caracal

----- The rules of the usage of the equation are the following: First i have to know what is the property of that distribution that it speaks about. If it is a force, then the magnitude of the force changes like F'/F = 1/L^2 E'/E = 1/L F'/F = 1/L^2 a'/a = 1/L etc. Then i could just LOOK the spatial distribution of the field without analysing it any further. The field just would have such transformation that it contracts isotropically - in all directions. And its magnitude in every place also increase by factor 1/L^2. And i could just LOOK the time evolution in graph and it would just have such transformation that every event runs faster. This is the idea. Like for example i could look what the hydrogen atom looks like and what its time evolution looks like and then i can transform them. But in order to use that equation: Then if the distribution is inverse square F = a/r^2 it transforms to F = (1/L^2) a L^2/r^2 = a/r^2. This means that all Force fields that are follow inverse square law remain unchanged in their shape and magnitude. There is one thing i didn't mention - when i compare conditions in two systems, i have to define the reference points of comparison. If i compare two hydrogen atoms without electrons, other which is transformed by factor L and other is normal, for example transformed by factor L<1, then i put the reference point of transformed atom L times closer to a center. Because of this, if the force field follows inverse square law, i get equation F'/F = 1/L^2 between the magnitudes of the forces in these two reference points. But if the property that has that kind of distribution would be energy, then its magnitude should change like E'/E = 1/L and i get E = a/r^2 -> (1/L) a L^2/r^2 = L a/r^2. That means that all energy distributions that follow inverse square law would transform to E' = L a/r^2 But if i want to compare two reference points, the one in contracted entity where it is is L times closer to the center - i get E'/E = 1/L between the magnitudes of energy in these two reference points. --- There is just new phenomenom present in the cosmological scale, that is the reason why friedmann equations would change. That is - the matter changes. I think i can temporarily accept that energy conservation principle does not hold - for the sake that other laws of nature holds. And i can always arbitrarily define that there is energy source. And maybe there is an energy source - in the structure of spacetime. I think I don't abandon physics - i just hypothetize that a new kind of phenomenom could be possible - and in cosmological theory - takes place.

Quote(Markus Hanke)"So can you provide a mathematical formalism that shows the mechanisms for shrinkage in the framework of the Standard Model (in a way that preserves the known laws of QFT), and show that this reproduces all available cosmological observations (not just redshift)?" Yes i can write mathematical formalism for my theory. But this idea may not be in the framework of standard model, i dont know that now. (this may not be a good text or good formalism, i suspect this a little) Part 1. I make hypothesis, that every physical object made of ordinary matter can have 'iso-transformations'. That physical object can be any object made of ordinary matter - particle, atom, some space vessel, any everyday object, or even planet or stellar object like asteroid or star. (I could mention here - i am not yet speculating that matter changes. But if it does, what would make some physical object to contract (or expand )isotropically instead of disintegrating into group of small parts? I suggested two reasons: Binding forces and quantum-mechanical adjustment when particles wave function changes towards spatially contracted wavefunction that has faster time evolution, it's allowed orbital also contracts.) I didn't use this word 'iso-transformation' before. It just means 'transformations that have certain similar properties' ------------------ 1a) I state that in that iso-transformation, every length s in the spatial distribution and every characteristic duration of any event t in time evolution, has transformation t -> L t s -> L s ,where i define L as 'a factor of transformation' , L > 0 This 1a) does not yet tell whether the transformation has single center. But the following 2) states that the transformation has center in 0,0,0 and that the transformation is isotropical around this center. 1b) The magnitudes of Several physical properties should change by following equations: notation: X'/X = FF means that for physical property XX, there is transformation X -> FF X such that X' = FF X where X' is transformed physical property X -> X' and FF is certain factor that is listed below for magnitudes of different physical properties: v'/v = 1 a'/a = 1/L E'/E = 1/L p'/p = 1/L m'/m = 1/L h'/h = 1 c'/c = 1 F'/F = 1/L^2 P'/P = 1/L^2 2) Any spatial and time dependent entity, field or distribution should transform into other form by following way: It has transformation in the magnitude, spatial distribution and time evolution: X(r,t) -> (X'/X) X(r/L,t/L) where r is vector (x,y,z) I describe here that the transformation center is at origin 0,0,0 and that the transformation of the spatial distribution of the field is isotropic and homogenous. For example time dependent 'step' energy distribution E = E(r,t) E = 1 , when 0<t<1 and 0<r<1 E = 0 , when t > 1 OR r > 1 will transform to E = 1/L ,when 0<t<L and 0<r<L E = 0 ,when t > L OR r > L , where 0<L<1 is some factor In case 0<L<1 the transformation would be isotropic contraction of spacial shape and transformation in time evolution such that all events in the field takes shorter time. In case L >1 the transformation would be isotropic expansion of spatial shape and transformation in time evolution such that all events in the field takes longer time. This is the formal representation of my theory. Hypothesis is that any physical object can have this kind of iso-transformations. This phenomenom is transformation. It is not only change in magnitude of certain physical properties but also transformation of spatial distributions and transformation of time evolutions of any field or distribution. --------- I could add here that i also came to conclusion from Schwarzchild radius formula and Coulomb law is that it looks like (GM)'/GM = L and (kQ1Q2)'/kQ1Q2 = 1 but i was not certain whether k'/k = 1 and Q'/Q = 1 or is it k'/k = L^2 and Q'/Q = 1/L. But what really is the situation in EM fields and gravitational field is that they can have transformation X(r,t) -> (X'/X) X(r/L,t/L). for example gravity pull 'field': g(r,t) -> (1/L)g(r/L,t/L) where r is place vector r = (x,y,z) or escape velocity 'field': v_esc(r,t) -> v_esc(r/L,t/L) Where the center of the transformation is at (0,0,0) note that later in cosmological theory i postulate that the rate of the transformation is subject to time dilations. --------- -------- Part 2. Then i try to use this theory to make cosmological theory. A) I make assumption that all matter in the observable universe transforms in the way L becomes smaller. L = L(t) , L(t0) = 1 , dL/dt < 0, L > 0 ,where t is time that stays at constant time rate I denote another function LL(t) that describes the proportional redshift according to time t that is now 'accelerating time' of contracting or transforming observer. LL is not same as L. I make fit to Hubble's law : LL(t) = 1 + 2.20*10^-18 1/s This is linear approximation and real LL(t) is unknown. I can make guess that LL(t) = exp(k(t-t0) but LL may be different and depend on some conditions. B)I assume that all matter has same contraction size and is contracting at same rate. This is not exactly true because of time dilation histories and time dilated matter contracts more slowly. For example non-rotating black holes do not contract at all. Theorems 1)I make theorem that A) and B) leads to Robertson-walker metric in flat space if there were no gravitation and ordinary expansion of space present. ds^2 = c^2dt - a(t)dr^2 ,Where a(t) = LL(t). In this time it is only 'pseudometric' - not real metric. LL(t) describes now 'apparent expansion' - because all the changes are in the observer. This would be the only observation we see unless we look into deep space, where we would see light coming from 'old matter' and unless we see somewhere matter that has transformed different rate due to its different time dilation history. Or unless there is differently transformed matter for other reason. 2)Theorem: Following observations: The old light coming from old matter has -redshift LLL(r) -decrease of momentum and energy of photon 1/LLL(r) -time dilation 1/LLL(r) The reason for these 3 observation is now that matter in the past had iso-transformation such that it had expansion by factor LLL. Also all light this matter had emitted had expansion LLL and time dilation already when it left from the source. 3)Theorem since light travels at the velocity c LLL(r) = 1 + k*r/c k = 2.20*10^-18 1/s this is also linear approximation. This is the redshift-distance relation. Real LLL(r) is unknown. 4)I make theorem that A) and B) and 2) leads to that Tolman test is passed. The surface brightness is relational to inverse 4th power of redshift. 5)There would be different kind of Friedmann equations. In deriving them i would have to account gravitation and possible 'ordinary' expansion of space. I wrote earlier in part 5) of the main text about predictions that are different from expanding space theory. Some of the predictions and comparing them to observations may actually falsify this cosmological part of the theory. --------- --------- Note that i haven't said anything about how the transformation actually takes place. But what would make some physical object to contract isotropically instead of disintegrating into group of small parts? I suggested two reasons: Binding forces and quantum-mechanical adjustment when particles wave function changes towards spatially contracted wavefunction that has faster time evolution, it's allowed orbital also contracts. Quote(Markus Hanke) By what mechanisms do these change? What determines the rates of change? What mechanism ensures that all changes are fine tuned exactly such that everything remains consistent? I dont know the mechanism for the change. I started with assumption that the rate of time is accelerating. I do have one idea. Could the spacetime consist in deep level a network of signals that are traveling at velocity of c or some kind of 'changing entities' that at very deep level changes in the velocity of c. The length- and timescale of these events may be extremely small. The size differences of these entities may be very high. Then, this network is just shrinking for some reason. All distances between the nodes or different entities gets smaller in a way that the network maintains it's shape. (or it may also disintegrate). That would lead to that the 'time' that is the duration of all events of the network would start to move faster also. This is i think a corollary - i don't answer to question why this kind of network would shrink. It may not be a finetuning. Spacetime could be that kind of entity that in spacetime, there are always certain laws of nature valid. such as Newton's 3 laws of dynamics, de Broglie equation, Heisenberg uncertainity principle, Equation of photons energy, Lorenz covariance and special theory of relativity. The change in properties of matter when it transforms or contracts may be just following from this. ---- Quote(Markus Hanke) "So energy is not locally conserved? How does this fit in with Noether’s theorem? And how does simply transforming the Lagrangian like this yield a spatial shrinkage of the system? " The energy conservation law doesn't hold in this transformation or change in properties. But if i would demand that to hold, then Heisenberg principle, de Broglie law or Photon energy law would not hold. What i think is that because of these laws have to hold, i have to give up energy conservation law. (But the Energy conservation principle still holds in the viewpoint of transformed or changed observer.) Instead of it, integral E*dt of any event stays constant here. This means that if some event have energy E(t) and it last time t1-t2, then integral (t1->t2)E dt = constant. Maybe this is more general conservation law. Or there is an energy source. Not only Lagrangian transforms, but every field or distribution, according to equation X(r,t) -> (X'/X)X(r/L,t/L) Why? the change should be in the structure of spacetime or space. The idea i have is that space or spacetime can transform like a picture in projection screen when someone moves projector closer or further away. But what is also needed is that the matter adjust to the change. In order to do this, matter i think needs strong binding forces and QM behavior. Atom or molecule would contract as a whole system because Electrons and nucleons, which have slightly shorter matter waves adjust to orbitals that are transformed to slightly smaller volume. Also if there are time dilations in electrons and nucleons or in fields it would make this situation different. (this may be too brief answer what i wrote here)

Sorry about this double reply. I didn't remember to say about time evolution of Lagrangaen, or Force or other things. The time evolution of things should change also. If for example radioactive nucleus has been transformed that way that its time moves 20 times faster, and has been transformed to 20 times smaller in all lengths isotropically and homogenously such a way that the contraction center is defined, and also other changes took place, then the expected characteristic half life of the remaining nuclei is 20 times shorter from that moment on. That change in time evolution also comes from that the space or spacetime has transformed into other form. there was a question in the title of this topic ' what would happen to space if the passage of time was accelerating?' I speculated that it could transform into certain form. That the acceleration of time would not be only change what would take place in space or spacetime.

I could add this science study here: There is one interesting science study about Quasar time dilations. https://arxiv.org/abs/1004.1824 MRS Hawking (2010) have studied quasars and he makes in this article a conclusion that quasars with different redshifts don't show signs of time dilation. What would be reason and explanation for that? He gives few possible explanations there. I have to say that i havent read it well though.

No. As I have already pointed out earlier, while some laws of physics may be scalable in that way, most are not scale invariant, most notably the laws of quantum physics don’t behave well under rescalings. You cannot ‘shrink’ atomic structures and composite particles and expect the physics to remain the same. For one thing, none of the fundamental interactions can be scaled, irrespective of how you fudge the fundamental constants; the whole concept of shrinking matter is pretty much dead right there. Even if that weren’t so, the wave equations that govern atomic structure do not scale as well - and neither do their solutions. And again, even if such rescalings were possible somehow, you’d come up against other issues. For example, if you shrink an atom while keeping its orbitals intact, the position of its electrons becomes more and more localised over time - which of course increases the uncertainty in their momenta. Eventually that uncertainty becomes large enough that electrons can jump orbitals (and fall back), leading to molecules becoming unstable, and ordinary matter emitting a continuous ‘glow’. Still further in the future, all atoms would become ionised; and still further, the hadrons within the nucleus would ‘dissolve’ into a quark-gluon plasma. Needless to say, we observe none of those things. Lastly, we actually have ways to check whether at least some of the fundamental constants might have had different values in the past (~2 billion years) - for example using natural fission reactors, such as at Oklo. The available data indicates that that was not the case. So no matter how you look at this, it simply doesn’t work. Even if it did, the model would generate many more problems and explanatory gaps than it solves. I am not changing physical properties only, i am also transforming the shape. In a way i think this transformation of shape to be similar than transformation of picture in projection screen, when the projector is pushed closer to the screen. I make any physical object to shrink homogenously and isotropically into smaller size, and then i change time rate,E,m,p,U,F,a,... by certain factors. timeinterval'/tinterval = L , v'/v = 1 E'/E = m'/m = p'/p = 1/L , F'/F = 1/L^2 , a'/a = 1/L h'/h = 1 c'/c = 1 This means that any field shrinks isotropically no matter what is their shape. After that i multiply for example E by 1/L and F by 1/L^2. You should use SI units and look the lagrangian in these units - why? because i looks like natural units defines m_p = 1 or that m_e = 1. you shouldn't do this definition, because all masses change like m'/m = 1/L in this transformation. The lagrangian should have dimension Joule in all its terms in SI units, is this true? If it is joule, The Lagrangian's 'magnitude' changes like Lag'/Lag = 1/L and the shape of lagrangian 'field' Lag(x,y,z) shrinks in 3 dimensions isotropically and homogenously. For example if it is a radially symmetric step function: if 0 < r < 1 Lag(x,y,z) = 1 if r > 1 Lag(x,y,z) = 0 it transforms to following: if 0 < r < L Lag(x,y,z) = 1/L if r > L Lag(x,y,z) = 0 And for example any force field F = F(r) where r is a vector transforms to following: F' = 1/L^2 F(Lr) (i put factor L in the argument of the force function and multiply the magnitude F then with 1/L^2) And any energy field E = E(r) where r is a vector transforms to following: E' = 1/L E(Lr) What is happening there is - the spacetime or space itself transforms into different shape. Or if not speaking that there is something is happening there, i could say that spacetime or space has a kind of iso-transformations. There exist objects that can have a 'transformation' relative to some other object. For example there are two similar space vessels, that are otherwise identical or almost identical, except that the other vessel has transformation relative to the other vessel. (and they may exists in same place side by side.) There is actually a principle or statement i didn't mention: the empty space should look similar to both space travelers, if there are space travelers inside those two space vessels.) --- In the viewpoint of non-transforming observer, when matter transforms and shrinks isotropically and other changes takes place, electrons should emit very long wave emission when it adjust to its new orbital, that is now slightly transformed into smaller in size, but it is far too long wavelength that it could be seen or measured. Nothing else should happen. Electron do get more localized by factor L but its mass, momentum and energy also increases by factor 1/L. This would make the uncertainity of momentum times uncertainty in place to be same = h/2pi . (But in the viewpoint of transforming observer he would just see this emission, nothing else.) None of the fundamental constants have changed in our environment in our perspective, But if we look to distant space, we would see there differently transformed matter - matter has been bigger in the past + other differences. But this image of the matter in the past actually i think 'should' look same same as if we imagine that distant object just have redshift and time dilation because of cosmic expansion of space ( and other effects coming from the expansion of space) This text above looks like i am repeating here. --- I could write here about two problems that i have noticed in this Shrinking matter theory: There is one question or problem about my theory in particle collision experiments. Should there be also created shrunk or differently transformed electrons and protons or other particles in particle collision experiments for example in CERN? My counter though to this is that in order to create shrunk, bigger or differently transformed particles in such experiments, maybe you would need this kind of particles to start with in the first place. There is a problem with solar system dynamics, what could actually falsify this theory. If matter shrinks, (and in my theory also the gravitation field shrinks), then in our viewpoint, planets should migrate about 330nm/AU/s away from the sun. This is i think different prediction from expanding space theory because this is not a force that can be neglected in gravitationally bound systems. It is apparent expansion of lengths due to shrinking of the length unit of the observer. that is roughly a velocity 330nm/AU/s - not a force. I am not sure what happens if this velocity that is pointing away from the sun would be added to numerical calculations. This migration rate is just the Hubble constant in units nm/AU/s (k = 2.20*10^-18 1/s). But radar measurements with messenger probe gives that astronomical unit increases only about 15cm/year. But maybe the gravity of other planets cancels this effect? On the other hand titan is preceding from saturn about 11cm/year and moon is preceding 3.8cm/year. According to this shrinkin magger theory if the velocity is just added to semimajor axis, the migration should be 8.4cm/year and 2.66cm/year at least. But are these titan and moon migration coming solely from tidal effects? That would mean that there is no room for my theory.

I still am not sure what you are asking. The reading is different but the difference in time rates are such that the clock is moving 20 times faster. According to relativity theories one possible way to do this would be that the park is in gravitation field and the space vessel is away from the field. Then the man's clock in the park could have 20 times slower time rate than space traveler in the vessel. I could here write about idea that spacetime could transform into different forms. This may be slightly repeating, But Well The idea i have in mind is that the other clock and the whole space vessel has been 'transformed'. Nothing in the theory of relativity forbids that that there is a entity called space vessel and clock inside that runs 20 times faster by definition. The theories describe only what kind of relative time dilations the clocks can have if they move relative to each other or the other is in deeper gravitation field and other is further away from the gravitational field. The question what i was thinking is that is it possible that the space vessel can 'transform' into other form that way that its natural time runs 20 times faster after the transformation in a way that it does not break certain laws of nature? Lets make thought experiment. Lets assume that The space vessel has transformed that way that its time run 20 times faster. Does this contradict with something? Here is the picture of the situation again: I look now some laws of nature: If this were the only change that take place in the transformation, then observer inside the vessel would measure that the velocity of light is 20 times slower. I think that this is what can't be. There is a possibility that all lengths in the vessel has contracted by factor 20 including the length unit that the space traveler in the vessel uses. He now measures that light's velocity is still same - 2998000km/s Also the Lorenz gamma factor of any object inside the vessel are still same. All velocities in fact in the vessel are still same. Special relativity works as usual inside the vessel. All moving things just have different natural time rates, different lengths and different masses. Special relativity tells only what is the relative changes if these things move at certain velocity inside the vessel. But if these two were the only changes that has taken the place in the transformation of the space vessel, then the space traveler would measure that any photon does not follow law E = hf = hc/lambda. I think that this also what can't be. It would be more meaningful to think that The law is still valid. It is possible if all the energies in the vessel have changed also. And it would be meaningful that planck constant is constant. The energies have to increase by factor 20 and planck constant have to stay constant. Next i would like to think that Newton's second law is still valid inside the vessel: F = ma and the kinetic energy equation is valid E = 0.5mv^2. Since velocities stay unchanged in transformation, all the masses should grow by factor 20. Any acceleration inside the vessel should be 20 times greater. If Newton's second law is still valid inside the vessel, then all forces should become greater by factor 400. By this far, it looks meaningful that space vessel can transform in a way that its time runs 20 times faster than the time of the man who is walking in the park - if certain changes in lengths,accelerations,masses,energies, and forces that are inside the space vessel take place. This is the 'invention' i suggest. Some physical object can 'transform' into other form in that kind of way that physical laws in or inside that object are still valid. While this thought experiment is going quite well this far, I make a big question: Can the transformation of the space vessel be even such that the space traveler inside the vessel does not notice anything changing in any laws of the physics inside the space vessel - if he does not look outside from the window? How this could be possible? There may be answer to this - the spacetime or space itself transforms into different form. But there are some questions. Is this transformation stable, does it leak or something? can it exist in ordinary place? what about empty space, does the space traveler measure some changes in the empty space, for example in vacuum energy? I think the answer is, the principle still may be possible - to all these questions. This is the reason i speak about a physical principle: The space vessel can be 'transformed' that way that its natural time rate is 20 faster and other changes. And the space traveler inside the vessel may not see the difference. The space traveler see the inverse changes in the environment. For example earths gravity pull is 20 times weaker. How about higher mass densities, do they lead to that the space vessel might collapse to a black hole if it would be say 100000000 times smaller and have 100000000 times greater natural time rate? Actually the gravitation constant changes too, in the case of space vessel by 1/200 times. it comes weaker by inverse of the square of the change in time rate. The answer would be according to this 'no'.

Yes i may have made too much text here in order to others to read it all but maybe they can read by fastreading. I made mistake in writing, i mean what i think Pauli exclusion principle between electrons in atomic scale distances 10^-10 ... 10^-15 is coming from EM forces between electrons, coulomb force, magnetic forces. (and also quantum fluctuations). Neutrons are fermions and obey Fermi-Dirac statistics but they don't have as strong coulomb and magnetic forces between them similarly than electrons do have, i think this is why they can pack together more than electrons, but they do obey pauli exclusion principle. This spin 1/2 and integer spin different behaviour had to do something with superposition of quantum wave functions, i remember.

banstrom is having his own conversation, i havent yet read it. --- quote(swansont) "Not good enough. The Pauli exclusion principle is predicated on identical particles, not "only tiny differences" If you are predicting differences between these particles, then they are not identical, and you are wrong." What i have understood, the Pauli exclusion principle, is it coming from coulomb repulsion. If there were no repulsion, the electrons could pack up much more closely, like neutrons can do. The exchange force is not a independent force, it is what i understand depending from coulomb repulsion. quantum fluctuations may make coulomb propulsion stronger or weaker or cause tunneling effects, but without propulsion there is no exchange force and electron degenerate pressure. And pauli exclusion principle would be not present in atomic length scales. (That would propably mean that the electrons in matter falls apart and becomes dust. ) Therefore unidentical electrons, what they would do, is that they could cause new kind of emission (and absorption) lines in atoms and molecules that could be observable? (The termodynamic motion of atoms may blur spectral lines thought.) Right? what kind of variation this theory predicts among the matter on the surface of earth , it is not clear to me at the moment. But what left me thinking is - what is the experimental accuracy that electrons are identical? There must be a limit in current experiments. This question is also a little more general interest to me, not only because of my theory. This statement or theory that electrons are identical is verified only by some experimental accuracy. If electrons have for example mass variety 1 +- 10^-26 , would it be in the range of measurements to see it or for example 1 +- 10^-18 ? or say 1 +- 10^-32 ? I tried to find information on this question are electrons verified to be identical and in which accuracy, from e.g physics stack exchange where only qualitative answers was given. The differences coming from this theory should be well observable in the cosmic ray and solar wind particles. Has anybody actually collected and measured the mass of solar wind protons or cosmic ray protons. Or their Electric charge? or that do particles generally change over time or from place to place by some other ways for some reason? this may have not been done. If i look to distant space with telescope and spectrometer and try to find different kind of matter there, in this theory, matter that is 'transformed' its spectral lines looks similar as a matter that has redshift or blueshift because of doppler effect or time dilation. Therefore this matter may be mistaken as matter with doppler effect or time dilation. Except that there may be somewhere ordinary atom nucleus that have one or more transformed electrons in its orbitals or transformed nucleus with some ordinary electrons in its orbitals. Quote(studiot)" What does the t' clock read ? If both clocks were running at the same rate then the t' clock reads (t + h) hours where h is a constant difference btween them. What now happens if you also apply the condition that t'/t = 20 , because the factor of 20 cannot be applied to the starting difference, h." the t' clock would read... I am not sure yet what you are asking... But well if i make following thought experiment if i concider that every proton can be thought as a clock. If two protons has been created in the big bang era and big bang is defined to have time t = 0 for both of the protons, it depends which place it has been what instant of time it would point after that. If the other proton has been traveling in space at a velocity of light for long enough and then decelerated to for example surface of earth at the present time, it may point only say few years when the other proton that has been on milky way and the surface of earth would point about 13.8 Billion years. But if the time has been accelerating, the rough estimate or linear approximation would be that time of proton on earth would run 1 + 13.8 Byrs * 0.0693 1/Byr = 1.9563 times faster than proton that was coming from space. or if the acceleration is exponential then roughtly exp(13.8*0.0693) = 2.6022 times faster. In that space vessel picture, If i reset both clock to have time t0 at some point of time and assume that the t' clock runs 20 times faster than clock t at the reset of clocks then at the reset t = constant1 t'= constant2 constant1 and constant2 mean time after for example big bang according to space vessel travelers clock and man's clock who is walking in the park. Then i assume that at some point of time clock t' has started to run 20 times faster than clock t by some unknown phenomenom. then after one second of the t time t = constant1 + 1s t'= constant2 + 20s The 'acceleration of elapsing proper time t' as a function of elapsing proper time t' - if it is fit to explain Hubble's law, would be 1 + 2.20*10^-18[1/s] * (t-t0) That is a linear approximation. It is so small change during 20 seconds that i can neglect it. If proper time is accelerating as a function of proper time itself such a way that if there were a clock that is not accelerating at all - for example a star traveler that travels in a circle near speed of light and he manages somehow to slow down, take a picture of the surrounding and then back to accelerate. And he takes picture of environment say every hour according to time in environment that was running certain way at the first lift-off moment, then according to this kind of 'clock' the time of some accelerating clock runs like t'-t0' = integral[t0->t] L(t)dt I could define 'a time that is not accelerating' that way like i did above. (quote)(Markus Hanke) "This is precisely the issue I’m pointing out to you - they do not cancel out. If you rescale, you end up with a different Lagrangian; this is why the idea doesn’t work. I’m not just claiming this for no reason - it can be mathematically shown that these interactions are not invariant under rescaling. We know this. What do you mean by rescaling? is it change in lengths or length+time or change in several or arbitrary selection of physical units and properties? I guess the unit of any Lagrangian is Joule in SI units? Or you say it is more complex than that? In this theory, If it is Joule in SI units, It should then change like LL'/LL = 1/L regardless of what terms does it contain. (But this is the viewpoint of observer outside of the box. In the viewpoint of observer inside the box, it stay unchanged like all other things according to equality principle.) ..... This may not be relevant,but: It looks like that if some quantity or its partial term is dimensionless in natural units that you were speaking of, it in this theory may not stay always unchanged. According to wikipedia, the natural unit system seems to be a system where c, h/2pi, G , k_b are set 1. In my theory, according to my deduction these quantities change by following way: c'/c = 1 h'/h = 1 k_b'/k_b = 1 but G'/G = L^2 -yes the gravitational constant should change. (actually i wasn't sure can i deduce from (GM)'/GM = L and m'/m = 1/L that G'/G = L^2) In particle physics, the natural unit system is where c, m_e, h/2pi and e0 is set 1 there other stay unchanged but the mass changes like m_e'/m_e = 1/L and in QCD c = m_p = h/2pi = 1 and e_0 = 1 or 4pie_0 = 1 others stay unchanged but m_p'/m_p = 1/L (Actually that is only so if Q'/Q = 1 and e_0'/e_0 = 1. I wasn't very sure whether it is for example Q'/Q = 1/L and e_0'/e_0 = 1/L^2. But i deduced that (kQ1Q2)'/(kQ1Q2) = 1) This means that if for example some formula term KK that is dimensionless in QCD natural units but contains term 1/m_p , this term should change like KK'/KK = L . If KK contains term m_p it should change like KK'/KK = 1/L and so on. i picked this example equation for Lagrangian L = a/r^2 - b/r from your discussion with bangstrom. Is this a Lagrangian in QCD natural units? if so, It may be that this term contains 1/m_p if its formula is expressed in SI units. But b does not contain 1/m_p. if it is so, then because m'/m = 1/LL and r'/r = L both terms would change like lag'/lag = 1/LL where LL is some factor. But this is the viewpoint of outside observer. In the viewpoint of observer inside the box lagrangian like all other things remain unchanged according to equality principle. It could be that this applies to other Lagrangians in strong and weak force as well- there could be m_p hidden in the formula in some of the terms, if they are expressed in natural units.? ... What if Coulomb law was something else more complex than just inverse square dependent of the distance? Then i couldn't deduce that (kQ1Q2)'/kQ1Q2 = 1 I just repeat here how i get the equations of change for E,m,p,h,c: I can deduce that E'/E = 1/L from the law for photon energy: E = hf and demanding h'/h =1 and m'/m = 1/L and p'/p = 1/L from equation lambda = h/p and the F'/F = 1/L^2 from Newton 2 Law F = ma. I also demand that c'/c = 1 when it has to be that s'/s = L and t'/t = L. Here what i do is that i demand certain laws of nature to hold. they are de Broglie equation, Photon energy equation, Newtons 2nd law, that c'/c = 1 and h'/h = 1. But back to the lagrangian, I above already wrote this, but I remember that in classical mechanics the Lagrangian has unit Joule in the usual SI units. If the strong interaction lagrangian Lag has dimension J in SI units, then according to the equations of change what i deduced in section 2) Lag'/Lag = 1/L if it is measured or observed by observer who hasn't shrunk. but if this lagrangian is measured by observer inside the box, that has shrunk, then according to equality principle that Lagrangian has not been changed at all. The equality principle - it is the idea what i suggest in part 1 of the main text. I am not sure if you have had a thought of it. This idea i have is not only about accelerating time and shrinking of matter together with changes in other properties, it is also about equality principle. This may be repeating. and i make a lot of text. I make here description of this principle: I forgot to say that the idea for equality principle i got when i was thinking the principles of equivalence and relativity in the theories of relativity. If there were a closed box and inside the box the time runs say 2 times faster than outside of the box and there are also other changes, like all lengths have been shrunk by factor 1/2, all energies and masses and momentum's have been increased by factor and other changes what i have deduced in section 2 - relative to the outside of the box, then - the equality principle states that if there were an observer inside of that box, and all changes above have been happened to him as well, he cannot by any means whatsoever deduce by looking any kind of things inside of the box, he cannot determine whether he has been shrunk or whether he still is normal and no shrinking has happened. There is absolutely no way to find out how small he is. That is the equality principle statement i have. How this is possible? it could be that the spacetime or space changes or transforms such a way that it is possible. Spacetime could be able to transform like a picture in projector screen, and if there were some entity in that picture, he would not be aware of that his picture has been transformed. But now not only the size of the things changes, but both the time rate and the all lengths changes. And the entity is not aware by any means that he has changed. He observes everything to be normal. The spacetime looks to be normal and nothing seems to be changed. While i may not be thinking enough while writing the above i have to say that maybe this equivalence principle can't be true for some reason. Maybe spacetime does not have this kind of property that it can transform. Comparison with equivalence principle and relativity principle: It is somewhat similar principle than equivalence principle in the theory of general relativity. What states that if there were an elevator in freefall in gravitational field, the person inside of the elevator would think he is in a place where no force or acceleration is moving the elevator. There is no way he can tell whether he is in freefall or just levitating in space or moving at constant velocity. (well at least in very small area in the gravitation field or in uniform gravitation field) And it is somewhat similar than relativity principle in the special relativity. The observer who is moving at constant velocity inside an elevator, cannot by any means determine whether he is moving at constant velocity or not. And also there is no absolute rest what Newton was thinking. In 'certain way', if some physical object change its timerate and size and other properties by certain way what i have described, it may be said that the physical object can have existence in different 'scales'. Observer inside that physical object, can't determine without looking outside, what is his scale. He can have scale 1000 or 1/1000 relative to world outside - but he can't determine which scale he has by doing measurements inside. It may be also that there exist no absolute scale at all. Some object may have scale 1/100000000 or 100000000. For example there may be at least in principle a proton that has scale 10000000 somewhere in the universe. I could mention here this : How this change takes place is a bit different story. Matter should somehow adjust to the changes in lengths in order to shrink isotropically, otherwise it would disintegrate. It may be the strong binding forces and Quantum mechanical behavior that makes it possible. For example electron that has transformed, has shorter matter-wavelength, therefore it adjust to closer to nucleus in atom in order to keep its quantum wave in standing wave motion.

(studiot) Let us stop right there, because there is your problem in a nutshell. Why is it 20 times ? Why not 20.000000001 or 19.99999999999 ? How does any observer determine when it is 20 times ?, because according to your hypothersis, this factor is continually changing. ...I am not sure what you are going for, and this answer may be outside of what you are asking. I don't know what kind of other change, process or mechanism could change the space vessel such a way that it has 20 times faster time relative the time in the park and on the surface of earth. I only describe how it would look in the viewpoint of outside observer- the man in the park - if the time would run faster in the vessel and if it would have shorter lengths and other changes i described before. But if the hypothesis is true that matter is changing over time and its time is accelerating in a way i described it, the following scenario would do it: Lets keep the space vessel far away in space away from the sun's and earth's gravitation field. Then its time runs slightly faster than time of a clock on the surface of earth. Lets keep it there for a very long time. If matter is shrinking in the way i described it and the time is accelerating, it would eventually gain 'transformation difference' relative to the matter on earth L = 1/20. It would have 20 times faster time rate and it would have all lengths 20 times shorter and other changes i described above. If the hypothesis is right, the transformation difference would be 1+2.20*10^-18 1/s * time difference - that is just a fit to Hubble's law and this factor 2.20*10^-18 is a number that is close to Hubble constant, maybe it should be slightly more because gravity pulls matter together. This time difference may be hard to calculate if the space vessel has had more complex history. In order to know what is the transformation difference of the matter in space vessel and how fast the time in the matter of the vessel runs relative to surrounding, the man in the park could just do measurement. could for example take a proton out of the vessel and weigth its mass. He could find out that the mass of that proton is 20 times greater than mass of the protons in the matter on the surface of earth. He could then conclude that the time of the space vessel must run 20 times faster than the time on the surrounding, on the surface of earth. He could measure also some characteristic time, like half-life of neutron in the matter of the space vessel and measure that this half-life is 20 times shorter than the half-life of neutron -He could pick and measure for example 100 000 neutrons in order to get their half-life. I dont know, it may be that i start to write out of the point here.

I have one picture that could share here, it is quite simple, not very fancy, but it could clarify this 'equality principle' what i am talking about. I earlier decided to leave this picture and its description out , but maybe i just share it now. I may start to repeat myself here. Lets imagine there is a space vessel that has 20 times faster time rate and that has contracted by factor 20 and lets imagine it is moving on the park. There is a space traveler inside of the space vessel. According to equality principle, this space traveler thinks that everything is normal inside the space vessel - all laws of nature are normal inside of the vessel. Following is a description how space traveler inside the vessel observes outside and how a man who is walking in the park observes the space vessel. ( according to the deduction i have made) The space traveler inside the vessel measures the changes in the outside of the vessel. The density of air is 20^4 = 160000 times smaller, the temperature of the sun is 300K and the temperature of air is 15K. He measures earth's gravity pull to be 0.5m/s^2. The mass of his vessel is 200kg and it has temperature 300 K. The density of the vessel is 3g/cm^3 The escape velocity on the surface of earth is 11.2km/s. The velocity of light is 300 000km/s everywhere. There is outside observer who is walking in the park and notices this space vessel. What he sees in this space vessel if he sees that its time is moving 20 times faster than his own time, he might see a clock inside the space vessel and notices that it is counting seconds 20 times faster. The space traveler and space vessel and all matter in it seems to have size 20 times smaller. The space vessel has high mass: 40 000 kg and its density is 20^4 = 160 000 times higher - 480000 g/cm^3. But the vessel has 20 times more energy in its fuel. The temperature of the vessel is high, 6000 K. The temperature of the air in the park is 300 K. Sun seems to have temperature 6000 K. The escape velocity on the surface of earth is 11.2km/s. The velocity of light is 300 000km/s everywhere. Gravity pull on the surface of earth is 9.81m/s^2.

Moderator note: It's mainstream physics and taken as true for purposes of discussion. This is not your thread, which is for discussion of caracal's proposal (even though it has been falsified), not yours or anyone else's Excuse me, but what makes you think that my theory falsified? i might have been drop out. There are two parts in my theory. Equivalence principle and the shrinking matter theory that is a fit to Hubble law. I would like to ask, do you see the equality principle what it is about, and understand what i am trying to say there? Quote(Beecee) I once had someone pushing a similar hypothetical. He called it his "shrinking rule" model. My point to that was we see light redshifted, (lengthened) which I saw as invalidating such thoughts. For example pioneer 10 had last successful communication with earth at 2002-4-27 when it was 80.22 AU away. If matter shrinks in the way i described, there should be redshift in pioneer 10:s signal. redshift = 1 + 2.20*10^-18 1/s * 1,50*10^11 m/AU * 80.22 AU / (2.998 * 10^8 m/s) = 1 + 8.830 * 10^-14 But in this theory the light emitted by for example table lamp does not get redshifted as time elapses if i put it on for say million years later. It is the equality principle what states that. Quote(Studiot) "The problem as I see it is that you are offering a rate of change with respect to itself, which is meaningless." What i am trying to do is to say in mathematical form that if the L = 1/2 ,then : -One hour inside the box runs out in 30 minutes in the perspective of outside observer, so the time rate is 2 times faster -All lengths and length unit is 2 times smaller. The meter looks like half meter in the viewpoint of outside observer -All energies and energy unit is 2 times greater. One Joule looks like two joules in the viewpoint of outside observer -All massses and mass unit is 2 times greater inside the box. One kg looks like 2 kg in the viewpoint of outside observer I dont know if there is standard notation for this kind of equations. How i write above mathematically is t_in/t_out = L s_in/s_out = L E_in/E_out = L m_in/m_out = L ,where L = 2 in this example. (Quote)(Swansont) "The protons on earth all came from somewhere else. Electrons, too. Does it stand to reason that according to your conjecture, all protons and all electrons would all have slightly different masses, depending on their history? But we know that they don’t - protons are identical, and electrons are identical. And we know that’s the case, because the Pauli exclusion principle only works for identical fermions. If these particles weren’t identical, we wouldn’t have atoms as we know them. But we do." The differences and variations in electrons mass in the matter on earth could be so small that they haven't been noticed. I just have a thought that pauli exclusion principle could work between electrons that has similar EM properties but slightly different mass. The only change could be that more massive electron may favor lower energy state slightly more than less massive. The electrons in matter should have sligth differences because they move in their orbital at high velocities that are different in different orbitals. For example lowest electrons in Uranium atom have high velocities. But on the other hand they may exchange their places sometimes what makes the differences to become more even. (Quote)(Markus Hanke) " And this is the problem, because, in natural units, the coupling constants in the weak and strong Lagrangians are dimensionless. So if you rescale lengths, the relative strengths of the various terms within the Lagrangian changes, and the whole thing breaks down. " This discussion start to look like yes-no discussion. This sounds simple to say but the equality prinicple is the hearth of my theory. Yes the time rate changes, and lengths changes but the equality principle states that observer inside the box does not notice any difference in anything. I deduce in the section 2) that in the viewpoint of observer outside of the box the lengths and time rate changes inside the box, but in fact acceleration, energy, momentum, mass, power, local forces, density should change also. This is because the certain laws of nature should hold. Velocity and Planck constant does not change. t'/t = L s'/s = L a'/a = 1/L E'/E = 1/L p'/p = 1/L m'/m = 1/L P'/P = 1/L^2 F'/F = 1/L^2 rho'/rho = 1/L^4 v'/v = 1 h'/h = 1 k'/k = 1 Q'/Q = 1 f'/f = 1/L I dont know what these coupling constants and lagrangians looks like, but if they are dimensionless, i guess they stay dimensionless and changes in different properties in the formula cancel each other out - in the viewpoint of observer that is outside of the box. for example fine structure constant is alpha = ke^2/hc . there the changes in different quantities are k'/k = 1 e'/e = 1 h'/h = 1 and c'/c = 1 so that makes alpha'/alpha = 1

(Studiot) I'm sorry to tell you that this is meaningless. You are confusing functional dependence with transformational equivalence. These are simply proportions. I dont know what would be the standard notation. (Lets think about situation that there is a box where time is moving faster and there are observer inside of that box. and that there is observer outside of the box whose time does not run faster) In words that equation above says that the proportion between infinitesimal time unit inside the box and time unit outside of the box is same as proportion between length unit inside the box and any length unit outside the box that is same as inverse of the proportion between energy unit inside the box and energy unit outside te box etc. What it means that inside the box time runs faster, all lengths are smaller by same factor and all energies ,momentum and masses are greater by inverse of the same factor dt'/dt = L s'/s = L E'/E = 1/L p'/p = 1/L m'/m = 1/L ,where L is some factor and 0 < L < 1 why the time units has to be infinitesimal? because if the time is accelerating, then the equation of change for elapsing time is changing when time elapses. that equation of change for elapsing time would be t' = integral[0->t] L(t)dt , where L(t) is some function. does this make sense? It should be so that it can be tested directly whether matter shrinks. The mass of the proton is known by many numbers of significance. M = 938.27208816(29) MeV/c^2 (from wikipedia) If one collects solar wind particles and cosmic ray particles and measure their mass, the mass should be slightly less than ordinary. These particles have been subject to time dilation and they have shrunk or contracted less in the past relative to similar particles on the surface of earth. The escape velocity on the surface of sun is 617.7km/s, that would make gravitational time dilation T/t = 1 -2.117*10^-6 since the sun is 4.6 Billion years old and the matter shrinks at the rate 1.0693 1/Byrs the transformation difference would be L = 1 + (2.117*10^-6*0.0693*4.6) = 1 + 6.75*10^-7 That means the proton in solar wind should have at least 1/L times less mass than ordinary proton. The mass of ordinary proton : 938.27208816(29) Mev/c^2 The mass of proton in sw : 938.27145... Mev/c^2 or less. The cosmic ray particle that has travelled 100 MLY in space near the velocity of light should have transformation difference L = 1 + 0.0693 * 0.1 = 1.00693 The mass of ordinary proton : 938.27208816(29) Mev/c^2 The mass of proton in CRays : 931.8146... Mev/c^2 If one runs particle accelerator for say 4 years and keeps its proton beam particles near the speed of light, the transformation difference between proton that has been in particle accelerator and ordinary proton would be L = 1 + 4 years *6.93*10^-11 1/year The mass of ordinary proton : 938.27208816(29) Mev/c^2 the mass of proton in pacc. : 938.27208790... Mev/c^2 I didn't find anything useful to say about W and S interactions so i left them out from this text. How i think is that the strong and weak interactions do not need to have any special properties. Why? This is how i think: The equality principle is the starting point here. The spacetime itself changes. It changes like for example projection in the screen if the projector is pushed closer to the screen, and second change would be that the time runs in the picture faster, that could be similar than if there is video player that is set to play a motion picture at faster speed. The object in the screen can have any kind of properties, right? similarly the object that has faster time rate and shorter length unit can have any properties whatsoever. Then, after this assumption, if i want to deduce how the objects inside the box changes exactly, i start to deduce how different kinematic and dynamical properties should change inside the box where time runs faster - in the viewpoint of observer outside the box. I demand certain laws of nature holds, what i do in part 2 in the text. But i have wrote only about gravitation and EM interaction, not about Strong and weak interaction. for example yukawa potential, that is one mathematical potential - if all lengths should contract, then if some object inside of the box has this kind of potential, i deduce that then the radius of this potential should also contract. This is quite long answer and maybe there is something wrong in my thinking.

What would happen to space if passage of time was accelerating? Equality principle and its consequences. Similarity of empty space. A Shrinking matter theory that might actually work. ---This is quite long representation. There may be some mistakes. Contents: Part I Two important principles: Equality principle and similarity of empty space Deriving equations of change for kinematic, dynamic properties and EM and gravitational properties starting from equality principle and demanding certain laws of nature to hold Transformation of spacetime Cross-interactions Part II Shrinking matter theory that might actually work (without causing any observed changes in local natural laws and nature constants except that there is matter that shrinks at different speed because of differences coming from slight time dilations.) Predictions of the shrinking matter theory 'A kind of Abstract': I have posted this kind of topic few years ago but there were many mistakes. I made this representation because i want put everything right. There are two parts in this text. In first part i speculate what kind of changes might take place in ordinary or normal spacetime if the passage of time was accelerating. In second part i fit this phenomenom to cosmology and i try to explain Hubble’s law and other cosmological observations. What is the key thought i want to deliver to you in this text? It is the thought that the spacetime could have ability to transform into certain forms in that way that local observer can’t observe the difference – that is what the equality principle is. Why i think this cosmological theory is worth of thought? Are there any observations that speak for it? Well, there is actually one good observation that could speak for especially this shrinking matter theory what i propose. MRS hawking has published in 2011 a study where he concludes that quasars do not exhibit effects of time dilation. (https://arxiv.org/abs/1004.1824) This theory explain this because it predicts that black holes do not shrink – the shrinking of matter depends on its proper time and black hole event horizon’s time has stopped. There is a list in part 6 of other predictions. Many of them are very slight, but in they are (just barely) in the range of observations. A notable thing in this shrinking matter theory is, that it keeps nature laws and nature constants unchanced, what is problem in an ‘ordinary’ shrinking matter theory. It does that that way that i assume a weird principle of space or spacetime to be true, what i call equality principle. Starting deduction from this principle, there are many changes that takes place at the same time, not only shrinking. It looks like this is possible to do – if certain changes takes place the shrinking observer would measure all nature laws to be constant. If all matter would shrink at the same rate everywhere almost only thing we would see is that all distances grow. Except that some of the matter that has shrunk differently due to its time dilation (or lack of it) in the past. For example black holes, matter in compact objects and matter that has relativistic velocities. And this matter have certain properties. Since time dilations are very small in solar system (of magnitude 10^-6 to 10^-9) and since the phenomenom is very weak (about 6.93*10^-11 1/year that is just Hubble constant), these differences in matter are extremely small. If matter in outer solar system or in the sun has spent 5 billion years in its place, the differences between matter in different places in solar system would be then about of magnitude 10^-8 (on the surface of sun) to 10^-10 (on the surface of moon). Another difference in this theory is that the observed expansion of all distances is not caused by force. You can approximate it as a velocity v = k*r, where k = 2.20 * 10^-18. The effect of the apparent expansion of distances should be visible in solar system. There is a problem in this prediction of this theory. It predicts that earth-sun distance should increase at velocity 2.20*10^-18 * 1AU , that would make roughly 10.4 meters per year. But it is observed that earth precedes from sun by only 10-15 cm per year by radar measurements – that is 100 times less. On the other hand earth-moon distance should grow 2.66cm/year at least and the observed change is 3.8cm/year. Also Titan-Saturn distance should grow 8.47cm/year at least and the observed change is 11cm/year. Maybe the gravitation of other planets explain why sun-earth distance does not grow? Or maybe there is something wrong in the theory. There is evidence in the distribution of Kuiber belt objects that Neptune has migrated outward in the past by 9 AU, maybe because of interaction with planetesimals and dust. The distributions of KBO shows that KBO s has been swept out by 3:2 resonance with migrating neptune (Malhotra 1993) : According this shrinking matter theory, Both Neptune and KBOs should have migrated slowly outward during the lifetime of solar system. Neptune should migrate 51.37km away from the sun per period and KBO:s should migrate by same factor. Has that migration left any visible marks to KB ? This shrinking matter theory gives surface brightness to dimish proportional to inverse 4th power of redshift similarly as in expanding space theory that has Robertson-Walker metric. This result is coming from that the time rate increases and energies increases at the same time when matter shrinks. (These changes are required if i demand certain laws of nature to hold for shrinking observer. Velocity of light should be constant for all observers and De Broglie equation l = h/p, Heisenberg uncertainity principle and Quantum of light equation E=hf to hold for all observers and to keep planck constant constant for all observers.) The equality principle - if it is true – might be a thought of the century. It tells that spacetime has unique property that no one has thought before. That is - If the passage of time accelerates, the spacetime can transform into certain form in that way that observer inside of the changing area –who is changing too - still measures all laws of nature to be same. If there were just one thing i would want you to think of , just think about this principle. Can it be true or not. Another important principle is the similarity of empty space. This principle – if it is true - makes possible that matter that has different rates of time, can coexist in same place. And the empty space around the matter still looks similar. Two important principles: Equality principle and similarity of empty space What would happen to space if passage of time was accelerating? This is the question i'd like to ask from you. I am not concidering here the question why the time would do that. Only thing i think is that there could be some process happening in the fundamental level in spacetime that changes the rate of time. There may not be mechanical explanation for the acceleration of time since it could happen in deep level in spacetime. I dont know answer to this ‘why’ question. But Newton didn't know what is the cause of gravity. Nobody knows why mass curves spacetime. Nobody knows what is the cause of particle-wave duality. This applies to many things in physics. But i state here that if the time rate do accelerate, there are certain consequences from this. I claim here that the passage of time could be so fundamental property of spacetime that if it would change, spacetime would maintains what i call an equality principle. Equality principle: all observers that have different time rates are equal that way that they all observe all laws of nature to have same form in their own coordinate and unit system and all constants of nature to have same values. They can't deduce what is their time rate without comparing themselves with another object that has different time rate. A special form of equality principle: Let there be an isolated box and an observer inside that box. Lets demand that the time inside the box is moving at different rate than outside. There is no gravitation or the box is in free fall in uniform gravitation field with constant gravity pull. Now the observer inside the box measures all laws of nature to have same form inside the box than what observer outside the box observes outside the box to be. I concider here the special form of equality principle. This equality principle is the basis of all deduction i do later here. The equality principle is strange principle. Spacetime would be very strange substance if it was true. In the setting of the special form of this principle - No matter how fast your time is going inside the box, you would still measure that everything inside the box is like if your time rate would be normal If this principle is maintained when time accelerates there are many consequences. It must be, that if in the viewpoint of observer inside the box whose time run faster all laws of nature have same form and all constants of nature are same, then in the viewpoint of observer outside the box whose time does not run faster, if he could see inside the box, there must be changes in the physical properties of matter and fields inside the box that has fast time rate. There is actually a way to deduce how they change by demanding certain laws of nature to hold. There is yet one another important principle that i state to hold: Similarity of empty space: That is, empty space looks similar in the viewpoint of all observers with different time rates. This principle makes possible that i can just talk about matter and fields, or any physical objects generally, while not caring much what happens in empty space in the area where time is moving faster. The empty space looks similar in that area than some other area where time rate is ‘ordinary’. If this principle holds, then matter that have different time rates, can be in the same place at the same time. Deriving equations of change Lets assume that there is a box and an observer inside box. And for some reason, the time inside of that box would start to run at different rate relative to the world outside of the box. 1. all lengths should contract by inverse factor - otherwise observer with faster passage of time would observe the velocity of light to become smaller. I demand that the velocity of light stays constant: c'/c = 1. I also demand that the Newton first law holds. That means that particles or physical objects do not change their velocities if there is no force affecting them. 2. all masses,momentum and energies should increase by same factor - otherwise the de broglie law lambda = h/p would not be valid and planck constant would change. Also the energy of photon would not be E = hf. I demand that Planck constant stays constant: h'/h = 1 and De Broglie equation lambda = h/p and Equation for photon energy E = hf hold. Also, if th principle of similarity of empty space holds, then I demand that the vacuum energy should look similar in the viewpoint of different observers with different time rates. Heisenberg uncertainity principle also should have same form: delta_p * delta_x = h/2pi . I think the vacuum energy distribution can be constant by following way: that the observer should change certain way when his time is accelerating. Demanding that Edt = E’dt’ and dpdx = dp’dx’ - That is – the measurement of some events energy * time of that event stays constant, and the measurement of uncertainty of momentum of some particle * the uncertainty of its place stays constant. This is possible when 2) is true. 1 and 2 can be expressed by following equation: \[ dt'/dt = s'/s = 1/(E'/E) = 1/(p'/p) = 1/(m'/m) \] ' states for new value and no ' states for old value. Both values are measured by observer outside of the box that has normal time rate. Dt is infinitesimally short time interval, s is either all lengths or length unit, and E,p,m are either all energies,momentums and masses or their units. From now on, i denote that \( dt’/dt = L \) ,where L is ‘factor of change’ 1 - means that the acceleration of time must be coming together with isotropic contraction of all lengths. Or disintegration of all lengths and places – that means that every thing contracts towards its own center. 2 – means that the acceleration of time also must be coming together with increase of mass, momentum and energy. If 2) should be true, the big principle in physics that i have to ‘leave out’ or allow to be broken here is energy conservation principle. (But alternatively you could always just define that there is some kind of energy source present where the energy comes from.) Note that the energy is still conserved in the viewpoint of changed observer inside the box. So i have to leave out this principle because i demand Heisenberg uncertainity principle and de broglie law and that planck constant is universal constant to be valid. Instead of energy conservation, \( E*dt \) stays constant. That is, the infinitesimal cut of energy of some event during infinitesimal time integral. There are basicly two different ways how all lengths can contract. Isotropic contraction and disintegration. And something that is a bit of both. Here i make leap of faith and assume that ordinary matter, planets, objects in solar systems and stars contract isotropically, but everything in solar system, star systems and in bigger things in cosmological length scales disintegrates. Interstellar gas might do something between these two possibilities. I assume that the binding forces in ordinary matter are high enough to cause isotropic contraction of matter instead of the disintegration. Also because of the quantum mechanical nature of the matter, when the matter-wavelength of a particles becomes smaller when their mass increases, they should shift to closer orbit of molecule, atom and nucleus in order to keep its matter-wave in standing wave motion. Following picture shows how different observers that have different time rate, have different isotropic contraction and different change in energies, observe properties of a UV light that has certain wavelength and frequency. What is not shown in pictures, these observers observe alsto the energy of a photon to change. Following quite simple but important picture demonstrates the equality principle. Lets look at situation that there are many observers inside of their own box. All of the observers with different time rates think that everything is normal inside the box – All laws of nature are normal and all nature constant have normal values. This picture shows also that different time rate comes together with isotropic contraction of all lengths in ordinary matter. (Note that if there was gravitation or acceleration present, then different observers would observe the gravity pull or inertial acceleration differently: g_observed_by_observer = L g_normal. So if g=10m/s^2 for L=1 observer, the other observers would observe that gravity pull to be 6m/s^2 and 4m/s^2.) Now, if this equality principle is valid and 1 and 2 are true, it has to be that other properties like kinetic and dynamic properties, electric charge, coulomb constant and gravitational constant and for example radius of proton and neutron, should change too. Lets deduce the kinematic and dynamical properties of particles first: \( v'/v = 1 \) – all velocities remain unchanged \( a'/a = 1/(dt'/dt) \)– all accelerations increase \( (da/dt)'/(da/dt) = 1/(dt'/dt)^2 \) the time derivative of acceleration increases by the square of the change \( f'/f = 1/(dt'/dt) \) – all frequencies increase Now how about forces? i demand that Newtons 2. law holds: F = ma (classical) or F = dp/dt (relativistic) => \( F'/F = m'a'/ma = 1/(dt'/dt)^2 \) or just noting that the time derivative of p must change like (dp/dt)’ = (1/L^2)(dp/dt) It is important to note that this equation of change for force apply only if both objects that put force to each other, belong to the same changed object or system – that has contracted isotropically. This may not apply to cross-interaction between two differently changed objects. In order to deduce the equations of change for gravitational and electromagnetic properties and nature constants in perfectly isotropic contraction, you need to compare two systems, an ordinary system, say electron orbiting single proton, and two stars orbiting each other, and system that has changed, and start with for example Swarczshild metric and Coulomb law. I demand first that Coulomb law holds : F_coulomb = kQ1Q2/r^2 \[ F_{coulomb}' = F_{coulomb} * 1/(dt'/dt)^2 = 1/L^2 \] \[ a = F_coulomb/m \] \[ r'/r = L \] \[ a'/a = 1/L \] => \( (kQ1Q2)'/(kQ1Q2) = 1 \) How to go further than this? I can demand that electric charge stays unchanged: Q'/Q = 1, then it must be that k'/k = 1 , E'/E = 1 and B'/B = 1. But is this Q'/Q = 1 true? Lets concider following situation: Electron annihilates with positron that has different time rate. If Q'/Q wouldnt be 1, then where would the excess charge go if the charge is conserved in this reaction? It could be that this kind of reactions are not allowed or there is some new particle present that carry that charge, or Q’/Q = 1. Or maybe the conservation of electric charge does not hold in this reaction. which one it would be? I assume that Q’/Q = 1. There is one argument also: it might be so because there might be some deep unknown reason in that electric charge is quantized while different particles with same charge has different masses. I earlier thought without thinking much that it might be that k'/k = L^2 and Q'/Q = 1/L => E'/E = 1/L and B'/B = 1/L (it could be actually that k'/k = A^2 and Q'/Q = 1/A for any A) Which one it would be? The difference between these two are in the cross-interactions. How about gravitation? Lets look what can be deduced when looking one specific property, I demand that the Schwarzchild radius of spherical nonrotating mass distribution for given mass M and G is r = GM/c^2 : It should be that: r'/r = L , like all distances s'/s = L. And Since c'/c =1, it must be that => (GM)'/(GM) = L How to get further than this? I now demand that M'/M = 1/L , that is, gravitational mass changes like inertial mass m'/m = 1/L . These could be two different things, but i demand that they are the same physical property. => G'/G = L^2 But i think this last equation is not needed, that is, G always comes with M or other similar property of the gravitational source, that is in Schwarchild metric and Newton approximation term ‘GM’. Now i can put all together. Note that all these equations of change actually apply only for system that has changed both homogenously and isotropically. dt'/dt = L s'/s = L E'/E = p'/p = m'/m = 1/L velocities v'/v = 1 accelerations a'/a = 1/(dt'/dt) frequencies f'/f = 1/(dt'/dt) wavelengths lambda'/lambda = (dt'/dt) density rho'/rho = 1/(dt'/dt)^4 Forces F'/F = 1/(dt'/dt)^2 if both of the objects that put force to each other belong to changed system (GM_grav)'/(GM_grav) = 1/L Gravitational constant G'/G = (dt'/dt)^2 Gravitational mass M_grav'/M_grav = 1/L Schwarzchild radius r'/r = L (kQ1Q2)'/(kQ1Q2) = 1 coulomb constant k'/k = 1 electric field E'/E = 1 magnetic field B'/B = 1 electric charge Q'/Q = 1 The following picture illustrates how outside observer, if he can see what is happening inside box that has faster timerate, would measure and see the properties of physical objects inside the box. What about strong and weak interactions? I wont go there, but the starting point would be again the equality principle and the equations of change for kinematic and dynamic properties. For example the demand of equality principle ,c'/c = 1 and s'/s=L is that radius of proton should change like r'/r = dt'/dt. Anwers to some questions: So the gravitation constant changes? Yes it comes from demand that equality principle holds. For example the Schwarzchild radius should decrease like all specific lengths inside the box. What happens in isotropic contraction is that the gravitation field contracts as a whole, and that can be thought same as if the term GM became weaker. Note that the gravitation constant changes only in the viewpoint of unchanged observer outside the box and it stays still constant in the viewpoint of observer inside the box. This makes possible that if the time inside the box was say 1000 000 000 times faster, the box wouldn’t collapse into a black hole. But does the equality principle and similarity of empty space hold if time rate is very fast? Lets put the change in the extreme: What if the time rate inside of the box is say 10^10 times faster? I think it could be so that the equality principle still holds! I could here talk about that spacetime has a new kind of dimension, so called 'time scale dimension' or 'scale dimension'. Does this change of energy violate energy conservation law? Note first that the volume where the energy is has shrunk in 3 dimensions. I dont know what would be the energy source of this change. It may be that the spacetime itself contain some kind of energy. There would also be following law instead of energy conservation: Edt = E'dt' = constant - that means Energy times infinitesimal time interval of time is constant. That actually keeps the energy-time form of heisenberg uncertainity principle valid. That principle states that a quantum mechanical system is there allowed to have high energy if it last for small amount of time that way that E*deltaT = constant. How about electron that is point-like according to current understanding? How does it look if its timerate is faster ? Well first maybe electron do have radius but it is extremely small, for example 10^-50 meters or say 100 times bigger than black hole with same mass. And electrons electric field may vanish or be smaller than inverse of the distance times constant in very close distances. Coulomb law may not be valid in the very close radius. In that case the em field of electron would not go to extremely high value in close distances. It is also possible that electron is already transformed particle, when its size can be smaller than black hole with same mass. Now if the passage of time was accelerating in some system like i speculate later, and if this change in the time rate depends on the proper time, it could depend on the time dilations inside the system how fast the changes take place in different places. Then the change couldn't be homogenous for the whole system. Then these equations of change do not exactly apply. This might be actually a problem in the shrinking matter theory what i represent later, because then for example the protons or gluons and quarks might change at different rate than electrons. What about vacuum energy? if the similarity of space - principle is valid, vacuum energy should be same for all observers who have different time rates. I think the answer is that Heisenberg's uncertainity principle has exactly same form for all observers: deltaE*deltat = h/2pi . Transformation of spacetime The general name for this phenomenom, where there are multiple changes in the area where the passage of time is faster in a way that the area maintains the equality principle – Could be “spacetime transformation” or “space transformation”. Transformation would just mean a change in properties. The term transformation is used in the field of optics. When some picture is changed if there is a lens system put between projector and screen, you can say that the picture is transformed by the lens system. Thermal expansion can be thought as a transformation of matter. All length contractions and time dilations that are present in the theories of relativity can be thought as transformation of all lengths and time rate. The idea that spacetime or space can in certain circuimstances transform into certain different forms is new in physics. Also the equality principle is a property that i think has not been presented earlier. Spacetime transformations may be a building block of new theories in physics. That is one reason i have interest to think about this subject. For example in solving the mystery of particle-wave duality. What i think of the particle-wave duality that it could be explained by some kind of pilot wave theory or Bohm theory. Particles may there have classical trajectories but those trajectories are difficult to predict. I may be that the electric fields of all particles have some kind of perturbations. That perturbation may for example cause all particles to have temporarily high kinetic energies that can also be taken away from the particle in short times – that could explain Heisenberg uncertainty principle and tunneling effect. The double slit experiment could be explained by that particle causes an otherwise unseen field around it, this perturbation, that travels throught the other slit and hits the particle after the slit – that cause the interference pattern behind the slit. Cross interactions But how about cross-interactions? I mean for example EM force and gravitation between ordinary object and object that has changed homogenously and isotropically by for example factor L ? Lets look first gravitation. Now i think about system of three objects, one with big mass M and others are two point-like objects that have very small masses m and m', but this second object has changed by factor L. When thinking equivalence principle that is the basis of Einsteins gravitation theory, i demand that both small objects should fall with equal gravitational acceleration in the gravitational field of object M. (Actually i am not sure is it really the case, but i just can’t think this through.) Lets use the Newtonian gravitation law that is still a good approximation in stellar systems. Lets look then situation that there is big object with mass M' that has changed by factor L and second object, that is point-like and has mass m. The gravity pull of big object should be now (GM)'/r'^2 = 1/L but remember that this is a situation where r' is L times smaller than r. The gravity pull in the distance of r is L^2 times weaker because the inverse square law of g : g = L GM/r^2 . (remember that L < 1) So the object that consist of ‘transformed matter’ should have weaker gravity pull than same kind of object that constists of normal matter. The EM -cross interaction case raises question is k'/k = 1 and Q'/Q = 1 or k'/k = L^2 and Q'/Q = 1/L. The conservation of electric charge and the quantization of electric charge, that is charges comes always with multiples of e, would speak for the first option. There may be some strange reason for this. These could be fundamental laws of nature, but are they? What happens when changed electron annihilates with normal positron? If the second option is true, where does the excess charge go? If the first option is true, then force between proton and changed electron is same than force between unchanged proton and unchanged electron. But changed electron would now accelerate less because it has more mass. So, IF Q’/Q = 1 and k’/k = 1 - This would be the only observed change in EM interactions of ‘transformed particle’ - it has 1/L times more mass. But what if the second option is true ? That Q'/Q = 1/L, E'/E = 1/L, B'/B = 1/L and k'/k = L^2 ? when changed electron is in the Electromagnetic field of ordinary proton, its mass-charge ratio is 1. That means it accelerates similarly as unchanged electron and for example it would go into similar path than ordinary electron in normal electric or magnetic field. This would mean that it is not possible to distinguish transformed electrons from ordinary electrons just by looking its trajectory in EM fields. You should weigth the electron in gravitation in order to notice that transformed electron has more mass than ordinary electron. But what happens to that ordinary proton in the EM field of changed electron? The electric and magnetic field of changed electron should be changed by factor 1/L. It means you could notice that transformed electrons (or protons) cause stronger EM fields than ordinary electrons (or protons) Shrinking matter theory (that might actually work) I got feedback from one man that shrinking matter theories fails because it would unavoidably mean that laws of nature and nature constants change over time and that is not what is observed. The starting point of this theory is that i assume that the passage of time is accelerating by factor \[ \frac{dt}{dt} = 1 + 2.20*10^-18 [1/s] \] This is linear approximation. The local observer observes all laws of nature to be unchanged because the area of the change in time rate keeps equality principle and similarity of empty space –principle is valid. I Claim that these principles are possible to keep valid if the changes i wrote about in part 2. takes place in the area where the time rate gets faster. This acceleration of time rate causes that matter shrinks in planets, stars and galaxies. I also assume that all matter shrinks at the same rate and all matter has same time rate. -Which is not actually exactly true because of time dilation differences. But the time dilation differences in for example solar system are very small because the escape velocities and orbital velocities of planets are small. The time dilations are significant in relativistic particles and compact objects like neutron stars and black holes. The velocity differences between galaxies are i think less than 5000 km/s, so the difference in time rate between galaxies are still quite small. So besides of these differences, only thing what we would see is that all distances appear to grow. But all matter is not shrinking at the same speed because of time dilation differences. So i make starting point assumption that the passage of time of all ordinary matter is accelerating in that way that space maintain equality principle. And principle of the similarity of empty space holds. i use the equations of change now. For any physical object: 1) dt'(t) = L(t)dt , where L(t) depends on the proper time or natural time of the object 2) s'/s = L(t) 3) E'/E = p'/p = m'/m = 1/L(t) (+all other equations of change) What is the cause of cosmological redshift and time dilation in this shrinking matter theory? They both are coming from that matter has been bigger and its passage of time has been slower in the past. In expanding space theory they come from that the signal that travels in empty space is stretching when the space is expanding. Following picture represents how shrinking matter theory explain that space appears to be expanding. White balls are astronomical objects like stars and planets. Black ball on the center is a black hole that does not shrink. The grid is a coordinate grid of the rest frame where all matter in the universe lies more or less. The grid is shrinking over time and all distances appear to grow for so called shrinking observer. Note that the stars and planets contracts towards their center isotropically. Also , in this theory the time rate is accelerating also. The velocity of light and in fact all velocities remain constant. I think these two changes in both meter-stick and time unit leads to Robertson-Walker metric. But that is now only apparent metric – all changes are in the matter in the universe. There are two different ways the space could change when the matter is shrinking – Isotropic contraction or disintegration. And there may be a grey zone that is between these two. I think it depends on the binding forces which way some physical object shrink. I think ordinary matter and matter in stars have enough strong binding forces and they shrink isotropically, but planetary systems, galaxies and space in cosmological scale very weak binding forces and they shrink that way that they disintegrate. Also the quantum systems would contract isotropically because the particles need adjust to smaller orbitals in order to have standing matter-wave. But what is then the apparent distance expansion as a function of elapsing time that is observed by ‘observer who shrinks’ ? Lets denote it by LL(t'), where t' is elapsing time for shrinking observer. You can make first linear approximation LL(t')=(1+k(t'-t0')) Then you can make exponential approximation LL(t')=exp(k(t'-t0)) If i assume that the proportional change for example in the observed wavelength of ligth is same for every infinitesimal time interval dt', this would lead to exponential law for LL. This argument would suite well together with equality principle: The proportional change in the wavelength of light is same for all different observers with different time rates. Hubble’s law, Tolman test and Quasar time dilation The Hubble redshift can now be explained in a way that observers own time rate, length unit and energy unit changes while photon does not change. There is a so called cosmological test as ‘Tolman test’– how does the surface brigthness P/A change. The answer is that the unit of power changes by factor 1/LL^2 and the cross section changes by factor 1/LL^2, that would make surface brightness change by factor 1/LL^4 that means it is changes proportional to inverse fourth power of redshift. This is i think same relation what you get in cosmology that has expanding space with Robertson-Walker metric. There is one astronomical reseach result that actually could be explained by this shrinking matter theory i have made here: MRS Hawking (2010) has measured frequency distributions of quasars that have different distances and his study has a result, that quasars do not exhibit effects of time dilation. (https://arxiv.org/abs/1004.1824) All frequency distributions are similar. This could suite together with shrinking matter theory because black holes do not shrink. IF we assume that the size distribution of black holes is same everywhere, BH at different distances should have same radius and same spin rate, and only the matter that is falling into BH would be different. That way that atoms and molecules of the falling gas have shrunk more and has faster time rate in closer distances than in far distances, and light coming from them should be redshifted. (Actually the ergosphere of BH does not have stopped time dilation but its time runs about 1% times slower than time far away from BH. ) Distance expansion Shrinking matter theory is different from expanding space also in that apparent expansion of distances is not caused by force. It is the change in observers own length unit. I dont know how to write together these two things, apparent distance expansion and gravity pull and solve the orbit of the planet: 1) s' = s0 (1 + k(t-t0)) or s0 * exp(k[t-t0]) - apparent expansion of all distances 2) d^2r/dt^2 = - GM/r^2 , when k -> 0 - gravity pull of the sun I think you can put this in to words by saying that during small time step the planet first is moved by gravity and after that – the second step is it appear 'magically' to gain more distance from the sun. I could make up numerical intergration by computer from this. Expansion of the universe and space in cosmological length scales How the space actually appear to expand then? Well there could be four phenomena influencing to the apparent and real expansion or contraction of space. The expansion of space that has started in big bang, gravity that pull matter together and this new phenomenom what i call 'distance expansion' r'=[1 + L(t'-t_0)]r_0. - and then there could be dark energy. It could be also so that there is no real expansion or contraction of space present. Also it could be that there is no dark energy present. Then there would be only gravitation and this distance expansion that both influence to that how the space looks expanding. The easiest case is a model universe, that does not have ‘ordinary expansion of space’ and has only dust that has very weak gravitation and this distance expansion. Then the scale factor that is completely coming from apparent distance expansion, would be just a(t') = LL(t'), keeping that the time dilation differences are small. If LL is exponential this is similar than whas it de Sitter space – that has only cosmological constant. If there would be only two phenomena that effect to observed expansion of space are the shrinking of matter and gravitation, what would be the time dependence of scale factor a(t)?. In the case where LL is exponential it should be possible to write an equation. I can’t write this equation here now. I think i could make again calculation for a(t') by taking small time steps and do numerical calculation. Again, If LL(t') is known, for example it is exponential function then it is possible to calculate the a(t'). But what is this constant k? I can make just a rough guess that k is about 5-10 % greater than Hubble constant H_0. The difference would come from that gravity is pulling matter together. Problems in this shrinking matter theory There is one problem with the time dilations of the particles. For example proton. Gluons inside proton might have significant time dilation - this would lead to that protons transform slower than electrons when their time is becoming faster. This should have been observed: the properties of electron and proton , like mass, are known in many significant numbers. Proton and electron should have nearly equal time dilation in order to this theory to work. But the time dilation in electron orbiting atom may not be a problem since electrons may exhange their place in atom. But do the gluons really have relativistic speeds inside proton? If so, that causes a problem, since this has not been observed. What is the limit between when some object contract isotropically and when the object disintegrates, i mean contract that way that its constituents contracts towards their own center? -I think it depends on the strength of binding forces in the matter and there is no clear limit. But since gravitation is about 36 magnitudes of order weaker than electromagnetic forces, i could say, that all solid matter and all matter in stars and planets contract isotropically and celestial systems consisting of stars and planets contracts that way that planets and stars contracts toward their center. Interstellar gas and dust may be somewhere between these two extremes, and they contract only partially as a whole object. Also the quantum nature of the matter causes that if the matter-wavelength of electrons in atoms decrease when their mass and momentum increase, they adjust to new orbit around the nucleus in order to matter-wave to have standing wave-motion. This might happen also inside the atom nucleus and inside protons and neutrons. When the universe was very young all matter was together. At some point of time they would have had enough binding forces that the universe would have shrunk as a whole isotropically. What made the universe to disintegrate that way that clumps of matter started to shrink towards their own center? I think this would require some kind of rip off or inflation to be present. The distance expansion that is not a force but roughly a velocity - should be visible in solar system and it should be 2.20*10^-18 1/s times any distance. If this all is tranferred to the increase of semimajor axis of a planet, earth should migrate 10.4m/year away from the sun. But it is observed that Astronomical unit is changing only by 15cm/year. On the other hand earth-moon distance should increase by at least 2.66cm/year - the observed change of earth-moon distance is 3.8cm/year. Saturn-Titan distance should increase by at least 8.47cm/year and the observed increase is 11cm/year. The distance between Neptune and Sun is not well known since Neptune has made only one Period after its discovery. What would explain why at least the inner solar system planets does not migrate as it is predicted by this theory? Is it so that the gravitation of other planets cancels this effect out? Or is this really a prediction of this theory? What about particle collisions? Why there are no transformed matter particles produced in those events? - Maybe they need this kind of matter in the first place. Predictions of shrinking matter theory Distance expansion. The distance expansion is r’ = r0 exp (k(t-t0)) or r’ = r0 (1+k(t-t0)) (linear approximation), where k = D* 6.93 * 10^-11 /year or 329 nm/s/AU or 10.37 m/year/AU. Distance expansion in solar system: Neptune-Sun distance: 311.7m/year and 51.37km/period Uranus-Sun distance: 199.0m/year and 16.72km/period Earth-Sun distance: 10.37m/year Jupiter-Sun distance: 53.96m/year and 640.0 m/period Earth-Moon distance: 2.66 cm/year Saturn-Titan distance:8.47 cm/year Delay effect in gravitation How about delay in gravity and EM interactions? Both of them travels at the velocity of light. This would cause that the gravity has delay effect – Gravitation is slightly stronger than Newton’s gravitation law- the effect is very small. F = (1+kc/r)GM1M2/r^2 or exponential approximation F = exp(kc/r)GM1M2/r^2 This is because the gravitation has been stronger in the past. (This formula does not apply if the gravitating object is compact star or black hole) Transformed matter. There should be ‘transformed matter’ in particles that have travelled long distances at very high velocities and in compact matter that is old. They have relative L greater than 1. On the other hand there is matter away from the influence of gravity that has L slightly less than 1 relative to matter on earth. Transformed particles have 1/L times mass of ordinary similar particle, L times half time and L times greater gravitation (if it can be measured) and L times the size (if it can be measured). The spectral lines of transformed matter are L times redshifted (or blueshifted) - that shift may be hard to distinguish from the spectral shift coming from doppler effect. The transformation difference is L = 1+(time difference)*k, where k = 6.93*10^-11 1/year Cosmic ray proton that has travelled 100 million LYrs in ultrarelativistic speed * L = 1.0693 - has 1/L times less mass than ordinary proton 300 million years old neutron star that has surface time dilation 0.7 L = 1 + 0.3*0.3*0.0693 = 1.006237 - Has L times stronger gravitation and L times more time dilation (at least- the time dilation at the center is higher and there may be convection) Sirius B – age 124 000 000 years with time dilation on its surface 1- 1.46*10^-5 L = 1 + (0.124 * 1.46*10^-5 * 0.124 ) = 1.00000013 - has L times stronger gravitation and L times more time dilation (at least) compared to the time of the birth of white dwarf Black hole that has age 1 billion years L = 1.0693 - thas L times stronger gravity and L times larger radius (at least for non-rotating BH) than when it was born (even when it is not feeded by any matter) Matter on the surface of sun and in solar wind – age 4.6 billion years, time dilation (missing) L = 1.00000073 - proton has 1/L times less mass and all matter has L times more time dilation (at least) and has L times redshifted spectral lines. Matter in asteroid belt asteroids. Age 5 Billion years, time dilation = 1 – 5.337* 10^-9 Relative to earth surface matter L = 1 - 0.0000000102 - Any particle in it Has 1/L times more mass than similar particle of earths matter. Spectral lines of transformed matter in milky way and other galaxies are either redshifted L>1 or blueshifted L<1 depending the ‘time difference’. this may be difficult to distinguish from doppler effect. The Friedmann equations I can’t solve this. But the ordinary Friedmann equations do not hold. There is new kind of phenomenom, that is 'apparent growth or expansion of all distances' that comes from that the observer himself is contracting: D = D0 * LL(t), where LL may be exponential function of time LL(t) = exp (k (t-t0)) Twin Paradox Second kind of twin paradox: The other twin has transformed matter relative to other twins matter because he has experienced less time – and therefore matter in him and his space vessel have contracted less than matter on earth. Atom Clock in Twin Paradox The atom clock that is carried by other twin that has travelled in space should have permanent time dilation relative to similar clock that is carried by other twin on earth. The factoral time dilation would be 1 - (time difference) * 6.93*10^-11 [1/year] . End.

...that would be good idea to contact or ask an expert like astronomer or historian about this subject. I try to do something and i think i update also this thread if i get answer from them. thank you for your comment

No one yet commented in this topic? How about more generally was there "ancient telescopes"? Well, maybe this is not a big thing and nothing new. As i seach from internet there are some writings about ancient time and ancient greek telescopes. So maybe there were some early grudely made ones around in ancient time. Maybe also this kind of reflector. The antikythera mechanism tells on the other hand that they may have been well made if they existed. Sorry about my bad english by the way.

Alexandrian lighthouse and off axis parabolic mirror - an antique time mirror telescope? hi all, I have not intented this as historical speculation, but more as technical and scientific speculation could certain kind of optical system, off axis parabolic mirror what i describe below later, have been used as telescope and to beam light in alexandrian lighthouse similarly as fresnel lens. I dont know why anyone haven’t thought this idea more. I show here three sources, two of them is a take from medieval time chinese book and arabian book from the description of alexandria, third one is a single picture from Kitab al-bulhan or ”Book of Wonders”. Both of them are very short descriptions, first one and second one are just few sentences and third one is only a badly drawn picture. I first mention that greek mathematican Diocles has studied parabolic concentrators in 2nd or 3rd century BC. There is not long way from these burning mirror to invention of telescope. https://en.wikipedia.org/wiki/Diocles_(mathematician) The First source: Chau Ju-Kua: his work on the Chinese and Arab trade: https://archive.org/details/cu31924023289345/page/n161/mode/2up page 162 or 146 in the book – Alexandria lines 15-22: ” On the summit there was a wondrous great mirror; if war-ships of other countries made a sudden attack, the mirror detected them beforehand, and the troops were ready in the time for duty. In recent years there came a foreigner, who asked to be given work in the guard-house of the tower; he was employed to sprinkle and sweep. For years no one entertained any suspicion of him, when suddenly one day he found an opportunity to steal the mirror and throw it into the sea, after which he made off” The second paragraph is likely just invented story. The description is short but gives accurate description of some kind of magnifying mirror that can be used as telescope. The second source: I didn’t manage to find ebook for this next writing that is english translation that i took from one web page. Abu Hamid Al-Gharnati, who visited Alexandria in 12th century describes the lighthouse by following: “The first tier is a square built on a platform. The second is octagonal and the third is round. All are built of hewn stone. On the top was a mirror of Chinese iron of seven cubits wide (364 cm) used to watch the movement of ships on the other side of the Mediterranean. If the ships were those of enemies, then watchmen in the Lighthouse waited until they came close to Alexandria, and when the sun started to set, they moved the mirror to face the sun and directed it onto the enemy ships to burn them in the sea. In the lower part of the Lighthouse is a gate about 20 cubits above the ground level; one climbs to it through an archway ramp of hewn stone”. In the first part of the description the mirror again is told to be used as telescope. It is also exaggeration how far it can see, thought there might be mirages in mediterranean sea that makes possible to see over horizon. The second part of this text, what is about the mirrors ability to burn ships, is likely story of imagination. I wonder why anyone haven’t thought this following concept. What i speculate is that this mirror has been off-axial parabolic mirror, that reflects light sideways into one point, maybe in 90 degree angle. The angular size of the mirror by looking from the focal point could have been as much as 2 x 17.5 = 45 degrees or even 22.5 + 35 = 57.5 degrees, before the viewer starts to be in front of reflecting area or the furthest part of the mirror becomes too elongated. With these values of angles the mirror is close to flat mirror that is in 45 degree angle from the viewer. If someone looks sideways this kind of mirror behind the focal point with eyepiece, it works as telescope. This kind of mirror can also beam light but it might not be as good as fresnel lens. During daytime it works similarly as parabolic solar cooker. It also can work as magnificator. The eyepiece of the telescope may have been another, smaller off-axial parabolic mirror or a lense. In principle using another off axis parabolic mirror behind focal point it is possible to make constant beam of light. i have drawn schematic picture in the attachment file. Here is also a link to schematic picture of off-axial parabolic scheffler reflector that reflects light in 90 degree angle. this is close to concept that i have in mind: https://ars.els-cdn.com/content/image/1-s2.0-S0038092X1930430X-gr1.jpg (This is a link that is not public web page) The scheffler concentrator, that is used in solar cooking, is somewhat close to this kind of mirror. This concentrator is however so badly made that it cannot be used as objective mirror in telescope. https://en.wikipedia.org/wiki/Wolfgang_Scheffler_(inventor) Maybe the mirror in pharos lighthouse didn’t get much attention and became forgotten or something happened to books that describe it. It may have been a secret at that time also. Why there is no technical description of such telescopes in antique time texts? The arabs may have kept this antique invention as secret, when they translated antique time books in ninth and tenth century. The reason for this would be that they think it is benefit in war. what do you think of this? The third source: Kitab Al Bulhan by Abd al-Hasan AL-Isfahani: https://archive.org/details/KitabAlBulhan/page/n17/mode/2up page 84 What this picture shows, is that picture maker had clearly in mind concept of mirror for sightseeing. And the posture of the woman, that she is looking into mirror sideways, may tell that she is looking to the off axis mirror telescope that reflects light in 90 degree at its center. The mirror is also black what is like in magnifying mirror when there is no lightsource near focal point. What is missing is the eyepiece. This is not very accurate drawing. I dont know if i am just imaging things here, but from the same book, for example pages 18 and 28 show strange looking man that seem to have strange magnified face. This may be a hint – they are looking through round mirror that way that their face is magnified. This hint tells that reader should not talk to anyone in detail about magnifying mirrors. Thought these faces and that rider that holds sword and someones head may just be weird illustrations. What is certain is that i can’t read the text in this book, its arabian.

I try to be very brief. What happens to matter if the mass of the electron, proton and neutron and their constituents increases by same factor? Lets look some of the properties in Bohr hydrogen model. I dont put formulas here but I tell the how they depend on the reduced mass. The orbital velocity, radius of orbit, energy, orbital period. All other properties except velocity, depends linearly to reduced mass or its inverse. If the mass of electron and proton increases by same factor,say “K” -the energy of energy levels increase by factor K -the radius of all energy level electron’s orbit decrease by factor 1/K -the orbital period time of electron decrease by factor 1/K The general trend seems to be that matter shrinks, its energy levels increases and duration of all events decreases. Now I make harsh generalization and claim that all matter, including quarks,gluons, proton and neutron, atom nucleus, atoms and molecules change by same ways than in Bohr model above if all mass of their smallest constituents change by same factor: their energies increase by factor K, their all lenghts decrease by factor 1/K and duration of all of their events decrease by factor 1/K. What would be the possible cause of such mass increase? There could be at least two possible causes: -Particles gather or absorb small particles, some kind of “mini particles” that are freely moving in space. -There is mass source in the particle itself that generally does not show itself in the form of mass, but can change to having mass when particle undergo some kind of structural change. (?) Lets now assume that all matter in the universe gain more mass at the same time by factor 1+Ht ,where H is Hubble constant. Let there also be an observer whose matter undergo such a change. This changes his units of the measure by following ways: -Unit of length decrease by factor 1/(1+Ht) -Unit of time decrease by factor 1/(1+Ht) -Unit of mass increase by factor 1+Ht -Unit of energy increase by factor 1+Ht And lets figure out how the unit of momentum changes: p = muv ,where u is Lorenz factor.Because unit of velocity does not change, the unit of momentum must change by factor 1+Ht. If such observer observes a photon that is moving in space, he would observe following changes: -Photons wavelength appear to have increased by factor 1+Ht -Photons frequency appear to have decreased by factor 1/(1+Ht) -Photons momentum appear to have decreased by factor 1/(1+Ht) -Photons energy appear to have decreased by factor 1/(1+Ht) This is same what would happen to photon if the space is expanding. So this change in the units of measurement could be alternative explanation to Hubble’s law. There is at least one problem in this hypothesis – it is the gravitational constant. If the units of measure of the observer changes, and the gravitational constant is universal constant, then the observer would observe that the gravitational constant appear to change. For example - If the observer observes black hole radius, it would appear to have increased by factor 1+Ht – like all lengths, even when the black hole is not gathering matter. This black hole radius is r = GM/c^2. The measurement of velocity stays constant, so the measurement black hole radius depend on term GM. So if r changes by factor 1+Ht, the measurement of the term GM should change also by same factor 1+Ht. I think this is not what is observed in the field of astronomy. There is one possible way out from this problem: The gravitational constant is not universal constant, but it depends on the kind of matter that is causing the gravity around it. Something changes in the property of matter to cause gravity when particles gains more mass in the way described above. That way that the gravitational constant could still appear to be constant in the viewpoint of the observer – around the observer in the matter that has gained same mass increase than himself. But now it would not be constant when the observer is observing distant matter when he is looking to cosmic window. This “relativity” of gravitational constant looks like relativity principle in the relativity theory. The gravitational constant depend on the kind of the matter and the viewpoint – and it is constant in the viewpoint of observer for the same kind of matter that the observer consists of. But it would also mean the following: If for example the earth would gain mass this way by factor of million if it is possible, it would not collapse to black hole since the gravitational constant of such matter would become weaker. Its time to stop.

i think the 1st Friedmann equation in flat space actually is the one i first proposed in co-transforming coordinates? why? because: -in this coordinate system all matter in the universe has relative L=1 in some given time -the gravity works as usual because the relative L=1 for all matter -this new phenomenom what i call "distance expansion", if it is exponential function, then it just gives constant term to Friedmann equation the only difference is that not all matter contracts at equal rate (compact matter like black holes and neutron stars, and ultrarelativistic matter like cosmic rays and jets) but if i assume amount of this matter to be small the Friedmann 1 equation should be same as in Lambda-CMD universe, where lambda is substituted by this constant. but in non-flat space i think i have to change the Friedmann equation since the curvature radius increases like r'/r = 1/L = e^(pt) I think the transformation equation math works exactly as i described. The L is dimensionless factor, what i call "transformation factor" the equation for velocity is v'/v = 1 , therefore the lorentz gamma factor also changes like u'/u = 1 therefore the proportional lorentz transformation of infinitesimals dt and ds is also invariant equation for frequency is f/f = 1/L since the dimension of frequency is 1/t and t'/t = L you can derive these transformation equations from these nature laws: t'/t = L s'/s = L E'/E = 1/L lambda = s f = 1/t v = s/t p = h/lambda F = ma E = mc^2 p = mvu (u is lorentz gamma factor) F = G m1m2 /r^2 F = k Q1Q2 / r^2 F = q (E + v x B) c = 1/ sqrt ( e u ) i have to answer better but i thought to write about these two things.

i am in hurry, but i make some statements here: -the key idea in the cosmological model is that 1. when particles contracts, the macroscopical objects will contract isotropically, that is why the contracting observer - like us cannot measure or observe whether he has been contracted or not 2. But matter does not contract isotropically in cosmological length scales - all concentrations of matter contracts towards their center. The matter kind of fragmentates, the concentration centers become all the time smaller and smaller. This causes that contracting observer measures that the universe is expanding in cosmological length scales. I call this as "apparent expansion" or "distance expansion" IF there were very little matter density in the universe, and its gravity was neglible then there should be only two cosmological phenomena: 1. Ordinary expansion of the space that is remnant of the big band 2. Apparent expansion of the space (that is actually an observation illusion and caused by the contraction of the meter stick of the observer) and i think then the scale factor that is observed by contracting observer should be then a= a0K * 1/L where K is some constant that describes the ordinary expansion and 1/L is so called "distance expansion" Other thing i say that these transformation equations that are on that table, such as f'/f = 1/L Are valid only when comparing two physical entities that are otherwise equal, say for example two stars, or two protons that would be otherwise equal but the other is perfectly contracted isotropically relative to the other. in other words, when the other is perfectly isotropical and homogenous transformation of the other. For example if the system of two stars contracts such that the both stars undergo isotropical contraction by factor L<1, but their distance remains fixed - then the whole system does not anymore contract isotropically - and for example the transformation equation for the distance between the star is not longer R'/R = L , while the radii of the stars still follow the equation r'/r = L thanks, i have to think about those issues you wrote.

i answer first to this and later to your other writings. You are mixing here two things. the k i use here has nothing to do with the curvature of the space, it is a constant factor parameter in the transformation factor function L, if L is decreasing exponential function of co-contracting time: [latex] L(t') = e^{-k(t'-t'_0)} [/latex] Contracting observer observes all cosmological distances grow simultaneusly such that [latex] R(t') = R_0 / L = R_0 \cdot e^{k(t'-t'_0)} [/latex] I could select ofher symbol instead of k, say p : [latex] L(t') = e^{-p(t'-t'_0)} [/latex] If i add the curvature in the equation, i should take into account that in the viewpoint of contracting observer, the curvature radius of the space R appear to increase (similarly as all other distances) such that: [latex] R_{curv}(t) = R_0 / L(t') = R_0 \cdot e^{p(t'-t'_0)} [/latex] and i think the curvature k is inverse of the curvature radius: [latex] k = 1/R [/latex] ,when [latex] k(t) = k_0 \cdot e^{-p(t'-t'_0)}[/latex] the term p^2 comes from that in the viewpoint of contracting observer, the space appears to expand more, and if the contraction of matter is exponential function of co-contracting time, the solution for vacuum universe is [latex](\frac{\dot{a}}{a})^2= p^2 [/latex] And then i claim a theorem that i can just add this vacuum solution term p^2 coming from contraction of matter to the ordinary Friedmann-equation In Lambda-CMD universe: so the Friedmann equation would be now: [latex]\frac{\dot{a}}{a})^2=\frac{8\pi G}{3}\rho-\frac{kc^2 e^{-p(t'-t'_0)}}{a^2} + p^2 + \Lambda [/latex] Or, if you define the lambda and k differently: [latex] H^2=(\frac{\dot{a}}{a})^2=\frac{8\pi G}{3}\rho-\frac{ke^{-p(t'-t'_0)}}{a^2} + p^2 + \frac{\Lambda}{3} [/latex] This is the 1st. friedmann equation only if the transformation factor function is exponential [latex] L(t) = e^{-k(t'-t'_0)} [/latex] This is also equation for space that has ordinary matter, radiation, curvature, cosmological constant - and this new particle contraction / matter contraction - phenomenon, assuming that nearly all matter has same proper time (postulate is that particle contraction depends on proper time), same transformation factor L and also same transformation factor change rate dL/dt ( which is not the case in compact stellar objects, relativistic particles and generally in all matter that has had different time dilation history. Due to different time dilation histories of the matter, there should be so called differently transformed matter in the universe. )

Problem: Rotating black hole that has different inertial mass than gravitational mass Kerr metric describes rotating black hole: [latex] c^2 d\tau ^2 = \left ( 1- \frac{r_s r}{\rho ^2} \right )c^2 dt^2 - \frac{\rho ^2}{\Delta }dr^2 - \rho ^2 d\theta ^2 - \left ( r^2 + \alpha ^2 + \frac{r_s r\alpha ^2}{\rho ^2}sin^2\theta \right )sin^2\theta d\phi ^2 + \frac{2r_s \alpha sin^2 \theta }{\rho ^2}c dt d\phi [/latex] ,where [latex]\alpha = \frac{J}{Mc} [/latex] [latex]\rho ^2 = r^2 + \alpha ^2cos^2\theta [/latex] [latex] \Delta = r^2 + r_s r + \alpha ^2 [/latex] Einstein's theory of gravitation has a postulate that gravitational mass is equal to inertial mass. In this cosmological model however the matter that has transformation difference relative to observer, appears to behave as if it had different inertial mass than gravitational mass: [latex] m_{inertia} \neq m_{gravitation} [/latex] for black holes that has transformation difference relative to ordinary matter according to particle contraction law, the apparent difference between the inertial and gravitational mass is: [latex] \frac{m_{inertial}}{m_{gravitational}}= e^{-6.93 * 10^{-11} \cdot T[years]} \approx (1 - 6.93*10^{-11} \cdot T[years]) [/latex] ,where T is the age of the black hole The problem is - how does Kerr metric change, if the black hole has different inertial mass than gravitational mass? At least this change affects to inertial momentum, and therefore to all properties that depend on it, [latex] (\alpha , \rho ,\Delta ) [/latex] The different inertial momentum affects to : - the form of ergosphere - frame dragging - Penrose mechanism / Penrose process

ok, thanks:) I came cross into one interesting thing that is related to quasars - according to few studies - quasars with different distances do not show signs of cosmological time dilation in their power spectrum. (On time dilation in quasar light curve M. R. S. Hawkins 1988) I am not sure if this has some natural explanation. In this model there are two new changes that should happen in quasars in cosmological time scale: 1 Black holes should grow at rate exp( Ht ) = exp (6.93* 10^-2 [1/Byears] * t [byears] ) relative to contracting observer (also their gravitation constant also changes such that G= L^2 and in cross interactions with ordinary matter G = L(?), and their mass decreases M=1/L relative to contracting observer) 2 the matter in quasar jet, being ultrarelativistic or relativistic, should gain transformation difference at rate if they travel long distances

Matter in neutron stars: The observations of pulsars and binary system neutron star may be able to prove or disprove this cosmological model. there are few thousand known pulsars currently. The gravitational time dilation inside non-rotating neutron star would be: [latex] ( \frac{\tau}{t_{inf}}) = \sqrt{ 1 - (\frac{1}{c^2}) ( \frac{GMr^2}{R^2} - \frac{3GM}{R})} [/latex] and you can see straight from this equation that the time dilation in the center is 3 times larger than on the surface. The real neutron star is rotating, so it has Kerr metric ? or different metric, and it is not currently known what kind of equation of state does the matter have inside the neutron star. If neutron star has mass m = 2 * mass of a sun and diameter 15 km, then its surface should have time dilation (1 - 0.1045) = (1 - D) According to particle contraction law what is the basis of this cosmological speculative model, that depends on the proper time of the matter, the matter in the neutron star should gain transformation difference relative to ordinary matter with no time dilation such that: [latex] D = 0.1045 [/latex] [latex] k = H = 6.93*10^{-11} [1/year] = 2.20 *10^{-18} [1/s] [/latex] [latex] L_{rel}=e^{HDt} = exp(0.1045* 6.93*10^{-11} [1/year] * t )= exp(7.240*10^{-12}[1/year]\cdot t[years]) [/latex] [latex] \approx( 1+7.240*10^{-12}[1/year]\cdot t[years])) [/latex] This should affect to the Newton's second law such that: 1. The gravitational acceleration of neutrons star in binary system should increase by factor 1/L 2. The moment of inertia of a pulsar should decrease by factor 1/L 3. The inertial mass of neutron star should decrease and since neutron star have more time dilation in the center than on its surface, maybe 3 times according to non-rotating case, then the effect may be approximately 3 times larger in the center of the neutron star. The older neutron star, the more time the matter has had time dilation and therefore the more it should have these 3 changes. Also the pulsation frequency of pulsar should decrease and its radius should grow - if the pulsar had homogenous time dilation then the decrease rate would be factor of 1/L and the increase of radius would be by factor L of course this is so only if i havent done any mistake.

again i may have made mistake but.... i dont have time to correct them now

(I have made mistakes in the gravitation interactions of transformed matter in earlier posts, i think i now get it right: -The gravitation of transformed matter changes such that - transformed matter causes equal gravitation force than ordinary matter, but its inertial mass has changed.) A Very Short Summary: If the universe is observed by contracting observer, the Friedmann 1.st equation would be: [latex] \left ( \frac{\dot{a}}{a} \right )^2 =\left ( \frac{8 \pi G}{3} \right ) (\frac{\rho_{m,0}}{a^3} + \frac{\rho_{r,0}}{a^4} ) +k^2 +\Lambda [/latex] , if the matter contracts such that transformation factor function is [latex] L(t') = e^{-kt'} [/latex] ,where t' is elapsing time of contracting observer. the term k^2 is very similar to cosmological constant and may therefore be a substitute for it. There is now however possible new density component, "transformed matter", which should be inserted to above equation. Transformed matter. Transformed matter has different transformation factor L than ordinary matter. It may be possible that the universe has already contained in early ages transformed matter, that has significant transformation difference relative to ordinary matter. This may be a candidate for dark matter. In principle the transformed matter may be both contracted matter L<1 or expanded matter L>1 Even if it is assumed that all matter has have relative transformation factors close to 1 in early universe,the time dilation differences causes compact and relativistic matte to gain so called transformation difference relative to ordinary matter (=matter that has L =1 in co-contracting coordinates ): This kind of process produces "relatively expanded matter" that has L>1 relative to ordinary matter. [latex] L_{relative} = \frac{L(\frac{\tau_1}{\tau_2}(t'-t'_0))}{L(t'-t'_0)} = e^{kD(t'-t'_0)} [/latex] ,where D describes relative time dilation difference and it is [latex] D = (1 - \tau_1 / \tau_2 ) [/latex] t' is elapsing time of contracting observer. According to transformation equations, the gravitational mass, gravitation constant and inertial mass change for this matter such that: [latex] m(t')/m(t_0) = \frac{1}{L_{relative}} = e^{-kD(t'-t'_0)} [/latex] and [latex] G(t')/G(t_0) = L_{relative}^2 = e^{2kD(t'-t'_0)} [/latex] and compact and relative matter have therefore density: [latex] \rho_{comp} = \frac{\rho_{comp,0}}{a^3} \cdot e^{-kD(t'-t'_0)} [/latex] In the gravitational interaction, the change in gravitation constant cancels the change in gravitational mass: [latex]F(t') = \sqrt{G_1 G_2} \frac{m_1(t') m_2(t') }{R(t')^2} = L_1 L_2 G(t'_0) \frac{L_1 m_1(t'_0) L_2 m_2(t'_0)}{R(t'_0)^2 a(t')^2} = F(t'_0) a(t)^{-2} [/latex] (note that R changes such that [latex] R(t') = a(t')R(t'_0) [/latex] when the universe expands) And the transformed matter causes equal gravitation force than ordinary matter (=matter that has L =1 in co-contracting coordinates ) But the Newtons second law changes for such matter such that: [latex] a(t') = (F/m(t_0)) e^{kD(t'-t'_0)} [/latex] -That is - compact and relativistic matter appears to cause equal gravitational force than ordinary matter, but it accelerates more easily. ( Its inertial mass have decreased) k is close to hubble constant H = 2.20 * 10^-18 1/s = 6.93 * 10^-11 1/year EDIT : i made some corrections