caracal Posted February 12, 2016 Share Posted February 12, 2016 (edited) Description of the hypothesized phenomenon: Local Isotropic length contraction that is associated with time contraction and energy expansion OR Local isotropic length expansion that is associated with time expansion and energy contraction OR Local velocity-invariant length contraction/expansion Hi everyone, i would like to talk here about one hypothetical phenomenon, what i have thought through many times and done many checks, does it violate something or not. In principle when it is examined how it fits together with the theories of relativity there is nothing badly wrong with it - it does not change Lorentz covariance and it does not change the form of the Einsteins field equation, which i show here briefly. There is one open question how it fits together with the principle of mass-energy equivalence. But i want to emphasize that it has never ever been observed in laboratory on in the nature. But it may be, that nobody have ever thought that it can exist and nobody has ever tried to find it. This phenomenon may belong to a larger class of phenomena, so called local space transformations, where some local area of space or some local physical object can transform into different forms which may include length contractions or expansions, time contractions or expansions, rotational transformations or for example space drift, and they can be nonhomogenous and time dependent -but i wont write about these. But generally some local area of the space or spacetime may have ability to transform into different kind of forms - under some conditions which i can honestly say that i am not aware of. Time dilations and length contractions or expansions in the theories of relativity can be thought as special types of space transformations: -Length contraction that is associated with time dilation and relative velocity -Gravitational Time dilation that is associated with gravitation And the theories of relativity describe the properties of these space transformations very accurately. Properties of isotropic velocity-invariant length contraction / expansion What i want to write about is the following transformation, that is hypothetical and it has never been observed anywhere in any laboratory, any test, or any observation. It is isotropic length contraction that is associated with time contraction and energy expansion. This LST (Local space transformation) can be described with transformation equations, which describe how different kind of physical quantities or observables transform. The mathematics of the transformation equation of this type of LST, when the transformation is homogenous,is exactly same as the mathematics of the unit conversions. You need to define 3 independent transformation equations to be able to derive all the other transformation equations similarly as you need to define 3 independent unit conversion equations to be able to derive all other unit conversion equations: (1) s'/s = L length transformation (2) t'/t = L time transformation (3) E'/E = 1/L energy transformation and by dimensional analysis, and with help of commonly known physical laws such as Newtons 3 laws, Coulomb law, Lorentz force law, Newtons Gravitation law you can now derive the transformation equations for the other quantities. I call this LST as velocity-invariant local length transformation, since it keeps all velocities invariant: v'/v = 1 Justification for the equations 1,2,3 How to justify these 3 equations? A) By looking the theory of relativity (1) and (2) implies that all velocities are invariant: v'/v = 1, and for this reason, (1) and (2) makes the line element equation in Minkowskian metric unchanged: ds^2 = c^dt^2 - dr^2 <=> ds'^2 = cdt'^2 - dr'^2 (3) -equation will make the Einstein field equation unchanged: All terms in Einsteins Field equation will transform like 1/L^4 B) By looking the observation of a photon: (1) and (2) equations will transform photon such that its frequency changes like 1/L and its wavelength changes like L, and (3) equation shows that photons energy is proportional to the change of the frequency and inverse proportional to the wavelength. This is logical, but you have to assume here that the Planck's constant is invariant. the equations (1), (2) and (3) actually makes the Planck constant invariant under this transformation: h'/h = 1 More Transformation equations The other transformation equations are: m'/m = 1/L mass v'/v = 1 velocity p'/p = 1/L momentum a'/a = 1/L acceleration F'/F = 1/L^2 local force (force of a a local event) P'/P = 1/L^2 local power (power of a local event) V'/V = 1/L^3 volume d'/d = 1/L^4 density Q'/Q = 1/L electric charge e'/e = 1/L fundamental electric charge G'/G = L^2 gravitation constant k'/k = L^2 Coulomb constant e'/e = 1/L^2 electric constant u'/u = L^2 magnetic constant c'/c = 1 velocity of light l'/l = L wavelength of light f'/f = 1/L frequency of light h'/h = 1 Planck's constant is invariant As you can see here, the Coulomb constant and Gravitation constant must change too. Local principle of relativity The most mystical thing of this type of transformation is - that it can satisfy the principle of relativity. The principle of relativity is weird property in the theory of relativity, that states that the laws of nature are identical in all reference frames (in special relativity) Basicly in this situation, this principle states that local observer measures all laws of nature to be normal by doing local measurements inside the area that has been transformed. The local observer is not able to deduce whether the local space has been transformed or not, and he cannot deduce the value of the transformation factor L by doing local measurements. In principle this kind of principle can be satisfied in homogenous, isotropic length contraction. This is of course a hypothesis and it may be debuted. Mass - energy equivalence and energy conservation As i wrote in the introduction, there is one issue on the mass- energy equivalence. According to mass- energy equivalence E = mc^2 , when the mass changes like 1/L, the energy content of the system should change also like 1/L. But when we look at for example hydrogen atom, the energy of this system will change like L - the Coulomb constant changes like L^2 and both charges changes like 1/L - these changes cancel each other out (if there is no delay in the interaction) But since the matter wave length of the electron changes like L, the electron will end up into closer orbit to proton, what would mean that the energy of the system changes like L. (EDIT: there may be deduction mistake in this section....) Transformed matter So this kind of transformation would change the properties of the matter in a way that is described by transformation equations - similarly as the unit conversion change the amplitudes of different observables. IF there were this kind of transformed matter in the interstellar medium, it would appear to have spectral lines exactly like ordinary matter with doppler shift. There is however one exception - in the clouds where there are two or several differently transformed matter particles presents, there should be additional weak spectral lines present due to electron transfitions between slightly differently transformed protons. Applying velocity-invariant isotropic length contraction to cosmological model I emphasize that I haven't presented here any kind of mechanism that can produce this hypothetical LST. There is one interesting possibility that this isotropic length contraction takes place in matter in cosmological time scale. It may be possible to construct cosmological model, where the expansion of the universe is totally or partly subtituted by the contraction of matter in the universe: s'/s = L(t) t'/t = L(t) E'/E = 1/L(t) Where L(t) is decreasing function of the proper time of the matter and L(now) = 1 You can crudely estimate that L(t) is exponential function such that: L(t) = exp (-Ht) , where H is parameter that is close to Hubble constant H0 = 2.20 * 10^-18 1/s Predictions of the cosmological model based on isotropic length contraction of matter This kind of hypothesis- that all matter contracts as a function of its proper time would explain following cosmological observations: -Robertson - Walker metric in flat space: ds^2 = c^2dt^2 - a(t) dr^2 -Cosmological red shift -Cosmological time dilation -Cosmological decrease of photon's energy -Thin light ray cross section grows proportional to (1+z) (increase in angular size) -Surface brightness decreases proportional to (1+z)^4 This hypothesis makes also clearly different predictions, this is because the proper time of the matter is subject to time dilation: (1) Since the weakly bound celestial object cannot contract as the matter contracts, the distances between celestial objects should grow as a function of time. This means that there is additional velocity component present in the dynamics of the solar system, which i call "distance expansion" v = HR , where R is the distance Distance expansions in solar system: -Earth - moon : HR = 2.63 cm/year -Earth - sun : HR = 10,4 m / year note that this is additional velocity component, and therefore it may not describe the true change in the distances. (2) As the matter contracts, the distances between the surfaces of two celestial objects will grow - all celestial objects appear to contract. Contraction of the sun: HD = 10.4 cm /year D = is the diameter of sun = 1 AU/100 (3) Atom clocks in satellites that have either time dilation or time expansion, should have additional time dilation or time expansion due to the different contraction velocities of the matter: dt'/dt = 1 + HD where D is relativistic time dilation factor. This time dilation wont perish, when the atom clock is brought back to surface of earth and compared to an identical atom clock, but it should be a permanent property of the atom clock. There are also more exotic predictions: -There should be differently transformed matter in cosmic rays and quasar jets that travel cosmological distances -There should be additional weak emission lines in interstellar clouds due to different time dilation histories of matter, due to electron transitions between differently transformed matter. -The black holes appear to grow at rate R( 1 + Ht) -Pulsars appear to slow down at rate (1 + HDt) where D is relativistic time dilation factor. Edited February 12, 2016 by caracal 1 Link to comment Share on other sites More sharing options...
swansont Posted February 12, 2016 Share Posted February 12, 2016 I call this LST as velocity-invariant local length transformation, since it keeps all velocities invariant: v'/v = 1 Justification for the equations 1,2,3 How to justify these 3 equations? A) By looking the theory of relativity (1) and (2) implies that all velocities are invariant: v'/v = 1, and for this reason, You lost me. Velocity is invariant? How does that work, exactly? Link to comment Share on other sites More sharing options...
caracal Posted February 12, 2016 Author Share Posted February 12, 2016 (edited) You lost me. Velocity is invariant? How does that work, exactly? The equations (1) s'/s = L (2) t'/t = L describe how in the transforming region, if it is observed by some non-transformed observer, how -the values of lenght and values of time , or -the unit of length and unit of time , or -the increment of length and increment of time changes. The transformation is a phenomenon that changes the actual values of the length and time, if they were observed by observer that does not transform. It may be more clear to use instead of using just s , s' and t , t' some subscript marking sunit or tunit or to use increments or differentials to make the point that the change applies to all lengths and all time intervals in the transforming region. The math for the trasformation equation for velocity is very simple: velocity is v = s/t , so if (1) s' = L s and(2) t' = Lt that implies that v' = s'/t' = s/t = v <=> v'/v = 1 In other words, all values, units or increments of the local velocities in the transforming area remain unchanged. In other words, all velocities remain invariant under this type of LST. Here is also an assumption that the transformation is homogenous in the region I give here an Example how the math in this velocity-invariant isotropic LST works: Lets imagine that there are two regions, A and B and inside these regions there are two observers OA and OB. If the region A transform relative to region B such that (1) sA/sB = 10 (2) tA/tB = 10 (3) EA/EB = 1/10 The observer OB will observe following changes in the area A: - length unit and all lenghts in region A are 10 times larger than his own lenght unit in region B - the time rate in region A is 10 times slower than in the region B - All energies in the region A are 10 times weaker than in region B - All other properties in the region A change by following amounts: * all accelerations are 10 times slower * all momentums are 10 times smaller * all local forces in events that are inside region A are all 100 times weaker * all powers in events that are inside region A are all 100 times weaker * all velocities remain exactly same * the planck constant remain exactly same * the fundamental charge is 10 times smaller * the gravitation constant and coulomb constant are 100 times stronger (EDIT in local events) But according to the local principle of relativity the observer OB will measure all lenghts , time intervals and energies as all other physical observables and laws of nature in his own region B perfectly normal. The observer OA will measure exactly the inverse changes in the region B, but again according to local principle of relativity, he will measure all physical observables and laws of nature in his own region A perfectly normal and unchanged. A More exotic example would be if you imagine that if space vessel somehow get contracted by this velocity invariant LST say by factor 100. This sounds like almost science fiction, but this is exactly what the local principle of relativity implies if this phenomenon is put into its extremes: How The pilot in the vessel would observe the conditions on the surface of earth: - Earths radius is 600000 km - the time appears to run 100 times slower on earth - the temperature of the air in the earth is 100 times smaller T = 3 K - sun appear to have surface temperature 60 K - the "light" of the sun has now 100 times longer wavelengths - earths gravitation pull is 100 times weaker: 9.81 cm/s² - escape velocity of the earth is exactly same 11km/s - the gravitation constant of earth is 100 00 times stronger (EDIT for local events) - the density of the matter on earth is 100 00 00 00 times smaller (EDIT the gravitation constant between two differently transformed regions/objects is propably the geometric mean Gab = (GaGb)1/2) On the other hand, a normal human would observe following properties in the 100 times contracted space vessel: -it is 100 times smaller -its time runs 100 times faster -its temperature is 300 00 K (if its assumed to be 300 K for the pilot) and if not thermally insulated, the vessel appears to glow more or less like black body in 300 00 K temperature -its mass is 100 times higher -it has 100 times more energy in fuel tank than normal vessel has -its density is 100 00 00 00 times greater This sounds more like space fantasy or science fiction, but if the phenomenon is put to its extremes this is exactly what the phenomenon should look like - if it satisfies the local principle of relativity and if the transformation is homogenous. In the hypothetical cosmological model i presented here - the relative factor L between two kind of material - if it changes in cosmological time scale may be very small: 1 + 2.2 * 10⁻18 1/s * t * D or 1 + 6.93 * 10⁻11 1/year * D * t(years), where the D is time dilation factor . That would mean for example that in order to have relative factor L = 1.07 , a space traveler should spend 1000 000 000 years in the vicinity of black hole or travel across the universe at light velocity for 1000 000 000 years. Edited February 12, 2016 by caracal Link to comment Share on other sites More sharing options...
caracal Posted February 15, 2016 Author Share Posted February 15, 2016 (edited) Cross interactions Hi all, there is one issue what i didn't mention in the transformation equations. All transformation equations for interaction properties such as forces and interaction constants apply only for local events, where all participating interactors belong to the transforming area. But those dont apply for interactions between two interactors that belong differently transformed regions or objects. For these situations, the equations for forces and interaction constants are propably the geometric means of the two. Cosmological model and 2 corrections to Newtonian Gravitation Law The cosmological model i presented above gives a prediction, that there There would be two corrections to newtonian gravitation 1. Distance expansion, that is a velocity component that has opposite direction than the gravity pull :vdistance expansion = HR . This distance expansion velocity is apparent effect that comes from the contraction of the matter, and contraction of the meter stick the local, "contracting oberver" uses. Weakly bond stellar objects do not contract isotropically when the matter contracts, therefore all distances between weakly bound objects appear to grow as a function of time for contracting observer. Note that distance expansion is NOT caused by any force, it is a velocity component. 2. Interaction delay term - If the matter contracts and changes the masses and gravitation constant of two bodies M1 and M2 , due to that the graviation effect travels at light velocity, there is a delay Tdelay = R/C in the gravitation interaction that causes transformation difference between real M1 and apparent M2 and real M2 and apparentM1 , and this cross interaction gives therefore there term L(0-Tdelay) > 1 in newtonian gravitation: FG = (1-HR/c) (-G M1M2 / R2 ) = GM1M2( -1/R^2 + (HR/c)/R) (this is linear approximation) (EDIT is it + or - ?) putting the two together: Corrections to Newtonian Gravitation: (1) vdistance expansion = HR weak repulsive velocity component due to distance expansion (that is NOT caused by any force) (2) FG = (1-HR/c) (-G M1M2 / R2 ) = GM1M2( -1/R2 + (HR/c)/R) weak force term (or factor) due to interaction delay (these are linear approximations, real values depend what kind of function L(t) is) where H is close to Hubble constant: H=2.20 * 10^-18 [1/s] and (H/c) =0.734 * 10^-26 [1/m] = 0.0776 * 10^-11 [1/Ly] = 7.76 *10^-10 [1/KLy] (at the moment i am not able to estimate directly how much would these two corrections would change galaxy dynamics) Edited February 15, 2016 by caracal Link to comment Share on other sites More sharing options...
Mordred Posted February 15, 2016 Share Posted February 15, 2016 (edited) How in the world can you have contraction that is not caused by any force? Secondly why are you not applying the thermodynamic laws? Is it because if you take any object and compress it you change the temperature? Which we don't see happening? It's great that your trying to use math to describe your model but your missing the key aspects in the FLRW metrics (that being the thermodynamic involvement) Now here is a problem I can immediately see wrong on your math. That being the Hubble constant itself. The Hubble constant is only constant throughout the observable universe at a specific moment in time. It's value changes these changes can be calculated. (Or measured). If you do the calculation you will find that Hubbles constant increases as you go back in time. [latex]H_z=H_o\sqrt{\Omega_m(1+z)^3+\Omega_{rad}(1+z)^4+\Omega_{\Lambda}}[/latex] You can use this formula to calculate the Hubbles constant then as opposed to now. For example at z=1100 CMB roughly Hubbles constant is. H today of 67.9 km/s/Mpc. Leads to ratio of H/H_O is 23257.149 multiplying this value by Hubbles constant today tells us H then 540894979.6 km/s/Mpc. how did you derive this equation? [latex] F_g = (1-\frac{HR}{c}) (\frac{-G M1m2}{R^2})[/latex] Why the minus sign for G? Either way the left hand side doesn't match the right hand side if you do a dimensional analysis. Edited February 15, 2016 by Mordred Link to comment Share on other sites More sharing options...
imatfaal Posted February 15, 2016 Share Posted February 15, 2016 ..how did you derive this equation? [latex] F_g = (1-\frac{HR}{c}) (\frac{-G M1m2}{R^2})[/latex] Why the minus sign for G? Either way the left hand side doesn't match the right hand side if you do a dimensional analysis. [latex] F_g = (1-\frac{HR}{c}) (\frac{-G M1m2}{R^2})[/latex] I am sure we agree that [latex] F_g = (\frac{-G M1m2}{R^2})[/latex] Is dimensionally correct - it is standard Newtonian Gravity (by the way I would also have a minus as it is the standard representation when no unit radial vector is present) and this [latex] (1-\frac{HR}{c})[/latex] is surely dimensionless [latex] (1-\frac{[s^{-1}][m]}{[m][s^{-1}]})[/latex] The idea looks like nonsense to me - but your comment was just raising a blue rag to a pedant Link to comment Share on other sites More sharing options...
Mordred Posted February 15, 2016 Share Posted February 15, 2016 Yeah I found where I did my error I was about to correct my post. Link to comment Share on other sites More sharing options...
imatfaal Posted February 15, 2016 Share Posted February 15, 2016 Yeah I found where I did my error I was about to correct my post. I learnt about dimensional analysis here - shows how lacking my formal science education was - so I take a perverse pleasure in looking at almost every equation that displays on my screen and just checking. My poor timing I am afraid Link to comment Share on other sites More sharing options...
Mordred Posted February 16, 2016 Share Posted February 16, 2016 (edited) It's a handy cross check on new formulas for sure. I don't think the formula is getting the desired results though. Maybe due to not knowing Hubbles constant varies increases as the observable universe gets smaller. I have run some calcs. For the calcs I have set M_1 and M_2 as 1 kg mass, radius size of observable universe at time of a specific value of z. To improve accuracy I'll use data from the Cosmo calc keeping the same degree of accuracy in units. So as the calc uses Gly I'll do the same. Z=1100 H/H_O=23257.146 radius 0.000619 Gly. H today 67.9 H then 67.9*23257.146. Result 4.11*10^-55 kg m/s^2. http://www.wolframalpha.com/input/?i=(1-+540894979.6+km%2Fsec%2FMegaparsec*0.000619+Gly%2F+c+)(G*1kg*1+kg%2F0.000619+Gly%5E2) Observable today from calc data observable universe 14.399932 Gly. H =67.9 5.1*10^-62 kg/m/s^2 I could be misreading what your doing here. "2. Interaction delay term - If the matter contracts and changes the masses and gravitation constant of two bodies M1 and M2 , due to that the graviation effect travels at light velocity, there is a delay Tdelay = R/C in the gravitation interaction that causes transformation difference between real M1 and apparent M2 and real M2 and apparentM1 , and this cross interaction gives therefore there term L(0-Tdelay) > 1 in newtonian gravitation:" Oh you specified local so lets use 1 metre I set 1 metre for R. Run 67.9 km/s/Mpc. getting 6.67*10-11 http://www.wolframalpha.com/input/?i=(1-+67.9++km%2Fsec%2FMegaparsec*+1+m%2F+c+)(+(-G*1kg*1kg)%2F1+m%5E2) For some reason wolframalpha links are parsing the full equation links However I'm still not seeing results that makes sense. Just noticed you specified G as 100* stronger but that still doesn't explain the numbers I'm getting. Edited February 16, 2016 by Mordred Link to comment Share on other sites More sharing options...
caracal Posted February 16, 2016 Author Share Posted February 16, 2016 (edited) How in the world can you have contraction that is not caused by any force? Secondly why are you not applying the thermodynamic laws? Is it because if you take any object and compress it you change the temperature? Which we don't see happening? It's great that your trying to use math to describe your model but your missing the key aspects in the FLRW metrics (that being the thermodynamic involvement) Now here is a problem I can immediately see wrong on your math. That being the Hubble constant itself. The Hubble constant is only constant throughout the observable universe at a specific moment in time. It's value changes these changes can be calculated. (Or measured). If you do the calculation you will find that Hubbles constant increases as you go back in time. [latex]H_z=H_o\sqrt{\Omega_m(1+z)^3+\Omega_{rad}(1+z)^4+\Omega_{\Lambda}}[/latex] You can use this formula to calculate the Hubbles constant then as opposed to now. For example at z=1100 CMB roughly Hubbles constant is. H today of 67.9 km/s/Mpc. Leads to ratio of H/H_O is 23257.149 multiplying this value by Hubbles constant today tells us H then 540894979.6 km/s/Mpc. how did you derive this equation? [latex] F_g = (1-\frac{HR}{c}) (\frac{-G M1m2}{R^2})[/latex] Why the minus sign for G? Either way the left hand side doesn't match the right hand side if you do a dimensional analysis. Imatfaal and Mordret, So you all decided to throw me all these question today? wow! ) I answer to you question Imatfaal - i cannot quite follow what mordret has written. Question (1) How in the world can you have contraction that is not caused by any force? Answer - This "distance expansion" is apparent effect that is caused by the contraction of the observers meter stick. So being apparent effect, it is not caused by any force. Also if you took the derivative from it, you get zero. Question (2) Secondly why are you not applying the thermodynamic laws? Is it because if you take any object and compress it you change the temperature? Which we don't see happening? Answer - as i wrote in section "local relativity principe" - because the transformed region satisfies the local relativity principle. Local observer cannot measure any differences in LOCAL laws of nature by doing LOCAL measurements. This is the key thing in the cosmological model. This is why we are not able to deduce have we been contracted in past or not and what is our transformation size now by doing only local measurements. The contraction factor L is changing, but as the matter contracts very slowly, you can in principle say that the transformation factor L is constant in short time scales. So this isotropic and homogenous contraction that is very close to constant in short time scales. does not have any effect to the thermodynamical laws as long as they are observed by LOCAL observer. Local observer does not measure any changes in laws of nature. There is one issue however: due to time dilation differences between electron and atom nuclei, electrons should contract slightly different rate than nuclei. The diffference rate is (1 + HDt) where D is time dilation factor. So it is very very small deviation process. This difference may however be balanced by for example electron exchange processes. Point (3) your missing the key aspects in the FLRW metrics (that being the thermodynamic involvement) Answer: - i havent derived friedman equations , but i have tried to explain the reason for FLRW metric : instead that the universe is expanding, the matter in the universe is contracting. This contraction may subtitute the whole expansion, or part of it. However there are different predictions, because the contraction of matter depends on the proper time of the matter, and all matter that are subject to time dilations, will therefore contract slightly slower. Point (4) Now here is a problem I can immediately see wrong on your math. That being the Hubble constant itself. The Hubble constant is only constant throughout the observable universe at a specific moment in time. Answer : There is now new function L(t), that is unknown function of time. This function tells how the matter contracts as a function of fixed or co-contracting time. L(now) = 1 similarly as a(now) = 1 and L(t) is decreasing function, such that L -> 0 when t -> infinity. You can crudely estimate that L(t) is decreasing exponential function of fixed time. Here you have to remember, that in this phenomenon, the time unit of the observer contracts too. The time starts to run faster. Which i think makes L(t) to be linear function as a function of co-contracting time L(t) = 1 - Ht. Here the H is close to H0 - the hubble constant at present time. However since i havent derived friedman equation, and take into account that gravity and possibly some expansion of the universe and possibly cosmological constant have effect to the scale factor a(t), i can only estimate crudely what is L(t0) or what is the linear approximation for L(t) from Hubble's law. Question (5) : how did you derive this equation? [latex] F_g = (1-\frac{HR}{c}) (\frac{-G M1m2}{R^2})[/latex] Why the minus sign for G? Answer: You can take linear approximation for L(t) by fitting it to Hubble's law: L(t) = (1 - Ht) a) The distance expansion is velocity component, that as i explained is only apparent effect that comes from two things: the contraction of the observer's own meter stick and the other thing is that weakly bound objects do not contract isotropically when the matter contract - they remain to their position - therefore contracting observer measures that all distances between weakly bound stellar objects appear to grow as a function of co-contracting time. actually i am not sure of the b) there may be deduction mistake b) The interaction term comes from the fact that as both particles M1 and M2 contracts, particle M2 "observers" that particle M1 is less contracted than M2 due to delay. There is apparent transformation difference between M2 and M1, and the relative transformation factor between M1 and M2 is Lrelative apparent = (1 + HR/c) where HR/c is delay time. (Observer in particle M1 observes similar apparent transformation difference in M1) This apparent transformation difference causes two things in apparent M1: 1. The apparent mass of M1' is M1'apparent = M1 /(1 + HR/c) 2. The gravitation constant of M1' is G1 apparent = (1 + HR/c)² (is this right?) Now if i put these inputs 1 and to 2 to newtonian gravitation law Newtonian gravitation law becomes: a) v = HR (distance expansion velocity component) b) FM1'->M2 = -(1 + HR/c) G M1M2/R² (but i am not sure about this actually) and the minus sign in the force just means that the force is opposite to the direction vector R as in normal vector form of newtons law (where there is actually R³ in the nominator and vector R in the above ) Point (6) Either way the left hand side doesn't match the right hand side if you do a dimensional analysis. Answer: the factor comes from transformation difference and it is actually same as Lrelative apparent . L is dimensionless factor and it should be dimensionless. So i am able to answer all these question except that i am not sure of b) in corrected Newtonian gravitation law. i have to think about it. these cross interactions between differently transformed particles are the thing i am not sure yet how they goes. Edited February 16, 2016 by caracal Link to comment Share on other sites More sharing options...
Mordred Posted February 16, 2016 Share Posted February 16, 2016 Sounds to me your idea still needs some work. Part of the reason I mentioned thermodynamics is that one of the most commonly missed pieces of evidence is that the universe has cooled. The reason I chose to post the equation I did is two reasons. One the formula shows how the density of radiation, matter and the Cosmological constant vary as the volume changes. Note they don't change at the same rate. Secondly it shows that Hubbles constant changes over time. (Which in turn gives you a tool to check your model.) After all your equations need to work at every point in expansion. (Radiation, matter and Lambda dominant eras) Ive seen models before where you have contracting matter as opposed to expansion. The ones I recall fail to account for the thermodynamic aspects particularly on the global scale. The other aspect they had trouble with is redshift itself. (Which is also temperature influenced) As far as what you've shown I see a lot of maybe this or not sure statements. I'm also unclear how to test your math, M1 real and apparent M2 real and apparent, changing G etc. Link to comment Share on other sites More sharing options...
caracal Posted February 16, 2016 Author Share Posted February 16, 2016 Mordred - I try to answer to these - this may be a little repetitive but i hope it clarifies you... Quote: One the formula shows how the density of radiation, matter and the Cosmological constant vary as the volume changes. Note they don't change at the same rate. No they do not change locally in the point of view of contracting observer, because the isotropic velocity invariant length contraction follows local relativity principle - they remain exactly the same for "contracting observer" as does all laws of nature. You have to note that there is two different kind of coordinate systems: 1) fixed lenght - fixed time coordinate system, and 2) co-contracting coordinate system . And two different kind of observers - 1) non-contracting observer and 2) contracting observer. The local contraction of the matter is only visible in the fixed coordinate system, not in the co-contracting coordinate system. But since all matter contracts at same rate (except matter with significant time dilation), we all as observers, we do measurements in the co-contracting coordinate system, and we all are "contracting observers", mainly : whose meter stick contracts, whose time contracts or start to run faster, and whose unit of energy increases. Contracting observer does not measure any changes in the local laws of the nature due to local relativity principle. But as he looks back in time by observing distant objects - he will observe transformation difference in the past. Now the important thing is that this transformation difference in the past (time dilation, length expansion, energy contraction) looks like relativistic doppler effect (time dilation and redshift). (exception is that matter with time dilation - for example matter in neutron star, or matter in relativistic jets of quasars - contract less than normal matter with less time dilation) contracting observer will measure also the distance expansion history by doing observations of distant objects - weakly bound objects were closer together in past. Putting these together the contracting observer observes, that the universe appears to be expanding or following Robertson Walker metrics ds^2 = c^2dt^2 -a(t) dr^2 (in flat space) - however in this hypothetic model this expansion is only apparent effect, that is caused by the transformation of the observer (change in observers length time and energy units). But in this case the gravity still has effect on this metric. Quote: Secondly it shows that Hubbles constant changes over time. (Which in turn gives you a tool to check your model.) Yes, and the way how it changes depends on gravity, and if the expansion of the universe is totally subtituted by the contraction of the matter (Robertson - Walker metric comes only from gravity and contraction of the matter) - what kind of function L(t) is and has been in the past and will be in the future, in co-contracting time. I dont know what the L(t) is, but i can estimate crudely that in fixed time it may be close to L(t) = exp[-kt] Quote: After all your equations need to work at every point in expansion. (Radiation, matter and Lambda dominant eras) In this model there may not be cosmological constant - if the contraction of matter is wanted to explain the apparent expansion solely. But you can put cosmological constant there if you assume that this contraction of matter is only a partial explanation for the apparent expansion of the universe. Quote: Ive seen models before where you have contracting matter as opposed to expansion. The ones I recall fail to account for the thermodynamic aspects particularly on the global scale In this model, there is three major transformations that took place in this velocity invariant local length contraction: s'/s = L(t) t'/t = L(t) E'/E = 1/L(t) and by dimensional analysis you can derive how other physical observables and properties changes. So also the time unit changes and energy unit changes. The key thing here is again that this transformation satisfies local relativity principle - because of this - in the viewpoint of contracting observer, nothing appears to change in the local space near the contracting observer. so there is no change in thermodynamics either. --- Quote: As far as what you've shown I see a lot of maybe this or not sure statements. I'm also unclear how to test your math, M1 real and apparent M2 real and apparent, changing G etc. This changing G has to be so, if the local relativity principle is valid. But according to same principle, the transformed observer or contracting observer does not measure any changes in G or any value in any property locally. This apparent M2 is a bit misleading term - it means that - when M1 and M2 both are contracting as a function of time according to the hypothesis that all matter is contracting as a function of time, in the viewpoint of M1, the M2 appears to have contracted less than M1, and since the gravitation travels at light velocity, M2 appears to have different gravitation field that M2 has in reality. (here i should use co-contracting time, i guess i used fixed time in there) I think it may be a very good idea to derive Friedmann equations. Link to comment Share on other sites More sharing options...
Mordred Posted February 16, 2016 Share Posted February 16, 2016 Yeah working it into the FLRW metric is definetely a needed step. For example at any value of a the scale factor I can give you the temperature. I can even calculate the number density of any elementary particle. (Bose-Einstein and Fermi-Dirac statistics) from that temperature. Secondly I don't see any relation that covers redshift and this is an extremely important aspect. The first portion of your equation doesn't have any significant influence upon the second portion until you hit roughly 10^25 meters using 67.9 km/s/Mpc. try it 67.9 km/s/Mpc *1 metre/c. Dang close to 1. What unit of measure do you draw the line between local to global? 1 metre, 1Mpc ? Link to comment Share on other sites More sharing options...
caracal Posted February 16, 2016 Author Share Posted February 16, 2016 (edited) Quote: Secondly I don't see any relation that covers redshift and this is an extremely important aspect. I can answer to this. 1. s'/s = L(t) 2. t'/t = L(t) 3. E'/E = L(t) 4. Particle contraction law hypothesis : all matter in universe contracts such that L(t) = exp (-kt) where t is fixed proper time Cosmological Observations: These following 3 observations are caused by the fact that the photon has infinite time dilation, and it does not contract, when the matter in the universe contracts. The contraction law does not have effect on the photons. Therefore contracting observer observes changes in the photons that travel long distances in space. A.Cosmological Redshift: (1+z)/z = 1/L(tem) where tem = D/c where D = distance and L(tem) is the relative transformation factor what the matter in distant universe had time interval (t0- tem) ago B.Cosmological Time dilation: Temitter/Tobserver = 1/L(tem) where Temitter is time unit the matter in distant universe had time intervat (t0 - tem) ago C.Cosmological Energy loss of photon: E'/E = L(tem) D.Cosmological growth of thin light ray cross section : D(t0)/D(temitted) = L(tem) - the cross section of thin light ray appears to grow This observation is due that while all matter in universe contracts, the cross section of the light ray does not contract at all - and this causes apparent effect, that contracting observer observes the cross section to grow. Quote: The first portion of your equation doesn't have any significant influence upon the second portion until you hit roughly 10^25 meters using 67.9 km/s/Mpc. Yes that is very small term. I dont know may these two effect be significant enough to cause differences in galactic dynamics, and be sufficient to have MOND type explanation to galactic rotation curves. Or are they far too small. if i calculate R when the two terms are equal : 1/R^2 = (H/c) 1/R <-> R = c/H = 2.998 * 10 ^8m/s / 2.20 * 10 ^-18 m/s = 1.36 * 10^26 m = 1.36 * 10^26 m / 9.46 * 10^15 Ly/m = 14.4 BLy Quote: What unit of measure do you draw the line between local to global? 1 metre, 1Mpc ? Well, if all matter in universe contracts at equal speed, then all matter have exactly relative L = 1 all the time for "contracting observer". then the whole universe is local = has same transformation factor. But when you look into the past by looking distant objects, you observe that matter in the past has had transformation difference L(tem) > 1 relative to local matter in present time. But concidering the distance expansion: 1) you can think that all planets and stars are local objects that contract very slowly, but isotropically, because matter is strongly bound together 2) while the solar system, gas clouds and galaxies - that is too weakly bound, does not contract isotropically when the matter contracts - the objects in these systems remain in their place in fixed coordinate system. So i guess this is where the limit is where contracting observer can see distance expansion, and where nothing at all due to that all matter contracts similarly as the observer. Edited February 16, 2016 by caracal Link to comment Share on other sites More sharing options...
Mordred Posted February 16, 2016 Share Posted February 16, 2016 (edited) Sorry the last post doesn't make any sense. Your saying there is no expansion. Yet matter contracts sufficient enough to cause a redshift illusion of z=1100?. If matter contracted that much every planet would be ablaze due to the increase in its density. Sorry I'm not buying it. Especially since you don't require the Cosmological constant to have an expanding universe. Radiation can and has caused expansion as well. Not to mention you completely ignored the reference to the scale factor and temperature. [latex]a\propto\frac{1}{T}[/latex] Have you ever looked at z to distance values? Its not linear Edited February 16, 2016 by Mordred Link to comment Share on other sites More sharing options...
caracal Posted February 16, 2016 Author Share Posted February 16, 2016 (edited) sorry, this is also a bit repetitve answer. Quote:Sorry the last post doesn't make any sense. Your saying there is no expansion. no i wrote that in the case where you subtitute the expansion of the universe and cosmological constant totally by the hypothesis that the matter is contracting - there is expansion, but this is only apparent, not real expansion. It is apparent expansion in the viewpoint of contracting observer, which we are too, but it is not real expansion - it is an apparent effect that is caused by two things: 1. the contraction of the observers own meter stick 2. Weakly gravitationally bound interstellar object do not contract isotropically, when all matter in them is contracting - but they remain to their place. If you think this situation in fixed coordinate system, what you see, is that celestial objects contracts, but their position remain to what they have been. Since the transformation changes not only time, length and energy, but are physical properties and interaction constants - you would see them changing such that this transformation function L(t) starts to get smaller from its initial value 1. Their time rate accelerates, their energies increases and so on. Here i assume that since the contraction of matter is very slow process, all celestial objects contracts isotropically. What you see is that for example the temperature of the objects - among all other energies - appears to grow. If there were a human on the surface of that planet, since he contracts too - if he were still alive after millions of years - you would see that his time would run faster and faster. But if you think this situation in the viewpoint of the contracting observer, such as we are, whose meter stick contracts what you see is that - due to relativity principle (which is the most important thing to understand here) - since almost all matter contracts at the same velocity - everything seems to be normal otherwise, but the distances between celestial objects appear to grow as a function of time. But One thing what you see as a contracting observer, is that when looking to distant space and also to the past, the distant matter appears to have had transformation difference relative to you. That means basicly : all lengths have been bigger, the time rate appears to have been slower in the distance, and all the energies seem to have been smaller - and also all other properties - And the other thing what you would see is the distance expansion. -but these two observation looks very closely to that you see that distant objects just appear to move away from you and they have also relativistic time dilation. And you observe cosmological redshift, cosmological time dilation and loss of energy in photons because your own units of measure changes while photon remain unchanged due to the fact that its proper time is always 0 after emission. Quote: If matter contracted that much every planet would be ablaze due to the increase in its density. No, again because of the relativity principle - assuming that all matter contracts nicely isotropically very slowly - including the matter in the observer - contracting observer does not observe any changes in local matter, but he measure all laws of nature being normal - and that nothing at all have been happened in local area. except the distance expansion of the celestial objects. There is no increase of density in co-contracting coordinates. (i just noticed there is a logical mistake in the "contraction of sun" - part in first post. the sun does not appear to contract and its density remains exactly same) Quote: Especially since you don't require the Cosmological constant to have an expanding universe Yes it may not be necessary. But you can still add the real expansion of the universe into the picture if you want that. And also cosmological constant. This may not be necessary however. The contraction of matter with good choice for L(t) may explain Robertson Walker metric without cosmological expansion and without cosmological constant. i am not exactly sure what this function L(t) should be then. Quote: Radiation can and has caused expansion as well. Yes of course if effect on the expansion or since it has gravitational influence. no problem. Quote: Not to mention you completely ignored the reference to the scale factor and temperature. I am not sure what you mean but - The transformation difference in the past will make also all energies in the window of past - to behave like L - that is - to decrease. This means also temperature. Also the distance expansion may spread gas clouds into larger volume when they lose temperature. Edited February 16, 2016 by caracal Link to comment Share on other sites More sharing options...
Mordred Posted February 16, 2016 Share Posted February 16, 2016 (edited) Z=1 proper distance now. (Using Planck 2013 values. Z=1 11064.707 Mly Z=2 17314.77 Mly Z=3 21225.6514 Mly Z=4 23933.6225 Mly Z=5 25943.908 Z=6 27510.4166 Z=7 28774.7706 Z=8 29822.8057 Z=9 30709.7325 Z=10 31472.9467 That should be enough to show the non linear relation. The problem is you need to compare what you would calculate and what the FLRW metric would calculate for the proper distance now and what the temperature and corresponding volume would be. Then you would also need to redefine the equations of state. Matter, radiation have different EoS values their density doesn't adjust at the same rate. Now I am mentioning these details as the FLRW metric works extremely well with relativity and thermodynamic relationships. I am pushing you in the direction of developing your model in the direction of that same rigor. Otherwise your model will fail. In order to do that you will need to compare your metric answers to the answers that the FLRW metric will get. The next problem is your going to need to address the distance to luminosity relations. As well as diameter distance measurement. Changing a few basic formulas is a bare minimal start. By the way radiation does have gravitational influence ( all energy/density does) even gravity waves The point you keep missing though is compression raises temperature, expansion lowers temperature. Your compressing matter, which will raise the temperature of matter. If you didn't recognize this formula then you haven't looked at the thermodynamic portion of the FLRW metric. [latex]a\propto\frac{1}{T}[/latex] If that's the case then I have to ask how will you account for BB nucleosynthesis? https://en.m.wikipedia.org/wiki/Equation_of_state_(cosmology) You should review the EoS Point being you can't assume your model will work with thermodynamics you must show it does Edited February 16, 2016 by Mordred Link to comment Share on other sites More sharing options...
caracal Posted February 17, 2016 Author Share Posted February 17, 2016 (edited) Quote: If you didn't recognize this formula then you haven't looked at the thermodynamic portion of the FLRW metric. But if my hypothesis brings up FLRW metric (in flat space), then i guess this dependency comes from there if FLRW metric is sufficient condition for it. (That FLRW metric is nearly the only result of the hypothesis - is really possible due to the relativity principle. the only two different prediction of the hypothesis is that due to time dilation differences, there should be differently transformed matter in the universe - and due to interaction delays - there may be very small additional term in interactions) Quote: The next problem is your going to need to address the distance to luminosity relations. As well as diameter distance measurement. I think this model satisfies the Tolman test - which is that surface brightness goes down proportional to (1+z)^-4 -energy loss of photon (1+z)^-1 -time dilation -> loss of number count of photons (1+z)^-1 -thin light ray cross section area appears to grow like (1+z)^2 -> energy flux per square meter appear to decrease like (1+z)^-2 and also This thin light ray cross section growth -> diameter growth proportional to (1+z) Edited February 17, 2016 by caracal Link to comment Share on other sites More sharing options...
Mordred Posted February 17, 2016 Share Posted February 17, 2016 (edited) Your not considering what is the emitter wavelength and peak. Just judging from the numbers your throwing in your making assumptions. Google Weins displacement law. You are modelling a compression of matter sufficient enough to cause an illusion of no cosmological constant. The cosmological constant has attributed to a huge volume change in expansion. You need to look at actual numbers those formulas apply to. You can't just assume the formulas will work without testing them. For example stars themselves will compress. They are made of matter. What happens to their blackbody temperature as a result of further compression? You can't tell me and expect me to believe that it will remain the same, nor that they won't heat up due to compression. In the FLRW, your changing the average density of matter. This will cause changes to the curvature constant. (You need to look at actual numbers and it's multimodel influence) ( so far I'm suggesting relatively easy formulas to consider. I haven't mentioned the Einstein field equations, Bose-Einstein statistics, Maxwell- Boltzmann statitstics. Let alone the Boltzmann constant.) Next point you need to clarify which particles compress. (What type of particles count as matter particles) What is the influence on quage theories. So(5)*So(3)*SO(2)*U(1) ? What is the influence on coupling constants? Ie coupling constant of the strong force and electromagnetic force,gravitational force? Believe me your just getting started. Stop and ask yourself "How many formulas use the gravitational constant? ". "How many formulas does a varying gravitational constant influence, in how many different fields of study"? (Speaking of gravitational constant...what tests have been performed to confirm the gravitational constant? How is it determined in the first place?) These are the types of questions you need to address when you suggest modifying something as fundamental to physics as the gravitational constant. ( then there is also the fine structure constant, which is also influenced by the Cosmological constant). "In the January 2007 issue of Science, Fixler et al. described a new measurement of the gravitational constant by atom interferometry, reporting a value of G = 6.693(34)×10−11 m3 kg−1 s−2.[8] An improved cold atom measurement by Rosi et al. was published in 2014 of G = 6.67191(99)×10−11 m3 kg−1 s−2." https://en.m.wikipedia.org/wiki/Gravitational_constant Why do these tests not note a change in the gravitational constant? Edited February 17, 2016 by Mordred Link to comment Share on other sites More sharing options...
caracal Posted February 17, 2016 Author Share Posted February 17, 2016 The weird part of the model is the local relativity principle, which i see that you may not fully understand or see. IT IS weird property. But this principle is the key reason why nothing appears to change in stars or planets when the matter contracts, if they are observed by observers consisting the same matter and who is also therefore contracting. I am assuming that this principle is applicaple to macroscopic scale, when the contraction of the particles is a very slow process. so even humans , and all normal matter, contract under isotropic velocity invariant lenght contraction Quote: Your not considering what is the emitter wavelength and peak. Just judging from the numbers your throwing in your making assumptions. Google Weins displacement law. The emitter in the past was less contracted. Assuming that all matter contracts at same rate - in the past the distant emitting matter had so called transformation difference L = 1 + (H/c)D (this linear aproximation) - in other words the emitter had isotropic velocity invariant length expansion relative to the observer in earth in present time. This changes the emitters wavelength and peak were both therefore different. But if there were an observer near the emitter that have exactly same transformation difference L = 1 + HD/c relative to observer here in earth, as he should have had since all normal matter contracts at equal rate, he would have measured no changes in wavelength, peak or temperature in the emitter, or any value whatsoever. Why? again because of the relativity principle. i assume that the relativity principle is applicaple to macroscopic level when the particle contraction is very slow process. The local relativity principle works similarly as relativity principle in the theory of relativity - Observer is not able to measure any changes in nature laws if he is in different inertial coordinate systems - and he not able to deduce his velocity without measuring relative velocities relative to some other object. This very odd principle is indeed the key subject in this model. IF the relativity principle would not be true, then you would have changes in the densities of stars and temperatures of the stars. And i would also agree that the model wouldnt work: there should be significant changes in stellar evolution and structures of the stars. Quote: For example stars themselves will compress. They are made of matter.Quote: What happens to their blackbody temperature as a result of further compression? Nothing, absolutely nothing when all matter contracts at the same rate, if the relativity principle is applied to macroscopic scale. local observer would observe absolutely nothing. But when you look at distant stars, since the matter were less contracted then, the matter had relative transformation difference to matter in the present day. However if there were local observer consisting of same matter, because of relativity principle - he would not observe any changes - and he would think that absolutely nothing is different. The distant star would just appear to have redshift and time dilation 1+z = 1 + HD/c (linear approximation) no changes in any conditions in the star otherwise Local observer in earth would think that the distant star must be either moving away from us, or the space between us and the star is expanding - if he would have never heard of isotropic velocity invariant lenght expansion/contraction Quote: You are modelling a compression of matter sufficient enough to cause an illusion of no cosmological constant. no, i am modelling alternative explanation for FLRW metric in flat space for remnant expansion from big band and cosmological constant: - which also explains changes in photonic radiation.This hypothesis gives explanation also for cosmological redshift, time dilation and energy loss of photons and so called Tolman surface brightness-redshift relation. The weird part of the model is the local relativity principle, which i see that you may not fully understand or see. IT IS weird property. I try to sum up my view here: I am modelling alternative explanation for FLRW metric in flat space. 1. My first starting point assumption is that All matter in universe is subject to isotropic length contraction . it is described by three main transformation equations: 1) s'/s = L length unit in 3d 2) t'/t = L time unit in 3d 3) p'/p = 1/L or E'/E = 1/L unit of momentum or unit of energy and second assumption is: 2. particle contraction law: the function L(t) is decreasing function of time. L(now) = 1 and L(infinity) -> 0 The linear approximation of L(t) can be fitted to hubbles law: L(t) = 1 - Ht where H is hubble constant in situation , if there were no radiation and matter in the universe (that is -if there were no gravitation) 3. The third assumption is that local isotropic velocity invariant length contraction satisfies so called local relativity principle: -The local principle of relativity states that if the transformation is homogenous and time independent, local observer is not able to see any changes in local laws of nature, and is not able to deduce what is the value for absolute L by doing local measurements. There is no absolute value for L and L can have only relative values. 4. Since L is very slow function, i assume that the local principle of relativity is applicable also to macroscopic scale in systems that are bound mainly by EM interactions Since the contraction of particles is very slow process, you can assume that even macroscopic objects, such as planets, stars and human society, all life forms in earth, are strongly enough bound due to electromagnetic and gravitational interaction, are all contracting isotropically according to the equations of velocity invariant length contaction, when the particles contract. IF this is true, then the principle of relativity is applicaple to macroscopic scale, not only scale of particles. The implication of this is - that we - as contracting objects, when we do measurements, we see the local world as if the L = 1 all the time. Also we dont see any change in density, in temperature or any other physical condition. We see the world as if nothing has happened on the earth. 5. Distance expansion However the solar system, planets , interstellar gas clouds and galaxies, are not strongly enough bound - and therefore they do not contract isotropically. What happens in the viewpoint of local observer, is that they appear to remain otherwise perfectly unchanged, no changes in density or temperature but their distances appear to grow. I call this effect a distance expansion, and this is the effect what causes FLRW metric. I dont know exactly where is the limit between weakly bound and strongly bound system. But the gravitation is many many magnitudes weaker than electromagnetic forces. When all matter is contracting at the same rate and speed, not even a macroscopic observer, who is contracting also, can see any local changes. But he can see distance expansion in the interstellar systems that are relatively weakly bound. this distance expansion looks exactly like the expansion of the universe and it is the (whole or partial) reason for observed FLRW metric. But in this model it is only apparent effect that is caused by the contraction of the lenght unit of the observer. About FLRW metrics - if expansion and lambda is substituded away there are still three sources for it: velocity invariant contraction of matter, gravitation effect of matter, and gravitation effect of radiation This hypothesis may either fully substitute cosmological constant and expansion of universe as a remnant of big bang, or subtitute it only partly, being a new effecting component. But it wont substitute the effect of matter and radiation to the FLRW metric. 1. The contraction of matter causes so called distance expansion - it is apparent effect in weakly bound systems that is observed by contracting observer, when all matter is contracting at the same velocity. IT does not cause any other effects. No other changes in density or temperature or gravitation constant. 2. The matter behaves almost exactly like in expanding universe (except matter that has long time dilation history: old neutron stars, old black holes, old cosmic rays - this matter starts to have very slowly so called transformation difference), 3. and the radiation (and any kind of ultrarelativistic radiation) is subject to isotropic length expansion (relative to contracting matter), since photons have proper time 0 always after emission. That means that: -Length unit of photon increases and therefore its wavelength increases -Time unit of photon decreases and therefore its frequency decreases -Energy unit of photon decreases and therefore it appear to have less energy (Also, since matter contracts, the meter stick of any contracting observer contracts, therefore the distance expansion causes that he measures for example the cross section of light to grow and spread into larger cross section.) So also the radiation behaves also like in expanding universe model. 3. You can still try add cosmological constant and remnant expansion of the universe from big band into friedman equation 4. I am not sure of this how it is exactly but there may be a very small effect on gravity due to interaction delay - gravitation travels at the speed of light. The compelling part of this model to me is the prediction of the existence of differently transformed matter. The main question is, Where is it? there should be some transformed protons in cosmic rays, and possibly some of them should be in the matter in earth. The time dilation differences may be very small in galactic dynamics, and the emission from the transformed matter may look similar than redshift or blueshift that is caused by relativistic doppler effect. There might be something different in the doppler shift distributions of the gas in galaxy, if the time dilation differences in galactic matter makes very slightly differently transformed matter. And in gas clouds where there is mixed gas of differently transformed particles, there might be some weak emission lines due to electron transitions between differently transformed protons. i can show that the theories of relativity at least do not contradict with this hypothetical isotropic velocity invariant lenght transformation: 1. in all metrics, the equation of the square of line element remain exactly same, since all terms change like L^2 ds^2 = c^2dt^2 - dr^2 <-> d(dLs)^2 = c^2(dLt)^2 - (dLr)^2 (minkowskian metric) (but it is also true schwarchild metric, kerr metric and Robertson-Walker metric) 2. The einstein's field equation remains exactly the same, since all terms change like 1/L^4 The Table of the changes of the different properties and constants: ------------------------------------------------------------------------------------------- G'/G = L^2 gravitation constant R'/R = L lengths t'/t = L times E'/E = 1/L energies d'/d = 1/L^4 densities V'/V = 1/L^3 volume p'/p = 1/L momentum a'/a = 1/L acceleration this means that the isotropically transformed test observer would measure the metric of spacetime exactly same in all metrics. Despite from that he has different meter stick, time unit and energy/momentum unit. Link to comment Share on other sites More sharing options...
Mordred Posted February 17, 2016 Share Posted February 17, 2016 (edited) no your wrong .. Please stop and actually crunch numbers IF the relativity principle would not be true, then you would have changes in the densities of stars and temperatures of the stars. And i would also agree that the model wouldnt work: there should be significant changes in stellar evolution and structures of the stars. Quote: For example stars themselves will compress. They are made of matter. Quote: What happens to their blackbody temperature as a result of further compression? Nothing, absolutely nothing when all matter contracts at the same rate, if the relativity principle is applied to macroscopic scale. local observer would observe absolutely nothing. But when you look at distant stars, since the matter were less contracted then, the matter had relative transformation difference to matter in the present day. However if there were local observer consisting of same matter, because of relativity principle - he would not observe any changes - and he would think that absolutely nothing is different. https://en.wikipedia.org/wiki/Wien%27s_displacement_law then google spectography and consider each element and its spectral index. then stop and ask yourself what is Z how is z derived ? your little patch work fixes in redshift relations in your last post don't cut it. If you were actually crunching numbers as I asked you would have discovered one KEY aspect. Hubbles law means we have a Hubble Horizon. which is smaller than the cosmological Horizon V=Hd and proper distance relations changes above the Hubble horizon. The apparent recessive velocity exceeds c above the Hubble horizon. course if you crunched the numbers you would have relaized that your patchwork fixes on redshift z wouldnt work,..... But then your assumptions on luminosity distance is also incorrect. http://www.google.ca/url?sa=t&source=web&cd=1&rct=j&q=high%20z%20apparent%20lumisosity%20increase&ved=0ahUKEwiF97uyk__KAhXGLmMKHeWQBSYQFggdMAA&url=http%3A%2F%2Farxiv.org%2Fpdf%2Fastro-ph%2F0505206&usg=AFQjCNE8qV8k1W7g3lt2Mw1ZgqLi5Z6E5g At high z there are corrections. This is why I have been stressing. "Don't assume your derived formulas are correct. Do the calculations over a good range and check" Compare those results to observation and calcs done by related metrics The other problem is your statements keep changing..... Read your posts in one post you stated the gravitational constant and Coulomb constant changes. The one value you gave for the gravitational constant was 100* current value. Then on your last post you state it doesn't change. I strongly suggest you rework your model be more clear on what changes and when. Then when you've tested your derivitaves post the results (with the actual numbers) Quite frankly there is too many changed statements for me to desire to decipher. The last point is your using the same prime and inprimed symbols used in relativity. We use relativity in all measurements for wavelength etc already. So which effects are a consequence of your model ie actual contraction. And which is the normal length contraction due to relativity? Try using different symbols to denote those specific to your model. If you have contraction whether or not its observer only or actual the measured temperature WILL CHANGE. That's why measured energy is also observer dependant. Aka REDSHIFT.... Now where does your model add further compression????????????? Edited February 17, 2016 by Mordred Link to comment Share on other sites More sharing options...
caracal Posted February 17, 2016 Author Share Posted February 17, 2016 yes i agree that this thread is becoming messy. This should be actually very simple model. 1. Velocity invariant isotropic length transformation of matter: s'/s = L(t) t'/t =L(t) E'/E = 1/L(t) 2. L(t) = 1 - kt (linear approximation) or L(t) = exp (-kt) (exponential guess) - the real L(t) is unknown to me. t is proper time 3. Local Relativity principle all other things should be derived from these. The local relativity principle is the hardest thing to accept here and it appears to be very weird thing. It basicly says that human can in principle contract say by factor 1000, and he still doesnt see or observe anything changed in himself (if he is isolated from environment). But we others will see all changes in him. How the space can have this kind of property? Link to comment Share on other sites More sharing options...
Mordred Posted February 17, 2016 Share Posted February 17, 2016 (edited) 3. Local Relativity principle all other things should be derived from these. The local relativity principle is the hardest thing to accept here and it appears to be very weird thing. It basicly says that human can in principle contract say by factor 1000, and he still doesnt see or observe anything changed in himself (if he is isolated from environment). But we others will see all changes in him. How the space can have this kind of property? well thats the crux its your model. yes a human can lose height near he end of the day but after 8 hours rest can regain that height. As far as planets etc we already account for this. Under density. In space we model the critical density, average density of matter, average density of radiation, average density of the Cosmological constant. Which allows us to develop the curvature constant. [latex]w=\frac{rho}{p}[/latex] [latex]\rho_{crit}=\frac{3c^2H^2}{8\pi G}[/latex] [latex]\Omega_{total}=\Omega_{rad}+\Omega_{matter}+\Omega_\Lambda[/latex] [latex]\Omega=\frac{P_{total}}{P_{crit}}[/latex] these evolve according to this equation. Note the terms under the square root. [latex]H_z=H_o\sqrt{\Omega_m(1+z)^3+\Omega_{rad}(1+z)^4+\Omega_{\Lambda}}[/latex] this means in volume change matter and radiation energy/mass density change as [latex]\rho_{radiation}\propto R^{-4}[/latex] [latex]\rho_{matter}\propto R^{-3}[/latex] [latex]\rho_{\Lambda}=constant[/latex] [latex]a=\frac{R}{R_o}=\frac{1}{(1+z)}[/latex] [latex]\rho=\frac{\rho_{r,o}}{a^4}+\frac{\rho_{m,o}}{a^3}+\rho_\Lambda[/latex] Now how is the above relations defined.. Iehow is each equation of state determined.... First take the first law of thermodynamics. [latex]dU=dW=dQ[/latex] U is internal energy W =work. As we dont need heat transfer Q we write this as [latex]DW=Fdr=pdV[/latex] Which leads to [latex]dU=-pdV.[/latex]. Which is the first law of thermodynamics for an ideal gas. [latex]U=\rho V[/latex] [latex]\dot{U}=\dot{\rho}V+{\rho}\dot{V}=-p\dot{V}[/latex] [latex]V\propto r^3[/latex] [latex]\frac{\dot{V}}{V}=3\frac{\dot{r}}{r}[/latex] Which leads to [latex]\dot{\rho}=-3(\rho+p)\frac{\dot{r}}{r}[/latex] We will use the last formula for both radiation and matter. Assuming density of matter [latex]\rho=\frac{M}{\frac{4}{3}\pi r^3}[/latex] if matter doesn't follow this ratio as per what I understand in your model that alters This relation [latex]\rho=\frac{dp}{dr}\dot{r}=-3\rho \frac{\dot{r}}{r}[/latex] Using the above equation the pressure due to matter gives an Eos of Pressure=0. Which makes sense as matter doesn't exert a lot of kinetic energy/momentum. For radiation we will need some further formulas. Visualize a wavelength as a vibration on a string. [latex]L=\frac{N\lambda}{2}[/latex] As we're dealing with relativistic particles [latex]c=f\lambda=f\frac{2L}{N}[/latex] substitute [latex]f=\frac{n}{2L}c[/latex] into Plancks formula [latex]U=\hbar w=hf[/latex] [latex]U=\frac{Nhc}{2}\frac{1}{L}\propto V^{-\frac{1}{3}}[/latex] Using [latex]dU=-pdV[/latex] using [latex]p=-\frac{dU}{dV}=\frac{1}{3}\frac{U}{V}[/latex] As well as [latex]\rho=\frac{U}{V}[/latex] leads to [latex]p=1/3\rho[/latex] for ultra relativistic radiation. so you tell me hw to fit your idea in. From the FLRW metric your distance relation follow as [latex]d{s^2}=-{c^2}d{t^2}+a{t^2}d{r^2}+{S,k}{r^2}d\Omega^2[/latex] [latex]S\kappa r= \begin{cases} R sin r/R & k=+1\\ r &k=0\\ R sin r/R &k=-1 \end {cases}[/latex] So I'm not following how you can apply local relativity, as you define it. Relativity is already applied in every aspect of measurement in Cosmology applications. The FLRW metric is 100% compatible with the Einstein field equations. We look for observer influences via redshift, not only cosmological, but also Doppler and gravitational redshift. The Sache-Wolfe effect is an application of gravitational redshift. Edited February 17, 2016 by Mordred Link to comment Share on other sites More sharing options...
caracal Posted February 19, 2016 Author Share Posted February 19, 2016 thanks i have done some basic work - densities and scale factor. but the full form of friedman equations is not there yet. First - there are two coordinate systems - 1 rigid and 2 co-contracting coordinate system------------------------------------------------1. in rigid/fixed coordinate system :------------------------------------------------time unit [latex] t_{rigid} = constant [/latex]lenght unit [latex] s_{rigid} = constant [/latex]energy unit [latex] E_{rigid} = constant [/latex]transformation factor of matter: L = L(t)transformation factor of radiation: L = 1time length and energy unit of matter:[latex] t' = t_{rigid} * L [/latex][latex] s' = s_{rigid} * L [/latex][latex] E' = E_{rigid} / L [/latex] -> density: [latex] d/d_0 = 1/L^{4} [/latex] time length and energy unit of radiation[latex] t' = t_{rigid} = constant [/latex][latex] s' = s_{rigid} = constant [/latex][latex] E' = E_{rigid} = constant [/latex] -> density = constant null expansion (= zero initial expansion)null lambdaactive gravity (matter + radiation)scale factor if null gravity : [latex] a_{null}(t) = 1 [/latex]density of matter if null gravity: [latex]p_{null}=\frac{p_0}{L^{4}a(t)_{null}^{3}} [/latex] density of radiation if null gravity: [latex]p_{null}=\frac{p_0}{a(t)_{null}^{4}} = p_0 = constant [/latex]change in gravitation forces in matter (no delay):----------------------------------------------------G' = G0 L^2 m' = m0 /Lr' = r0 (r is constant)[latex]F' = G' m_1'm_2'/r'^{2} = Gm_1m_2/r^{2}=F[/latex]changes in G and m1 , m2 cancel each other out.-> no changes in gravitation even when the mass increases if there is no delay-> matter and radiation behaves as if it has no density dependency of L->density of matter [latex] p=\frac{p_0}{a(t)^{3}}[/latex]density of radiation [latex] p=\frac{p_0}{a(t)^{4}}[/latex]-> 1st friedman equation (no delay): [latex] (\frac{dH}{dt})^{2}=(\frac{8\pi G}{3})(\frac{p_{m,0}}{a^{3}}+(\frac{p_{r,0}}{a^{4}})) [/latex]Change in gravitation forces in matter (delay)-----------------------------------------------------There comes factor 1/L(r/c) where r is efective distance[latex]F = (\frac{1}{L(r/c)})Gm_1m_2/r^{2}[/latex]->newton's theorem for spherical mass distribution is no longer validhow to derive friedman equations from modified gravity?--------------------------------------------------2. in co-contracting coordinate system--------------------------------------------------time unit :[latex]t' = t_{rigid} * L [/latex]lenght unit [latex]s' = s_{rigid} * L [/latex]Energy unit [latex]E' = E_{rigid} / L [/latex]Infinitesimal time interval equal to [latex]dT' = dT_{rigid}/L(t_{rigid})[/latex]time interval T' equal to T_rigid = [latex] T' = \int_{0}^{T}{dt/L(t))} [/latex](co-contracting time t' is accelerating relative to rigid time t_rigid)transformation factor of matter L = 1transformation factor of radiation [latex] L = 1/L(t') [/latex]null lambdaapparent expansion: 1/L(t')active gravity (matter + radiation)scale factor if null gravity : [latex] a(t')_{nullG} =\frac{1}{L(t')} [/latex]density of matter [latex] p=\frac{p_0}{a(t)^{3}}[/latex]density of radiation [latex] p=\frac{p_0}{a(t)^{4}}[/latex] similarly as in expanding universe. change in gravitation forces in matter (no delay):----------------------------------------------------G' = G0 since L = 1m' = m0 since L = 1r' = r0 (r is constant) [latex] F' = G' m_1'm_2'/r'^{2} = Gm_1m_2/r^{2}=F [/latex]-> no changes in gravity when there is no delay-> 1st Friedman equation (no delay): [latex](\frac{dH}{dt})^{2}=(\frac{8\pi G}{3})(\frac{p_{m,0}}{a^{3}}+(\frac{p_{r,0}}{a^{4}}))[/latex]+ a term coming from apparent expansion what is [latex] a(t')_{nullG} = 1/L(t)[/latex] (what kind of term is it?)Change in gravitation forces in matter (delay)-----------------------------------------------------There comes factor 1/L(r/c) where r is efective distance[latex]F = (\frac{1}{L(r/c)})Gm_1m_2/r^{2}[/latex]->newton's theorem for spherical mass distribution is no longer validhow to derive friedman equations from modified gravity?scale factor if delay term in gravity : a(t) = ? 1 Link to comment Share on other sites More sharing options...
Mordred Posted February 19, 2016 Share Posted February 19, 2016 (edited) OK this is much better to follow glad to see you switched to latex. I'll have to look at the math later on. I would recommend at first glance changing the symbol for energy density from p to use \rho. [latex]\rho[/latex] p is the common symbol for pressure or momentum. For now lets treat your modelling as a toy universe we can check how it matches up to reality later on. toy model building is a good training exercisethat one can learn a ton from. I have one question though, how familiar are you with GR in particular the Einstein field equations.? this is going to be the tricky level to work out the new FLRW metric. by the way +1 for recognizing the importance of the math in model building Training (textbook Style Articles) http://arxiv.org/pdf/hep-ph/0004188v1.pdf :"ASTROPHYSICS AND COSMOLOGY"- A compilation of cosmology by Juan Garcıa-Bellidohttp://arxiv.org/abs/astro-ph/0409426 An overview of Cosmology Julien Lesgourgueshttp://arxiv.org/pdf/hep-th/0503203.pdf "Particle Physics and Inflationary Cosmology" by Andrei Lindehttp://www.wiese.itp.unibe.ch/lectures/universe.pdf:" Particle Physics of the Early universe" by Uwe-Jens Wiese Thermodynamics, Big bang Nucleosynthesishttp://www.blau.itp.unibe.ch/newlecturesGR.pdf "Lecture Notes on General Relativity" Matthias Blau this material will help in your model building several of the steps are described within, it will give you some study aids to understand better the formulas your manipulating.. currently at work atm so I'll have to get back to assist you later on Edited February 19, 2016 by Mordred Link to comment Share on other sites More sharing options...
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