substitutematerials

appreciate it Mordred [math] z=\frac {H_0l^2}{c+\frac {1}{2}(1+q_0)H^2_0l^2/c^2+O (H^3_0l^3)} [/math] What's the O here? And l? Forgive me if they are self evident.

I did maim that equation a bit, thanks for the correction. I also put the first (1+z) under the square root when it should not have been. My argument is that these degrees are freedom are more bugs than features- since total Omega appears to be so close to 1, and consequently curvature so close to flat and k so close to 0, we have a difficult task to explain how we landed in a universe so precisely balanced. We need inflation to explain this away. Not to mention that Lambda is a pretty huge and exotic addition of energy to our model to achieve this balance, and generate a negative value for q. These are pretty big patches to yield a result- a universe with no curvature- that suggests a simpler explanation.

Sure, but doesn't ad-hoc fitting of equations usually involve adding constants and additional terms to make an equation fit? For instance, feed some data points of redshift versus lookback time from the lightcone calculator into mycurvefit.com. It will generate an equation in the symmetrical sigmoidal form: [math]y=d+\frac{a-d}{1-(x/c)^b}[/math] parameterized with the following coefficients and substituted variables: [math]z=804991698.025728+\frac{39.3188685672713-804991698.025728}{1-(t/13.8074359611365)^{9100.00062385681}}[/math] This a pretty terrible fit, I welcome a better one. It's good enough to illustrate the point that ad hoc equation fitting involves lots of free parameters. And looks more like this: [math]t_l=\frac{1}{67.9}\int_{0}^{z}\frac{dz'}{\sqrt{{(1+z'){0.307(1+z')^3}+0.0013(z+1')^2+0.693}}}[/math] than this: [math]z=\frac{-ln(1-t)}{\sqrt{1-t^2}}[/math]

any further thoughts? Strange, I would just say that the non-local and retro-causal behavior of quantum events can only be described as well-explained by existing theory in the sense that it is mathematically circumscribed: we can predict outcomes. It is not well explained in physical terms, which is why QM physicists are sometimes implored to 'shut up and calculate'. I'm sure this is an acceptable stage for scientific understanding to pass through. Lorentz derived the mathematical transformations of time and length that special relativity would later explain. Kepler derived the math of elliptical orbits before Newton explained the nature of the force that caused them. We get so much more when we make intuitive sense of what the numbers are telling us. This thread is a tangent to the paper I presented. While I can imagine some of these quantum behaviors to emerge in a locally expanding space, or stationary light model, my work is a cosmological theory. So this may have been a clumsy place to introduce the idea. All the topics I've started on scienceforums relate to this theory, although hopefully they have some merit as good thought experiments too. Is the close fit of my model to our present one, in the relationship of various distance scales to redshift, and the evolution of temperature over time, at all interesting to the esteemed members of this forum? Also I'm embarrassed to issue a correction, which I already issued in the numerical analysis thread in the cosmology section, which is that the Co-Moving distance equation should read: [math]X=ct_{lb}(1+\frac{\int_{0}^{t}(z)dt}{t})[/math] (t_o) for the time of the observer, was written where (t_lb) for lookback time is in the above, the units of time should be the same as those used for the speed of light. This error is also in the attached pdf, and in light of this and future edits, I'll just post a link to the sharelatex website where I am working on it: Stationary Light

Yes Mordred, those 2 links are about a quantum mechanical experiment, and have no reference to expansion, nor do they need to in the conventional picture, because, like you say, 70 km/sec/mpc is a vanishingly small rate, and it should be completely constrained on local scales by all the forces that hold the environment of the experiment together. What I am saying is that 70 km/sec/mpc is not the rate of expansion. In my hypothesis, H_o is a time dilation that stems from the fact that we are measuring time against the expanding medium of space- because I have equated light's transmission with the expanding medium. [math] H_o={\dot\dot}\tau[/math] The Hubble parameter is the second derivative of proper time (tau) with respect to cosmic time. Units of distance in the numerator and denominator can be cancelled to yield 2.31E-18 sec^-1. This change in time is transformable to a scaling factor, but it emerges geometrically from the fact the we are measuring the rate of time against a constantly expanding medium. The analogy that I employ here is that the space is like audio tape for light waves, except that the tape plays destructively, by stretching across the observer. When the time elapsed since an event is small relative to the cosmic age, the distortion is miniscule. But on larger scales it becomes significant- it is the source of the cosmological redshift, and is given by the equation I've posted several times: [math]z=\frac{-ln(1-t)}{\sqrt{1-t^2}}[/math] The derivation of this equation is in the attached paper. The change in wavelength of photons does not come from spatial expansion in this model- it comes from this second order scaling. Stationary_Light.pdf I have crunched actual numbers as best as I know how: SL supernova table.tiff The above attachment is a short table of supernovas from the SCP paper, computing the various distance scales to compare to values generated by the Wright calculator, and showing a mean disagreement of .007 between the models. The equations used for the (SL) columns are listed elsewhere in this thread, with the addition of the standard distance modulus to convert apparent magnitude to absolute magnitude: [math]M=m-5(log_{10}(D_l)-5)[/math] Another way to compare to conventional cosmology is by the evolution of background temperature, using [math]K_e=(z+1)K_o[/math] and 2.73 Kelvins as the measured background temperature presently. For the CMB, with z of 1089, recombination would be centered around 590,000 years after the Big Bang, and the light arriving now from that event would have been emitted from a co-moving distance of 52.6 glyr. The comparisons to the lightcone calculator are an age of 373,000 years and co-moving distance of 45.33 glyr. Reaching back to a single second after the big bang, we can calculate that the temperature, assuming adiabatic expansion since then, the temperature would be 51.56 gigakelvins, within the order of magnitude estimated by lambdaCDM of 100 gigakelvins. This evolution of temperature is important in models of Big Bang Nucleosynthesis. Finally, I would just say that, like the original post in this thread, quantum mechanical behavior suggests that there is something wrong with the simple picture of light traveling through static space. I don't think we need to just accept things that don't make sense, relying entirely on mathematical efficacy. Deeper truths await us if we can truly proceed from intelligible first principles. Thanks again guys SL supernova table.tiff Stationary_Light.pdf

The part of my proposal that you are missing Mordred is that light doesn't travel across space. I'm proposing that light is borne on expanding space. This is a major change to the laws of physics, yes. Of course I'm not proposing that the Earth and Sun are moving apart at the speed of light; as Strange has gathered, I am ascribing a physicality to space that is not defined by the distance between any 2 particular objects. This is what I'm doing. And I'm claiming that we measure and detect this expansion all the time, because that's how light 'gets around'. When we view light, we are viewing a past moment that has expanded in volume to encompass our present position. In this way, a telescope is not 'like' a time machine, it is a time machine. Hence the retrocausality of quantum mechanics. Assume for the sake of a thought experiment that the universe is finite, and has a edge. If this was the case, we would say that that edge is receding from any observer as the universe expands. This is a relationship to space itself, and not any particular object. We could make a similar statement about the Hubble horizon, or the observable horizon. In this hypothetical finite universe, any physical, intact object with a real volume will occupy a particular fraction of the entire volume of space. After time has elapsed, that object will (obviously) still measure its own volume to be the same, but the fraction of the whole that it now occupies has become smaller, since the universe as whole grew in the interim. But you could still refer to that earlier fractional volume of space, formerly occupied by the object, which would appear to be radiating away from the physical object as the universe grew. I'll make one more post later to explain why I think redshift emerges naturally from this model, then I'll let it rest. Assume for the sake of a thought experiment that the universe is finite, and has a edge. If this was the case, we would say that that edge is receding from any observer as the universe expands. This is a relationship to space itself, and not any particular object. In this hypothetical finite universe, any physical, intact object with a real volume will occupy a particular fraction of the entire volume of space. After time has elapsed, that object will (obviously) still measure its own volume to be the same, but the fraction of the whole that it now occupies has become smaller, since the universe as whole grew in the interim. But you could still refer to that earlier fractional volume of space, formerly occupied by the object, which would appear to be radiating away from the physical object as the universe grew.

Hey guys, surely 'complete garbage' is an overly strong dismissal- I realize that this idea is a very wrong description of present theory, but I don't believe the statement is logically incoherent. You doth protest too much. There are many ideas that are brought to these sites that are not self-consistent or even capable of evaluation, and I pretty strongly believe this idea at least rises about that level of gibberish. I can formulate a clear mental picture of what it means to be "standing where the sun was eight minutes ago". It is not different than saying "I am standing where the big bang occurred," except for the radical shift in the actual dynamics of spatial expansion. Back to your point about path integrals Strange, I have been doing some reading, and as far as I can tell, at least the double slit experiment hasn't really been tested yet to the precision needed in order to confirm or deny the importance of non-classical photon paths in the path integral calculation, since their probabilities would be very low. Some recent work is tackling this almost as we speak- I think the general experimental setup is to add a third slit and look for the effect of photons weaving through multiple slits on their path to the detector. So I will hazard, without caution, that you have actually identified an experiment that would produce a relevant yay or nay to this image: If locally expanding space is the principle that underlies path integral formalism, then we should only see evidence for classical light path probabilities in any experimental setup. here are some links: https://arxiv.org/abs/1308.2022 arxiv.org/abs/1610.06401v1 (not yet peer reviewed) Do you know of any other experimental arrangement where the path integral requires computing non-classical paths, say in particle accelerators? Thanks again for looking at this, guys. And Mordred, I will read the links you sent. I certainly want to have a complete understanding of the LambdaCDM configuration of the FLRW metric. What I am proposing here is clearly a dramatic deviation from that framework, which is why I began the topic in speculations.

The speed, like the speed of light, is relative to the observer's inertial frame, and is radial in all directions. No. They are all moving away from space they formerly occupied. It doesn't have to mean anything to the the distance measured between them. Can you imagine this alternative or does it seem non-sensical? This is an excellent question, just the kind I hoped to get here. It is the same as the point you brought up with the Feynman Path Integral, and I don't have a ready explanation for why future paths would also be relevant.

I can mostly wrap my head around this last post, I think I'm basically familiar with those relations. My equations do not allow for any curvature of space (k), they assume flatness apriori as far as can tell. I realized I posted an error in my co-moving equation, it should read: where (t_lb) is lookback time in the units of time used in the speed of light, not (t_o) as is in the earlier post. I agree that the FLRW math is not too onerous. In calling my test equations simple, I'm referring to the lack of free parameters I guess. No need to define the various components of omega to yield a similar redshift /light-travel-time relationship. It could be nothing more than a coincidence though, that's what I hope to determine.

Hi Mordred, I realize that my proposal is in clear disagreement with how we understand spatial expansion to work at present. The below explanation will hopefully explain how my mental image of a different conception works, for the purpose of speculation. Every point is moving away from it's past position at a fixed speed. I am 300,000 kilometers away from the space I was inhabiting one second ago, which has expanded by that radius to form a sphere surrounding me. The radius of this sphere is the distance light could have 'traveled' in the elapsed time. Likewise a point on the sun's surface has expanded to form a sphere eight light-minutes in radius. Because the Earth and the sun maintain static distances from each other, they are overlapping each other's expanding pasts. This is why I see light from the sun: I am standing where the sun was eight minutes ago. You might ask why one would want to perform these mental gymnastics rather just referring to the well accepted explanation,"light traveled across static space from the sun to the Earth; it took eight minutes to cross the void." One reason I find the alternate vision compelling is that the locally expanding space scenario fits what we see at the quantum level- that the photon is somehow still engaged with the entire volume of its potential paths until absorption, and that the interaction with the photon is as if it is an interaction with the past moment of emission itself as shown in entanglement scenarios, as if we are touching the past, retrocausally.

What I'm saying is that light is propagated by the expansion of space. On some level, this is true in conventional cosmology- since light from the CMB has traveled 45 glyr to reach us in only 13.8 gyr, I think we can say that most of its motion was borne on the expanding fabric of space. Of course any observer along the interval will measure the speed of light at c, but in the simplest interpretation of Speed = Distance/Time, the effective speed of the traveling photon was X/t. I am taking it a step further and saying that all of the apparent motion of light is due to expanding space, which happens locally at c, and at on larger scales can be averaged to X/t. The speed of light is the speed of the expanding medium, the speed of information.

The lightcone calculator is really great, the table functionality is excellent. It's nice to have the more current data sets as well. The Hubble horizon now is ~13.8 glyr in comoving coordinates, correct? So corresponding to a z of about 1.5. It seems to me that my equation toes the line for longer than that, starting to get kind of bad in the z=8 territory. It's within the right order of magnitude even as far back as 1 second after the big bang though. But again, I'm not a statistician, I can't say if this is an easy to generate coincidence, or perhaps a truly useful equation since it is so simple.

It's a goofy way of saying that no time elapses for the photon. I don't think what I am proposing is the same as the predetermination of the spin. The spin is in a superposition until it is detected, and so does not violate Bell's inequality. What I am proposing is very similar to the retrocausal solution to Bell's Inequality, talked about here by Huw Price and Ken Wharton, https://aeon.co/essays/can-retrocausality-solve-the-puzzle-of-action-at-a-distance and here https://www.youtube.com/watch?v=bXMJ2Z90teQ and peer reviewed https://arxiv.org/abs/1508.01140 Agreed, I definitely do need to read up on the path integral. I've been working on this for a while. It is certainly true that what I am proposing is not consistent with an FLRW derived model of the universe. I don't think there is any conflict with General Relativity as a local solution, in regions of asymmetrical distribution of mass. Of course there better not be a conflict in these cases, since it is pretty well tested at this point. Here are the basic equations that would describe distance scales in my model: [math] z=\frac{-ln(1-t)}{\sqrt{1-t^2}} [/math] [math] X= ct_o(1+\frac{\int_{0}^{t}(z)dt}{t}) [/math] [math] D_l=X(1+z) [/math] where (z) is the cosmological redshift, (t) is the lookback or light travel time expressed with the present being 0 and the origin being 1, (X) is the Co-moving distance, (t_o) is the cosmic time of the observer and (D_l) is the luminosity distance. You can see this has no free parameters except for the present age of the universe. The graph parallels LamdaCDM pretty well, I am working with Mordred over in this thread on comparing values with the lightcone calculator. I've generated a graph here showing a comparison. I can tell you that for the type 1a data from the Perlmutter study, this equation agrees within a fraction of a percent. It begins to diverge more substantially after z=8 or so, but the very early universe is quite similar, with the age of the universe at the CMB being off by a factor of 2, and the temperature at one second after the big bang being off by a factor of 4. It seems to me that being in the right order of magnitude at this point is meaningful. The metaphor I resort to is that space is like an audiotape of lightwaves, which we play by stretching, rather than just moving it as in a tape player. Since we are stretching and distorting the record through the act of playback, we naturally observe a lengthening of distant events- they take longer to unfold, and are shifted in 'pitch'. This is the source of the redshift in this model. When the time elapsed since the event is short compared to the age of the universe, this effect is negligable. I have a paper explaining the derivation of the first equation as well. Thanks again for your thoughtful consideration.

Thanks for the detailed consideration of my speculation, Strange. I appreciate it. My conjecture is not that the distance between astronomical objects doesn't change with spatial expansion, but that it needn't. Objects like the Earth and the sun can be decoupled from expansion, and maintain static distances, but that doesn't change the fact that space is expanding through and around them. It is a global property in this regard. Very distant objects can recede from each other in this model, as we observe. While it is a can of worms, a necessary condition for this is that mass density and gravitation do not impact the progress of expansion. Hence the speculations forum. I've confused things by referring to the size of a photon. Really the idea is: all points in space expand to become volumes. no. Expansion in this model is a constant. The effect of the photon's absorption emerges at a single point in the future, but the expanded spatial volume doesn't collapse with the waveform of the photon. The universe remains larger than before. This is quite perplexing to me; I have stumbled on it for a while. How is a superluminal path included in the list of possible paths? Does this mean that a third slit placed behind the detector would need to be accounted for in the interference pattern of a hypothetical test? What if the test is controlled for a given light travel time, rejecting inputs with a long enough light delay to have encountered the third slit? The photon is stuck in the past moment. The point in space and time has expanded to come in contact with the present observer. When the observer determines the spin or polarization, she is determining what happened at the moment of its inception. She is interacting with the past itself, which has grown in volume to encompass her position, as well as the position of the entangled photon. This is my big idea.

Thanks Mordred, I'll spend some time with this. As a preliminary measure I added some values from your calculator to my graph, and changed the time of present to reflect the default values (the real present is the time at z=0 from the chart, correct? The Hubble age being the simple 1/Ho?) Just a cursory look suggests that the values in your chart versus my heuristic deviate slightly more between z=10 and z=25 than when compared to Ned's Wright's calculator, but the they re-converge comparably well as we get to higher z values.

Bump Anybody willing to flex their math muscles? Imatfaal, Mordred? Can you generate a comparable fit with a different equation? We can integrate this equation to get co-moving distance (X) also, if that's a more meaningful comparison... [math] X=ct_o(1+\frac{\int_{0}^{t}(z)dt}{t}) [/math]

Hi Everybody, Please try out this speculative explanation of various quantum effects. It takes this as its main non-standard assumption: the expansion of space does not necessitate a changing distance between any two particular physical objects, and expansion occurs on all scales in the universe. Imagine that a photon begins as a point, but expands it radius by c(t), i.e. the photon gets bigger over time, until an interaction occurs somewhere on its expanding surface. The interaction can only happen at one particular point on the shell of the enlarged photon because the energy of the photon is quantized- it can only give up its energy once. However, the probability of the photon arriving at that particular point on its shell is influenced by all potential events within the sphere, since the expanding photon has grown through them. This explains the fact that a single photon will interfere with itself in the double slit experiment, having appeared to "take all available paths" before choosing it's actual path. We can take this a step further and say that it is not the photon that is expanding, but space itself. The deeper meaning of this is that a point from the past interacts with a larger volume in the future. Now we can move on to entanglement, which describes the scenario in which determining the property of one entangled photon will simultaneously determine that of its entangled partner, regardless of the distance separating them. This is because the observer is actually interacting with the past moment when the photons were entangled. The point-moment, the event of entangled emission, has grown in volume, such that the observer's measurement is essentially retro-causal. This is the real meaning of spatial expansion, and the cause of entanglement: a point in the past becomes a larger volume in the future. The observer of entanglement is interacting with the past. This also makes some sense if we imagine the photon's perspective from a relativistic framework. Since the photon moves at c, it experiences no passage of time. It is emitted and absorbed instantaneously. It has not traveled- instead, the moment of its emission has expanded in volume until the moment of its absorption. Consequently, I'm offering that quantum effects are evidence of local spatial expansion. Anybody?

I believe it's actually the opposite- flatness comes from a state of precise balance in the Friedman equations. Any tiny deviation from perfect flatness should magnify itself over cosmic history. This is part of the reason it is surprising that we observe such flatness in the present era.

I think you're right, I shouldn't be invoking an extra dimension. But the mental image sort of demands another dimension for the surface to curve in. I suppose you can just imagine a distorted coordinate grid like a Mercator projection on a flat map of Earth, but this seems like a formalism and so isn't quite as satisfying.

I see this as simply a limitation of our spatial minds. Mathematically, we can address any number of dimensions, but we must resort to lower dimensional metaphors to mentally picture it. I can picture a 3 dimensional cube, but I can't picture a 4 dimensional cube. I can however resort to a metaphor of a 2 dimensional square being extended to a 3 dimensional cube, and thus I can imagine a similar transformation of a cube into 4 dimensions. I can picture a curvature of a 2 dimensional surface, and extend that metaphorically into a 3 dimensional curvature in 4 dimensional space. That said, we don't see any observational evidence for global curvature in the universe, i.e. parallel lines remain parallel as far as we can see, apart from local effects of gravitational objects. This means we either have a profoundly precise density of mass-energy in the universe, or an exotic inflation process took place to smooth out our section of the whole universe, or maybe- curvature actually is not possible on global scale in our universe. The last possibility is not conventional science.

Can you guys test drive this heuristic equation relating cosmological redshift (z) to light travel time (t)? [math]z=\frac{-ln(1-t)}{\sqrt{1-t^2}}[/math] It seems to mirror LambdaCDM well, but I don't know enough about statistical analysis to really assess it. Light travel time (t) is written with the present equal to zero and the origin of time as 1; multiply by the age of the universe in desired units to get a real time. The equation has no free parameters and is quite simple, so I think its interesting that it seems to fit so well. Useful maybe? I'm generating light-travel times for comparison using Ned Wright's cosmology calculator with default settings. The equation is difficult to solve for light travel time (t) for a given (z), but Mathway can generate roots numerically if the equation is written like this and a value is entered for z: [math]ln\frac{1}{1-t}-z\sqrt{2-2t-(1-t)^2}=0[/math] also here is a graph fitting the equation against some points plotted from the CosmoCalc. Thanks!

Are there any theories right now as to why the observable universe is so close to flat, and consequently mass-energy is so close to the critical density, other than inflation? Or are the only mainstream options a.) we are in a tiny portion of the entire universe that has been stretched flat by inflation or b.) density is randomly fine-tuned?

Thanks HallsofIvy, I'm not much of a mathematician myself, but I've put this to other maths people IRL and they've said the same thing.

Can anybody solve this equation for x? [math]y=\frac{-ln(1-x)}{\sqrt{1-x^2}}[/math] the best I can do is to rearrange to this: [math]ln\frac{1}{1-x}-y\sqrt{2-2x-(1-x)^2}=0[/math] and then take the roots numerically using the mathway website. Any help is much appreciated!

This could certainly be my hangup. But at the same time, I feel like the statement about the big bang happening everywhere rests on such a premise: that the original planck length volume has 'stretched' to the present size of the universe, whatever size that may be. A coordinate system could be drawn in the original volume which could undergo transformation to present coordinates.