That is exactly what we would see if our ruler were contracting. The wavelength of light emitted farther back in time will look longer, when compared to our "calibrated" instruments.

Thank you for considering the proposal to first look at a direction-resolved Hubble law.

I'm not sure that I fully understand the question but my understanding of the CMB is that it is radiation left over from the time in the early Universe when matter and radiation decoupled and parted ways and there ceased to be thermal equilibrium. The effect of continuing expansion of the Universe effectively "cooled" the radiation independently of matter at a time before there were stars and galaxies. In forming stars by contraction under gravity matter is heated not cooled.

If SPIRAL we would predict a stable CMB temp or a very slight trend down in temp, but not as fast as it would drop under SCM.

aside for refining what is the current conventional norm based on advances in technology,

Is there any evidence for increase or decrease since we began to measure the CMB temp. after margin of error for any variance from pure black-body, outside 'interference' and instrumentation.. ?

if under a contracting universe the OP, or the current conventional view expanding universe the temp would trend , and we would predict if a static (no ongoing cosmic expansion or contraction) it would stay stable or slowly go down to normal 1 LY a year 'leakage' as predicted under SPIRAL cosmological redshift hypothesis.

Todd,  Good question.  If you can wait for about a billion years, the answer will be obvious. Actually, your question implies that we must choose between two different models of the universe.  The standard cosmological model assumes that the universe started as a singularity, then had a Planck epoch, inflation, etc.  This assumes that in the early universe there was some form of contact  with distant parts of the universe which are now beyond the particle horizon (for example, gravitational or radiation contact).  This is the standard Big Bang model. This  model assumes that the universe is getting bigger and our rulers are constant. 

The other model assumes that the universe started in the most energetic state that spacetime can support - Planck energy density which is about 10112 J/m3.  There is no singularity  and this explains the homogeneity of the universe without needing inflation. The rest of the explanation is beyond the scope of this post, but the result is that our rulers shrink. More distant parts of the universe are continuously coming into view.  For example, in this model, there was a time when the matter currently in the Andromeda galaxy was beyond our horizon. Then when it first came into view it had a large redshift.  

 Today, the most distant galaxy observed has a redshift of about Z = 12.  If the universe is expanding according to the standard cosmic model, this galaxy will increase its redshift and eventually disappear with infinite redshift when it crosses our particle horizon. The other alternative predicts a different fate.   If our rulers are shrinking, then in the future this galaxy will have the counter intuitive effect of appearing to become more distant because of our rulers shrinking, but also having a redshift less than12.  This is counter intuitive but it is explained in chapters 13 and 14 of the book titled "The Universe Is Only Spacetime" available from my ResearchGate home page.  The bottom line is that we will have to wait a long time to obtain experimental proof that answers your question.  

 John

Remi,

I could also argue that the universe is contracting and my ruler is contracting faster. However, there is some logic to my hypothesis, and that is. If it is correct, it is consistent with thermodynamics and there is no need for a mysterious Dark Energy to explain accelerated expansion. It is all just matter getting cooler over the centuries. 

The best path to falsifying the hypothesis I've heard yet, is to determine if there is any anisotropy in the Hubble Constant. Because, my hypothesis would inherently lead to an isotropic expansion.

There is no chance to falsify the shrinking meter hypothesis in GR.  Simply because from point of view of GR philosophy, it makes no difference.  All systems of coordinates are on equal foot, none is preferred.  So, the one where all galaxies remain at fixed places x,y,z, but rulers are shrinking, is as good as any system of coordinates where galaxies fly away.  

The FLRW coordinates are, BTW, those which correspond to shrinking rulers.  And even in GR we can prefer this system of coordinates as that which has a higher symmetry.  

To falsify one or another one needs a different theory of gravity, one which has a fixed background so that it makes sense to claim that rulers shrink relative to this background.  See http://ilja-schmelzer.de/gravity/ for such a theory of gravity. Such a background may be necessary to quantize gravity.  

Henri Poincare made a similar conjecture 100 years ago. He imagined a Gedanken Experiment of a universe 2 meters in diameter where the center is extremely hot and the periphery extremely cold (zero K). As one rockets outward the spacecraft shrinks and the boundary of spacetime is never reached, a continuous time version of the Zeno Paradox.

In more modern times Hawking and Penrose established the "No Boundary, Boundary" Theorem, which effectively disables a meter stick being able to "measure" the ever expanding edge.

More succinctly, I think the shrinking ruler and the expanding spacetime are group symmetric inverses of each other.

Suppose the universe is expanding, then if I want to keep the the distance between any two stars fixed I have to redefine the unit of length continuously. Let us take two stars which are 1 light year away from each other. After a time t years, the distance becomes 2 light years. Then expansion rate is 1/t light years per year. The meter stick should also expand at this rate and then we should conclude that "nothing has happened".  I don't think meter stick should contract.

On the other hand if the universe is fixed but we want to forcefully conclude that it is expanding, then meter stick should shrink, we cannot know the difference.

Thank you Dr. Vento! I would agree with your last statement, that's probably what I was thinking but didn't know the terminology. I'll check it out.

If there is no way to tell the difference, then there Is no difference and no consequence of being unable to make the determination. It seems unlikely.

Expanding universe has a wealth of theories and proposed mechanisms. Contracting meter stick needs a proposed mechanism to be seriously considered. First you need to say in what frame the meter stick is not moving with respect to the CMB, and in what frame the contraction is being suggested.

Space has a set of properties that can be measured or calculated. For every property  change of one type there are several other properties that respond with other changes.

For your question the answer must not include speed or distance like vibration amplitude, but may include vibration frequency, also possibly vibration mode.

So I suggest the difference can be distinguished, but not with conventional science, only with leading edge technologies that probe the properties and limitations of properties for space and time.

Jerry,

My goal is to relate it to temperature, such that the meter stick is cooling and contracting at a rate of 6.8 nanometers/century. It may be that it is in equilibrium with the CMB and that as the CMB temperature decreases, so does the length scale of our meter stick. I have not completed that derivation yet. I'm still fishing for the critical details that must be met, so I appreciate your input. 

I think I'll work another angle.  I also had also thought of a fixed point from which Jerry Decker mentioned, and I like his frequency suggestion.  However I think I have found a much simpler approach.  The Linear Doppler Effect.  These equations are in any freshman textbook: (fixed position, spacetime moving away; moving forward position, fixed spacetime; and last moving backward fixed position, moving forward spacetime).

If we take some associative frequency, say converting the Hubble Constant to a frequency, and playing with the 3 equations, maybe a Noetherian symmetry will reveal itself. 

Mathematically the two viewpoints look the same, since only dimensionless ratios matter. Measured in units of the size of the universe, its size is constant while the hydrogen atom shrinks. Measured in units of the Bohr radius the hydrogen atom is constant while the universe expands.

But the focus, and with it additional predictions and correlations, is different. With an expanding universe you will try compare with other cosmological phenomena, like the development of structure and long distance propagation of light. With a shrinking meter stick you would try to look for additional evidence in the physics of atoms and materials.

Fortunately, one does not have to know everything about nature to explain a specific detail. Isn't that nice?

Todd> "The Hubble constant is equivalent to a ruler, 1-meter in length on Earth, contracting 6.8 nanometers per century."

Well, that is another fuzzy way (not quite as silly as the one involving megaparsecs) to say that the Hubble constant is the inverse of 14.5 * 10**9 years. :-) [Which implies that I think 6.9 nm is a _much more_ accurate number...]

one way to test if the universe is expanding

vs one that is not 

is by comparing a star or galaxy that is subject to cosmological redshift (CR) to one that is not.

under SCM the CR indicates ongoing cosmic expansion away from us.

under SPIRAL CR hypothesis it does not.

so if a star 5k LY away no CR /not moving away

and another 6k LY away with CR assumed by SCM to be moving away, if they hold their relative positions to each other it would indicate some SPIRAL conclusions:

the object with CR is not moving away and CR is not evidence of ongoing cosmic expansion.

the universe is not expanding as is assumed, because of prevalent CR of distant stars, as we see CR does not equate to expanding away..

SPIRAL explains what the CR is evidence of (past but not ongoing cosmic expansion, that ended the number of years ago = to the number of LY distance that the prevalent CR begins from us outside our galaxy.

addendum due to some points made by George D.:

'Hi George,

5k and 6k were used as even outside our galaxy the prevalent CR does not begin till between 5k and 6k so 5k and under no prevalent CR, over 6k prevalent CR 

keep in mind out galaxy is disc like so not a sphere.

If as you indicate there are no other galaxies within 5K LY distance from us using individual stars was also presented as an option.

Your point about one of the two object we want to compare in the test being 'gravitational bound' and the other not, is a valid concern.

if we do identify 2 stars one 5k LY with no CR and one 6k LY w/ CR in a position where we can compare their relationship over a ample time (a few years?)

why assume the one w/o CR is gravitational bound? it just may be there is no ongoing cosmic expansion, and the one w/ CR is also not moving away, it just has CR due to past, but not ongoing CR as explained by SPIRAL.'

Book 'SPIRAL' cosmological redshift hypothesis and model

Todd different materials shrink at different rates when cooling, even metals of different alloys have different thermal expansion. In your question I suggest you include several meter sticks of different alloys at the same temperature. Then the shrinkage rates are different. It you choose 100 alloys you get 100 answers for meter sticks, but in cosmology you only get 30 TOE estimates for cosmic expansion, and only one standard model. A mismatch is created by simple construction, similar to the way arguments between Einstein and Bohr were resolved.

Standards of measure are specified at a temperature for a specific alloy compared to a specific number of wavelengths of a precisely defined color of light waves emitted by a specific atom at a specific temperature in a specific emission band.

Cosmology has been built up by systematic testing of ideas. To put your question into an untested zone, it is necessary to challenge the constants of nature along with the properties of space and time as a group all at once, which I often do.

Jerry,

Good points, I had not considered this. However, in the PV Model, K affects space-time uniformly at the sub-atomic scale. Inter-atomic bonding and molecular bonds are all contracted by the same factor  delta_x/sqrt(K). 

Likewise, all materials are immersed in the CMB and are in thermal equilibrium with the vacuum field. In this regard, matter obeys the ideal gas law, P*V~T. So in order for different alloys to have different contractions for the same temperature change, there must be some variation in P*V that is "different" for those alloys. 

As I said, I have not derived this relationship to temperature yet. It's a hunch I have, but it's not fully baked yet. Thanks!

Just to note:  There is an important difference between the usual everyday shortening of rulers caused by shrinking temperature and the effects we see in the universe:  The shortening of rulers caused by temperature depends on the material.  This makes it possible to measure temperature, simply by combining different materials and observing that they shrink differently.  

In the universe, at least as far as the GR equivalence principle holds, this is impossible. This does not invalidate the idea of shrinking rulers instead of flying away galaxies, but adds a property of this shrinking:  Universality.  All rulers shrink in the same way.  This makes it impossible to build a thermometer-like device to measure this shrinking.  

Todd PV~RT only applies to gases and a few other special cases, most accurately at low pressure and high temperature. Other materials have different equations of state or correction factors for the gas laws.

I suggest that vacuum space also has an equation of state, but not the gas law, although it makes a useful example. PV represents mechanical energy and RT represents thermal energy. A number of people have worked on different aspects of vacuum stress energy and curvature. Einstein's field equations are similar to the gas law, where one energy term is equal to another energy term.  Other researchers have worked on ZPE and flat space models. The missing point for vacuum space is the curvature represents a type of energy like PV or a compressed spring, measurable separately from the balancing energy that caused the curvature.

In GR we have an Ideal set of equations of state like ideal gas law that works well in ordinary cases, but are missing the correction factors and different equations of state for unusual situations.

In high speed studies that I do often, the failing of ideal laws lead to infinities, suggesting the laws become non ideal at extremely high energy, or some other law becomes significant. In your question it seems to me that  you are missing an answer that needs non ideal laws, while the question seems to be asking for an answer based on ideal laws.

Thanks Jerry, you gave me some good ideas on this! This question is based on the Hubble Constant, which is a linear equation. So the ideal law is the one I applied. I understand fully what you are saying and there is a paper I need to go back and review, where the author derived Einstein's field equations and said it was an "equation of state". So I need to correlate that "inversely" to matter, rather than vacuum in my model.

A couple of interesting points to note: if metre sticks shrank but spacings not related to matter were unaffected, we should see galaxies and star systems expanding too, but what then happens to orbital energy? Is it still conserved?

Second, the length of a metal rod is determined by inter-atomic forces which are EM in nature. A metre stick, and all other matter, will shrink if there is a slowly reducing speed of light, but as Ilya mentioned, this too can simply be seen as an aspect of your choice of coordinates.

There is a lot more subtlety in this question than first meets the eye.

TD: That is exactly what we would see if our ruler were contracting. The wavelength of light emitted farther back in time will look longer, when compared to our "calibrated" instruments.

Not entirely. Naively, a spectral line from a distant atom would have the same wavelength as from a local source so should also be measured as longer. If we calibrate our instruments using a spectral line, the metre stick would be stabilised. I think you can't just change the metre stick alone, you need other changes too.

That meter sticks shrink will be, clearly, caused by changes in the fundamental forces which hold them together.  So, everything else hold together by the same forces shrinks too.  This covers everything which is hold together by forces, like planets, stars, galaxies, and even local  galaxy clusters.  So, we will not see them expanding.  

If the metre stick shrinks then so will the Earth and Sun, but their mass should remain the same, they aren't shedding atoms (however, what about gravitational binding energy?).

If the Earth's mass and kinetic energy stay the same, so does its orbital speed. If the Sun's mass stays the same, the radius of the Earth's orbit must also stay the same by Kepler's Laws. If the radius stays the same but the metre shrinks, we would observe the orbit increasing as a ratio to the the metre. To prevent that, the value of G would have to change in a definite relation to the change of the metre.

Other thought experiments should be able to identify further changes in other constants necessary to avoid measurable discrepancies like this.

George,

See my paper on Quantum Gravity, or any of Hal Puthoff's papers on the PV Model of GR. These things do change. Longitudinal mass will change, along with acceleration and velocities, while the "forces" remain invariant. So the orbital radius will contract, along with the scale of the sun and the earth, and the mass of both, and the binding energy. Everything will scale uniformly with an increase in the refractive index, K. As matter contracts, it appears to us that space is expanding. The FRW space-time is based on a scaling variable, "a". Whether you consider this the scale of the universe, or the scale of a meter stick, doesn't make any difference to the equation. It's a matter of choice, interpretation and opinion.

Exactly, just as the same effect can be obtained by a change of coordinates in GR.

AS: CMBR has origin in the quantum vacuum where is always NOW

Light takes a non-zero time to reach us from any non-zero distance so we can never observe any light that is emitted now, we can only ever see the past.

Your suggestion that the CMBR has a vacuum origin fails to explain the thermal spectrum, I explained this to Otto Rossler in another thread so I'll repeat that with his original comment here, where I talk of "", read it as "the quantum vacuum":

OER: The whole cosmos must then have a mean temperature everywhere. The latter would be "holding hands" everywhere with more or less the same temperature elsewhere, but the more distant parts would not contribute to the locally valid peak directly

If that were the case, we would see thermal radiation from sources scattered throughout space but with similar temperatures. To understand what that means, analyse it as a series of shells centred on our location. If each shell has the same thickness, it has a volume (hence number of sources) proportional to the square of its distance but the luminosity of each is diminished by the square of its distance so you might naively expect each shell to contribute equal amounts to what we observe. However, if one shell contributes say 1% of the black body intensity, it also absorbs 1% of the radiation from more distant sources, effectively shadowing them, so the actual contribution falls as a slow exponential.

That however creates a problem. Each shell is also subject to redshift proportional to its distance (at low z) which means that we would see the high frequency end of the total spectrum as looking thermal in shape but at too low a level from the nearby shells, but then becoming almost flat but falling exponentially at low frequencies due to the redshifted more distant shells.

The bottom line is that you can play a bit with the exponential decay but you can never reproduce anything like a black body curve, it is always too broad and too low.

Todd the properties of space and time must be better understood to answer your question. In equations of state the constants must become variables at extreme distance, energy, or speed, or we need additional laws to cover those cases.  it is not widely known that Albert Einstein required the velocity of light to decrease in a gravity field. Peter Bergmann always claimed the direction would change but not the speed. He did include the Einstein version in a graph of his book on gravity, but represented it as the view of a distant observer in flat space, much like you have presented PV theory.  Max Born and Richard Tolman took the Einstein point of view, and Born expressed clearly the speed changes in a gravity field according to Einstein representation.

Equation 107 of Einstein's technical book can be expressed for a central mass instead of a mass density.

 c/c0 =  1 - 2MG / rc02

This form relates to invariant Planck's constant at high speed in my version of PV.

 c/c0 = 1 -2MG/rc02 + v2/c2

Far from the central mass a reverse curvature is represented by the kinetic energy similar to the practice in QFT to use Lagrangian Densities for kinetic energy fields in space around a fast moving object, expressed with the Klein Gordon equation. The previous equation becomes.

 c/c0 = 1 + v2/c2

It relates to invariant Planck's constant for a traveler.

h = dE / df

This is a warp field of reversed  curvature created for the traveler by high speed. Light speed increases locally for the traveler but is always greater than local velocity.

Planck's constant must become a local variable in any situation where these last two equations are not valid for the traveler, in order to satisfy the established equations of energy and momentum derived from many years of accelerator experiments at high energy.

Notice there is predicted a maximum critical speed of light for c of 2c0 at which answers for energy and momentum become complex math, meaning 4 dimensions cannot contain any additional increase of velocity as viewed by the traveler.

The warp field elongates to a worm hole for the traveler, but not viewed as such by the distant observer in flat space. It is a minimum of 6 dimensions, three of space and three of time or a coordinate transformation from space like to time like dimensions.

As you know I have experimented with models of variable Planck constant in PV at extreme speeds that give similar results, but different critical speeds for c in one case almost as high as 4c0 ( actually 3.9548.. ). This is the limit of Heisenberg Uncertainty.

hbar = dE / df

The implication of your question is that there should be opportunities for advancement of science related to understanding of space and time, especially the non linearity observable by a traveler at high speed in deep space where experiments can be made to choose between the competing models.

Your question does not get an answer from conventional wisdom and established science, but it does get an answer from the leading edge of technology. This is why we propose the deep space expeditions and develop different models to predict the performance of people and equipment at high speed. There is something powerful be discovered, and high speed from prolonged acceleration is the safest way to generate the required field energy.

Todd: Perhaps I am not understanding your question. Are you suggesting that the Universe is not expanding but appears to be because rulers are shrinking due to the cosmic background radiation cooling? If so, at the risk of being irrelevant, my question is: if the Universe is not expanding, why is the cosmic background radiation cooling? I find myself unable to consider the hypothesis without some answer to that.

Hi John, how do you/we know the CMB is cooling?

(per SPIRAL (no ongoing cosmic expansion) CMB is cooling very slowly due to 1 LY per year of 'leakage' from the end of our spherical universe (that approximates our visible universe) so not due to any ongoing cosmic expansion.)

Thanks, Roger! Sorry I don’t have time to make a full study of your SPIRAL theory; I gather that it involves new physics, e.g., “1 LY per year of 'leakage' from the end of our spherical universe”. Unless the leakage is into pure nothingness (energy just lost), it sounds like the energy is leaking somewhere, in which case it sounds like expansion.

I looked at one of your previous remarks: “the CR is evidence of (past but not ongoing cosmic expansion, that ended the number of years ago”. So expansion is consistent with SPIRAL; is there a concise and simple way to explain the mechanism that stopped the expansion? And was the expansion originally due to a Big-Bang-like event?

My impression is that Todd’s question involved explaining an apparent-but-not-real expansion without introducing new physics.

Hi John,

SPIRAL holds a big bang cosmic expansion/inflation event early in the history of the universe, and no subsequent ongoing cosmic expansion.

CMB i assume moves at the speed of light so if no ongoing cosmic expansion the CMB at d i assume keep dissipating at the speed of light beyond the edge of the the edge of the universe that was by the end of the cosmic expansion..

As far as SPIRAL cosmological redshift hypothesis and some related speculation: 

SPIRAL the CR is lagging light (limited to light speed) that could not keep up with the proto stras/galaxies during the cosmic inflation event.

I do not know the mechanism (that our One common designer /creator aka G-d employed) that caused the cosmic expansion /inflation to begin or to stop.

Those who know science well I assume could hypothesize far better than I.

Something to do w the ten utterances of creation, that string theory may touch on i suppose.

In Distant Starlight and Torah we reference Pirkei De'Rebbi Eliezer regarding the meaning of the SHaKKai name of G-d, as revealed already to Abram ham long before revelation at Sinai as referring to Sh-Amar-Di = who said enough to end the cosmic expansion.

I assume the inflation mechanism reached equilibrium. The universe certainly had reached it's optimal size for the purpose at hand, and knowing motive can be useful when investigating the who, what, when, where. /how. :) ) 

Todd if Hubble's Law is linear at great distance, meaning H is constant, and measurements are proper in the frame of Earth, then an acceleration can be inferred.

v = H D

v = dD / dt

a = dv / dt

a = H v

a = H2 D

In your question the length of the competing meter stick must be decreasing, but not uniformly. It must follow the reverse of the acceleration equation at different places along the length to be indistinguishable from an expanding universe. The non uniformity is small according to H2 but significant and possibly measurable. It is difficult to imagine as a thermal gradient not extinguished by conduction in such a slow process.

This reasoning brings concern that acceleration is largest at the greatest distance, suggesting that reverse curvature intensifies with speed, a concept that I have been trying to establish.

Jerry,

Your math does not agree with the Friedmann equation. The perceived acceleration in the Hubble constant comes from the time coordinate. As you look back in time, the objects are larger because our ruler has shank since then. It is linear. 

The relatively NEW supernovae data that suggests that the universe is accelerating is in addition to the Hubble constant, it's not the Hubble constant.

John W. F.,

In my model, the universe was never a singularity, but it still started out hot and dense. As matter cooled and contracted, it eventually got to this point, where matter is uniformly contracting at ~ 6.8 nm/meter per century. According to some of the other responders, the Friedmann equation can be interpreted either way, because the length scale "a" in the equation is arbitrary. It could be the size of the Universe, or it could be the size of our meter stick. It depends which coordinate system you choose. 

As far as I'm concerned, this question has been answered to my satisfaction. 

JD: Todd if Hubble's Law is linear at great distance,..

It is, if the universe is homogeneous and isotropic.

JD: meaning H is constant

It is not. For a matter- or radiation-dominated universe, H falls as the inverse of the cosmological age. The law is linear because it refers to proper distance which is measured along a surface of common age. See the explanation on Prof. Ned Wright's tutorial.

http://www.astro.ucla.edu/~wright/cosmo_02.htm#MD

Todd I suggest the Hubble Law is non linear in ways that answer your question, by placing virtually impossible non linearity constraints along the length of the meter stick.

GD has given a reference link that agrees with my interpretation ( v = dD/dt ). Also if there is no Hubble acceleration then HD would be constant and v would be constant.

Usually Hubble constant is assumed ( H = 1/t ) for cosmic time, but this is just the case of constant velocity and no acceleration. H must vary slightly from (1/t) to comply with any one of the competing theories and GD "falls as the inverse of the cosmological age".

Suppose  H = 1/t + B    for constant B.

Acceleration is   a =  B ( D/t + v)

Constant B can be as small as you like but greater than zero in this case of expanding universe. Other models get a somewhat different H.

Hubble variables are all defined as proper measurements in Earth frame, which eliminates relativistic transformations, but makes Hubble law a bit artificial.

About Freidman equation, I have disparaged FLRW family of metrics in other threads for their disagreement with other families of metrics that are rigorously integrated from Einstein Maxwell equations, also for the assumption of dark energy that isn't found or measured, to rescue FLRW in ways that are not needed in rigorously integrated metrics.  It is relativity not related to Hubble Law. 

For Todd's question I offer the several theories of expanding universe and the Hubble non linear law that goes with them to distinguish between expansion of the cosmos and shrinking of a meter stick non uniformly along the length. 

H = 1/a(t) da(t)/dt

where a(t) is the scale factor. Dark energy means H tends to a constant hence a a(t) tends to an exponential. The speed and acceleration then also tend to exponential. There is no analytic solution unfortunately but your "1/t+B" gives a qualitative indication.

Your variable B as the asymptotic value of H is sqrt(lambda / 3) where lambda is Einstein's Cosmological Constant.

https://en.wikipedia.org/wiki/Scale_factor_%28cosmology%29#Dark_energy-dominated_era

Jerry> I have disparaged FLRW family of metrics

Why??  FLRW solutions can be derived in an equally respectable manner than other ones, and match observations much better. Nice, analytic expressions can be found for the most popular model, cold matter plus dark energy. Light (Maxwell equations/relativistic matter) has been a irrelevant contribution for a very long time, even in comparison with the observed cold matter.

Please, read the file in:

ROTATING SPASE OF THE UNIVERSE, AS A SOURCE OF DARK ENERGY AND DARK MATTER.

https://hal.archives-ouvertes.fr/hal-01329145v1

GD thanks for the explanation. Many functions of H are offered to me, but lack the data for comparison of predicted acceleration, or deceleration in the past. The H function I used is possibly the simplest that provides for velocity to change with time for objects and groups. Most likely the function is polynomial in (1/T) to account for the expansion phases. Even if it isn't polynomial a series expansion is usually possible with infinite series, which in this case with very small H, the higher order terms should quickly become insignificant.

Valery the concept of a rotating universe with kinetic energy of rotation taking the place of dark energy is interesting but fails the homogeneous and isotropic requirement. Since there would be an axis of rotation, not all distant objects would be treated equally because of different distances from the axis. About 6 years ago there was suggestion of a preferred axis of rotation for the universe based on studies of fine structure at a distance. My objection to it was historical, but strengthened by the apparent axis passing through the South Magnetic Pole of Earth, which I thought was unlikely, and a step backward in science. The fine structure data could be interpreted as small displacement of magnetic and gravity fields of Earth repelling each other. Most GR metrics predict this for magnetic monopoles, but not for dipoles. FLRW predicts the opposite that gravity and EM attract each other, both making positive curvature. I suggested at the time of fine structure publication that Earth magnetic poles are far enough apart to act as monopoles in the near field, repelling gravity enough to account for the fine structure data, and in agreement with GR.

 Kåre the derivation of FLRW would be OK with me if the assumptions were reconsidered about curvature of electric and magnetic fields. FLRW family treats all known energy including EM as an addition to strength of gravity. Then it needs dark energy to counteract the combine curvatures. Albert Einstein did not do this. Neither do the metrics that are rigorously integrated from Einstein Maxwell equations. Example is Kerr-Schild family of metrics, which nearly every researcher accepts as valid. All of these rigorously derived metrics apply EM to weaken gravity, by integration, not by assumption.. Einstein in his technical book beginning with equation 107 shows that light speed is a variable in changing curvature and slows down when approaching a gravity field. His prediction of light passing the sun in the next paragraph is confirmed several times by different people. FLRW is widely accepted without question, except I question it when it ignores Maxwell and opposes Einstein.

All that is necessary to cause acceleration without dark energy on a large scale is for radiant EM energy to slightly exceed gravity potential energy in deep space regions far from mass concentrations including dust of the FLRW metric.

Todd: “As matter cooled and contracted, it eventually got to this point, where matter is uniformly contracting at ~ 6.8 nm/meter per century.”

I still have not seen a reason why the Universe is cooling if it is not expanding. I guess I agree with the others about the scale parameter in the FLRW metric being able to go either way, but it seems to me that the cooling of the cosmic background radiation resolves the ambiguity. The Universe is by definition (usually) a closed system, so there’s no reason for a largely decoupled radiation field (i.e., the CMBR) to cool if its container is not expanding.

Sorry for the delay, by the way; ResearchGate did not inform me that you had responded to my question, as I thought it was supposed to.

Jerry> Example is Kerr-Schild family of metrics, which nearly every researcher accepts as valid. All of these rigorously derived metrics apply EM to weaken gravity

Can you please explain to me where electromagnetism enter into the derivation of the Kerr metric?

 Kåre the Kerr-Schild family of metrics has several cases that include electricity and/or magnetism either as point sources, or as potential fields. The Kerr metric is in the family, but does not contain electromagnetism. In the cases that do such as Kerr-Newman, Maxwell equations enter in as partial differentials and are integrated simultaneously with Einstein field equations. Here are references In RG.

https://www.researchgate.net/publication/252575345_Einstein-Maxwell_fields_of_the_Kerr-Schild_and_generalized_Kerr-Schild_class

https://www.researchgate.net/publication/222246060_A_class_of_solutions_of_Einstein-Maxwell_equations

Reissner-Nordström is the simplest member of the family with electromagnetic fields and easiest for some of the readers to understand since it is not rotating. Peter Bergmann gave a fairly complete derivation in his 1942 book on Relativity, also available in the 1976 Dover edition beginning on page 204. It follows closely to the Nordström version of 1918, and is remarkable in that the Maxwell equations go in and the square of the electric charge emerges as a constant of integration weakening gravity unambiguously. Here is another fairly simple representation of Reissner-Nordström extended to show a conventional view of how magnetic monopoles oppose gravity. 

Reissner-Nordströmom Metric, Gulmammad Mammadov, Department of Physics, Syracuse University, Syracuse, NY 13244-1130, USA,  May 04, 2009.

Quite a few other derivations are available on line. Here is a review of Kerr-Newman.

arXiv:1410.6626v1 [gr-qc] 24 Oct 2014

The Bergmann presentation is a significant starting place, because it shows in sufficient detail there is no other way to interpret the electromagnetic component other than as weakening gravity. All of the Kerr-Schild family that include electricity and/or magnetism reach this same conclusion, but with more complicated math that not everyone can follow unambiguously.

FRW also has alternative derivation in recent publications.

arXiv:gr-qc/0407080v3 6 Jan 2005

At equation 27 the EM energy is added to intensify the gravitational stress energy in disagreement with  Kerr-Schild, and with no explanation why, except it has always been done that way in Friedman family of metrics. It is simply an arbitrary assumption that is seldom challenged.

I suggest to the readers that in equation 27 the EM energy could be just as easily subtracted from gravitational stress energy on the grounds that fully integrated metrics reach that conclusion from emerging parameters when Maxwell equations are simultaneously integrated with Einstein field equations. It would give a different FRW, probably not needing dark energy, but in agreement with Kerr-Schild, of which it would become a special member.

Article Einstein-Maxwell fields of the Kerr-Schild and generalized K...

Article A class of solutions of Einstein-Maxwell equations

Ilja and Jerry, 

I ask you to reference Appendix B of Milonni's book, "The Quantum Vacuum". That's the idea of temperature dependence I am referring to. 

Todd I'm in the group that doesn't find a mechanism for cooling other than by expansion.

Consider the ways we measure temperature. It can be a differential change of volume or a voltage potential of millivolts. There are enough redundant ways that measure of temperature is not compromised by indeterminate distance, unless the complete set of measurable quantities is discredited, which was not your question.

In Appendix B of Milonni's book, "The Quantum Vacuum" thermal radiation pressure on a free atom is discussed. I go a bit further and ascribe a reverse space curvature to the radiant energy. Radiant heat in vacuum is made up of  long wave length radio waves. So it looks like part of your question, not part of an answer.

I prefer vibration frequencies and counting of cycles on a clock as the best answer that does not depend on amplitude or distance. In the micro world everything vibrates with an energy. The frequencies and amplitudes change with stress. Curvature varies with energy density, of which Temperature is a contributor.

By eliminating distance in a temperature measurement, your question is answered. There is a fundamental principle and a practical mechanism for deciding between a shrinking meter stick and an expanding cosmos. 

Dear Todd

Your question is really important because if instead of an expanding universe what happens is that bodies are decreasing in size, than current model is just a modern version of Ptolemy model, with dark energy in the role of celestial spheres to explain global motion, dark matter in the role of epicycles to explain "anomalous" local motions, a universe split in two, an invariant local one made of known stuff and a changing distant one made of unknown stuff. Really similar, don't you think?

There is a very clear answer to your question. Let me point the essential aspects

A decrease of the length of the bodies is a consequence of the decrease of mass and charge of particles, using a classic atomic model. Such decrease would imply decrease of size and decrease of time unit because light speed is invariant in the process. When mass, charge, length and time decrease at the same rate, then the non-dimensional combination of them hold invariant, holding physical laws (pi-theorem). Temperature is independent of the process because it depends only on the state of systems, having the same value for the same state, whatever mass and charge of particles. Therefore, in this case, bodies would decrease in size and we could not detect it by local experiments; but we will see an expanding space and the redshift of distant radiation, emitted when atoms where bigger.

I have a paper that on this (Article A self-similar model of the Universe unveils the nature of dark energy

The diference between using my model and the current one is like the diference between using Newton model and Ptolemy one. I know it because I made this 30 years ago and kept researching. You can't imagine what is ahead to be discovered. I have a second paper in vixra, it can give you and idea, and that is just the second of seven, all as unexpected as those two. I am now finishing a much better version of my paper, but publishing in a scientific journal is not easy because I am an engineer not affiliated to a research institution.

Dear Todd J Desiato , thank you for your question. Additionally, some CMB anomaly about symmetries and inhomogeneity: https://www.researchgate.net/post/CMB_Anomaly_Cosmic_Microwave_Background_Symmetries_and_Inaumogienity Thanks to Alfredo Oliveira , Jerry Decker , Kåre Olaussen and all for useful answers.

@ All

On contracting Universe model, one can propose potential of nature V(x)= - x^6 ,8 ....

Interestingly quantum analysis reflects real energy . Surprisingly paper in PRL & J.Phys A

give two different expressions for energy .

So my doubt is which one is correct ?

Secondly possible model must consider

mass dependent potential. Any move in this direction might give some interesting new findings.

B.Rath