I had a discussion on this general topic with someone not long ago.

The important point, in my view, is to distinguish between the invariance of a theory vs. the invariance of a specific solution.

Take cosmology, for instance. General relativity as a theory is fully diffeomorphism invariant. There is no preferred frame, no preferred coordinate chart. The equations remain the same. Same goes for Maxwell's theory.

However, when you solve those equations, you may introduce initial or boundary conditions that break this symmetry. Specifically, the FLRW solution in cosmology is constructed by assuming spatial isotropy and homogeneity, but no isotropy or homogeneity in the time direction.

So right there, we picked a solution with properties that identify a preferred frame by definition. And if this solution happens to describe the physical universe correctly, then the physical universe has a preferred frame, despite the fact that the underlying theory doesn't.

Personally, I don't find this particularly profound or mysterious. As a much more mundane example, here on the surface of the Earth clearly we have a preferred frame. Even though the laws of classical mechanics are invariant under an arbitrary spatial rotation, clearly its solutions as applied to terrestrial events are not invariant under rotations in anything other than the horizontal plane.

Experiments involving Planck-scale energies may very well produce exotic results, but I don't think this has much to do with the preferred frame of the FLRW metric.

I had a discussion on this general topic with someone not long ago.

The important point, in my view, is to distinguish between the invariance of a theory vs. the invariance of a specific solution.

Take cosmology, for instance. General relativity as a theory is fully diffeomorphism invariant. There is no preferred frame, no preferred coordinate chart. The equations remain the same. Same goes for Maxwell's theory.

However, when you solve those equations, you may introduce initial or boundary conditions that break this symmetry. Specifically, the FLRW solution in cosmology is constructed by assuming spatial isotropy and homogeneity, but no isotropy or homogeneity in the time direction.

So right there, we picked a solution with properties that identify a preferred frame by definition. And if this solution happens to describe the physical universe correctly, then the physical universe has a preferred frame, despite the fact that the underlying theory doesn't.

Personally, I don't find this particularly profound or mysterious. As a much more mundane example, here on the surface of the Earth clearly we have a preferred frame. Even though the laws of classical mechanics are invariant under an arbitrary spatial rotation, clearly its solutions as applied to terrestrial events are not invariant under rotations in anything other than the horizontal plane.

Experiments involving Planck-scale energies may very well produce exotic results, but I don't think this has much to do with the preferred frame of the FLRW metric.

There are no preferred frame of reference as mentioned by Prof. Toth. If particle energy exceeds Planck energy its wavelength will cross the limit of Compton wavelength and the particle wave will collapse and unmanifest to human senses.

V. T. and Vikram,    The reason that I ask this question is that I believe that the question has far reaching implications if there are ultra-relativistic frames of reference relative to the CMB rest frame where the laws of physics break down. For example, string theory is based on three mathematical assumptions. One of these is Lorentz invariance which implies that the laws of physics are the same for all uniformly moving observers (even in the most ultra-relativistic frames of reference). For example, can a Higgs boson exist in a frame of reference if it would appear to have a de Broglie wavelength shorter than Planck length in the CMB rest frame? Can a gamma ray photon exist in a frame of reference if the photon would appear to possess more than Planck energy in the CMB rest frame? This is probing the structure of spacetime and if there are any limits on Lorentz invariance.

If I am in a closed spacecraft, I do not know my frame of reference relative to the CMB rest frame. However, I can do experiments to determine whether there are any changes in the laws of physics which might occur if some virtual particle pairs cannot exist in my frame of reference. Field theory visualized zero point energy existing at all frequencies up to Planck frequency. This seems to imply a symmetrical distribution of frequencies up to Planck frequency as seen from some preferred frame of reference which is probably the CMB rest frame.

The universe has fundamental limits. For example, the maximum force that can be applied to a physical object is Planck force (ignoring numerical factors near 1). This is the force between two equal mass black holes as they are about to merge. It is proposed that Planck frequency and Planck length are similar fundamental limits which reference the CMB rest frame.

John: Your comment reminded me of the paper by Drummond and Hathrell, (PRD V22N2 1980), where they discuss vacuum polarization in curved spacetime and conclude that photons are now described by an effective Lagrangian that is Lorentz-violating. They specifically discuss, among other cases, the case of an FLRW universe. Perhaps it might prove interesting/useful to try to model your ultrarelativistic spaceship using their approach?

This ultra-relativistic frames of reference seems to violate the conservative idea that the velocity of light is same in all frames of refrence. If the de Broglie wavelength is shorter than the Planck length than it will require the particle to travel faster than the speed of light which is crossing the Compton wavelength limit. Experimental proof of particles travelling faster than the speed of light will lend support to the idea of ultra-relativistic frames of reference. In this connection following article by Shalender Singh can be of some interest. 

Article Extended principle of relativity beyond speed of light and a...

There are lots of arguments in favour of preferred frames and preferred coordinates, and I'm starting now to write a book collecting them all. The most powerful and easy to understand argument is up to now the violation of Bell's inequality.  Every realistic explanation of this violation requires a preferred frame.  

So those who argue for the non-existence of a preferred frame have to give up realism and realistic causality.  Without a good reason - because there exist realistic interpretations for quantum theory, namely de Broglie-Bohm theory.  Thus, one cannot blame quantum strangeness as a justification for rejecting realism.

John, very interesting question, thanks for bringing it up. Of course, it has been discussed countless number of times, yet there seem to be new facets to it. Other replies take it in various directions, too. Let me chime in with my two cents. From my prospective, the issue breaks down  into two -- and not very connected -- questions.

(1) Is there a preferred frame in our Universe? (I mean, no bulls*t frame, in respect to which one can measure -- using existing technologies -- one's velocity in a direct, explicit way, no "thought experiment"...) The answer to this question is a resounding "yes", there is one! It is the CMB (cosmic microwave background) radiation, or relic radiation; by now there are plenty of accumulated research data on its (averaged) isotropy (with respect to its rest-frame), slight fluctuations, a lot of details (we even know by now  tiny velocity of our galaxy with respect to its rest-frame), etc. Thsoe reports are published by huge collaborative groups (sorry, don't have references at hand). Furthermore, it is not just that cold EM-radiation (about 2.725 degree in Kelvin); by now we also know that CMB essentially imposes  almost similar  isotropy on the matter -- I am talking here about GZK (Greisen, Zacepin, and Kuzmin) limit in observable high-energy protons and neutrons in cosmic rays.

(2) In view of (1) --  is special relativity still true, in particular in that no speed of energy transfer faster than speed of light in vacuum exists?  Well, no credible experimental data so far suggest otherwise.  In my own understanding, I personally came to the comfortable point that there is no actual contradiction between (1) and (2). After all, special relativity (SR) never claimed that "preferred frame" is non-existing. The only thing that SR postulated was that an "unloaded" vacuum is not a "preferred frame".  Now, if we (or the big ONE who is/was tinkering with our Universe), put something else in that vacuum -- it is our (or HIS) business; the light doesn't care, and doesn't pay too much attention to the "pie-filling". Just a trivial mundane example: in our little neck of wood  we definitely have a "preferred frame" -- it is our Earth; yet it doesn't affect our physics in laser wave propagation, in super-duper accellerators, etc -- all of which are solidly based on special relativity...

What does "rest frame of the CMB background" mean? Light doesn't have a rest frame or to say it a different way, every unaccelerated frame sees light at the same speed.

James: It's the frame in which the CMB is isotropic.

By the "rest frame of the CMB background" one just means the frame in which the CMB is isotropic. Observed from Earth it is the frame in which the dipole anisotropy is subtracted away. It is a mere convention.

To Charles Francis: thanks; I looked into Toth's post. I found no contradiction between his and my posts; good to see that my view (as simple as it is) is not far from others who thought of this issue.

To Charles: "bean-counting"... My friend, you want to be a self-appointed judge and expert, be my guest. This is an alive discussion; I don't remember anybody appointing you for the position of the "king-of-the-hill", who can make a judgement of other people "language" and  assign who failed and who won. Of course, with ten or so papers behind your belt, you could feel like an Einstein successor, but as you may guess it will be up to others people in the field to make this judgement. I wish you to become a shining star in the field, although at this point I haven't seen any indication of that outside of this forum. Meanwhile, there would be nothing wrong if you learn how to speak to your colleagues and be part of scientific discussion.

I confess that I had in mind an answer when I proposed this question. For a long time I have been developing a model of the universe constructed only out of 4 dimensional spacetime. An overview of this model is available as a preprint of a paper to be published by Springer in December (see link below). The key step in developing this model is the characterization of zero point energy (ZPE). Spacetime has impedance of c3/G obtained from gravitational wave equations. The uncertainty principle allows waves in spacetime to have a displacement amplitude equal to Planck length and Planck time. All frequencies up to Planck frequency exist in ZPE. However, this statement implies a preferred frame of reference where the frequencies of ZPE are seen as being symmetrically distributed.

This might seem as wild speculation, but this approach has yielded numerous predictions which are correct. For example, the model yields predictions into a connection between the gravitational force and the electrostatic force. For example, this paper gives 9 equations which show that the gravitational force between fundamental particles can be expressed as the square of the electrostatic force when both forces are expressed in the natural units of the particles. This relationship was predicted by the spacetime based model of particles, fields and forces. Gravity is modeled as a nonlinear effect that scales as wave amplitude squared.  This yields the curvature of spacetime and the correct relationship to the electrostatic force. Another prediction discussed in a related book is that all frames of reference are not equal. ZPE is symmetrical only when seen from the CMB rest frame. Moving relative to the CMB rest frame does not have noticeable effects if the special relativity gamma is not so large as to affect the formation of virtual particle pairs. However at extreme frames of reference there is an unsymmetrical effect on the formation of virtual particle pairs. The prediction is that the laws of physics would be affected in frames substantially displaced from the CMB rest frame..

http://onlyspacetime.com/QM-Foundation.pdf

@ Toth

"So right there, we picked a solution with properties that identify a preferred frame by definition. And if this solution happens to describe the physical universe correctly, then the physical universe has a preferred frame, despite the fact that the underlying theory doesn't."

I completely agree...

Hi John! I suppose it depends on the exact statistics, but the "boring" answer might be that this sort of local galaxy-frame distribution doesn't //always// suggest local preferred frames for the physics carried out in those regions – we might also expect locally-biased distributions based on statistical behaviour.

For instance, the planets circling our sun all pretty much circle in the same direction. This doesn't necessarily mean that there's a massively-preferred local frame for rotation (although there will be some sort of effect due to the dragging effect of the rotating Sun and planets) ... it's more likely to mean that interactions between the particles that coalesced to form those planets had time to interact and exchange momentum though direct collisions or radiation and be influenced by local averages.

So if you're a particle orbiting in the proto-solar-system gascloud, and you're orbiting in the same direction as the majority of other particles, then you'll be a happy particle ... but if you're orbiting the other way, you're orbit is going to be repeatedly changed by collisions until you end up travelling pretty much in the same direction as your neighbours. It's the most stable solution.

In an early hot dense universe, any regions that move "quickly" wrt their neighbours will tend to be slowed by collisions and other interactions with less-quickly-moving matter, creating a similar averaging effect. If the most stable solutions have galaxies forming in conditions that have a minimum velocity wrt their immediate neighbours  (the ones that don't are more likely to be destroyed by collisions), then you might expect galaxies on average to tend to be roughly stationary wrt surrounding local averages, and wrt background.

So you could conceivably have emerging statistical averages for the large-scale distribution of matter in local frames, without the field-physics in those regions showing a preferential bias for those frames.

A more interesting (but more speculative) answer might be that although we assume that all particles moving at a given velocity will continue at that velocity until disturbed, I don't know whether this necessarily holds true for particles travelling at more than background lightspeed.

In acoustic metrics there seems to be a nice balancing effect for a fast-moving particle between the opposing velocity-based effects of the changed apparent distribution of background matter and the gravitomagnetic effects of that moving background material, which seem to create frame-invariance as an emergent effect.

However, I don't know (one way or the other) whether that mechanism still operates perfectly once a particle is moving faster than background c wrt a uniform distribution of  background matter. If an acoustic metric turns out NOT to extend frame invariance past cBackground , then that might also create a local bias on the behaviour of slow particles in the region.

And (again in a hypothetical universe that allows ultrafast particles) there's also the possibility that ultrafast particles might be braked by Cerenkhov radiation or it's non-EM versions, again creating a bias centred on the local average.

I don't know the reason why  the planets circling our sun all pretty much circle in the same direction.because I am not an astronomer, but I don't believe the conjecture that interactions between the particles that coalesced to form those planets had time to interact and exchange momentum though direct collisions or radiation and be influenced by local averages. That I think is unlikely.

In order to find noticeable differences in the laws of physics extreme reference frames (like CMB) aren' t required but usual reference frames are sufficient. A different  conclusion depends on a wrong interpretation of the Relativity. Let us begin saying the term "equivalent"  is generic and it has to be specified.

The Principle of Relativity, the only really valid, affirms an invariance (not a simple equivalence) of laws of physics with respect to all inertial reference frames, after that a reference frame at rest has been supposed and defined. Therefore an absolute resting reference frame doesn' exist but exists only a reference frame that is supposed at rest. As per this definition of reference frame supposed at rest, we can define inertial reference frames that don't would have meaning in the absence of that definition.

The Principle defined in General Relativity isn't a principle of relativity because it isn't based upon a principle of invariance, but on the contrary it is based upon a principle of covariance. This principle of covariance doesn't define an invariance of laws of physics with respect to accelerated (non-inertial) reference frames but a simple equivalence concerning the possibility to write the same law of physics with respect to all accelerated (non-inertial) reference frames, without that the principle of invariance is respected. Consequently firstly it is necessary to do a distinction between relativity (=invariance) and simple equivalence in GR (=covariance).

Experimental observations of CMB with relative small anysotropies would have to consider also Doppler spectra (redshift and blueshift) besides thermal spectrum of blackbody and anyway they have no meaning with respect to the initial question.

The other problem with CMB as a prefered reference frame is that there is no reason to suppose that it is inertial. The apparent motion of the Earth with respect to the CMB could equally be explained by differential expansion caused by a concentration of matter on one side and a void on the other. A frame of reference which has different accelerations in different patches is definitely not inertial.

Andy, no, this is not a problem. Simply in GR there is no such notion as "inertial frame" anyway. Then, if one introduces a preferred frame, one automatically introduces a notion of time dilation and distortion of tulers, because it answers the quetions "distortion relative to what". As a consequence, the expansion of the universe, accelerated or not, is interpreted as a shrinking of the rulers. 

Of course, I know that in some local approximation some aspects (all those which ignore curvature) can be described with approximately inertial local frames.

But the context of the discussion was about the global aspects of the CMBR frame. So, such local inertial frames are irrelevant here. 

The statement "local inertial frame" can be accepted in the order of General Relativity. Outside GR that statement has no meaning. As usual the predominant viewpoint becomes absolute truth.

Charles, of course "CMB-preferred system of coordinates" would be, of course, more accurate, but, as it often happens, the shorter but less accurate "CMB frame" is the established notion. Which is not that problematic, because these CMB-preferred coordinates define, everywhere, locally (where SR is applicabla) a frame in which the CMB radiation is isotropic. 

Charles, your definition of "local inertial frame" derives from the fact that according to GR inertial reference frames exist only locally. My room is certainly a local inertial frame according to Galileo's definition that has nothing in common with GR.

Your room isn't an inertial frame - the Earth's gravitational field acts within it.

Eric, is true, there is the Earth's gravitational field, but it is the same for all points of the Earth at equal distance from the Earth's centre. The same thing is valid with respect to the rotatory motion and to orbital motion of the Earth. Consequently the whole Earth can be assumed as an inertial reference frame. Suppose now that the Earth is immobile in the universe (for the sake of argument) and then the Earth can be assumed as a resting inertial reference frame for describing the inertial field of all inertial reference frames with respect to the Earth. This is the great scientific progress of the Galilean relativity that Einstein accepted only partially. The concept of inertial reference frame isn't absolute.

If your room is a laboratory on the ground floor of a skyscraper and there's another laboratory on the top floor, the 'laws of physics' in the two laboratories won't be the same (the gravitational field is different). So they can't both be regarded as inertial frames.

Ilja, the CMB is not isotropic as measured. It is assumed isotropic because the universe is assumed to be homogenus and isotropic. Locally the universe is neither. On one side we have the Virgo and Comma superclusters. on the other a big empty space. The mass/enmergy tensor which determines the expansion rate is different on the two sides of the galaxy. By ignoring observation and adjusting things to fit the dogma we give our location a boost to make the CMB isotropic. The problem with this is that we must then postulate a "great attractor" to account for all the motions. The attractor is conveniently situated behind the galactic centre where we can not see it. Occam did warn us about multiplying entities. Improved observations are making the great attractor as a concentration of mass less likely so we get speculation that it is some sort of leakage from another part of the "multiverse." That is the problem with multiplying entities there is no end to it.

The CMB is not itself a frame of any sort: it is a hum in the radio spectrum. The space through which the CMB is travelling is a frame of some sort. It is certainly local because that is the only place we can see it. The local mass/energy tensor is not isotropic so neither is the CMB. The only frame I have got is where I am now with my clock running at sixty seconds to the minute and my eyeballs right on the leading edge of the expanding universe. This frame is covariant because it goes with me wherever I go and however you may describe the coordinate patch I inhabit from one moment to the next. My space is Euclidean. That you all live in a twisted space with dogy clocks is not your fault. It is just because you are not me. My experiments always obey the laws of physics. If they look strange to you that again is because are not me. You may think your physics is the right one but it will look odd to me. GR may be a way to adjust your physics so it mtches my proper physics done in proper time.

I would say that not all frames of reference are equivalent.  They would have to have the same forces on them.

No the CMB is not isotropic. Look at the raw data. To make it isotropic we have to assume motion relative to the CMB. The only reason for assuming this motion is to make the CMB isotropic. Before believing that it is isotropic then independant observation of the supposed motion would be needed. The observation is that the CMB is not isotropic and there is a just so story to make it fit with the supposed isotropy.

Last time I heard isotropy means same in all directions. The CMB is manifestly not the same temperature in all directions until it has been corrected to to remove these temperature differences by the supposed motion. This is not the same as independantly observing motion then correcting the anisotropic CMB and finding it is really isotropic. Show me the independant evidence for motion relative to the CMB and I will accept what you say. Until them I will say that the observed CMB is not isotropic.

Andy,

The CMB exhibits a dipole anisotropy. The temperature varies minutely over the sky in such a way that it is maximally blueshifted in one direction and maximally

redshifted in the opposite direction.

The hot Big Bang cosmology predicts that the CMB should be essentially

isotropic, since it originated in the last scattering surface, which has now receded to a redshift of z~1090 in all directions.

In the standard model the expansion is spherically symmetric, so it is quite clear that the dipole anisotropy cannot be of cosmological origin. Rather, it is well explained by our motion `against' the radiation in the direction of maximal

blueshift with relative velocity v..

Thus there is a frame in which the CMB is isotropic and which is comoving with the expansion of the Universe..To a fundamental observer at rest in the comoving frame, the Universe must appear isotropic if it is homogeneous. Although

general relativity was constructed to be explicitly frame independent, the comoving frame in which the CMB is isotropic is observationally convenient.

The interpretation today is that the Galaxy moves relative to our Local Galaxy Group and our motion relative to the CMB is 369+-0.9 km/s. The velocity vectors add up to a peculiar motion of the Galaxy of about 550 km/s, and a peculiar motion of the Local Group of about 630 km/s. Thus the dipole anisotropy seen by an Earth-based observer tells us that we and the Local Group are part of a larger, gravitationally bound system.

The speed of light is equal to the universal constant c in all frames of reference. However, it does not follow that all frames of reference are Lorentz invariant if the term all includes even frames with extremely large values of gamma (γ) from special relativity. For example, the current record for the highest energy photon ever observed is a 12 TeV gamma ray (∿ 2×10-6 J) which has wavelength of about 10-19 m. This energy photon is permitted in our frame of reference, but it would not be permitted in any frame of reference which exceeded about γ ≈ 1016 relative to the CMB. The reason is that this photon would have a wavelength less than Planck length when viewed in the CMB rest frame and the energy would exceed Planck energy. Spacetime cannot propagate photons with this characteristic because Planck units such as Planck length and Planck energy represent limits placed by spacetime. This implies that the laws of physics change in these extreme frames of reference.

String theory is based on three starting assumptions which are expressed as mathematical equations. These are 1) Lorentz invariance, [the laws of physics are the same in all uniformly moving frames of reference] 2) analyticity [a smoothness criteria for the scattering of high energy particles after a collision] and 3) unitarity [all probabilities always add up to one]. The contention is that Lorentz invariance is not a valid assumption for all uniformly moving frames of reference. Therefore, since string theory incorporates this erroneous assumption, any analysis incorporating this assumption is questionable.

John,

I don't follow your argument that a photon of energy 12 TeV in our frame of reference would not be permitted in any frame of reference which exceeded about γ ≈ 10^16 relative to the CMB. Because of  Lorentz invariance, that photon would be permitted,( in a frame of reference which exceeded about γ ≈ 10^16), but it would not appear to have energy 12 TeV. Or, is that what you said but I misunderstood?

The CMB question is full of interesting considerations. Firstly to the initial question  "Are all frames of reference truly equivalent?", we would have to add now other interesting questions: 1. Which is the effective physical source of CMB?  2. Is the CMB a resting reference frame?  A certain consideration that we can do is that different experimental observations have to be in accord. They seem to show definitively the presence of numerous anisotropies in different observed spectra that have different origin. In particular Doppler spectra prove the redshift celestial front goes away while the blueshift celestial front moves near and consequently it would involve the expansion of the universe isn't homogenous in all zones of space relative to the same direction. It means the galactic system to which the sun belongs is the most slow among all observed galactic sytems and it would pose serious problems for the BigBang theory and for the Hubble law. 

Certainly, as J. Macken has pointed out, these considerations raise also an other problem at level of fundamental physics on the Lorentz invariance. Analysing the photon energy, he claims the Lorentz factor must have an upper bound  gM=10^16, as per deductions relative to the Planck length and to rest CMB. Consequently he derives laws of physics have to change relative to extreme reference frames like CMB. Substantially he suggests a process of re-normalization of the Lorentz factor through a generalization of laws of physics relative to extreme physical situations. At last he concludes string theory, the most accredited theory for post-modern physicists, isn't  a solution to the question because it is based upon the Lorentz classical invariance.

I agree with Macken's a few conclusions and I disagree with others. I agree for instance the string theory isn't a valid alternative and I agree also the Lorentz invariance has serious problems. I disagree nevertheless with the upper bound  gM because it would involve an upper bound vM  also for the speed equal to  vM=c SQRT(1 - 1/gM2) that is hardly acceptable.

In the Theory of Reference Frames this question is solved by a new group of transformations, alternatively to LT, that is valid in the space-time-mass domain whether for inertial reference frames or for non-inertial reference frames. It allows to eliminate also all singularities that are present in predominant theories at present.

Matts, I am interested in these recent comments you made:

The interpretation today is that the Galaxy moves relative to our Local Galaxy Group and our motion relative to the CMB is 369+-0.9 km/s. The velocity vectors add up to a peculiar motion of the Galaxy of about 550 km/s, and a peculiar motion of the Local Group of about 630 km/s. Thus the dipole anisotropy seen by an Earth-based observer tells us that we and the Local Group are part of a larger, gravitationally bound system.

How do you define peculiar motions here if they are different to those relative to the CMB? What is this system to which the Local Group is gravitationally bound and did you ignore or take account of the future influence of dark energy here? Voyager 1 has left the Solar System and is moving away from the Sun with a speed of ~17km/s. Its peculiar velocity does not mean that it is gravitationally bound either to the Sun or any nearby star.

Robin,

The peculiar velocities I mentioned have not been determined with respect to CMB, they come from the use of Hubble's linear law on galaxies within the Local Supercluster (LSC) which cab be used to predict the dipole motion.

On the other hand, one also observes deceleration of

the expansion in the local universe due to the lumpiness of matter. For instance, the local group clearly feels the overdensity of the Virgo cluster at a distance of about 17 Mpc, falling towards it with a peculiar velocity of about 630 km/s.

It has been argued that the peculiar velocities in the LSC cannot be understood without the pull of the neighbouring Hydra--Centaurus supercluster and perhaps a still larger overdensity in the supergalactic plane, a rich cluster (the A3627) nicknamed `the Great Attractor' at a distance of 79 Mpc. The greatness of the latter has been questioned..

It should be clear from this that one needs to go to even greater distances, beyond the influences of local overdensities, to determine a value for the cosmologically important deceleration parameter q_0. Within the LSC it is safe to conclude that only the linear term in Hubble's law is necessary., and no dark energy needs to be taken into account.

Matts, thanks for your answer but I don't think it is safe to ignore dark energy's influence - see http://arxiv.org/abs/1006.0555. I agree that we have an anomalous motion in the direction of Virgo (about 220 km/s) but it is insufficient to overcome the effects of the accelerating cosmic expansion. The effective repulsion due to dark energy is already (at least) four times larger than Virgo's gravitational attraction and this cluster is already receding from us at 1000km/s. Since the discovery that the expansion of the universe is accelerating it has become clear that galaxy clusters are the largest bound structures of the universe (rather than superclusters) and neither the Milky Way nor the Local Group belong to one.

Matts,  Sorry, I did not express my reasoning well. I am going to give two different sets of reasons. The first is merely reasonable contentions. 1) Photons with wavelength less than Planck length (energy exceeding Planck) are not allowed when viewed from the CMB rest frame of reference. 2) The relativistic Doppler shift equation works in all frames of reference. 3) In order for the universe to exhibit Lorentz invariance, the laws of physics must be the same in all frames of reference. 4) The CMB rest frame is a reasonable preferred frame of reference which would permit photons near Planck energy to propagate homogeneously in any direction. 6) Rapidly moving frames of reference relative to the CMB rest frame are predicted to exhibit different physical properties for photons near Planck energy compared to the CMB rest frame. This difference stems from the contention in point #1.

The second set of reasons more tightly woven.  It is based on the model of the universe stated in the paper obtained from the link below. This paper will be published in December and makes the case that everything in the universe (all particles, fields and forces) are all different manifestations of 4 dimensional spacetime. In pages 13 to 15 of this paper this contention is extended to charged particles, electric fields and photons. A new constant of nature is proposed which converts electrical charge (Coulomb) to a distortion of spacetime. When this charge conversion constant is applied to the impedance of free space (Zo ≈ 377 Ω) it converts to the impedance of spacetime Zs=c3/G which is the impedance encountered by gravitational waves as they propagate through the medium of spacetime. The implication is that photons are also a wave propagation in the medium of spacetime. The particle-like property of photons is associated with quantized angular momentum. Ultimately, the quantum mechanical property of spacetime (zero point energy) is quantified and calculated. This leads to the contention that the properties of spacetime are only homogeneous when viewed from the CMB rest frame. However, these differences in physical experiments would only become obvious in extreme frames of reference with special relativity gamma exceeding about γ ≈ 1015.

http://onlyspacetime.com/QM-Foundation.pdf

In certain modified gravity theories like MOND, all frames of reference are not equivalent. For example, if you're in a spacecraft orbiting the Sun, you're freely falling. If you do a gravitational experiment (measure force between two 1kg masses 1m apart), you get the result predicted by Newtonian gravity. But, if the spacecraft was taken to a point say halfway towards Andromeda, and the thrusters were off (so you're also freely falling), then the force measurement would yield a higher answer. The reason is the external field effect. The external gravitational field upon the spacecraft - even if it is perfectly uniform (so there are no tidal forces) - can weaken the internal self-gravity of the two masses.

This idea seems to work reasonably well with astrophysical observations. For example, the escape speed from the Milky Way can be calculated assuming an external field strong enough to explain the present motion of the MW with respect to the CMB (or by calculating the forces from some nearby heavy galaxies like Andromeda).

http://arxiv.org/abs/astro-ph/0702275

So no, I don't think all frames of reference are equivalent. I think it's like if 100 years ago people had only looked at classical gases and said absolute temperatures weren't important, only relative ones. So adding one unit of T takes the same energy, whatever T is in absolute terms. Thus, absolute values of T cease to have meaning.

In reality, at low temperatures this classical result breaks down. This is why we use the freezing point of water as a special temperature scale.

I think it is the same with gravity - general relativity is a classical gravity theory, so it works at high energies (in this case, high accelerations, which means there's lots of energy in the gravitational field). But if there's very little energy in it (i.e. very low accelerations), then the theory breaks down.

I don't much understand this theoretically, but I gave a lecture recently about the observational evidence behind why modifying general relativity at low acceleration might be a good idea.

https://www.youtube.com/watch?v=-eCahykEy1A&hd=1

After interesting questions on Equivalent Reference Frames and on CMB, Indranil Banik's comment induces to pose a new interesting question: Are negative absolute Kelvin temperatures possible?

It is known that in classical thermodynamics the answer is negative.

@Daniele you wrote

"After interesting questions on Equivalent Reference Frames and on CMB, Indranil Banik's comment induces to pose a new interesting question: Are negative absolute Kelvin temperatures possible?"

He was talking about "specific heat", negative Kelvin do not make sense..

Indranil wrote:

"adding one unit of T takes the same energy, whatever T is in absolute terms"

"at low temperatures this classical result breaks down"

This is one of the "marvellous" effects of Quantum physics and the relation with the vacuum energy... The entropy does not diverge when approaching to 0 Kelvin... The behaviour near the absolute 0 is completely different from the  behaviour at higher temperatures.

There is a sharp discontinuity on the relation of the specfic heat...adding one unit of T at very low temperatures  takes a very different amount of energy as Indranil reported.

Thanks Robert, your suggestion is very useful. It seems to me that the statement in the link you have suggested "a system with a truly negative temperature in absolute terms on the Kelvin scale is hotter than any system with a positive temperature" has to be carefully considered and understood. What is your interpretation?

Stefano, it is possible that I have misinterpreted Indranil BaniK's words, but outside classical thermodynamics the question exists anyway. Consequently I would want to invite also you to think on that statement.

Daniele, If a system with negative temperature comes into contact with  a system with positive temperature, energy flows from the domain with negative temperature, which decreases, into the domain with positive temperature, which increases. Then, a moment happens when the temperature reaches the limit -oo and immediately becomes oo. The same energy flow continues, and the following processes are as usual, from higher temperature to lower temperature.  

Negative temperature is simply a mathematical artefact which follows from the very unusual property of physical systems that an increase of energy leads to a descrease of the number of possible states. 

If I have understood well, Ilja and Robert, you agree with the consideration that temperatures  T

Daniele, there is no bastion to fall, because negative temperatures are simply  an automatic consequence of the definitions if we have such a strange system where we have less states with higher energy than with lower energy. Moreover, you can find this in standard textbooks of thermodynamics and statistics. 

To create such a strange system in practice would be extremely difficult, because you would have to isolate these strange degrees of freedom completely. But how to prevent them from interacting with the device itself? The device consists of matter, and matter which behaves in a normal way.

Ilja, for one second I believed we could talk the same scientific language. Please, let you verify if in your textbooks there is the third principle of thermodynamics. Thanks.

Robert, for me it is sufficient to know that negative temperatures on the Kelvin scale are possible independently of physical processes. Thanks for your notices.

Thanks I learned something new...then..

I agree, Robert  Anyway it shows an anomalous behavior with respect to standard behaviors. The important consideration is that at least in one case that behavior has been verified experimentally. I think it can represent a new chapter of thermodynamics and of physics. It is interesting to observe the different behavior at negative Kelvin temperatures with respect to positive Kelvin temperatures relative to heat exchanges.

In the order of the Theory of Reference Frames I have demonstrated a similar behavior for electrodynamic elementary particles that for greater speeds than the critical speed have a different behavior with respect to smaller speeds. Also here this different behavior regards energy exchanges and it is due to the fact electrodynamic masses and energies are negative for greater speeds than the critical speed, that is a zone of instability for particle. I can deduce that also physical systems at negative kelvin temperatures are unstable systems.

A way to lower the entropy of other systems...

A new chapter that in 1950 wasn't developed. It isn't the first time that it happens. There are numerous examples of ideas understood much time after (for example the Boole algebra). I believe this possibility.

Stefano, if you have good ideas, let you go on.

Dear Daniele,

right now I'm  finding flaws in the extension of the WEP proposed and applied by Einstein, like Synge, Fock and others argued... and I'm working on the quality of intertial systems.. since not all the inertial systems so far classified as such in GRT are equivalent for performing experiments .. GRT is a great theory but it's only  a sophisticated extension of classical mechanics.  At  the base of everyting  is  the "least action principle" the gist of  rational mechanics which got a new life with QED. There is already enough to keep me busy for  ages.

Stefano, anyway my support to go on is always valid. I did that encouragement because I think you are a young researcher. It is right you follow your way.

Thanks Daniele..

Re. negative temperatures. Negative temperatures are discussed in detail in the half-century old Theoretical Physics series by Landau and Lifshitz (Vol 5., para. 73, in particular). They cite research that was done even earlier, in the early 1950s. Their discussion is about negative temperatures realized using magnetic moments in a crystal lattice, but more recently, a system exhibiting negative temperature behavior using motional degrees of freedom was also realized (http://www.sciencemag.org/content/339/6115/52).

Dear V.T. Toth, your notice is very interesting and regards a more recent paper (January 2013) than the paper that has been indicated by Robert Low (1950). If one paper could be a chance, now two papers begin to do an evidence. Anyway I am always more convinced that the subject on the negative Kelvin temperatures represents a new chapter of thermodynamics and physics. I know many researchers don't know or don't subscribe the Theory of Reference Frames, but I ascertain that it can give a valid theoretical legitimation to negative Kelvin temperatures. Anyway thanks for your notice.

I would argue that no two reference frames are the same and there for not two reference frames are equivalent. 

Robert, then we are in good company. I would propose a common study for searching for understanding the theoretical reason of those negative tempeatures. Do you have some idea or did you find it in some of those papers?

George, I would want to insist that the concept "equivalent" is generic. Do you think two inertial reference frames (i.e. the difference of speed between the two frames is a constant rectilinear speed) aren' t equivalent with respect to the invariance of laws of physics? For me the question is which type of invariance. In classical physics the invariance was defined by Galilean.Newtonian Transformations (even if between Galileo and Newton some difference there was), in modern physics that invariance is defined by Lorentz's Transformations and In the Theory of Reference Frames that invariance is defined by Transformations in the Space-Time-Mass Domain.

Robert, I would want to say your explanation isn't completely satisfactory because differentials don't give in general values but trends and your explanation is acceptable only if your system is working at Kelvin zero. But above all I would want to say your explanation isn't a "theoretical reason" but a random interpretation that, like all random interpretations, says nothing on the physical reason of the system..

In the context of cosmology, there's also an interesting concept of "apparent temperature" (as in, the apparent temperature of a black hole horizon under GR1915 according to a distant reference-observer is set at zero, even though this may not be the temperature that you'd measure locally at this location when you actually fall through the horizon, especially if you're accompanied by a lot of hot infalling accretion disk material).

So we're used to assigning "apparent" temperatures to remote locations and systems according to how we measure the distant visible physics from here-and-now, rather than calcualating what a local observer might measure (or might have measured when the signals were originally generated).

If we stay with that astronomical/cosmological convention of using "apparent"  temperatures, then once we extrapolate through something like a cosmological horizon, we can enter a realm of negative "apparent" assigned temperatures.

Those assigned negative apparent temperatures aren't directly observable, but they do affect the apparent temperature of other physics in the region that //is// observable ... so for instance, a gas cloud at the very edge of our observable universe that's pretty much stationary wrt the local average speed might be assigned a very low Kelvin temperature by us, if it recedes from us faster than neighbouring material then its apparent temperature (as judged by its radiation seen here-and-now) will be lower, and it it recedes from us fast enough to be behind an effective cosmological horizon, then it can be assigned a negative apparent temperature.

Even though the cloud wouldn't then be directly visible, its nominal "apparent" temperature value could be justified by pointing out that the cloud can still mix and merge with a different cloud with a lower recession velocity and positive apparent temperature value that //is// visible.

So at the fringes, a small fast-receding negative-apparent-temperature cloud can "cool" a larger positive-apparent-temperature cloud by giving it a greater recession velocity and redshift, and if the faster-receding "negative" cloud is moving fast enough, or has enough mass, it can make the final mixed cloud recede fast enough to also be behind a cosmological horizon, also with a negative assigned apparent temperature.

So for descriptions of the "apparent" physics of a region intersected by a "leaky" cosmological or acoustic horizon, negative numbers can have a use. They also tend to be associated with negative numbers for the nominal "apparent" rate of timeflow of a system, even though no such time-reversal can be seen directly (normally due to a shielding horizon), and even though we might deduce that no such time-reversal //really// happens – it's more of an observerspace "projective artefact" trick for calculating things for "non-visible" physics that have visible  consequences.

Eric B., your comment on negative Kelvin temperatures brings again the discussion into the cosmological context. Your considerations on the concept of "apparent temperature" are very interesting and that concept seems to derive from the fact that it is the result of a calculation rather than the result of a local measure that clearly isn't feasible. As per the Robert L. and V.T. Toth information we know negative Kelvin temperatures have been proved through real experiments and consequently, I think, we could deduce that also in cosmological ambit, and not only for black holes, the negative Kelvin temperatures are real and not only apparent. As per my theoretical considerations the concept of negative K temperature may be connected with the concept of unstable thermodynamic system, on all scales from the microscopic to macroscopic, and like this the Kelvin zero would become a kind of critical temperature rather than a lower bound, like the critical speed of light and the critical electrodynamic mass. In next mounths I will search for formalizing in a paper some of these new ideas but I think we are opening a gateway above all for future generations of researchers.

Eric, it seems you have not understoos the main point about the thing named "negative temperature" - namely that this is better understood as something with temperature higher than oo, not below 0. This system will not eat energy from the normal environment if it interacts with it, but will give some energy and heat the environment. 

Ilja, I think you will have to study better the mathematical concept of infinite.

This question is a key to understanding QFT where kinetic energy is represented as a dot product of two field vectors. It needs a definition of zero velocity like the one being discussed here, to put kinetic energy in space curvature. Without it QFT remains incomplete.

The answers are important to my proposal to express kinetic energy as a local space field as Albert Einstein recommended in 1949, Autobiographical Notes.

https://www.researchgate.net/post/Is_Kinetic_Energy_Carried_In_A_Stress_Energy_Field_Of_Space

My opinion is that a zero velocity can be defined any where based on the local readings of essentially equal CMB temperatures in all directions. It doesn't make a preferred frame, but it does make a preferred velocity reference which supports kinetic field energy.