Exploring Relativity: The Conundrum of Absolute Rest Frames in a 2D Universe

[jcsd]

I do! (Because the isotropic frame has a 'special' local physics - see my last post)

Garth

That's why I said most

 

[jcsd]

Thanks everyone (so far).

I understand that it is possible to determine one's velocity (speed and direction) wrt the CMBR, at least here on Earth. No one has yet shown (jcsd aside, but only in general terms) that this determination is independent of one's current position in the universe (if I'm orbiting the M87 SMBH, can I make the same determination? Is the result of that determination the same as the one I make from here on Earth? What about if I'm near one of those really distant HUDF galaxies?).

Of course, I will measure my velocity wrt the CMBR in terms of my local rulers and clocks, and can convert to xc (0 <= x < 1) - but how do I then get an absolute ruler and clock? And (esp Aether) - if my clock is calibrated by the apparent age of the universe (from where I am), can you show that a) this is (cosmology) model independent, and b) the same no matter where I might be?

I also see that no one has tried to give me an in principle way to determine the (absolute) origin and directions of any (spatial) axes.

Here's part of the rub though, if we look back at the assumptions we made we assumed that the universe was completely isotropic and completely homogenous which it cleraly is only on a global scale, so if anyone says we can define an absolute frame from the CMBR I'd like to know what they'd do about the fact that the universe is slightly (though ceryainly enough to be important) 'lumpy'.

 

[Nereid]

And the cosmic clock, measuring t cosmological time since the Big Bang, is in fact a thermometer measuring the CMB monopole temperature T (degrees K) with
t = 13.4 x 2.725/T Gyr.

Garth

That's good Garth ... no matter where I am, I can determine the CMBR's equivalent blackbody temperature (do we all measure it as 2.725K? even if we're deep inside an SMBH's gravity well??).

However, how do we all - no matter when or where in the universe - determine the 13.4 Gyr? Doesn't our choice of cosmological models to use to (eventually) arrive at this figure depend a great deal on when and where we are?

 

[Garth]

That's good Garth ... no matter where I am, I can determine the CMBR's equivalent blackbody temperature (do we all measure it as 2.725K? even if we're deep inside an SMBH's gravity well??).

However, how do we all - no matter when or where in the universe - determine the 13.4 Gyr? Doesn't our choice of cosmological models to use to (eventually) arrive at this figure depend a great deal on when and where we are?

I am sorry everybody I have made a mistake, (it is late Friday night here, but that's no excuse)
I have conflated a result from SCC: (R ~ t) with the standard theory.
In the standard theory R ~ t^n where n = 1/2 for a radiation dominated universe and n = 2/3 for a matter dominated universe.
The energy density of a photon gas is proportional to T^4 and also proportional to R^-4, so T ~ 1/R and therefore t ~ T^-n .

Therefore the cosmological clock actually obeys
t = 13.4 x (2.725/T)^n Gyr. where n is determined by substituting the appropriate equation of state into the cosmological field equations.

The units are defined by local standards. In a deep gravitational well the CMB would appear blue shifted but the local clocks would suffer a partial compensating gravitational time dilation. In a freely coasting universe such as SCC such compensation would be complete.

Note: In such a 'well' the CMB would be generally greatly distorted from isotropy, therefire it would require a high velocity to place yourself in an CMB-isotropic frame.


Garth

 

[Nereid]

This thread may well start to break into several separate strands, all of which would be fascinating. If that happens, and if posters agree, I will create new threads so that this one doesn't get too overloaded and confusing.

Could we first explore the Aether (and yogi? and 4Newton??) approach? Observations can tell one's velocity wrt the CMBR. Garth has suggested that the temperature of the CMBR can be used to determine the age of the universe (actually, only the time from the surface of last scattering to now?), and so an absolute clock may be built (well, maybe ... let's come back to that). What I'm curious about is: how does one determine the age of the universe without using GR (for observational data, assume you have only the CMBR temperature)?

 

[Aether]

What I'm curious about is: how does one determine the age of the universe without using GR (for observational data, assume you have only the CMBR temperature)?

The function that Garth gave for cosmological time as a function of the CMB monopole temperature comes from F(L)RW cosmology which is based on GR.

The CMB monopole temperature evolves over cosmological time, but at any given instant it is supposed to have the same value in all frames. I referred to this property as instantaneous Lorentz invariance in an earlier post, but I am looking for a better name for it. I have developed a transform, I call it a universal transform, in which such quantities are invariant over universal transforms in complex space-time, which is just another name for what I call the aether. I think that such a distinction is meaningful depending on whether or not one has access to a cosmic clock. The interesting effects come to life when transforming across non-zero spans of cosmological time, and in the various integrals and derivatives with respect to cosmological time. I call this aetherdynamics in its classical formulation, and aetherodynamics in its quantized formulation. Has anyone else done this before?

This is why I say that SR must not be extrapolated across any significant span of time.

My current estimate of the age of the universe based on aetherodynamics is 11.14 Gyr. This calculation does not require any reference to GR, but it does lead me to suspect that the curvature tensor per se is inadequate for computations involving complex space-time, or the aether. So, enter curvature spinors.

 

[Garth]

The function that Garth gave for cosmological time as a function of the CMB monopole temperature comes from F(L)RW cosmology which is based on GR.

Actually the type of time, atomic time, ephemeris time etc. is defined by the means of measuring it.

Thus whereas my second, corrected, formula
t = 13.4 x (2.725/T)^n Gyr
could be the basis of a cosmological time clock, albeit a very imprecise one, which if GR is correct, will also tell atomic time, the original formula
t' = 13.4 x 2.725/T Gyr
can also be used to define a time, t', which is called conformal time! According to this clock the universe will expand stricly linearly in any cosmological theory. R(t') = t'.

Garth

 

[Aether]

...my second, corrected, formula
t = 13.4 x (2.725/T)^n Gyr
could be the basis of a cosmological time clock, albeit a very imprecise one, which if GR is correct, will also tell atomic time...

Garth,
Is it not the case that such a cosmological time clock would only agree with atomic clocks in the CMB rest frame, and thus provide a means for comparing one's proper time to cosmological time? The CMB dipole anisotropy also happens to be useful for this, but other types of cosmic clock mechanisms might not have such redundancy.

 

[Chronos]

Hmmm. I thought it would be a fairly matter to translate away the motion of Earth relative to the CMBR. Unfortunately, I'm running into trouble picturing a coordinate system where the Earth is stationary and the CMBR is in motion that is consistent with the RWF metric. I must ponder this.

 

[Nereid]

Given what yogi said:

[...] LR (Lorentz Relativity), and MLET (modified Lorentz Ether Theory), Non rotating Earth center as a preferred frame, and a frame that has zero velocity with respect to the CBR (a point and velocity where the CBR is isotropic). All experiments that confirm the Lorentz transforms are also consistent with Selleri transforms, and some other cosmological theories [...]

, and 4Newton's apparent endorsement of these ideas, I'm curious to know how one can determine the age of the universe (or the time since the decoupling of matter and radiation) using LR, MLET, Selleri transforms, 'and some other cosmological theories' ... using only the CMBR (monpole) temperature. I'm also interested in how the age determined using these non-GR approaches compares with ~13.4 Gy.

 

[yogi]

Nereid -The existence of a preferred frame impacts some of SR - but it leaves much of the formalism intack - for example, if mass modified space - then we might question whether MMx and Kennedy-Thorndike over and back type experiments add any support to the verification of SR - since all such experiments have been conducted in the moving frame of the Earth which is rendered locally isotropic by the Earth's mass (this is different from the ether drag hypothesis since it is a conditioning of the local space rather than a dragging of some substance which is disproven by aberration)

A second possibility - The existence of a preferred frame based upon a location and velocity where the CBR is isotroptic. Experiments conducted in such a frame would be consistent with the invariance of the spacetime interval between the isotroptic CBR frame and an inertial frame in motion wrt thereto - but the derivation of the covariance of the interval could not be based upon Einsteins's second postulate. The significance of any preferred frame, whether CBR or matter centered, is that the preferred frame would provide a physical starting point for explaining time dilation, the triplet paradox and other questions which arise when trying to fit the experimental results with a theory that shifts from observational kinematics to real time losses. SR does not provide a mechanism - if motion wrt to some preferred frame is different than motion with respect to any and every inertial frame - then physics will have a new basis for investigating the properties of space.

 

[Chronos]

I think it would be more accurate to term the CMBR as a convenient reference frame, not preferred. Basically, you can do the same translation with any reference frame [earth is a pretty popular one too]. Were that not true, would we not see a seasonal anisotropy in solar radiation? And what about frame dragging? Gravity probe b will answer that question pretty convincingly [and will not show any selective seasonal variations IMO]. The CMBR temperature also makes a lousy clock. It only tells you how much the universe has expanded since the BB, not how long it took.

 

[Garth]

I think it would be more accurate to term the CMBR as a convenient reference frame, not preferred.

Firstly: congratulations Chronos, you deserved it!

The isotropic CMB frame can indeed be called a convenient frame. After all it is that one adopted by nearly all cosmological solutions to Einstein’s field equations as the cosmological co-moving frame in which the universe is isotropic and homogeneous. However there is also the question of whether physical laws take on any special characteristics in this frame. I believe there is. As I posted above and on the “The Cosmological Twin Paradox” thread the effect of space-time curvature and therefore the presence of matter in the rest of the universe endows this frame with a special property.

Consider the cosmological twin paradox again. Two inertial observers with clocks encounter each other at high mutual velocity. By the Principle of Relativity (PR) each thinks they are at rest and the other moving, each thinks the other’s clock is slower than theirs. There is nothing to distinguish between them except that coincidentally one of them is at rest in the cosmological co-moving frame.

For the sake of the argument the universe is closed.

After a very long time they encounter each other again. Each one thinks the other has circumnavigated the compact space of the universe. And as they pass they compare clocks. By the PR each one expects the other to have recorded the shorter time interval. But in fact which one has? Obviously the one not in the cosmological co-moving frame.

The topology of the compact space of the universe endows one of our observers the one in the cosmological co-moving frame with a special property, his clock actually records the longest proper time between all such “twin” encounters.

In this sense, local clock rate, the cosmological co-moving frame can be thought of as a preferred frame can it not?

Garth

 

[Aether]

Firstly: congratulations Chronos, you deserved it!

...However there is also the question of whether physical laws take on any special characteristics in this frame. I believe there is.Garth

Congratulations Chronos, and Zz!

Ok, I have written up a paper entitled "Evidence for a Locally Preferred Frame of Reference" which gives the details of my analysis of the published ionization potentials of the elements. The standard deviation between the observed data (for the first twenty-nine elements) and the predicted values using SRT is $$\sigma = 97.9 eV$$. The worst case standard deviation between the observed data (for the first twenty-nine elements) and the predicted values taking the CMB rest frame as a locally preferred frame is $$\sigma = 0.22 eV$$. That's a better fit by a factor of 445!

Now, I need someone to endorse me at arXiv.org so that I can submit the paper there. Then you will be able to read it, and your criticisms are welcome. Is there anyone here who can help me get an endorsement?

 

[Nereid]

Nereid -The existence of a preferred frame impacts some of SR - but it leaves much of the formalism intack - for example, if mass modified space - then we might question whether MMx and Kennedy-Thorndike over and back type experiments add any support to the verification of SR - since all such experiments have been conducted in the moving frame of the Earth which is rendered locally isotropic by the Earth's mass (this is different from the ether drag hypothesis since it is a conditioning of the local space rather than a dragging of some substance which is disproven by aberration)

A second possibility - The existence of a preferred frame based upon a location and velocity where the CBR is isotroptic. Experiments conducted in such a frame would be consistent with the invariance of the spacetime interval between the isotroptic CBR frame and an inertial frame in motion wrt thereto - but the derivation of the covariance of the interval could not be based upon Einsteins's second postulate. The significance of any preferred frame, whether CBR or matter centered, is that the preferred frame would provide a physical starting point for explaining time dilation, the triplet paradox and other questions which arise when trying to fit the experimental results with a theory that shifts from observational kinematics to real time losses. SR does not provide a mechanism - if motion wrt to some preferred frame is different than motion with respect to any and every inertial frame - then physics will have a new basis for investigating the properties of space.

Hmm, since SR is a special case within GR, I wonder whether the existence of a preferred frame has impacts as profound in GR as in SR?

But haven't you created a somewhat circular case? You rely (at least partly) on GR to determine the nature of the CMBR (and the age of the universe?), yet you rely on the CMBR as a preferred frame to show that GR cannot be right!

In any of the SR-alternatives you mentioned earlier, how do you derive the age of the universe from the CMBR (monopole) temperature? How do such estimates compare with 13.4 Gy?

Another thing: Aether has told us what the motion of the solar system barycentre is wrt the CMBR (per WMAP); how do you determine what the locations in the universe are for which the CMBR is isotropic? How do you assure yourself that they will all measure the same temperature? Don't you first need a cosmological model - consistent with observations - before you can start to answer these questions?

 

[yogi]

Nereid - perhaps I am missing something in your questions. I do not see why GR cannot be correct and there still be one or more preferred frames. To my way to thinking, the conditioning of local space by matter implies a detectable, measurable spacetime attribute that is different from spacetime far removed from matter - one of those characteristics might be local light isotrophy. This impacts the generality of SR, that is, the symmetry is observable only when the matter conditioning field exists (a local condition), but it does not influence the modus operandi of time dilation in GR. While it is often said that SR is a special case of GR, there is a difference (primarily in the assumptions made to derive the equations). GR seeks and offers a physical explanation of gravity independent of the second hypothesis of SR; SR tells us how relative motion leads to different perceptions, but we get to these same results with Lorentz ether theory and other transforms based upon a preferred frame. Should it ever be demonstrated that the second hypothesis in SR is incorrect in a free-space MMx environment (e.g., the discovery of a preferred frame), it would not invalidate GR - nor would it invalidate any of the the many SR consequences that are based upon the invariance of the spacetime interval. The SR experiments neither validate nor invalidate the slippage term vx/c^2 as this factor is canceled out in the formulation of the temporal rate differences as determined by high speed particle lifetimes.

 

[Garth]

Just to throw in a little light relief how about this eprint out today?
"The Einstein Postulates: 1905-2005 A Critical Review of the Evidence"
Reginald T. Cahill (Flinders University)
http://arxiv.org/abs/physics/0412039
From the abstract

While the relativistic effects are well established experimentally it is now known that numerous experiments, beginning with the Michelson-Morley experiment of 1887, have always shown that the postulates themselves are false, namely that there is a detectable local preferred frame of reference.

Going back to the discussion above, I would argue that if there is a preferred frame in which the laws of physics take on a unique aspect (as I have argued with the Cosmological Twin Paradox) then it would affect GR rather than SR.

I do not see how a preferred frame can appear in SR as any preferred frame must be linked to the presence of matter, "to hang it on", and SR is framed in the pristine flat space-time in the absence of gravitational masses.

However it is when we move from SR to GR by considering the effect of stress-energy-momentum on space-time that a preferred frame may creep in. If it does then the GR postulate that would be challenged would be the equivalence principle as physics in the freely falling frame would no longer be locally those of SR. This would then affect the conservation of energy-momentum.

Garth

 

[Rob Woodside]

Much of the noise in this thread comes from people talking at cross purposes because they have different notions of preferred and absolute frames.

As someone said a preferred frame is a convenient frame- a frame where things look physically or mathematically simple. Physically these include the global inertial frames of Newtonian mechanics or special relativity and the local inertial frames of general relativity. Mathematically perferred frames include Schwarzschild coordinates for a spherical star and Boyer-Lindquist coordinates for rotating black holes. In fact any published metric tensor is given as coordinate functions of a preferred frame. This includes the isotropic CMB frame.

However, cosmologists have followed Newton's dictum "time is defined to make motion look simple." They infer spatial expansion with a uniform time from red shift data on distant galaxies. One could equally well say that spatial distances remain fixed but recent clocks tick more quickly than old clocks. A photon's frequency is a frozen clock rate of the emitting atom. An early distant atom has a slower clock rate than a modern earthly one. Since the frequency times the wavelength is the constant speed of light, the wavelength of the old photon is longer since the clock rate is faster when it is absorbed at earth. Apart from Newton's dictum, I can't see how to tell these two scenarios apart.

Some posters have used absolute frames interchangeably with preferred frames and this has raised the hackles on other posters. They are NOT interchangeable. The word "absolute" has special connotations from Newtonian mechanics. Newton's first law gives the constant speed straight lines needed to set up the coordinate lines of an inertial frame. Newton was well aware of Galileo' principle of relativity and he knew that two inertial frames could slide through each other at a constant speed. Not knowing of a maximum speed that would be the same in all inertial frames, he turned to religion. Since his God was omniscient and omnipresent, just one of these frames would be God's sensorium, but which one? It was obvious to him that it should be the frame of the fixed stars. This frame in which the aether was at rest defined the absolute space and time. It was called absolute because velocities were now not just relative to some inertial frame, but were absolute with respect to the rest frame of the aether. Further, when viewing in one inertial frame the rods and clocks tied to another inertial frame they would appear identical to those in the viewing frame. There was no length contraction or time dilation, space and time were immutable. It is these old connotations that raise a red flag every time the word absolute is used.

 

[ZapperZ]

Just to throw in a little light relief how about this eprint out today?
"The Einstein Postulates: 1905-2005 A Critical Review of the Evidence"
Reginald T. Cahill (Flinders University)
http://arxiv.org/abs/physics/0412039
From the abstract

I would seriously suggest (i) that you wait till this thing is actually accepted for publication and (ii) look at all the "evidence" he cited, and then look at all the evidence that *I* have listed in my Journals, and see for yourself which one is more convincing. Has he been asleep the past 10 years and missed ALL (not even ONE) of the most recent evidence before he put this up? What does that tell you about how up-to-date he is on keeping up with all the experimental evidence?

Honestly, people! We need to be a bit more discriminating on our sources here! If not, any quack who either have a website or could somehow wrangle onto ArXiv would get free publicity on here!

Zz.

 

[Nereid]

Much of the noise in this thread comes from people talking at cross purposes because they have different notions of preferred and absolute frames.

Excellent post Rob! However, I prefer, perhaps because it's convenient, to not be so absolute in saying that it's noise

I think there are different strands to our discussion here, several (all?) of which are very worthwhile.

For example, if there is a claim that the CMBR somehow allows an absolute or preferred (no one challenges the statement that it is convenient, do they?) frame, then let's see that claim in detail ... and let's ask the proposers to make clear what assumptions about the CMBR and the universe that they must make to establish their claim. OTOH, if there are folk who claim that the CMBR allows us to easily (!) identify "the cosmological co-moving frame in which the universe is isotropic and homogeneous" (thank you Garth), but that this does not lead to problems with the core postulates of GR, let's hear their case too (I think we already have, but there may still be some doubt).

OTTH (Harry Truman would turn in his grave), if there are cosmological models which use modified GR (or even modified Newtonian dynamics ) - and which are consistent with the observational data - it is interesting to learn (well, interesting to me at least) the extent to which 'preferred' and 'absolute' make sense in these models (Garth has already said quite a bit about his SCC in this regard; do we have any MOND supporters here?)

 

[Garth]

I would seriously suggest (i) that you wait till this thing is actually accepted for publication and (ii) look at all the "evidence" he cited, and then look at all the evidence that *I* have listed in my Journals, and see for yourself which one is more convincing. Has he been asleep the past 10 years and missed ALL (not even ONE) of the most recent evidence before he put this up? What does that tell you about how up-to-date he is on keeping up with all the experimental evidence?

Honestly, people! We need to be a bit more discriminating on our sources here! If not, any quack who either have a website or could somehow wrangle onto ArXiv would get free publicity on here!

Zz.

I said "Just to throw in a little light relief "

Garth!

 

[Rob Woodside]

Excellent post Rob! However, I prefer, perhaps because it's convenient, to not be so absolute in saying that it's noise

Thanks for the Kind words. There is much less noise here than at SPR.

 

[Aether]

I'm particularly interested in seeing how - in principle! - it [CMBR] could be used to create an absolute ruler and clock, oh, and an absolute set of coordinate directions (orthogonal or not) would be nice, as too would an absolute origin for the coordinate system and clock.

Please be sure to explain why the procedures you describe would yield the same results whether I'm here on Earth, somewhere in the Bootes void, orbiting M87's SMBH (just so I don't get sucked in), or somewhere in the vicinity of one of the primordial galaxies in the HUDF field (z ~=8). {Garth's cosmological paradox method is not permitted; you can't assume anything about the geometry}

To make an absolute clock one seems to need a specific cosmological model in combination with an instantaneously Lorentz invariant observable quantity like the CMB monopole, but not necessarily that one since there are other examples of such quantities and no guarantee that most supposedly Lorentz invariant quantites aren't evolving over cosmological time. I mean, without our cosmological model to tell us different, the CMB monopole would almost certainly be listed right along with all of the other fundamental physical constants. http://arxiv.org/abs/gr-qc/0211052

Given an absolute clock and a specific cosmological model, then a minimium CMB monopole temperature $$T_{min}$$ can be defined for a closed universe, and this can be used to define the units for both the absolute clock $$T(OneBigTick) = T_{min}$$ and the absolute ruler $$R(T_{min}) = OneFurPiece$$.

So a closed universe has a preferred frame of reference! It has so by virtue of its topology, which is finite yet unbounded.

It is interesting that a closed universe is also a condition of Garth's preferred frame. I am not sure about how to define the units of an absolute clock or an absolute ruler, in anything other than a closed universe, without being arbitrary.

Any absolute set of coordinate directions is bound to be arbitrary, unless there is something of cosmological significance about the odd alignment of the CMB multipole that nobody has told us about yet. As a group, humans are predisposed to favor a dextral orientation (e.g., right hand rule) in lots of circumstances.

The absolute origin for the clock is given by the cosmological model, and the spatial origin for the coordinate system is the center of mass of the universe.

By absolute I mean with respect to the matter and energy distribution of a closed universe.

 

[windscar]

I am amussed that you mentioned light being the absulote rest frame of the universe. I have also considered this. If your thinking about two objects in this frame of reference, I would say that both object observe them being at rest and moveing at a constant speed at the same time. Therefore, they would both see each other's time going slower relative to each other. And the actual time dilation wouldn't be able to be resovled unless you found out which object accelerated. I have read that as an object accelerates, the intervals of light you see while observeing the other object could change how you see their speed of time through difference in doppler shift's. So I guess it could depend on from which side of the sphere you observed the other object. One direction would be faster and from the other side would be slower if not equadistant from each other along the sphere. It would depend from what side they met up from each other.