Does Special Relativity Suggest a Predetermined Future?

[yogi]

Came across an article of interest claiming SR implies the future is predetermined. The salient argument is summarized below:

We start with the notion that we cannot attribute reality to the future since it is yet to be determined. Nor can we claim that what we see is real in the present because, if we are looking at distant light sources, we only see them as they were in the past. One definition of reality would be: “all that exists, now, here and elsewhere” This avoids things that do not exist anymore and things that do not yet exist.

Consider a Minkowski diagram having space as abscissae and time in ordinates. At time t = 0 an observer J located at the origin of an inertial system S would regard as objectively real all events that lie on the X axis (i.e., simultaneous with the presence of J at the origin at t = 0). But if another inertial frame S1 is considered that is in uniform motion v wrt to S, an observer J1 at rest in S1 must attribute reality to all events happening at his present time t1 = 0. These events are different from those constituting the reality of J. Given the complete symmetry demanded by SR, if the reality line of J1 passes through the origin 0, all the events on the X1 axis whose equation is t1 = 0 with inclination determined by the relative velocity v can be considered equally real as those on the X axis.. In other words J1 will attribute reality to events in J’s future which are not part of his present reality.

To make it more meaningful, consider other observers P1 and P2 at different points along the positive X axis. These are all equivalent in their description of their present reality since the time t = 0 is the same for all of them. It is seen that the reality line of J1 will be intersected by the personal future(s) of P1 and P2 (you will need to draw the point X1 above X and a line from the origin through X1 with p1 and p2 somewhere spaced somewhere along the positive x axis, then dotted lines up from p1 and p2 to intersect the 0-X1 axis ...sorry the drawing gets scrambled when I copy it from the clipboard).

Since there can be an infinite number of reality lines corresponding to different velocity frames that all pass through the origin - each representing the present for some legitimate inertial observer - is the future fixed in every detail?'''''''

ct '''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''' X1
!
!
!____________________________________ X
0 ...p1 ......p2

 

[Hurkyl]

Implication of determinism isn't peculiar to SR; the same can be said about classical mechanics, GR, and even QM (when phrased properly).

Such arguments come with the implicit assumption that there is a deterministic description of some piece of space-time, and then use time evolution formulae to extend that determinism to other parts of space-time (possibly all). While the various theories admit such a case, none require it.

P.S. I didn't really follow the particular argument you were trying to make.

 

[RandallB]

yogi
P1 and P2 can only obeserve the past of others including each other.
With the one time exception of when they are in the same place.

P1 only sees P2's past within the common ref frame unless P2 comes by for a visit in the current place and time.
Same applies to other ref frame members. In fact all ref frames has a part of it visiting P1's current place and time. All other part only share their past with P1. As P1 does the same for them.

 

[ohwilleke]

My intuition is that there is a unit of measurement flaw in the determinism argument for SR. In otherwords, the time scales aren't well calibrated and that apples and oranges in different calibrations are being compared.

Also, while all classical theories are deterministic, it doesn't necessarily follow that the SR piece of the classical theory is the lynchpin that creates the determinism.

Finally, I've never heard any coherent argument that QM is deterministic. Indeed, one of the best arguments for non-determinism is that QM is inherently stochastic and that the notion of "chaos" (i.e. sensistivity to initial conditions in certain non-linear systems) makes it possible for the stochastic underpinnings of QM to make themselves felt at the macroscopic level.

 

[yogi]

The diagram is confusing because it gets corrupted when I paste to the forum. Anyway - to clarify (maybe) just consider the X axis as coincident with the "now" line of J and ct orthogonal to the X axis - we can consider J to be at the origin ct = 0 and X = 0. Another frame in which J1 is at rest also passes through the same origin - but this frame has a velocity v wrt to J. So we can represent the "now" line of J1 as a sloped line connecting the origin with X1. Since according to SR, this is equally real from the standpoint of J1 as are the events that lie along the X axis are real to J. As time progresses the observers p1 and later p2 will intersect the line from 0 to X1 - when they do they will be arriving at a spacetime point that was a "now" event for J1 at an earlier time. Does that clarify or confuse?

 

[Hurkyl]

Wrap your diagram in code tags. e.g.

[ code ]
/
/
/
/
/
[ /code ]

becomes

    /
   /
  /
 /
/

 

[chronon]

The argument goes as follows: Suppose that event B is in the future of event A. Then there is an event C which is spacelike separated both from A and from B. Thus a suitably moving observer at A would see C as 'now' and a suitably moving observer at C would see B as 'now'. If we assume that what is happening 'now' is already determined, then B should be already determined at A.

I would argue against this as follows: suppose we assume that freewill exists - I make a decision after A which changes what happens at B. Is there anything it the above argument which contradicts this? No there isn't. I would say that the problem is believing in some special significance to 'now' at distant locations - I think of all events which have spacelike separation from me as having the same significance.

 

[Aether]

I would say that the problem is believing in some special significance to 'now' at distant locations - I think of all events which have spacelike separation from me as having the same significance.

There is a special significance to 'now' at distant locations, chronon (e.g., cosmological time). SR does not strictly apply anywhere in the real world, it is a local approximation to GR, which isn't rock-solid itself.

SR is only valid in the limit as the space-time volume under scrutiny goes to zero, so you can't extrapolate SR "to all events which have a spacelike separation from me" and still be talking about the real world. For example, in flat space-time, satellites do not orbit planets, planets do not orbit stars, etc..

 

[RandallB]

Then there is an event C which is spacelike separated both from A and from B.
Thus a suitably moving observer at A would see C as 'now' and a suitably moving observer at C would see B as 'now'.

Dosn't "Spacelike seperated" mean there is no moving obeserver that is able to could see now as common between A & C or B & C.

If they could by definition they couldn't be "Spacelike seperated" could they?

RB

 

[Hurkyl]

There is a special significance to 'now' at distant locations, chronon (e.g., cosmological time).

Not in GR.

 

[Aether]

Not in GR.

Care to elaborate, Hurkyl? Here is an example of where I am coming from:

http://www.lakeheadu.ca/~physwww/courses/Astro/2330/Cosmology/Gene.htm][/PLAIN]

IMPLICATIONS FROM GENERAL RELATIVITY...Einstein's equations coupled with the cosmological principle imply that the large scale structure of the universe can be separated into a cosmological time ( t ) , a length scaling factor that depends on time ( a(t) ), and a single curvature parameter (k) which has the value +1 for a closed universe, 0 for a flat universe, and -1 for an open universe.

Cosmological time is defined as the time shown on clocks that move only with the expansion of the universe. The isotropy of space implies that cosmological time defined in this way does not depend on the spatial location of the clocks. The cosmological principle allows us to consider space and time separately.

 

[chronon]

General relativity actually allows a wide choice of coordinate systems (and most of the mathematics of GR consists of converting between them). Cosmologists choose a coordinate system where the time is given by the proper time of an object moving with the expansion. This emphasises the homogeneity and isotropy of the universe, but I would still see it as a choice rather than as having physical significance. I've written more about this on my website, especially at http://www.chronon.org/Articles/milne_cosmology.html.

I would note that if you do believe in a preferred time coordinate, then the SR argument for determinism no longer applies.

 

[Hurkyl]

It's merely a choice of coordinate chart -- they have picked a (family of) coordinate charts that are convenient for explaining the large scale structure of the universe. It's no different than picking a frame in SR that is convenient for analyzing an SR problem.

It's important to note that physical clocks cannot agree with the time coordinate of such a chart -- in an extreme case, it would have to pass through a black hole and come out! Even in the mild case, it would have its rate of time altered by local gravitational fields. Actually, I don't think it's even possible to locally work out in which direction it's supposed to be travelling, as it is buffeted by local gravitational fields.

 

[Aether]

The WMAP team's estimate for the age of the universe at 13.4Gyr, based on the CMB monopole, is one example of a real cosmological clock. This is a physical clock, and it is easy to work out locally, using the CMB dipole anisotropy, in which direction it is supposed to be traveling. By "locally", do you mean to restrict the clock from receiving signals from outside itself?

So, are you saying that the CMB monopole does not have the same value at the same cosmological time regardless of spatial coordinates (within our universe)?

Do you agree that the CMB monopole is simultaneously observable at any given cosmological time t, and will be seen to have the same value, at all spatial locations, for any arbitrary inertial frame, and for any local gravitational conditions within our universe?

 

[russ_watters]

I'm not sure what you are saying is correct, but assuming it is, why should we care? What's so great about that particular frame of reference? Seems to me it is only relevant to cosmologists (and then still not for many things). I can't think of anyone else who would use it over a heliocentric or geocentric frame. Since we live in the geocentric frame, its virtually always the most important.

 

[Chronos]

I think there is a difference between an absolute [preferred] reference frame and a convenient reference frame. If you strictly apply the rules of SR, it's apparent [at least to me] the CMB is merely a convenient reference frame, not absolute. The rules apply in exactly the same way as they do in any other reference frame. I find the term 'cosmological time' unsettling because I have seen it used in a way that implies it is a somehow superior way to keep time. I object to that notion. It may be conceptually simpler, but it is mathematically indistinguishable from any other clock.

 

[Aether]

I'm not sure what you are saying is correct, but assuming it is, why should we care?

Most of what I said in my last post was in the form of three questions, and that is because I am not sure that it is all correct myself; but it is to the best of my understanding at this time. I hope that it is OK with you if, as I am studying GR and cosmology on my own, that I can continue to ask such questions here.

What's so great about that particular frame of reference? Seems to me it is only relevant to cosmologists (and then still not for many things). I can't think of anyone else who would use it over a heliocentric or geocentric frame. Since we live in the geocentric frame, its virtually always the most important.

Isn't it enough to say that it is relevant to cosmologists? When a scientist attempts to extrapolate SR principles across vast distances, then they have stepped into the realm of cosmology. When chronon, for example, says that:

I would say that the problem is believing in some special significance to 'now' at distant locations - I think of all events which have spacelike separation from me as having the same significance.

then he has clearly entered into the realm of cosmology, and the cosmological principle applies. I have not objected, so far, to anyone's use of heliocentric or geocentric frames when the scope of their observations haven't expanded to encompass the entire universe (and beyond).

 

[Aether]

I think there is a difference between an absolute [preferred] reference frame and a convenient reference frame. If you strictly apply the rules of SR, it's apparent [at least to me] the CMB is merely a convenient reference frame, not absolute. The rules apply in exactly the same way as they do in any other reference frame. I find the term 'cosmological time' unsettling because I have seen it used in a way that implies it is a somehow superior way to keep time. I object to that notion. It may be conceptually simpler, but it is mathematically indistinguishable from any other clock.

I also find the term cosmological time unsettling, and that is why I keep bringing it up. I was unaware of the concept myself until about three or four months ago.

Why do you say that a cosmological clock is mathematically indistinguishable from any other clock? A proper time clock runs slower with increased velocity, but a cosmological clock does not (as I understand it). The 13.4Gyr estimate for the age of the universe, based on the CMB monopole temperature, does not depend on the velocity of the observer; the CMB dipole anisotropy does, but that is easily compensated for.

 

[russ_watters]

Isn't it enough to say that it is relevant to cosmologists? When a scientist attempts to extrapolate SR principles across vast distances, then they have stepped into the realm of cosmology.

I asked the question because you seem to be implying that the CMB constitutes a Universal reference frame, ie one contrary to Special Relativity. If such a frame existed, it would be important to everyone, not just cosmologists.

My understanding of this is a little thin, but it sounds like "cosmological time" is just Earth time corrected for our motion through the CMB (and gravity?). Yes, certainly, then any clock that is corrected for its motion through the CMB (and gravity?) would tick at the same rate, but that does not imply cosmological time has any special significance. In fact, its an empty assertion, logically identical to saying that any clock corrected to show Earth time will show Earth time. True, but useless.

 

[Aether]

I asked the question because you seem to be implying that the CMB constitutes a Universal reference frame, ie one contrary to Special Relativity. If such a frame existed, it would be important to everyone, not just cosmologists.

My understanding of this is a little thin, but it sounds like "cosmological time" is just Earth time corrected for our motion through the CMB (and gravity?). Yes, certainly, then any clock that is corrected for its motion through the CMB (and gravity?) would tick at the same rate, but that does not imply cosmological time has any special significance. In fact, its an empty assertion, logically identical to saying that any clock corrected to show Earth time will show Earth time. True, but useless.

OK, so a cosmological clock based on the CMB monopole gives the same output as a Universal Clock should, but the step of extracting the CMB dipole anisotropy somehow profoundly distinguishes between the two types of clock? Can you explain the nature of this distinction in greater detail, or give a link to where such an explanation is posted?

 

[Chronos]

Pardon the intrusion, Russ. I have too much free time.

OK, so a cosmological clock based on the CMB monopole gives the same output as a Universal Clock should..

Huh? What led you to draw that conclusion? Russ said nothing of the sort. There is no such thing as a universal clock under SR, and nothing in the CMB data implies the existence of such a clock.

..but the step of extracting the CMB dipole anisotropy somehow profoundly distinguishes between the two types of clock?

What step is that? The CMB dipole anisotropy offers nothing to suggest it is profoundly different from any other clock. You might as well say the moon, or your wristwatch, is profoundly different from any other reference frame. SR rules apply exactly the same in the CMB reference frame as they do in any other reference frame.

Can you explain the nature of this distinction in greater detail, or give a link to where such an explanation is posted?

There is no distinction and none has been claimed.

 

[Aether]

Pardon the intrusion, Russ. I have too much free time.Huh? What led you to draw that conclusion? Russ said nothing of the sort. There is no such thing as a universal clock under SR, and nothing in the CMB data implies the existence of such a clock.

What would be the signature of a Universal Clock, if one existed? It seems to me that the necessary and sufficient condition for a Universal Clock is that it measures a universal time coordinate that is independent of location, velocity, and perhaps local space-time curvature. The CMB data not only implies the existence of such a clock, but the theory has apparently been reduced to actual practice with the WMAP team's estimate of 13.4Gyr for the age of the universe. btw, I suspect that I am missing something here, and that you guys are all right about this, but none of you have come close to explaining why yet.

What step is that?

The CMB monopole is the basis for the WMAP team's estimate of the age of the Universe of 13.4Gyr, and that is an example of a cosmological clock. To isolate the monopole, a dipole anisotropy that is usually attributed to the motion of the solar system with respect to the CMB has to be measured and removed from the data.

The CMB dipole anisotropy offers nothing to suggest it is profoundly different from any other clock. You might as well say the moon, or your wristwatch, is profoundly different from any other reference frame. SR rules apply exactly the same in the CMB reference frame as they do in any other reference frame.There is no distinction and none has been claimed.

Cosmological time based on the CMB monopole temperature is locally Lorentz invariant. This is an atypical case for the qualification of Lorentz invariance with "locally". SR-like rules apply only instantaneously, but (after replacing the SR-metric with the F(L)RW metric, or a better one) they can be applied across all spatial coordinates at one instant of cosmological time. However, they do not apply across any span of cosmological time because the CMB monopole evolves with time.

 

[Nereid]

'cosmological time' = 'time measured in a co-moving frame'?

This page, from Ned Wright's cosmology tutorial may help.

 

[Aether]

'cosmological time' = 'time measured in a co-moving frame'?

This page, from Ned Wright's cosmology tutorial may help.

So it would seem. On p. 67 of Peacock, Cosmological Physics (Cambridge University Press, 1999), he says: "COSMOLOGICAL TIME: The first point to note is that something suspiciously like a universal time exists in an isotropic universe. Consider a set of observers in different locations, all of whom are at rest with respect to matter in their vicinity (these characters are usually termed fundamental observers)...We can define a global time coordinate t, which is the time measured by the clocks of these observers - i.e. t is the proper time measured by an observer at rest with respect to the local matter distribution."

I don't see where either Peacock or Ned Wright actually say unambiguously that this is what is called cosmological time, but let's say that it is until some new information says otherwise. This is not what I am talking about, so I will henceforth use the term universal time to refer to the t that I am talking about. What's the difference? A fundamental observer measures both cosmological time (as defined by Peacock) and the local CMB dipole anisotropy, and then is able to transform cosmological time into universal time (which, btw, looks like a duck, walks like a duck, and appears to also quack like a duck).

So, is the CMB monopole temperature the same for all fundamental observers at the same cosmological time, or at the same universal time?

 

[russ_watters]

Pardon the intrusion, Russ. I have too much free time.

By all means - I've been waiting for it! I'm an engineer, not a physicist, and though I think I see something here, I'm not at all certain I have all of this right. I've been hoping one of our experts would jump in where I left off.

What would be the signature of a Universal Clock, if one existed? It seems to me that the necessary and sufficient condition for a Universal Clock is that it measures a universal time coordinate that is independent of location, velocity, and perhaps local space-time curvature. The CMB data not only implies the existence of such a clock, but the theory has apparently been reduced to actual practice with the WMAP team's estimate of 13.4Gyr for the age of the universe. btw, I suspect that I am missing something here, and that you guys are all right about this, but none of you have come close to explaining why yet.

What's the difference? A fundamental observer measures both cosmological time and the local CMB dipole anisotropy, and then is able to transform cosmological time into universal time.

The problem is, you could also reference all time calculations to my watch (or a clock somewhere in Greenwich, England) and arrive at the same result! Anyone in the universe who knows where they are and how fast they are moving in relation to my watch can use my watch as The Universal Timepiece if they so choose. That's how GPS clocks work: they are adjusted to stay synchronized with a clock in a different frame. That's one of the main purposes of Relativity - it enables you to synchronize clocks in different frames.

The fact that the CMB permeates the universe does not mean that its The Universal Reference Frame. Once you get into it, what can you say? You're stationary. Stationary with respect to what (to be stationary you have to have something to measure it from)? Stationary with respect to yourself. Guess what - I'm already stationary with respect to myself!

I think the problem here may be how you're arriving at this: a Universal Clock, if it existed, would be a device you could build and run in this reference frame and would show the same time as an identical clock in another reference frame. By taking your measurements in one frame, of a phenomena that is happening in another (the CMB), what you're really doing is declaring that other frame to be the Universal Reference Frame and the time measured by a clock in that frame to be Universal Time. The reality is that there is no basis for this declaration.

 

[Hurkyl]

Aether: I've been mentally playing with what you described, and I've concluded that it is not well-defined -- it depends on a choice of at least one "right" observer.


One model over which I've mulled is a conical universe. We can envision this universe as a cone in three dimensions (2 space and 1 time), with the axis of the cone being timelike.

It appears obvious that there is a distinguished class of observers on this cone: their worldlines are simply straight lines that originate from the vertex of the cone, and we can define an apparently universal intrinsic time coordinate by computing the proper time along these distinguished worldlines.

However, appearances are deceiving. There is actually a large class of observers -- you can start with any geodesic eminating from the vertex that spirals around the cone, and get a similarly "distinguished" class of observers (geometrically, their worldlines are formed by rotating this first geodesic). These observers are also moving "with the universal expansion", and their clocks will disagree with the clocks of the first class we noticed.

 

[Aether]

There is actually a large class of observers -- you can start with any geodesic eminating from the vertex that spirals around the cone, and get a similarly "distinguished" class of observers (geometrically, their worldlines are formed by rotating this first geodesic). These observers are also moving "with the universal expansion", and their clocks will disagree with the clocks of the first class we noticed.

Hurkyl, The WMAP satellite was spiraling through space-time all the while it was collecting its data, but that didn't stop the mission team from measuring the CMB monopole temperature and estimating the age of the universe at 13.4Gyr. So, would all of these cone-world observers be able to measure the same value of the CMB monopole temperature at the same time or not?

 

[Aether]

The fact that the CMB permeates the universe does not mean that its The Universal Reference Frame. Once you get into it, what can you say? You're stationary. Stationary with respect to what (to be stationary you have to have something to measure it from)? Stationary with respect to yourself. Guess what - I'm already stationary with respect to myself!

Once you get into the Universal Reference Frame, if it exists, then I would expect $$d\tau/dt=1$$ (e.g., we could send a probe to this reference frame, and an identical probe to the diametrically opposed reference frame wrt us, let them loiter 'there' for awhile, bring them back, and compare clocks). Stationary with respect to the center of mass of the universe, stationary with respect to the centroid of the particle horizon, etc..

I think the problem here may be how you're arriving at this: a Universal Clock, if it existed, would be a device you could build and run in this reference frame and would show the same time as an identical clock in another reference frame. By taking your measurements in one frame, of a phenomena that is happening in another (the CMB), what you're really doing is declaring that other frame to be the Universal Reference Frame and the time measured by a clock in that frame to be Universal Time. The reality is that there is no basis for this declaration.

There is actually a large class of observers -- you can start with any geodesic eminating from the vertex that spirals around the cone, and get a similarly "distinguished" class of observers (geometrically, their worldlines are formed by rotating this first geodesic). These observers are also moving "with the universal expansion", and their clocks will disagree with the clocks of the first class we noticed.

OK, you have convinced me that the CMB rest frame is not necessarily 'The' Universal Reference Frame (uncommon first name, 'The'), but it still appears to be one of many possible absolute reference frames with the distinguishing feature that it is easily located with existing technology. Are you both stipulating that the CMB monopole clock is an absolute clock, that there can be an arbitrary number of such absolute clocks, but with the reservation that none of them are selected out yet as being The Universal Clock? If not, what does the CMB monopole clock lack that a true absolute clock mustn't other than a universal unit of time (which I still have up my sleeve)?

 

[Aether]

Once you get into the Universal Reference Frame, if it exists, then I would expect $$d\tau/dt=1$$ (e.g., we could send a probe to this reference frame, and an identical probe to the diametrically opposed reference frame wrt us, let them loiter 'there' for awhile, bring them back, and compare clocks).

Actually, bringing these probes back together would just guarantee a null result. Using the CMB monopole temperature T as a reference, it might be interesting to measure $$dT/d\tau$$ in several different frames for example. I suspect that the gradient of the CMB monopole is going to turn out to be precisely whatever is necessary to confirm SR, but want to know this for sure.

 

[russ_watters]

OK, you have convinced me that the CMB rest frame is not necessarily 'The' Universal Reference Frame (uncommon first name, 'The'), but it still appears to be one of many possible absolute reference frames with the distinguishing feature that it is easily located with existing technology.

My watch is also easily located and observed. Buts not an in absolute reference frame, and neither is the CMB:

Are you both stipulating that the CMB monopole clock is an absolute clock, that there can be an arbitrary number of such absolute clocks, but with the reservation that none of them are selected out yet as being The Universal Clock? If not, what does the CMB monopole clock lack that a true absolute clock mustn't other than a universal unit of time (which I still have up my sleeve)?

Well, isn't that an obvious contradiction? If there is more than one, then none of them can be "absolute clocks."

 

[Aether]

Well, isn't that an obvious contradiction? If there is more than one, then none of them can be "absolute clocks."

I contacted Ned Wright, and he was kind enough to respond with this:

Actually conformal time is different: $$d\eta = dt/a(t)$$ where t is the cosmic time and $$\eta$$ is the conformal time.

It's easy to define cosmic time since almost everything in the Universe is almost comoving. In other words, the actual solution is less symmetric than the theory. Even in SR you can define a universal time for any reference frame -- it is just that it can't be an invariant definition of time that everybody in all reference frames would agree on. But since in this Universe everybody is comoving we don't have a problem.

So, there is apparently no contradiction in saying that you can define an absolute universal time for any reference frame. The trick seems to be in finding an invariant universal unit of time that each observer can agree to scale to.

 

[Chronos]

So, there is apparently no contradiction in saying that you can define an absolute universal time for any reference frame. The trick seems to be in finding an invariant universal unit of time that each observer can agree to scale to.

No more a trick than building a perpetual motion machine that works. It is impossible.

 

[Aether]

No more a trick than building a perpetual motion machine that works. It is impossible.

Perhaps, I just want to see why exactly. For example, if each observer can estimate the present age of the universe, and supposing that they can also estimate the age of the universe when the expansion reverses (this depends on a specific cosmological model for a closed universe), then why can't they all set their clocks to the same scale by normalizing their current age estimates upon division by their age of maximum expansion estimate? Why would this dimensionless ratio vary from one inertial frame to another?

For example, on p. 738 of MTW (Gravitation, Misner, Thorne, and Wheeler) in Box 27.4 there is given "A Typical Cosmological Model Compatible with Astronomical Observatons and with Einstein's Conception of Cosmology". This model gives a time from start to today of 10E9 yr. and a time from start to maximum expansion of 29.76E9 yr., and this yields a dimensionless ratio of 0.3360 which is (I suppose) frame independent.

 

[pervect]

It's not a mater of "scaling". Different observers have different ideas of simultaneity. This makes it impossible to define a universal notion of time, except by fiat. At the expense of making life difficult for everyone else, one could in principle declare one particular class of observers to be "special" or "priveleged", and declare that everyone should use their concept of time. This will require most observers to use rather unpleasant anisotropic coordinate systems, however.

 

[russ_watters]

It's not a mater of "scaling". Different observers have different ideas of simultaneity. This makes it impossible to define a universal notion of time, except by fiat.

...which is exactly how GPS does it: they arbitrarily decided on a ground station to synchronze to. Think about it, Aether - a GPS clock always stays synchronized with its ground-based counterpart. Its calibrated that way because its simpler to operate. Using the same knowledge of your position and speed relative to that clock (and an arbitrary determination of simultaneity), anyone anywhere in the universe could synchronize permanently to that clock. Calibrating the tick rate alone isn't enough and using the Big Bang as the starting point won't provide synchronization.

Perhaps, I just want to see why exactly. For example, if each observer can estimate the present age of the universe, and supposing that they can also estimate the age of the universe when the expansion reverses (this depends on a specific cosmological model for a closed universe), then why can't they all set their clocks to the same scale by normalizing their current age estimates upon division by their age of maximum expansion estimate? Why would this dimensionless ratio vary from one inertial frame to another?

They can. I think what you are missing is simply that that choice of datum is no less arbitrary than any other choice and it does not eliminate clock synchronization issues - it makes them worse by adding a 3rd frame to synchronize to. Even after synchronizing to this 3rd frame, those engineers who designed the GPS system still have to do additional work to synchronize the satellites with the ground station.

edit: narrative thought experiment...

You and your buddy synchronize watches accordng to this Universal Clock of yours. Your buddy flies to the moon. He's changed frames so he resynchronizes. You open a data connection to his onboard computer and notice his computer clock is 1.28 seconds slow. When you ask him about it, he checks and says your clock is 1.28 seconds slow. How do you rectify that?

But then things get worse. You try to measure the distance to his ship, but your calculations don't match his. So he recalibrates his instruments and finds that the speed of light is no longer C because he's using a clock in a different reference frame to measure the speed in his frame. This variation in C is sufficient to cause his computer to improperly control the fusion reactor powering his ship (its output depends on C) and his ship explodes.