Does Special Relativity Suggest a Predetermined Future?

[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.

 

[pervect]

...which is exactly how GPS does it: they arbitrarily decided on a ground station to synchronze to.

GPS time (and TAI time) are good examples of the sort of trouble one can get into with clock synchronization. One can more or less consider that the "reference clock" for GPS time time (also, for TAI time) is a clock on the north or south pole. This clock isn't moving with respect to the center of the Earth (though it keeps slightly different time because of gravitational time dilation).

Momentum will NOT BE CONSERVED in a system of physics that uses GPS clock synchronizations to measure velocities when one uses the simple formula

p = mv

One can use the simple relation p=mv only if one has an Einsteinian clock synchronization. There are many options, but because most peole find it much easier to keep p=mv than to muck around with anisotrpic velocity-momentum tensors (Using anisotropic velocity-momentum tesors means that. one re-adjusts the momentum velocity relationships so that an object moving east-west with "velocity" v (said velocity being measured with GPS clock synch) has a different ratio of momentum/mass than an object moving west-east with the same "velocity").

The usual option is simply not to use GPS clock synchronizations to measure velocities, much as one does not include time zones when one is measuring velocities. If an object is moving slow enough, the difference in GPS/ einsteinian synchronization methods may not be critical to a particular experiment, but it will become more and more important as the velocity increases.

 

[Aether]

Thank you, all. I have printed out this entire thread and will study everything carefully. If anyone has a link or reference to a thorough discussion of similar issues, I would also like to see that. Chronos, there is perpetual motion everywhere at both the atomic level and the astronomical level.

 

[pervect]

One thing I should clarify - given that the reference clock for GPS/TAI time is at the pole, the place on Earth where you run into the biggest synchronization problems is at the equator. This happens simply because the equator is moving relative to the poles.

 

[yogi]

Of point - at page 249 of the Jan issue of nature: The cosmological principle ... furnishes a preferred time coordinate; any observer can define a clock in terms of the local density of matter at their location. This defines cosmological time. All observers using this clock see the same matter density at any particular time. This simplifies the four dimensional machinery of Einstein's theory into a much simplier 3 + 1
structure, and removes much of the complexity that arises where no special choice of time coordinates is obvious. Space-times compatible with the cosmological principle must have the same geometry at each point on the surface of constant time. The space-time may be expanding or contracting..."

 

[Chronos]

Thank you, all. I have printed out this entire thread and will study everything carefully. If anyone has a link or reference to a thorough discussion of similar issues, I would also like to see that. Chronos, there is perpetual motion everywhere at both the atomic level and the astronomical level.

Your argument is compelling. Electrons orbit atomic nuclei. Since electrons move, an energy source is required. Since energy and mass are equivalent, atomic nuclei must sacrifice mass over time to power the motion of their electrons. Old atoms are therefore less massive than young atoms. I'm trying to follow your logic, but it's like tracking buffalo with the wind at your back. You can smell where they came from, but not where they're going.

 

[Aether]

Your argument is compelling. Electrons orbit atomic nuclei. Since electrons move, an energy source is required. Since energy and mass are equivalent, atomic nuclei must sacrifice mass over time to power the motion of their electrons. Old atoms are therefore less massive than young atoms. I'm trying to follow your logic, but it's like tracking buffalo with the wind at your back. You can smell where they came from, but not where they're going.

This logic points to a symmetry higher than that of local Lorentz invariance.

http://groups-beta.google.com/group/sci.physics.relativity/msg/a6f110865893d962]The[/PLAIN] basic symmetry of SR is Lorentz invariance, and the essence of SR is encapsulated in the statement that the laws of physics are locally Lorentz invariant (i.e. unchanged under the operation of any member of the Lorentz group). This is an instance of the modern approach to symmetries: a symmetry principle states that something remains unchanged when a specific type of operation is performed. Note that Einstein's original two postulates for SR are both symmetry principles.

Einstein was instrumental in bringing the importance of symmetries to the forefront of modern physics, and SR is an excellent example of the power of symmetry groups in determining the possible structure of physical laws: considerations of group theory alone plus the simple observation that pion beams exist are sufficient to derive the equations of SR. In addition, an assumption of Lorentz symmetry and the guess that electrodynamics is the simplest possible gauge theory is enough to derive the Maxwell's equations. Symmetry principles are a very powerful (nay indispensable) tool in modern theoretical physics.

And none of the ether theories contain such a symmetry as a fundamental part of the theory (LET has an "accidental" Lorentz symmetry, but it is not a principle of the theory). It is highly doubtful that any of the modern theories of physics would have been discovered without the symmetry principles of SR leading the way -- modern gauge theories are direct descendants of the geometrical description of SR; this includes both GR and the Standard Model. Such a geometrical description is not possible in any ether theory (geometry is inherently coordinate independent, but the ether is not).

 

[Hurkyl]

Since electrons move, an energy source is required.

You're just recasting a classic paradox of classical mechanics: when a charge accelerates, it emits radiation, so the electron must be continuously emitting radiation (because it undergoes acceleration to orbit the nucleus).


In an important sense, electrons in an atom are not moving -- they are smeared out in a stationary electron cloud, which results in stationary charge and current distributions.

 

[Aether]

In an important sense, electrons in an atom are not moving -- they are smeared out in a stationary electron cloud, which results in stationary charge and current distributions.

The x^4 coordinate is changing at the rate of ic.

 

[selfAdjoint]

True but so is the x⁴ coordinate of the nucleus, the apparatus, the lab, the earth, the visible universe and presumably all those elephants.

Electrons are not orbiting because if they were, they would be accelerating, and so by EM they would be radiating, which they don't. It was this conundrum which led Bohr to the old quantum theory.

 

[Aether]

True but so is the x⁴ coordinate of the nucleus, the apparatus, the lab, the earth, the visible universe and presumably all those elephants.

Electrons are not orbiting because if they were, they would be accelerating, and so by EM they would be radiating, which they don't. It was this conundrum which led Bohr to the old quantum theory.

Elephants from elsewhere?

If, according to EM and for a charged particle, d²xⁱ/dt²\neq0 implies that it is radiating, then what does d²x⁴/dt²\neq0 imply?

 

[Hurkyl]

\neq


Other issues aside, acceleration 4-vectors are always space-like. In particular, it cannot be the case that the three spatial components of acceleration are zero, but the time component is nonzero.

 

[Aether]

Other issues aside, acceleration 4-vectors are always space-like. In particular, it cannot be the case that the three spatial components of acceleration are zero, but the time component is nonzero.

The Pioneer anomaly is consistent with d²x⁴/dt²=ia_P.