Could there be an absolute 'state of reference?'

[PeterDonis]

Peter, I'll try to answer this the best I can, but I'm not a mathematician.

Then you shouldn't be making claims about what the math of SR says or doesn't say.

According to einstein (actually the Lorentz transformations) a moving clock runs slower than one that isn't moving, right?

This is the way it's often described, yes, but IMO it's a bad description, because it leaves out too much information.

Also, it's not a good idea to talk about some vague, unspecified scenario. Let's talk instead about a concrete scenario: the train and the embankment. In the Einstein example that I think you were referring to in the other thread, we had the following, IIRC:

(1) An observer at the center of the train, which is moving along a track parallel to the embankment.

(2) An observer standing on the embankment. The two observers pass each other (i.e., they are co-located, since we are ignoring all but one spatial dimension) at some particular instant.

(3) Two lightning strikes that hit particular points on the embankment at particular instants.

(4) Light from those two lightning strikes travels to the observer on the embankment; the light from both strikes reaches him at the same instant. This happens *after* the two observers pass each other.

So we have four events of interest: event A, the first lightning strike hitting the embankment; event B, the second lightning strike hitting the embankment; event O, the two observers passing each other; and event L, the light from the two lightning strikes reaching the observer on the embankment.

Mathematically, the way we model this is to first pick a frame of reference, and then assign each event of interest coordinates in that frame of reference. I'll do that below.

The LT tells you that, right? What the LT does NOT, and CAN NOT, tell you is which of two objects is relatively motionless. The math can't tell you that.

I'm not sure what this means. There will be some velocity $v$ in the math, which represents the relative velocity of two observers or objects. In our train-embankment scenario, it represents the relative velocity of the train and the embankment; and we would use that $v$ in the Lorentz transformation formulas to convert coordinates of events in the embankment frame to coordinates of events in the train frame. If you are saying that that process does not pick out either frame as "motionless", you are correct. If you're saying something else, you'll need to clarify what it is before I can respond to it.

either way, one clock will be slower than the other.

But which clock it will be depends on which frame you choose. More precisely, that's true as long as the relative motion between the two frames is the same, which is the case for our train-embankment scenario. In other scenarios, where that's not the case, there might be an invariant sense in which one clock runs slower than the other. It depends on the scenario.

If the guy on the train is moving, his clock will be slower. If the guy on the embankment is moving, then, per the LT, his clock will be slower.

This is just another way of saying what I said just now, that which clock runs slower depends on which frame you choose. Choosing a frame amounts to choosing which object you are going to assume to be "motionless" for purposes of your calculation. But the physics doesn't care which frame you choose; they're all equivalent. The only reason to choose one at all is to do a particular calculation. See below.

Which one is slower? The one which is moving. To me, that is a question of physics, not mathematics.

No, it's a question of properly understanding what "moving" means.

Let me work through the train-embankment example more explicitly, to illustrate what I said above. Suppose that we know, from actual measurements made by the observer on the embankment, that the coordinates of the four events of interest, in the embankment frame (i.e., the frame in which the embankment is motionless) are:

Event O: $(t, x) = (0, 0)$

Event A: $(t, x) = (0, -1)$

Event B: $(t, x) = (0, 1)$

Event L: $(t, x) = (1, 0)$

Note that I am using units in which the speed of light is 1; for example, distance could be in feet and time in nanoseconds, or distance in kilometers and time in light-kilometers (the time it takes light to travel 1 kilometer, or 1/300,000 of a second), or whatever. The specific units don't matter for this discussion; I'll just call them "units".

Note also that, as you can see from the above, 1 unit of time elapses in the embankment frame between event O and event L. Physically, this means that 1 unit of time elapses on the embankment observer's clock between the train observer passing him and the light from the two lightning strikes reaching him.

Now, if we know the velocity $v$ of the train relative to the embankment, we can use the Lorentz transformation to obtain the coordinates of these three events in the train frame (i.e., the frame in which the train is motionless). The transformation equations are:

$$
t' = \gamma \left( t - v x \right)
$$

$$
x' = \gamma \left( x - v t \right)
$$

where $\gamma = 1 / \sqrt{ 1 - v^2 }$.

Applying these to the above coordinates gives:

Event O: $(t', x') = (0, 0)$

Event A: $(t', x') = (\gamma v, \gamma)$

Event B: $(t', x') = (- \gamma v, \gamma)$

Event L: $(t', x') = (\gamma, - \gamma v)$

To see how these numbers show that "moving clocks run slower", observe that, in the train frame, the observer on the embankment is moving, so the elapsed time by his clock (1 unit) between event O and event L is less than the coordinate time between those two events in the train frame ($\gamma$ units). So, relative to the train, the embankment clock does indeed show "time dilation". (And notice how I reversed things, by showing how the *embankment* clock runs slow relative to the train frame, rather than how the train clock runs slow relative to the embankment frame? That was to illustrate that which clock is "moving" and runs slow is a matter of choice of frame; the physics is the same either way.)

But notice how much that description leaves out. First, it leaves out the fact that event L has a different *spatial location*, in the train frame, than event O (because in the train frame, the embankment is moving). Second, it leaves out relativity of simultaneity: notice that events A and B have *different* time coordinates, in the train frame, whereas they have the same time coordinate (they are simultaneous) in the embankment frame. (Physically, this is because we specified that light from the two lightning strikes reach the observer on the *embankment* at the same instant. If we had specified that light from the two lightning strikes reached the observer on the *train* at the same instant, we would have obtained different coordinates for events A and B.) To really understand what's going on, you have to include *all* the physics, not just time dilation.

 

[Layman]

Time to meet some real physicists! The effects of time dilation are completely symmetric. They each see the other's clocks as running slow.

I completely agree that each will "see" the other's clock as running slow, IF, and only if, each assumes that he is motionless and the other is moving. Otherwise, no.

But questions still exist apart from what a person will "see." I put "see" in scarequotes because we are not talking about actual observation. We are talking about calculations BASED ON certain given permises (which may or may not be true).

Take the global positioning system. Ignoring the distorted time effects created by gravity, we ASSUME that a clock on the satellite will run slower because we assume that it is moving relative to us (and NOT that we are moving relative to it). As it turns out, our assumptions are right. The clock on the satellite DOES, in fact, run slower. Why? Presumably because it is moving. It has the "moving clock," not us.

 

[WannabeNewton]

Why? Presumably because it is moving. It has the "moving clock," not us.

You do realize if you boost to the rest frame of the clock in orbit, the central clock will now be in orbit and it will have a time dilation factor attached to it right? So your argument makes no sense. The only thing absolute in your scenario is the fact that one clock accelerates whereas the other is inertial. This doesn't affect the kinematical time dilation which only depends on relative velocity.

 

[PeterDonis]

Ignoring the distorted time effects created by gravity, we ASSUME that a clock on the satellite will run slower because we assume that it is moving relative to us (and NOT that we are moving relative to it). As it turns out, our assumptions are right. The clock on the satellite DOES, in fact, run slower. Why? Presumably because it is moving. It has the "moving clock," not us.

This is a different sense of "moving" than the train and embankment example. The GPS satellites are in closed orbits; they return to the same position, relative to someone on the surface of the Earth, periodically. That gives a common reference from which to measure elapsed time, by measuring elapsed time between one time the satellite passes and the next; it's not the same as the train and the embankment, where the two observers only pass each other once. In cases like GPS (or the "twin paradox"), where the two observers meet more than once, you can use the elapsed time between meetings as an invariant measure of which clock "runs slower". But you can't do that if the observers only meet up once.

 

[A.T.]

I don't recall saying any such thing, A.T.

It was just a few hours ago:

My question was merely addressing a guy on a moving train, on earth, claiming that he was motionless. In that case, the "absolute" frame is obviously the surface of the earth.

So, our Earth defines the absolute frame?

 

[Layman]

It was just a few hours ago:


So, our Earth defines the absolute frame?

A.T. that is out of context, and you are misreading the intent. I was responding to a specific question, and, in each post, the word "absolute" was put in quote marks, indicating that this frame was being TREATED AS absolute, without regard for the factual question of whether is was in fact absolute.

 

[A.T.]

Ignoring the distorted time effects created by gravity...

You cannot ignore that, because in curved space-time the inertial frames that SRT talks about exist only locally. You cannot apply SRT over a large area like the orbit of satellite.

 

[ZapperZ]

Let's cut to the chase. There is no absolute reference frame based on all the physics that we know.

Now, if you have a specific paper or physics that can contradict that, please use it and make the exact citation. Otherwise, this thread is meandering in the misuse and misinterpretation of Special Relativity.

Zz.

 

[A.T.]

the word "absolute" was put in quote marks, indicating that this frame was being TREATED AS absolute, without regard for the factual question of whether is was in fact absolute.

So by "obviously absolute" you actually mean "without regard for the factual question of whether is was in fact absolute"?

 

[Layman]

...one clock accelerates whereas the other is inertial. This doesn't affect the kinematical time dilation which only depends on relative velocity.

I agree with this, and it is my understanding that experiments at CERN, Fermilab, etc. have conclusively established this (i.e., that acceleration has no effect on time dilataion). Yet I still run into many who assert otherwise.

As for the part of your quote that I omitted, Wannabe, I don't understand why you say my comment makes no sense. Moving clocks run slow (per the LT). You can arbitrarily SAY (without any justification whatsoever) that this or that clock is moving, and the other isn't, but that doesn't make it so.

Same with the Keating experiment. Have you seen the youtube video with them actually on a plane? They are predicting, at every stage, just how much slower their clock will be than the Earth clock when they land. And their predictions are correct. Their clock showed less time elapsed, not the Earth clock. Of course they did NOT assume they were stationary when in the air. In that sense, they were violating the dictates of SRT.

 

[Layman]

So by "obviously absolute" you actually mean "without regard for the factual question of whether is was in fact absolute"?

Yes, as I recall. The question was about which rest frame was being treated as absolute.

 

[WannabeNewton]

Moving clocks run slow (per the LT). You can arbitrarily SAY (without any justification whatsoever) that this or that clock is moving, and the other isn't, but that doesn't make it so.

Doesn't make what so? The point is "moving clock" requires a frame of reference for it to move relative to. The time dilation is with respect to that frame.

They are predicting, at every stage, just how much slower their clock will be than the Earth clock when they land. And their predictions are correct. Their clock showed less time elapsed, not the Earth clock. Of course they did NOT assume they were stationary when in the air. In that sense, they were violating the dictates of SRT.

Nono, this is a different concept. See Peter's previous reply.

 

[A.T.]

The question was about which rest frame was being treated as absolute.

If you can choose which frame is "treated as absolute", then there is no absolute frame.

 

[Layman]

Doesn't make what so? The point is "moving clock" requires a frame of reference for it to move relative to. The time dilation is with respect to that frame.

Not sure what you are trying to say here. Isn't is universally agreed, in twin paradox discussions, that the traveling twin will be absolutely (not "relatively") younger than the stay at home twin? The contention is NOT that each twin will be younger than the other. Here again, the difference CANNOT be ascribed to acceleration because, as you yourself noted, this does not affect time dilation (only speed does)>

 

[Dale]

Well, Dale, from my point of view, that is not an "explanation," it is an assertion. Can you actually "explain" it?

Sure. The first postulate states that the laws of physics are the same in all inertial frames. Therefore, any observer can use any inertial frame and be assured that the same laws of physics will work. That inertial frame may be the one where he is at rest, but it doesn't have to be.

I commented that IF both the person on the train and the person on the embankment assumed that the train was moving, and not the earth, then they would not calculate the speed of light to be isotropic, would agree on simultaneity, etc. Why is this wrong?

It is wrong because they would both calculate the speed of light to be isotropic. That is the second postulate.

 

[Dale]

But, either way, one clock will be slower than the other. If the guy on the train is moving, his clock will be slower. If the guy on the embankment is moving, then, per the LT, his clock will be slower.

I wouldn't say I'm an LET "proponent."

I would, for all practical purposes here anyway.

 

[Layman]

Layman: "I commented that IF both the person on the train and the person on the embankment assumed that the train was moving, and not the earth, then they would not calculate the speed of light to be isotropic, would agree on simultaneity, etc. Why is this wrong?"

Dale: "It is wrong because they would both calculate the speed of light to be isotropic. That is the second postulate."

I disagree Dale. Under the circumstances I set forth, they would agree on simultaneity. The "second postulate" only works for two different observers if each assume that he is at rest and the other party is not. But I changed that assumption. That changes the conclusions about simultaneity. Without saying one or the other is "correct," I am simply noting that the conclusions will be different, based on what is (or is not) assumed.

 

[WannabeNewton]

Not sure what you are trying to say here. Isn't is universally agreed, in twin paradox discussions, that the traveling twin will be absolutely (not "relatively") younger than the stay at home twin? The contention is NOT that each twin will be younger than the other. Here again, the difference CANNOT be ascribed to acceleration because, as you yourself noted, this does not affect time dilation (only speed does)>

But that isn't an example of time dilation. Let's go back to your first example. We have an inertial observer in free space and another observer in circular orbit starting and ending at the inertial observer. Now imagine a cylinder with symmetry axis aligned with the rotation axis of the circular orbit. The world-line of the inertial observer is simply a straight line striation on the cylinder parallel to the symmetry axis. On the other hand the world-line of the circulating observer is a helical striation that wraps around the symmetry axis. Initially the helix and straight line intersect at some point on the cylinder and after one period of the orbit they intersect again. Measuring the Lorentzian lengths of the helix and straight line between these two endpoints corresponds to measuring the proper time read by a clock carried by the circulating observer (Lorentzian length of helix) and that read by a clock carried by the inertial observer (Lorentzian length of straight line). This is indeed absolute because it refers only to the world-lines of the respective observers and world-lines are absolute objects embedded in space-time.

However this is not the same thing as kinematical time dilation which is a statement about coordinate time. If I boost to the rigid extended frame of the circulating observer then the inertial observer will, in this frame, be moving in a retrograde circular orbit and will have a time dilation factor attached to his clock. If I stay in the global inertial frame of the inertial observer then the circulating observer will instead have (the exact same) time dilation factor attached to his clock. This is entirely relative and symmetrical as it applies between the global inertial frame of the inertial observer and the instantaneously comoving inertial frames of the circulating observer. You can verify this through a simple calculation.

 

[Layman]

I would, for all practical purposes here anyway.

Dale, discussing other theories (like discussing differing religions, for example) and noting the differences in theories and how they arise does not mean you are "propounding" one or the other. But such exercises do, I think, help one see what theoretic possibilities are available.

 

[A.T.]

Under the circumstances I set forth, they would agree on simultaneity.

If both use the same reference frame they will agree on frame dependent quantities.

The "second postulate" only works for two different observers...

It always works, but is rather moot if everyone uses the same reference frame.

 

[Layman]

But that isn't an example of time dilation.

Why isn't it? Without getting overly technical, I would just say that, in the SRT context, time dilation (and it's converse, contraction) is merely a function of differing relative speeds. Two clock which are not in the same inertial frame will record time differently (with the faster moving clock running slower, time-wise).

 

[ChrisVer]

Can I make a similar question to what is being discussed in the main thread?
In principle we can always define a reference frame (equivalent to the rest), but isn't that frame defined only locally? For example, a big enough/extended object will be subject to tidal forces of a gravitational field, so in that case the body can really "feel" the gravitation.
In that sense, if we define a reference frame at a small region U in spacetime, how can we be sure it can be connected (or related) to some other region U', if the one is subject to those forces while the other is not?

 

[WannabeNewton]

Why isn't it?

I've already explained why above.

 

[A.T.]

Two clock which are not in the same inertial frame will record time differently

Not true in general. There are frames where both will run at the same rate.

 

[WannabeNewton]

In principle we can always define a reference frame (equivalent to the rest), but isn't that frame defined only locally? For example, a big enough/extended object will be subject to tidal forces of a gravitational field, so in that case the body can really "feel" the gravitation.

When talking about extended bodies we have to in general talk about frame fields as opposed to frames. If the extended body is undergoing Born rigid motion (e.g. Born rigid rotation) then we can define a frame field for the body using Lie transport so that the spatial axes of the local Lorentz frames constituting the frame field rigidly lock onto one another and form an extended (global) reference frame. If the motion isn't Born rigid then the best we can do is refer to the individual local Lorentz frames making up the frame field.

 

[Layman]

I've already explained why above.

Well, I'm sorry. I missed your point, I guess. If the difference in aging that is expected to occur in the twin paradox is NOT a case of time dilation to you, then obviously you and I have different notions (definitions) of what "time dilation" is.

 

[Layman]

Here are two of the rules that I was referring to:

•Challenges to mainstream theories (relativity, the Big Bang, etc.) that go beyond current professional discussion
•Attempts to promote or resuscitate theories that have been discredited or superseded (e.g. Lorentz ether theory)

Going way back to respond to this, G.H. It is my understanding that theories of relative motion which posit absolute simultaneity produce predictions which are 100% in accord with the predictions of the SRT. I don't think you can call such theories "discredited." Perhaps "superseded" in the sense that such theories are not as "popular" as SRT, I don't know.

But, subjective attributes like "popularity" aside, all experimental evidence that I am aware of shows these to be currently viable theories of relative motion. Every experiment which "confirms" SRT also "confirms these theories. Kinda like the Copernican and ptolemic theories, in some respects.

 

[PAllen]

Going way back to respond to this, G.H. It is my understanding that theories of relative motion which posit absolute simultaneity produce predictions which are 100% in accord with the predictions of the SRT. I don't think you can call such theories "discredited." Perhaps "superseded" in the sense that such theories are not as "popular" as SRT, I don't know.

But, subjective attributes like "popularity" aside, all experimental evidence that I am aware of shows these to be currently viable theories of relative motion. Every experiment which "confirms" SRT also "confirms these theories. Kinda like the Copernican and ptolemic theories, in some respects.

Such theories are LET, and are banned from this forum per rules you agreed to. George quoted the exact text of the rule you agreed to. Yes, LET is just like Ptolemaic theories - completely discredited in modern scientific discourse.

Also, note that the absolute simultaneity in theories that match observations is, in principle unobservable. Thus, such theories are equivalent to the statement like: "the standard model of particle physics is true because unicorns exist in a parallel universe". That is, they are outside of science - their core concept is inherently unverifiable.

 

[Nugatory]

Well, I'm sorry. I missed your point, I guess. If the difference in aging that is expected to occur in the twin paradox is NOT a case of time dilation to you, then obviously you and I have different notions (definitions) of what "time dilation" is.

Differential aging, as in the twin paradox, and time dilation are different phenomena (although they are are obviously related).

The paradox in the twin paradox is what happens if you try to interpret the differential aging as time dilation. The problem is that at all times during the journey, traveler's time dilation calculation correctly says that time is passing more slowly for stay-at-home; and stay-at-home's time dilation equally correctly says that time is passing more slowly for traveler. That's not a very promising start for deciding which twin in fact ages more during the journey.

 

[Layman]

Differential aging, as in the twin paradox, and time dilation are different phenomena (although they are are obviously related).

The paradox in the twin paradox is what happens if you try to interpret the differential aging as time dilation. The problem is that at all times during the journey, traveler's time dilation calculation correctly says that time is passing more slowly for stay-at-home; and stay-at-home's time dilation equally correctly says that time is passing more slowly for traveler. That's not a very promising start for deciding which twin in fact ages more during the journey.

I wouldn't say they are merely "related," myself. They are the same thing. What started out as the "clock paradox" later became (due to Lagvin, I believe) the "twin paradox," because he personalized the question. But in each case, the issue is identical, i.e., the differing rates at which time passes for moving objects (clocks) or observers.

I agree that's it's not a promising start. At the end of the day, when you remove all the subterfuge and attempts to obscure what's happening, I believe the "solution" is simply that the rocket is indeed the one moving, not the earth. Of course, that's exactly what the LT predicts, as Al pointed out very early.

The problem arises, as I see it, from the issue I raised in my (now closed) thread. You really can't logically say that each clock is slower than the other, and it is (in many cases) hostile to common sense, experience, and physical "laws" (such as the conservation of momentum) to claim that an object (e.g. a train) or an observer (e.g. a passenger) is NOT moving with respect to the earth. That claim is what generates the "paradox"