Why is Time DILATION Called Time DILATION?

[ghwellsjr]

...
Let me explain why I am partial to this way of thinking.

Refering back to Einstein's paper http://www.fourmilab.ch/etexts/einstein/specrel/www/, I see in Section 4:
- He writes "A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other which has remained at B by ¹/₂ tv²/c²"
- He does not state that the clock stationary at B could similarly be considered slower by the moving clock A in its own rest frame (which is strange since he does say that about length contraction earlier). I am not saying he meant it would not happen, just that he does not stress that part

He does not say that "B could similarly be considered slower by the moving clock A" because A is not at rest in an Inertial Reference Frame (IRF).

- Nevertheless, he then goes on to talk about one clock at the equator and another at a pole of Earth, and concludes that the equator one "must go more slowly, by a very small amount".

This last part to me implies a clear objective reality. He seems to tacitly state that in any real situation the stationary and moving clocks would become clear, the situation will be aymmetric, and real relative time dilation will show up between the clocks (unless the conditions of both clocks are really completely symmetrical). Moreover, such difference between the clocks is an ongoing and predictable amount at any point of the journey of the moving clock.

Also, the equator/pole relative time dilation happens even though the two clocks never get together at a location.

Would you say my thinking is correct, or is there something wrong with it?

There is something wrong with your thinking.

All IRF's will agree that the total amount of time difference per rotation of the Earth between the clock on the equator and the clock at the pole will be the same but they will not agree on the time dilations of the two clocks.

In the IRF in which the pole clock is at rest, it is not time dilated and the equator clock is time dilated by a constant amount, the same as the ratio of the accumulated times after one day.

But in other IRF's, the pole clock can have a constant time dilation while the equator clock has a fluctuating time dilation.

Observers cannot observe time dilation because it is a function of the chosen IRF.

 

[ghwellsjr]

What is "real relative time dilation"?

Experimentally proven and measurable differential aging between clocks.

What I meant:
"Experimentally proven and measurable" = "real"
"Relative time dilation" = "differential aging"

Time Dilation is not the same as Differential Aging.

The reason Differential Aging requires the two clocks to have a face-to-face meeting at the beginning and ending of the measurement interval is to remove any assumptions about clock synchronization. You may have found some specific examples where the Time Dilation factor for a particular Inertial Reference Frame (IRF) is equal to the Differential Aging factor, you cannot extrapolate to all other general examples. Even for the same example where it does work, picking a different IRF will make it not work.

 

[ghwellsjr]

There is a nuance here that I am not sure has been addressed adequately (I admit I haven't read the whole thread). Imagine the turnaround twin deriving the rate of the distant clock as described. Assume, for simplicity, instant turnaround. Then, throughout the trip they consider the stay at home clock running slow. For example, from 1 pm (when they separate) to 2 pm on their clock the see a redshifted clock going from e.g. 1 pm to 1:15 pm, and they figure it is slow (but by less than visual after correction for 'pure doppler'). Then, from 2 pm to 3 pm (at which point they re-unite), they see the stay at home clock advance uniformly from 1:15 pm to e.g. 3:15 pm. Correcting for doppler, it is considered to run slow during this whole time - yet advances more than their own clock.

I have made some diagrams to illustrate this example. I'm assuming that each twin either sends a light signal to the other one every 15 minutes (quarter hour) or that we just pay attention to the image of each twin at 15-minute intervals.

To summarize your scenario, the traveling twin leaves at a high speed such that his observation of the Earth twin's clock is Doppler shifted to the point that he sees it running at 1/4 of his own on the outbound portion of his trip which takes one hour. (This fixes the speed of the traveling twin to be 0.882353c.) That means the traveling twin will send out four signals during this portion of the trip (not counting the initial one when he starts) and he will just be receiving the first signal from the Earth twin when he gets ready to turn around. Since the inbound portion of the trip also takes one hour, the inbound speed will be the same and the Doppler shift will be the reciprocal of the outbound Doppler shift. I realize that you were just using an example when you said that the traveling twin will see two hours pass on the Earth twin's clock but it is actually going to be four hours.

We can easily calculate the differential aging of the twins by simply taking the average of the two Doppler shifts since the time for the traveling twin is the same for the outbound and inbound portions of the trip. The average of 1/4 and 4 is 4.25 divided by 2 or 2.125. This is also the gamma at the speed of 0.882353c.

I show the Earth twin's progress as a heavy blue line with dots every 15-minutes indicating when he sends out a signal depicted as a yellow line traveling at c towards the traveling twin. The traveling twin is shown as a heavy black line with dots every 15-minutes indicating when he sends out a signal depicted as a thin black line traveling at c towards the Earth twin.

The first diagram is for the Earth's Inertial Reference Frame (IRF) in which the Earth twin is at rest and in which his clock is not time dilated so the blue dots are spaced identically to the coordinate grid lines at 15-minute intervals. However, since the traveling twin's speed is 0.882c, his clock is time dilated by gamma or 2.125 and the black dots are spaced at every 2.125 of the coordinate time. This is easy to see precisely if you consider the entire trip takes 2 hours or 8 quarter hours and if we multiply 8 by 2.125 we get 17 which is the coordinate time at the end of the trip.

The next diagram is for the IRF in which the traveling twin is at rest during the outbound portion of the trip. This diagram was generated by taking the coordinates of each event depicted in the first diagram and using the Lorentz Transformation equations to generate a new set of coordinates for an IRF moving at 0.882353c with respect to the first IRF. It depicts exactly the same information that was contained in the first diagram.

Note that now the black traveling twin's clock is not time dilated during the outbound portion of the trip and so the first five dots line up with the coordinate grid lines (look down in the lower right corner). However the blue Earth twin's clock is time dilated by the same amount that applied for the traveling twin in the first diagram. Also note that the Doppler signals are sent out and received in exactly the same way as in the first diagram even though they travel at c in this IRF and may have different distances to go.

The third diagram is for the IRF in which the traveling twin is at rest during his inbound portion of the trip. Again, this was generated simply by taking the coordinates for all the events from the first IRF but transformed to a speed of -0.882353c. Similar comments could be made about the how the clocks are time dilated differently than in the other two IRF's and yet all the Doppler signals are sent and received identically.

Obviously, the resolution, is that to use this standard approach for removing Doppler, they must also accept the standard approach to simultaneity, which says that much of the blueshifted history occurred before the turnaround, even though seen after and indistinguishable from the period they consider the distant clock running slow (this is unsurprising, due to finite light speed). With a non-instant turnaround, you would consider this to be delayed reception of the remote clock running fast during the turnaround.

The key point is that for a significant period after turnaround (even for non-instant turnaround), after the turnaround twin is inertial, they must interpret the signals they receive in a way that is cognizant of the fact of their turnaround - if they want to avoid a logical contradiction, while still using the standard removal of doppler convention.

Personally, I prefer to give much less emphasis the uniqueness, let alone, objective reality of this interpretation. I consider that time dilation is a coordinate dependent, non-observable quantity whose character is a matter of convention - the choice of coordinates.

Great comments. Hopefully, this will enable arindamsinha to see the difference between Time Dilation and Differential Aging.

 

[arindamsinha]

If there is no face-to-face ( ie co-located) comparison, you are talking about something which cannot be observed which is a waste of time. If the worldlines of the clocks involved are known, then the elapsed time on the clocks are invariants whose values are easily calculated.

I explained this with the thought experiment in post #15. Co-location is not necessary for establishing differential aging. Signals exchanged at the speed of light between distant locations can establish the same.

What exactly is 'co-location' anyway? Can you define it in terms of 'observations' not using signals at the speed of light?

You won't find any new physics by looking at time dilation - it is a coordinate dependent effect and not physical. Differential ageing is physical.

I am trying to have a discussion on existing physics - terminologies and interpretations. Not looking for 'new physics' here, as you so sweetly call it.

If time dilation is just the 'apparent, or coordinate-dependent' effect, what use is it anyway, since it must be symmetrical between two bodies? As you mention, it is not 'physical', meaning it is an 'apparent' effect depending on 'where you observe it from' - analogous to 'parallax error'. Both are very readily understandable and correctable using Newtonian mechanics and common sense. It would appear using Doppler effect even in Newtonian mechanics.

"Differential aging" or "relative time dilation" is the real essense of relativity theory, in my opinion. I don't understand why people make such a big fuss about separating "time dilation" and "differential aging". When Einstein talked about "time dilation" he was clearly talking about "differential aging". If it was just a coordinate-dependent observational phenomenon, it would have been within the purview of Newtonian mechanics anyway, using Doppler effects.

1) Since the traveling twin's clock is essentially stopped during the trip, it will end up 10 seconds behind the Earth twin's clock when they do the synchronization verification test you described.

But having answered this, it doesn't help me understand what you are saying.

Thanks for taking this up and answering the question.

I was trying to establish that velocity-based differential aging between two bodies (and agreement on the same by both), is not dependent on the moving twin coming back to origin to be 'co-located' with the stationary twin to 'compare clocks'. It can be done at any point during the traveling twin's journey using light-signals.

He does not say that "B could similarly be considered slower by the moving clock A" because A is not at rest in an Inertial Reference Frame (IRF).

You misunderstood me. I said A in 'its own rest frame' (which of course is an IRF as well, and A is at rest in that IRF, in the situation considered). As I said, he didn't deny it, but just that he didn't stress it, and then went on to an example where there is a clearly established stationary and moving frame - which I found very interesting.

There is something wrong with your thinking.

Subjective. Can you point out exactly what?

All IRF's will agree that the total amount of time difference per rotation of the Earth between the clock on the equator and the clock at the pole will be the same but they will not agree on the time dilations of the two clocks.

In the IRF in which the pole clock is at rest, it is not time dilated and the equator clock is time dilated by a constant amount, the same as the ratio of the accumulated times after one day.

But in other IRF's, the pole clock can have a constant time dilation while the equator clock has a fluctuating time dilation.

Observers cannot observe time dilation because it is a function of the chosen IRF.

This is a SR situation we are discussing. So, without bringing in GR or acceleration, what prevents us from seeing the polar clock as 'rotating' w.r.t. an IRF fixed to a point on the equator?

 

[Nugatory]

This is a SR situation we are discussing. So, without bringing in GR or acceleration, what prevents us from seeing the polar clock as 'rotating' w.r.t. an IRF fixed to a point on the equator?

By "fixed to a point on the equator", you mean that there is a point on the equator that is at rest in the frame, right? No such frame can be inertial because it is accelerating, and I see no way to discuss it without considering the acceleration.

(We need not bring in GR, of course)

 

[Mentz114]

If there is no face-to-face ( ie co-located) comparison, you are talking about something which cannot be observed which is a waste of time. If the worldlines of the clocks involved are known, then the elapsed time on the clocks are invariants whose values are easily calculated.

I explained this with the thought experiment in post #15. Co-location is not necessary for establishing differential aging. Signals exchanged at the speed of light between distant locations can establish the same.

What exactly is 'co-location' anyway? Can you define it in terms of 'observations' not using signals at the speed of light?

You're ignoring what I said. There is no need to 'establish' differential aging. It follows from the fact that every worldline has its own invariant proper time.

If time dilation is just the 'apparent, or coordinate-dependent' effect, what use is it anyway, since it must be symmetrical between two bodies? As you mention, it is not 'physical', meaning it is an 'apparent' effect depending on 'where you observe it from' - analogous to 'parallax error'. Both are very readily understandable and correctable using Newtonian mechanics and common sense. It would appear using Doppler effect even in Newtonian mechanics.

Now you're agreeing with me and contradicting yourself.

"Differential aging" or "relative time dilation" is the real essense of relativity theory, in my opinion. I don't understand why people make such a big fuss about separating "time dilation" and "differential aging". When Einstein talked about "time dilation" he was clearly talking about "differential aging".

Wrong. Einstein called differential aging 'the clock paradox'.

Your thinking is very woolly. Stick to invariants. Time dilation is not an invariant.

 

[PAllen]

The case of a equatorial and polar observer is really a case of twin differential aging not just time dilation because the equatorial observer keeps returning to a fixed point in the polar observer's rest frame. In exchanging signals, the polar observer is effectively getting slightly delayed information about this 'twin' situation. As a result, the accumulated average time difference between polar and equatorial clock is invariant, not observer dependent.

If two observers simply move past each other at some relative speed, each forever considers the others clock to be slow, and other observer's have various different conclusions about which clock is faster.

Note, the non-inertial character of the equatorial clock must be considered (you can't consider them the origin of a coordinate system that can use the Lorentz transform or the Minkowski metric). However, since you are interested in invariant features (exchange of signals with information), you can do the analysis most simply in any inertial frame (e.g. the polar inertial frame). This frame is sufficient for computing any actual observation or measurement made by the equatorial observer. Note also, that a frame in which the Earth was moving at .999c would be almost as simple to use, and would compute identical results for the behavior of exchanged signals and world line proper time information they carry. However, it would differ radically on 'time dilation' applicable to the polar and equatorial clocks.

 

[arindamsinha]

By "fixed to a point on the equator", you mean that there is a point on the equator that is at rest in the frame, right? No such frame can be inertial because it is accelerating, and I see no way to discuss it without considering the acceleration.

@Nugatory - Since in SR there is no preferred frame of reference, what is the 'point on the equator' accelerating w.r.t. to? Einstein does not refer to any acceleration at all in his example. There is a way to discuss it without considering any acceleration - a preferred IRF from which both observers' velocities are measured. The polar point has no velocity in this IRF, the equatorial point does. I believe this is implicit in Einstein's example.

The case of a equatorial and polar observer is really a case of twin differential aging not just time dilation because the equatorial observer keeps returning to a fixed point in the polar observer's rest frame.

@PAllen - Absolutely correct, but w.r.t. what frame is the equatorial observer returning to the same point? We are talking about a single preferred IRF w.r.t. which we are looking at both observers, I think you will agree.

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A lot of discussion in this thread seems to be about differentiating the terminologies of "time dilation" and "differential aging". My understanding is that "time dilation" is just a combination of the classical Doppler effect combined with "differential aging". Would you agree?

 

[Nugatory]

@Nugatory - Since in SR there is no preferred frame of reference, what is the 'point on the equator' accelerating w.r.t. to?

Unlike velocity, acceleration does not have to be defined with respect to something else.

In SR (and GR with a more careful definition of "acceleration") an accelerated frame and a non-inertial frame are the same thing, so if I can observe non-inertial behavior I know that I'm being accelerated - even if there's nothing else around for the acceleration to be relative to. The most natural way to for me at the equator to measure my radial acceleration towards the center of the Earth due to the Earth's rotation is to study the behavior of an object moving in the radial direction; it will move eastward in violation of the law of inertia and I'll know that I'm not in an inertial frame. A sensitive enough accelerometer would also do the trick; and the accelerometer reading is the position of a needle on a scale, and that has to be an invariant fact not relative to anything else.

 

[ghwellsjr]

1) Since the traveling twin's clock is essentially stopped during the trip, it will end up 10 seconds behind the Earth twin's clock when they do the synchronization verification test you described.

But having answered this, it doesn't help me understand what you are saying.

Thanks for taking this up and answering the question.

I was trying to establish that velocity-based differential aging between two bodies (and agreement on the same by both), is not dependent on the moving twin coming back to origin to be 'co-located' with the stationary twin to 'compare clocks'. It can be done at any point during the traveling twin's journey using light-signals.

This is not true. Here is a diagram that depicts a similar situation to the one you proposed except that it uses the same parameters as the one in post #33 but without the moving twin returning:

You are giving preference to this one frame, the Inertial Reference Frame (IRF) in which the "stationary" twin remains inertial. In this IRF, the differential aging after the moving twin comes to mutual rest with the "stationary" twin is 4.5 quarter hours (a little over an hour) with the moving twin younger. But look at this diagram in which the moving twin is inertial during his moving portion of the trip:

Here there is a different criterion for what is simultaneous and now the stationary twin is the one that is younger by slightly over 2 quarter hours (a little over a half hour).

Of course, every IRF will show the same results for whatever light signals are exchanged between the twins, but that is not sufficient to establish unambiguous simultaneity and that's what you have to do to determine differential aging. Differential aging is answering the question, between this coordinate time and that coordinate time, what is the difference in how two observers age? Even if the two observers agree with each other because they implicitly are using their mutual rest IRF, that doesn't mean the question has been answered the same for all other IRF's. The only way for all IRF's to get the same answer is if the two observers are colocated at the first coordinate time and again colocated at the last coordinate time, (not necessarily the same location, not necessarily even at rest in the same IRF nor do the observers even have to be in mutual rest at either time). All this is simply to remove any ambiguity about simultaneity issues at the start and the end of the process.

He does not say that "B could similarly be considered slower by the moving clock A" because A is not at rest in an Inertial Reference Frame (IRF).

You misunderstood me. I said A in 'its own rest frame' (which of course is an IRF as well, and A is at rest in that IRF, in the situation considered). As I said, he didn't deny it, but just that he didn't stress it, and then went on to an example where there is a clearly established stationary and moving frame - which I found very interesting.

The clock moving in a circle is constantly accelerating. If it weren't, it would go in a straight line. It has to accelerate in order to move in a circle. It is not inertial. It cannot be at rest in an IRF. Einstein only considered a single reference frame when discussing the differential tick rate of the two clocks and he did not address the issue of the differential aging.

Subjective. Can you point out exactly what?

You don't have a correct idea of what Time Dilation is nor of what Differential Aging is and I suspect you don't understand Relativistic Doppler

This is a SR situation we are discussing. So, without bringing in GR or acceleration, what prevents us from seeing the polar clock as 'rotating' w.r.t. an IRF fixed to a point on the equator?

I've never brought GR into the discussion but somehow you seem to associate acceleration with GR. I'm not sure you understand what acceleration is. The clock on the equator is accelerating in order to maintain a circular path. You could, if you wanted to (I don't) consider a non-inertial frame in which the equator clock is at rest and in which the pole clock is moving but I don't think you're ready for that.

 

[PAllen]

@PAllen - Absolutely correct, but w.r.t. what frame is the equatorial observer returning to the same point? We are talking about a single preferred IRF w.r.t. which we are looking at both observers, I think you will agree.

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A lot of discussion in this thread seems to be about differentiating the terminologies of "time dilation" and "differential aging". My understanding is that "time dilation" is just a combination of the classical Doppler effect combined with "differential aging". Would you agree?

The 'twin like' feature of the equatorial path is that it has periodic intersections with an inertial space time path that has zero relative velocity compared to the polar observer's (presumed) inertial space time path. This circumstance is true in every coordinate system or reference frame.

You have the concept of time dilation backwards. Differential aging and Doppler are the invariant observables. Time dilation is a feature of the how a particular clock's time relates to coordinate time; it can then be used to compute the invariants: differential aging, clock time between two physically identifiable events, and Doppler.