Is velocity the reason for the time dilation effect?

[PeterDonis]

Calling differential aging a "real" effect and time dilation not a "real" effect means that a "real" effect is caused, explained, and calculated using effects that are not "real".

No, it isn't. You are thinking of it backwards. The invariants are where all the actual physics is contained; and the invariants are also all you actually need to calculate answers. You do not need "time dilation" to either calculate or explain the actual physics.

For example, the explanation of differential aging is simple: different worldlines between the same pair of events can have different lengths. This is no more mysterious than the fact that different routes between two points on Earth can have different lengths. There is no more need to invoke "time dilation" to explain differential aging than there is a need to invoke "distance dilation" to explain why two different roads connecting the same pair of points on Earth have different lengths.

 

[FactChecker]

For example, the explanation of differential aging is simple: different worldlines between the same pair of events can have different lengths.

Ok. We have a differential length. Do the Lorentz transformations give a formula for the differential aging in terms of the differential length?

Another question I have is whether a third IRF would agree that the differential aging has the same value? It seems that if the Earth twin and the traveljng twin agree on a differential age, then a third IRF observer would disagree on the value of the differential aging. Does that complicate the statement that differential aging is frame independent?

 

[PeterDonis]

Do the Lorentz transformations give a formula for the differential aging in terms of the differential length?

You don't use Lorentz transformations to compute the length of a worldline.

whether a third IRF would agree that the differential aging has the same value?

Differential aging is an invariant. It's the same no matter what frame you use--it doesn't even have to be an inertial frame. That's what "invariant" means.

 

[Ibix]

Do the Lorentz transformations give a formula for the differential aging in terms of the differential length?

The "length" of the worldlines is the elapsed time along those worldlines (give or take a factor of $c$). The Lorentz transforms don't really come into it.

Another question I have is whether a third IRF would agree that the differential aging has the same value?

Of course - if the twins zero their clocks when they separate and compare them when they meet again, all frames had better agree what the clocks say, since it's a direct observable.

 

[Dale]

I can understand the importance of distinguishing frame independent effects from frame dependent effects. But one thing bothers me. Calling differential aging a "real" effect and time dilation not a "real" effect means that a "real" effect is caused, explained, and calculated using effects that are not "real". It seems like there could be some better terminology.

Personally, I consider the word “real” to be a philosophical term which is best avoided altogether. (Except as part of the mathematical term “real number”.) One of the main differences between interpretations is what they consider to be “real” and not, so if you avoid the word “real” it will help you to write interpretation-neutral statements

 

[cianfa72]

One of the main differences between interpretations is what they consider to be “real” and not, so if you avoid the word “real” it will help you to write interpretation-neutral statements

See also this thread Is time dilation a real effect?

 

[FactChecker]

You don't use Lorentz transformations to compute the length of a worldline.


Differential aging is an invariant. It's the same no matter what frame you use--it doesn't even have to be an inertial frame. That's what "invariant" means.

Thanks! I see the difference. "Time dilation" is definitely frame dependent. "Differential aging" is a comparison between two proper times, which is not frame dependent. I was too casual (lazy?) to correctly understand the term "differential aging".

 

[Dale]

I like the term “differential aging” as it does clarify the invariant vs frame variant distinction. As far as I know, however, it is a term that is just used here on PF

 

[PeterDonis]

As far as I know, however, it is a term that is just used here on PF

Google turns up a number of papers by one E. Minguzzi which use the term, although it's not clear that their usage is the same as ours here. I have not seen the term in any textbooks or any of the classic papers in the field.

 

[Sagittarius A-Star]

Personally, I consider the word “real” to be a philosophical term which is best avoided altogether. (Except as part of the mathematical term “real number”.)

The adjective "real" can also have the meaning, that time dilation is no accident of convention.

This 'time dilation', like length contraction, is no accident of convention but a real effect. Moving clocks really do go slow. If a standard clock is taken at uniform speed $v$ through an inertial frame $S$ along a straight line from point $A$ to point $B$ and back again to $A$, the elapsed time $T_0$ indicated on the moving clock will be related to the elapsed time $T$ indicated on the clock fixed at $A$ by the Eq. (21) ...

Source:
http://www.scholarpedia.org/article/Special_relativity:_kinematics#Special_relativistic_kinematics

 

[cianfa72]

Isn't the above in post#45 just a restatement of twin paradox or "differential aging" ?

 

[PeterDonis]

The adjective "real" can also have the meaning, that time dilation is no accident of convention.

As has already been pointed out, the term "time dilation" is ambiguous. The Rindler quote is referring to "time dilation" in the sense of what has been called in this thread "differential aging", and which is invariant and does not depend on any choice of convention. But "time dilation" can also be, and usually is, used to refer to a difference in the relationship of proper time to coordinate time, and that depends on your choice of coordinates, which is a convention.

Isn't the above in post#45 just a restatement of twin paradox or "differential aging" ?

Yes. See above.

 

[Ibix]

The adjective "real" can also have the meaning, that time dilation is no accident of convention.

Sabine Hossenfelder used this convention in her (rather poor) "I explain relativity" video. I had no idea it had been used by Rindler. I have to say I don't like it. "Time dilation" and "real time dilation" seems to me like "mass" and "relativistic mass" - an obvious source of confusion.

 

[Sagittarius A-Star]

Isn't the above in post#45 just a restatement of twin paradox or "differential aging" ?

Yes. But Rindler uses the twin paradox as argument, that time dilation in general is no accident of convention.

 

[Sagittarius A-Star]

But "time dilation" can also be, and usually is, used to refer to a difference in the relationship of proper time to coordinate time, and that depends on your choice of coordinates, which is a convention.

In this case it's magnitude depends on a convention, but not it's existence at certain velocities.

 

[Sagittarius A-Star]

Sabine Hossenfelder used this convention in her (rather poor) "I explain relativity" video.

No, she doesn't (see below).

I had no idea it had been used by Rindler. I have to say I don't like it. "Time dilation" and "real time dilation" seems to me like "mass" and "relativistic mass" - an obvious source of confusion.

Rindler didn't distinguish between "Time dilation" and "real time dilation". He wrote that time dilation is a real effect.

 

[PeterDonis]

Rindler uses the twin paradox as argument, that time dilation in general is no accident of convention.

No, not "time dilation in general"--only "time dilation" by Rindler's definition. Which, as has already been said, is what we in this thread have called "differential aging"--i.e., an invariant. He is not saying that "time dilation" by the other definition (the frame-dependent one) is "no accident of convention".

Rindler didn't distinguish between "Time dilation" and "real time dilation". He wrote that time dilation is a real effect.

Whether RIndler explicitly distinguished the two meanings of the term "time dilation" is irrelevant. He explicitly defined what he meant by the term, and, as above, it is what we are calling "differential aging". That is the only kind of "time dilation" that he claimed was a "real effect".

 

[PeterDonis]

In this case it's magnitude depends on a convention, but not it's existence at certain velocities.

If by this you mean that there will be a difference in time dilation factor between two worldlines in any frame, that is not correct. Given two inertial worldlines in flat spacetime, their time dilation factors will be the same in the inertial frame called the Loedel frame, in which each worldline is moving at the same speed, but in opposite directions. AFAIK it is possible more generally to construct a coordinate chart such that both of a given pair of worldlines, which need not be inertial (and the spacetime need not be flat), will have the same relationship of proper time to coordinate time, but in general the chart will not correspond to an inertial frame.

 

[Sagittarius A-Star]

He is not saying that "time dilation" by the other definition (the frame-dependent one) is "no accident of convention".

He describes in his scenario the differential aging as a two-way time dilation. Logically, the resulting age difference must be the sum of the (frame-dependent) time-dilations in forward and backward direction. Therefore it is not possible to define the clock-synchronization for his reference-frame in such a way, that the (frame-dependent) time-dilations in both directions disappear.

 

[PeterDonis]

He describes in his scenario the differential aging as a two-way time dilation.

No, he uses the term "time dilation" to mean what we are calling "differential aging".

Logically, the resulting age difference must be the sum of the (frame-dependent) time-dilations in forward and backward direction. Therefore it is not possible to define the clock-synchronization for his reference-frame in such a way, that the (frame-dependent) time-dilations in both directions disappear.

Sorry, but at this point you are simply repeating errors. Look up the term "Loedel diagram".

 

[PeterDonis]

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