Time dilation why or how, Special Relativity causes

[PeterDonis]

I mean that I've never seen a statement whereby the measure S of a space-time interval varies depending on the path followed end-to-end, I've never seen a statement whereby what a clock measures is nothing else than S along a definite path. These are things you don't find in presentations of SR easily accessible by non-physicists.

Ah, I see. Yes, pop science or layman's presentations of SR (like pop science or layman's presentations of science in general) don't take the same care as textbooks or scientific papers do. That's why you shouldn't try to learn a science from pop science or layman's presentations. Textbooks on SR, at least the ones I'm familiar with, do address these points.

In the Newtonian context, there is no doubt that what a clock measures relates to an interval alongside the time axis.

No, this is not correct. In Newtonian physics, clocks measure absolute time, which is not linked to the "time axis" of any inertial frame. (It can't be, because the "time axes" of different inertial frames are different, but absolute time is the same in all of them.) It appears that your confusion about terminology in SR arises from a confusion about terminology in Newtonian physics.

The semantics of “time interval” points to an interval alongside the time axis

No, it doesn't. See above.

As a further point, the semantics of "time interval", or any such term involving "time", has to change when you go from Newtonian physics to SR, because SR does not have absolute time. So your general argument that we should adjust the semantics of terms like "time interval" so they match the Newtonian semantics is not valid, because it can't be done.

 

[Sugdub]

And it should not, because that is by definition what a clock does. ... Again you have it backwards, the "fault" here if there is one is not in calling what the clock measures "time", but calling the time axis "time".

Excellent. I'm ready to follow whichever representation system provided it is internally consistent. According to your suggestion, clocks will be said measuring “time” intervals and thus the twins will effectively "age" differently. Clocks will follow geodesic lines in a 4-dimensions manifold, its geometrical structure (curvature) being dependent on the prevailing physical conditions, and this will in turn determine the coordinate axes (curved lines).

However “time dilation” will need re-naming since it won't deal any longer with a “time” interval and the coordinates of today's “space-time” which will no longer be called “space” and “time”. That's fine with me. For what concerns this specific thread, I found today's language being inconsistent because the terms "time dilation" and "proper time" can't both refer to a time interval. Also the path followed by the clock did not coincide with the "time" coordinate axis. Again the maths are correct but the language used by physicists was so far inconsistent.
Should the above be acceptable by physicists, I think it positively resolves my long-lasting discrepancy. Thanks a lot.

 

[PeterDonis]

Clocks will follow geodesic lines in a 4-dimensions manifold

No. Clocks can follow any timelike worldline. There is no requirement that it be a geodesic. The traveling twin's clock in the twin paradox follows a non-geodesic worldline.

geometrical structure (curvature) being dependent on the prevailing physical conditions

Yes, if by "prevailing physical conditions" you mean "the stress-energy tensor".

this will in turn determine the coordinate axes

No. Coordinates are an arbitrary choice; there is no requirement that a particular set of coordinate axes must be chosen.

“time dilation” will need re-naming since it won't deal any longer with a “time” interval and the coordinates of today's “space-time” which will no longer be called “space” and “time”.

I don't understand how you're getting any of this out of what we've been saying. Your understanding of how the terms "time" and "space" are used is incorrect, and we've been telling you so for many posts now. In the particular passage you quoted, Orodruin was not saying that the "time axis" of a coordinate chart is not a "time" coordinate; he was saying that coordinates are an arbitrary choice, so you should stop fixating on the "time axis" of an arbitrarily chosen coordinate chart, and start thinking about actual observables, like what a clock reads as it follows a particular timelike curve.

I found today's language being inconsistent because the terms "time dilation" and "proper time" can't both refer to a time interval.

No, you found it inconsistent because your understanding of it is incorrect.

the path followed by the clock did not coincide with the "time" coordinate axis.

So what? Coordinates are an arbitrary choice.

the maths are correct but the language used by physicists was so far inconsistent.

No, your understanding of the language is incorrect.

Should the above be acceptable by physicists

Not likely since it's based on an incorrect understanding of the issues involved.

 

[nitsuj]

... I think it is misleading to claim that a clock measures a time interval. I'm the only one defending this, so far.

In turn do you find it misleading to claim a ruler measures length? In other words do you find your perspective makes sense when seen from the perspective of length?

 

[Dale]

Where has it been explained that a clock measures amounts of the S quantity, i.e. amounts of “space-time”? I can't remember any presentation of SR, any lecture heading in this direction.

It is in any mainstream SR or GR textbook, it is even in the Wikipedia entry on proper time.

For me the wording “proper time” is not only highly misleading, it is symptomatic of a misconception about what gets actually measured: why did physicists introduce this wording whereas “space-time” was already available and fully appropriate?

All proper times are spacetime intervals, but not all spacetime intervals are proper time. Proper time is the spacetime interval along a purely timelike world line. There are spacelike, null, and mixed worldlines also.

Complaining about bad terminology is fruitless. Even widespread disagreement with a term can be insufficient, for example"relativistic mass". If all the top scientists can't get rid of "relativistic mass" then you are not going to be able to get rid of "proper time". Besides, it is a useful term, with a more specific meaning than just spacetime interval.

Subtracting S' from S is certainly possible, but this so-called “difference in ageing” can in no way be considered as a difference in the age of the twins.

Of course it can. The human body can be used as a clock. Not a very accurate clock, but a clock nonetheless.

 

[Dale]

I referred to “a pair of time-like physical events”. This is certainly not correct: “time-like” relates to the pair, not to individual events. So a better wording would be “a time-like pair of physical events”, with “time-like” indicating that there exists an inertial frame of reference in which the physical events at stake are represented as being co-located. Hopefully this is what you call a “timelike path” and the following statement will be backed-up: “ A clock delivers an invariant measure of the space-time interval along a path connecting a time-like pair of physical events”. Please let me know.

The correct wording is "a pair of timelike separated events", but I understood what you meant to begin with so I didn't make a big deal of it. It is the separation that is timelike, the events are just events. Timelike separated events have a timelike path which connects them, and a timelike path is a path whose tangent vector is timelike at all events along the path.

I would not use the description in terms of inertial frames since there may not be a global inertial frame at all if you are dealing with GR. However, if you are in flat spacetime and if you have a pair of timelike separated events using the general definition, then your definition follows.

Yes, a clock measures the spacetime interval along its worldline, and that is invariant.

Let's now come back to my post #53 and consider the “ageing” of the twins along their respective journeys. There is absolutely no doubt that the word “ageing” has been chosen because it designates what we usually consider being an increase in the age of the twins, hence a “time” interval. Now we must acknowledge that “ageing” actually designates an increase in S, an amount of space-time, the measure of a space-time interval.

Yes.

Subtracting S' from S is certainly possible, but this so-called “difference in ageing” can in no way be considered as a difference in the age of the twins.

Sure it can. Both S' and S are invariant numbers, true in any frame, they both represent ages, they have the same units and so forth, so subtracting them is a well-defined operation. If I am 40 and my wife is 37 then everyone I know would consider the difference in our age to be 3 years.

How could that lead to a statement whereby one of the twins comes back “younger” than the other?

The word "younger" means less age.

The only way would be to isolate the “time” components of S and S' respectively and to subtract one from the other

Why would you need to do that. Subtracting the spacetime interval, or proper time is sufficient. No need to take an invariant and break it into components.

... but first, one would need to ascertain that it is physically meaningful to breakdown S and S' onto the same base of the same manifold (I've never seen any consideration about this) and second, one would have to ascertain that the difference between both “time” components is frame-invariant (which I believe is not true: only the difference between S and S' is frame-invariant).

I see no benefit it breaking it into components

Both twins have a different life history life history. A comparison can certainly be drawn, but no objective qualification of the difference can be made in terms of a frame-invariant time interval. So a statement whereby one of the twins comes back “younger” or “ages less” propagates an erroneous conclusion.

What is erroneous? Seems fully justfied to me

However your inputs show that semantic characterisations accounting for a “time” interval are necessarily frame-variant. Therefore I think such expressions should be firmly rejected.

I don't follow either the "semnatic characterisation" or the resulting "firmly rejected"