I Lasting effects of Mass and Distance Dilation

[Jkreider48]

We know that time dilation is "real" in the sense that a subject at relativistic speeds or gravitational changes are measurable even when the subject returns to an "at rest" state. But are there lasting effects with mass and distance dilation under the same circumstances?

 

[Ibix]

This is something of a misapprehension. The difference between a clock and a ruler is that the clock has a memory. The tick rates of two clocks are identical if they are at rest, but if one has moved away and returned then it may have accumulated less time.

The analogous situation in terms of distance is laying out a tape measure straight and another with kinks in it, so it runs parallel to the first for a while, then leads away and back before running parallel again. The distance measures before the kinks might well match. The ones after the kink will be evenly and equally spaced, but the will not match up.

 

[Jkreider48]

Thank you, but I'm not sure I understand what you're saying. I'm envisioning twins, identical weight, shape, etc. Both have a rule of the same weight and length. One stays home, the other goes on a trip at relativistic speeds and returns. I already know when the traveler twin returns home, he's younger than his brother. But are there any telltale signs of mass or distance dilation upon returning? Are the two rulers the same weight and length?

 

[Ibix]

Are the two rulers the same weight and length?

Yes, and their clocks tick at the same rate. It's only because the clocks have memory (their accumulated count) that there is a difference you can see after the return.

You get the same effect with distance measurement if you set up a situation where one end of the tape measure "remembers" that the middle parts of the tape measures weren't parallel. In fact, apart from switching the $x$ and $t$ for $x$ and $y$ so the sign of the squared interval is opposite, the maths is identical.

 

[Jkreider48]

I get it that when traveling at relativistic speeds lengths and masses will dilate. Upon return, however, there is no longer any dilation. For time, the returnee is younger than his twin. Is there any such indication that the returned twin had experienced dilation of mass or length?

 

[Ibix]

In modern terminology, mass means the invariant mass, which doesn't change. Relativistic mass changes, but outside popsci nobody has used that term for decades. It caused too much confusion.

If you can devise a distance measurement that remembers its history then you can in principle show some evidence. For example, if you did the twin paradox in a car the odometer would show less distance travelled than the milage according to the map (by about two parts in $10^{14}$ for highway speeds). Again, this is an effect of a device with a memory, not a lingering effect of relativistic travel.

 

[berkeman]

But are there lasting effects with mass and distance dilation under the same circumstances?

But are there any telltale signs of mass or distance dilation upon returning? Are the two rulers the same weight and length?

Is there any such indication that the returned twin had experienced dilation of mass or length?

Echo Echo Echo Echo Echo

 

[Jkreider48]

In modern terminology, mass means the invariant mass, which doesn't change. Relativistic mass changes, but outside popsci nobody has used that term for decades. It caused too much confusion.

If you can devise a distance measurement that remembers its history then you can in principle show some evidence. For example, if you did the twin paradox in a car the odometer would show less distance travelled than the milage according to the map (by about two parts in $10^{14}$ for highway speeds). Again, this is an effect of a device with a memory, not a lingering effect of relativistic travel.

Great! That's what I was looking for. Thank you for your time (and patience).

 

[PeroK]

I get it that when traveling at relativistic speeds lengths and masses will dilate.

Note there is no such thing as "travelling at relativistic speed". All inertial motion is relative. Velocity-based time dilation and length contraction are fully symmetric. If you measure a moving clock to be dilated and its length contracted, then an observer at rest relative to the clock will measure your time to be dilated and you to be length contracted in the direction of your relative motion.

Moreover, relativistic mass is generally not used in modern physics. If we do allow the concept, then likewise your mass will increase as measured by an observer moving relative to you. Which shows that relative motion cannot change your mass.

 

[PeterDonis]

when traveling at relativistic speeds lengths and masses will dilate.

No, this is not correct.

Here is what is correct: if an object is moving at relativistic speeds relative to you, then it will seem to you that its clock runs slow, its length is contracted, and its mass is increased (there are caveats to both of these statements, somewhat more to the latter, but those can be ignored for this discussion). But to the object itself, nothing changes; its clock ticks at one second per second, its length and mass are the same.

In the case of the twins, the reason one is younger than the other when they meet again has nothing to do with any change in the twins themselves; it has to do purely with the fact that they take two different paths through spacetime that have different lengths. Their clocks each record the "distance traveled" along their paths through spacetime, just as a car's odometer records the distance traveled along the car's path through space. Two clocks that take different paths through spacetime of different lengths between the same two events (the clocks carried by the twins) will record different elapsed times ("distances through spacetime") just as the odometers of two cars that take different paths through space between the same two places (say two different routes from New York to Los Angeles) will record different distances traveled. The cars themselves don't change; it's not that one's odometer "runs slower" than the other. It's entirely a matter of geometry: the lengths of the paths traveled.

 

[Jkreider48]

Okay, I get that. But, as I understand it, the twin that returns to his at rest, observer brother and IS now younger of the two twins. This is a real, tangible, lasting attribute (for the lack of a better word) of a person that traveled at high velocity to include near light speed. However, the observer also measured his mass and length as dilated (per the Lorentz transformation equations) while his twin was traveling and witnesses those attributes return to normal as he slows, stops and comes to reunite with him. There is no evidence of the change in mass and lengths that the observer saw during the flight. No shortened ruler, no stretch marks, no stressed-out bones. BUT there IS evidence of the time dilation upon his return. This is what I'm trying to be clear on. Time dilation not only appears to happen, it actually did happen and, as "ibix" said early, "the clock has a memory" but length and mass don't.

Maybe it's semantics or my lack of the contemporary vernacular or something, but I think my question is answered, though we seem to have taken the long way around the barn to get there. Thank you to all who contributed to help me be clear on this.

 

[PeterDonis]

as I understand it, the twin that returns to his at rest, observer brother and IS now younger of the two twins.

That's true.

This is a real, tangible, lasting attribute

Yes, but it's due to the different paths through spacetime that the twins travel, not to any change in one twin vs. the other. Just as, when two cars take different routes between two points, their odometers registering different mileage traveled is not a change in the odometers; it's just a difference in the path lengths.

the observer also measured his mass and length as dilated

Nobody observes their own mass, length, or clock tick rate to change.

there IS evidence of the time dilation upon his return.

No. The evidence is not of "time dilation". It's of differential aging--different path lengths through spacetime. It is not evidence that anything changed about the traveling twin's clock. It is only evidence that that clock followed a shorter path through spacetime than the stay at home twin's clock.

Please think carefully about this in the light of the odometer analogy I gave. If two cars take different routes between two points, and their odometers register different mileage, nobody attributes that to one odometer being "dilated" with respect to the other. Both odometers register one mile per mile traveled. They just traveled a different number of miles because of the different routes.

 

[PeterDonis]

Maybe it's semantics or my lack of the contemporary vernacular or something, but I think my question is answered

I'm not sure you are correctly interpreting the answers you've been given. See my post #12.

 

[Jkreider48]

(I'm beginning to think I should change my level from Intermediate to Basic).

What I said, "The observer also measured his mass and length..." was badly worded, by "his" I meant his brother's (the observed twin) mass and length.

there IS evidence of the time dilation upon his return.

And you said:
No. The evidence is not of "time dilation". It's of differential aging--different path lengths through spacetime.
-----
Isn't this just semantics? Isn't the amount of differential aging the same as would be indicated by the time dilation equation?

 

[PeroK]

(I'm beginning to think I should change my level from Intermediate to Basic).

What I said, "The observer also measured his mass and length..." was badly worded, by "his" I meant his brother's (the observed twin) mass and length.


And you said:
No. The evidence is not of "time dilation". It's of differential aging--different path lengths through spacetime.
-----
Isn't this just semantics? Isn't the amount of differential aging the same as would be indicated by the time dilation equation?

It's not semantics. Imagine that both twins go on symmetrical journeys in opposite directions. When they return to Earth they are the same age. Yet, each has measured the other as time dilated throughout the journey.

 

[Jkreider48]

I get that, but it is not my point. In your example, of course there's no differential, but, ah hah, when they return to Earth, they meet for the first time their long lost, forgotten, brother, who, as it happens is their triplet brother and now this triplet brother is older than the traveling "twins". Older by just the amount the at rest triplet measured while they were gone and as each of the traveling twins measure on their own clocks. True?

 

[PeroK]

I get that, but it is not my point. In your example, of course there's no differential, but, ah hah, when they return to Earth, they meet for the first time their long lost, forgotten, brother, who, as it happens is their triplet brother and now this triplet brother is older than the traveling "twins". Older by just the amount the at rest triplet measured while they were gone and as each of the traveling twins measure on their own clocks. True?

You'll need to explain why time dilation doesn't always lead to differential ageing.

Okay, sometimes you can use the time dilation formula to calculate the amount of differential ageing.

The twin paradox, in fact, questions why one twin is younger given the reciprocity of time dilation. And it's not because one twin is "really" moving.

 

[Ibix]

I get that, but it is not my point. In your example, of course there's no differential, but, ah hah, when they return to Earth, they meet for the first time their long lost, forgotten, brother, who, as it happens is their triplet brother and now this triplet brother is older than the traveling "twins".

It's not exactly a coincidence, but it's a special case where pretending that time dilation and differential aging are the same thing works. The point of the twin paradox is to point out that the travelling twin sees the stay-at-home twin as fast moving, so measures the stay-at-home's clocks ticking slowly due to time dilation - but that reasoning fails for him because the stay-at-home ends up older.

 

[pervect]

We know that time dilation is "real" in the sense that a subject at relativistic speeds or gravitational changes are measurable even when the subject returns to an "at rest" state. But are there lasting effects with mass and distance dilation under the same circumstances?

The way I prefer to talk about the undeniable "real" aspects of time dilation is to talk about differential aging. For instance, if a twin travels around the galaxy at relativistic speeds and then returns, they will have aged less. So, one can argue about the "reality" of time dilation, because it's talking about quantities that are not observer independent, but one can't make the same argument about differential aging. Differential aging means, literally, that one twin in the twin paradox ages less - they age differently. This statement is always true regardless of any human choices of "reference frame".

The status of "time dilation" is much less clear. The term "real" gets overloaded a bit, so rather than saying time dilation is "not real", I will say that the concept is observer dependent, as one needs to specify an observer to even talk about "time dilation".

I have not seen it discussed much, but I suppose one could do something roughly similar with distance, in that the total distance measured by the travelling twin is shorter, to correspond with his shorter elapsed time. But it's not a very good analogy though - there is an important difference. Proper time is an invariant quantity that does not depend on the observer, as I noted earlier. But the sort of distance I was talking about above is not "proper distance", it is an observer dependent quantity that requires one to specify a frame of reference, not an entity that exists independent of the human choice of reference frames.

There is a notion of proper distance similar to the notion of proper time, by the way - and the answer is different if one uses it.

I hope this is of some help.

 

[PeterDonis]

Isn't this just semantics?

No.

Isn't the amount of differential aging the same as would be indicated by the time dilation equation?

In the particular idealized special case you are talking about, you can indeed use a simple "time dilation equation" to calculate the differential aging.

But that is a particular idealized special case. It doesn't generalize. Also, the "time dilation equation" is coordinate dependent, whereas differential aging is not; it's invariant.

Consider again the odometer analogy. If you have a simple scenario where twin A drives his car along a straight line from point A to point B, while twin B travels along the two equal length sides of an isosceles triangle with line AB as its base and point C as its apex, you can write down a "odometer dilation" equation that will let you calculate how many more miles twin B's odometer will register. (Here twin B, the "traveling twin", covers more miles instead of less because the geometry of space is Euclidean, whereas the geometry of spacetime is Minkowskian.) But such an equation would only apply to that special case and would not generalize, and nobody would think that this "odometer dilation" reflected anything real about the respective odometers of twin A and twin B. It's just a property of the geometry involved.

See this article for more on the general spacetime geometry viewpoint:

https://www.physicsforums.com/threads/when-discussing-the-twin-paradox-read-this-first.1048697/

 

[jbriggs444]

Isn't this just semantics? Isn't the amount of differential aging the same as would be indicated by the time dilation equation?

No. It is not just semantics. Differential aging and time dilation are different things. Related, as you note, but different.

Differential aging refers to the accumulated discrepancy in two clock readings. Importantly, the two clocks must start and end co-located. Or at least nearby -- if we want to consider things like orbiting clocks.

Time dilation refers to the instantaneous rate discrepancy between the two clock readings. Importantly, a simultaneity convention must be used to decide what clock reading over here corresponds to that clock reading over there. The two twins do not share a single natural simultaneity convention.

Differential aging is an invariant effect. All frames of reference will agree on what the two clocks should read upon being re-united.

Time dilation is a coordinate-relative effect. Various inertial frames of reference will disagree about which twin is time dilated and when.

 

[Nugatory]

Isn't this just semantics? Isn't the amount of differential aging the same as would be indicated by the time dilation equation?

No. They are different and unrelated phenomena.

To see this, consider that at every moment of the entire journey the traveling twin considers themselves to be at rest while the earth twin is moving; therefore the earth twin's time is dilated, the earth twin's clock runs slower; and the earth twin is expected to be younger at the reunion. But the earth twin considers themselves to be at rest while the traveler is moving; therefore it is the traveler whose time is dilated and ought to be younger at the reunion. And this is what makes the Twin Paradox a "paradox" - we have two seemingly equally valid arguments leading to contradictory conclusions.

All relativity "paradoxes" are the result of misapplying/misunderstanding some aspect of the theory, and in this case the mistake is thinking that we're dealing with a time dilation effect. We aren't. The difference in the twins' ages at reunion is unrelated to the time dilation that says that they both find that the other's clock is running slow throughout the trip.

This would be a good time for you to take a look at the sticky at the top of the forum - the section on the "time gap" analysis shows how symmetrical time dilation is consistent with differential aging but does not cause it.

 

[Jkreider48]

Ah HA. Thank you.

 

[A.T.]

But are there lasting effects with mass and distance dilation under the same circumstances?

- If you compress a spring, it will be permanently more massive.

- If you accelerate a rope, while preventing it from contracting, it will break and remain broken.

 

[PeterDonis]

- If you compress a spring, it will be permanently more massive

This doesn't have anything to do with what the OP is calling "mass dilation". The OP is talking about "relativistic mass", which is a coordinate effect (and not a good way to understand mass). What you are talking about here is an increase in the invariant mass of the spring. Not the same thing.

- If you accelerate a rope, while preventing it from contracting, it will break and remain broken.

This is also not the same as what the OP is talking about. What you are doing here is stretching the rope, by forcing all of its parts to have exactly the same proper acceleration. This is an invariant effect (the expansion tensor of the congruence of worldlines that describes the rope's motion is positive), and is not the same as length contraction (which is a coordinate effect).

 

[A.T.]

The OP is talking about "relativistic mass", which is a coordinate effect (and not a good way to understand mass). What you are talking about here is an increase in the invariant mass of the spring. Not the same thing.

The increase in "relativistic mass" during acceleration is due to the energy that is added to the object. If all the energy for acceleration is stored on board from the start (like in a spring powered toy car), there is no increase of "relativistic mass" during acceleration.

What you are doing here is stretching the rope,

In its initial rest frame the rope isn't being stretched, it keeps a constant total length. Yet it breaks, in that frame too. And the explanation in that frame is that the fields that keep the rope together are contracting.

 

[PeterDonis]

The increase in "relativistic mass" during acceleration is due to the energy that is added to the object.

Please don't confuse the OP any further than they already are. Relativistic mass is an outdated concept and should not be used. An accelerating object does not have to have any "energy added" in the sense of increasing its invariant mass; indeed, in the most common case, a rocket, its invariant mass decreases as it accelerates.

Yes, in the object's initial rest frame, its energy increases. But that's frame dependent, and one of the central lessons of relativity is that frame-dependent quantities have no physical meaning. The physics is in the invariants. So that's what should be focused on.

If all the energy for acceleration is stored on board from the start (like in a spring powered toy car), there is no increase of "relativistic mass" during acceleration.

Again, "relativistic mass" is an outdated concept. Please don't confuse the OP further.

In its initial rest frame the rope isn't being stretched, it keeps a constant total length. Yet it breaks, in that frame too.

Frame-dependent quantities have no physical meaning. The physics is in the invariants. The relevant invariant in this case is the positive expansion scalar of the congruence of worldlines that describes the rope. That is the invariant that says that the rope is "stretched", and it is the same in every frame, since it's an invariant.

And the explanation in that frame is that the fields that keep the rope together are contracting.

And the problem with this "explanation" is that it doesn't explain why the rope itself doesn't contract as well, since the fields that keep it together are contracting.

Frame dependent "explanations" always run into problems like this, because, as I've said, frame-dependent quantities have no physical meaning. Plus, having to switch explanations if you switch frames denies the principle of relativity, which is that the laws of physics are the same in all frames. The same laws should lead to the same explanations.

 

[A.T.]

Again, "relativistic mass" is an outdated concept.

Sure but so what? The OP asked about it.

And the problem with this "explanation" is that it doesn't explain why the rope itself doesn't contract as well, since the fields that keep it together are contracting.

Its ends are kept at constant distance in the initial rest frame. That's a boundary condition.

Plus, having to switch explanations if you switch frames denies the principle of relativity,

When two space ships collide, each of them can claim to have been at rest, while that other one bumped into them, as an explanation for the accident. Frame dependent explanations don't deny the principle of relativity, they follow from it.

 

[PeterDonis]

The OP asked about it.

And the correct answer is to tell the OP that it's an outdated concept.

 

[PeterDonis]

Its ends are kept at constant distance in the initial rest frame. That's a boundary condition.

A frame-dependent one, yes. But the congruence of worldlines that describes the rope can be specified without needing to use any frame-dependent quantities. For example, one could specify the length along a spacelike curve orthogonal to the congruence of worldlines, from the front worldline to the rear one.

When two space ships collide, each of them can claim to have been at rest, while that other one bumped into them, as an explanation for the accident.

Neither of these are explanations. They're descriptions. Frame dependent descriptions are often a crutch that people find they need to use; but they don't explain anything.

The explanation of whatever actual physical changes happen to the ships in the collision--dents, breaking of the hulls, etc--will involve invariants.