I Lasting effects of Mass and Distance Dilation

[PeterDonis]

The physics is in the invariants.

Which, btw, gives a simple way to respond to the OP's questions:

There are no invariants that correspond to "time dilation", "mass dilation", "distance dilation", etc. Or, to put it another way, describing an object in a particular state of motion in two different frames does not change any invariants about the object.

In the standard twin paradox scenario, the key invariants are geometric: the lengths along the paths in spacetime that the two twins follow. It's basically just the Minkowski spacetime version of the triangle inequality. There are no invariants anywhere in the problem that correspond to the traveling twin's clock "running slow", or his mass being "increased", or his length being "shortened".

 

[A.T.]

And the correct answer is to tell the OP that it's an outdated concept.

The OP didn't ask whether the concept is outdated. So it's not an answer to the OP's question.

But the congruence of worldlines that describes the rope ...

Neither of these are explanations. They're descriptions.

So is the congruence of worldlines, as you write above. Explanations are based on descriptions.

Your preferred explanations might sound great and elegant to you. But to many people asking about this, they are just completely abstract, and don't easily to translate into physical quantities they know and understand.

 

[PeterDonis]

The OP didn't ask whether the concept is outdated.

So what? It is. The OP evidently didn't know that. Now they do.

they are just completely abstract, and don't easily to translate into physical quantities they know and understand

I already gave the direct physical meaning of the expansion scalar: it's the invariant that corresponds to the rope being stretched. That's a physical quantity that should be easy to understand.

 

[Jkreider48]

Every time I think I get it; I don't get it. Let me first see if I understand this now and, if I do, then I'll have another question.

The time dilation equations attributed to Special Relativity are merely a phenomenon of the "at rest" observer of something moving at great velocity. They have nothing to do or say about what's happen to those doing the moving. The fact that the travel, once returning to "at rest" shows less aging is because of dilations (for the lack of whatever might be the proper term) cause by phenomenons described in General Relativity.
True?

 

[PeroK]

Every time I think I get it; I don't get it. Let me first see if I understand this now and, if I do, then I'll have another question.

The time dilation equations attributed to Special Relativity are merely a phenomenon of the "at rest" observer of something moving at great velocity. They have nothing to do or say about what's happen to those doing the moving. The fact that the travel, once returning to "at rest" shows less aging is because of dilations (for the lack of whatever might be the proper term) cause by phenomenons described in General Relativity.
True?

Velocity is relative. There is no concept of being absolutely at rest or absolutely moving at great velocity.

Velocity based time dilation is symmetric.

Differential ageing is fundamentally different from time dilation.

I said all that 30 posts ago, but it's worth repeating.

 

[Jkreider48]

No offence, PeroK, but you seem to me to be ignoring my question. Let me try to be more precise.

In the situation where person A observes person B moving at great velocity (from person A's perspective), person A needs to use the dilation equations to assess what they, person A, "sees" as the person B's Time passage, mass and length changes. These constructs/formulas/transformations/whathaveyou, came out of special relativity. True?

The fact that when Person B returns to Person A, that Person B will have experienced that less time has passed, than Person A experienced while Person B was traveling. True?

If so, is this phenomenon due to attributes described in General Relativity?

 

[PeterDonis]

In the situation where person A observes person B moving at great velocity (from person A's perspective), person A needs to use the dilation equations to assess what they, person A, "sees" as the person B's Time passage, mass and length changes. These constructs/formulas/transformations/whathaveyou, came out of special relativity. True?

No, not true. If person A and person B are spatially separated, there is no physically meaningful way of saying "what time it is" for either person "as seen by" the other. All such constructs are coordinate dependent and have no physical meaning. Ignore them. Forget them.

The fact that when Person B returns to Person A, that Person B will have experienced that less time has passed, than Person A experienced while Person B was traveling. True?

True, if by "less time has passed", you mean "less time elapsed on Person B's clock when they meet again, as compared to Person A's clock".

If so, is this phenomenon due to attributes described in General Relativity?

It's due to the different lengths of the paths the two people take through spacetime. I've said that repeatedly.

 

[Ibix]

In the situation where person A observes person B moving at great velocity (from person A's perspective), person A needs to use the dilation equations to assess what they, person A, "sees" as the person B's Time passage, mass and length changes. These constructs/formulas/transformations/whathaveyou, came out of special relativity. True?

Imagine a long straight road with markers every 100m. Imagine another long straight road with markers every 100m that crosses the first at a slight angle. Walk past the crossing to the next marker and look at the other road. Its equivalent marker will be behind you (level with $100\cos(\theta)$, in fact, if $\theta$ is the angle between the roads). Go to the next marker and look again - the equivalent marker will be even further behind you.

Now go back to the crossing and go up the other road to the first marker and look at the original road. Again, its equivalent marker will be level with somewhere behind you. And the same if you proceed to the next marker. So, from both roads, the markers on the other road are early. This phenomenon, in spacetime instead of space, is the root of time dilation. It's symmetric, and it depends entirely on the fact that the two roads imply different ideas of how to measure "level with me" - or in spacetime, observers in relative motion have different ideas how to measure "at the same time".

Thinking of the roads again, imagine one road turns and heads back towards the other. As you walk along it you'll still see that you pass more markers on the other road, and that will be true on both roads. But when you get to the second crossing, you'll find that how far you walked depends which road was taken. There's no ambiguity. That phenomenon is the basis of differential aging.

When thinking about spacetime, you measure elapsed time along a path through ot, not distance. And the rules of geometry it obeys mean that the straight path is the longer distance. But apart from those things, the analogy between the roads and the twin paradox is very, very close.

 

[PeroK]

If so, is this phenomenon due to attributes described in General Relativity?

General Relativity describes curved spacetime. I.e. gravity.

Nothing in this thread requires GR to be explained.

In fact, if you study GR then velocity-based time dilation, length contraction and relativistic mass don't feature.

 

[Nugatory]

The fact that the travel, once returning to "at rest" shows less aging is because of dilations (for the lack of whatever might be the proper term) cause by phenomenons described in General Relativity.

No. There are no “dilations” involved (and also no general relativivity, this all special relativity stuff). The traveler’s clock advances at the rate of one second per second, just like a car’s odometer counts off one mile for every mile the car the car drives. Both the odometer and the clock have a “memory” because they’re counting the miles and seconds; we can look at them and see how many they’ve counted since we last looked.

Time dilation is a different phenomenon, a consequence of relativity of simultaneity. We have two clocks A and B, moving relative to one another. As they pass one another, we set them both to 12:00 noon. Then someone at rest relative to clock A and watching clock B through a telescope calculates that at the same time that clock A read 1:00 clock B read 12:30 (note that this is a calculation - we have to allow for light travel time between B and our telescope). Thus clock B is running slow by a factor of two.
Meanwhile, someone at rest relative to clock B and watching clock A through their telescope calculates that at the same time B read 12:30, clock A read 12:15; that is, clock A is the one that is running slow.

So: they disagree about what clock A reads at the same time that clock B read 12:30. This is relativity of simultaneity, and it is how they both find that the other clock is dilated. Time dilation has nothing to do with the actual tick rates of the clocks (which are tautologically one second per second), it’s all about how we define “at the same time”.

(If you are not already comfortable with the relativity of simultaneity, spend some time understanding it. It is a critical piece of special relativity, without which you cannot make sense of time dilation and length contraction)

 

[Nugatory]

If so, is this phenomenon due to attributes described in General Relativity?

No, it’s all Special Relativity.
And it all requires relativity of simultaneity to make sense of it. My previous post was about how time dilation is a manifestation of RoS, and similar arguments apply to length contraction: the length of something is the distance between where its endpoints are at the same time. Relativistic mass increase (which you would be well-advised to unlearn - we figured out a half century ago that it’s a bad way of explaining the relationship between force and acceleration for objects in relative motion) is that way too, but it’s easier to advise you to unlearn it than to go through the complete explanation and then tell you to forget the whole concept.

 

[A.T.]

... that Person B will have experienced that less time has passed, than Person A experienced while Person B was traveling. True?

Yes it's true.

If so, is this phenomenon due to attributes described in General Relativity?

If you want to describe the whole process continuously from B's perspective, you have to use non-inertial coordinates, where resting clocks at different locations tick at different rates. There are different ways to define such coordinates and the analysis is more difficult. That's why you see responses trying to steer you away from that, and seemingly dodging the question. Whether you see this type of analysis as part of SR or GR doesn't really matter.

 

[Jkreider48]

Thank you.

 

[Herman Trivilino]

BUT there IS evidence of the time dilation upon his return.

There is evidence of the effects of time dilation, but time dilation itself only occurs when there is relative motion. There is also evidence of the effects of the relativity of simultaneity. You are ignoring the relativity of simultaneity in your analysis of the twin paradox, which is precisely why it's called a paradox. Once you account for the relativity of simultaneity the paradox is resolved.

If you sketch up the spacetime diagram of the situation you can see all this, and then understand that geometrically the difference in their ages is due to the fact that they took different paths through spacetime.

It would be a far more efficient use of your time and energy to study the analysis of the twin paradox from the sources already mentioned by others: https://www.physicsforums.com/insights/when-discussing-the-twin-paradox-read-this-first/

 

[Jkreider48]

Thank you (all) for your assistance on this issue. The purpose my current interest is that I'm writing an article for a few people that expressed interest in this, but they are much more "science challenged" than I am. I'm not trying to get a degree in astro-physics. I wrote something I called, "The Cosmos in a Nutshell" back in the 90s.
My nephew asked me if I still had the article I wrote for him back then. I didn't, so I told him I'd rewrite it.

However, there is a proverbial "S**T load" of stuff that's been discovered, confirmed or modified since then. I didn't talk about Relativity last time, but it seems important now, hence, the question. Between all of you (and a boost from ChatGPT), I've been able to get a broad enough picture that I expect can be watered down enough so my nephew doesn't freak out when he reads it. The plan, with this piece of information and others, is to hit it very broadly about what appears to happen and leave a more detailed discussion (including some of the math) for the appendix. I was having trouble with what, actually, constituted "broadly". It's been 45 years since I pushed my pencil through an "Intergration" and so the math slowed me down quite a bit.

Anyway, thank you all for your help.

 

[Nugatory]

(and a boost from ChatGPT)

Be very cautious about accepting help from ChatGPT. It is designed to arrange words in plausible-sounding ways that resemble how they're arranged elsewhere on the internet, not in correct statements.

For example, last time I asked "How does the twin paradox show time dilation?" it's answer looked convincing but was completely wrong.

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