I Another Time Dilation Question

[InquiringMind]

TL;DR Summary

Twin Paradox Question

I'm confused about something about the Twin Paradox. To keep it simple, let's ignore acceleration and deceleration.

Twin "A" heads for a point in space 5 light years away and returns at near the speed of light, while twin "B" remains on earth. Approximately 10 years passes for Twin "B" for the 10 light year trip. Due to time dilation, time slows down for the traveler Twin "A" so, when he returns, he has not aged as much as earthbound Twin "B". This is where I get lost. Although time is slower for traveler Twin "A", he is still making a 10 light year trip near the speed of light. So why isn't he also 10 years older when he returns, and the same age as his twin?

 

[Nugatory]

So why isn't he also 10 years older when he returns, and the same age as his twin?

That’s what makes it a “paradox”, and the resolution of the paradox is that:
1) it’s easy to misanalyze the problem when we use the time dilation formula without understanding its limitations. That’s what happening here.
2) This isn’t a time dilation problem, so it is more easily understood if you don’t start with the time dilation formula. Instead try the sticky FAQ at the top of this subforum: https://www.physicsforums.com/threads/when-discussing-the-twin-paradox-read-this-first.1048697/
3) As with almost all relativity “paradoxes”, the problem is failing to consider the relativity of simultaneity. In this case, space twin and earth twin disagree about what the earth clock reads before and after the turnaround. The “time gap” section of the FAQ addresses this.

 

[Ibix]

So why isn't he also 10 years older when he returns, and the same age as his twin?

The first key insight in relativity is understanding that "space" and "time" are combined into spacetime, and there isn't One True Way to think of space and time separately anymore. The second is to realise that a clock is to spacetime as an odometer is to space - it measures the "length" of the path it took through spacetime.

With the latter insight, things like the twin paradox are kind of trivial. The twins didn't take the same path through spacetime from departure to return, so why would you expect the "length" of that path (their own measured times) to be equal? The travelling twin just took a shorter path. That is fundamentally why the twins aren't the same age, although there's a bit of maths needed to justify the claim. That extra maths is probably why popular sources often use the "time runs slow for the travelling twin" explanation. (The whole point of the twin paradox, by the way, is to demonstrate the shortcomings of that approach, so they then have to do a lot of scurrying around to patch up the problems they were supposed to be learning to avoid...)

But it's the first insight that's directly relevant to your question. No, the traveller has not travelled ten light years by his own measurements. He stayed still and the destination came to him at near the speed of light. Then he accelerated briefly and home came to him at near the speed of light. Explaining in detail exactly how he can interpret this is quite complex (understanding interpretation of observations for observers who acelerate actually lead towards general relativity, which is a whole other ball game of maths requirements). But in each inertial phase he would interpret the distance between home and destination as much, much shorter than 5ly - effectively this is the phenomenon called length contraction. Thus he is unsurprised that his own clocks read less than ten years - the destination wasn't far away to begin with.

 

[Sagittarius A-Star]

So why isn't he also 10 years older when he returns, and the same age as his twin?

That's because an absolute time does not exist. Each twin has his own time, called "proper time". Not the time-interval between the two meeting-events is invariant, but the spacetime-interval between both events.

 

[pervect]

TL;DR Summary: Twin Paradox Question

I'm confused about something about the Twin Paradox. To keep it simple, let's ignore acceleration and deceleration.

Twin "A" heads for a point in space 5 light years away and returns at near the speed of light, while twin "B" remains on earth. Approximately 10 years passes for Twin "B" for the 10 light year trip. Due to time dilation, time slows down for the traveler Twin "A" so, when he returns, he has not aged as much as earthbound Twin "B". This is where I get lost. Although time is slower for traveler Twin "A", he is still making a 10 light year trip near the speed of light. So why isn't he also 10 years older when he returns, and the same age as his twin?

I'm not sure if this observation will help, but the distance from start to destination being five light years in Earth's frame (the frame of twin B) does not imply that the distance from start to destination is five light years in some other frame. Specifically, the distance can be shorter in a moving frame.

Twin A does not have a single frame, a more exact (and tedious) answer would need better descriptions of what frames you are using. I can make a reasonable guess as to what you _might_ be using, but it'd still be a guess.

There are several ways to work out the problem, in terms of "time dilation" style explanations you need to include time dilation, length contraction, and the relativity of simultaneity. Frequently the third part gets lost :(.

You can also chug through the Lorentz transform equations, if you are familiar with them.

There are other approaches as well, such as concentrating on what twin A "sees" during his journey, which can be interpreted as the doppler shift of some beacon broadcasting from the definition. Pick your favorite approach and stick with it, but as far as your specific approaches goes, only taking into account time dilation won't work because you've ignored the other two effects I've mentioned, length contraction and the Relativity of Simultaneity.

 

[Herman Trivilino]

TL;DR Summary: Twin Paradox Question

he is still making a 10 light year trip

No. The distance is ten light years in the rest frame of the staying twin but much less than that in the rest frame of the traveling twin.

Distance is not absolute, it's relative. It only makes sense when you state what frame is being used to make the measurement. There is no such thing as the "true" distance.

 

[DaveC426913]

I'll chime in with a "me too" answer, in case other didn't do it for you.

• Twin A has accelerated to near c (measured relative to his point of departure).
• He observes that he is stationary (by definition) and everything else is rushing toward him, that includes his turnaround target, and everything in between.
• Because everything in his path is moving relativistically, everything he sees is length compressed.
• That includes the distance from his point of departure to his turnaround target.
• From the moment he reaches near c, which might be on Day 1 - he measures his target to be - not 5 light years away but an easy 5 light weeks distant.
• In other words, he doesn't have to travel 5 light years out and back - the trip is a very short distance for him - 5 light weeks.
• Thus, when he arrives back home, he has - correctly - aged only 5 weeks.

TL;DR: by moving at a relativistic velocity, Twin A's actual measured journey is length compressed from 5 light years to 5 light weeks. And he correctly only ages 5 weeks during each 5 light week leg of his trip.

Diagrammatically:

 

[phinds]

Due to time dilation, time slows down for the traveler

@InquiringMind, just to be sure you understand ... NO ... time does NOT slow down for the traveler. This is a very common misconception but you are confusing time dilation with differential aging.

Both twins see their clocks ticking at the same one second per second, it's just that, as has already been pointed out, they take different paths through spacetime and so age at the same rate but by differing amounts.

 

[GR86]

I'll chime in with a "me too" answer, in case other didn't do it for you.

• Twin A has accelerated to near c (measured relative to his point of departure).
• He observes that he is stationary (by definition) and everything else is rushing toward him, that includes his turnaround target, and everything in between.
• Because everything in his path is moving relativistically, everything he sees is length compressed.
• That includes the distance from his point of departure to his turnaround target.
• From the moment he reaches near c, which might be on Day 1 - he measures his target to be - not 5 light years away but an easy 5 light weeks distant.
• In other words, he doesn't have to travel 5 light years out and back - the trip is a very short distance for him - 5 light weeks.
• Thus, when he arrives back home, he has - correctly - aged only 5 weeks.

TL;DR: by moving at a relativistic velocity, Twin A's actual measured journey is length compressed from 5 light years to 5 light weeks. And he correctly only ages 5 weeks during each 5 light week leg of his trip.

Diagrammatically:

View attachment 356215

I joined this forum today specifically for questions like this. Correct me if im wrong. Relativity claims that all velocity is relative, meaning there no objective motion. Anything "moving" is only moving in relation to something else, but it works both ways always. This is where the twin paradox seems to be misinterpreted no? The traveling twin doesn't experience time dilation due to velocity, as the earth and the first twin can be said to be moving near the speed of light in relation to the traveling twin.

What's actually happening is the acceleration of the rocket behaves like gravity, distorting time to a greater degree than the gravity on earth, assuming the traveling twin is under more than 1g of force. In fact, if the traveling twin only accelerated at 1g the entire trip, his time would pass at exactly the same rate as the twin on earth. So unless im missing something, why do people insist it's due to "speed" being close the the speed of light? It can't be, as velocity is ALWAYS relative and both objects are said to be in motion. It's only when you introduce acceleration does time dilation become asymmetrical and cause differences in the passage of time between two perspectives.

This has bothered me for a long time. Am i missing something or are people conflating velocity with acceleration?

 

[PeterDonis]

What's actually happening is the acceleration of the rocket behaves like gravity

This is one explanation, but it's limited.

Please read the article linked to in post #2. It has the title it has for a reason. It addresses your question.

 

[GR86]

This is one explanation, but it's limited.

Please read the article linked to in post #2. It has the title it has for a reason. It addresses your question.

So i think i understood the article. It's saying that spacetime geometry suggests it's path distance that cause the asymmetrical passage of time. I assume, meaning as the speed of light is approached, the traveling twin's perspective sees the universe compress and therefore his path is shorter (when comparing relative distances between the two twins), which equates to less passage of time. Im probably butchered that summary but assuming it's correct, that's where i find the inconsistency.

Since velocity is relative, it's not the traveling twin's motion that compresses space by his perspective, it's his acceleration right? If two ships fly past eachother at 300m m/s relatively, both cannot have compression of the universe from their POV. If there is no asymmetrical input, there cannot be asymmetrical output, so to speak. It's only when a difference between the two is presented will the outcome differ, such as each being under differing levels of gravity/acceleration.

I guess what im saying is, it doesn't make sense to suggest the compression of space based solely on velocity since that is relative. Acceleration and gravity fields are not relative, they are asymmetrical, and therefore allow the differences of time dilation proposed in the twin paradox. Am i misunderstanding something or does this make sense?

 

[phinds]

Since velocity is relative, it's not the traveling twin's motion that compresses space by his perspective, it's his acceleration right?

Wrong. The twin paradox does not depend on acceleration. Poke around. There are dozens** of threads that talk about the "paradox" and some of them explain why acceleration is not the issue. Better yet, do as @PeterDonis suggested an read the link that @Nugatory posted in #2.

**EDIT: actually, it's probably hundreds.

 

[Ibix]

So i think i understood the article. It's saying that spacetime geometry suggests it's path distance that cause the asymmetrical passage of time

I don't think you did understand it. The key point is that distance through space and "distance" through spacetime are different things. Distance through space is a relative concept because you can "slice" 4d spacetime into a stack of 3d slices that you could call space at one instant in many different ways. If my slices are at an "angle" to yours then we have different definitions of space, different definitions of being stationary in space, different definitions of distance through space, and different definitions of being at the same instant, and different definitions of the rate of passage of time.

We need to pick a slicing (technically called a foliation) of spacetime to be able to talk about distance and to be able to compare clocks that aren't at the same place. But we don't need to pick a slicing to measure the "distance" along a path through spacetime nor to compare readings of clocks that are in the same place. It turns out that the "distance" along a path through spacetime is the elapsed time on a clock that followed that path.

The whole of the twin paradox is therefore trivial: the twins followed different paths, the "distance" along those paths was different, and therefore they had different elapsed times.


The complexity is in demonstrating that "distance" through spacetime is a meaningful concept distinct from distance through space, that it corresponds to elapsed time on a clock, and dealing with the consequences of the differences between the "distance" through spacetime and distance through space. (Those differences are why I keep putting scare quotes around "distance" - it does have some different properties, which is what makes 4d spacetime different from a 4d space.) Conceptually, though, it's very little different from the idea that you can draw two paths from point A to point B on a piece of paper and the paths need not be the same length. All "why" and "what causes it" questions do turn out to have the same answer in both the space and spacetime cases. So what would you accept as an answer to what causes two different paths on a piece of paper to have different lengths?

 

[GR86]

With the latter insight, things like the twin paradox are kind of trivial. The twins didn't take the same path through spacetime from departure to return, so why would you expect the "length" of that path (their own measured times) to be equal? The travelling twin just took a shorter path. That is fundamentally why the twins aren't the same age, although there's a bit of maths needed to justify the claim. That extra maths is probably why popular sources often use the "time runs slow for the travelling twin" explanation. (The whole point of the twin paradox, by the way, is to demonstrate the shortcomings of that approach, so they then have to do a lot of scurrying around to patch up the problems they were supposed to be learning to avoid...)

But isn't that effectively what's happening, time is slower for the traveler than the one on earth? It's impossible yes but if the two twins COULD instantaneously see eachother during the trip, the twin on earth would see the traveling twin moving very slowly, and visa versa. Differences in relative time passage, as an observer would experience them, are real. We see it in real time with satellites that are under lesser gravitational fields in earth's orbit, and the clocks must be adjusted for time dilation.

Time on the moon is slightly faster than that on earth as it's within a weaker gravitational field. For me, i prefer to discuss concepts as close to how we would experience them. I know the math is there but not everybody wants to dive into that. For anybody who says we cant discuss physics without the math, do we really think Newton was doing equations for a falling apple?

 

[PeterDonis]

spacetime geometry suggests it's path distance that cause the asymmetrical passage of time.

It's a lot more than a "suggestion". It's the physical fact.

I assume, meaning as the speed of light is approached, the traveling twin's perspective

No. Spacetime geometry and path lengths of worldlines have nothing to do with "perspective". They are invariants.

it's not the traveling twin's motion that compresses space by his perspective, it's his acceleration right?

It's neither. "Compression of space" is not a physical thing. It's a coordinate convention. You're barking up the wrong tree. Spacetime geometry and path lengths of worldlines have nothing whatever to do with "compression of space".

Am i misunderstanding something

Yes. See above.

isn't that effectively what's happening, time is slower for the traveler than the one on earth?

No. Spacetime geometry and path lengths of worldlines have nothing to do with "time is slower". Time runs at the same rate for both twins--one second per second along their worldlines. The reason the traveling twin is younger when they meet again is that his worldline is shorter--it has fewer seconds along it.

An analogy that's been used in other threads might be helpful here: two people who take car trips between the same two points on Earth, say New York and Chicago, by different routes. One car's odometer reads less elapsed distance than the other when they meet again. That has nothing to do with that car's odometer "running slower"; both odometers register distance at the same rate, one mile per mile. One car's odometer reads fewer miles because it took a path that was shorter, because of geometry.

 

[PeterDonis]

I'll chime in with a "me too" answer, in case other didn't do it for you.

Unfortunately, I think this answer causes more confusion than it solves.

 

[jbriggs444]

As @PeterDonis points out, "time dilation" is a coordinate effect. It has to do with how we assign my coordinates to your physical clock. And how the other fellow assigns his coordinates to my physical clock.

The essential difficulty is that there is no physical way to unambiguously know what time it really is "right now, over there". Any clock synchronization technique you can think up will depend on some underlying assumption. Usually an assumption about a standard of rest.

If I synchronize clocks based on the assumption that I am at rest, I will match up your clock readings with my clock readings in such a way that your clock appears to run slow.

If you synchronize clocks based on the assumption that you are at rest, you will match up your clock readings with my clock readings in such a way that my clock appears to run slow.

When one of us (me, let's say) turns around, my synchronization assumption goes out the window. I have a new standard of rest. My idea of what time it is "right now, over there" has changed. It will turn out that my new "right now, over there" will have swept forward across your time line, leaving a big swath of your time unaccounted for on my chronology.

When we meet again, I will expect your clock to have less time elapsed because I will have failed to add in the missing time that should have been accounted for at my turnaround.

 

[Herman Trivilino]

The traveling twin doesn't experience time dilation due to velocity, as the earth and the first twin can be said to be moving near the speed of light in relation to the traveling twin.

He doesn't experience time dilation, he observes it. He will observe the staying twin's clocks to be running slow compared to his, just as the staying twin will observe the traveling twin's clocks to be running slow compared to hers. Time dilation is symmetrical. This seems paradoxical until you understand it. And understanding the symmetry of time dilation requires understand the relativity of simultaneity.

Perhaps you are thinking the traveling twin experiences time dilation because he ends up being younger when the twins reunite. But that effect is due to the difference in the spacetime path lengths of the two twins, and unlike time dilation, it's something that is not symmetrical. But it's simply a way to explain the difference in ages of the twins. Another way to do it is to consider both time dilation and the relativity of simultaneity, but before you can do that you have to do what I described in the first paragraph. You can't just gloss over it and expect to somehow reach an understanding. You have instead to expend the mental effort necessary to learn it. Which can be accomplished as there has been much written about it in textbooks on special relativity.

If two ships fly past each other at 300m m/s relatively, both cannot have compression of the universe from their POV.

Each will observe lengths contracted in the other's rest frame. You talk about the rest of the universe but you need to be more specific. If there is a single distant star along their line of relative motion, each will observe the distance between the other's ship and the distant star to be contracted. Again, just as in time dilation, it's an effect each person observes happening to the other person.

And by the way, these effects happen at all speeds, not just speeds that are high compared to the speed of light. It's just that the slower the speed the smaller the effect. But if you have accurate enough measuring instruments you can detect them at speeds much much slower than the speed of light. The GPS satellites, for example, each carry atomic clocks that can measure time dilation at relatively slow speeds. Engineers have to take these effects into consideration when operating the GPS. Otherwise the GPS in your car wouldn't be able track your position very well. Instead of telling you what intersection you are near, it would only be able to tell you what city you are in.

These relativistic effects are not just the theoretical considerations they were when these effects were first being discussed more than a century ago. They are also a fact of modern life for thousands of engineers, technicians, and scientists working at hundreds of locations around our world.

 

[Ibix]

It's impossible yes but if the two twins COULD instantaneously see eachother during the trip

...then relativity would not be a correct theory and we would live in a very different universe. You cannot just override one of the fundamental principles on which a theory is based without completely re-writing it. In this case you are simply assuming that there's a physical meaning to "instantaneously" in the sense of "at the same time over a distance". That is not what relativity describes, and does not appear to be the universe we live in.

In reality, the twins can only watch each other through telescopes and correct for the changing light speed delay. How they do that correction involves some assumptions, and difering assumptions will give different "age now" figures. Any sensible procedure will tell the stay-at-home that the traveller is aging at a steady sow rate (although he is not required to be sensible and other answers are possible), but almost any sensible procedure will tell the traveller that the stay-at-home ages at a variable rate, sometimes slower, sometimes faster. But the exact pattern depends on assumptions.

Differences in relative time passage, as an observer would experience them, are real. We see it in real time with satellites that are under lesser gravitational fields in earth's orbit, and the clocks must be adjusted for time dilation.

Sort of. Nobody "experiences differences in time passage". They always experience time at one second per second. They may sometimes measure other clocks to be ticking fast or slow, but there's a lot of flexibility in how they can choose to measure other clock rates.

Note that the example of the GPS clocks involves clocks going in circles. Just like the twin paradox, they return to their start positions, so there's a non-arbitrary way to determine whether they're older or younger than a stay-at-home clock would have been. In between, it suits our purposes to treat them as ticking at a constant rate - but that's a choice made because it makes the maths easier.

Time on the moon is slightly faster than that on earth as it's within a weaker gravitational field.

Again, this statement is kind of true, but depends on assumptions that aren't really correct (that the Earth/Moon spacetime is one of the stationary spacetimes, which it isn't) but the consequences aren't evident in such weak gravitational fields. Saying "time is faster on the Moon than the Earth" is wrong but won't bite. Saying "time is faster on the lighter neutron star of a tight binary pair" will lead you into a world of inconsistent nonsense.

For me, i prefer to discuss concepts as close to how we would experience them.

That's basically why all of physics is in invariant quantities - things you can directly measure in an assumption free way. Time dilation is not one of these things. Nor is length contraction. They largely exist as concepts in relativity because they got cemented into pop-knowledge about relativity before we really understood the depth of the changes that relativity wrought on our view of the world. They're basically irrelevant beyond Relativity 101, and there's a school of thought that they should basically be relegated to "history of the development of relativity".

do we really think Newton was doing equations for a falling apple?

Newton's study of gravity led him to develop an entire new field of mathematics, calculus. So yes, we have a few suspicions that he was thinking mathematically.

 

[PeroK]

It's not a paradox because their journeys were never symmetrical—one took the direct, "longest" route through time, while the other took a shorter shortcut by travelling through space.

However, the first postulate of SR says that there is no concept of absolute (inertial) motion through space. Neither twin is moving through space any more fundamentally than the other.

 

[weirdoguy]

one took the direct, "longest" route through time, while the other took a shorter shortcut by travelling through space.

That is misleading, or even wrong. Things "move" through spacetime, that is - they have worldlines. And the "lenght" of these worldlines is proportional to proper time. Worldline of one of the twins is shorter (in terms of spacetime metric) then of the other. End of story.

 

[Histspec]

Things "move" through spacetime, that is - they have worldlines. And the "lenght" of these worldlines is proportional to proper time. Worldline of one of the twins is shorter (in terms of spacetime metric) then of the other. End of story.

All of which was already explained by Laue in 1911:
https://en.wikisource.org/wiki/Tran...the_Theory_of_Relativity_and_their_Refutation

Einstein's experiment, however, is represented by a curved worldline, which (in a worldpoint A) decomposes into a row of curves, and all of them will be re-united at a worldpoint B to a single line. Of all curves connecting the points A and B having time-like direction throughout, the straight connection has the longest proper time; that is the meaning of Einstein's consideration.

Hopefully we don't have to wait another 110+ years before everybody understands this.

 

[Meir Achuz]

 

[Meir Achuz]

This image may help. The brother on Earth follows the vertical line. The traveling brother moves out the x-axis, and then returns. On a map, he would have traveled further. But, in space time, s^2=t^2-x^2, so he has traveled a shorter space-time 'distance'.