I Confusion regarding acceleration in SR

[Kontilera]

I’ve just realized something is wrong with my understanding of SR and I would really appreciate if you helped me sort it out. :)

This won’t be a post with loads of formulas, rather the confusion is a conceptual.

One way to describe my confusion is to put it into the twin paradox, although it’s not the common questions that most people have when encountering this ”paradox” for the first time..

So, let's say Bob and Alice are passing each other in the standard twin-paradox-scenario.
Both are in their own spaceship, meeting each other in a perfectly flat spacetime somewhere in outer space.

Both Bob and Alice are experiencing the other persons time as ”passing slower”.

When Bob decides to go back to Alice he has to accelerate.
This is where my confusion comes in.

When Bob accelerates he is going from one inertial frame to another, in a continuously manner.
This means that he he would be able to observe Alice, he would experience her time passing in ”ultrarapid”.

After the acceleration he will agree to the fact that more time has passed for Alice compared to his own measure.

It’s the whole acceleration part that seems strange.
From the point of view of how I under stand Lorentz transformations it seems fine.

But the light from Alice that Bob receives during (and right after) the acceleration seems independent of whether he accelerated or not.
Thus he ”should” see basically the same actions from Alice, in the same speed, as he would if he not accelerated.

The light that was about to reach Bob from Alice in the coming seconds are independent of his motion. (The wavelength might be shifted but that seems to be irrelevant.)

So my question is: How can Bobs view of what is simultaneous with his actions change so fast, when the light reaching him is independent of his almost instant acceleration?I hope you understand my confusion!

Thanks!

 

[A.T.]

How can Bobs view of what is simultaneous with his actions change so fast, when the light reaching him is

"Bob's frame simultaneity" and "What Bob sees" are different things. Simultaneity is just a convention, especially for accelerating frames.

 

[jedishrfu]

Checkout this video from minute physics on the twin paradox:

 

[Orodruin]

"Bob's frame simultaneity" and "What Bob sees" are different things. Simultaneity is just a convention, especially for accelerating frames.

In fact, to expand on that, the rate at which Bob actually sees Alice's clock tick is given by the Doppler formula, not the time dilation formula.

 

[Nugatory]

So my question is: How can Bobs view of what is simultaneous with his actions change so fast, when the light reaching him is independent of his almost instant acceleration?

What you are describing is not the twin paradox, but the "andromeda paradox". Google will find some good explanations.

When we choose to work in one reference frame instead of another, we're just changing the way that we label the time and place of distant events. We can change these labels by as much as we want as quickly as we want.

 

[Kontilera]

Checkout this video from minute physics on the twin paradox:

This video is exactly what I´m talking about, although he does not adress my confusion at all.
During the "almost instantaneous acceleration" the traveller sees time passing much faster on Earth since coordinate axes are changing direction during the acceleration. But! Let's say the total acceleration took about 1 microsecond. How does this acceleration change the observations that he was about to make? The light that was about to be reached him is still traveling towards him, and will be observed directly after the acceleration.

I.e. in what sense is that time not accounted for? :/

 

[Kontilera]

It seems to me that it cannot only be explained by doppler shift, but I am sure I´m wrong.
I just need to grasp what's wrong with my line of thought.

To make it more concrete we can use the example in the youtube video above.
If I´m the traveller, the moment before I start to make my acceleration I will observe Earth as it was 3.1999 seconds after I left.
Then, making my "almost instant" acceleration, I will observe Earth as it was 6.800001 seconds after I left.

How can this be?
The light that was heading towards me and was about to reach me in this short acceleration interval seems to mysteriously have changed.

 

[Kontilera]

What you are describing is not the twin paradox, but the "andromeda paradox". Google will find some good explanations.

When we choose to work in one reference frame instead of another, we're just changing the way that we label the time and place of distant events. We can change these labels by as much as we want as quickly as we want.

Yes, that seems to be somewhat similar to my confusion.
I will read more about it later. Thanks.

 

[anorlunda]

It is really hard to textile questions like this with words . Draw diagrams.

 

[jedishrfu]

How about this diagram? Jim is stationary on the Earth and Pam is in the drivers seat of the spaceship.

 

[Kontilera]

It is really hard to textile questions like this with words . Draw diagrams.

I agree, but I think that watching the youtube clip (3 and a half minute long) and reading post #7 it the best way to understand what I´m aiming at.

I will try to draw a nice diagram later. :)

 

[alejandromeira]

When the traveling twin changes your diection, must to have an acceleration, (of enormeus magnitude). Then because the equivalence principle, during this acceleration, your time go slowly than the time of your twin at rest.
Note that just before this acceleration the twin traveling think that your brother is younger.
Is a good exercise plot this in a minkosky diagram (I have do this some weeks ago), and also is very interesting, draw the radio communications signals betwenn the Earth and the spaceship and the inverses, like in a previous post.

 

[Kontilera]

How about this diagram? Jim is stationary on the Earth and Pam is in the drivers seat of the spaceship.

View attachment 226414

Hmm, how will this "Jim sends greetings"-diagram add up with the diagram drawn in the youtube video.
In the youtube video Pams notion of what is simultanous on Earth (after she has accelerated) will be ahead of her own time.

 

[alejandromeira]

I was very happy, when i have made this work. I always love relativity and now y can learn about that. Work is in the images.

 

[jartsa]

So my question is: How can Bobs view of what is simultaneous with his actions change so fast, when the light reaching him is independent of his almost instant acceleration?

Bob's view of which far away events are simultaneous with his actions changes fast, while the change is slow regarding nearby events.

It's just as simple as gravitational time dilation. Clocks run very fast far away in the uphill direction, according to Bob.

 

[Kontilera]

Bob's view of which far away events are simultaneous with his actions changes fast, while the change is slow regarding nearby events.

It's just as simple as gravitational time dilation. Clocks run very fast far away in the uphill direction, according to Bob.

Yes, but how does Bob calculate what is simultaneous on earth?
He has to check what he observes and take into account the time it took for the light to reach him.

If the acceleration is almost instant the length between him and Earth is the same as before the acceleration (length contracted or not).
And the light itself, traveling towards him, cannot magically change to display other events that are "more into the future".

Thus, looking at the small time interval around the acceleration: he observes the same thing as he would have done without the acceleration and his calculations for the simultaneous events on Earth is the same as well.

 

[Kontilera]

I was very happy, when i have made this work. I always love relativity and now y can learn about that. Work is in the images.

Thanks!
I will wait until I get home and take a careful look at these. :)

 

[alejandromeira]

I submit you the statement of the problem, traslation is from spanish. The numbers in the problem are well selected for easy calculus.

PROBLEM
In New Year day of 2050, Danae go out from the Earth to alpla-Centaurus, 4 light-years away from the Earth, Danae travel with an speed of 0.8c. Just Danae make your goal, she cames back to the Earth at the same velocity, and landing in the same point the New Year of 2060.
Danae has a twin, Apolo, that stand at rest in the Earth. They agreed to communicate by radio signals every day of the new year, until Danae cames back.

You must construct the space-time diagram for the voyage and the radio signals. Also you can use the lorentz contraction or dilation of time for calculations.
I'm sorry for my English

 

[jartsa]

Yes, but how does Bob calculate what is simultaneous on earth?
He has to check what he observes and take into account the time it took for the light to reach him.

If the acceleration is almost instant the length between him and Earth is the same as before the acceleration (length contracted or not).
And the light itself, traveling towards him, cannot magically change to display other events that are "more into the future".

Thus, looking at the small time interval around the acceleration: he observes the same thing as he would have done without the acceleration and his calculations for the simultaneous events on Earth is the same as well.

Bob before the acceleration "The light that is hitting my eyes now left the Earth when the Earth was 6 light-seconds away from me, so it's 6 seconds old, so the event I see happening now happened 6 seconds ago". Let's say the event is the 1984 Olympics 100 final start.

Bob after the acceleration "The light that is hitting my eyes now left the Earth when the Earth was 30 light seconds away from me, so it's 30 second old, so the event I see happening now happened 30 seconds ago" It's still the 1984 Olympics 100 final start.

So the event shifted 24 seconds towards the past. Same shift happened to all events in the Earth's history, according to Bob.Note: I did not make any error there, even if it seems so at first glance. ;)

One may wonder how does the light travel through 6 light-seconds of space or 30 light-seconds of space exactly the same way? Hmm ... Let's say there is some interstellar dust between Bob and the earth.

Bob before the acceleration: The Earth is standing still and so is the dust.
Bob after the acceleration: The Earth is moving towards me and so is the dust.
Because of time dilation the photon - dust collision rate goes down as the light - dust system moves faster. That sounds like a good answer to the question.

 

[Kontilera]

Bob before the acceleration "The light that is hitting my eyes now left the Earth when the Earth was 6 light-seconds away from me, so it's 6 seconds old, so the event I see happening now happened 6 seconds ago". Let's say the event is the 1984 Olympics 100 final start.

Bob after the acceleration "The light that is hitting my eyes now left the Earth when the Earth was 30 light seconds away from me, so it's 30 second old, so the event I see happening now happened 30 seconds ago" It's still the 1984 Olympics 100 final start.

So the event shifted 24 seconds towards the past. Same shift happened to all events in the Earth's history, according to Bob.

Why is there such a big difference in how far away Earth was if we are playing with the idea of an almost instant acceleration and that Bob makes these statements right before and right after the acceleration?

 

[Kontilera]

I feel that I understand the twin paradox perfectly when looking at the signaling diagram and the plane-of-simultanity diagram seperate. But I can't figure out how they can be compatible with each other.
Lets say Bob looks at Earth right before the acceleration.
He observes the 1984 Olympics 100 final start and that Earth is 10 light days away.
Using his formula:

(The time it is on earth) = (The time I observe on earth) + (The time it took the light to reach me)

He concludes that the 1984 Olympics 100 final start was exactly 10 days ago.

Now he makes his super fast, mind blowing, acceleration. Which in the Earth reference frame may have taken 1 microsecond and only moved him about some meters. (I don't won't do the calculations here cause you get the idea of what I´m getting at.)

After the acceleration he (according to the signaling diagram) will observe a moment that is slightly later that the start of the Olympics final. Maybe the difference is some microseconds..

He will again use his formula to calculate the correct time on earth.
The time he observes on Earth is only some microseconds later and the time it took light to reach him is the same (assuming that the acceleration is "symmetrically performed".)

Thus, I cannot grasp (within this perspective of the problem) how he can claim that the simultaneous events on Earth changed so much due to the acceleration..

 

[Janus]

Yes, that seems to be somewhat similar to my confusion.
I will read more about it later. Thanks.

There are two issues here: What Bob and Alice visually see and what Bob or Alice would determine about each other's clock. What they see, is in part determined by the distance between them. If they are at rest with respect to each other, and 1 light hr apart, Bob might see Alice's clock read one hr behind his and Alice might see Bob's clock reading 1 hr behind hers, but they also both know that the light carrying that information took an hr to reach them, and that in that hr the other person's clock advanced by 1 hr, and thus actually reads the same as their clock at any given moment.

If they are moving away or towards each other, it's a bit more complex. The distance between them is changing between them and thus so is the light propagation time. This causes a Doppler effect, which causes each of them to see the other person's clock run slow if they are receding and run fast if they are approaching. On top of this, there is time dilation, with which according to both of them causes the other person's clock to run slow regardless of whether they are receding or approaching. This is what is left over after you account for the Doppler effect.
Most of the time when Relativity is discussed it is assumed we are not dealing with what is being visually seen by the observers, but what they determine is happening to the other clock after they have factored out any light propagation times.

So in you example, Bob would not visually see Alice's clock run fast or jump forward during his near instantaneous acceleration. He sees the same light both before and after. But what that light is telling him as to what time is "really is" on Alice's clock does change.

To see how this works, we will work out an example. Bob passes Alice at 0.8c. He travels 0.8 light years from Alice ( as measured by Alice) then returns.
According to Alice, just using time dilation alone, Bob will have aged 1.2 years upon return, at a steady rate of 0.6 as fast as herself. She however, would not visually see his clock do this if she where watching the whole time. She would actually see it tick at a rate of 1/3 as fast as hers for 1.8 years and then 3 times as fast for 0.2 year. This is due to the combined effect of time dilation, Doppler shift and light propagation delay.
As she watches him recede the combination of Doppler effect and time dilation ( called Relativistic Doppler shift) has her seeing his clock run 1/3 the rate of her own. Now while it only takes 1 year for him to reach the turn around point, it is 0.8 light years away, which means it takes another 0.8 years before she see this event. In other words, she sees the outbound trip as taking 1.8 years. This also means that by the time she visually sees Bob's turn around, He is already most of the way back to here on his return leg, following closely behind that same light from turn around. He arrives back after a total of 2 years, so she sees the whole of his return trip compressed into 0.2 years seeing his clock advance 0.6 years in that time.

What does Bob see? Well first off, due to length contraction, he measures the distance from Himself and Alice at turn around as only being 0.48 ly, which, at 0.8c takes 0.6 years to cross. During this time, he visually sees Alice's clock run 1/3 as fast as his own and thus see's it read 0.2 year. He does his turnaround acceleration, after which he still reads 0.16 yrs on Alice's clock. But since he is the one that made the change of velocity, he does not have to wait to see the effects of his velocity change on the relativistic Doppler shift. He immediately starts seeing Alice's clock running 3 times as fast of his own. In the 0.6 years it takes by his clock to rejoin Alice, he will see her age 3*0.6 = 1.8 year, for a total of 2 years.

Now just before turn around, Bob sees Alice's clock read 0.2 years, but if you factor out the Doppler effect component, this means that Alice's clock reads 0.48 years due to time dilation alone according to Bob "at that moment".

Upon rejoining Alice, Alice's clock reads 2 years. The time dilation for Alice's clock according to Bob during the return trip is the same as it was was for the out bound trip. 2 - 0.48 = 1.52, which means at the start of the return leg, even though he visually saw Alice' clock read 0.2 years, it "really: read 1.52 yrs at that moment according to him. Thus during the turnaround acceleration, the " at this moment" time on Alice's clock jumped from 0.48 years to 1.52 years according to Bob.
This shift is due to Bob's changing of inertial frames, even though he doesn't visually see any shift in Alice's clock other than in the Doppler rate ( going from running slow to running fast)

 

[jartsa]

Why is there such a big difference in how far away Earth was if we are playing with the idea of an almost instant acceleration and that Bob makes these statements right before and right after the acceleration?

If the Earth moves towards Bob at speed 0.9 c and light from Earth moves towards Bob at speed c, then light is gaining distance to the Earth at rate 0.1 c.

"It has taken quite a long time for the distance to become as large as it is now" , Bob thinks.

 

[pervect]

I’ve just realized something is wrong with my understanding of SR and I would really appreciate if you helped me sort it out. :)

...

When Bob accelerates he is going from one inertial frame to another, in a continuously manner.
This means that he he would be able to observe Alice, he would experience her time passing in ”ultrarapid”.

Bob can't directly "experience" Alice's time.

But the light from Alice that Bob receives during (and right after) the acceleration seems independent of whether he accelerated or not.
Thus he ”should” see basically the same actions from Alice, in the same speed, as he would if he not accelerated.

Here are some hints as to way to tackle the problem.

A) Assume Alice sends out regular clock signals. You can imagine each signal is timetamped with Alice's time
B) Compute when (according to Bob's clock) he receives each timestamped signal.
C) Space-time diagrams may be of some help - posters have already drawn some for you, but you may not understand them unless you draw some yourself. They don't have to be pretty. Compare what you draw to what other posters have drawn.

In part two of your post, you talk about "the light from Alice that Bob recieves". In part one of your post, you are talking about somethign else, "what Bob experiences". This is apparently a different notion form what you talk about in part 2, the signals that Bob recieves. As you point out, there is nothing ultra-rapid going on in part 2, but there is something ultra-rapid going on in part 1.

What you need to think about is what you mean by the notion you write about in part 1, which is different from the notion in part 2. How is it different?

Hint. The notion that you use in part 1 most likely involves the concept of simultaneity. Can you phrase your question in part 1 in terms that involve the word "simultaneous"?

 

[Janus]

I feel that I understand the twin paradox perfectly when looking at the signaling diagram and the plane-of-simultanity diagram seperate. But I can't figure out how they can be compatible with each other.
Lets say Bob looks at Earth right before the acceleration.
He observes the 1984 Olympics 100 final start and that Earth is 10 light days away.
Using his formula:

(The time it is on earth) = (The time I observe on earth) + (The time it took the light to reach me)

He concludes that the 1984 Olympics 100 final start was exactly 10 days ago.

Now he makes his super fast, mind blowing, acceleration. Which in the Earth reference frame may have taken 1 microsecond and only moved him about some meters. (I don't won't do the calculations here cause you get the idea of what I´m getting at.)

After the acceleration he (according to the signaling diagram) will observe a moment that is slightly later that the start of the Olympics final. Maybe the difference is some microseconds..

He will again use his formula to calculate the correct time on earth.
The time he observes on Earth is only some microseconds later and the time it took light to reach him is the same (assuming that the acceleration is "symmetrically performed".)

Thus, I cannot grasp (within this perspective of the problem) how he can claim that the simultaneous events on Earth changed so much due to the acceleration..

Let's address this by considering two clocks in an accelerating rocket. One one in the nose and one in the tail. They are communicating by light signal.
Light signals leave the nose clock toward the tail. But between emission and reception, the rocket has changed velocity. Ergo, the tail is moving at a different velocity at reception of the signal than the nose was moving at emission. This results in the tail seeing a Doppler shift in the light coming from the nose. And since the relative velocity change was towards the nose, it is a blue shift. Conversely, the nose will see a red shift coming from the tail of the Ship. Now, as I mentioned in the Earlier post, Doppler effect is normally associated with changing distance between the observer and source ( You extract the time dilation component from Relativistic Doppler shift by factoring out this part), But in this case, there is no change in distance involved. The tail does not see the nose clock running fast because it is approaching, nor does the Nose clock see the Tail clock run slow because it is receding. In all real respects, the tail clock does run slower than the Nose clock. The further apart the clocks the greater the difference in tick rate This is the equivalent of a higher clock running faster than a lower clock in a gravitational field.

This is not restricted to just clocks accelerating with the ship, as far as an observer in the accelerating ship is concerned, all clocks in the direction of the acceleration run fast regardless of whether or not they share the acceleration.

Another way to look at it is that acceleration can be treated a rotation in space-time. If you are standing facing an object that is 4 m in front of you, and then do a 180 degree turn, it shifts to being 4 m behind you. Rotations in space-time can involve such "shifts" in time as well as in space.

 

[PeterDonis]

Why is there such a big difference in how far away Earth was if we are playing with the idea of an almost instant acceleration and that Bob makes these statements right before and right after the acceleration?

Because "how far away the Earth is" is not an absolute fact. When Bob changes direction, and "how far away the Earth is" for him changes drastically as a result, he isn't changing anything about the earth, or about his location in spacetime relative to the earth. He is only changing his own state of motion. In other words, "how far away the Earth is" for him depends on his state of motion. That means "how far away the Earth is" does not work in relativity the way your intuitions are telling you it ought to work.

 

[alejandromeira]

Of course there are a relativistic Doppler redshift when Bob go away, and blueshift when Bob comes back.
But what Bob see from Alice, and Alice see from Bob is given for the radio signals (for example a photograf of each clock). I've uploaded a minkosky diagram that shows every new year felicitation. On can read in the axis the times when the signals where receipted for one or another, one can draw as may signals as you wont, and read all these times. I don't understand what is the problem.

Also. If the reference frame changes instantantly, then the Alice cloock Instantly goes forward, when Bob perceive that? On can read this in the radio signal diagram also. Note, that the shape of the radio signal diagram is different in the outgoing trip. and the return trip.

But the change in direction can't not be instantly, and then must take a time, and the minkowsky diagram will have a rounded area. In this area if one trace the marks in the t-axis at rest (from the another Sistem of Reference), one will see how the rest-cloock runs faster. I don't know if my intepretation is ok, but I interprete this in the sense that these acceleration is like a gravitational field and then the rest clock must run faster than the Bob's clock.

Then in the return trip one can observe that returns special relativity and Alice and Bob see that the clock of the anoter goes slowly.

Ok, I see this problem clearly, so surely something idea escapes me.

There are another pos when I write:

Another way to look at it is that acceleration can be treated a rotation in space-time. If you are standing facing an object that is 4 m in front of you, and then do a 180 degree turn, it shifts to being 4 m behind you. Rotations in space-time can involve such "shifts" in time as well as in space.

Of course for Bob is all the Universe that is rotating around he. I'm not an expert but in the notes that I've read for make the minkosky diagrams, said that this has a great importance.
Edit: I'm sorry for my English.

 

[sweet springs]

GR says in gravity generated by acceleration the higher, the faster time goes. higher is farther here.

 

[sweet springs]

Say at turning point you Bob cross with return ship and transmit your clock time for synclonization and all the data observed from the Earth to return ship captain asking him to see Alice so that you can go on journey. Captain find that he already knows what happened next on Earth with hIs own observation hitherto.

 

[sophiecentaur]

So the resolution of the paradox would seem to be based on which of the two twins has undergone some acceleration during the experiment. One of them has 'stepped outside' Special Relativity conditions and the amount of the 'time disparity' would have to depend on the amount of Energy that has been put into the exercise in reversing the velocity of the moving twin.

 

[Orodruin]

So the resolution of the paradox would seem to be based on which of the two twins has undergone some acceleration during the experiment. One of them has 'stepped outside' Special Relativity conditions and the amount of the 'time disparity' would have to depend on the amount of Energy that has been put into the exercise in reversing the velocity of the moving twin.

No, acceleration is not the key issue and SR is perfectly capable of handling it. The key issue in how the paradox arises in the first place is a misapplication of what statements made in the theory actually mean.

Geometrically, the accelerating twin having a shorter proper time is equivalent to a curved path being longer. Is it longer because the pen had to change or is it longer because you had to move the pen a longer distance to draw it?

 

[Nugatory]

GR says in gravity generated by acceleration the higher, the faster time goes. higher is farther here.

That's not a prediction of GR. It's a prediction of SR, which is all that's needed to handle acceleration and the inertial forces that appear in accelerating frames. As long as there is no gravitating mass present, GR is never needed.

 

[sweet springs]

I didn't say it necessary .. I would like to say
GR also works.

 

[PeterDonis]

I didn't say it necessary .. I would like to say
GR also works.

A better way of stating the point @Nugatory was making is that in flat spacetime, "GR" is the same thing as "SR". They are not two different theories; they are the same theory.

 

[sophiecentaur]

The key issue in how the paradox arises in the first place is a misapplication of what statements made in the theory actually mean.

OK it's still within SR - sorted. But the essence of who ages slower (the asymmetry) is to do with the Energy / Work expended on him/her. The 'missing' bit in the diagram, during the instant acceleration explains the process well.

 

[Orodruin]

OK it's still within SR - sorted. But the essence of who ages slower (the asymmetry) is to do with the Energy / Work expended on him/her.

I disagree. You can construct "twin paradoxes" without any acceleration by using three observers.

 

[stevendaryl]

OK it's still within SR - sorted. But the essence of who ages slower (the asymmetry) is to do with the Energy / Work expended on him/her. The 'missing' bit in the diagram, during the instant acceleration explains the process well.

It's true in flat spacetime that you can always tell which of two twins has aged the least by which one accelerated, but I wouldn't call that the "essence", since in a simple generalization of flat spacetime, you can have a twin paradox with no acceleration. If you generalize SR to a "cylindrical" universe (by saying that the point with coordinates $x=0, t=0$ in some frame is identified with the point $x=L, t=0$), then you can have two twins, one of who sits at $x=0$ and the other who travels at constant velocity in the $x$ direction. When they get back together, the "traveling" twin will be younger. But neither accelerates.

 

[jbriggs444]

But the essence of who ages slower (the asymmetry) is to do with the Energy / Work expended on him/her.

But an acceleration that takes an outward velocity and produces an inward velocity of equal magnitude requires zero work.

 

[SiennaTheGr8]

It's true in flat spacetime that you can always tell which of two twins has aged the least by which one accelerated, but I wouldn't call that the "essence", since in a simple generalization of flat spacetime, you can have a twin paradox with no acceleration.

Or one where both twins accelerate!

 

[sophiecentaur]

If you generalize SR to a "cylindrical" universe

But I suggest that the twins paradox would not be a paradox when the curvature was involved. For a start, all distances could be Modulo(The circumference of the Universe)

 

[stevendaryl]

But I suggest that the twins paradox would not be a paradox when the curvature was involved. For a start, all distances could be Modulo(The circumference of the Universe)

I'm not sure how that helps. But it seems to me to be equally paradoxical. You have one twin, Alice, at rest. You have a second twin, Bob, moving away at 99% of the speed of light. From Alice's point of view, Bob is aging slower, and from Bob's point of view, Alice is aging slower. It's just as paradoxical as the flat space version. But eventually, Bob will meet up with Alice from the other direction, and one of them will be older than the other. I don't see how viewing distances modulo the circumference of the universe helps.

 

[A.T.]

he can claim that the simultaneous events on Earth changed so much due to the acceleration..

Since it's just a convention, he can claim whatever he wants. He is not actually physically affected by those distant events at the time he claims they happen.

 

[sophiecentaur]

I'm not sure how that helps. But it seems to me to be equally paradoxical. You have one twin, Alice, at rest. You have a second twin, Bob, moving away at 99% of the speed of light. From Alice's point of view, Bob is aging slower, and from Bob's point of view, Alice is aging slower. It's just as paradoxical as the flat space version. But eventually, Bob will meet up with Alice from the other direction, and one of them will be older than the other. I don't see how viewing distances modulo the circumference of the universe helps.

If you change the Cylindrical Universe to ants on the surface of the Earth then there are loads of 'surprises' about relative lengths of journeys but I wouldn't say that they are paradoxes. But perhaps the ants would think of them in that way.
Perhaps we have done this to death. There is no limit to how many scenarios we could think up. With Bob moving away fast around the cylinder (and Alice moving equally fast away from him, they could both meet on the other side but they would each see the other one as younger (in years) rather than just observing their clocks being slow as they go past each other. Isn't that an even more paradoxical paradox if they could be standing next to each other and both be older and younger than their twin? I hope I've missed something obvious about this because it's quite uncomfortable to contemplate.

 

[A.T.]

I hope I've missed something obvious about this because it's quite uncomfortable to contemplate.

In the cylindrical universe there would be a preferred frame globally.

 

[stevendaryl]

If you change the Cylindrical Universe to ants on the surface of the Earth then there are loads of 'surprises' about relative lengths of journeys but I wouldn't say that they are paradoxes. But perhaps the ants would think of them in that way.
Perhaps we have done this to death. There is no limit to how many scenarios we could think up. With Bob moving away fast around the cylinder (and Alice moving equally fast away from him, they could both meet on the other side but they would each see the other one as younger (in years) rather than just observing their clocks being slow as they go past each other. Isn't that an even more paradoxical paradox if they could be standing next to each other and both be older and younger than their twin? I hope I've missed something obvious about this because it's quite uncomfortable to contemplate.

Well, the point of introducing the cylindrical universe was just to show that acceleration isn't really necessary for the paradox; differential aging can happen even when nobody accelerates.

The cylindrical universe is interesting because it's actually equivalent in every way to an infinite flat universe with periodic boundary conditions. Alice sitting on Earth can look through a powerful telescope and see, far away, another copy of the Earth, and beyond that, another copy and another copy, ad infinitum. After adjusting for the delay for light to travel such a distance, she would compute that all the Earths are the same age. Similarly, there is an infinite line of Bobs all the same age, traveling at the same velocity. Each Bob travels from one Earth to the next, and when he arrives, he is younger than the Alice of that Earth.

From the perspective of Bob, though, things are weirder. He also sees a line of infinitely many Earths, and infinitely many Alices and infinitely many Bobs. But the difference for Bob is that looking in one direction, each Alice is older than the last. From his point of view, his Alice leaves and a second, older Alice starts moving toward him. The second Alice is aging slower than Bob is, but she starts out older, so when she gets to Bob, she's still older than he is.

 

[Kontilera]

Okey, I feel like I need to explain some missunderstandings about the whole thread now. :)First of all, I've taken SR and GR courses on university level.
And I feel like I do understand the SR and at least some GR.

The twin paradox itself is not a problem for me. I understand that the acceleration boosts Bobs inertial frame of reference. That his notion of what direction time has changes and that he will realize that he his the younger one when he travels back to earth.
My fault is that I put my confusion into a twin-paradox-context and now it feels like many people want to explain the twin paradox for me.
An effort I, of course, am very, very thankful for!
My confusion is about what you do see when you do change your inertial frame of reference by accelerating, if we play with the thought that our telescopes could give us a good resolution on very large distances.

Take the scenario described by Penrose in 'The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics' as an example. In this case he discusses a potential invation of Earth by the civilization in the andromeda galaxy.

"Two people pass each other on the street; and according to one of the two people, an Andromedean space fleet has already set off on its journey, while to the other, the decision as to whether or not the journey will actually take place has not yet been made. How can there still be some uncertainty as to the outcome of that decision? If to either person the decision has already been made, then surely there cannot be any uncertainty. The launching of the space fleet is an inevitability. In fact neither of the people can yet know of the launching of the space fleet. They can know only later, when telescopic observations from Earth reveal that the fleet is indeed on its way. Then they can hark back to that chance encounter, and come to the conclusion that at that time, according to one of them, the decision lay in the uncertain future, while to the other, it lay in the certain past. Was there then any uncertainty about that future? Or was the future of both people already "fixed"?" - R. Penrose

Wikipedia solves this "paradox" by stating:

"The "paradox" consists of two observers who are, from their conscious perspective, in the same place and at the same instant having different sets of events in their "present moment". Notice that neither observer can actually "see" what is happening in Andromeda, because light from Andromeda (and the hypothetical alien fleet) will take 2.5 million years to reach Earth. The argument is not about what can be "seen"; it is purely about what events different observers consider to occur in the present moment."

My question is: If they see the same thing in the andromeda galaxy. Then how can the person approaching the Andromeda galaxy even justify that his present is simultaneous to the fleet already moving? I mean, when calculating your simultaneous universe I assume that you can use the formula:

What the time is now in Andromeda = The time I observe right now in Andromeda + The time that the andromeda people experience that it took for light to reach me.

You might say that the second term here changes due to time dilation and length contraction... but that doesn't seem to solve the problem, because those effects are independent of the sign of the velocity. So if one person is walking with the velocity +v and the other one is walking with the velocity -v, they will both experience those effects but still disagree of what is simultaneous in the Andromeda galaxy.

 

[sophiecentaur]

according to one of the two people, an Andromedean space fleet has already set off on its journey,

Do you mean he just thought it was a possibility and happened to voice that exactly the 2.5 million years before Earth observers happened to spot the fleet? If that was just a random idea then why is it of any consequence? Plenty of people are convinced they dreamed about the winner's name and the actually manage to back the winner. How does that fit in with this stuff? Clearly, Penrose had a serious message there.

 

[jartsa]

What the time is now in Andromeda = The time I observe right now in Andromeda + The time that the andromeda people experience that it took for light to reach me.

You might say that the second term here changes due to time dilation and length contraction... but that doesn't seem to solve the problem, because those effects are independent of the sign of the velocity. So if one person is walking with the velocity +v and the other one is walking with the velocity -v, they will both experience those effects but still disagree of what is simultaneous in the Andromeda galaxy.

Let's use the same Olympics sprint example as before, and the same Bob that acceletes.

Bob before acceleration: "At this moment on Earth people should be saying the Olympic event is happening right now. And those people should be saying that Bob is one light day away"

Bob after acceleration: "At this moment on Earth people should be saying the Olympic event was two weeks ago. And those people should still be saying that Bob is one light day away. And then they should say that two weeks ago Bob was 10 light days away. Because at the time of the Olympic event Bob started moving towards the Earth quite fast".

 

[alejandromeira]

My confusion is about what you do see when you do change your inertial frame of reference by accelerating, if we play with the thought that our telescopes could give us a good resolution on very large distances.

Unfortunately light don't have infinite speed, and then all these questions have to be solved with the minkowsky diagram for radio signals, and the equations of the contraction of length and dilation of time.
We can perfectly know the time measured in andromeda when our radio signal comes out and when it arrives, (we can know ablolutely the time meausured in both reference frames).

In a real world, the acceleration is not instantaneous, and the trajectory of the traveling twin, in the Minkowsky diagram, will be rounded in the area of acceleration. In this area we can draw their axes, if we do it and we extend the traveling X axis until we cut the T axis at rest, we will see how the time of the resting twin begins to increase. Specifically, at the point of V = 0 for the traveler, the time at rest is half of what the trip takes. Later it is symmetric about the outward trip.

The question of when we 'perceive' it by the telescope, then we would have to go back to the other Minkowsky diagram of the radio signals.

Regarding Penrose's paradox, in that case I have to say clearly that I do not understand anything about that.

 

[Kontilera]

Do you mean he just thought it was a possibility and happened to voice that exactly the 2.5 million years before Earth observers happened to spot the fleet? If that was just a random idea then why is it of any consequence? Plenty of people are convinced they dreamed about the winner's name and the actually manage to back the winner. How does that fit in with this stuff? Clearly, Penrose had a serious message there.

No, I´m with you. Of course he cannot observe whether the fleet leaves the Andromeda galaxy or not.
But if you watch the minutephysics video that seems to be the explanation.

As for me I´m trying to ask: In what sense is the future of the Andromeda galaxy part of his 'present-universe' if he can't observe it and none of the terms in my pseudoequation changes?