# Confusion regarding acceleration in SR

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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, lets 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!

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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.

Orodruin
Mentor
Checkout this video from minute physics on the twin paradox:

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"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.

Mentor
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! Lets 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 travelling 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 whats 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.

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

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

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BvU
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.

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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, travelling 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, travelling 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 ... Lets 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.

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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 cant 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 dont wont 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..

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Yes, that seems to be somewhat similar to my confusion.
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)

BvU
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.

Staff Emeritus
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"?

Staff Emeritus
Gold Member
I feel that I understand the twin paradox perfectly when looking at the signaling diagram and the plane-of-simultanity diagram seperate. But I cant 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 dont wont 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.

Mentor
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.

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Gold Member
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.

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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?

Mentor
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.

Mentor
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.

SiennaTheGr8, sweet springs and Orodruin