Hi,

I am having a hard time getting my head around the time slowing down bit of the theory, and I could do with someone explaining it to me.

From my understanding, the faster you travel the slower time gets right?
but also any frame of reference is valid, so speed is again relative.
and direction of travel has nothing to do with the effect right?

In that case I cant figure what happens in the following situation.

We have 2 Probes A and B, each carries an atomic clock, and their sychronized.

Probe A accelarates away from Probe B at .5c (relative to probe B) for 1 year, then returns again at 0.5c arriving exactly 2 years later as measured by its internal clock.

Now here is my confusion since any point of reference is valid.

From Probe A's reference point, Probe B is the one moving meaning its clock should be slower.
From Probe B's reference point, Probe A is the one moving meaning its clock should be slower.

Which one is right? if they both started with a time of 0, how many days/seconds would have passed and how can I work it out?

This has always baffled me, as it seems a paradox both can't be right.

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Dale
Mentor
This is called the "twins paradox" and is one of the most common questions. I would recommend reading the usenet FAQ by John Baez on the topic and a brief search here to see if any of the MANY threads speak to you.

G01
Homework Helper
Gold Member

The symmetry of the situation is broken when one of the clocks invariably had to accelerate to turn around. In that case, we have an accelerating frame and the problem is not correctly handled by special relativity, which only deals with inertial frames. Thus, we will find that the clock that actually accelerated will have recorded less time.

The symmetry of the situation is broken when one of the clocks invariably had to accelerate to turn around. In that case, we have an accelerating frame and the problem is not correctly handled by special relativity, which only deals with inertial frames. Thus, we will find that the clock that actually accelerated will have recorded less time.
Interesting, I wish someone would do a decent experiment to prove this.

On a side note, what about time-dilation between planets i.e. earth and mars.
Does time flow at different speeds?

The symmetry of the situation is broken when one of the clocks invariably had to accelerate to turn around. In that case, we have an accelerating frame and the problem is not correctly handled by special relativity, which only deals with inertial frames. Thus, we will find that the clock that actually accelerated will have recorded less time.
I'm CONFUSED! I have read (in this forum) some posts which state that it is the acceleration/deceleration which causes the time dilation, and I read other posts which say that even relative velocity (without acceleration) causes time dilation. Which is it, or is it BOTH?

I can easily devise a thought experiment which contains a "traveling twin" and a "stay-at-home twin" and which contains a method of comparing their respective ages after a journey by the "traveling twin", WITHOUT introducing either acceleration or deceleration into the scenario.

Al68
I'm CONFUSED! I have read (in this forum) some posts which state that it is the acceleration/deceleration which causes the time dilation, and I read other posts which say that even relative velocity (without acceleration) causes time dilation. Which is it, or is it BOTH?
It's the latter. Time dilation is the result of relative velocity. The difference in elapsed times is the (indirect) result of acceleration.

Time dilation refers to the rate of a moving clock relative to a stationary clock in a chosen reference frame, so each clock is time dilated relative to the other frame. The total elapsed time between events is the combination of a clock's rate and the path length. Remember that in the twins paradox, the total distance traveled is greater for the earth twin than for the ship's twin.

Fredrik
Staff Emeritus
Gold Member

The symmetry of the situation is broken when one of the clocks invariably had to accelerate to turn around. In that case, we have an accelerating frame and the problem is not correctly handled by special relativity, which only deals with inertial frames. Thus, we will find that the clock that actually accelerated will have recorded less time.
The part I colored red is wrong. As long as we're talking about Minkowski spacetime, it's SR.

From my understanding, the faster you travel the slower time gets right?
Does time flow at different speeds?
A much better way to think about these things is "a clock measures the proper time of the curve in spacetime that represents its motion". So clocks are always doing what they're supposed to, no matter how they move.

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relative velocity causes time dilation
relative velocity also causes relativity of simultaneity
change in relative velocity causes a change in relativity of simultaneity. This causes clocks at different distances from the accelerating rocket to run at different rates. some may even run backwards

so its both

Fredrik said:
G01 said:

The symmetry of the situation is broken when one of the clocks invariably had to accelerate to turn around. In that case, we have an accelerating frame and the problem is not correctly handled by special relativity, which only deals with inertial frames. Thus, we will find that the clock that actually accelerated will have recorded less time.
The part I colored red is wrong. As long as we're talking about Minkowski spacetime, it's SR.
seconded

I'm CONFUSED!
I can easily devise a thought experiment which contains a "traveling twin" and a "stay-at-home twin" and which contains a method of comparing their respective ages after a journey by the "traveling twin", WITHOUT introducing either acceleration or deceleration into the scenario.

Maheinste.

you can certainly solve it without taking accel or decel into account.
but can you understand or explain to a beginner why the traveling twin sees the stationary twin age more even though relativity says that all motion is relative.

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Maheinste.
Well, my thought experiment is somewhat lengthy, but if I understand the earlier reply, acceleration/deceleration isn't needed to cause time dilation. My thought experiment was simply my way to illustrate a twin-paradox scenario in which the ages of the twins can be compared after the traveling twin's journey, without the traveling twin having to accelerate or decelerate.

Well, my thought experiment is somewhat lengthy, but if I understand the earlier reply, acceleration/deceleration isn't needed to cause time dilation. My thought experiment was simply my way to illustrate a twin-paradox scenario in which the ages of the twins can be compared after the traveling twin's journey, without the traveling twin having to accelerate or decelerate.
But if the traveller does not accelerate his journey never starts and if he does not then decelerate his journey never ends.

Matheinste.

But if the traveller does not accelerate his journey never starts and if he does not then decelerate his journey never ends.

Matheinste.

In my thought experiment, the two don't need to be twins. All that I want is to construct a scenario in which the age DIFFERENCE between two persons CHANGES after one of them has undergone a long trip. In my scenario, the "traveler" has already gone through his acceleration long prior to reaching a point alongside the "stay-at-home" on Earth. At that instant, the relative ages of the two can be known. The traveler continues at his constant velocity until passing a point on Planet X. He does not decelerate. As he reaches that point, an observer on Planet X notes the traveler's age. The age of the traveler is transmitted back to Earth.

Now, all that needs to be known is the distance from Earth to Planet X, the speed of the traveler, the time in Earth years that it would have taken the traveler to reach Planet X, and the age of the traveler at the time that he passed a point on Planet X and the current age of the stay-at-home.

This can reveal the CHANGE in the age DIFFERENCE of the two.

In my thought experiment, the two don't need to be twins. All that I want is to construct a scenario in which the age DIFFERENCE between two persons CHANGES after one of them has undergone a long trip. In my scenario, the "traveler" has already gone through his acceleration long prior to reaching a point alongside the "stay-at-home" on Earth. At that instant, the relative ages of the two can be known. The traveler continues at his constant velocity until passing a point on Planet X. He does not decelerate. As he reaches that point, an observer on Planet X notes the traveler's age. The age of the traveler is transmitted back to Earth.

Now, all that needs to be known is the distance from Earth to Planet X, the speed of the traveler, the time in Earth years that it would have taken the traveler to reach Planet X, and the age of the traveler at the time that he passed a point on Planet X and the current age of the stay-at-home.

This can reveal the CHANGE in the age DIFFERENCE of the two.
The fact that the acceleration occurred at a distant point in time doesn't change the fact that we're still talking about acceleration. The point is that while accelerating, Relativistic effects occur... and their separation in time from your comparison only matters in terms of who was born at the relevant time to be able to make an initial clock-synch.

We know what the stationary twin will calculate for the traveling twins age.
the traveling twins calculation of the stationary twins age and how he arrives at it is the real question

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The fact that the acceleration occurred at a distant point in time doesn't change the fact that we're still talking about acceleration. The point is that while accelerating, Relativistic effects occur... and their separation in time from your comparison only matters in terms of who was born at the relevant time to be able to make an initial clock-synch.
I don't care that the traveler had to BEGIN his trip by accelerating. I'm only interested in the portion of the time dilation (with respect to a stay-at-home person) that occurs AFTER the traveler reaches a constant velocity. In my earlier post, I asked whether constant relative velocity (without regard to acceleration) would result in time dilation, and I understood the answer to be "yes".

I don't care that the traveler had to BEGIN his trip by accelerating. I'm only interested in the portion of the time dilation (with respect to a stay-at-home person) that occurs AFTER the traveler reaches a constant velocity. In my earlier post, I asked whether constant relative velocity (without regard to acceleration) would result in time dilation, and I understood the answer to be "yes".
Yes, in this scenario both are moving inertially and so only time dilation is relevant. Each reckons the others clock to be running slower than his own, and the clocks in the others rest frame to be out of synch. It has, of course, nothing to do with the differential ageing paradox.

Matheinste.

Yes, in this scenario both are moving inertially and so only time dilation is relevant. Each reckons the others clock to be running slower than his own, and the clocks in the others rest frame to be out of synch. It has, of course, nothing to do with the differential ageing paradox.

Matheinste.
I'm even more confused now. What do you mean when you say that it has nothing to do with the differential ageing paradox? In my scenario, even without accelerating, won't the traveler age slower than the stay-at-home? As I stated before, I had a reply to my earlier question which said that constant velocity WILL result in time dilation.

Janus
Staff Emeritus
Gold Member
I'm even more confused now. What do you mean when you say that it has nothing to do with the differential ageing paradox? In my scenario, even without accelerating, won't the traveler age slower than the stay-at-home? As I stated before, I had a reply to my earlier question which said that constant velocity WILL result in time dilation.
With constant velocity, which twin ages slower i5 frame dependent. Each says that the other ages slower.

So let's go over your scenario:

In my scenario, the "traveler" has already gone through his acceleration long prior to reaching a point alongside the "stay-at-home" on Earth. At that instant, the relative ages of the two can be known. The traveler continues at his constant velocity until passing a point on Planet X. He does not decelerate. As he reaches that point, an observer on Planet X notes the traveler's age. The age of the traveler is transmitted back to Earth.

Now, all that needs to be known is the distance from Earth to Planet X, the speed of the traveler, the time in Earth years that it would have taken the traveler to reach Planet X, and the age of the traveler at the time that he passed a point on Planet X and the current age of the stay-at-home.
All of this works fine, as long as you only consider things from the frame of the Earth and Planet X.

But here's what happens according to the traveler. As he passes Earth, he notes the time on Earth's clock. Since he is moving with respect to both Earth and Planet X, two things are noted. One is that the distance between the Earth and Planet X will be shorter for him than it is as measured by the Earth. This is because of length contraction. In addition, The clocks on Earth and Planet X will not be in sync; Planet X's clock will be ahead of Earth's. This is due to the Relativity of Simultaneity.

While traveling to planet X, both Earth's and Planet X's clocks will run slow compared to his. When he gets to Planet X, he notes what his clock reads( which will equal the length contacted distance divided by his speed relative to the planets.). This will be less than what Planet X's clock reads, but that is only because Planet X's clock had a head start to begin with. Earth's clock will read less time than his.

The signal is sent. From the Traveler's frame, the Earth is fleeing away from him at some high speed and the signal has to chase after it. So even though the Earth's clock ticks slower than his, by the time that the light signal reaches it, the Earth clock will have advanced quite a bit.

For example. Assume the distance between planets is 10 ly as measured from Earth. At 0.866c, it will take the traveler 11.55 yrs to travel the distance according to the Earth clock Planet X clocks. Time dilation will slow the traveler's clock by half, so 5.77 yrs pass on the traveler's clock. The signal takes 10 yrs to get back to Earth, and So Earth gets the signal 21.55 yrs after the traveler passed Planet X. This is what happens according the stay at home frame.

Here's what happens according to the traveling frame:

As the Earth passes beneath him, the distance to Planet X is 5 ly and the clock on Planet X already reads 8.66 years. It takes 5.77 yrs until Planet X passes beneath him, during which time, 2.88 yrs passes on the Earth and Planet X clocks. Thus 11.55 yrs shows on the Planet X clock and 2.88 yrs shows on the Earth Clock at this instant.

The signal is sent. Earth is 5 ly away and fleeing away at 0.866c. It will take 5ly/(1c-0.866c) = 37.31 yrs by the traveler's clock for the signal to reach Earth, during which time 18.67 years pass on the Earth clock. Add this to the 2.88 yr that The earth clock already read and the signal arrives when the Earth clock reads 21.55 yrs, the same time as seen from the Earth frame. However, from the traveler's frame, the stay at home twin has always aged less than him.

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Just pick up a copy of "The Elegant Universe" and read the portion about the two 'astronauts' in various scenarios. Anyone can grasp that reading of this issue, and it covers the accelerated and constant scenarios.

I have another thought..

Two satellites in orbit of something, they are orbiting in different directions.
Now that means that their relative speed is constantly changing, what happens to time?

Both thrusted the same, both experience the same accelaration to start, so who has the slower time, who has the faster time.

As the Earth passes beneath him, the distance to Planet X is 5 ly and the clock on Planet X already reads 8.66 years. It takes 5.77 yrs until Planet X passes beneath him, during which time, 2.88 yrs passes on the Earth and Planet X clocks. Thus 11.55 yrs shows on the Planet X clock and 2.88 yrs shows on the Earth Clock at this instant.

The signal is sent. Earth is 5 ly away and fleeing away at 0.866c. It will take 5ly/(1c-0.866c) = 37.31 yrs by the traveler's clock for the signal to reach Earth, during which time 18.67 years pass on the Earth clock. Add this to the 2.88 yr that The earth clock already read and the signal arrives when the Earth clock reads 21.55 yrs, the same time as seen from the Earth frame. However, from the traveler's frame, the stay at home twin has always aged less than him.
What happens if the ship stops at planet X, no longer is earth fleeing away at .866c, so a signal sent will take 10 years by the travellers clock and 10 years by the earth clock, arriving only 12.88 years after departure?

In addition, The clocks on Earth and Planet X will not be in sync; Planet X's clock will be ahead of Earth's. This is due to the Relativity of Simultaneity.

Ok, before I go any further, let me ask this: Why do the clocks on Earth and Planet X HAVE to be out of sync? What if I have someone on a planet that is equidistant from both Earth and Planet X send simultaneous signals to both planets to set their clocks together? The signal would take the same length of time to reach Earth as it would to reach Planet X, so that both clocks would be set to the same starting time.