Confused about time slowing down

[MrXavia]

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 can't 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.

Thanks in advance for explaining!

 

[Dale]

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]

The short answer is:

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.

 

[MrXavia]

The short answer is:

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?

 

[LBrandt]

The short answer is:

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]

The short answer is:

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.

There are lots of threads about the twin paradox already. This is one of them.

 

[granpa]

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

The short answer is:

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

 

[matheinste]

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.

What is your thought experiment?

Maheinste.

 

[granpa]

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.

 

[LBrandt]

What is your thought experiment?

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.

 

[matheinste]

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.

 

[LBrandt]

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.

 

[nismaratwork]

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.

 

[granpa]

but that doest address the real point of the twins paradox.
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

 

[LBrandt]

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".

 

[matheinste]

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.

 

[LBrandt]

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]

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.

 

[nismaratwork]

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.

 

[MrXavia]

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.

 

[MrXavia]

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?

 

[granpa]

it really isn't all that complicated. you are confusing yourself
my suggestion is that you learn to draw spacetime diagrams

https://www.physicsforums.com/showthread.php?t=314080

 

[nismaratwork]

OK... read beginning on page 28. If you don't get it then, you're not going to in my view. http://books.google.com/books?id=FH...=1&sqi=2&ved=0CBIQ6AEwAA#v=onepage&q&f=false"

 

[LBrandt]

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.

 

[matheinste]

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.

Yes, but if the clocks on Earth and the other planet at rest in the same frame are synchronised to an observer (planet/transmitter) also at rest in that frame, then they cannot be synchronized as far as an observer moving relative to them is concerned. This is absolutely basic to SR. Even if you could arrange to start them at the same time according to some observer moving relative to them, they would not remain synchronized for that observer.

Matheinste.

 

[LBrandt]

Yes, but if the clocks on Earth and the other planet at rest in the same frame are synchronised to an observer (planet/transmitter) also at rest in that frame, then they cannot be synchronized as far as an observer moving relative to them is concerned. This is absolutely basic to SR. Even if you could arrange to start them at the same time according to some observer moving relative to them, they would not remain synchronized for that observer.

Matheinste.

All that my scenario requires is that when the traveler "passes" a point on Planet X, his AGE at that point can be documented. If so, then the calculations can be made back on Earth (I don't care WHEN they're made) to determine whether the traveler aged slower than the stay-at-home DURING his constant velocity trip.

 

[matheinste]

All that my scenario requires is that when the traveler "passes" a point on Planet X, his AGE at that point can be documented. If so, then the calculations can be made back on Earth (I don't care WHEN they're made) to determine whether the traveler aged slower than the stay-at-home DURING his constant velocity trip.

If the Earth (for our present purposes) and the traveller are each at rest in inertial frames of reference which are moving relative to each, then being at rest or moving is meaningless.

Matheinste.

 

[Janus]

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.

Again, this is only true for someone at rest with respect to Earth and Planet X.

This will not be true as far as the Traveler is concerned. Remember, the speed of light is a constant relative to any inertial frame. Thus according for the traveler, the two signals travel at c relative to him (not Earth and Planet X). Thus Earth is fleeing away from its signal and Planet X is rushing towards its signal. Planet X gets its signal first, and its clock starts running from the Agreed upon starting value first. By the time that Earth has gotten its signal, quite a bit of time has already past on Planet X.

 

[Janus]

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?

Then the ship has undergone an acceleration and changed inertial reference frames. Form the Traveler's perspective, the Earth clock jumps forward to read the same as Planet X's clock.

 

[LBrandt]

Again, this is only true for someone at rest with respect to Earth and Planet X.

This will not be true as far as the Traveler is concerned. Remember, the speed of light is a constant relative to any inertial frame. Thus according for the traveler, the two signals travel at c relative to him (not Earth and Planet X). Thus Earth is fleeing away from its signal and Planet X is rushing towards its signal. Planet X gets its signal first, and its clock starts running from the Agreed upon starting value first. By the time that Earth has gotten its signal, quite a bit of time has already past on Planet X.

That doesn't make sense to me at all. Let's forget a traveler for the moment. I can visualize a clock on Earth and a clock on Planet X being set in sync simply by having simultaneous signals sent from a THIRD planet that is equidistant from both Earth and Planet X. Forgetting travelers, forgetting relativity, forgetting everything, I can do that! Surely, you will allow that scenario.

 

[nismaratwork]

That doesn't make sense to me at all. Let's forget a traveler for the moment. I can visualize a clock on Earth and a clock on Planet X being set in sync simply by having simultaneous signals sent from a THIRD planet that is equidistant from both Earth and Planet X. Forgetting travelers, forgetting relativity, forgetting everything, I can do that! Surely, you will allow that scenario.

If you forget relativity then your question is no longer meaningful! You can add an infinite array of intermediate planets, and your "difference" will become smaller and smaller at each step, but it's never eliminated. What you would require is that light not be the upper 'speed limit' at work, and have a means to send signals faster than light. That in essence, removes the entire need for and concept of, Relativity.

 

[granpa]

http://en.wikipedia.org/wiki/Relativity_of_simultaneity

this is what confuses all beginners. Rather than argue with the people here you would be better off taking the time to learn about this first.

 

[Janus]

That doesn't make sense to me at all. Let's forget a traveler for the moment. I can visualize a clock on Earth and a clock on Planet X being set in sync simply by having simultaneous signals sent from a THIRD planet that is equidistant from both Earth and Planet X. Forgetting travelers, forgetting relativity, forgetting everything, I can do that! Surely, you will allow that scenario.

I never said that you couldn't. The problem is that not everyone will agree that the Earth clock and Planet X clock are in sync.

Much of Relativity doesn't seem to make sense when compared to everyday experience.

We expect it to be the same time in Atlanta and New York regardless of whether we are standing along the road between them or driving along the road between them. Relativity says otherwise. It says that if you are driving from one to the other, it will not be the same time in the two cities. We just don't notice it because at the speed of a car the difference is too small to measure.

Relativity requires that we rethink how we consider time and space and toss out some of the notions about it that we got by observing the slow moving world around us.

 

[nismaratwork]

I really think the link I gave to The Elegant Universe's relativity section is a pretty simple and straightforward explanation. *shrug*