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Offline DoctorBeaver

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Acceleration & ageing
« on: 12/10/2007 08:02:33 »
I found this on another forum. Is he right?

"The point of that paradox is to show that it's not the speed that makes the difference, it's the acceleration.

It is true that both twins move away from each other at near light speed from each others' point of view... but only one twin experienced the acceleration. The other did not. The twin that stayed on Earth did not accelerate or decelerate. The twin that flew away then came back did. That is why he did not age while the other did.

If both twins had accelerated away in different directions, then came back, both would be the same age."


Consider this:-

2 people accelerate off in different spaceships to near-lightspeed. 1 immediately decelerates to a standstill while the other keeps going at a constant speed for a while. When the 2nd person decelerates and returns, will he not have aged less than the first?


 

another_someone

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Acceleration & ageing
« Reply #1 on: 12/10/2007 13:11:53 »
It is the acceleration that causes the change of reference, but how long you remain in that other frame of reference is another matter.

Although what I am trying to work out is what someone who is born on one of the spaceships while they are speeding apart (and so has no knowledge of the first acceleration) will perceive?
 

Offline DoctorBeaver

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« Reply #2 on: 12/10/2007 14:12:06 »
I'm aware that acceleration causes the change of reference; but, surely, it is the actual speed that causes time dilation. Consider this diagram:-



The x axis = time and the y axis = speed for each plot. In the first, the spaceship accelerates to near c, then immediately decelerates to a stop. In the 2nd, the spaceship accelerates to near c, maintains that speed for a while, then decelerates to a stop. The total time taken is the same for both.

Assuming both spaceships take an equal time to accelerate to near c (same max speed for both) and decelerate to a stop, would both passengers age at the same rate? I would have thought that the passenger in B would age slower as near c speed is maintained for longer.

Photons travel at c and for a photon, time is irrelevant - everything happens at once. They neither accelerate nor decelerate (OK, they do, but to all intents and purposes they don't) yet time dilation applies.
« Last Edit: 12/10/2007 14:14:31 by DoctorBeaver »
 

another_someone

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« Reply #3 on: 12/10/2007 14:29:55 »
I'm aware that acceleration causes the change of reference; but, surely, it is the actual speed that causes time dilation. Consider this diagram:-



You can regard speed as equivalent to integral of acceleration, and the time at a given speed as being the time between accelerations; so they are probably roughly the same thing.

The problem with using speed is that there is no absolute reference for speed, but there is an absolute reference for acceleration (although there is still a problem with distinguishing acceleration from deceleration).  Thus calculating the integral of acceleration is meaningful, but working out your speed without knowing your acceleration history is not possible.

Photons travel at c and for a photon, time is irrelevant - everything happens at once. They neither accelerate nor decelerate (OK, they do, but to all intents and purposes they don't) yet time dilation applies.

Actually, this leads to another interesting question:

Since all photons, which are travelling at the speed of light, are travelling at equal speed with reference to us; does it mean that we all travel at equal speed in relation to the photons - i.e. that a photon cannot distinguish between the speed of a different objects which to our perception are travelling at very different speeds.  Does it then follow that simply because all photons appear to be travelling the same speed to us, they may not perceive each other to be travelling at the same speed.  Possibly not a question one can answer unless one becomes a photon.
 

Offline DoctorBeaver

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« Reply #4 on: 12/10/2007 14:33:21 »
I asked a question about that a while back regarding how photons travelling line astern perceive each other.
 

another_someone

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« Reply #5 on: 12/10/2007 14:43:05 »
I asked a question about that a while back regarding how photons travelling line astern perceive each other.

If you mean this, it not really the same question.

You were asking whether one photon perceives another photon as travelling at the speed of light.  I was rather asking whether one photon could perceive another photon as travelling at subluminal speeds (e.g. maybe 30m/s).
 

lyner

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« Reply #6 on: 12/10/2007 14:58:40 »
We did one of these not long ago.
The actual effect on time (how many seconds adrift, you get)  can be calculated on the basis of the speed difference and the time it's going for.
You need acceleration times time to get to that speed.
Surely the guy on the accelerating space ship will just feel perfectly normal. (Unless he is accelerating so fast that the blood rushed to his feet.)
 

Offline DoctorBeaver

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« Reply #7 on: 12/10/2007 17:37:17 »
So am I right or wrong?  ???
 

lyner

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« Reply #8 on: 12/10/2007 17:44:36 »
You are right, in as far as you can't have one without the other!
Someone has to accelerate at some point for this effect to occur.
The twins can't get back together without it.
 

Offline DoctorBeaver

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« Reply #9 on: 12/10/2007 18:42:01 »
What about the point that George raised where someone is born on the moving spaceship. They would not have experienced the initial acceleration. If someone was born on Earth at the same time and then a message was sent to the spaceship on the Earth-born child's first birthday, would the child on the spaceship be experiencing their first birthday aswell or would they be younger?
 

Offline thebrain13

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« Reply #10 on: 12/10/2007 19:23:47 »
george, the thing about the baby is, it has no way of knowing how old the other "stationary" object is, Unless they get together for tea later. So to answer your question, whoever accelerates after the baby is born will determine which frame of reference has aged more or less.
 

Offline thebrain13

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« Reply #11 on: 12/10/2007 19:36:23 »
think about this, lets say one spaceship takes off at .9c, then later another spaceship takes off at .95c and catches it. the spaceship that took of second would age less because it had to travel faster to catch the ship. the initial acceleration that seperates objects doesnt matter, its who accelerates second to get them back to where they need to be that matters.

You see it doesnt matter that the baby had accelerated in his past, because once he accelerated he set a new precedent in the acceleration needed to reunite them.
 

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« Reply #12 on: 12/10/2007 19:42:23 »
george, the thing about the baby is, it has no way of knowing how old the other "stationary" object is, Unless they get together for tea later. So to answer your question, whoever accelerates after the baby is born will determine which frame of reference has aged more or less.

I had thought about that, but the problem I see is this.

Suppose we have two babies born in two frames of reference - neither knows which one is travelling faster, the only know there is a relative speed between them.  Now one of the babies feels an acceleration, and the two are now travelling the same speed.  Nice and simple - yes?  But was that really an acceleration, or a deceleration?
 

Offline DoctorBeaver

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« Reply #13 on: 12/10/2007 20:02:32 »
I'm getting out of my depth here  [V]
 

Offline thebrain13

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« Reply #14 on: 12/10/2007 20:11:12 »
since all i know is that there are two observers traveling with respect to one another, the one that you said changed speed is the one that would be viewed as accelerated.

your problem is that you are assuming a reference frame that you didn't mention, that would determine which one was traveling faster "relative to it" in the first place. If you tell me it's parameters, i can answer your question.
« Last Edit: 12/10/2007 20:20:27 by thebrain13 »
 

Offline DoctorBeaver

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« Reply #15 on: 12/10/2007 20:26:26 »
thebrain - I was assuming that both set out from Earth. 1 accelerated then immediately decelerated. The other accelerated, maintained speed for a while, and then decelerated. I was just wondering how time dilation would affect each of them.
 

Offline thebrain13

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« Reply #16 on: 12/10/2007 20:43:27 »
the beauty of relativity is that all frames of reference from all time periods will agree "once you bring them back togeter" if objects are floating away from each other, they will both say that the other object has aged less than them.

In your experiment that you explained, assuming all objects are traveling in the same direction with respect to one another, they would all view each other as aged less than themselves, the outermost observers (the earth and the object that decelerated second) would view each other as the most time dilated, and both would view the center object as less time dilated.

If you brought all three objects back together on earth, the time dilation would be dependent on  how long they traveled away from one another and at what speed, so once they returned the object that traveled the farthest away from earth would be the youngest and the one that traveled not so far would be younger than the earthlings but not as much younger.

 

Offline DoctorBeaver

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« Reply #17 on: 12/10/2007 20:53:49 »

If you brought all three objects back together on earth, the time dilation would be dependent on  how long they traveled away from one another and at what speed, so once they returned the object that traveled the farthest away from earth would be the youngest and the one that traveled not so far would be younger than the earthlings but not as much younger.



That's exactly what I was asking. In my diagram, B would have travelled further as it maintained near-c speed for a while whereas A decelerated straight away.

So it's not just acceleration that causes time dilation.
 

lyner

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« Reply #18 on: 12/10/2007 23:35:09 »
I think that, somewhere in here, you have forgotten that your two individuals can only do this experiment if they can establish a common time and place where they actually meet up. in some way. They can be moving, relative to each other when they meet, if you like.
We had this all out before.
I claimed that it involves GR, because of the acceleration but someone (can't remember who) said that you didn't need GR if you were an observer in an inertial frame, somewhere. But I argued that, for this stuff to happen someone has to experience the effects of GR - i.e. the guy who accelerates - and someone has to accelerate for it to happen.
The issue of the twin who is traveling at birth is, I think, irrelevant because his frame has accelerated at some point - whether he was alive at the time or not.

As for this comment
Quote
thebrain - I was assuming that both set out from Earth. 1 accelerated then immediately decelerated. The other accelerated, maintained speed for a while, and then decelerated. I was just wondering how time dilation would affect each of them.
, they can't be at the same place at the end of the experiment, so can they establish how much adrift their clocks are? The one that traveled  faster for longer would experience the greater time dilation, I think.
 

Offline DoctorBeaver

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« Reply #19 on: 13/10/2007 11:46:46 »
They can be at the same place at the end if they make cirular trips out from Earth & then return. B's loop would obviously be much bigger than A's.
 

another_someone

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« Reply #20 on: 13/10/2007 12:15:23 »
They can be at the same place at the end if they make cirular trips out from Earth & then return. B's loop would obviously be much bigger than A's.

But if you are travelling in a circle then you are under constant acceleration, which is very different from the inertial reference frames that special relativity addresses.
 

Offline DoctorBeaver

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« Reply #21 on: 13/10/2007 18:31:03 »
They can be at the same place at the end if they make cirular trips out from Earth & then return. B's loop would obviously be much bigger than A's.

But if you are travelling in a circle then you are under constant acceleration, which is very different from the inertial reference frames that special relativity addresses.

Good point; to which I had given no consideration. TUT! @ me   [:I]
 

Offline thebrain13

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« Reply #22 on: 13/10/2007 21:48:26 »
sophiecentaur, it doesnt matter that the baby had accelerated at some point, it wouldnt affect anything. The babys frame of reference is altered relative to the initial frame of reference. Or to put it another way, time dilation occurs before and after the babys birth. Once the baby is born it sets a new precedent for simultaneity(it was born in a different time frame than the initial one). Relativity works the same in all frames of reference from wherever and whenever you look at it. the initial observer would view a different time dilation than the baby because they started their time experiments from different times and locations.
 

Offline thebrain13

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« Reply #23 on: 13/10/2007 21:51:14 »
Also, acceleration of the experiment does not alter time dilation directly, but the changing of velocities, due to acceleration does.
 

lyner

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« Reply #24 on: 13/10/2007 23:46:26 »
I think this is going in circles.
Acceleration just introduces GR. What's the problem?
 

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