Explaining the twin paradox with special relativity and doppler effect.

[CasualKilla]

I have been thinking about a way to explain the twin paradox, I came across a video where both twins have synchronized clocks that emit a light pulse every 1 minute. When they are moving apart, both the earth twin and the spaceship twin experience doppler shifted pulse of 2 minutes.(v = 0.87c). Then when the spaceship twin turns around, he experiences doppler shifted pulse from the earth every 30 seconds. The earth however, still receives the the 2 minute pulses until the information that spaceship twin has turned around reaches them (depends of distance), after which earth also receives 2 minute pulses.

 

When the twins gets back together, both agree that earth twin sent more pulses. Thus space twin is indeed younger.

 

Now I do not find this a satisfactory explanation, since the same argument can be made for say a fast car with a 1hz siren and a stationary observer with another 1Hz siren. We know for certain at these low speeds there will be almost negligible time dilation, but the car will measure more beeps from the stationary object, since it will also take a while for the sound information to travel back to the observer to tell him he has turned around.

 

Is this argument fallacious, or am I getting something wrong?

 

I think I see the problem with this explanation, since it does not address the fact that both twins experience the same time dilatation relative to the other, ie they both observe the other going at 1/2 speed. Then pulls a bait and switch by showing you that one twin received less pulses than he sends out, making you assume that their times where different without even using relativity in the first place.

 

Another thing, this explanation seems to use the fact that light is the tool used for observation. Is this what Einstein intended, or can an observer observe things "instantly" without relying on the delay cause by the finite speed of light?

Edited March 26, 2015 by CasualKilla

[swansont]

Is this argument fallacious, or am I getting something wrong?

Option b. Do the math.

Another thing, this explanation seems to use the fact that light is the tool used for observation. Is this what Einstein intended, or can an observer observe things "instantly" without relying on the delay cause by the finite speed of light?

You can never transmit information faster than c

[CasualKilla]

Option b. Do the math.

 

You can never transmit information faster than c

I did, they both experience the same time dilatation, since the relative motion is same for both. If it could be so simply solved it wouldn't be a paradox would it...

[xyzt]

I did, they both experience the same time dilatation, since the relative motion is same for both.

 

 

But their motion is not symmetric, one is accelerated, the other one is not. You need to learn to make the distinction.

Edited March 26, 2015 by xyzt

[CasualKilla]

You can never transmit information faster than c

That is interesting since then observation would just mean detecting the photons, how do we know objects actually change length, perhaps it is just how we perceive the photons? For example, fly near the speed of light, then you see stars changing shape, but for all we know that star may already be dead, we are just changing how we observe the photons..

But their motion is not symmetric, one is accelerated, the other one is not. You need to learn to make the distinction.

Yes, but that is general relativity. Do you need to go there to solve the paradox?

Edited March 26, 2015 by CasualKilla

[xyzt]

That is interesting since then observation would just mean detecting the photons, how do we know objects actually change length, perhaps it is just how we perceive the photons?

Yes, but that is general relativity. Do you need to go there to solve the paradox?

No, you do not need GR, SR handles accelerated motion just fine. You only need to learn to make the distinction between the twins. So far, you haven't.

[Janus]

I have been thinking about a way to explain the twin paradox, I came across a video where both twins have synchronized clocks that emit a light pulse every 1 minute. When they are moving apart, both the earth twin and the spaceship twin experience doppler shifted pulse of 2 minutes.(v = 0.87c). Then when the spaceship twin turns around, he experiences doppler shifted pulse from the earth every 30 seconds. The earth however, still receives the the 2 minute pulses until the information that spaceship twin has turned around reaches them (depends of distance), after which earth also receives 2 minute pulses.

 

When the twins gets back together, both agree that earth twin sent more pulses. Thus space twin is indeed younger.

 

Now I do not find this a satisfactory explanation, since the same argument can be made for say a fast car with a 1hz siren and a stationary observer with another 1Hz siren. We know for certain at these low speeds there will be almost negligible time dilation, but the car will measure more beeps from the stationary object, since it will also take a while for the sound information to travel back to the observer to tell him he has turned around.

 

Is this argument fallacious, or am I getting something wrong?

 

I think I see the problem with this explanation, since it does not address the fact that both twins experience the same time dilatation relative to the other, ie they both observe the other going at 1/2 speed. Then pulls a bait and switch by showing you that one twin received less pulses than he sends out, making you assume that their times where different without even using relativity in the first place.

 

Another thing, this explanation seems to use the fact that light is the tool used for observation. Is this what Einstein intended, or can an observer observe things "instantly" without relying on the delay cause by the finite speed of light?

The problem with your car and siren example is that you use different formulas to calculate Doppler shift for sound, which requires a medium than you do for light, which does not.

 

The classical Doppler shift formula for sound is:

 

[math]F= \frac{c+v_r}{c+v_s} f_0[/math]

 

here c is the speed of sound in the medium, Vr is the speed of the receiver, and Vs the speed of the source.

 

So for example, if our car travels at 50m/s and the speed of sound is 340m/s, we get the following result:

 

As we(the receiver) listen to the receding siren, we hear it reduced in frequency to ~87.18Hz. We will assume that the car travels away from us for 10 sec by its own clock before returning. This means that it sends out 10 x 100=1000 "beats" on the outward leg and another 1000 on the inward leg.

It will take us 1000/87.18= 11.47 sec to hear the 1000 beats of the outbound leg. we then hear the siren shift to ~1.172Hz. It will take us 1000/1.17 = ~8.53 sec to hear the 1000 beats of the return leg.

Thus it will take us 11.47+8.53 = 20 sec to hear the 2000 beats sent out by the 100Hz siren in 20 of its own seconds.

 

If we are traveling with the car listening to the other siren, we hear the following:

 

For ten seconds, we hear a frequency of 85.3Hz and count 853 beats. For the next ten seconds we hear a frequency of 114.7Hz and and hears 1147 beats.

Thus we hear 853+1147= 2000 beats sent out by the at rest siren. Someone in the car or at rest count the same number of beats coming from the other siren.

 

One thing to point out here is that, because of the need of a medium to carry sound, the Doppler shift is not reciprocal between car and the at rest siren. While they are separating, the at rest observer hears a frequency of 87.17Hz from the car, while the car hears 85.3Hz from the stationary siren. There is a similar difference during the return legs.

 

Now the Doppler shift for light, where there is no medium to consider, is the following.

 

[math]F= \sqrt{ \frac{c-\frac{v}{c}}{c+\frac{v}{c}}}f_0[/math]

 

where c is the speed of light and v the relative between source and receiver. Note that we no longer need to distinguish between source and receiver velocity.

as a result, this formula does gives reciprocal results. Both observers measure the same Doppler shift when separating or closing in on each other.

 

If we repeat the above car siren test with light(instead of a 100Hz sound we have a light flashing at 100Hz), and boost v up to 0.147c (this keeps the ratio between v and the speed of light the same as between the speed of the car and sound in the first example), wqe get the following results:

 

Our "stationary" observer sees the car light flash at a rate of 86.2Hz for the outbound leg and it takes ~11.6 sec to see first 1000 flashes.

He then sees the the car light flash at a rate of 116Hz and takes 8.62 sec to see the next 1000 flashes. total time to sees 2000 flashes is 11.6+8.62=20.22 sec, during which time its own light flashes 2022 times.

 

The car sees this:

 

while receding, he sees the stationary light flash at 86.2Hz. During the 10 sec it takes for his own light to flash 1000 times, he sees 862 flashes.

He then sees the stationary light flash at 116hz for another ten seconds and flash 1160 times while his own light flashes 1000 times.

Thus he sees the stationary light flash 862+1160 = 2022 times for his own light flashing 2000 times. Both observers agree how many flashes occurred for both during the entire duration.

This also agrees with the time dilation factor for 0.147c which is 0.989, and 2000/2022 = 0.989

 

As to your objection that this does not square with the idea that both observer should conclude that the other clock should be the one running slow, this is not the case.

There is more to this than just time dilation, there is also length contraction and the Relativity of Simultaneity to consider. You have to factor in these effects also when looking at the total elapsed time for both observers.

 

As for using light for our observations. The means by which the observations are made are not important. Light is just the simplest means of doing so in these examples. Light happens to travel at the invariant speed of the universe. It is the fact that such a finite invariant speed exists that leads to the effects of Relativity, not that we can use light to demonstrate them.

Edited March 26, 2015 by Janus

[CasualKilla]

No, you do not need GR, SR handles accelerated motion just fine. You only need to learn to make the distinction between the twins. So far, you haven't.

One experiences acceleration, sure, but what if there was a worm hole that allowed him to change direction instantly, lets remove that variable completely.

[swansont]

I did, they both experience the same time dilatation, since the relative motion is same for both. If it could be so simply solved it wouldn't be a paradox would it...

 

There is no time dilation for the siren example. Janus has done the math for you.

[CasualKilla]

The problem with your car and siren example is that you use different formulas to calculate Doppler shift for sound, which requires a medium than you do for light, which does not.

 

The classical Doppler shift formula for sound is:

 

[math]F= \frac{c+v_r}{c+v_s} f_0[/math]

 

here c is the speed of sound in the medium, Vr is the speed of the receiver, and Vs the speed of the source.

 

So for example, if our car travels at 50m/s and the speed of sound is 340m/s, we get the following result:

 

As we(the receiver) listen to the receding siren, we hear it reduced in frequency to ~87.18Hz. We will assume that the car travels away from us for 10 sec by its own clock before returning. This means that it sends out 10 x 100=1000 "beats" on the outward leg and another 1000 on the inward leg.

It will take us 1000/87.18= 11.47 sec to hear the 1000 beats of the outbound leg. we then hear the siren shift to ~1.172Hz. It will take us 1000/1.17 = ~8.53 sec to hear the 1000 beats of the return leg.

Thus it will take us 11.47+8.53 = 20 sec to hear the 2000 beats sent out by the 100Hz siren in 20 of its own seconds.

 

If we are traveling with the car listening to the other siren, we hear the following:

 

For ten seconds, we hear a frequency of 85.3Hz and count 853 beats. For the next ten seconds we hear a frequency of 114.7Hz and and hears 1147 beats.

Thus we hear 853+1147= 2000 beats sent out by the at rest siren. Someone in the car or at rest count the same number of beats coming from the other siren.

 

One thing to point out here is that, because of the need of a medium to carry sound, the Doppler shift is not reciprocal between car and the at rest siren. While they are separating, the at rest observer hears a frequency of 87.17Hz from the car, while the car hears 85.3Hz from the stationary siren. There is a similar difference during the return legs.

 

Now the Doppler shift for light, where there is no medium to consider, is the following.

 

[math]F= \sqrt{ \frac{c-\frac{v}{c}}{c+\frac{v}{c}}}f_0[/math]

 

where c is the speed of light and v the relative between source and receiver. Note that we no longer need to distinguish between source and receiver velocity.

as a result, this formula does gives reciprocal results. Both observers measure the same Doppler shift when separating or closing in on each other.

 

If we repeat the above car siren test with light(instead of a 100Hz sound we have a light flashing at 100Hz), and boost v up to 0.147c (this keeps the ratio between v and the speed of light the same as between the speed of the car and sound in the first example), wqe get the following results:

 

Our "stationary" observer sees the car light flash at a rate of 86.2Hz for the outbound leg and it takes ~11.6 sec to see first 1000 flashes.

He then sees the the car light flash at a rate of 116Hz and takes 8.62 sec to see the next 1000 flashes. total time to sees 2000 flashes is 11.6+8.62=20.22 sec, during which time its own light flashes 2022 times.

 

The car sees this:

 

while receding, he sees the stationary light flash at 86.2Hz. During the 10 sec it takes for his own light to flash 1000 times, he sees 862 flashes.

He then sees the stationary light flash at 116hz for another ten seconds and flash 1160 times while his own light flashes 1000 times.

Thus he sees the stationary light flash 862+1160 = 2022 times for his own light flashing 2000 times. Both observers agree how many flashes occurred for both during the entire duration.

This also agrees with the time dilation factor for 0.147c which is 0.989, and 2000/2022 = 0.989

 

As to your objection that this does not square with the idea that both observer should conclude that the other clock should be the one running slow, this is not the case.

There is more to this than just time dilation, there is also length contraction and the Relativity of Simultaneity to consider. You have to factor in these effects also when looking at the total elapsed time for both observers.

 

As for using light for our observations. The means by which the observations are made are not important. Light is just the simplest means of doing so in these examples. Light happens to travel at the invariant speed of the universe. It is the fact that such a finite invariant speed exists that leads to the effects of Relativity, not that we can use light to demonstrate them.

Firstly, great response, thank you very much. I will be re-reading several times.

 

Just another comment on the observation though, when using special relativity, we assign relative speeds, distances etc. and then we can get the relative times and distances for each reference object. Does this assume perfect information of objects, even though the objects may be lightyears apart, therefore there can be no way to determine the actual values of both objects in the same instant. Then results are obtained, but these are not the observed results, we need to wait a couple lightyears to check if our prediction were right? Are we measuring the effect on incoming light from objects, or the objects themselves?

 

There is no time dilation for the siren example. Janus has done the math for you.

Was not talking about the siren example, I was just trying to show why I found the doppler effect explanation of the paradox silly. I admit my logic was flawed on the siren example, but that is not my question. I regret posting that siren example, I knew it was not correct, but I was thinking that perhaps it was incorrect for the same reason the doppler shift twin paradox explanation was incorrect.

Edited March 26, 2015 by CasualKilla

[swansont]

Was not talking about the siren example

 

I was.

Firstly, great response, thank you very much. I will be re-reading several times.

 

Just another comment on the observation though, when using special relativity, we assign relative speeds, distances etc. and then we can get the relative times and distances for each reference object. Does this assume perfect information of objects, even though the objects may be lightyears apart, therefore there can be no way to determine the actual values of both objects in the same instant. Then results are obtained, but these are not the observed results, we need to wait a couple lightyears to check if our prediction were right? Are we measuring the effect on incoming light from objects, or the objects themselves?

Yes, it relies on perfect information. It's a thought experiment/prediction. Whether you are discussing the objects or the signals from them depends on the context of the discussion. The doppler-shifted signal explanation is quite obviously discussing the signals, but you can analyze the trip itself as well.

[CasualKilla]

 

I was.

 

Yes, it relies on perfect information. It's a thought experiment/prediction. Whether you are discussing the objects or the signals from them depends on the context of the discussion. The doppler-shifted signal explanation is quite obviously discussing the signals, but you can analyze the trip itself as well.

Do you think it is legit though? The doppler explanation seems to work even if the twins experience no time dilation, it is simply the light changing frequency, and then uses the finite speed of light to explain why beeps are different.

[swansont]

Do you think it is legit though? The doppler explanation seems to work even if the twins experience no time dilation, it is simply the light changing frequency, and then uses the finite speed of light to explain why beeps are different.

 

But the twin did experience time dilation. A factor of 0.989, that Janus mentioned. That will cause the faster clock to flash 1.011 times faster relative to the slow one. 2022 flashes instead of 2000.

 

if you want to work a non-relativistic example you would need to use a much lower speed, and there would be a much smaller Doppler shift.

[xyzt]

One experiences acceleration, sure, but what if there was a worm hole that allowed him to change direction instantly, lets remove that variable completely.

No, they don't, the situation is STILL asymmetric, one twin changed direction, the other one didn't. You don't seem to want to learn.

[MigL]

If you could remove the 'acceleration' part from the twin paradox by making use of a wormhole, you would have all the ingredients needed for a time machine.

See some of Kip Thorne's research.

[CasualKilla]

No, they don't, the situation is STILL asymmetric, one twin changed direction, the other one didn't. You don't seem to want to learn.

You seem quite happy with the explanation that "one twin is different", but you can't seem to articulate why that makes a difference (within special relativity). Relative velocities remain the same at all points. If I did not want to learn, I would not have posted this thread in the first place, that is a rather stupid claim.

 

But the twin did experience time dilation. A factor of 0.989, that Janus mentioned. That will cause the faster clock to flash 1.011 times faster relative to the slow one. 2022 flashes instead of 2000.

 

if you want to work a non-relativistic example you would need to use a much lower speed, and there would be a much smaller Doppler shift.

Is doppler shift of light caused by time dilation, length contraction, or both?

Edited March 27, 2015 by CasualKilla

[swansont]

 

Is doppler shift of light caused by time dilation, length contraction, or both?

 

Neither. They are all the result of relative motion combined with the invariance of c

[xyzt]

You seem quite happy with the explanation that "one twin is different", but you can't seem to articulate why that makes a difference (within special relativity). Relative velocities remain the same at all points. If I did not want to learn, I would not have posted this thread in the first place, that is a rather stupid claim.

Is doppler shift of light caused by time dilation, length contraction, or both?

Giving me negative feedbacks like a coward will not change anything. The reason the twin that turns around accumulates less time is the faCt that while he turns around the other twin accumulates extra time.

Edited March 27, 2015 by xyzt

[swansont]

Relative velocities remain the same at all points.

 

No, they don't. Relative speed does, but one twin turns around. That's a change in sign of the relative velocity.

[CasualKilla]

Giving me negative feedbacks like a coward will not change anything. The reason the twin that turns around accumulates less time is the fcat that while he turns around the other twin accumulates extra time.

I gave you negative feedback because I out of 4 posts, not a single one added any value and you were getting rude and personal. I stand by it.

 

 

No, they don't. Relative speed does, but one twin turns around. That's a change in sign of the relative velocity.

I do not see where is special relative the sign makes any difference in the calculations. I am open to that idea, please just show me your logic.

Edited March 27, 2015 by CasualKilla

[Phi for All]

!

Moderator Note

Attitude affects behavior, people. Let's stay focused and civil.

[xyzt]

I gave you negative feedback because I out of 4 posts, not a single one added any value and you were getting rude and personal. I stand by it.

 

I do not see where is special relative the sign makes any difference in the calculations. I am open to that idea, please just show me your logic.

The fact that you don't understand the answers doesn't mean that they do not explain your misunderstandings.

[CasualKilla]

The fact that you don't understand the answers doesn't mean that they do not explain your misunderstandings.

Agreed. But perhaps you would like to elaborate on your answer. I agree than twin B experiences acceleration, but in this paradox we only consider special relativity. In that case, ok the velocity goes negetive, fine, I agree, but I do not see how to extrapolate that to solve the paradox.

[xyzt]

Agreed. But perhaps you would like to elaborate on your answer. I agree than twin B experiences acceleration, but in this paradox we only consider special relativity. In that case, ok the velocity goes negetive, fine, I agree, but I do not see how to extrapolate that to solve the paradox.

Well, you will need to take back your gratuitous negative feedbacks first.Like I said earlier, SR handles accelerated motion.

Edited March 27, 2015 by xyzt

[CasualKilla]

Well, you will need to take back your gratuitous negative feedbacks first.

Still stand by that. Ok no hard feelings then, you don't have to respond if you don't want to.