Get confused about time dilation

[asdff529]

When the observer B is traveling at a very high speed, the observer A on the ground will record a time dilation.
But at the same time,from the point of view of B, A is also traveling at a very high speed relative to B.
Here comes the question:does that mean they both record the time dilation,which seems to be illogical.

 

[Doc Al]

does that mean they both record the time dilation

Yes, both "see" the other's clock as running slowly.

which seems to be illogical.

In order for things to be less "illogical", and to realize that there is no contradiction, you must consider all of the relativistic effects, including length contraction and the relativity of simultaneity, not just time dilation. (The big one that most folks miss is the relativity of simultaneity.)

 

[facenian]

As Landau explains there is no contradiction since both observers compare distinct watches(L.D. Landau Vol II)

 

[Nugatory]

When the observer B is traveling at a very high speed, the observer A on the ground will record a time dilation.
But at the same time,from the point of view of B, A is also traveling at a very high speed relative to A.
Here comes the question:does that mean they both record the time dilation,which seems to be illogical.

It will make sense if you also consider the relativity of simultaneity. Search this forum and you will find many examples.

 

[asdff529]

My teacher gives me an explanation about this:
A moving clock(observer B) runs slower actually means it is slower comparing to two stationary clocks at different locations.
Does it have something to do with relativity of simultaneity?
I also heard of Hafele-Keating experiment.And it comes out one clock is actually slower than the other clock.
Doesn't it contradict that both "see" the other's clock as running slowly?

 

[ghwellsjr]

When the observer B is traveling at a very high speed, the observer A on the ground will record a time dilation.
But at the same time,from the point of view of B, A is also traveling at a very high speed relative to B.
Here comes the question:does that mean they both record the time dilation,which seems to be illogical.

In order to understand how each observer can record the same Time Dilation of the other observer, you have to understand what "record" means. It doesn't mean record with a video camera or with your eyes because Time Dilation cannot be seen optically. What can be seen is called Relativistic Doppler. Recording Time Dilation requires a combination of optical signalling, optical measurements, an assumption about the speed of light and calculations.

 

[Nugatory]

I also heard of Hafele-Keating experiment.And it comes out one clock is actually slower than the other clock.
Doesn't it contradict that both "see" the other's clock as running slowly?

It does not. The Hafele-Keating experiment is a different setup than the one that you started this thread with, so it's not surprising that it gives a different result.

I very strongly urge you to figure out the easy case that you started with, in which relativity of simultaneity makes it possible for both observers to correctly and consistently see the other clock running slow, first. Only after you have a solid understanding of that problem are you ready to take on the H-K experiment.

(and a hint: the only way of saying that one clock is running slower than another involves comparing what the two clocks read at the same time)

 

[ChrisVer]

It is not illogical. If the one was to measure a different time dilation for the other, then this would mean that the one is somewhat privileged over the other.
The fact that both of them measures the same time dilation, is actually an illustration of the Lorentz symmetry.
Think of them communicating with light signals.
When A sends a signal with frequency $v_{em}$ the B will receive a signal with frequency $v_{obs}$.
Doing the opposit, if B sends a signal with frequency $v_{em}'$ then A will receive a signal with frequency $v_{obs}'$
Now if $v_{em}' = v_{em}$ then the $v_{obs} = v_{obs}'$
and the frequency redshift (relativistic doppler effect) is connected to time dilation measurement, since time dilation will give a different time interval between the two wave crests for emitted and observed light.

 

[Doc Al]

My teacher gives me an explanation about this:
A moving clock(observer B) runs slower actually means it is slower comparing to two stationary clocks at different locations.

That's a useful way to think of it.

Does it have something to do with relativity of simultaneity?

Absolutely! One way to set up an example of "observing" time dilation is as follows. You, on the ground, set up clocks at points A and B, far apart. Now let that moving clock (in a rocket, say) move along, passing your A clock and then your B clock. You set things up so that when the rocket passes next to each clock, some mechanism at each clock records the time showing on the moving clock and the time showing on your clocks.

So some imaginary data might be as follows. When the rocket passes clock A, both the rocket clock and clock A show a reading of 1 pm. When the rocket clock passes clock B, the rocket clock shows 1:20 pm and clock B shows 1:30 pm. So, using this data, you calculate that the moving clock must be running slow, since it only shows 20 minutes having passed when you have clearly measured 30 minutes by your clocks. (As ghwellsjr explained, you don't directly "see" the time dilation, there are calculations and assumptions involved. That's why I put "see" in quotes.)

So what does the guy in the rocket say about all this? Well, relativity works for him too, so his observations must allow him to conclude that as measured by his clocks it is your clocks that are running slowly. That's where the relativity of simultaneity comes in. Whereas you have arranged things so that the clock at A and the clock at B are synchronized according to you, the rocket observer would measure that clock B is set ahead of clock A. So, according to the rocket observer, when clock A shows 1 pm, clock B already shows 1:17 pm. (I'm just making up data here, but it would be something like that.) So, when the rocket measures the time to get from A to B, he gets 20 minutes, but he would say that clock B only went from 1:17 to 1:30 during his trip, so a time of only 13 minutes elapsed on your clocks. That leads him to conclude that your clocks are running slow, when compared to his.

I also heard of Hafele-Keating experiment.And it comes out one clock is actually slower than the other clock.
Doesn't it contradict that both "see" the other's clock as running slowly?

No. As others have noted, that's a bit more complicated than simple time dilation. So stick to the simple case first.

 

[PeterDonis]

the frequency redshift (relativistic doppler effect) is connected to time dilation measurement, since time dilation will give a different time interval between the two wave crests for emitted and observed light.

Be careful. This intuitive picture works fine for two observers moving away from each other; they both see a Doppler redshift and they each measure the other's clock as time dilated.

But if the observers are moving towards each other, they both see a Doppler blueshift--they see (as in, directly see with their eyes or a telescope) the other's clock ticking faster, not slower. To obtain the time dilation, they have to apply a correction to the observed Doppler shift, and it's not as intuitively obvious that that works in the case of a Doppler blueshift.

(Of course the calculations work out, in both cases--you also have to correct the Doppler redshift observation to obtain the usual time dilation in the case of observers moving apart. But this discussion isn't really about the math, it's about how to intuitively understand what the math is telling you.)

 

[ChrisVer]

Be careful. This intuitive picture works fine for two observers moving away from each other; they both see a Doppler redshift and they each measure the other's clock as time dilated.

But if the observers are moving towards each other, they both see a Doppler blueshift--they see (as in, directly see with their eyes or a telescope) the other's clock ticking faster, not slower. To obtain the time dilation, they have to apply a correction to the observed Doppler shift, and it's not as intuitively obvious that that works in the case of a Doppler blueshift.

(Of course the calculations work out, in both cases--you also have to correct the Doppler redshift observation to obtain the usual time dilation in the case of observers moving apart. But this discussion isn't really about the math, it's about how to intuitively understand what the math is telling you.)

Well in maths everything can work out fine. You can also do that with any kind of velocity of observer A relative to observer B (even with angles) to derive the Doppler shift (blue or red I guess), by applying appropriate boosts on your photon 4-momentum.
So i guess understanding the maths for the special case, you can go and have a deeper look on the maths for the more general case and understand it better.
Afterall, everything is because of Lorentz symmetry (I used the word boost), which connects A and B and none of them are any "privileged" ref.frame.