Time Dilation: 2 Clocks in Same Ref Frame?

[maxpower2020]

Question about time dilation. What if two clocks used the same reference frame? For instance, 2 countdown clocks using a particular pulsar as a measure of time. One stays here, the other is sent 100 million miles away at a very high velocity. Would they still reach 000 at the same time?

 

[Dale]

In the usual meaning that scenario would involve only a single clock: the pulsar.

 

[Ibix]

What if two clocks used the same reference frame?

This is rather confused. Clocks measure their own proper time - they don't use reference frames.

For instance, 2 countdown clocks using a particular pulsar as a measure of time.

These aren't really clocks, if I understand your setup. They're basically counters attached to telescopes and they count the pulsar flashes they see.

One stays here, the other is sent 100 million miles away at a very high velocity. Would they still reach 000 at the same time?

Depends where they are in relation to the pulsar and what you mean by "the same time". If the counter that you move goes directly towards the pulsar then it will see pulses earlier than the stationary counter, so will finish earlier. If the counter moves directly away then it will receive pulses later and finish later. If it moves in any other direction then it's frame dependent - there exists a frame in which they finish simultaneously, but there are frames in which either counter finishes first.

There can be advantages to this approach to timekeeping, although there are some changes that need to be made to your process. But it really doesn't work well for moving clocks, and it definitely doesn't save you from the relativity of simultaneity.

 

[phinds]

Question about time dilation. What if two clocks used the same reference frame? For instance, 2 countdown clocks using a particular pulsar as a measure of time. One stays here, the other is sent 100 million miles away at a very high velocity. Would they still reach 000 at the same time?

Suppose one were sent directly toward the pulsar and one directly away from it. Do you think it would take the same amount of time for each to accumulate the same number of pulsar-ticks?

EDIT: I see ibix beat me to it.

 

[maxpower2020]

This is rather confused. Clocks measure their own proper time - they don't use reference frames.

Okay I understand more and am confused even more. First off measurement of time is totally arbitrary, it depends on what we all agree upon. Our clocks on Earth are measured in our gravity, and in our reference frame, and on a agreed upon definition of a second.

These aren't really clocks, if I understand your setup. They're basically counters attached to telescopes and they count the pulsar flashes they see.

Is not a cesium clock (or any other) just a frequency counter?

I do get the the different velocities, and looking forward to thinking this through. I love learning new things. Even when I find out I was wrong, it means I learned something new. And this is part of a bigger question I want to ask, but I want to get my foundations right first,

 

[maxpower2020]

My original thought certainly drifted, but thanks I have a lot of new stuff to think about. My original thought was if there was any way to keep 2 clocks in sync, one here one there. And it doesn't matter what the intervals are, as long as they agree. I know we have the physics and the math to deal with it, like GPS, but is there any way to do it at great distances, real time with accuracy? Or on the other hand, reliably deal with any inaccuracies?

 

[Dale]

Is not a cesium clock (or any other) just a frequency counter?

Yes, it is called a “frequency standard”. A clock is a frequency standard with a counter, but the frequency standard is the thing that makes a clock a clock.

In your OP there was only one frequency standard, the pulsar. You had two counters, but the one frequency standard makes it one clock.

 

[Ibix]

Okay I understand more and am confused even more. First off measurement of time is totally arbitrary, it depends on what we all agree upon. Our clocks on Earth are measured in our gravity, and in our reference frame, and on a agreed upon definition of a second.

Measurement of time is not arbitrary. The units used are, sure. But once you've agreed that, a second is a second is a second and had nothing to do with reference frames, gravity, or anything else. All that kind of thing comes in when you want to work out what my clock says at the same time yours says 12.00.00. Furthermore, two correctly calibrated clocks sitting side by side will tick at the same rate. That isn't arbitrary behaviour.

But you asked about clocks "using the same reference frame". Reference frames are abstract concepts used to analyse or describe experiments. Clocks are physical devices that do what they do regardless of the reference frame you analyse them with.

Is not a cesium clock (or any other) just a frequency counter?

Not quite. It's a frequency counter with a stable cyclic process - a source of pulses with a fixed frequency. Your counters aren't attached to the source, so they don't see a fixed frequency due to the Doppler effect - so they will sometimes count at the same rate as a clock sitting next to them and sometimes won't. So they aren't really clocks.

My original thought was if there was any way to keep 2 clocks in sync, one here one there.

A great many ways, most giving different results. One of the lessons of relativity that seems to be the hardest to learn is that "synchronised clocks" is not a complete concept. You need to specify your synchronisation process and the states of motion of the clocks that are being synchronised. And you need to accept that no process gives clocks that everyone will reasonably describe as synchronised.

Your approach could be turned into a clock synchronisation procedure by measuring the distance to the pulsar and correcting for both the distance and the rate of change. However, this ends up just being a difficult to implement version of (probably) Einstein synchronisation in the pulsar rest frame since it depends on how you define distance to the pulsar (and that gets very messy close to the pulsar because it's a large object).

 

[Grinkle]

Please, I'd like to confirm the invoked frame is in these two statements -

so will finish earlier.

Do you think it would take the same amount of time

I think maybe its an earthbound telescope watching both counters? Or is it either counter? Or all three?

 

[Ibix]

Please, I'd like to confirm the invoked frame is in these two statements -

Mine was a specific statement about when the pulsar and both counters are in a straight line ("the counter that you move goes directly towards the pulsar"). In this case the reception events of a particular pulse are null separated and order is invariant. When the three are not colinear then the reception events are spacelike separated and the order depends on frame.

 

[maxpower2020]

Took a little thinking but now I'm starting to understand. I really appreciate the answers and the time spent helping me get a handle on my question.

 

[Mister T]

Our clocks on Earth are measured in our gravity, and in our reference frame, and on a agreed upon definition of a second.

It makes no difference which reference frame you use to take the measurement. The clock measures the passage of its own (i.e. proper) time, something that's the same in all reference frames.