Synchronizing clocks in different frames of reference.

[geordief]

Suppose we have two reference frames that are not at rest wrt each other (even accelerating).

Is there any way at all that a observers in their respective frames can agree upon  a mutual time?

Is there any way at all for the to synchronize clocks ,if only for the one instant?

Edited March 11, 2021 by geordief

[swansont]

Synchronize? No, because that implies frequency and phase are the same. 

You can set them to the same value, as a one-off, by accounting for light-travel-time delays. (and we also do this in thought experiments all the time)

Make the readout agree? Yes, we do it with GPS. Since the satellite clocks run faster than the ground clocks, the oscillators on the satellite clocks is set to be at a lower frequency. After a time T on the ground the satellite clock will also display T, even though the time passed on the satellite is > T.

e.g if the net time dilation were a factor of 2, you set the satellite clock oscillator to 5 MHz, while the ground clock is at 10 MHz

[geordief]

 

11 minutes ago, swansont said:

You can set them to the same value, as a one-off, by accounting for light-travel-time delays. (and we also do this in thought experiments all the time)

 

Well ,I was wondering whether it was possible  to set a ground clock and a distant  clock to the same time at a particular instant and thereafter  the distant clock approaches the ground clock directly** in freefall.

Will the two clocks still show the same time when they meet?

 

** ie no lateral movement but all movement is along the shortest path.

[studiot]

22 minutes ago, geordief said:

at a particular instant

What instant would that be ?

Or rather one might ask whose instant ?

[Janus]

2 hours ago, geordief said:

Suppose we have two reference frames that are not at rest wrt each other (even accelerating).

Is there any way at all that a observers in their respective frames can agree upon  a mutual time?

Is there any way at all for the to synchronize clocks ,if only for the one instant?

You could set things up so that, from a given frame, the clocks started and ended "in sync", but this would require artificially adjusting the tick rate of the clocks. Thus you could get this as measured from the rest frame of the lower row of clocks.

All the clocks in both rows remain in sync.

However, when you transition to the rest frame of the upper row of clocks, you get this:

The only moment when any two clocks read the same is when they are passing each other.

[geordief]

Is there anything special in the (temporal) relationship between a massive body and an object freefalling towards its centre of mass  without any lateral motion?

 

I had it in mind that their clocks might tick at the same rate but it seems that they don't.

 

What about if their distance is artificially maintained  through acceleration?

Do their clocks tick at the same rate for that duration?

 

 

 

[Markus Hanke]

12 hours ago, geordief said:

What about if their distance is artificially maintained  through acceleration?

Do their clocks tick at the same rate for that duration?

Not unless you artificially make it so. If one of the clocks experiences acceleration and the other one does not, then there will be time dilation between the two.

[geordief]

5 hours ago, Markus Hanke said:

Not unless you artificially make it so. If one of the clocks experiences acceleration and the other one does not, then there will be time dilation between the two.

(hope I am not just  repeating myself)

If the one clock is in freefall(my earlier scenario).

21 hours ago, geordief said:

Well ,I was wondering whether it was possible  to set a ground clock and a distant  clock to the same time at a particular instant and thereafter  the distant clock approaches the ground clock directly** in freefall.

 

,it does not experience acceleration yet still ticks at a different rate...

 

Is that because the two clocks are still in relative motion?

 

And so the only time they tick at the same rate is  when they  are both at rest and also experience no (different?) acceleration?

[studiot]

Perhaps you would like to think about the proposed situation.

One clock is in 'freefall'.

So how is it 'approaching the other clock', which is not in freefall ?

 

You need to choose one inertial coordinate system, declare that one to be at rest and then relate the motions of everything else to that system.

Edited March 12, 2021 by studiot

[Bufofrog]

51 minutes ago, geordief said:

it does not experience acceleration yet still ticks at a different rate...

Is that because the two clocks are still in relative motion?

Yes

54 minutes ago, geordief said:

And so the only time they tick at the same rate is  when they  are both at rest and also experience no (different?) acceleration?

Both clocks tick at the same rate if they are at rest relative to each other.  IOW for an observer a moving clock ticks slower.

I assume when you say acceleration you are referring to a gravitational potential since one clock accelerating would mean that the clocks were in relative motion.

If 2 clocks are not in relative motion to each other but are in 2 different gravitational potentials then the clocks will also tick at different rates.  So there are 2 kinds of time dilation, relative motion time dilation (SR) and gravitational time dilation (GR).

 

 

 

[geordief]

40 minutes ago, Bufofrog said:

So there are 2 kinds of time dilation, relative motion time dilation (SR) and gravitational time dilation (GR).

Is there a connection between those two kinds of time dilation?

Is it simply that  the one  cause is the derivative of the other ?

[swansont]

7 minutes ago, geordief said:

Is there a connection between those two kinds of time dilation?

Is it simply that  the one  cause is the derivative of the other ?

You can have one without the other; there's no inherent connection.

[geordief]

4 minutes ago, swansont said:

You can have one without the other; there's no inherent connection

You ca't have acceleration  without implied motion can you?

[Bufofrog]

3 minutes ago, geordief said:

You ca't have acceleration  without implied motion can you?

If two people are in the same reference frame, the only way they can develop relative motion is for at least one of the people to accelerate.  I am trying to answer in a way that does not get into semantics and have the answer to a simple question become confusing.

[geordief]

4 minutes ago, Bufofrog said:

If two people are in the same reference frame, the only way they can develop relative motion is for at least one of the people to accelerate.  I am trying to answer in a way that does not get into semantics and have the answer to a simple question become confusing.

So does that not suggest that the two causes of time dilation have a connected cause?

Is there a sense in which they are entirely distinct?

Edited March 12, 2021 by geordief

[swansont]

 

39 minutes ago, geordief said:

You ca't have acceleration  without implied motion can you?

In GR being stationary in a gravitational field is an accelerated frame.  Your speed is zero but you are accelerating at g

[geordief]

4 minutes ago, swansont said:

 

In GR being stationary in a gravitational field is an accelerated frame.  Your speed is zero but you are accelerating at g

Your speed is only zero wrt  the centre of gravity of the field.

You are in motion wrt all other points.

Anything  to that?

[swansont]

12 minutes ago, geordief said:

Your speed is only zero wrt  the centre of gravity of the field.

You are in motion wrt all other points.

Anything  to that?

 

This is the scenario that launched this part of the discussion:

1 hour ago, Bufofrog said:

If 2 clocks are not in relative motion to each other but are in 2 different gravitational potentials then the clocks will also tick at different rates.   

IOW, nothing is in motion in this situation.

[dimreepr]

34 minutes ago, geordief said:

Your speed is only zero wrt  the centre of gravity of the field.

You are in motion wrt all other points.

Anything  to that?

Only if, someone with zero understanding tried to explain it...

[Bufofrog]

1 hour ago, geordief said:

Your speed is only zero wrt  the centre of gravity of the field.

You are in motion wrt all other points.

Anything  to that?

It sounds like you are confusing yourself on this point.  Look at it like gravity is trying to accelerate you towards the center of the earth but the earths surface is holding you back.  IOW your weight is the force you are exerting on the surface of the earth which is your mass times the acceleration due to gravity (9.8 m/s^2).

Hope that helps.

[geordief]

4 hours ago, Bufofrog said:

I assume when you say acceleration you are referring to a gravitational potential since one clock accelerating would mean  that the clocks were in relative motion

Actually ,no I didn't have that  particular scenario in mind.I was just  very generally thinking of two clocks  that ,either one or both accelerated.

And that ,if they did accelerate (under their own steam and provided possibly that they did not both accelerate "equally" )  then they would tick at different rates.

 

5 hours ago, studiot said:

Perhaps you would like to think about the proposed situation.

One clock is in 'freefall'.

So how is it 'approaching the other clock', which is not in freefall ?

 

You need to choose one inertial coordinate system, declare that one to be at rest and then relate the motions of everything else to that system.

Sorry ,I missed your post.I will have a look at it a bit later.

@studiot

I don't see the problem with my scenario. Can you not have  a clock on the surface of the Earth and another at rest wrt it at say 1 light second from it (or from the centre of the Earth)?

This second clock will ,  from rest move towards the first clock and eventually they will come together.

 

I realize now that these two clocks will tick at different rates ,but when I asked the question I imagined the opposite might be the case (and the freefall might have kept them aligned)

 

(The inertial coordinate system I was using was that of the "Earth bound" clock)

[swansont]

1 hour ago, geordief said:

 (The inertial coordinate system I was using was that of the "Earth bound" clock)

An earthbound clock is not in an inertial frame, though there are many situations where one can treat it as inertial. But there are others where this will get you into trouble. You have to be careful, and know when the "inertial" assumption is valid.

e.g. in the Hafele-Keating experiment, none of the clocks are in inertial frames, which is why the kinetic effects are different for the eastbound vs westbound clocks, relative to the earthbound clocks.

[geordief]

9 minutes ago, swansont said:

An earthbound clock is not in an inertial frame, though there are many situations where one can treat it as inertial. But there are others where this will get you into trouble. You have to be careful, and know when the "inertial" assumption is valid.

e.g. in the Hafele-Keating experiment, none of the clocks are in inertial frames, which is why the kinetic effects are different for the eastbound vs westbound clocks, relative to the earthbound clocks.

Should /could I have placed the "earthbound" clock at the centre of the Earth?

[swansont]

1 hour ago, geordief said:

Should /could I have placed the "earthbound" clock at the centre of the Earth?

A clock at the center of the earth will run at a different rate than one at the surface (and we have to account for elevation differences). And since all real clocks are going to be at/near the surface, that's the situation we usually look at.

[Markus Hanke]

12 hours ago, geordief said:

And that ,if they did accelerate (under their own steam and provided possibly that they did not both accelerate "equally" )  then they would tick at different rates.

I think (but maybe that’s just me) that the notion of “tick rate” is not particularly helpful, since no ideal clock can ever tick at anything other than “1 second per second” in its own frame, irrespective of where it is and how it moves. It is only when you compare the total accumulated time between two shared events that differences become apparent. “Tick rate” is one of those notions that, even though everyone routinely uses it, all too easily lends itself to misinterpretation.

Now, the total accumulated time a clock records as it travels from event A to event B is identical to the geometric length of the world line it traces out while connecting these events - so it is actually a geometric quantity. This is true regardless of what the geometry of the underlying spacetime is, so it applies whether or not there is gravity present. So what is the meaning of acceleration then? If you have two events A and B in spacetime, the longest (!) possible world line that connects these is always that which represents a test clock in free fall (i.e. inertial motion) - such world lines are called geodesics. Hence, given that the absence of any acceleration yields the longest possible world line and thus the most accumulated time on your clock, the presence of acceleration at any point of the clock’s journey will shorten its world line between the same two events - so the clock will accumulate less time. This is just precisely what we see as time dilation (due to acceleration). So, proper acceleration can thus be understood as the degree by which a world line differs from being a geodesic, or alternatively, the degree by wich motion deviates from being free fall. Or in a somewhat more fancy way, it’s a parameter that picks out a world line in a 1-parameter family of all (physically realisable, sharing the same boundary conditions) world lines connecting two given events in spacetime.

Note that this type of time dilation has nothing to do with spacetime curvature - it’s simply about how you choose to connect two given events.