Einstein-Poincare Clock Synchronization Convention

[PainterGuy]

TL;DR Summary

I have a question about clock synchronization which is directly related to the simultaneity. One could say that clock synchronization is the main pillar of special relativity because this is the 'convention' which makes the speed of light constant for all observers, and moreover it is the convention which is used to define an inertial frame of reference in the special relativity.

Hi,

There are three clocks - Clock A, Clock B, and Clock C. The distance, D, between each clock is 6 light-second. The clocks are situated in a frame of reference which is moving toward the right at speed of 0.5c where 'c' is taken to be 300000000 m/s. Please look here: https://imagizer.imageshack.com/img921/4197/EaNwTf.jpg

The clocks are to be synchronized according to Einstein-Poincare scheme of synchronization. Clock A is situated in the middle of other two clocks. Clock A sends pulses to both other clocks at 12:00:00

For Clock B, the time of round trip is:
from A to B:
(c+0.5c)t=6 light-second
1.5ct=6 light-second
t=4 seconds
from B to A:
t=12 seconds
Therefore, total round trip time is: 16 seconds. It is assumed that one way trip time taken by the pulse is 16/2=8 seconds.

For Clock C, the time of round trip is:
from A to C:
t=12 seconds
from C to A:
t=4 seconds
Total round trip time is 16 seconds and therefore one way trip time is 16/2=8 seconds.

If the clocks are synchronized then Clock B should have shown 12:00:00 plus 00:00:08, i.e. 12:00:08, on the arrival of pulse. Similarly, Clock C should have also shown 12:00:08 when it received the pulse if it was synchronized with Clock A.

Am I following the synchronization procedure correctly? Could you please help me with it?

 

[PeterDonis]

There are three clocks - Clock A, Clock B, and Clock C. The distance, D, between each clock is 6 light-second.

Distance in what frame? You have already been told in several previous threads that, if you do not specify a frame, "distance" and "time" have no meaning.

The clocks are situated in a frame of reference which is moving toward the right at speed of 0.5c

Moving relative to what? Are the clocks all at rest relative to each other?

You have already been told in several previous threads that there is no such thing as "moving" in an absolute sense; you have to specify what motion and speed are relative to, otherwise those terms have no meaning.

Clock A sends pulses to both other clocks at 12:00:00

12:00:00 according to what? According to Clock A? According to some frame? Which frame?

You really, really need to stop leaving out necessary information when you describe a scenario.

For Clock B, the time of round trip is

Relative to what frame?

or Clock C, the time of round trip is

Relative to what frame?

Am I following the synchronization procedure correctly?

You haven't even specified a well-defined scenario yet. See comments above. Until you do, your questions are not answerable.

 

[PainterGuy]

Distance in what frame? You have already been told in several previous threads that, if you do not specify a frame, "distance" and "time" have no meaning.

The frame of reference is the one in which clocks are situated and are at rest with respect to each other.

Moving relative to what? Are the clocks all at rest relative to each other?

Moving to the right at speed of 0.5c with respect to a stationary observer who is located in a different inertial frame of reference.

12:00:00 according to what? According to Clock A? According to some frame? Which frame?

According to Clock A and according to the same frame of reference in which clocks are located.

Relative to what frame?

Relative to the frame in which clocks are located.

I hope it's clear now. Thank you.

 

[jbriggs444]

So you have three synchronized clocks at rest with respect to one another in a row at 6 light-second intervals. You ask about the round trip time between the first two. It is obviously 12 seconds.

Any motion of clocks or frame as judged by some other observer is utterly irrelevant.

Synchronization of the clocks is also irrelevant. You are measuring round trip times. Clock synchronization does not enter in.

 

[Nugatory]

The clocks are situated in a frame of reference which is moving toward the right at speed of 0.5c where 'c' is taken to be 300000000 m/s.

Saying things are “situated in” a frame is sloppy and inaccurate language, and is a source of endless confusion. Everything is always “in” every possible frame, so saying that something is in a particular frame is pointless - it’s in every frame, so of course that thing is in some particular frame.

Let’s try restating your question without the slop.
We have three clocks that are at rest relative to one another, and using the frame in which they are at rest they are separated by 6 light-seconds. We will call this frame R (for Rest).

We synchronize the clocks using the Einstein clock synchronization protocol. The central clock A emits a flash of light in both directions when it reads 11:00:00. When the flash arrives at clocks B and C we set them both to 11:00:06 (because we know that the distance between them using frame R is 6 light-seconds). The clocks are now synchronized with respect to frame R; that is, using frame R’s definition of “at the same time”, all three clocks read the same thing at the same time.

OK, now we’ve completed the setup, so we can get on with your thought experiment.

When clock A reads 12:00:00 it sends another flash of light both directions. It’s easy to analyze this situation using frame R, and we see that the flash arrives at clocks B and C when they both read 12:00:06.

There is another frame, which we call frame M (for Moving). If we use this frame to describe the situation, the clocks are all moving at speed .5c and they are not synchronized; that is, using frame M’s definition of “at the same time”, the three clocks do not read the same thing at the same time. Furthermore the distance between the clocks is not 6 light-seconds. It is something less because of length contraction.

Nonetheless, you can use frame M to calculate what clocks B and C read when the flash reaches them. Do the calculation carefully, allowing for time dilation, length contraction, and that clocks B and C do not read 12:00:00 at the same time that A reads 12:00:00 and the flash is emitted... and you will find that clocks B and C each read 12:00:06 at the two different times that the flashes are received.

When you try this, I suggest that you use a speed of .6c instead of .5c and separate the clocks by 1 light-minute using frame R (so the clocks will read 12:01:00 when the flashes arrive) - the calculations come out a lot easier that way. If you do I’ll even tell you what clocks B and C read at the same time (using frame M’s definition of “at the same time”) that clock A reads 12:00:00. B reads 12:00:45 and C reads 11:59:15 .

(I did that calculation of the times on clock B and C in my head, so would be grateful if someone less prone than I to sloppy mental arithmetic would check them)

 

[PainterGuy]

So you have three synchronized clocks at rest with respect to one another in a row at 6 light-second intervals. You ask about the round trip time between the first two. It is obviously 12 seconds.

How do we follow this convention? Are we supposed to know the distance, D, between two clocks or points beforehand, and from that one theoretically calculates the round trip time and then synchronize the clocks? If one is supposed to follow the convention theoretically and assign the times based on calculation then round trip should be 12 seconds. I agree with this.

Thank you!

 

[Nugatory]

Are we supposed to know the distance, D, between two clocks or points beforehand,

I thought about mentioning this subtlety in my earlier long post, decided that post was already too long. There are several ways of knowing the distance, all more or less equivalent.
1: Get a meter stick, then slowly and at your leisure measure the distance before you perform the synchronization.
2: Put a mirror at A and B. A sends the signal at time 12:00:00, B receives it and reflects it back to A, and then A reflects it back to B. Now A and B both have a complete round trip time so they both know the distance and hence the light travel time.
3: Use a round-trip light signal from A to B and back again to measure the distance; then use whatever communication method you like (carrier pigeon, message in a bottle, morse code, postal service, courier, radio broadcast, semaphore signals, ...) to tell B what the distance is. Then perform the clock synchronization procedure.

There are plenty of other variations on these methods... But you will note that they require that the clocks be at rest relative to one another and all yield the distance using the frame in which they are at rest

 

[PeterDonis]

The frame of reference is the one in which clocks are situated and are at rest with respect to each other.

Then the clocks are at rest in this frame, not moving at 0.5c.

Moving to the right at speed of 0.5c with respect to a stationary observer who is located in a different inertial frame of reference.

Ok, but then your calculations are mixing values from two different frames, which is wrong.

Relative to the frame in which clocks are located.

Ok, but then your travel times are wrong.

 

[pervect]

Summary:: I have a question about clock synchronization which is directly related to the simultaneity. One could say that clock synchronization is the main pillar of special relativity because this is the 'convention' which makes the speed of light constant for all observers, and moreover it is the convention which is used to define an inertial frame of reference in the special relativity.

I wouldn't describe clock synchronization as a "main pillar of special relativity". It actually is a convention, and as a convention, it doesn't actually affect physical measurements , just how they are communicated and discusssed.

I don't want to downplay the amount of confusion not following standard conventions can cause for students and readers who are used to to them, including used to using formulae that rely on following the conventions. But the confusion can affect Newtonian physics as well as special relativity.

Let me give an example. Suppose one were measuring the speeds of airplanes, flying from LA to New York and back again, in the US. Furthermore, suppose one used wall clocks (one keeping Pacific Standard Time, one keeping Eastern Standard Time) to note the time of arrivals and departures.

One might falsely conclude that in one direction of travel, the flights were much faster than the other. But actually they are not, in any meaningful physical sense. By not following the conventions, one has created confusion.

If one uses proper time instead of coordinate time, by putting a clock on the plane to measure the travel time rather than using a two-clock method, the difference mostly disappears. One might still notice a small effect with physical origins due to the direction of prevailing winds.

Many experiments can be formulated with one clock rather than two, allowing synchronization conventions to be generally bypassed. There are some exceptions- one can't make a clock travel at the speed of light, for instance, and often it is inconvenient to use one clock. But for the most part, using two clocks rather than one is a matter of covenience, and related to isssues such as minimizing the effect of vibration and bumps on how the clocks keep time.

One example of a Newtonian formula that fails if clocks are not properly synchronized is p=mv, p being the momentum, m being the mass, and v the velocity. If the velocity is measured by clocks that are not synchronized in a standard manner, this relationship is not true. This shows up in the airplane case I discussed above. The two airplanes really have the same momentum regardless of which direction the apply - the artifical numbers that don't follow standard conventions might cause an unwary person to conclude otherwise. Most likely the error would be caught if the person was familiar with Newtonian physics. The situation is mostly the same for SR as it is for Newton, it's just that people who are unfamiliar with SR are more likely to not realize they are making a silly mistake.

So it's not really a relativistic issue - a lot of non-relativistic formula also break down if clocks are improperly synchronized. For small synchronization errors, it only really matters for very high speeds a 1 millisecond error on a 5 hour trip isn't significant, but if the trip time is only 10 milliseconds, the error is much more significant.

In the airplane example, using a large several hour clock synchronization error might lead one to the erroneous conclusion that two airplanes flying in different directions had different amounts of physical momentum, when in actuality one is simply reporting the speed of the airplane in a matter that is confusing because it doesn't follow the expected conventions for how we expect speeds to be reported. And standard formulas, such as p=mv, require one to use the standard conventions in order to get correct results.

 

[Orodruin]

I wouldn't describe clock synchronization as a "main pillar of special relativity". It actually is a convention, and as a convention, it doesn't actually affect physical measurements , just how they are communicated and discusssed.

This is a very important comment. In fact, clock synchronization really has nothing to do with special relativity itself, only with the construction of coordinate systems on spacetime. However, SR is independent of any coordinate system.

It also has nothing to do with the speed of light - only the coordinate speed of light. Of course one can choose to work only in coordinate frames where the coordinate speed is the same as the physical speed, but this is certainly not required.

 

[Ibix]

I agree with both @pervect and @Orodruin, about the importance of clock synchronisation to relativity (or lack of importance). But it's true that clock synchronisation is critically important to understanding how inertial reference frames are defined, and it's at least arguable that understanding it is more important than understanding time dilation or length contraction. The idea that there isn't a unique meaning to "now" was certainly the thing I found it hardest to get into my head.

 

[Orodruin]

The idea that there isn't a unique meaning to "now" was certainly the thing I found it hardest to get into my head.

You and 99.99% of all people when they start learning relativity.

 

[PainterGuy]

Thank you!

I thought about mentioning this subtlety in my earlier long post, decided that post was already too long. There are several ways of knowing the distance, all more or less equivalent.
1: Get a meter stick, then slowly and at your leisure measure the distance before you perform the synchronization.

I'd prefer this old school method.

2: Put a mirror at A and B. A sends the signal at time 12:00:00, B receives it and reflects it back to A, and then A reflects it back to B. Now A and B both have a complete round trip time so they both know the distance and hence the light travel time.
3: Use a round-trip light signal from A to B and back again to measure the distance; then use whatever communication method you like (carrier pigeon, message in a bottle, morse code, postal service, courier, radio broadcast, semaphore signals, ...) to tell B what the distance is. Then perform the clock synchronization procedure.

Both of these methods create conceptual problems for me. I don't think one can measure the correct distance this way. Let me elaborate on it below.

Please note the following. The speed of light is independent of the motion of source and it is always constant in vacuum. The Earth goes around the sun at speed of 200 kilometers per second. One can ignore the rotational speed which is 460 meters per second at the equator.

In the pages below, I have highlighted the main parts in green. Berne and Lucerne lie almost along a straight line where Lucerne is 60 kilometers toward east of Berne.

Page #1: https://imagizer.imageshack.com/img924/9313/GFsPS4.jpg
Page #2: https://imagizer.imageshack.com/img923/6910/fOTlWV.jpg

Let me put this confusion in a related context. If you fly on a plane from from Berne to Lucerne, one might think the plane has to cover more distance going toward east in direction of Lucerne. This does not happen because plane, air in which plane flies, earth, and everything else move along at same speed. If the plane is flying at speed of 0.25 km per second toward Lucerne then it is moving speed of (0.25 + 200 ) km per second from perspective of someone in space. This is the reason that if you are hovering over a spot, you and the spot remain aligned because both you and spot are co-moving. The same goes for the journey from Lucerne to Berne. The following are useful links to this discussion.
1: https://www.sciencealert.com/Earth-spins-to-the-east-why-isn-t-it-faster-to-fly-west
2: https://www.forbes.com/sites/quora/...-does-not-affect-latitudinal-airplane-travel/

Here comes the confusion. When a light signal is sent from Berne to Lucerne, as soon as light signal leaves its source, then it's only light and space (ignoring air). Light signal is not co-moving with anything as was plane. Light signal is not a plane and it is not co-moving with anything else. In my view, light signal does have to travel more distance from Berne to Lucerne because Lucerne is moving away from the light signal therefore light has to travel through more space. After reflection of signal, on way back to Berne, the situation would get reversed. You would end with distance of 60.00003 km between Berne and Lucerne which is wrong. It should have been 60 km. The difference is small because the distance between Berne and Lucerns is comparatively small, just 60 km.

From Berne to Lucerne:
ct = 200t+60
=> 300000t-200t=60
=> t = 200.1334 us

From Lucerne to Berne:
ct = 60-200t
=>t=199.8668 us

Total round trip time: 200.1334 us + t=199.8668 us = 400.0002 us
Round trip distance: 300000 km/sec * 400.0002/10^6 sec = 120.00006 km
One way distance: 120.00006 / 2 =60.00003 km

 

[jbriggs444]

The speed of light is independent of the motion of source and it is always constant in vacuum.

Not just constant. Invariant.

It travels at the same speed no matter what frame of reference you use to measure it. Including the frame of reference in which Berne and Lucerne are at rest.

 

[PainterGuy]

I wouldn't like to steer this thread into a different direction because in the end I'd get more confused. On the other hand, I don't have enough knowledge to contribute effectively.

I wouldn't describe clock synchronization as a "main pillar of special relativity". It actually is a convention, and as a convention, it doesn't actually affect physical measurements , just how they are communicated and discusssed.

I don't want to downplay the amount of confusion not following standard conventions can cause for students and readers who are used to to them, including used to using formulae that rely on following the conventions. But the confusion can affect Newtonian physics as well as special relativity.

Your own post from 2005 is quite helpful and relevant here: https://www.physicsforums.com/threads/einsteins-clock-synchronization-convention.86985/post-730537

This synchronization convention is what makes the postulate of special relativity that speed of light is constant and same in all inertial frames of reference. You can argue that it's not a pillar but it's still extremely important.

Peter Galison's book is also helpful to this discussion: Einstein's Clocks, Poincare's Maps: Empires of Time.

The idea that there isn't a unique meaning to "now" was certainly the thing I found it hardest to get into my head.

Mathematically, "now" is somewhat hard to define. Even when you listen to someone, your "now" becomes the past of that someone . Langauge and mathematics encode time differently. In my humble view, this "now" was one of the factors which also contributed toward the development of special theory of relativity.

Thank you!

 

[PeterDonis]

Both of these methods create conceptual problems for me.

You are having conceptual problems because you keep refusing to use the correct conceptual tools in the correct way. See below.

I don't think one can measure the correct distance this way.

Your unwillingness to use the correct conceptual tools is leading you to erroneous conclusions like this one. See below.

The Earth goes around the sun at speed of 200 kilometers per second. One can ignore the rotational speed which is 460 meters per second at the equator.

You keep on leaving out which frame when you say these things. The two speeds you mention here are relative to two different frames; thinking of both of them as "speeds" without qualification is going to lead you to wrong answers.

You can't possibly understand physics if you are unwilling to use the correct conceptual tools in the correct way, like forcing yourself to explicitly specify a frame every time you give a distance, time, or speed.

Lucerne is 60 kilometers toward east of Berne.

In what frame? Note that the frame you are implicitly using here is different from both of the frames you implicitly used above.

You can't possibly reason correctly with a mess like this, so it's no wonder you're obtaining wrong conclusions.

 

[Nugatory]

I'd prefer this old school method.

Sure... Nothing wrong with it in a thought experiment. It captures our intuitive notion of the distance between the two clocks, and that's why you prefer it. If you think about it for a moment, you'll see that this method of measuring requires that the clocks be at rest relative to us while we're doing the measurement; this is a procedure for measuring the distance between the two clocks using frame R, not an any other frame.

Please note the following. The speed of light is independent of the motion of source and it is always constant in vacuum. The Earth goes around the sun at speed of 200 kilometers per second. One can ignore the rotational speed which is 460 meters per second at the equator...

None of this is even slightly relevant. We're measuring the distance between the two clocks according to frame R. In that frame the clocks are at rest so if the round-trip time between them is 12 seconds they are separated by six light-seconds using that frame.

Let me put this confusion in a related context. If you fly on a plane from from Berne to Lucerne, one might think the plane has to cover more distance going toward east in direction of Lucerne. This does not happen because plane, air in which plane flies, earth, and everything else move along at same speed.

Careful... You've just made a frame-dependent statement. Using the frame in which the surface of the Earth is at rest, the plane covers the same distance flying east or west. Using the frame in which the surface of the Earth is moving at 200 km/sec, the plane covers a longer distance flying east than flying west.

Thus it is incorrect to say "the plane has to cover more distance going toward East" and it is incorrect to say "this does not happen". Correct statements would be "Using the frame in which the Earth is at rest, the plane covers the same distance in both directions" and "Using the frame in which the Earth is movig to the east at 200 km/sec, the plane covers a longer distance flying east than flying west". None of this has anything to do with Einstein's theory, it's Galilean relativity, discovered and analyzed by Galileo centuries ago. If this isn't making sense to you, you should study Galiean relativity until it does make sense to you - it's silly to try to understand 20th century physics before you understand what was already known in the 16th century.

In my view, light signal does have to travel more distance from Berne to Lucerne because Lucerne is moving away from the light signal therefore light has to travel through more space.

This is true using the frame in which the Earth is moving. It is not true using the frame in which the Earth is at rest. The only twist that Einstein's relativity adds to Galilean relativity is that the light signal is moving at speed $c$ using the frame in which th Earth is at rest and also using the frame in which the Earth is moving. If Galilean relativity were exactly correct, the light signal would not be moving at the same speed using both frames.

 

[PainterGuy]

Thank you very much!

When a light signal is sent from Berne to Lucerne, as soon as light signal leaves its source, then it's only light and space (ignoring air). Light signal is not co-moving with anything as was plane. Light signal is not a plane and it is not co-moving with anything else. In my view, light signal does have to travel more distance from Berne to Lucerne because Lucerne is moving away from the light signal therefore light has to travel through more space. After reflection of signal, on way back to Berne, the situation would get reversed. You would end with distance of 60.00003 km between Berne and Lucerne which is wrong. It should have been 60 km. The difference is small because the distance between Berne and Lucerns is comparatively small, just 60 km.

From Berne to Lucerne:
ct = 200t+60
=> 300000t-200t=60
=> t = 200.1334 us

From Lucerne to Berne:
ct = 60-200t
=>t=199.8668 us

The equations above show that where I was going wrong. Writing "ct+200t" or "ct-200t" suggests that the speed of light is source dependent. The main confusion was how I had been writing the mentioned equations. When light signal is sent from Berne to Lucerne, the moment light signal gets to Lucerne, Lucerne does have moved by 'x' amount from its original position. After reflection, the moment light signal gets back to Berne, Berne has moved by the same '-x' amount as well. As Earth is almost in uniform motion therefore it doesn't make much sense and is not necessary to say that Berne or Lucerns have moved from their 'original' positions; and one doesn't need to refer to any other frame of reference.

I should have better written it as follows.

From Berne to Lucerne:
ct = 60 + x

From Lucerne to Berne:
ct = 60 - x

(ct+ct)=(60+x)+(60-x)
=>2ct=120
=>ct=60
=>t=60/c=200 us

 

[PainterGuy]

Einstein-Poincare synchronization of clocks convention is what makes the postulate of special relativity that the speed of light is constant and same in all inertial frames of reference true.

I don't think, practically, one can use light signals to synchronize clocks. I think using radio waves instead of light signals would do the purpose. In other words, how is this convention of synchronization using light signals applied practically? I'm sure they make use of it in real life! :)

I wouldn't be surprised to know that different countries like USA, UK, Russia and Chine use their own master clocks. What master clock is used by the US? Global Positioning System is also operated by the US. Are the GPS clocks slave to some other master clock(s)? Is it NIST-F2 which is used as a master clock by the US, https://en.wikipedia.org/wiki/NIST-F2? If NIST-F2 is the master clock then what other master clock(s) it compares its time with? Or, is it the clock network of NIST-F1, NIST-F2 and GPS clocks serving as a master clock network? This is relevant here: https://en.wikipedia.org/wiki/International_Atomic_Time#Operation

Thank you!

 

[PeterDonis]

Einstein-Poincare synchronization of clocks convention is what makes the postulate of special relativity that the speed of light is constant and same in all inertial frames of reference true.

I don't think, practically, one can use light signals to synchronize clocks. I think using radio waves instead of light signals would do the purpose. In other words, how is this convention of synchronization using light signals applied practically? I'm sure they make use of it in real life! :)

@PainterGuy, you are in no position to be making pronouncements about SR, either theoretical or practical. You keep drawing incorrect conclusions and ignoring the feedback you are getting from experts. There is no point in continuing discussion under those circumstances.

Thread closed.

(P.S.: You do realize that "radio waves" and "light signals" are the same kind of thing, right? They are both electromagnetic radiation, and they both travel at the SR invariant speed in vacuum.)

 

[Nugatory]

Einstein-Poincare synchronization of clocks convention is what makes the postulate of special relativity that the speed of light is constant and same in all inertial frames of reference true.

That is exactly backwards. Einstein-Poincare synchronization works because we assume that the speed of light is the same in all inertial frames. We used this assumption when we were synchronizing the clocks in post #5 above: it’s how we concluded that if the clocks were separated by six light-seconds (using the frame in which they were at rest) then the light-travel time between them (using that frame) would be six seconds.

 

[Nugatory]

I don't think, practically, one can use light signals to synchronize clocks. I think using radio waves instead of light signals would do the purpose.

PeterDonis has already reminded you that visible light and radio signals are both light signals, so when we speak of a “light signal” that could be either visible light, or radio, or any of the other forms of electromagnetic radiation.

These days we generally use radio frequencies to broadcast time signals but many of the experiments during the 19th and early 20th century that led to relativity used visible light - it was easier to work with using pre-silicon technology. And even today when we’re doing really accurate distance measurements using round-trip light travel times, we use visible light.