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# Relativity and Cosmology

This is a Blog on relativity and cosmology for engineers and the like. You are welcome to comment upon or question anything said on my website (http://www.relativity-4-engineers.com), in the eBook or in the snippets I post here.

Comments/questions of a general nature should preferably be posted to the FAQ section of this Blog (http://cr4.globalspec.com/blogentry/316/Relativity-Cosmology-FAQ).

A complete index to the Relativity and Cosmology Blog can be viewed here: http://cr4.globalspec.com/blog/browse/22/Relativity-and-Cosmology"

Regards, Jorrie

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### Einstein Clocks and the Sagnac Effect

Posted November 10, 2011 4:00 AM by Jorrie

Einstein's clock synchronization method is based on the principle that, in every inertial frame, the one-way speed of light in vacuum is the same as its average round-trip speed.(a)

In synchronization terms, it means the following. Let clocks A and B be at rest in an inertial frame; measure the coordinate distance d between two clocks; send a time-stamped light pulse from A to B; at the instant of reception, add the propagation delay (d/c) to the time stamp and set clock B accordingly. Clocks A and B are now 'Einstein-synchronized' in that inertial frame.

The relativistic principle and hence Einstein's method of clock synchronization is a convention, not an absolute truth.(b) This may sound like relativistic heresy, but there are other valid ways of synchronizing clocks - it is just that none works as well as Einstein's.(c) This Blog article attempts to show why by means of the Sagnac effect.

The figure (right)(d) is largely self-explanatory. The two red arrows represent two signals moving in opposite directions at speed k relative to the blue ring. If the ring is non-rotating, each signal will circumnavigate the ring in time t = 2Πr/k, as measured by a laboratory clock.

In Newtonian mechanics, this is also true if the ring is rotating, because in the lab frame, the difference in the distances that the signals have to travel in the two directions exactly cancels the apparent faster or slower speed of the signals (u = v ± k), depending on signal direction. Signals traveling in opposite directions arrive at the same time and remain in phase; hence there should be no Sagnac effect. This Newtonian result is in conflict with observations of the Sagnac effect.

In Einstein dynamics, the principles are the same, accept that we cannot simply add the speed of the signal to the speed of the ring, i.e. u = v ± k does not work. We must use the relativistic speed addition equation u = (v±k)/(1±kv/c2). This gives a definite difference in the time for signals circumnavigating the rotating ring in opposite directions: Δt = 4Πrν/(c2-v2), as measured in the inertial laboratory frame.(d,e)

This time difference is independent of the speed of the signals (k) and just depends on the radius and the rotation rate of the ring. Hence, in contrast to classical Galileo/Newton theory, Einstein's theory does predict the Sagnac effect and it agrees with all experiments performed so far. The Sagnac effect is a very simple proof that the Einstein clock synchronization method works. But, why is it the best scheme?

The answer is simple: by convention, it forces light to propagate at the same speed in both directions around the ring. All other clock synchronization schemes imply that light moves at different speeds in the two directions. As we have seen, in Newton mechanics this results in zero Sagnac effect. In others, having time dilation and Lorent contraction, like Lorentz ether theory (LET), it results in horribly complex equations for the observed Sagnac effect.(f)

Einstein clocks are cool...

-J

PS: see reply #29 below for a summary of the topic.

Notes:

(a) More precisely stated: the observed one-way speed of light in vacuum is constant and isotropic in every inertial frame.

(b) A very good discussion of the conventionality of relativity can be found in this Wiki and also in this Blog entry.

(c) One alternative clock synchronization is due to Selleri, which has preferred inertial frame, but with time dilation and Lorentz contraction in any other frame. It is discussed in "The relativistic Sagnac Effect: two derivations", section 3.5. The paper contains a complete mathematical treatment.

(d) I borrowed the graphics from a physicsinsights.org article, which is excellent for a introductory discussion of the Sagnac effect and shows the calculations involved. It is a lot more accessible than "The relativistic Sagnac Effect: two derivations" in (b) above.

(e) Because v2 « c2 in the usual Sagnac interferometers, v2 is normally ignored and just Δt = 4Πrν/c2 is used. This is precisely double the Einstein clock synchronization offset between the transmitter and the receiver for each direction.

(f) For an example, see eq. (23) of "The relativistic Sagnac Effect", referenced in endnote (c). Note that the equations given there are for time as measured by a ring clock and not a lab clock, as used above, but there is only a factor γ difference.

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#1

### Re: Einstein Clocks and the Sagnac Effect

11/10/2011 11:05 PM

Face it, the reason clocks show different times for one way transmission of light verses two way is that in the two way you average out any gain and delay. You can't do this with one way measurements, it doesn't let you cheat. Tell me, if light is constant regardless of emitting object speed, then why does light from on oncoming train shift blue and one from a receding train shift red? The train has no effect on the light remember, or hmmm, does it? Couldn't be simple c+v or c-V could it? Nah, that would be ridiculous wouldn't it that light might actually give two different measurements depending on velocity towards or away as does every other known thing that exists, even though you get a Doppler shift for that very reason. All GPS clocks are adjusted within the stationary ECI frame and work with exceptional precision, yet they do indeed show different two way transmission of light speed.

http://vixra.org/pdf/1008.0035v1.pdf

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### Re: Einstein Clocks and the Sagnac Effect

11/11/2011 1:31 AM

sjw40364, did you read anything that I wrote above? Did you consult any of the references?

Your core question has been answered in all of them. I repeat the main theme:

The one way speed of light depends on the clock synchronization convention that you adopt and as such it can never be measured in absolute terms.

-J

PS: It looks like the author that you referenced does not understand the way the Sagnac effect has been implemented in the GPS receivers. He demonstrably does not understand relativity either.

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#3

### Re: Einstein Clocks and the Sagnac Effect

11/11/2011 2:43 AM

That's a little tough Jorrie!!

Give us mere mortals a little time to digest it all.

Perhaps a practical example... We are engineers not theoreticians.

A real life example of time stamped light pulses could be the data stream on a ranging radar, right? Where the distance is inferred by the data slip on the PRNS data?

I promise that I will eventually read it all.

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#4

### Re: Einstein Clocks and the Sagnac Effect

11/11/2011 3:33 AM

Hi Wal, with PRNS I presume you are referring to pseudo random noise codes in radar?

There is another meaning, namely "Partially Resolved Numerical Simulation", of which I doubt the applicability here.

You must remember that ranging radars use the two-way speed of light, not one-way, AFAIK. I will think about a suitable one-way example, though.

As a matter of fact, ranging radars assume Einstein's clock synchronization, otherwise they will be fairly useless. The radar distance is taken as half the total time delay divided by c.

-J

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#5

### Re: Einstein Clocks and the Sagnac Effect

11/11/2011 4:01 AM

PRNS=Pseudo random number stream AKA PRBS=Pseudo random bit stream

Not all two way though where spacecraft transmit their data embedded beacons, but then that's not really radar is it but it is a earth based reference ranging technique with a free running (previously synchronised) clock on board the spacecraft. Again your point on clock synchronisation is apparent and demonstrable.

Or have I lost the point?

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#6

### Re: Einstein Clocks and the Sagnac Effect

11/11/2011 4:30 AM

Yep, GPS uses exactly what you said, but their clocks are all 'forced synchronized' to GPS master (ground) time, as you well know.

One way speed of light/distance measurement and time-stamps are indeed used by the receiver algorithms to determine a location on Earth. Apart from other things, they also take into account the Sagnac effect due to Earth's rotation.

The anti-relativity fraternity tie themselves into knots around this, trying in vain to "prove relativity wrong" by means of GPS - usually through some misunderstanding or misrepresentation.

-J

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#7

### Re: Einstein Clocks and the Sagnac Effect

11/11/2011 10:59 AM

Tell me. since the earth is spinning on its axis, and rotating around the Sun which is rotating around the galaxy, which is moving through space, where is that non-rotating spot you need for the principle of equivalence? That you actually believe you can consider any frame to be non-rotating or non-moving shows the error in your thinking. We have no concept of what either of those two realities are because we have never observed one non-rotating or non-moving object, ever. Pick any spot on the earth, it has 3 rotations and one forward velocity. So why are you not using the Lorentz equations to adjust clocks on the Earth due to its velocity around its axis, its velocity around the Sun and its velocity around the galaxy and the galaxies velocity through space? Are you saying the Lorentz equation does not apply to a moving clock except when it leaves the earth? That magically all clocks on earth are free from this effect? Or have you perhaps chosen the Earth as a preferred frame of reference without claiming it as such?

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#8

### Re: Einstein Clocks and the Sagnac Effect

11/11/2011 11:13 AM

Make it easy all the way around.............just go digital.

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#9

### Re: Einstein Clocks and the Sagnac Effect

11/11/2011 10:48 PM

CJW, unless you stay on-topic, showing that you have at least read what was written or referenced, this has been your last surviving post to this blog. You have not asked one question that is relevant to the topic under discussion here, so sadly, there will be no answers coming your way.

-J

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#10

### Re: Einstein Clocks and the Sagnac Effect

11/12/2011 1:59 AM

So let me see if i have this straight: Though we know there is no universal frame of reference and therefore never any need for more than two frames of reference for an experiment, for the explanation of this experiment, we're going to add a third frame of reference outside of the emitter and receiver and call it "proper time". In regard to this third frame of reference the light beam is traveling a different distance so that is why it is out of sync. Does that about sum it up?

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#11

### Re: Einstein Clocks and the Sagnac Effect

11/12/2011 2:30 AM

Some good questions, at last...

"Does that about sum it up?" Not quite.

"Though we know there is no universal frame of reference ..."

We only know there is no absolute frame of reference detectable. There is a 'universal frame of reference' - the frame where the CMB radiation is isotropic, but it is just another inertial frame in which cosmological calculations are the most convenient.

"and therefore never any need for more than two frames of reference for an experiment, ..."

There is never the need for more than one frame of reference. You choose the most appropriate frame for your experiment and do all calculations in that frame. It is OK to jump between frames, if convenient, provided that you do the transforms from the one to the other(s) correctly, according to your chosen clock synchronization convention.

"... for the explanation of this experiment, we're going to add a third frame of reference outside of the emitter and receiver and call it "proper time"".

Yea, provided you choose that frame correctly. 'Proper time' has a very strict definition in that it is measured by a clock that is physically present at both events being observed.

"In regard to this third frame of reference the light beam is traveling a different distance so that is why it is out of sync."

You need to state what is out of sync with what. Frames can't be out of sync; clocks can go out of sync with each other. So which of the clocks in the OP are you referring to?

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#12

### Re: Einstein Clocks and the Sagnac Effect

11/12/2011 3:32 AM

So to explain this experiment we are going to add an uneeded clock so that we can explain why the two light rays traveling in different directions are out of sync with the third clock, which is unnecessary to begin with. Since the two synchronized clocks show the light rays arrive at two different times we add a third unnecessary clock, call it proper time, and then use that clock to explain the discrepancy. Since the only clocks needed are one at the emitter and one at the receiver, why are we adding this third clock and calling it proper time (a preferred frame) again? Did I miss something or are we just throwing the third clock in so one light ray has further to travel according to it (but it is unnecessary to begin with), so apparently we can throw out any measurements from this unnecessary clock and only rely on the two necessary clocks. Unless of course you need this third clock and its preferred frame to make the discrepancy disappear? But wait, there is no preferred frame so either of the two frames of the other clocks will work just as well, but no, they don't do they, but, but....

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#13

### Re: Einstein Clocks and the Sagnac Effect

11/12/2011 6:34 AM

"Did I miss something or are we just throwing the third clock in so one light ray has further to travel according to it (but it is unnecessary to begin with) ..."

You seem to be missing the whole point of this thread. What third clock appears in my article?

I'm firstly describing two clocks in some inertial frame, being synchronized by the Einstein method. Then, to illustrate the validity of the method, I continue with the Sagnac effect, where the same two clocks are now sitting next to each other on a fiber-optic ring. No third clock anywhere. I just decided to analyze the Sagnac effect with the non-rotating lab frame as reference.

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#14

### Re: Einstein Clocks and the Sagnac Effect

11/12/2011 12:58 PM

The non-rotating lab frame which is a third clock and your now preferred frame (proper time). How is that frame non-rotating since the surface of the earth rotates around the Earth's axis, which rotates around the Sun, which rotates around the galaxy? Hence neither you nor I can even conceive of non-rotation or non-moving as we have no experience of either. Of course you want to use this rotation to show why the Sagnac effect fits relativity, then claim the lab is a non-rotating frame so it fits relativity too.

The principle of equivalence is this: "We may incorporate these ideas into the principle of equivalence, which is this: In a freely falling (nonrotating) laboratory occupying a small region of spacetime, the laws of physics are the laws of special relativity."

You be sure to let me know when you find that small region of space-time that is non-rotating and I will certainly agree that the laws of physics there are the laws of special relativity. If you need to we can also discuss how gravity causes an acceleration of objects so the Earth orbiting the Sun can not be considered in free-fall. But when you find a spot free of all gravity and rotation do let me know.

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#17

### Re: Einstein Clocks and the Sagnac Effect

11/12/2011 11:36 PM

"The non-rotating lab frame which is a third clock and your now preferred frame (proper time)"

My 'lab frame' does not have a clock, just an observer.

"How is that frame non-rotating since the surface of the earth rotates around the Earth's axis, ..."

It's in space and non-rotating relative to the distant stars. Piece of cake - ask NASA.

"Hence neither you nor I can even conceive of non-rotation or non-moving as we have no experience of either."

Speak for yourself, because we as relativists can; we simply add the qualifier "relative to such or such", Then things are easy. My thoughts go out to "absolute framers", who do not have that luxury.

The rest of your reply is off-topic, so I will reply to that in a new thread under General, which you will love... I will no longer tolerate a complete diversion here, but have fun on that new 'dedicated' thread.

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#15

### Re: Einstein Clocks and the Sagnac Effect

11/12/2011 4:57 PM

People have a preferred frame, the frame they are in, relativity does not.

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#16

### Re: Einstein Clocks and the Sagnac Effect

11/12/2011 5:20 PM

Agreed, yet you must add a third frame, prefer its measurements over the receivers frame or you cannot explain the velocity of light without contradiction. Since there is no preferred frame and the 3rd frame is unnecessary, the two synchronized clocks should be all that is needed. yet they show light does not travel at the same velocity, but you can't accept that so you throw in a 3rd frame and call it the proper frame so you can backstep around the problem. Double talk and sleight of hand.

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#18

### Re: Einstein Clocks and the Sagnac Effect

11/13/2011 12:45 AM

I will delete further diversions here.

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#19

### Re: Einstein Clocks and the Sagnac Effect

11/14/2011 4:46 AM

StandardsGuy wrote on another thread: "I would like your response to this link, if it is not too much trouble. I can't even understand the summary."

I'm responding here, because it's the topic of this Blog entry.

Post's Sagnac Effect is a very scholarly, textbook-quality paper of the late 1960s. It includes just about every angle of the Sagnac effect and its applications. Apart from present accuracy of experiments that's better, I could spot nothing that really changed since then.

Post clearly shows why low-speed rotations can be approximated to the standard 'classical' equations, but that the relativistic equation must be used for relativistic rotations. He also clearly shows the difference between the equations for the two frames of reference, as discussed in the physicsinsights.org article that I referenced in the OP.

You are welcome to ask specifics if needed.

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#20

### Re: Einstein Clocks and the Sagnac Effect

11/14/2011 8:51 PM

Thanks, Jorrie

In the link on this post:

In fact, it's impossible to exactly synchronize all Earth clocks such that light pulses sent between pairs of clocks will appear to have the same velocity regardless of the direction they're going in. The errors due to the rotation of the slowly turning Earth are so small they're not normally of consequence, however.

But in the neutrino speed test they might be of consequence. Could this be the problem in the apparent neutrino speed>c problem?

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#21

### Re: Einstein Clocks and the Sagnac Effect

11/14/2011 10:59 PM

Hi S.

No, the short answer is: "too small and in the wrong direction", for the neutrinos at least. Since the around-the-equator Sagnac effect is some 200 ns on 40,000 km, it must be less than half a nanosecond on the 70 km path. So even if they forgot to include it, or did it in the wrong direction, it's still insignificant.

The clocks at CERN an the Opera tunnel were synchronized by the standard international methods, which takes the Sagnac effect into account. Since the Opera site is in a tunnel, they had to 'slow-transport' a reference clock from a Swiss timing center to inside the tunnel. That setup has been scrutinized many times.

-J

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#22

### Re: Einstein Clocks and the Sagnac Effect

11/14/2011 11:48 PM

A further comment on "it's impossible to exactly synchronize all Earth clocks such that light pulses sent between pairs of clocks will appear to have the same velocity regardless of the direction they're going in." seems in order.

The 'anti-club' misreads this as saying that the local speed of light on Earth's surface is not isotropic. They fail to recognize that locally, clocks are synchronized by the Einstein method, ensuring local isotropy. It is just not valid globally, i.e., if you do that from clock to clock around the world, you have to bring in Sagnac, like in the GPS time sync protocol - else you have a discontinuity.

For the benefit of the 'anti-club' - as I wrote before: we choose the clock synchronization scheme that fits the purpose best. There are no absolute methods to follow, just 'best methods'. UTC-time is one global method and GPS-time another.

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#23

### Re: Einstein Clocks and the Sagnac Effect

11/15/2011 8:05 PM

Isn't light isotropic to all moving frames regardless of the frames velocity, so that all clocks should measure speed c with regard to light with no adjustments at all if that clock is used as the measuring frame?

According to standard definition: "It generalizes Galileo's principle of relativity-that all uniform motion is relative, and that there is no absolute and well-defined state of rest (no privileged reference frames)-from mechanics to all the laws of physics, including both the laws of mechanics and of electrodynamics, whatever they may be. Special relativity incorporates the principle that the speed of light is the same for all inertial observers regardless of the state of motion of the source."

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#24

### Re: Einstein Clocks and the Sagnac Effect

11/16/2011 12:41 AM

"Isn't light isotropic to all moving frames regardless of the frames velocity, so that all clocks should measure speed c with regard to light with no adjustments at all if that clock is used as the measuring frame?"

One more time (and I'll be as clear as I can manage):

Light propagation is not isotropic in rotating frames. At many points on a rotating ring you can set up momentarily co-moving inertial frames; in each frame you can Einstein-synchronize its own clocks and light then propagates isotropically in that frame. But, now you have a large number of inertial frames, all moving relative to each other, and each with its own clocks sync'd in its own frame, but not in any of the other inertial frames.

Have you missed the fact that light is isotropic in inertial frames only because Einstein made it so by choosing the simplest convention for clock sync in inertial frames? Did you notice that I wrote above that you can choose any other scheme you like, but you will make life difficult for yourself?

On a rotating sphere without gravity, you cannot synchronize clocks in any consistent way. Luckily, on Earth we have an equi-potential surface where gravity and velocity time dilation cancel and all clocks sitting on the surface tick at the same rate. So we can synchronize them, by applying a Sagnac correction to the Einstein method, for every pair of clocks individually, because the correction is different for different directions and latitudes.

This now becomes the most useful clock synchronization scheme -"sleight of hand", yes, but proper and great! So useful it is that we preset the actual GPS space vehicle clocks to also run closely in sync with this scheme. Obviously, light will not seem to propagate isotropically in this frame, but we know exactly how to handle that.

We could have chosen another sync scheme, but that would have complicated our lives considerable. The results would however have been the same, because as long as we can define a frame properly, we can calculate anything relative to it.

This is why some calculations are done in the (inertial) ECI frame, where light do propagate isotropically. Some calcs are simpler there and we can at any time jump from the ECEF to the ECI and back, provided we do the transformations relativistically correctly. There are obviously no clocks permanently 'sitting' in the ECI frame - other than 'paper clocks'. Clocks are on Earth, on GPS satellites and inside vehicles of all sorts.

Many of the likes of Hatch and Wang misinterpret these simple facts and than shout 'foul'...

-J

PS: GPS is obviously complex and if one really wants to know what is going on, especially from the receiver side, you must read something like Ashby and Weiss (NIST Technical Note 1385). This one is tough going, 51 pages of information and discussion...

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#25

### Re: Einstein Clocks and the Sagnac Effect

11/16/2011 8:41 PM

So quit deleting my posts and answer the question.

1) Do GPS clocks show light to be isotropic before or after correction?

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#26

### Re: Einstein Clocks and the Sagnac Effect

11/16/2011 11:50 PM

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#27

### Re: Einstein Clocks and the Sagnac Effect

11/17/2011 9:57 PM

So only after applying clock synchronization?

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#28

### Re: Einstein Clocks and the Sagnac Effect

11/17/2011 10:47 PM

No. See #24.

For the absolutely final time: light propagation is isotropic in an inertial frame and only when clocks are Einstein-synchronized in that inertial frame. GPS clocks are not in an inertial frame, nor are they Einstein-synchronized. There are no clocks in the inertial (ECI) frame...

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#31

### Re: Einstein Clocks and the Sagnac Effect

11/19/2011 5:34 PM

Yah, I am sure our galaxies motion through space, the Sun around the galaxy, and the earth around the Sun can be considered to be non-inertial in your book. Smoke and mirrors.

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#29

### Re: Einstein Clocks - Summary

11/18/2011 5:15 AM

This thread has probably run its useful course, but because of some potential confusion,(a) I will briefly summarize it here.

1. Einstein clocks - a convention

I defined "Einstein clocks" as sitting at rest in some inertial frame and are synchronized by sending a time-stamped light pulse between them; add the light travel time to the time-stamp, assuming the one-way speed of light to be c. Set the receiver clock accordingly.

I may have added to this: reverse the process and verify that the original clock is indeed in sync with the synchronized clock. The method is a pure convention, originally brought in by Einstein (although I guess that Galileo must have used the same convention, just with "infinite speed of light".)

There are other valid ways of synchronizing clocks in inertial frames, but they do not produce such a simple, yet consistent result.

2. The Sagnac effect

The time it takes for light to travel in opposite directions around a length-wise rotating path is not the same for the two directions. The reason is that we cannot 'Einstein-synchronize' clocks in a rotating reference frame. Light simply does not propagate isotropically relative to any rotating frame of reference. It takes longer to go around with the rotation than against it.

On gravitating bodies with spin, there exists an equi-potential surface on which clocks can be synchronized, but in this case we must compensate the Einstein synchronization by a Sagnac effect, which depends on the direction between the clocks and the rotation rate of the body.

There is a small relativistic correction to for high-speed rotation, but other than that, classical Newton predicts the same Sagnac effect as classical Einstein. This is why Sagnac is sometimes called a non-relativistic effect in the literature. Rotating frames are seldom very relativistic.

3. Rotation versus linear movement

Rotation is an absolute effect in the sense that it can be measured in a coordinate-independent way. All inertial observers in the universe will agree that Earth is rotating and can calculate its rotational rate.

Linear movement is a relative effect, and what 'moves' and what not, and at what speed, depends on in which inertial frame the observation is made.

The Sagnac effect measures rotation rate, not linear movement. The Sagnac effect in a non-rotating interferometer is zero, irrespective of relative inertial movements.

The Sagnac effect is sometimes viewed as equivalent to clock desynchronization in linear (inertial) movement. This is true in the usual approximations employed for low speeds, but is not true in the full relativistic treatment of the two effects.

4. "Preferred" versus "absolute" frames of reference

It is OK to have a 'preferred' reference frame for a specific observation, or for calculations, because it makes things simpler. It does not mean that such a frame is 'preferred' by physics, because then it would have been the 'absolute' reference frame (e.g. the ether frame).

If such a frame exists, we seem to be incapable of detecting it in our 4-dimensional spacetime. Non-detection does of course not rule out the existence of such a frame.

Inertial frames are all equivalent, but rotating frames are not. Most dramatically, the speed of light differs for different rotation rates and positions in the frame (i.e. the coordinates of the observer and the observed effect).

Clocks can be 'Einstein synchronized' in any inertial frame. They cannot be synchronized in a rotating frame, except for specific cases, e.g. an equi-potential surface, like Earth's geoid. Moreover, each inertial frame has its own definition of when clocks are synchronized.

5. Conclusions

This is not an exhaustive summary, just most of the issues that came up during discussions in this Blog.(b)

Comments for further clarification are welcome.

-J

(a) Although SJW created some diversion and possible confusion, his comments did force a more thorough treatment and more references than what I initially planned. Being a Blog with comments, the discussions tend to get disjointed - hence this attempts to summarize the salient points.

(b) I must emphasize that this Blog was not about the GPS, but about the Sagnac effect. The Sagnac effect is present in the GPS system because it is a rotating system, but the purpose here was ordinary, down-to-earth Sagnac interferometers. SJW brought in GPS in the link he gave in the first comment, so some aspects were addressed. It more properly belongs to one of the "misconceptions" Blogs.

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#30

### Re: Einstein Clocks - Summary

11/18/2011 3:35 PM

So create an electromagnetic wheel (no Friction) driven by pulse bursts that react to gravity (for proper time) attach a single light source (bright LED) to the wheel and shine that light into equal length fiber-optic cables attached to a clock face. Whalla a light clock that keeps perfect time.

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#32

### Re: Einstein Clocks - Summary

11/19/2011 5:53 PM

So you are saying GPS clocks do not stay synchronized with one another?

ECI Frame:

Earth-centered inertial (ECI) coordinate frames have their origins at the center of mass of the Earth. ECI frames are called inertial in contrast to the Earth-centered, Earth-fixed (ECEF) frames which rotate in inertial space in order to remain fixed with respect to the surface of the Earth. It is convenient to represent the positions and velocities of terrestrial objects in ECEF coordinates or with latitude, longitude, and altitude. However, for objects in space, the equations of motion that describe orbital motion are simpler in a non-rotating frame such as ECI. The ECI frame is also useful for specifying the direction toward celestial objects.

ECI coordinate frames are not truly inertial since the Earth itself is accelerating as it travels in its orbit about the Sun. In many cases, it may be assumed that the ECI frame is inertial without adverse effect.

So it's inertial when you need it to be and non-inertial when you need it to be. Smoke and mirrors.

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#33

### Re: Einstein Clocks - Summary

11/20/2011 2:30 AM

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#34

### Re: Einstein Clocks - Summary

11/20/2011 8:41 PM

No thanks, I've had enough smoke and mirrors, you just keep believeing light is constant to all frames and continue to be surprised at results like CERN. You can't even accept the empirical data when it has been repeated twice, with exactly the same result, because you need it to be in error.

So a spacecraft traveling through space under no acceleration would be an inertial frame, yet the earth traveling around the Sun and with the Sun around the galaxy and with the galaxy through space is non-inertial frame, unless you need to calculate SV orbits, then it's inertial.

Yes, I've had enough smoke and mirrors.

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#36

### Re: Einstein Clocks - Summary

11/21/2011 12:12 PM

On the money GA!!!!!

The same as my kids. There is one truth which is theirs, even when evidence is provided to dispute their truth, they only believe in what they feel to be true, often not backed by real fact but assumed fact.

Even Einstein looked at all truths before making a statement of assumption that may not be true.

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#37

### Re: Einstein Clocks - Summary

11/21/2011 6:45 PM

And even Einstein was so unsure of his theories he was positive they would all be overturned, understood them so little he could not even solve them. Was so unsatisfied with them and having to fake his tensor that he worked up to the day he died trying to correct his mistake. Einstein formulated his theory on the idea that the universe was staic, not expanding, could nat make it work so threw in a tensor that is not even a tensor to make it work, and then only if one precisely pick the coordinates, any other coordinates fail.

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#35

### Re: Einstein Clocks and the Sagnac Effect

11/20/2011 10:02 PM

Who'd have thought that there was so much intrigue and emotion in the world of physics.?

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#38

### Re: Einstein Clocks and the Sagnac Effect

11/21/2011 9:33 PM

Jorrie,

I suggest you close these related threads. They have run their useful course.

-S

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#39

### Re: Einstein Clocks and the Sagnac Effect

11/21/2011 10:53 PM

Hi S, good idea, thx. :))

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