Einstein's Clock Synchronization Convention

[Aether]

Again, what are dA, dB, and dC? You seem to have introduced these symbols without defining them.

I defined them in posts #79 & #83. However, in #79 I used dv where I meant \textbf{v} dt, and didn't make the vectors bold. So, my apologies for causing confusion in that way.

Why did you get rid of the "d"? That makes even less sense, how do infinitesimal displacements along the x,y, and z lead to a non-infinitesimal velocity vector? And you didn't address my point about one side of your equation being a vector and the other being a scalar.

You're right about the notation. I changed it to: \textbf{v} dt=dx+dy+dt. Both sides of the equation are vectors.

Shouldn't this go in the Independent Research forum, anyway?

This forum looks like a great idea, but I wasn't looking to get into an open discussion of my own personal theories at this time. I was merely attempting to answer all of your questions as I have been doing all along. Your questions and comments have been generally helpful, and I appreciate that.

 

[DrGreg]

Technical note on vectors in TEX

I noticed in some posts in this thread that on this site's TEX system \bold text is sometimes hard to distinguish from normal italic TEX.

I'd suggest using \textbf instead.

\textbf r = (x, y)

Or, if you prefer, \vec

\vec r = (x, y)

 

[DrGreg]

If I understand correctly what Paul Dirac is saying (and I think I do because I have several of his subsequently published papers and articles in Nature where he says explicitly that "an ether is rather forced upon us" or words to that effect) then I don't see why we can't represent \textbf c_0 dt as a vector, and d \textbf s =\textbf c_0 dt-dx-dy-dz as a vector. I understand that for many practical purposes this would be a meaningless complication, but for my purposes I would like to figure out how to do it correctly. On second thought, it may be the vector \textbf c_0 dt that should be held invariant in the transformation that I'm trying to develop.

I preface my remarks by saying I don't know a lot about quantum theory. This website has a separate forum devoted to the subject.

In quantum theory particles do not have an exact position or momentum. There is always some error in any measurment you make. The more accurately you measure one, the less accurately you measure the other.

So if you try to measure a quantum particle's velocity by measuring \delta x / \delta t, for very, very, very, small \delta x and \delta tyou are doomed to failure because the errors will overwhelm the tiny difference you are trying to measure. So "instantaneous velocity" calculated this way is pretty meaningless. Your best bet is to measure a whole sequence of distances and times, plot them on a graph and perform a straight line curve fit. This averages out all the measurement errors.

In this forum I assume that all particles are "classical" particles postulated to have a precise position and momentum.

Mansouri-Sexl add three arbitrary synchronization parameters to the LET transformation equation for the t coordinate; one for each direction in space. Making \textbf c_0 dt a vector may imply three time coordinates; one for each direction in space.

No they are not saying anything of the sort. The three parameters are something you, the observer, decide when you choose how to synchronize your clocks, they are not extra dimensions of anything.

 

[Aether]

In this forum I assume that all particles are "classical" particles postulated to have a precise position and momentum.

OK. What is the right term (Minkowski geometry? Topology?) for that science which emcompasses all possible coordinate systems (e.g., from which new coordinate systems may be contructed), all types of particles, which directly addresses all questions of Lorentz symmetry and violations thereof, and of which relativity is an infinitesimally thin slice (e.g., that it explicitly applies only to inertial frames and classical particles)?

No they are not saying anything of the sort. The three parameters are something you, the observer, decide when you choose how to synchronize your clocks, they are not extra dimensions of anything.

That's right. Only the first sentence describes what Mansouri-Sexl are saying. The second sentence follows it so that the two may be compared to show that there is a precedent for parameterizing the time coordinate with three arbitrary components, one for each direction in space.

 

[Jimmy Snyder]

Just a friendly reminder, the first postulate of the special theory of relativity, namely that the speed of light c is the same in all inertial frames, only holds true in view of Einstein's clock synchronization convention.

Do I have this right? These guys are trying to prove that a postulate is true? By the way, it's the second postulate. Who are these guys?

 

[Aether]

Do I have this right? These guys are trying to prove that a postulate is true?

Mansouri-Sexl do not try to prove, by experiment, that the postulate is true. On page 499 of their first paper they say "When clocks are synchronized according to the Einstein procedure the equality of the velocity of light in two opposite directions is trivial and cannot be the subject of an experiment."

By the way, it's the second postulate.

One of my GR textbooks, A Short Course in General Relativity, by Foster & Nightingale, lists the speed of light postulate first.

Who are these guys?

They developed a popular test theory of special relativity and published it in 1977. Since then, most published experiments testing for violations of local Lorentz invariance have referenced their work.

After lengthy discussion, I see more clearly now that the key limitation of the constancy of the speed of light postulate is that it is only true "in all inertial frames". Inertial frames are coordinate systems in which the speed of light is defined to be constant in all directions, and that is the end of it. There can be no such thing as an experiment to verify that this is true. If someone claims that there is, then they are not observing this explicit limitation that is built into the postulate. That would be like saying that "experiments have proven that the inches on an english ruler really are inches, so there".

 

[Aether]

The primary reason to synchronize clocks is to be able to measure velocities. When we demand that an object of mass m and velocity v moving north have an equal and opposite momentum to an object of mass m and velocity v moving south, we require Einsteinan clock synchronization.

Empirically, this means that we require an two objects of equal masses moving at the same speed in opposite directions to stop when they collide inelastically.

It is indeed *possible* to use non-Einsteinain clock synchronizations, and under some circumstances it is more-or-less forced on us. In such circumstances, one must not remember that momentum is not isotropic.

Note that Newton's laws assume that momentum is isotropic (an isotropic function of velocity). Therfore Newton's laws (with the definition of momentum as p=mv) cannot be used unless Einstein's clock synchronization is used. Some other definition of momentum other than p=mv must be used if it is to remain a conserved quantity when non-standard clock synchronizations are used.

The ability to use Newton's laws at low velocities was what motivated Einstein to define his method of clock synchronization.

pervect, I agree with you now. I did not fully appreciate that it is the very definition of what an inertial reference frame represents which causes momentum to be conserved as p=mv rather than a law of nature per se. That is as interesting to me as is the fact that the constancy of the speed of light is an artifact of the definition of an inertial frame.

I interpreted "Empirically, this means that we require an two objects of equal masses moving at the same speed in opposite directions to stop when they collide inelastically" to imply that SR and LET were not empirically equivalent, but I see now that by this you were correctly defining how "at the same speed in opposite directions" is used to define an intertial frame.

 

[Jimmy Snyder]

One of my GR textbooks, A Short Course in General Relativity, by Foster & Nightingale, lists the speed of light postulate first.

One of Einstein's papers, 'On the Electrodynamics of Moving Bodies', lists it second.

There can be no such thing as an experiment to verify that this [postulate] is true.

Do you know of a postulate that has been proven true?

 

[Aether]

One of Einstein's papers, 'On the Electrodynamics of Moving Bodies', lists it second.

OK.

Do you know of a postulate that has been proven true?

If you have a point to make, then please make it.

 

[DrGreg]

In this forum I assume that all particles are "classical" particles postulated to have a precise position and momentum.

Aether, I said this simply to suggest that if you want to discuss the subtleties of quantum theory, it would be a good idea to do that in the Quantum Theory forum of this website.

 

[Aether]

Aether, I said this simply to suggest that if you want to discuss the subtleties of quantum theory, it would be a good idea to do that in the Quantum Theory forum of this website.

I know, and agree. However, if QM is built on relativity (or at least an assumption of Lorentz symmetry) then it's not exactly what I am looking for any more than relativity per se. That is not intended as a criticism of either theory. I simply want to keep each theory within its proper context so as not to be tripped up by inadvertent applications of these theories outside of their proper domain, and am asking what is the appropriate global perspective from which to build new theories?

 

[Jimmy Snyder]

If you have a point to make, then please make it.

My point is that postulates are never proven true. I asked you if you knew of a counterexample because I knew that there aren't any. I hoped that by my asking this question, you would come to realize what my point was without my telling you. It's a method of argumentation first practiced by Socrates, and described by Plato. It tends to fall to pieces when challenged in this way.

 

[Aether]

My point is that postulates are never proven true. I asked you if you knew of a counterexample because I knew that there aren't any. I hoped that by my asking this question, you would come to realize what my point was without my telling you. It's a method of argumentation first practiced by Socrates, and described by Plato. It tends to fall to pieces when challenged in this way.

OK, here is a counterexample of Copernicus' 7 Postulates. I would judge that at least some of them have been proven to be true.

(from the Commentariolus)

There is no one centre of all the celestial circles or spheres.

The centre of the Earth is not the centre of the Universe, but only of gravity and the lunar sphere.

All the spheres rotate about the Sun as their midpoint, and so the centre of the Universe is near the Sun.

The Earth's distance from the Sun is...imperceptible when compared with the loftiness of the firmament [of fixed stars].

An apparent motion of the firmament is the result, not of the firmament itself moving, but of the Earth's motion. The Earth... goes through a complete rotation on its axis each day, while the firmament and highest heaven remain unaltered.

What appear to us as [annual] motions of the Sun result, not from its moving itself, but from the [linear] motion of the Earth and its sphere, with which we travel around the Sun just like any other planet. The Earth has, accordingly, more than one motion.

The apparent retrogradations and [returns to] direct motions of the planets are the result, not of their own motion, but of the Earth's. The motion of the Earth alone, therefore, is enough to explain many apparent anomalies in the heavens

 

[Jimmy Snyder]

Here is the Britannica article on the word 'axiom'. Postulates are unprovable by definition. Counterexamples cannot exist.

In mathematics or logic, an unprovable rule or first principle accepted as true because it is self-evident or particularly useful (e.g., “Nothing can both be and not be at the same time and in the same respect”).

The term is often used interchangeably with postulate, though the latter term is sometimes reserved for mathematical applications (such as the postulates of Euclidean geometry). It should be contrasted with a theorem, which requires a rigorous proof.

http://www.britannica.com/ebc/article-9356242?query=postulate&ct=

 

[Aether]

Here is the Britannica article on the word 'axiom'. Postulates are unprovable by definition.

OK, but why are you showing me an article on the word 'axiom' to convince me of something about the word 'postulate'?

Counterexamples cannot exist.

I just showed you a counterexample. I wouldn't be surprised if there was some formal context in which what you are saying is correct, but you haven't put your statement within such a context. This is similar to where this thread is ending up; the speed of light postulate is true within the context of inertial reference frames, but not outside of that context.

We recently had a discussion of this as it relates specifically to special relativity in the 'Consistency of the speed of light thread', have you looked at that? Someone may have said something there that you can use to make your point.

 

[reilly]

There's always the simple minded observation that, as far as I know, the conventional approach to SR has served us well for about a century. So, why change, unless there are strong empirical reasons to do so?

As pervect suggests, anything but the standard synchronization of clocks, is a matter of General Relativity. Any consistent set of conventions for synchronization must map into the standard one, and vica versa, and the transformations will be nonlinear. That is, off beat conventions will lead to non-inertial frames, basically by definition.

Again, the canonical approach will be modified or thrown out only when it fails to pass an empirical test.
Regards,
Reilly Atkinson

 

[Jimmy Snyder]

OK, but why are you showing me an article on the word 'axiom' to convince me of something about the word 'postulate'?

For two reasons.
1. Because as the article says: "The term (axiom) is often used interchangeably with postulate". The difference is in the field, not in the meaning.
2. Because the postulates as stated in Einstein's original paper on SR (On the Electrodynamics of Moving Bodies) are to be understood in this way.

Examples of this sort, together with the unsuccessful attempts to discover any motion of the Earth relatively to the "light medium,'' suggest that the phenomena of electrodynamics as well as of mechanics possesses no properties corresponding to the idea of absolute rest. They suggest rather that, as has already been shown to the first order of small quantities, the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good. We will raise this conjecture (the purport of which will hereafter be called the "Principle of Relativity'') to the status of a postulate, and also introduce another postulate, which is only apparently irreconcilable with the former, namely, that light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body. These two postulates suffice for the attainment of a simple and consistent theory of the electrodynamics of moving bodies based on Maxwell's theory for stationary bodies.

 

[Aether]

For two reasons.
1. Because as the article says: "The term (axiom) is often used interchangeably with postulate". The difference is in the field, not in the meaning.

You would have to show me a definition of 'postulate' rather than 'axiom' before I would consider it relevant.

2. Because the postulates as stated in Einstein's original paper on SR (On the Electrodynamics of Moving Bodies) are to be understood in this way.

That quote contains the word 'postulate', but it doesn't say that the postulates are unprovable. You would have to show me a quote from a source like that which actually says something explicit to that effect, like this: "It is standard practice in the field of physics to label any unprovable assumption as a 'postulate', and of course what we mean by that is that counterexamples can't exist".

I looked up 'postulate' in several dictionaries, and all I saw was "a proposition taken for granted to be true". That doesn't necessarily mean that I couldn't also prove the proposition to be true also. Your definition of "axiom" on the other hand actually says that it is "unprovable". Show me a definition of 'postulate' that says that.

It's a method of argumentation first practiced by Socrates, and described by Plato. It tends to fall to pieces when challenged in this way.

Go back and see if either Socrates or Plato indicated which end of the argument was supposed to "fall to pieces when challenged in this way".

 

[Aether]

There's always the simple minded observation that, as far as I know, the conventional approach to SR has served us well for about a century. So, why change, unless there are strong empirical reasons to do so?

No reason to change unless there are strong empirical reasons to do so. However, the proliferation of crackpots may be a strong empirical reason for teachers to take care to keep SR clearly within the context of inertial reference systems. Some percentage of students is going find the relativity of simultaneity hard to accept, and quite rightly so, outside of this context; and for every genuine crackpot there may be a thousand others who just gave up trying to understand. Be prepared to give the right answer on this question. The constancy of the speed of light and the relativity of simultaneity are not what experiments prove, they are mathematical, as opposed to physical, properties of coordinate systems called "inertial reference frames".

Again, the canonical approach will be modified or thrown out only when it fails to pass an empirical test.

That is as it should be, except that alternate approaches will always need to be explored by those who would design and carry out new empirical tests.

Thank you for your help DrGreg, Hans, pervect, Hurkyl, JesseM, and to everyone else who participated. If I had a typist, I would thank them to, but I did all the typing on this end myself.