Is 'time' a measurable variable?

[Doctordick]

Originally Posted by Qfwfq

Quite central to SR, actually, I don't see how you can say that:

Yes, I see your confusion quite clearly. My position is that you are just too immersed in the conventional rationalizations of modern physics to see the problem I am trying to point out.

Originally Posted by Qfwfq

If you don't understand, look up any text of analytic mechanics (hamiltonian and lagrangian formulation) and then any real treatment of QM.

You see, my position is that you are simply far too immersed in the details of the conventional physics rhetoric to see the big picture. You seem to have a love for simple representations of complex ideas such as which actually expresses very little sans the professional training sufficient to interpret the intention. I am moved to give you the "Hamiltonian principle" as I was taught it

Where delta means a path variation along the integration path. Of course, both T and V are presumed to be represented as path dependent variables. The common verbal reference for "T" and "V" are "kinetic" and potential "energy". What is important here is that the frame of reference need not be the standard Euclidean frame. One can work in all kinds of frames (commonly selected because they simplify the constraints on the problem of interest) and the resultant equations can become quite non-linear; but that has little to do with the fundamental concepts embedded in the idea. They are most commonly seen (by anybody used to working with them) as variations in the expression of V, including both time dependent and momentum dependent terms. However, the variations can also on occasion be seen as changes in T such as the effective kinetic energy which arises in superconducting circumstances. What is important here is that all of these alterations are mathematical conveniences which go to simplify the representation of the problem. In which case I would say that these cases in general represent something more constrained than "any possible potential energy" (or, in the same vein, any possible kinetic energy).

Originally Posted by Qfwfq

You appear to misunderstand the idea that "conventional physics" has of potential energy.

I would disagree with you quite strongly on that.

Originally Posted by Qfwfq

... the only really essential constant factor is the imaginary unit!

Now that is an oversimplification if I ever heard one.

Originally Posted by Qfwfq

The Klein-Gordon equation is not of the Hamiltonian form and I don't know how you can say it is, when it is plainly in quadratic form, which is the reason it can't describe a both conserved and positive-definite probability density.

Let us just say it was my oversimplification of what they were trying to do.

Initially the reference "Fock space" rang no bells in my mind so I googled it. However, when I saw the reference to the "Hartree-Fock method" it definitely did ring a bell. Fock was a Russian and I probably didn't know much about him because the competence of Russian research was not emphasized in the early sixties. I am sure a lot of changes have occurred since I left the profession (including the emphasis placed on particular ideas) the but they don't seem to have gotten any closer to understanding reality than they were then.

You commented about a graduate student who liked to research everything to death. I had my own compulsion when I was a graduate student. I was quite a fast and prolific reader and, whenever I had to read a journal reference, I usually read the whole volume rather than just the article which was being referenced. It lead to a rather unusual perspective of physics. If one just reads the referenced stuff, you get the impression physicists are smart people. If you read the whole journal volume, you get the impression that most of the published stuff isn't worth the paper it's printed on. After I got my Ph.D. I had no interest in publishing unless I had something worthwhile to say; I had better things to do with my life. I was certainly convinced the professionals had little to offer.

Originally Posted by Qfwfq

... made me hope you were able to derive RQFT from your model.

That would be "relativistic quantum field theory" which, in my head is rather an oxymoron.

It was long long ago but I know I read something written by Newton regarding the issue of "field theories" (and, after all, he was sort of the originator of the idea with his gravitational theory). He said something along the lines of "even though action at a distance is clearly an impossibility, the idea of a gravitational theory provided a very convenient mathematical mechanism". Now, though he never made it clear as to why he thought such a thing was impossible, I find it a very reasonable comment. By the way, that is one of the reasons I think he would have seen the necessity of special relativity had he happened to think about setting physically separate clocks (I am sure you remember the discussion we had earlier). I always thought Newton was a pretty sharp observer who managed to put together some rather diverse information others seemed able to ignore.

But, back to "field theory". It seems to me that exchange forces provide a much more general mechanism which one might expect to yield universal application. I don't believe "field theory" will ever be more than a mathematically convenient approximation. But, again, that is no more than an opinion and opinions are a dime a dozen.

Have fun -- Dick

[Erasmus00]

Originally Posted by Doctordick

You seem to have a love for simple representations of complex ideas such as which actually expresses very little sans the professional training sufficient to interpret the intention. I am moved to give you the "Hamiltonian principle" as I was taught it

Where delta means a path variation along the integration path. Of course, both T and V are presumed to be represented as path dependent variables. The common verbal reference for "T" and "V" are "kinetic" and potential "energy".

Just a quick note. You are confusing Hamilton's principle for lagrangian mechanics with the Hamiltonian. Your variational method above is a variation of the lagrangian (T-V).

The hamiltonian is defined by a legendred transformation of the lagrangian (L=T-V) We replace with the momentum defined by



And hence we get



Here script L is the lagrangian, q is the coordinate, p is the momentum defined as above and script H is the hamiltonian. Your equations of motion then are





The hamiltonian usually (but not always)comes out just the total energy, but it is defined in terms of two seperate coordinates p and q instead of q and the linked qdot.

This then opens up the idea of canonical transformations in analytical mechanics, because you can transform coordiantes and momentas independantly.

It is this Hamiltonian that becomes the operator in quantum mechanics that Q was referring to. I believe he as asking what happened to your equation in the cases when the Hamiltonian was not simply the total energy of a system.
-Will

[Qfwfq]

Originally Posted by Doctordick

Yes, I see your confusion quite clearly. My position is that you are just too immersed in the conventional rationalizations of modern physics to see the problem I am trying to point out.

Now, let's get this straight, this is your usual manner of dodging and making up excuses for yourself. I say that, since X is actually quite central to SR (as understood by academia), I consequently can't see how you can claim that academia aren't aware of it or of Y, which is closely related to X. You call this "my confusion" and blame it on my conventionality and my inability to see your greater picture; this is sniping. You quite simply make false statements about academic understanding of space-time, and don't explain yourself sufficiently when asked for clarification. You then blame the same thing when I tell you what to look up, in order to clear up your misunderstanding of what I said.

This kind of deceptive reply is unwelcome behaviour Dick, n-th little warning.

[Qfwfq]

Now, back to the debate:

Originally Posted by Doctordick

You seem to have a love for simple representations of complex ideas such as which actually expresses very little sans the professional training sufficient to interpret the intention. I am moved to give you the "Hamiltonian principle" as I was taught it

Moved to give me something that's fundamental to classic and quantum mechanics, in an elementary form that I first found in Feynman vol. I while at my first year?

I am moved to give you the explanation of what tells you very little "sans the professional training sufficient to interpret the intention", as it is one of the things fundamental to the whole of quantum mechanics. You may write it more pedantly:



and even put in the right proportionality constants (such as an ) if you dislike natural units. H is the hamiltonaian operator, which in the case familiar to you is the operator form of. Make the replacement (with the operator for p being the usual gradient) and see what you get. Familiar? Now the operator is only good for a scalar particle and the potential is only a way of treating interactions that (or in cases where they) lend themselves to be so described. There is nothing universal about it, but the form above is much more fundamental.

The reason the imaginary unit has a qualitative rather than quantitative importance is that, for each energy eigenvalue, it flips between exponential decay and constant-amplitude oscilation at a frequency proportional to the energy. So, you make statements about what the conventional academic views of physics are, and disagree with my statements about what they are, but it increasingly appears that you have a very limited knowledge on which to base your statements and judge mine.

If you googled "Fock space" and came up with a reference to the "Hartree-Fock method" then I must presumed you didn't type the wo words inside quotation marks. This link came first in my results, very, very basic and simple. Considering you say that you're quite a fast and prolific reader and usually read the whole volume rather than just the article, you could further that with Schweber's book which is very pedantic about construction of Fock space and then even Bjørken-Drell which examines Feynman diagrams plentiful. You might find out that "relativistic quantum field theory" is not an oxymoron but just the quantum way of treating "fields" as being "particles" and vice-versa and quite the idea of the "exchange forces" you believe in. Never heard of virtual particles?

[Doctordick]

Hi Will, it's nice to hear from you. Have you looked at my dissertation on the need for special relativistic transformations within my picture and can you comprehend the reason why the approach you wanted to follow was not applicable to the geometry I use? I think some of your comments bear directly on that issue of geometric representation.

Believe me, I am well aware of Lagrange and Hamiltonian mechanics. If you go back and examine the roots of that work, you will discover that the central issue was originally the conundrum residing in the equality between inertial mass and gravitational mass. One of the most important aspects of Newton's work was the existence of what we used to call pseudo forces (apparently an idea which has fallen into disuse, at least that is the impression I have gotten). Pseudo forces were apparent forces which were a simple consequence of not working in an inertial frame. The most telling characteristic of a pseudo force was the fact that the magnitude of the force on any object was absolutely proportional to the acceleration. This was true for the simple reason that the acceleration was a consequence of the non inertial frame of reference and thus had nothing at all to do with mass of the object itself (from the perspective of an inertial frame, the free path of the relevant object was a simple straight line).

At the time, the identity between the inertial mass and the gravitational mass was taken as a very strong indication that the gravitational force was a pseudo force: i.e., a consequence of working in the wrong frame of reference. Much geometric work was expended in an attempt to discover a geometry which would yield gravity as a pseudo force. All this with the idea, put forth by Poincareé's, that geometry is nothing more than a convenience in representation. During that work, great strides were made in using implied relations related to general coordinate transformations to solve some rather complex problems which were otherwise totally intractable; however, the gravitational issue was never unraveled.

Eventually, Maupertuis proved that there existed no geometry with a Euclidean metric which would yield gravity as a pseudo force; however, by that time the work in geometric transforms had acquired a life of its own and, as you have implied, the classical work of Lagrange and Hamilton led straight into the modern realm of quantum mechanics. It was in fact the great accomplishment of reducing gravity to a pseudo force which gave Einstein's theory the final push into "fact" (as seen by the academy). If I may quote a respected book, Adler, Bazin and Schiffer, Introduction to General Relativity, McGraw-Hill Co., New York, 1965, p. 3. According to them, Einstein proved that "a reduction of gravitational theory to geodesic motion in an appropriate geometry could be carried out only in the four-dimensional space-time continuum of [Einstein's] relativity theory". They imply that it was the somewhat strange (might I say "unreal") character of this geometry which broke Maupertuis' proof.

However, if you look at the proof, you will discover that the crux of the thing is the fact that entities having different velocities must follow different paths. Einstein's approach works because this very issue is avoided (exactly what is the velocity of an object through the space-time continuum anyway). In Einstein's general picture ordinary spacial velocity is nothing more than a direction in his geometry. In order to achieve this result, Einstein had to sacrifice the issue of time as fundamental concept. I know, you think I am mad, but consider the facts: in Einstein's perspective, time is totally identified with a somewhat strange coordinate in the proper geometry of the universe. Yet they manage to use time as if it is still a parameter of evolution (and please, don't give me the standard rationalizations, I am well aware of them all). I say they do this because, if they presented their geometry as the universal abstract structure they claim it to be, the existence of that sacrifice would become obvious and the hood wink would be over.

I, on the other hand, noticed that mass behaved, analytically speaking at least, exactly like quantized momentum (it makes a lot of express relations simpler). And allowing a dimension for that component of momentum utterly removes the issue of "velocity" from the picture (velocity becomes nothing more than the relative angle between that quantization axis and the direction of motion of the relevant object). It also makes any interaction relationship look like an EM field (that is, all interactions propagate at exactly the same velocity). And finally, it defeats that proof by Maupertuis. Since everything moves at the same velocity, it is entirely possible that there exists a geometry (a four dimensional Euclidean geometry) which makes gravity a pseudo force.

Not only does such a geometry exist, I can display it explicitly and, as I didn't have to sacrifice the time parameter of temporal evolution in order to accomplish the result, general relativistic quantum mechanics becomes a simple straight forward step.

Oh, and regarding your question,"I believe he as asking what happened to your equation in the cases when the Hamiltonian was not simply the total energy of a system", since classical mechanics and its three dimensional representation is an exact approximation to my equation so long as relativistic velocities are not significant, all of the work based on classical mechanics goes through exactly as it did originally so the answer is simply "nothing different from what is in the books". One can even say the relativistic generalization go through though the route now goes down to nonrelativistic relations and then back up (a rather wasted way to get there).

Originally Posted by Qfwfq

This kind of deceptive reply is unwelcome behaviour Dick, n-th little warning.

No deception of any kind was intended. I am sorry you took it that way.

Originally Posted by Qfwfq

Now, back to the debate:

I am curious as to what you think we are debating.

Originally Posted by Qfwfq

So, you make statements about what the conventional academic views of physics are, and disagree with my statements about what they are, but it increasingly appears that you have a very limited knowledge on which to base your statements and judge mine.

So I guess I have totally failed to reach you. Sorry about that, but it has at least moved me to post some of the stuff I have deduced.

Originally Posted by Qfwfq

If you googled "Fock space" and came up with a reference to the "Hartree-Fock method" then I must presumed you didn't type the two words inside quotation marks.

Oh but I did; but I didn't stop there. I have no interest in reading that stuff as I find nothing there that carries our understanding of the universe beyond where it was when I left forty years ago and I have no expectations of success down that path. I was just commenting that I had used the Hartree-Fock method in my work with Oak Ridge as a graduate student.

Originally Posted by Qfwfq

You might find out that "relativistic quantum field theory" is not an oxymoron but just the quantum way of treating "fields" as being "particles" and vice-versa and quite the idea of the "exchange forces" you believe in. Never heard of virtual particles?

I said, "in my head is rather an oxymoron" which was intended to convey the fact that it was an opinion. Personally, I think it's pretty dumb to start with "fields" and work out quantization. It's putting the horse before the cart. And what's this garbage, " Never heard of virtual particles?" what the devil do you think mediates exchange forces? And you don't need fields to have exchange forces; have you ever done any actual calculations based on Feynman diagrams? Nothing tee's me off more than people who toss around Feynman diagrams like they know what they are talking about when they couldn't do the first calculation implied by the diagram.

I knew I was asking too much when I expected a serious examination of my deduction of Dirac's equation. Your n-th warning will be sufficient. Bye!

Have fun -- Dick

PS, if anyone out there is still interested in anything I have to say, let me know, I'll still check this forum out now and then. I may even post the derivation of Maxwell's equations as the constraint on the behavior of the expectations of gamma if I see any interest.

[Qfwfq]

Well Dick, I only meant that exchange forces are somewhat the essence of the thing that you judge to be an oxymoron. You appeared to be contradicting yourself in the space of a few lines. You should try to be clear about what you say, clear enough for the common mortals.

If you know all about the method, perhaps you've seen that it successfully predicts the Coulomb potential. Yet, you plainly said you knew nothing of Fock space. I guess you consider it an oxymoron simply because you don't see the reason it's called quantum field theory.

[Southtown]

Originally Posted by EWright

Time is most certainly a measurable variable.

Oh, come on. Prove it...

Originally Posted by EWright

Newton was right... Einstein was too.

Right how?

[Doctordick]

Originally Posted by Qfwfq

If you know all about the method, perhaps you've seen that it successfully predicts the Coulomb potential. Yet, you plainly said you knew nothing of Fock space. I guess you consider it an oxymoron simply because you don't see the reason it's called quantum field theory.

No, my position is that the idea of quantum field theory is based on the quantization of field theories. This places preeminence on the field theories. I hold that quantum theory, properly developed, is the correct approach. Field theories are only approximations and thus quantization of fields is simply the wrong attack. After the universal success of quantum theory, I am astonished with the common presumption that something else is more fundamental. But that’s just an opinion.

Have fun -- Dick

[HydrogenBond]

Everyone makes time much harder than it has to be. If one looks at quanta of energy they define distinct measures of distance and time that we measure as wavelength and frequency. These two combined define the magnitude of the energy (plus Plancks constant). As such, energy is composed of distance and time potential both of which are quantatized variables. These are quanta of nature.

The bias of tradition typcially defines distance and time as only reference values that we use to compare things. But even when we compare things, it is usually requires energy, such as light for the eyes, to make these measurements. The energy is defining what we measure and the energy contains both distance and time potential. If one took away all affects of energy when making measurements of distance and time one would not be able to make any measurement.

[Doctordick]

Originally Posted by HydrogenBond

Everyone makes time much harder than it has to be. If one looks at quanta of energy they define distinct measures of distance and time that we measure as wavelength and frequency. These two combined define the magnitude of the energy (plus Plancks constant). As such, energy is composed of distance and time potential both of which are quantatized variables. These are quanta of nature.

The problem with that definition (which, by the way, is essentially the standard physics perspective) is that it fails to represent a very important aspect of what is ordinarily thought of as time! Your perspective grows directly out of the common physics concept that “clocks measure time”. Please note the title of this thread, “Is ‘time’ a measurable variable?” If you presume “time is what clocks measure” (which is exactly what you are doing when you begin to talk about “energy”, “measures of distance and time”, and/or Plank’s constant) the answer is of course “YES, what you have defined is a measurable variable” (the thing you have define is measurable!)

However, that is not the aspect of time which I had in mind when I started this thread. If you look through this thread you will find comment after comment about the “flow of time”, “the perception of time” or perhaps “the arrow of time”. The evidence of confusion is overwhelming and it is utterly ridiculous to hold that no confusion exists. I say that the confusion arises because people do not understand what they are talking about and relativity itself is the most powerful indicator of this fact.

The concept “clocks measure time” works fine so long as the clock moves with frame of reference being used to describe the universe (including the issue of simultaneity by the way). However, the issue of simultaneity does not transform from reference frame to reference frame in Einstein’s picture. This means that the concept “simultaneous” can not be used in his picture.

The problem with throwing out the concept of simultaneity is that is disallows specification of “the present” (i.e., that simultaneous boundary between the past and the future) which is, in fact, a very important aspect of the concept of “time”. It is the existence of that boundary which is being talked about when people refer to “the flow of time”. “the perception of time” or “the arrow of time”.

Einstein’s picture is a four dimensional geometry with “time” (what clocks measure) as an imaginary axis. What I have done is add a fifth dimension, to represent time, and let “tau” (what a clock measures) be a real axis (totally equivalent to x,y and z). Define mass to be momentum in the tau direction and examine the physical consequences of such a picture.

Please note that the fact that all experiments are performed with equipment constructed with mass quantized entities will project out that tau dimension. As a consequence, the information content of the two pictures is equivalent: i.e., we both end up with four independent axes.

It turns out that, in such a picture, time is not a measurable variable (and use of clocks to define time yield what is refered to as the twin paradox); however, the behavior of clocks ends up being exactly the same as what is seen in Einstein’s picture.

The issue of relativity (physical law being independent of your frame of reference, and that includes the behavior of clocks which must also behave in a manner independent of their frame of reference) leads everyone to reckon events in their own frames of reference against their personal clocks (clocks at rest in their personal frame) and call the reference time. This is exactly what leads to the confusion and their failure to see the simple all encompassing solution to the issue of relativity which I have discovered.

Have fun -- Dick