A Revolutionary Idea: Rethinking Time Measurement in Physics

[Hurkyl]

Simultaneity itself is a pre-relativistic notion of time! Simultaneity has no bearing on any physics experiment which can be performed (any experiment which can be performed can be seen as a collection of interactions between specific events). Simultaneity is no more then a convenient concept used to describe the universe in pre-relativistic terms.

And the notion is modified for the purposes of SR. It is a convenient term to denote that the coordinate time corresponding to two events is the same. Again, I'll point out that crackpots have a heck of a time grasping this point, but when discussing in the context of relativity, I can't say I've ever seen a physicist use "simultaneity" to refer to the pre-relativistic notion.

How would Hurkyl propose to set up these "synchronized" atomic clocks if his kids kept tossing them around? That is a serious question believe it or not. When we get to fundamentals, even the smallest "tossing around" is significant. Since no clock, even our "ideal" clock, is disconnected from the universe, interactions exist which "toss it around".

Theoretically, put bounds on the error. Practically, implement periodic resynchronization. (GPS, I belive, is a great example of this!)


I'm somewhat surprised you haven't brought up the "no clock theorem" since it represents a serious theoretical sticky point, instead of a mere semantic issue, but then again, discussions of its ramifications beyond "any clock will run backwards occasionally" are probably beyond most of the people here. (including myself)

They invariably fail to include the phrase "in the clocks rest frame". If they would always include that phrase, I would have no argument with their presentations at all.

Do you also insist that people say something like "Where '+' is the standard addition operator on the integers and '1' is the multiplicative identity" when people write expressions like "1+1"?

My problem is that, the moment I say, "clocks do not measure time" or "time is not a measurable variable", everybody just goes ballistic and the discussion is over.

To me (and I presume to some others), you appear to be merely arguing semantics. The short form of your point, as I currently understand it, is "Physicists don't explicitly state things like 'in the clock's rest frame', therefore they must not understand that this clause is needed," which, frankly, seems silly.

 

[Hurkyl]

How would Hurkyl propose to set up these "synchronized" atomic clocks

And as another possibility, who cares about synchronization anyways? As long as things stay somewhat nicely arranged, they'll still measure a general relativistic coordinate chart.

 

[russ_watters]

And as another possibility, who cares about synchronization anyways? As long as things stay somewhat nicely arranged, they'll still measure a general relativistic coordinate chart.

Interesting side-note: on US Navy ships, the chronographs are never reset (synchronized) unless the batteries are changed. Even then, its not that important to precisely set them. Its far better to let them run at whatever rate they run and record the variation from day to day - that way you know what the error rate is.

Whether dealing with SR or ship's chronographs, synchronization is best done on paper.

In any case, I've been lurking in this thread (Hurky is doing just fine - no need to bust his groove), and I agree with Hurkyl. DrD, you're arguing a pretty trivial (non-existent) semantic issue. And your thought experiment doesn't say anything new, surprising, or useful.

 

[DrChinese]

Clocks, all clocks, actually directly measure "proper time", not time. We can only set up our classical relativistic coordinate system by making some very involved constraints on those clocks. These constraints are designed to assure the experimenter that their readings do indeed correspond to time. That constraint is actually very simple. Since what all clocks actually measure is proper time along their path (the integral of $$\frac{-i}{c}\sqrt{dx^2 +dy^2 +dz^2- c^2 dt^2}$$ along that path) we must make sure that the terms dx, dy, and dz vanish: i.e., the clock must be absolutely at rest in our proposed coordinate system.

No matter how we try, DrD remains in his ego trip. I will give one last try to see if we can get some substance...

Why bother with your constraint - i.e. that we minimize dx/dy/dz? This is a fairly severe constraint. Nice if you can have it, but in many cases not possible. That is in fact the entire purpose of relativity, as you should know - to resolve such differences in a manner which fits with experiment.

So how is the world different when your constraint is in place, and the terms are held to a minimum? Are we able to see a unification of gravity and electrodynamics? Anything like that? I am trying to understand the benefit of adopting your premise. Assuming that we agree that what is measured by a clock is "proper time" and not time itself. Honestly, I don't really see that statement as a stretch anyway.

 

[Doctordick]

So you want something serious to think about?

Thank you Dr Chinese. I appreciate your effort.

Here’s a tip, if you're relying on math to explain your thought experiment. What you have is a piss-poorly designed thought experiment.

No, I would say rather that your comment implies that you are not comfortable with mathematics. Let me quote Feynman, "mathematics is the distilled essence of logic."

One wonders at the stupidity of starting a thread with a thrown clock, then posting that in your system all clocks have to be at rest.

Not if that issue is the central issue I want to talk about. I want to talk about something which in your head is stupid! Ok, if you don't want to talk about it, don't bother me.

To me (and I presume to some others), you appear to be merely arguing semantics. The short form of your point, as I currently understand it, is "Physicists don't explicitly state things like 'in the clock's rest frame', therefore they must not understand that this clause is needed," which, frankly, seems silly.

Forty years ago I also thought the need to point that out was silly; however, over the years I have come to realize that it is exactly the issue which has prevented the physics community from seeing what I see.

My single greatest complaint with web forums is that the members never expose their education level. That makes it very difficult to cast one's comments at a level the reader can understand. As above, Oracle has finally made it quite clear that he really isn't comfortable with analytical thought. Now you haven't made your range of comprehension clear yet but, as you are apparently the only one reading this thread who has any comprehension of the real issues of relativity, I will proceed as if you have the background to understand a difficult subject.

I hope you have your thinking cap on. Earlier, I brought up the subject of parametric representation of space time lines. Though you have not commented on that issue, your general comments imply you understand enough to follow a presentation based on such a representation. I hope that is a correct assessment.

Let us consider a relativisticly correct solution to a problem. Now this can be an experimentalist's describing the results of an actual experiment or a theorist's analytical result of a hypothetical situation. In any case, accurately expressing the solution requires specifying the coordinate system of the real or hypothetical observer (the coordinate system or frame of reference within which the results are to be expressed). Now, if a correct solution has been obtained, then that solution can be expressed as a set of space-time lines in the referenced coordinate system (a specific line for each specific significant element in the solution).

Now I need to point out that the problem referred to here can run the gamut from the trajectory of a macroscopic object through a collection of massive gravitational sources to a QED calculation of fundamental phenomena involving Feynman's inclusions of virtual particles and the consequences of their impact on results. Even if the number of elements included the solution of that problem run to numbers far beyond what we want to explicitly write down, from an analytical perspective, the solution can be expressed as a collection of space-time lines in that observer's coordinate system.

We are talking about expressing information here. The coordinate system we choose to use, in the final analysis, is nothing more or less than a reference system used to express that information. So, in deference to modern physics, let us use the space-time continuum introduced by Einstein: the coordinates will be x,y,z and t. The signature of the coordinate system will be taken to be three real coordinates and one imaginary coordinate. Depending on the problem being solved, the coordinate system can either be a standard Minkowski space or, if general relativity is involved, the Riemann generalization of that space.

If that is the case, then the solution of the problem (and it doesn't make any difference what the problem is) can be explicitly displayed by a set of parametric representations of the space-time lines of the elements significant to that solution.

$$x_1 = f_{x_1} (\alpha_1)$$, $$y_1 = f_{y_1} (\alpha_1)$$, $$z_1 = f_{z_1} (\alpha_1)$$ and $$t_1 = f_{t_1} (\alpha_1)$$ --- entity #1
$$x_2 = f_{x_2} (\alpha_2)$$, $$y_2 = f_{y_2} (\alpha_2)$$, $$z_2 = f_{z_2} (\alpha_2)$$ and $$t_2 = f_{t_2} (\alpha_2)$$ --- entity #2
$$x_3 = f_{x_3} (\alpha_3)$$, $$y_3 = f_{y_3} (\alpha_3)$$, $$z_3 = f_{z_3} (\alpha_3)$$ and $$t_3 = f_{t_3} (\alpha_3)$$ --- entity #3
…
$$x_n = f_{x_n} (\alpha_n)$$, $$y_n = f_{y_n} (\alpha_n)$$, $$z_n = f_{z_n} (\alpha_n)$$ and $$t_n = f_{t_n} (\alpha_n)$$ --- entity #n
…

Now I presume, you will concede that all relativisticly correct answers to any physics problem could be so expressed. That is, all the information contained in the solution to the problem is contained in the set of parametric expressions above which clearly express the space-time lines in the relevant "approved" coordinate system applicable to the associated problem.

{I have cut this into two parts as apparently the forum will not allow excessively long posts -- read on below}

 

[Doctordick]

Sorry about that!

I seem to be having trouble with one of my latex expressions. I keep getting a fault on the post. I will post the rest of the note as soon as I can find the problem.

Sorry about that -- Dick

 

[Doctordick]

Now, here is where we get inventive. Let us, in our heads, attach an ideal clock to each and every entity associated with the solution above. Let us not worry at all about synchronizing these clocks (I would suggest that the concept of synchronization in this situation is rather meaningless) as the only significant issue is the rate at which these clocks run in the observer's coordinate system.

Let us establish the zero on the ith clock via an arbitrary reference to a value of $$\alpha_i$$ used in the parametric expressions above. Then, the readings on all the clocks are explicitly specified. They can be explicitly expressed by the parametric expression $\tau_i\, =\, f_{\tau_i} (\alpha_i)$ where $f_{\tau_i} (\alpha_i)$ is given by the definite integral of $\{ \frac{-i}{c} \sqrt{dx_i ^2 +dy_i ^2 +dz_i ^2 -c^2 dt_i ^2} \}$ integrated from that arbitrary reference value of $\alpha_i$ established above to the specific value of $\alpha_i$ of interest.

Thus it is that we can add another specific variable to the set x, y, z, and t given above. For every specific value of $\alpha_i$, not only does our representation yield specific values for $x_i ,\, y_i ,\, z_i$ and $t_i$, it also yields (by construction) a specific value for $\tau_i$.

There is but one more step to set this thing up for analysis. In order for the entities presumed to be significant in the solution of this problem to actually be necessary to the solution, there must exist interactions between those various entities. The correct solution must include specification of the event specific to each and every significant interaction (that is in fact the fundamental difficulty in doing the integrals associated with Feynman's expansion of the virtual particle interactions in QED).

These interactions are "events": i.e., they are specified in the parametric representation above by naming the two entities of interest (entity j and entity k for example) and then specifying the value of $\alpha_j$ and $\alpha_k$ which denote the specific event of interest. It is the existence of these events which allow us to relate the reading on any given clock to the reading on any other clock in a specific way: i.e., the time of the interaction as seen from the two different entities is a significant factor.

What one must realize is that the coordinate system used to display this information is actually a rather arbitrary construct. We have, in the above description, five variables associated with every value of $\alpha_i$ . Four of these are coordinates of the observer's coordinate system and the fifth constitutes the reading on a specific ideal clock. The relationship between the change in the reading on the clock and the change in the coordinate positions in the reference frame is set by the metric of the coordinate system; that is to say, ideal clocks "always" measure "proper time". Another way to express the same thing is to understand that there is an absolute physical relationship internal to the five variables under discussion.

At this point I ask you to make a subtle shift in your perspective. What we are talking about here is any arbitrary relativisticly correct solution to some physics problem. All of the information pertinent to the solution is contained in the parametric expressions discussed and the interaction information (the significant event specification). The actual coordinate system serves no purpose beyond allowing the observer to conceptualize the meaning of the coordinate variables and visualize these parametric lines as trajectories in a space he finds familiar.

Let me instead put forth an alternate coordinate system consisting of a different collection of four variables. I will choose to display the information in a coordinate system consisting of the values of x, y, z and $\tau$. In order to maintain the absolute physical relationship internal to the five variables under discussion, it is necessary to relate changes in the fifth variable to changes in the four I have chosen as coordinates in my representation. The relationship which is to be maintained must be exactly the same relationship imbedded in the original representation: i.e., $d \tau_i = \{ \frac{-i}{c} \sqrt{dx_i ^2 + dy_i ^2 + dz_i ^2 -c^2 dt_i ^2} \}$ or, simply rearranging terms, $cdt = \sqrt{dx_i ^2 + dy_i ^2 + dz_i ^2 + c^2 d \tau_i ^2} \}$.

This suggests a very interesting geometrical relationship between the five variables. In the original geometry, $\tau$ was a measure of length along lines in the geometry (Einstein's "invariant interval", or at least a time-like representation of it). If our intention is to use a geometry, the interpretation of which will maintain that absolute physical relationship between the five variables, then it behooves us to set the relation as the metric of the geometry. I personally find it quite surprising that such a move suggests that the pertinent geometry is Euclidian.

Why is that surprising? Well, we are talking about a relativisticly correct description of an arbitrary physics problem (note that the correctness of the solution includes general relativity). To come to the conclusion that the solution to that problem is easily represented in a Euclidian geometry is counter to every presentation of relativity I have ever seen. We need to examine this geometry very carefully.

{The final part will appear presently!}

 

[Doctordick]

The final bit!

The geometry has some strange aspects. Since the purpose of the geometry is supposed to allow the observer to conceptualize the meaning of the coordinate variables and visualize the parametric lines as trajectories in a space he finds familiar, we must make sure we understand exactly what interpretation we are to put on this representation. Remember, there has been no change whatsoever in the information being represented; it is no more than a different representation of exactly the same information represented in the original solution.

A straight forward interpretation would seem to be to let x,y and z be the standard coordinate axes we are used to and let t be exactly what we ordinarily interpret as time. Up to here that would certainly be consistent with the interpretation in the original presentation. The problem with that straight forward interpretation is that it leads to some seemingly unreasonable conclusions.

First, cdt is a differential measure along the paths of our entities. This would imply that everything in the universe proceeds along its trajectory at the speed of light. This is bothersome because our mental image of the universe generally has things moving at velocities considerably less than c.

Secondly, $c\tau$ would be a real axis, as real as x, y or z and this geometry is thus a four dimensional Euclidian geometry. Again, this is bothersome because our mental image of the universe is three dimensional; how can there be a fourth axis of which we are unaware.

Once again, I assert that there can be nothing wrong with the representation, only with our interpretation as the information expressed is exactly the correct solution to the relevant problem discussed at the beginning. What must be in error is our interpretation of the representation. Let me put forth an interpretation which clarifies the problem.

Suppose the universe here represented is exactly a conventional four dimensional Euclidian universe where everything moves at exactly c. Suppose further that every entity of interest to us is momentum quantized in the $\tau$ direction. Exactly what are the consequences of such a hypothesis? The consequence is actually rather straight forward: if the momentum in the $\tau$ direction is quantized (the uncertainty in $\tau$ momentum is zero), then the uncertainty in $\tau$ must be infinite.

A little algebra concerning the momentum vector and the definition of that $\tau$ axis leads immediately to the fact that momentum in the $\tau$ direction has to be mass. It follows directly that, as all our experiments are done in laboratories constructed of mass quantized entities with tools consisting of mass quantized equipment, we cannot possibly detect motion in the $\tau$ direction. An analysis of the character of the spatial wave functions will yield the conclusion that only motion perpendicular to $\tau$ is detectable.

It is then quite clear that most things will appear to be moving at velocities less than c as only the component of their motion perpendicular to $\tau$ is detectable. This also solves another difficulty in interpretation which I have not yet mentioned. Remember that $\tau$ was the reading on that ideal clock attached to our entities.

Now I am sure you are all familiar with what is usually called the twin paradox. One twin goes off to some star and returns. When he gets back, his clock does not agree with his twin's clock. The problem here is that, if this is a conventional Euclidian coordinate system, interactions should occur whenever two entities exist at the same specific point in the coordinate system. Since one of the coordinates is the reading on the clock, when they interact, the reading should be the same. Well, quantum mechanics clears that issue off the table immediately as they both consist of mass quantized constructs and their $\tau$ position is completely unknowable.

All it takes is a little serious effort to translate any real experiment into this representation. Once the translation is correctly accomplished, the results of any experiment are exactly what is observed which is as it must be because I have laid out exactly how the two different representations are related to one another.

There is a second interesting result. The identity between inertial mass and gravitational mass has always implied gravity was a geometric effect (I hope the readers are sufficiently educated to understand that comment). From Newton's time, it was held as very probable that gravity existed because we were not using a valid "inertial" coordinate system. For many years, mathematicians searched for the geometry which would achieve that result with consistent failure (if you look into the history of Hamiltonian mechanics, you will find that its roots lie in that effort). Eventually, a man named Maurpertuis proved that no such geometry existed (but thankfully, the work on the mathematical relations went on or we wouldn't have quantum mechanics).

One of Einstein's great break-throughs was his demonstration that Maurpertuis was wrong. There did indeed exist a geometry which would make gravity a geometric effect; that geometry is central to his theory of general relativity. It is always presented as if Einstein's success was a consequence of Maupertuis' failure to consider geometries with imaginary axes. But, if you go back to Maupertuis' proof, you will discover that a key point in that proof revolves around the fact that different objects can have different velocities. Note that if everything moves at the velocity c (as they do in the representation above) then his proof does not apply.

Actually, it is not difficult at all to generate a distortion in the geometry I have presented which makes gravity a geometric effect. What is nice about my approach is that quantum mechanics applies at every stage.

Now if you can follow that then you clearly have a mind open to new ideas and, most probably an education sufficient to think it out for yourself.

Have fun -- Dick

 

[Oracleing]

No, I would say rather that your comment implies that you are not comfortable with mathematics. Let me quote Feynman, "mathematics is the distilled essence of logic."

Tell you what if you every make a claim that I do not agree with that I need mathematics to prove you incorrect eat my own keyboard.

Not if that issue is the central issue I want to talk about. I want to talk about something which in your head is stupid! Ok, if you don't want to talk about it, don't bother me.

Sorry I don’t think that’s the way forums work, but then that’s not such a surprise, I would thought someone who starts a thread called “A Thought Experiment” in a forum called Theory Development” may have actually thought about their posts.
.

My single greatest complaint with web forums is that the members never expose their education level.

You know you’ve actually helped me understand something, I’ve been to many forums where you get people promoting their own crackpot ideas, but I’ve never really understood when they start making claims about the elitist education establishment not accepting their radically new ideas…. I understand now, people like you.

That makes it very difficult to cast one's comments at a level the reader can understand. As above, Oracle has finally made it quite clear that he really isn't comfortable with analytical thought.

? You design a thought experiment…. With a claim like “What is important here is that the reading on the clock has absolutely nothing to do with the "time" used in the description of the experiment in anyone's frame of reference!”

I point out that if you use a light clock, it certainly does have some thing to do with the "time" used in the description of the experiment in anyone's frame of reference.

But I’m not comfortable with analytical thought

I will not bore you with having to read another long post with questions you fail to answer…. This bit of your multi-post says it all.

Now I am sure you are all familiar with what is usually called the twin paradox. One twin goes off to some star and returns. When he gets back, his clock does not agree with his twin's clock. The problem here is that, if this is a conventional Euclidian coordinate system, interactions should occur whenever two entities exist at the same specific point in the coordinate system. Since one of the coordinates is the reading on the clock, when they interact, the reading should be the same. Well, quantum mechanics clears that issue off the table immediately as they both consist of mass quantized constructs and their position is completely unknowable.

Are you telling me that one of the benefits of your system is, the answer to the twins paradox difference in time, is “completely unknowable”

BTW you do know the clocks should not agree, don’t you?

Oracle

 

[DrChinese]

Ok, the first pieces look pretty good. I will continue to study.

 

[Hurkyl]

So to summarize up until the "final bit", your program is to, in a particular reference frame, take the worldlines of all of the entities in interest, and then replot them by replacing the coordinate time parameter with the proper time parameter, and note that the coordinate time of the original reference frame can be recovered as Euclidean arclength in this new representation.

Right?

My single greatest complaint with web forums is that the members never expose their education level.

It's generally more trouble than it's worth. Say that you're a PhD and you get accused of being part of the brainwashed orthodoxy. Say that you're a layman, and you get summarily dismissed as being incapable of understanding anything.

 

[Rut Roh]

Quote by Doctordick: Finally, to Rut Roh, I hope you understand why I found Antonio Lao's post to be off subject.

I came to accept the fact that I am not a mind reader a long time ago. That defect means I tend to ask questions. I have my theory on why you tossed out Antonio Lao's post, I was asking yours.

Quote fro Hurkyl: Say that you're a layman, and you get summarily dismissed as being incapable of understanding anything.

I agree 100% with this. Some people leave their personal info blank and up to questioning minds. Some fill those blanks with crap to fend off pre-fabricated ideals. I prefer to look at the posts and respond or not respond on that only.

BTW DoctorDick: If you really knew who I was, you would **** your pants.

 

[Doctordick]

Hi Hurkyl,

So to summarize up until the "final bit", your program is to, in a particular reference frame, take the worldlines of all of the entities in interest, and then replot them by replacing the coordinate time parameter with the proper time parameter, and note that the coordinate time of the original reference frame can be recovered as Euclidean arclength in this new representation.

Right?

Absolutly correct!

It's generally more trouble than it's worth. Say that you're a PhD and you get accused of being part of the brainwashed orthodoxy. Say that you're a layman, and you get summarily dismissed as being incapable of understanding anything.

More trouble to who?

I have my theory on why you tossed out Antonio Lao's post, I was asking yours.

I had to go back and re-read it as I did not remember what he said. Now that I have looked at it, I feel it was emotional clap trap loaded with physics nuances. Nothing that he said had any bearing on the discussion here.

Some fill those blanks with crap to fend off pre-fabricated ideals. I prefer to look at the posts and respond or not respond on that only.

You're right, I agree with you that a lot of what is posted is out and out bull; but a decently run forum could eliminate that by sectioning it out properly. The forum owners could certainly require a decent registration. I suppose you must like being in the dark.

BTW DoctorDick: If you really knew who I was, you would **** your pants.

Well you seem to have a high opinion of your status! If I had any interest in such things, I would not have lived the life I have lived. If you have to resort to those kinds of comments, you must have an extremely poor self image.

I have a sign over my desk which says "Knowledge is Power" in large letters and below it in small letters it says "the most popular abuse of that power is to use it to hide stupidity". I have a suspicion it applies directly to you.

DrChinese; I appreciate your response immensely!

Have fun -- Dick

 

[pallidin]

Is not "time" dependent upon the physicality of it's device and it's expression within locality? Surely, time is a dualistic beast.

 

[UltraPi1]

Just thought I would repeat it.

A clock is a measure of time, but a peanut butter and jelly sandwiich can measure time also. The point here is that existence is a measure of time.

 

[Rut Roh]

Wow! OK... I'm beginning to get it...

You present your views in out of the box expanded thinking, but also are taking responses as strict literal.

At least that would account for how confusing this whole thing is.

 

[ophecleide]

My single greatest complaint with web forums is that the members never expose their education level.

I am an undergraduate student at the Colorado School of Mines and I have background in multivariable calculus (including vector calculus) and calculus-based mechanics and E&M as well as some basic chemistry. I also read a lot of articles, and do a little research on my own, so I have some background in modern physics.

There, that's one less thing to complain about.

I managed to follow most of your argument, although it took me a few minutes to figure out that you were referring to the reading on the clock as a value rather than considering the changing of the value on the clock an event in itself.

Simultaneity itself is a pre-relativistic notion of time!

If two 'events' (refered to as $$\alpha$$ in your equations) have the same value of t, doesn't that make them simultaneous?

 

[Hurkyl]

This would imply that everything in the universe proceeds along its trajectory at the speed of light.

...

It is then quite clear that most things will appear to be moving at velocities less than c as only the component of their motion perpendicular to τ is detectable.

I don't have any trouble with this; I haven't bothered to follow the details in your system, but a similar statement can be made in the ordinary Minowski geometry, and on occasion I've tried using said approach to explain SR oddities on this forum.

The consequence is actually rather straight forward: if the momentum in the τ direction is quantized (the uncertainty in τ momentum is zero), then the uncertainty in τ must be infinite.

Now this I do have trouble with. We agreed τ is what clocks measure, right? If the uncertainty in τ was infinite, would it not follow that it is impossible to read a clock?

 

[Russell E. Rierson]

That fact must be true as the functioning of the clock is determined by physical laws and those physical laws are (from the axioms of relativity itself) independent of your frame of reference! The functioning of that "ideal" clock cannot possibly be a function of your frame of reference!

Einstein was forced to throw out the cherished notion of absolute time. Different observers in relative motion, at constant velocity, percieve the sequence of events differently.

Every particle in the universe carries its own intrinsic measure of time, called the proper time, if my interpretation is correct.

An interval between two events is called timelike, lightlike, or spacelike depending on whether the Lorentz interval

[Dt]^2 - [Dx]^2 = [Dt']^2 - [Dx']^2

is positive, zero, or negative.

The proper time along a curved world line from event A to event B is smaller than the proper time along the straight "t" axis from A to B in a spacetime diagram with Lorentz geometry. Hence, the stay at home twin is the one that is the biologically older person when the traveling twin returns.

 

[UltraPi1]

Every particle in the universe carries its own intrinsic measure of time, called the proper time, if my interpretation is correct.

More like - Every fundamental entity carries with it a measure of time, and each measure can be different. All fundamental entities move at a constant {{{ C }}} giving rise to their various measurements. Thus - It would not be time that changes, but it's measurement. Movement of a particle changes that measurement.

 

[Rut Roh]

ROFLMAO @ Luis Hamburgh...

confutatis gets extra stars for creativity!

 

[Doctordick]

I am an undergraduate student at the Colorado School of Mines and I have background in multivariable calculus (including vector calculus) and calculus-based mechanics and E&M as well as some basic chemistry. I also read a lot of articles, and do a little research on my own, so I have some background in modern physics.

I appreciate that; thank you very much.

If two 'events' (refered to as in your equations) have the same value of t, doesn't that make them simultaneous?

Watch out; generalizations are very dangerous. Whenever you define a concept, you must be very careful that you thoroughly understand all the ramifications of that concept. If you don't, you can easily be lead astray and may come to erroneous conclusions.

In this procedure, I started with a standard Einsteinian coordinate system set up by some observer. That coordinate system included a coordinate called t. From the perspective of that observer, all points with identical t are "simultaneous". However, anyone familiar with relativity knows that there exists an infinite set of coordinate systems (set up by different observers) describing exactly the same circumstance, all of which would have very different collections of "simultaneous" events. However, all of these observers would none the less agree about the simultaneity of certain specific events! For example, the decay of a free neutron and the production of the decay products would occur at the same time in everyone's coordinate system.

Essentially what we are talking about there is a single event involving several different space-time lines. The same thing occurs in my coordinate system and, if we wish, we can set those conceptual "ideal" clocks to have exactly the same readings when that event occurs; however, if we try to do that throughout the coordinate system, we will invariably fail as t is path length in this geometry and the readings on the various clocks will depend on the path length and it is quite easy to find different paths leading to the same point.

Notice that each parametric representation of a line has its own parameter, $\alpha_i$ and one might be very tempted to use the clock reading as that parameter but it won't work. Since dt is path length in this geometry, the specific value of t is defined by a definite integral and requires specification of the start point for the integral. We could, by proper selection of start points on each separate line, reproduce exactly the time in the original representation but the process would be extremely cumbersome and not very useful.

There is another definition of simultaneity which one might find more useful to an observer. As all information of concern to the observer eventually arrives at the observer, one could use the event marking that arrival as the definition of simultaneity. In many ways, that is a better definition of simultaneity than the standard physics definition. It certainly makes it clear that different observers will disagree as to what is simultaneous and yet fits very well with our anthropomorphic senses.

There are some mental tricks which can be used to quickly deduce results of various circumstances but, at the moment, until you get a clear understanding of the representation, I don't think I should go into those.

Now this I do have trouble with. We agreed $\tau$ is what clocks measure, right? If the uncertainty in $\tau$ was infinite, would it not follow that it is impossible to read a clock?

You are also being led astray through generalization. You must look carefully at exactly how a clock functions in this geometry. It will take me a little while but I will produce a clock design in this picture for you to examine.

If anyone could give me a little guidance on inserting diagrams (standard GIF files) on this forum, I could post the design here.

On the other hand, this thread seems to be drawing trolls!

Have fun -- Dick

 

[Oracleing]

In this procedure, I started with a standard Einsteinian coordinate system set up by some observer. That coordinate system included a coordinate called t. From the perspective of that observer, all points with identical t are "simultaneous". However, anyone familiar with relativity knows that there exists an infinite set of coordinate systems (set up by different observers) describing exactly the same circumstance, all of which would have very different collections of "simultaneous" events. However, all of these observers would none the less agree about the simultaneity of certain specific events! For example, the decay of a free neutron and the production of the decay products would occur at the same time in everyone's coordinate system.

?

Do you really think that two observers, one in say a heavily gravitational time dilated state, and one who’s not, would see your decay of a free neutron and the production of the decay products happening at the same time.

You may like to do some research on particle decay in accelerators.

On the other hand, this thread seems to be drawing trolls!

??

Oracle

 

[Russell E. Rierson]

On the other hand, this thread seems to be drawing trolls!

Watch out! vague generalizations can be very dangerous.

Who is the troll ...specifically?

 

[Peter Pan]

sorry all! needed to post to subcribe to this thread. i am enjoying this debate a lot.

 

[Russell E. Rierson]

Could "Scooby Doo"syllablism correspond to "troll" phenomena?

A mathematical description of time probably has no physical interpretation, unless, as Dr. Dick explains, a lucid definition/understanding of time, can be agreed upon.

So if Einstein says that "the train arrives here at ten o'clock" he means that the pointing of the small hand of his clock to the ten and the arrival of the train are "simultaneous events"... where the clock and the event, are in close proximity.

This definition of time appears to be OK when defining time for the place where the clock is located, but it is insufficient for defining time for a series of events at different locations, i.e. to evaluate times of events occurring at locations remote from the clock.

If for a location A of space, there is a clock, with an observer, and the observer at A can determine the time values of events in the immediate proximity of A by observing the positions of the hands of the clock which are simultaneous with the events at location A.

If at another location in space, point B, with an identical clock, the observer at B can determine the time values in the immediate proximity of B. But the time of an event at A cannot compare to the time of an event at B since a common time for both A and B is yet to be defined.

According to Einstein, the time it takes a ray of light to travel from A to B equals the time it takes the ray to travel from B to A. Let the ray of light start at the A time "TA" from A to B, it arrives at the B time "TB" and is reflected back in the direction of A, where it arrives at the A time "T'A".



TB - TA = T'A - T'B

A "synchronous" definition of time is arrived at?

2AB/[T'A - TA] = c, the speed of light in vacuum.



Distance is a property between objects in space. Duration is a distance between events in time. Spacetime is a relational structure; The structure
of space is possibly a distributive lattice. A lattice is a
partially ordered set, closed under least upper and greatest lower
bounds.

Any lattice which is isomorphic to a collection of sets, closed
under complementation and intersection, is a Boolean
algebra.

Is it possible to derive Einstein's field equations
strictly in terms of quantum mechanical operators? using n-dimensional
cross sections of cotangent vectors?


What is needed is a tensor equation which is parallel
to "wave" equations described in terms of a covariant
d'Alembertian operator. An alternative description for the general
relativistic space-time, that allows for "compressional" waves,
rather than allowing only "transverse" waves.

 

[Doctordick]

An Ideal Clock in the Eucledian perspective.

I appologize to all as I apparently cannot post the gif diagrams essential to the clock design. Hurkyl's concern was answered by private mail. If anyone else is seriously interested, you know how to reach me.

Sorry about that -- Dick

 

[Hurkyl]

You should be able to attach a .gif to any post; but it may have to wait and be approved by Greg first.

 

[Doctordick]

Ideal Eucldian Clock -- Part I

You should be able to attach a .gif to any post; but it may have to wait and be approved by Greg first.

So here it is. I'll delete it if the gif files don't show up in a few days.

[size="+2"]Analysis of an Ideal Clock
[/size] by Richard D. Stafford, Ph.D.​

In the following, I will totally neglect microscopic phenomena except to assume that microscopic interactions exist and that these interactions, whatever they are, are capable of generating and maintaining the existence of objects whose structures are macroscopically stable over distances and times of interest. I will use the term "event" to refer to a general point on the line segment specifying the path of a microscopic entity being described in my geometry.

My clock will consist of two components: a mirror assembly and an oscillator. Both can be seen as macroscopic assemblies of events. The oscillator will have zero rest mass; therefore, every event which is part of the oscillator will be in a zero eigenstate¹ of momentum in the $\tau$ direction (the oscillator can be seen as a macroscopic collection of photons). The mirror assembly will be massive: i.e., every event making up the mirror will be in a non zero eigenstate of rest mass; thus it also follows that every event making up the mirror assembly must be in a non zero eigenstate of momentum in the $\tau$ direction.

Since every event involved in this discussion is momentum quantized in the $\tau$ direction, the microscopic structure must be periodic in the $\tau$ direction. This clearly requires that the macroscopic cross section of both structures perpendicular to $\tau$ must be uniform and their extension in the $\tau$ direction must be infinite. This being the case, a description of their three dimensional cross-section completely describes their macroscopic shape. Our "clock" will be defined to be the entity pictured below.

http://home.jam.rr.com/dicksfiles/clock.gif
​

This clock is further defined by the following constraints: all events making up the mirror assembly have |$k_{\tau}$| large and $k_x$, $k_y$, $k_z$ negligible on a macroscopic scale. On the other hand, events making up the oscillator will have $k_{\tau}\equiv0$, non-negligible $k_y$ and negligible $k_x$, $k_z$. Furthermore, $k_y$ of the oscillator will be negligible with respect to $k_y$ of the mirror. We are free to make these assertions as we are defining an entity and, in the absence of contradiction, anything is certainly possible.

First, the consequences of quantum mechanics must be included from the ground up. The fundamental interaction equation is a many body wave equation. Since we are neglecting microscopic phenomena except for the assumption that they maintain the macroscopic structure, at a macroscopic level we can look at the ray optics limit of the microscopic solutions². Now consider the relationship between momentum and velocity; in the ray optic limit, their directions are the same³. It follows that, in macroscopic terms, although every event has exactly the same speed through the geometry⁴, the mirror is moving parallel to the $\tau$ axis while the oscillator is moving parallel to the y axis. Since our assembly is infinite and uniform in the $\tau$ direction, motion in the $\tau$ direction yields no changes in the structure of our clock. If we now postulate that microscopic interactions between the mirror and oscillator are capable of reversing the sign of the oscillator's momentum upon contact with the mirror, the oscillator will bounce back and forth between the legs of the mirror assembly. Our clock will clearly have a period of $\frac{2L_0}{c}$.

Since every event in the system described has non-negligible momentum only in the ($y,\tau$) plane, we can display all dynamic phenomena while considering only that plane. Thus, let us examine our clock as it appears in that ($y,\tau$) plane, paying particular attention to the associated velocity vectors. Notice that although no constraint has been imposed on the sign of the momentum of events making up the mirror, each event making up the mirror must have momentum either in the plus or minus $\tau$ direction. As the sum of all events must maintain a coherent whole (by definition, our object is coherent over the time and space considered) we need only focus on the collection of events having the same sign. For the sake of graphic representation, I choose that sign to be positive.

In any case where the interactions necessary to maintain the existence of my entity are negligible⁵, we can conclude that the velocity of the mirror (or those components we have focused on) is exactly c in the positive $\tau$ direction⁶.

Following is a $\tau,\,y$ cut of our clock at the midpoint of the oscillator perpendicular to the x,z plane:

http://home.jam.rr.com/dicksfiles/restcloc.gif
​

Note that T, the period of our clock, is identical to 1/c times the distance the mirror moves in the $\tau$ direction during one clock cycle. Although actual position in the $\tau$ direction is meaningless, (as the entire object is infinite and uniform in that direction), our clock is actually measuring displacement of the mirror over time in that direction: i.e., we can infer that the mirror has moved a distance 2L₀ in the $\tau$ direction during one complete cycle.

Our mechanism is certainly analogous to a clock since it will keep time if we can count the number of times the oscillator bounces back and forth. Furthermore, the image is clearly that of a massless object (a coherent pulse of photons?) bouncing back and forth between two reflective surfaces of a massive mirror, the common construction of an accurate clock under the conventional physics viewpoint.

{Part II will follow below!}

 

[Hurkyl]

There should be a "manage attachments" button when you post a new reply; that will attach them if you don't want to link them.

 

[Doctordick]

Ideal Eucldian Clock --- Part II

Now let us consider an identical moving clock. In this case, $k_y$ of the mirror is no longer negligible.

http://home.jam.rr.com/dicksfiles/movecloc.gif
​

Since all objects are uniform and infinite in the $\tau$ direction, we may suppress drawing the objects themselves. Instead, we may deal entirely with the displacement vectors ($\vec{V}c$). It should be clear that these vectors contain all relevant information needed to predict the time evolution of our device. It is only necessary to remember that anytime the displacement vectors lead to identical (x,y,z) coordinates, microscopic interactions can occur between our macroscopic objects (because all macroscopic objects are infinite and uniform in the $\tau$ direction). Please note that, in this particular case, x and z of every point in the picture is always identical so we need only concern our selves with the y coordinate of the displacement vectors.

http://home.jam.rr.com/dicksfiles/clocvect.gif
​

Note that the length of the moving clock is shown to be L'. This has been done because we know that the geometry must yield (by construction) a result totally consistent with the Lorenz contracted macroscopic solution if interactions with the rest of the universe may be neglected: i.e., when we solve the microscopic problem in the moving clocks system we want the length of the clock (when transformed into the original rest system) to be L₀. Only in the case where we can set the length (as seen from the rest system) to be L' can we call the clocks identical. This will require $L'=L_0\sqrt{1-\beta^2}$, where $\beta$ is defined to be the sine of the angle between the $\tau$ axis and the path of the clock⁷ Since all velocities are c, it follows directly that d₁ + d₂ = S.

Notice that the following geometric figure is embedded in the previous diagram.

http://home.jam.rr.com/dicksfiles/showdiog.gif
​

Once again we discover that one clock cycle measures exactly the length of time it takes the mirror to move the distance 2L₀ in the $\tau$ direction. Although our clock was designed to measure time, it appears that what is actually being measured is inferred displacement in the $\tau$ direction.

At this point it seems quite rational to point out that no one in the history of the world has ever been able to create a real manufactured device which will actually measure time. It can not be done because, although it is an absolute law that interactions can only occur between objects which exist at the same time, time can not be specifed absolutely as it is a relavistic thing which depends on your coordinate system). All so called clocks actually measure what a modern physicist calls proper time. He is able to define time only in his own rest frame. In that case dx = dy = dz = 0 and he can call what the clock measures "time" as, in that case and that case only, the two parameters ($\tau$ and t) are universally proportional. It should be noted that all clocks measure "proper time" exactly, even when in an arbitrarily accelerated frame! I have always found it rather strange that this fact was never pointed out to me during my graduate studies. It seems to me to be a very powerful statement.

End Notes
[size="-1"]

1. David Park, Introduction to the Quantum Theory, McGraw-Hill, Inc., NY, 1964, p.67.
2. Herbert Goldstein, Ph.D., Classical Mechanics, Addison-Wesley Publishing Co. Inc., Reading, Mass., 1959, p. 312.
3. Messiah, Quantum Mechanics, John Wiley and Sons, Inc., New York, 1966, p. 55.
4. I will use c to represent this velocity though I can show that there is a serious assumption in its actual value which we might discuss later.
5. The interactions are negligible if I can consider any subset of events making up the mirror as objects: i.e., the subsets form an analyzable universe unto themselves.
6. It can be shown that inclusion of these interactions will give rise to effects commonly attributed to general relativity.
7. This forces the apparent velocity of the clock to be beta times c.
[/size]

Have fun -- Dick

 

[Doctordick]

There should be a "manage attachments" button when you post a new reply; that will attach them if you don't want to link them.

Yes, I see it now. It didn't occur to me that the part II should be thought of as an attachment. Live and learn.

Thanks -- Dick

 

[Doctordick]

Though very few seem to be much interested in criticizing my alternate coordinate system for examining relativistic phenomena, for those who do have some interest in the perspective, I have managed to get you access to those gif files associated with the "Ideal Clock" design (evidently direct image posting is off limits). They appear as URLs which, if you click on them, will open a window containing the graphic.

There have been a lot of comments on this forum about speeds in excess of the speed of light. With regard to that, my representation makes the issue quite clear. As time is not a coordinate axis but rather a path length measurement, measuring it is a completely local phenomena and (as a specific numerical measurement) is only meaningful to the observer himself. On the other hand, the fact that things must exist at the "same time" in order to interact is still an absolute universal rule.

What the above means is that time has once again achieved the role it played in Newtonian mechanics: it is fundamentally a parameter specified by the observer to denote the distribution of events which he regards as simultaneous. Please note that all scientists familiar with relativity have made much of the fact that this can always be done without violating causality: i.e., simultaneity is in the eye of the beholder.

Since time is now merely a parameter of motion, if one wants to look at a set of interacting events over time (in their personal reference frame), they can construct exactly the same kind of diagram common to freshman physics analysis of motion: i.e., introduce time as a dimension on graphic representation of the motion.

My exposition on an ideal clock above is a good practice example to see what I am talking about. The most serious difficulty is that one cannot exclude the $\tau$ axis as its existence always has profound consequences. This means that the simplest diagram one can create has three dimensions, x, $\tau$ and t. What is important here is that, since time is a measure of path length, moving rapidly perpendicular to $\tau$ makes your x motion a significant component of your change in time: i.e., the faster you go, the more quickly you go into the future (as compared to the reading on your own clock).

As an aside, the twin paradox is still resolved by the inclusion of acceleration (which would fall into the category of general relativity) which I won't go into at the moment. If anyone has any questions about it, I will go into the representation of general relativistic phenomena from this perspective; however, you should make an attempt to understand special relativistic phenomena from this perspective first.

The great power of my perspective is that it reinstates the concept of "simultaneous" collapse of the wave function in quantum mechanics, another phenomena which is in the eye of the beholder. The collapse of the wave function occurs when the observer knows what the outcome of the situation is. Just as time is a local construct conceived of by the observer, the wave function describing a phenomena is also a local construct devised by the observer.

That is exactly why a covariant representation of quantum mechanics is so involved; the wave function describing the expectations of the observer is no more universal than is the specification of simultaneity as seen by the observer. Easy conversion is only possible when d$\tau$ and dt are linearly related to one another (special relativity). What my geometry does is to make representation of relativisticly correct set of distributed interactions easy to display from the observers perspective (well, at least somewhat easy).

Have fun -- Dick

 

[Antonio Lao]

Doctordick:On the other hand, the fact that things must exist at the "same time" in order to interact is still an absolute universal rule.

Only interaction by direct physical contact requires "same time." Interaction by quanta of force field is limited by light speed.

 

[Doctordick]

Relativistic Quantum Mechanics!

Hi Russell,

I have just finished learning latex code and was going through my old posts correcting what I put down to my intentions and decided I should respond to your post.

According to Einstein, the time it takes a ray of light to travel from A to B equals the time it takes the ray to travel from B to A. Let the ray of light start at the A time "TA" from A to B, it arrives at the B time "TB" and is reflected back in the direction of A, where it arrives at the A time "T'A".

TB - TA = T'A - T'B

A "synchronous" definition of time is arrived at?

2AB/[T'A - TA] = c, the speed of light in vacuum.

There is nothing wrong with such an approach at all except that it presumes there exists no special coordinate system. This perspective is rather all pervading even though, in the final analysis it is a mentally compartmentalized position. Certainly the distant stars provide a reference for a "center of momentum" coordinate system as special. It is clear that it would be quite reasonable to do calculations in a frame not rotating with respect with those distant stars (particularly if your interest was the orbits of the planets of the solar system). Now if they were to do so, it is clear that they would not find the speed of light on the Earth to the west to be the same as the speed of light to the east as they would be moving in their chosen reference frame.

Not a serious issue, except when one is trying to get down to fundamentals. If one wants to be absolutely correct, these kinds of issues must be thought about.

Is it possible to derive Einstein's field equations
strictly in terms of quantum mechanical operators?

It certainly is as I have done it (in essense anyway as my coordinate system is quite different from his). I need to make a slight intellectual correction to that statement: except for the fact that my results and Einstein's are slightly different. Who has made the error is still an open question as the required experiment to tell the difference is beyond current technology.

using n-dimensional
cross sections of cotangent vectors?

No, that is not the way I did it.

What is needed is a tensor equation which is parallel
to "wave" equations described in terms of a covariant d'Alembertian operator. An alternative description for the general relativistic space-time, that allows for "compressional" waves, rather than allowing only "transverse" waves.

Is that an opinion or a fact? If it is a fact, then I would like to see your derivation of general relativistic quantum mechanics. If it is not a fact, then it is only an opinion.

If you wish, I will give you my derivation of general relativistic quantum mechanics. But, before I do so, I need to know your education as without that knowledge I would have to start with freshman physics.

Have fun -- Dick