Is 'time' a measurable variable?

[ldsoftwaresteve]

DoctorDick:

It does, but I really can't communicate with you without knowing exactly where you fail to understand my math. I don't think there is any real difficulty there as none of the mathematics I use is really very far beyond what is taught in ordinary calculus and algebra. I just need to know where the problems are coming in. Mathematics is nothing more than logic.

Thanks. It's my education level and my level of understanding of mathematics. But what little I do know one thing I did like is how you use mathematics. Knowing some of it and understanding it are different. You understand the language. But it's starting to dawn on me what you are talking about and that's exciting. I've seen lots of people pretend to understand but when they show they are unable to use something...well, lol, that's the end of that. The framed paper on the wall behind them only means they've been exposed to a fraction of what's there. They wave that around, bludgeon people with it, get what they want and move on...and miss the point of the whole friggin thing.

I'm embarassed to admit to what I'm confused about. A puzzle in one of Ray Smullyan's books about the person looking at a picture ("brothers and sisters have I none....") is a beautiful illustration of my confusion. It's the referents. If I can't get those straight, I'm screwed. It took me over a day to figure it out (Smullyan's) which is a testament to the ability(or lack thereof) to grapple the referents. I suspect that's always the key to removing confusion and accessing the information below the conscious level.

You referred to us as a tribe of indians incapable of comprehending math :hyper: and you were right, well at least I'm one of those indians.

We're back to the original thread again.

Just out of curiosity, exactly what do you think my "premises" are (that is, beyond the premise that mathematics is a trustworthy mechanism of communication and that "an explanation" is the single most fundamental concept behind understanding anything)?

Your referents again. These are your basic definitions, the elements you're working with and the bricks in your structure. I guess it's how you treat them, use them, and build on them too. You'll say that's the mathematics, but from my point of view that's where most here are getting lost (which proves that there aren't many here that are that much better than me..)

 

1. A is a set. "What is to be explained."

2. B(tk) is a finite unordered collection of elements of A. "A hypothetical collection of information obtained from A."

3. C is a finite collection of sets B(tk). "What is known about A: i.e., our given known information."

 

But then you throw in the constraint "the only thing we know is that we know nothing at all" and I have to say it confused me a lot. By casting doubt on C, don't you cast doubt on B and A? Help me out here.

 

"Note that in mathematics, a set can be thought of as any collection of distinct things considered as a whole and thus can be anything. Furthermore, I have used tk as a stand in for a sort of pseudo time. The sole purpose of tk is to denote the order with which the information obtained from A was obtained and should not be thought of as implying any other common aspect of what is thought of as time. Lastly, if any information is conveyed by order in the elements of A that information will be in C via different B's. This allows B to be defined as an unordered collection of elements of A. "

I like the way you're working with events here. You concern yourself with the 'order' of those events. In an earlier post you spoke of how Newton referenced time as sort of an evolutionary thing, i.e. the order, correct? Causal connections would be included here by virtue of their sequential nature?

"The second fundamental component is the representation of an arbitrary method of obtaining expectations: i.e., the representation of the "explanation" itself. I will define the expectations to be the probability that a particular B(tk) will become a member of C: written as P(B(tk)). It should be clear that, in order to analyze an actual explanation, we need a way of referring to the specific elements of A which define B(tk). That would be so that we may know and discuss what we are dealing with."

My son pointed out to me that you are using accepted probability formulas. Very nice idea. Probably S.O.P. for educated folks but for me, well, let's just say it's new.

When I have the referents nailed down, I'll dig further. By the way, I reserve the right to wander aimlously down any and all blind alleys. (those are my 'happy place' :lol: )

Thanks for not giving up just yet.

[Little Bang]

Dick, I tend to agree with a great deal of what you imply. I'll sum it up by saying that time is simply an address lable we place on an event to know when it happened with respect to our frame of reference.

[Doctordick]

I'm sorry Will. Sometimes it is very frustrating to be misunderstood. I do get the distinct feeling that you are seriously trying to understand me. I will see if I can answer your questions in a way which makes sense to you. But first, let me make a couple complaints on your reaction to some of my comments.

Thats because it isn't the field of science, but maybe more correctly the philosophy of science.

The assumption that measured distances in one direction are identical to measured distances in an orthogonal direction is a very real constraint on what models you might create to explain your experiments and a constraint which should not be stepped into lightly. To conform to our experiments, what is required is that the structure of two measuring devices lying perpendicular to one another must be such that the physics of the universe in one direction must be the same as the physics of the universe rotated into the other direction. The measuring devices themselves must be a solution to the proposed laws of physics. This is a real experimental issue and not merely a philosophical one as it has great influence on the possible models to be considered.

There is no way to prove whether or not reality is "real." (Consider Des Cartes idea that a vengeful demon could be messing with all our senses, or the more modern idea of a brain in a jar being manipulated).

This issue can not even be discussed unless you first define "real". Without a definition, I sincerely do not know what you are talking about.

Which is why I asked for clarification.

Essentially, what I said was that you don't understand my model well enough for me to clarify the issue. It is not at all a trivial issue and can not be clarified via a simple waving of hands. The clarification comes directly from a careful examination of the solutions to my fundamental equation.

 

The Lorentz transformations do not stem from the assumption that a unique coordinate system can be set up! Rather, it allows us to take into account the same situation from several different observers.

Only if those two observers set up their personal coordinate systems as instructed by Einstein. In that case, the proper conversion from one observer to another is given by the Lorentz transformations. Exactly the same thing is true in my presentation. The observers can indeed set up their coordinate systems as instructed by Einstein and then use the Lorentz transformations to compare their experimental results. However, in my model, I do not instruct them to do so. In my model I allow them to use any clock they wish (moving in any way they want) and state that, so long as they make their calculations according to the proper laws of physics, they will all get the same results (that would be the actual results observed in the experiments, not necessarily their mathematical representation of those results).

 

That is not at all in contradiction to Einstein's concept of relativity. Anyone familiar with physics certainly knows that they need not be in the coordinate system at rest with respect to the phenomena being examined in the experiment in order to calculate the mathematical results of that experiment as seen from a rest frame supposedly at rest with respect to the experiment. That fact is the very essence of the concept of relativity. As far as the laws of physics are concerned, the frame of reference being used is immaterial to calculation. Use a frame, and the results of your calculation, if correct, will be displayed in that frame.

If space is curved, which you imply with your statement that it isn't absolutely flat, then you need SEVERAL sets of coordinates to cover space, and therefore it is essential to have some idea of a coordinate transformation.

Again I will say, you can use any coordinate system you wish, rectilinear, curved, logarithmic or whatever. If your "Laws of physics" are properly laid out in that coordinate system, your calculated results will be correct. It's a tautological statement concerning the requirements of a valid expression of the laws, not a conclusion. Depending on a particular problem, the representation can be simple in one representation and complex in another. That is an entirely different issue.

I feel as if this is another dodge. Here is a specific question: what does your theory predict for the energy density of the vacuum? How do you avoid the divergences that come about in QFT?

It is not a dodge; it is only by examining the solutions to my equation that one can discover the consequences of these subtle factors. The energy density of a vacuum is a concept which is only valid in approximation as a perfect vacuum cannot exist in my model. Also, field theories are a conceptual construct which have some very clear difficulties and are only useful as an approximate solution to any given problem. Both Newton and Einstein expressed opinions that field theories could not be the final statement so I am not in bad company by rejecting them as an ideal representation.

I've put in a fair amount of time to try and understand your relativity model and your universal explanation model.

Perhaps one problem might be that you appear to think these are two different models. They are not, the presentations constitute different aspects of the same model.

When I ran into problems I asked questions as clearly as I could for which I seldom received direct answers, and often received comments that could easily be perceived as insults.

The answers to many of your questions lie in understanding the solutions to my equation. Though the equation seems quite trivial, finding solutions is a hairy problem which I hate to approach before obtaining recognition that the equation itself is a necessary constraint on any explanation. Finally, I had no intention of insulting anyone; the problem is that I sometimes reach the end of my patience without communicating what I am trying to say. I am getting better as I discover the reasons people do not understand what I am saying. I thank you for having to patience to indulge my difficulties.

Gosh Doc, where do you get things like that? Are you able to support such claims?

Straight out of academic physics. What everyone seems to overlook is that I am talking about problems with the ideal concepts, not problems with the simple common everyday implementation. Just as Newton's coordinate system (Euclidean geometry) was brought into question by the fine detail of setting moving clocks to agree, I bring Einstein's coordinate system (the space-time continuum) into question through the fine detail of Einstein's assumptions. As I said above, "The assumption that both can be standards of time assumes the clocks do not accelerate with regard to one another (i.e., space is absolutely flat) which is violated by the very existence of the clocks." You should recognize that as a fact as all clock require some sort of mechanism to function and that mechanism must include state changes which require the existence of massive entities. The existence of those entities imply the space-time in which they exist is not flat. Not in the ideal sense at least. We have a problem with the ideal, not with common implementations.

1. A is a set. "What is to be explained."

2. B(tk) is a finite unordered collection of elements of A. "A hypothetical collection of information obtained from A."

3. C is a finite collection of sets B(tk). "What is known about A: i.e., our given known information."

 

But then you throw in the constraint "the only thing we know is that we know nothing at all" and I have to say it confused me a lot. By casting doubt on C, don't you cast doubt on B and A? Help me out here.

You are right, the referents are the problem here. English is a difficult language to communicate with (as are all human languages except for mathematics) as the definitions are vague and inconsistent. I am clearly being vague and/or inconsistent through my use of the term "known". I am indeed using it with two very different referents. In the case of, "the only thing we know is that we know nothing at all", I am including the concept of understanding what it is we know. When I use it in the definition of C I am using it with the definition "knowledge is justified true belief". (Someone put that forward and I think I can seriously live with that definition.) However, even using that definition, there exist some issues which I think are seldom approached. There are some aspects of knowing so defined which need to be cleaned up. First, one can certainly attach a name to a specific "justified true belief". Does that imply it is not a "justified true belief" before the name was attached? In the same vein, it is possible that a "justified true belief" can be understood. Does that imply it is not a "justified true belief" before it has been understood? That is exactly why I consider C to be an unknown to be represented by a symbol without any explicit definition.

Causal connections would be included here by virtue of their sequential nature?

Well certainly causal connections can not be presumed if the causes and consequences are out of order so order is essential to such a concept. Secondly, causal connections are the very essence of explanation itself. Can an explanation exist without any causal connections?

When I have the referents nailed down, I'll dig further. By the way, I reserve the right to wander aimlessly down any and all blind alleys. (those are my 'happy place' :eek: )

Thanks for not giving up just yet.

Wander where you will. I am always interested in the strange places the mind can go when given free rein. You can ask my wife about that one; she finds it quite entertaining sometimes. :D

Dick, I tend to agree with a great deal of what you imply. I'll sum it up by saying that time is simply an address label we place on an event to know when it happened with respect to our frame of reference.

Very close to my intention. Glad to have your reading this.

 

Have fun -- Dick

[Qfwfq]

Straight out of academic physics.

Good grief, I ask you to support your Strange Claims and you dodge, dodge, dodge...

 

What everyone seems to overlook is that I am talking about problems with the ideal concepts, not problems with the simple common everyday implementation.

I was talking about your statements, which were about what you seem to call "academic physics" and simply don't hold up, and I know will be futile to challenge. At least you attempt to support one of them:

As I said above, "The assumption that both can be standards of time assumes the clocks do not accelerate with regard to one another (i.e., space is absolutely flat) which is violated by the very existence of the clocks." You should recognize that as a fact as all clock require some sort of mechanism to function and that mechanism must include state changes which require the existence of massive entities. The existence of those entities imply the space-time in which they exist is not flat. Not in the ideal sense at least. We have a problem with the ideal, not with common implementations.

I imagined it would be something like that but, sheeeesh, are you absolutely serious?

 

Man I've heard many a critique of things, such as the equivalence principle being inaccurate because gravity isn't a quite uniform field, but this one is far more amusing! If you are talking about problems with the ideal concepts, not problems with the simple common everyday implementation, then you should at least get them straight.

 

I'd be curious to know where you get: "The existence of the Lorentz transformation comes directly from the assumption that a unique coordinate system can be set up" from too.

[Doctordick]

"Sorry, this post has lost some url references to my web site which no longer exists!" Life is tough all over.

 

I imagined it would be something like that but, sheeeesh, are you absolutely serious?

Now "sheeeesh" is certainly a cogent and rational argument for not examining my work and it eventually seems to be resorted to by all members of the academic faith. :lol: :lol:

 

Yes, I certainly am serious and ridicule is not a rational argument against a new and original idea. You, above anyone else here, ought to be aware of the fact that seemingly trivial fundamental problems in "ideal" representations can lead to deep and profound consequences. For example, Newton's failure to consider the problem of setting clocks to agree given a finite speed of light caused him to overlook the finer points of relativity. Had he looked at the issue carefully, I am quite sure he would have realized that the idea of reality being a three dimensional Euclidean universe had to be erroneous. :naughty:

 

It was the simple failure to examine the "trivial fundamental problem in an ideal representation" which allowed the error to exist until the success of Maxwell's equations pointed out a major inconsistency in the view in a way so obvious it could no longer be overlooked. The assumption that two clock moving with respect to each other can be set to agree seems, even today, to be a rather obvious fact to anyone who has not studied modern relativity. That is exactly why we have such a problem convincing the average layman that his Newtonian view is wrong. :D

 

I find the fact that you cannot comprehend the failure of an ideal reference frame can have serious consequences to be a serious error in your outlook. ;)

 

Idsoftwaresteve,

 

I appreciate your interest and outlook immensely as it provides me with practice at being clearer; practice I certainly need. No one seems to understand what I am doing in my paper, A Universal Analytical Model of Explanation Itself and maybe I can provide an acceptable hand waving argument which will at least allow you to understand what it is all about. :shrug:

 

My paper can be seen as a exposition on the following steps:

 

The first step is to change the representation of "an explanation" into a numerical representation. Now anyone familiar with computers should be completely aware of the fact that any information can be represented through a numerical representation. So representing the information we have to work with as a set of numbers should be seen as an obvious step which makes no assumptions whatsoever about the explanation. The only serious issue to keep in mind here is that absolutely all the information available is to be in that numerical representation: i.e., there is no way to obtain the information except by deciphering the numerical representation.

 

The next step I take is to transform the numerical representation into points on the x axis. This step however introduces a difficult fundamental problem as information can be lost if multiple occurrences of a given number exist in the elements of B(t). That is the reason I introduce the tau axis. Without the tau axis, there is no way of using points to represent all possibilities. I think if you carefully read the presentation up to the differentials:

 

you should find most of what I say pretty rational. The differentials are common functional relationships deduced in everyday physics via symmetry considerations so you really need not worry about them (though my approach to those symmetry issues is a bit askew of the norm). They are a direct consequence of what is called "shift symmetry": the fact that the selected origin cannot have any effect on the complete solution.

 

It is the Dirac delta function relationship

 

which is the new thing I introduce which cannot be found in any text of physics. The Dirac delta function can be seen as a function which is zero everywhere except when the argument vanishes (goes to zero) where it spikes to infinity. Though it is an infinitely high with a width of zero, it is defined to have an area under the curve of one. You might take a look at a somewhat straight forward development of the function.

 

Quoting directly from my paper,

It follows that, if the two arguments of any term of the sum

 

are identical, the sum is explicitly infinite. Thus it is that the only case which satisfies the constraint F=0 occurs when no point in the plane appears twice. This proves a D exists for any possible collection of elements in B.

What I proved was that, no matter what points existed in the element of C represented by B(t), there existed a second set of points D which, under the "law", "rule" or "constraint" (call it what you will)

 

applied to the entire set of points (points taken from both C and D) would constrain the points representing the element of C to exactly what they were.

 

Now, let's move to the next issue: the function

 

simply taken by itself certainly is not zero; however, if all of the delta functions happen to be zero (that is, no two reference points are the same) then F will be zero. And, for that case and that case only, there exists a set of points D which will constrain B(t) to your expectations no matter what those expectation might be.

 

Secondly, by definition, the function [math]\Psi[/math] will vanish for any argument which does not appear in your expectation as it's magnitude represents your expectation.

 

Thus it follows, as the night the day, that the product [math]F \Psi[/math] will vanish over the entire domain of the possible arguments if [math]\Psi[/math] is indeed the correct representation of your expectations derived from your explanation.

 

And of course there is no physics here. No deduction can result in anything not contained in the original specifications from which the deduction was derived and I took extreme care to assure that absolutely no internally consistent explanation was excluded by the model. Nonetheless, there is something very significant encased in my result. All explanations are created with two very different components: what is presumed to exist and what laws the things that exist must obey. What I have demonstrated here is that no matter what reality happens to be (that would be represented by C, which you can think of as the facts which must be explained), there always exists a set of hypothetical entities (that would be represented by D, which you can think of as the entities presumed to exist in your explanation) such that the rule F=0 will yield exactly what is observed. What exists must be solutions to my equation and that may be determined by solving it: i.e., every solution to that equation which exists constitutes a description of the outcome of an experiment which can be performed. The physics lies in solving that equation. :eek_big:

 

Any reasonable person will admit that changing the rules can change what must exist and changing what exists can change the rules. That is, it is a well known fact that a trade off exists between the two components. What I have proved is that, if one sets down the rule as being F=0 as I have defined it, there always exists a set of entities who's existence will in fact yield your expectations no matter what those expectations are. Under that rule, physics becomes the problem of discovering what exists, a much more straight forward problem than allowing both the rules and what exists to vary. It is also very much in line with what scientists actually do. In fact, if you look at the progress of physics, you will see that suggesting the existence of new entities is much preferred to changing the rules. However, scientists do occasionally change the rules but only when the new rule is considerably simpler than the old one. :shrug:

 

Finally, I would suggest that my F=0 is a pretty simple rule; certainly a lot simpler than what is currently being taught in physics. What I am looking for is someone capable of comprehending the validity of the equation I have deduced. If I ever find such a person, I will explain to them how to work out the solutions. The solutions turn out to be absolutely astounding. I would say personally that Maxwell's success was nothing compared to my discovery. That equation is a TOE except for one single fact: it's not a theory, it's a deduction. :phones:

 

Have fun -- Dick

[ldsoftwaresteve]

DoctorDick:

I appreciate your interest and outlook immensely as it provides me with practice at being clearer; practice I certainly need. No one seems to understand what I am doing in my paper, A Universal Analytical Model of Explanation Itself and maybe I can provide an acceptable hand waving argument which will at least allow you to understand what it is all about.

You're very welcome. I'm chuckling at the use of 'hand-waving' and I'll figure out what that means sooner or later. I have offered myself up as a sort of Judas goat because I think you have something important to say and the meaning behind it is more important than how I am seen by others. :) And I am not an altruist, quite selfish as a matter of fact.

All of this is a lovely puzzle to me Dick and my method is to pick away at the edges, try to get my arms around the meanings, and flesh it out over a period of time (I'm slow in other words). Also, I'm a harmonizer and love to play background music if I hear an interesting melody.

The next step I take is to transform the numerical representation into points on the x axis. This step however introduces a difficult fundamental problem as information can be lost if multiple occurrences of a given number exist in the elements of B(t). That is the reason I introduce the tau axis. Without the tau axis, there is no way of using points to represent all possibilities with points.

I actually was able to visualize this part and understood how overlapping information would get lost without the tau axis. Now I have to admit the clarity of my visualization was similar to trying to count deer in my headlights on a foggy night... :)

The Dirac delta function can be seen as a function which is zero everywhere except when the argument vanishes (goes to zero) where it spikes to infinity. Though it is an infinitely high with a width of zero, it is defined to have an area under the curve of one. You might take a look at a somewhat straight forward development of the function.

I'll bully my son into helping me glimpse what this is all about. Now I have a grandson to take to the beach.

[Doctordick]

I'll bully my son into helping me glimpse what this is all about. Now I have a grandson to take to the beach.

Youth is wasted on the young! It's too bad that the comprehension of what life is all about comes so late. But we can still enjoy it even if there is little we can do to change it. I was the eldest of four children and you know parents are are a bit loose with their tongues before they figure out that the kids listen to everything they say. That is to say, I knew about all the family skeletons that my siblings never heard of. When I was a child, I thought that all that was in the past and that "those kinds of mistakes" could not possibly happen again. Three generations later, I see that nothing has changed at all; every mistake made by my ancestors has been made again by their decendents. Life is life and we just have to learn to appreciate it. Hope you had fun at the beach.

 

But back to "what this is all about". I was quite impressed with the fact that you comprehended how overlapping information would get lost without the tau axis. That is a very important issue which I think many people miss. Another issue everyone seems to miss is the fact that every explanation of anything includes made up entities charged with being the carriers of causality. Their actual existence is only justified with the success of the explanation. That is, their existence is the basis of my set D: entities, concepts or ideas required for the explanation to make sense whereas C consists merely of the things which "must" be explained (the actual experiences of our lives, not the interpretation of those experiences). C and D consist of what we think is so. A new explanation can change D but it cannot change C, it can only change our interpretation of C. If people cannot comprehend that, they simply cannot comprehend what I am talking about.

 

Another subtle point, which I have not mentioned before but I think you might comprehend, is that the representation of C as points on the x axis is not the only kind of "point" representation conceivable. One could also collect those numbers in pairs and represent the information as points in an (x,y) plain (you should see that necessity of adding the tau axis still exists). All that happens in my representation is that B(t) becomes a set of points in a real (x,y, tau) space. Likewise, one can just as easily collect those numbers in triplets and represent the information as points in an (x,y,z) space. Again the tau axis is still necessary so one ends up with the representation where B(t) is a set of points in a real (x,y,z, tau) space.

 

If one then adds the Dirac delta function as an interaction between those points, the universe being described becomes a four dimensional gas of dust motes of zero dimension. That's a rather simple minded model of the universe but it clearly satisfies my equation (expanded to two more dimensions). In order to talk about any real observations of such a universe, that tau axis has to be integrated out of the problem and the final result turns out to be identical to what we see. But to understand that, one must be able to do the mathematics. Since the actual mathematics is apt to be beyond you I leave you with my model of "an explanation"; something I think you are maybe getting close to comprehending.

 

Have fun -- Dick

[ldsoftwaresteve]

DoctorDick:

Another issue everyone seems to miss is the fact that every explanation of anything includes made up entities charged with being the carriers of causality.

the order of and evolution of events?

Their actual existence is only justified with the success of the explanation.

The explanation predicts correctly, therefore the causal functions can be presumed as justified beliefs (knowledge)? I'm trying to use some terms the way you use them.

If one then adds the Dirac delta function as an interaction between those points

Is that the purpose of the Dirac delta function...the entity charged with being the carrier of causality?

[Qfwfq]

For example, Newton's failure to consider the problem of setting clocks to agree given a finite speed of light caused him to overlook the finer points of relativity. Had he looked at the issue carefully, I am quite sure he would have realized that the idea of reality being a three dimensional Euclidean universe had to be erroneous.

Before Maxwell's equations?

 

On the basis of exactly what, known at the time, could he have inferred such a thing?

[Qfwfq]

I'll bully my son into helping me glimpse what this is all about.

Go easy on the poor fellow, now! :(

[jpittelo]

Do you mean an "observable" in the mathematical sense ?...then, I think because of the time evolution operator (Schreodinger equ. derived), it's not, because it's not commutative, but anti-commutative : T=-T*

[Qfwfq]

I think because of the time evolution operator (Schreodinger equ. derived), it's not, because it's not commutative, but anti-commutative : T=-T*

The time evolution operator is unitary.

 

The condition T = -T* would mean that T is i times a self-adjoint operator, this is not a property of the time evolution operator.

[jpittelo]

Oh, sorry. I'm not used anymore to the scrupulous usage of vocabulary in science, because since my graduation, in 2003, I got just pushed out of the academic world..I meant a "time operator", that would give the time coordinate...sorry, parameter : T(Psi(x,t))=t*Psi(x,t)..the application of the operator T on Psi. The time evolution operator is defined as : U=exp(-iHt)...where H is the Hamiltonian H=H*, hence inv(U)=U*, but we have T=-T*..because of the "i" in the Schreodinger equation (sesquilinear forms)

 

But, in classical mechanics does observalbe mean : i can look at my watch, or any watch in fact ? (like primary school questions)

[Qfwfq]

I see what you mean now, [math]\norm T\Psi(x,t)=t*\Psi(x,t)[/math] is the multiplication operator but it would be self-adjoint, just like the same thing for x, or for p and E in energy-momentum representation. I don't see why the i in the Schrödinger equation would change that, apart from the fact that it doesn't suit a Lorentz-covariant description, it is actually the equation of time evolution:

 

[math]\Psi(t)=e^{-iHt}\Psi(0)[/math]

 

is really just an alternative form of the Schrödinger equation.

 

But, in classical mechanics does observalbe mean : i can look at my watch, or any watch in fact ? (like primary school questions)

In classical mechanics there isn't really a definition like there is in quantum formalism. It's more like... something that you can measure. :shrug:

[jpittelo]

Just consider the Schroedinger equation :

 

[math] -\hbar^2\frac{\partial^2}{\partial x^2}\psi(x,t)+V(x,t)\psi(x,t)=i\hbar\frac{\partial}{\partial t}\psi(x,t) [/math]

 

Hermite conjugation of the equation gives, let [math]\phi(x,t)=\psi(x,t)*[/math] :

 

[math] -\hbar^2\frac{\partial^2}{\partial x^2}\phi(x,t)+V(x,t)\phi(x,t)=-i\hbar\frac{\partial}{\partial t}\phi(x,t) [/math]

 

Hence the equation is not conserved, because of time reversal on the right hand-side, due to the presence of the imaginary "i"; except if you put a [math] anti-hermitean [/math] Time-operator : [math] \hat{T}*=-\hat{T} [/math], which restores the time sign on the right handside.

 

However, anti-symmetric matrices on R for example, can have imaginary eigenvalues, which is quite disturbing in a lab, to measure an "imaginary" date in the complex plane.

[Doctordick]

Sorry I didn't see your post. I presumed I wouldn't have anyone to talk to until Steve got back from his trip.

Before Maxwell's equations?

Why of course before Maxwell's equations. The difficulty existed prior to the introduction of Maxwell's equations; it just wasn't noticed until they tried to fit Maxwell's equations into their mental picture.

On the basis of exactly what, known at the time, could he have inferred such a thing?

Well, in my opinion, Newton was a very astute thinker. All you would have had to do is point his mind towards the difficulty and I am quite sure he would have seen it. First of all, he certainly believed in the concept of relativity (actually a concept introduced by Galileo when he pointed out that a stone dropped from the crow's nest on a ship would hit the same point on the deck whether the ship was moving or not). Newton himself showed that centrifugal force was a consequence of the general relativistic transformation from an inertial frame to a rotating frame.

 

People seem to miss the fact that the concept of relativity existed long before Einstein. In fact, it was exactly the problem with Maxwell's equations which brought the problems with Euclidean relativity (how one transfers measurements from one frame of reference to another) into the open light. And, Einstein's "special relativity" was called "special" because initially, Einstein could not generate the required "general" transformation (he had to omit accelerated frames which were very important to Newton's vision of Euclidean relativity).

 

But back to the point that Newton could have recognized the difficulty had he happened to think of the problem of setting his clocks from an ideal perspective. Let us set up a thought experiment using nothing not known by Newton. First, as I commented, Newton certainly believed in "relativity": the idea that the description of physical experiments could be transformed into alternate frames of reference. Secondly, he knew the speed of light was finite as he himself observed the difference in the apparent orbits of the moons of Jupiter caused by the finite speed of light.

 

All one would have had to do is describe a thought experiment involving examination of the same experiment from a rest position and a moving carriage as described in an ideal circumstance (both being inertial frames). Let the two examiners each possess a glass plate set parallel to the direction of motion an infinitesimal distance apart, one at rest with respect to observer number one and the other at rest with respect to observer number two. Let them each set up a coordinate system (make it a polar coordinate system with theta equal zero in the direction of motion for simplicity) on their respective glass plates and reckon their times from a infinitely accurate clock positioned at the origin of their coordinate system setting t=0 to the moment the two origins are in the same position.

 

Now let the two observers examine a phenomena which takes place between the two plates, recording the time and position of the significant events in that phenomena. I think we are all pretty sure we know exactly what Newton would initially do: he would presume to describe the phenomena via the rest observers measurements and then use Euclidean general relativity to transform the measurements into the moving observers coordinate system. Now all we have to do is point out the physical problems in that solution: essentially the problem of determining who is actually at rest.

 

He has obviously made the assumption that measurements in the direction of travel are the same for both observers. Challenge him to prove that those measurements have to be the same: i.e., that the acceleration to the other frame did not change the characteristics of the measurement devices used by that observer. If he responds that relativity itself requires they be the same then one can shift to the problem of defining time at the various positions in the coordinate system. No matter what he suggests, a problem with his solution can be brought up as it simply is not an internally self consistent solution and I believe Newton would have been able to see that fact.

 

Special relativity can be deduced directly from the idea that the speed of light is the same for both observers. Challenge Newton to show how an observer in an inertial frame could prove that he was moving with respect to the light. I think that a little time with the problem would have made him seriously worry about the situation. But that's just my opinion; I certainly could be wrong.

 

Have fun -- Dick

[Qfwfq]

Do you perhaps, quite implicitly, have Newton supposing there to be no whatsoever possibility of communicating information faster than light? He speculated much upon the nature of light but I don't see what could have even remotely suggested such a thing to him.

He has obviously made the assumption that measurements in the direction of travel are the same for both observers.

He certainly has, like all natural philosophers before 1905, considering it "a perfectly natural thing to suppose" in lack of any contrary reason.

 

Challenge him to prove that those measurements have to be the same: i.e., that the acceleration to the other frame did not change the characteristics of the measurement devices used by that observer.

I'm sure Newton would have replied that he was unable to prove this logically, without evidence which, at the time, appeared so far in support.

 

No matter what he suggests, a problem with his solution can be brought up as it simply is not an internally self consistent solution and I believe Newton would have been able to see that fact.

I don't see a lack of internal self-consistance, only a switch of axiom.

 

Special relativity can be deduced directly from the idea that the speed of light is the same for both observers.

Which was the prime Ansatz in Einstein's 1905 paper as well as the more formal approach of Minkowski. But what reason could Newton have possibly found, to adopt it instead of the above one? I haven't been able to find such a reason in your Gedankenexperiment.

 

Challenge Newton to show how an observer in an inertial frame could prove that he was moving with respect to the light.

Prove that he was moving with respect to the light? Once again you say something quite ambiguous. Without exactly knowing your intended meaning I'm at a loss to know what to make of it.