An “analytical-metaphysical” take on Special Relativity!

[Doctordick]

Originally Posted by Bombadil

In fact if they did not give the same expectations one of them would seem to have to be flawed or at least incomplete.

That is the central issue of special relativity: how does one transfer the measurements made in one inertial frame of reference to those made in a second inertial frame of reference moving with respect to the first. It is the actual measurements of the actual phenomena which is of significance. Central to the whole question is the idea that physics (the explanation of reality which is physics) must allow us to explain how that is to be accomplished. The explanation (the physics itself) is not to be changed. Any “change” would clearly be seen as a flaw.

Originally Posted by Bombadil

I assume that by, “by excellent I mean that the nature of the phenomena behind these measures is presumed to be well understood.” that you mean that the object must behave the same over any particular measurement. That is if something is measured at one time and then at a latter time then the measurements will agree or if a particular event is measured at one time the same event will have the same measurements at a latter time. And so by using such a property to define a measure a unit measure will always have the same properties (they will be considered to be the same length) in any frame.

No I do not mean any such thing. That is why I put it the way I did! How these measures are to be established is of utterly no consequence so long as the the procedure used is not confused by either party; that they will agree that the procedure being used is the “correct” procedure as per their explanation of reality (their “physics”). My presentation is much more open to alternate possibilities than is your statement.

Originally Posted by Bombadil

Now since any flaw-free explanation must be scale invariant there must exist frames in which two rods defined to be a unit of measurement by any particular event that is the same property of the explanation was used to define the units of measure.

That sentence just doesn't make any sense to me. The flaw-free explanation is scale invariant when the entire universe is included. If you have a solution (an explanation) and that explanation includes a “scale” obtained by some procedure (internal to that universe) and you change the scale of the entire universe, the scale used in that explanation changes in exactly the same way. That is scale invariance. The problem arises when the two observers are leaving out different pieces of the universe (which is exactly what they are doing when they each propose their frame of reference is inertially “at rest”): i.e., they are presuming that the motion of the far away portions of the universe are of no significance to their physics (their explanation). The consequence of that fact is that, to quote you, “the observers will not agree on what they see” if their personal universes are scale invariant. The obvious answer is that they can not be scale invariant. Their “Physics” must establish a mechanism which “explains” the transformation required.

Originally Posted by Bombadil

So the solution is that if the scale of the flaw-free explanations differ by exactly the Lorentz transformation then both observers can measure the same events and while their measurements will not agree they will agree on what happened if the measurements are transformed into any particular reference frame.

Let us say that their explanations of what happened will agree if those explanation include such a transformation.

Originally Posted by Bombadil

This does not however prove that the explanation obeys the Lorenz transformation only that if it does then there is no frame that is proffered over any other frame and that measurements in one frame can be changed to any other frame.

I think you have the horse on entirely the wrong side of the cart here. You should have said, “This does not however prove that the explanation obeys the Lorenz transformation; only that, if it does not, the explanation is flawed in that “the rest of the universe can not be omitted”. It is entirely possible that the proper “physics” (the flaw-free explanation requires information about the rest of the universe).

We already know that the background microwave radiation sets up a unique frame of reference wherein the common inertial frames used in physics are not at rest. People today commonly speak about the motion of our solar system or our galaxy through the universe so there is very definitely a “preferred” inertial frame. What they don't talk about is the possibility that the “laws of physics” could be a function of that motion. I am afraid my presentation leaves that issue open. Einsteinian relativity presumes such a thing is impossible; however, no such independence of that frame has ever actually been proved. As a matter of fact, when and if we get into general relativity, the issue rises again in a somewhat different form.

Originally Posted by Bombadil

So this is what the reason for using an element that has zero movement in the direction is for. It gives a very convenient way to define time or distance assuming that one has already been defined, because such elements will have the same speed no matter what frame they are in after speed has been defined. Its speed is in fact scale invariant, that is, no matter what the scale of the equation is after speed has been defined it’s speed will be the same in any frame. And so it can be used in any reference frame and the same result will be arrived at. However the speed being invariant is not necessary, all that is necessary is that objects in different frames behave in the same way independent of the scale.

Once again, I find your statement rather askew of what I am saying. I think everything would be clearer if you just left this paragraph out. I certainly would not agree with it.

Originally Posted by Bombadil

Now since Schrödinger’s equation is a solution to the fundamental equation this allows you to define a particular object in a rest frame to be a unit of distance.

Again I find your statement confused. Schrödinger's equation being an approximate solution to my equation implies that “objects” (the structure of which physics explains through Schrödinger's equation) can also be an approximate solution to my equation: i.e., what we call “physical objects” can exist and will obey standard Newtonian rules.

Originally Posted by Bombadil

The question then becomes the problem of moving such an object from one frame into any other frame.

The question then becomes the problem of examining such an object from two different frames. There is no problem of moving such an object: movement from one inertial frame to another occurs all the time in Newtonian mechanics.

Originally Posted by Bombadil

This shows that there exists a way on moving from one frame to any other frame that is adding momentum to the fundamental equation. Now when we compare this to the Schrödinger equation, adding momentum in this way results in adding velocity to a object to change it to a new reference frame.

Yes, but the solution is only flaw-free in the original inertial frame: i.e., these are your expectations if you take the position that the moving frame is “wrong”.

Originally Posted by Bombadil

So all that is being used is that energy and momentum will behave like they do in Newtonian physics and that it is possible to form objects?

Yes!

Originally Posted by Bombadil

So in effect since movement along the direction has no effect in the finale analysis of the problem and any difference from zero of the terms would just be integrated out and so would make no difference in the final analysis of the problem. So there is no reason to assume that there is any reason that the mass operators will sum to zero as it will have no effect in the final analysis of the problem.

Essentially yes.

Originally Posted by Bombadil

But isn’t it also true that if we where to try and define simultaneity in any other way then the results would still have to differ from one frame to another. Unless of course, we define simultaneity to only exist in a particular frame and use it as the rest frame and do all of our calculations in that frame which is not a practical solution to the problem.

Yes, I would have to agree with that; however, you need to define “a practical solution”. Remember, we are talking about an explanation which yields our expectations. An explanation is flaw-free if it does indeed yield our expectations. If, as the basis of our explanation, we are going to presume that there is nothing in our “local” measurements which can identify that preferred frame, then our explanation must include exactly the relativistic transformations we have deduced.

What you have to comprehend is the fact that our solutions (the problems physics can solve exactly) can not be “general many body problems” and are essentially restricted to interactions between two bodies, the things our physics can explain are totally limited to phenomena which obey the transformations we have deduced. Essentially, this can not be taken to imply our expectations are correct. We may perhaps discover events which contradict a physics deduced under such a constraint. In particular, the assumption that such transformations of physics to relativistic velocities compared to the rest frame of the background microwave radiation will have no consequences is an assumption. One which I suspect is in error and I will explain that problem when I get into general relativity.

Have fun -- Dick

[modest]

Originally Posted by Doctordick

Could I interest you in going through my presentation line by line?

Sorry for the delay.

I've been telling Michael Mooney for some time that he should not pass judgment on relativity without first understanding it. Taking my own advice I would like to withhold any bias or opinion on your formalism until I understand it which is not yet the case. To be honest: for as much time as I've spent on Hypography, I've avoided examining your work probably because it seems like a rather involved undertaking.

Originally Posted by Doctordick

I will show explicitly that my picture is not only totally consistent with special relativity but actually requires that special relativity be valid.

My knee jerk reaction and my first question: if your fundamental equation can be used to derive a space-time then would I be correct that you would not object to using it—at the very least as a matter of convenience. I realize this question sidesteps the point of your presentation, but I'd just like to be sure you're not rejecting the utility of Minkowski.

Originally Posted by Doctordick

It turns out that we are quite lucky in that the consequences of the above symmetry have already been completely worked out long ago by others. Notice that, if one ignores the Dirac delta function (as it has no spacial extension) my fundamental equation is a simple linear wave equation in four dimensions with wave solutions of fixed velocity. The constraint spoken of above is exactly the same constraint placed on the conventional Euclidean mental model of the universe by the fixed speed of light in Maxwell's equations. As we all know, if we constrain ourselves to linear scale changes, it turns out that there exists one very simple (and unique) relativistic transformation which maintains a given fixed velocity for all reference frames moving with constant velocity with respect to one another.

Taking as a postulate (simply because I have no idea how you derived these things) that some wave propagates at a fixed and finite speed for multiple inertial frames then I have no doubt the Lorentz transformations can and must be derived.

Originally Posted by Doctordick

We need to have a formula for translating coordinate points in the first frame, , into the identical points represented in the second frame, which have to be in a way which continues the validity of the fundamental equation. In order to do that, I will use the fact that the fundamental equation is (sans interactions) a wave equation where the wave velocity, v_? is constant; thus, we can use an opening circumstance where (at t=0), , the wave function of an object consisting of a single element (i.e., all interactions with the rest of the universe are being ignored), consists of a spike at the origin in both frames and is zero elsewhere (that means we are starting with the origins of both frames of reference exactly aligned origins). Anyone familiar with wave equations understands that the solution here is quite simple, is thereafter a spike at r=tv_? (where r is the radius of a four dimensional sphere centered on the origin) and zero elsewhere from then on. (Think of a flashbulb going off at the moment the origins of the two coordinate systems are exactly in the same point and then picture the sphere of light expanding at the speed of light.) The fact that our case is a four dimensional sphere is only of passing significance here, as we are still speaking of uniform radial expansion: i.e., the radius to that pulse of probability must be given by . Please notice that this means that once a scale is set for one coordinate, it is likewise set for all the others (otherwise we wouldn't have a sphere).

Inertial frames of reference are Euclidean in both classic and relativistic mechanics and there being 4 proposed spatial dimensions then I can certainly accept would make a 3-sphere in S. If time and velocity are typical (Newtonian) and the probability wave/sphere expands at v_? then I understand and agree r = v_?t.

The question I guess I have is how your fundamental equation insists that the origin of S' remain the origin of our 3-sphere as time progresses. In other words: why isn't the sphere moving in S'? It almost feels like you've asserted the principle of relativity. It would help me to see how you rule out the possibility of where v_? would be constant relative to the center of the sphere but not relative to S'. That case of course giving x' = x-vt and t' = t.

And... speaking of Galilean transformations:

Originally Posted by Doctordick

At this point, we have deduced the fact that observers from coordinate systems moving with respect to one another will totally agree with the transformations implied by the standard relativistic relationships. Virtually the only difference lies with the actual limiting velocity. Is v_? required to be c?

Before we can actually answer that question, we need to know exactly where the number “c” came from. The speed of light is c, thus it is, in our analysis, the apparent speed of that massless oscillator (what we have called v_?, the propagation velocity given to the changes of that probability function). It should be clear that the actual value of this velocity requires not only the definition of a clock (which we have done) but also a specification of a standard unit of time. It is here where the difference between my analysis and the conventional approach show up. In my approach, t is a free evolution parameter having absolutely nothing to do with actual physics of the issue. The velocity v_? can have any value one wishes (defining the standard unit of time or length is an open issue); however, once those units are defined, v_? will be exactly the apparent velocity of a massless entity and the limiting maximum velocity of any physical object in those specific units and that is exactly the underlying definition of c.

Where c approaches infinity the Lorentz transformations approach the Galilean transformations,



Usually it is left to observation to show that the invariant speed is finite. Wikipedia goes as far as saying experiment is necessary,

Originally Posted by wikipedia—Lorentz Transformations

If then we get the Galilean-Newtonian kinematics with the Galilean transformation, where time is absolute, , and the relative velocity v of two inertial frames is not limited...

Only experiment can answer the question which of the two possibilities, or , is realized in our world. The experiments measuring the speed of light, first performed by a Danish physicist Ole Rømer, show that it is finite, and the Michelson–Morley experiment showed that it is an absolute speed, and thus that .

But, your post seems to leave open the possibility of an infinite v_?. Is this not an issue?

~modest

[Doctordick]

Originally Posted by modest

I've avoided examining your work probably because it seems like a rather involved undertaking.

Actually, my work is quite simple; what makes it involved is the great number of things which flow from it.

Originally Posted by modest

My knee jerk reaction and my first question: if your fundamental equation can be used to derive a space-time then would I be correct that you would not object to using it—at the very least as a matter of convenience. I realize this question sidesteps the point of your presentation, but I'd just like to be sure you're not rejecting the utility of Minkowski.

I am not. In fact, I have essentially spent most of Sunday trying to find an exchange I had with Erasmus00 concerning exactly this issue which you really should read. That is one of the problems with the structure of these forums. There is essentially no way to find a specific discussion even when you know exactly what was being said: the search function does not produce posts but only threads. There is no organization of the exchanges what so ever. I try to keep a database on where my posts are and what they are about but I have let it get out of date. It takes time to keep it up to date. If I knew the bash shell a little better, I could probably write a bash script to do it for me but I am too busy (or maybe too old) to get competent in bash.

At any rate, he and I have discussed the fact that my picture and Einstein's are isomorphic with regard to any specific observations. I managed to convince him of the truth of that statement but he still didn't see any value in it and dropped out of the discussion.

Originally Posted by modest

Taking as a postulate (simply because I have no idea how you derived these things) that some wave propagates at a fixed and finite speed for multiple inertial frames then I have no doubt the Lorentz transformations can and must be derived.

You should really look at the derivation of my fundamental equation as, without understanding the necessity of that result the whole thing seems to be a bit “off the wall”. My original web site no longer exists but that derivation has been put on WiKipedia. Sans the interaction term, that is nothing more than a standard four dimensional wave equation.

Originally Posted by modest

I understand and agree r = v_?t.

Then we see eye to eye insofar as that paragraph is concerned.

Originally Posted by modest

It almost feels like you've asserted the principle of relativity. It would help me to see how you rule out the possibility of where v_? would be constant relative to the center of the sphere but not relative to S'.

I would comment that, to anyone who understands relativity and why Maxwell's equations require these transformations (and you are certainly a member of that set), asserting that the fundamental equation is a wave equation with constant velocity is exactly equivalent to asserting the principal of relativity (or rather, the problem relativity was created to solve). That is why I suggest you closely follow my deduction of that fundamental equation; the issue of relativity is embedded in the equation itself.

The equation is invalid because because it requires the moving observer (the observer in the primed frame) to know his frame is moving. In my derivation of my fundamental equation, the equation is only valid in the rest frame of the universe. Since it is not talking about “correct” answers but rather about “expectations” the issue arises as to what happens if the two observers ignore the data which sets their frames of reference apart (for example, rotation of the earth, movement of the earth through the galaxy or possibly the microwave background radiation).

In that case, they would each presume their reference frame to be at rest with respect to the universe and clearly any physical phenomena which did not depend upon the validity of their frames being “true” rest frames of the universe would be erroneous (their expressions of the fundamental equations would be different). There is a contradiction here which can only be removed by taking advantage of the scale invariance of that equation.

Originally Posted by modest

But, your post seems to leave open the possibility of an infinite v_?. Is this not an issue?

No, it is not an issue for two explicit reasons. First, you need to understand the deduction of the fundamental equation. The constant K, which is essentially the inverse of v_?, is a free parameter of the deduction. Infinite v_? would essentially amount to the case K=0. That implies that the magnitude of the momentum of the individual entities making up the universe vanishes identically. The only conclusion which can be drawn from that is that “no change whatsoever can occur”; that demands an exactly static universe.

And, secondly, the fundamental equation is essentially scale invariant. Since t is a free evolution parameter, the actual change per unit time is set by two issues, the actual scale used for distance (which is defined by some specific solution to the equation) and the scale used for time (which is simply picked to describe some convenient repeating phenomena). That is, your explanation of the universe itself (as expressed by ) sets the explicit value of v_? (whatever it is, it is a finite constant set by your physics). So why don't we just call it “c” for convenience?

Have fun -- Dick

[Bombadil]

Originally Posted by Doctordick

No I do not mean any such thing. That is why I put it the way I did! How these measures are to be established is of utterly no consequence so long as the the procedure used is not confused by either party; that they will agree that the procedure being used is the “correct” procedure as per their explanation of reality (their “physics”). My presentation is much more open to alternate possibilities than is your statement.

So all that is necessary to insure that measurements in one frame will agree when transformed to a new frame with the measurements made in the new frame is that the same procedure is used in both frames to arrive at their units of measure. It doesn’t matter how the units used are defined as long as they are made in the same way since in order for a flaw-free explanation to exist in both frames their laws of physics (their explanations) must agree when their measurements are transformed to a single frame.

Now in the case in which the measurements that the observers make do not follow the Lorenz transformation, the only possibility is that one or both of the observers are using a flawed explanation.

I’m somewhat puzzled though by exactly what the scale invariance is, it seems that it is stating that no matter how you define distance and time that the same explanation will be a valid explanation and as long as you use the same units it doesn’t matter what they are. Or in other words it doesn’t matter how we define length along any axis as along as it is consistent with the explanation. I’m wondering if this is the case because it seems that the scale invariance vanishes when we define a system of units.

Originally Posted by Doctordick

That sentence just doesn't make any sense to me. The flaw-free explanation is scale invariant when the entire universe is included. If you have a solution (an explanation) and that explanation includes a “scale” obtained by some procedure (internal to that universe) and you change the scale of the entire universe, the scale used in that explanation changes in exactly the same way. That is scale invariance. The problem arises when the two observers are leaving out different pieces of the universe (which is exactly what they are doing when they each propose their frame of reference is inertially “at rest”): i.e., they are presuming that the motion of the far away portions of the universe are of no significance to their physics (their explanation). The consequence of that fact is that, to quote you, “the observers will not agree on what they see” if their personal universes are scale invariant. The obvious answer is that they can not be scale invariant. Their “Physics” must establish a mechanism which “explains” the transformation required.

So since both observers are leaving out different parts of the universe when they define the units of there explanations they will not agree on there explanations (that is the units defined using one explanation will not be consistent with the other) but in order for both explanations to be flaw-free they must differ by nothing more then the scale (this corresponds to the scale of objects in their explanation) and in order for them to see the same event and agree on what happened in any particular frame that scale must be the same as what is defined by the Lorenz transformation.

Now the actual scaling of the fundamental equation is just a consequence of the transformation used to change the explanation in one frame to a new frame while still keeping the fundamental equation valid.

Originally Posted by Doctordick

I think you have the horse on entirely the wrong side of the cart here. You should have said, “This does not however prove that the explanation obeys the Lorenz transformation; only that, if it does not, the explanation is flawed in that “the rest of the universe can not be omitted”. It is entirely possible that the proper “physics” (the flaw-free explanation requires information about the rest of the universe).

But isn’t the issue of if any flaw-free explanations can obey the Lorenz transformation still open or is the fact that if they do, observers in different frames will agree on the measurements when transformed to the same reference frame enough to insure that two different flaw-free explanations will obey the Lorenz transformation. Basically I’m asking how do we know that the measurements in one frame can be transformed to any other frame even if both explanations are flaw-free. It seems that this may be equivalent to asking if all flaw-free explanations differ only by a scale.

Originally Posted by Doctordick

The question then becomes the problem of examining such an object from two different frames. There is no problem of moving such an object: movement from one inertial frame to another occurs all the time in Newtonian mechanics.

This still seems to leave open the question can an object in one frame be moved to any other frame. That is are there frames that an object in one frame can’t be moved into from some other frame. Or can an object in any frame be moved to any other frame.

Originally Posted by Doctordick

Yes, but the solution is only flaw-free in the original inertial frame: i.e., these are your expectations if you take the position that the moving frame is “wrong”.

Isn’t it still an open issue though that is if we can call the moving frame wrong or not it may be that there are no wrong frames only incomplete explanations or it may be as you seem to be suggesting that there is in fact a unique frame that is the only frame in which the fundamental equation is valid in.

[Doctordick]

I am sorry Bombadil, but I very much get the impression that some very important aspects of my presentation are just missing their mark. It seems to me that you are just attacking the problem from the wrong direction. I suspect there are two issues in play here. First, I suspect that your understanding of mathematics does not include much experience solving difficult differential equations. The single most important issue there is that no general solution to a many body problem has ever been found. The validity of my fundamental equation can not be judged through its solutions because those solutions simply are not available to us. Its validity rests entirely on my deduction and nothing else.

If you followed my deduction of the fundamental equation, you would understand that it is no more than a proof that any explanation of anything can be interpreted in a way which obeys that equation. That is, any ontological basis may be translated into a set of points in that Euclidean space I have set up. As Anssi has realized, what we are really talking about is a general epistemological construct consistent with that hypothetical ontological basis. Persistence is the central issue of any epistemological construct. Those points which make up a given present (defined to be new knowledge added to the past, “what we knew or thought we knew” ) are simply presumed to be a new distribution of the previous present. Each time slice is presumed to consist of exactly the same elements which made up the previous slice (indicated by the use of the same index i ); however, the presumed persistence says that they existed between those time slices. This is the central issue behind the dual identification: identification via the index “i” with the further numerical label x_i being plotted. That continuation which presumes existence between “presents” yields an epistemological construct which can model absolutely any explanation which can be conceived.

The epistemological construct is no more than a vast collection of point entities moving around in a Euclidean space. That epistemological construct is clearly flaw-free because it is clearly consistent with the fundamental equation I deduced: i.e., point entities traveling in straight lines except for point interactions (scattering) caused by the Dirac delta function interactions. But it is also a solution of utterly no use as I still can not solve the many body problem so represented. (Though I have shown that absolutely any "physical" representation of the universe can be represented by such a thing. See my geometric proof.)

But what I have done is to show that Schrödinger's Equation is an approximation to my equation given some rather simple and straight forward assumptions (assumptions totally consistent with the assumptions used in all applications of Schrödinger's Equation). What this leads me to is my definitions of mass, momentum, energy and (even more significant when it comes to constructing a mental picture consistent with my equation) “objects”. This gives me the power to transform this “flaw-free” epistemological construct into my personal world view (that solution to the problem provided to me by “squirrel thought” the correctness of which I can not check).

That any conceivable explanation can be so interpreted is the central issue; not what that explanation is to the person who dreamt it up. When you attempt to give me your explanation of anything, I make an attempt to understand what you are telling me. If that explanation is flaw-free (and I would certainly presume it is or I wouldn't bother trying to understand it as trying to understand a flawed explanation is clearly a waste of time) then your communication of your explanation can be interpreted in such a way that it obeys my equation. That is the first step! What you must remember is that your world view includes the meanings of the words you use and the mechanism you use to convey those words (sounds or electronic signals or even your own senses).

Your world view is the whole magillah. I likewise possess a world view and my interpretations of the communications you put forth are just another piece of my world view. There exists no evidence at all that there is any “real” correlation between your explanation (your method of keeping track of your expectations) and my explanation of what I think I know. What I know of “other people” is no more than the explanation I have managed to construct in my own mind (my mind itself being such a construction). We are each perceiving the others view through our own solution to the problem; our own personal explanation of our experiences.

Are any of those explanations flaw-free? Well of course not; neither of us is all knowing and our abilities to actually analyze our own world views are so far below the requirements of such a feat that it is ridiculous to even suggest attempting such a feat. But, what I do know (as I have proved it) is that any “flaw-free” explanation must be a solution to my fundamental equation. I can use this to examine certain aspects of the problem of understanding.

The fact that any solution of Schrödinger's equation is an approximate solution to my equation implies that I have some facts about my world view (and yours) which can not be countered. First, that the universe can always be seen as a collection of energy quantized massless entities interacting via point scattering (the Dirac delta function); essentially a gas of such point “noumena” (to accord Anssi a little credit). And, second, that if we constrain our examinations to entities which are momentum quantized in the tau direction (collections of noumena which are mass quantized) we are presented with the possibility that collections of these “noumena” can remain in close proximity for extended times (collections I have dubbed “objects”). Furthermore, these objects will approximately obey Newton's mechanics.

Well, where does that get us? You and I have already reached (even before we had our first conversation) the fact that one huge portion of our world-view is constructed of objects which obey Newton's equations and, through advanced concepts of quantum mechanics (essentially Schrödinger's equation plus the many extensions which have been proposed) chemical theory, and thus the field of biology. I am not saying that any of these fields are flawless; merely that they are all connected by a logical thread in agreement with our experiences with the universe we find ourselves in.

Thus it behooves us to speak of such things in terms of my fundamental equation. This thread was dedicated to the simple issue that my fundamental equation is valid “only in the rest frame of the universe”. If it is possible for two observers to define personal rest frames which are moving with respect to one another (something held, in our scientific community, as easily arranged) a very specific constraint exists on the transformations of measurements between those two frames. That constraint is exactly the constraint commonly held as “special relativity”. What you were supposed to do with this thread was to follow the logic of the deduction of that constraint; not go off in wild directions as to the interpretations which can be attached to that fact.

Originally Posted by Bombadil

Now in the case in which the measurements that the observers make do not follow the Lorenz transformation, the only possibility is that one or both of the observers are using a flawed explanation.

If that transformation is not part of their explanation then their explanation is certainly flawed.

Originally Posted by Bombadil

Now the actual scaling of the fundamental equation is just a consequence of the transformation used to change the explanation in one frame to a new frame while still keeping the fundamental equation valid.

Again, you seem to have the horse on the wrong side of the cart. Any flaw-free explanation of anything can be interpreted as a solution to that fundamental equation (which is only valid in the rest frame of the universe). It isn't a question of “keeping the fundamental equation valid”, it is a question of so interpreting their explanations.

Originally Posted by Bombadil

Basically I’m asking how do we know that the measurements in one frame can be transformed to any other frame even if both explanations are flaw-free.

The method of performing the transformation is part of the explanation! If it does not conform to the relativistic transformation, the explanation can be simply declared flawed.

Originally Posted by Bombadil

This still seems to leave open the question can an object in one frame be moved to any other frame. That is are there frames that an object in one frame can’t be moved into from some other frame.

Tell me, does your world view include the possibility of two inertial frames moving with respect to one another? And does your world view include the possibility that an object originally in one frame can be moved to the other: i.e., can acceleration exist?

Originally Posted by Bombadil

... or it may be as you seem to be suggesting that there is in fact a unique frame that is the only frame in which the fundamental equation is valid in.

The fundamental equation is valid only in the rest frame of the universe. That does not require a unique frame for two reasons; first I defined “time” to be what we know and “the present” to be “a change in what we know”; it follows that “what we know” is continually changing and thus it is entirely possible that the “rest frame of the universe” may change. And secondly, whenever an attempt to explain any specific phenomena is undertaken, great quantities of information concerning the universe are commonly ignored (we work out the problem in a mental environment which clearly presumes a “universe” consisting of considerably less than what is defined to be “The Universe”).

What I am getting at here is that my proof that Schrödinger's equation is an approximation to my fundamental equation allows me to talk about phenomena actually described by Newtonian mechanics as possible solutions to my fundamental equation (at least roughly approximate solutions). It is this fact which allows me to do thought experiments with flaw-free explanations. It should be clear to you that my fundamental equation is not itself solvable.

Have fun – Dick

[modest]

Originally Posted by Doctordick

You should really look at the derivation of my fundamental equation as, without understanding the necessity of that result the whole thing seems to be a bit “off the wall”. My original web site no longer exists but that derivation has been put on WiKipedia. Sans the interaction term, that is nothing more than a standard four dimensional wave equation.

I agree that's the next step for me. While the derivation in the OP seems sound to me, it is firmly based on the character of something I know nothing about. As I say, your post seems to take as a postulate that some certain wave has a fixed speed regardless of frame of reference. So long as that speed is finite I agree the Lorentz transformations are the only logical conclusion.

Before I get to your fundamental equation I might have some questions about this metric you're using. My confusion is right now all in my head and I'd have to work at putting it down in a post... if you think this is the wrong thread for discussing that metric then let me know.

Originally Posted by Doctordick

The equation is invalid because because it requires the moving observer (the observer in the primed frame) to know his frame is moving.

Well, I certainly agree But, in another thread you're saying that the moving train frame can decide to use the fixed frame of the platform in defining simultaneity. By your own objection, this would require the person in the train to know they are moving and thus not be a valid approach.


Actually, If you can indulge me, I might get this conversation on the metric started.

Defining tau loosely as what clocks measure and x as what a ruler measures and the metric where c=1 and y & z are omitted we might plot something like:

S is not moving in x while S' is. The red lines are light emitted from S and detected at S'. Taking things slowly, I'll just ask one question: what is the change in tau between the detection events for S'? Is there enough information (as I've said nothing about time) to answer this question?

I appreciate your help on this. I'd really like to understand this alternative view of relativity and it's not coming to me intuitively.

~modest

[Doctordick]

Originally Posted by modest

My confusion is right now all in my head and I'd have to work at putting it down in a post... if you think this is the wrong thread for discussing that metric then let me know.

No, it is a fine place to discuss your difficulties. Please go and read the opening post to this thread. You will find almost exactly your diagram in that opening post (with some subtle but very important differences).

Originally Posted by modest

But, in another thread you're saying that the moving train frame can decide to use the fixed frame of the platform in defining simultaneity. By your own objection, this would require the person in the train to know they are moving and thus not be a valid approach.

Then perhaps we are confusing the meaning of the term “know” here. English is not really a very exact means of expressing ideas. If you substitute the word “presume” for the word “know” perhaps the confusion would kind of dissipate a bit. What we are really talking about here is the ability to perform a valid change in our frame of reference.

It is Einstein's contention that there exists no preferred frame of reference (insofar as the laws of physics are concerned). That is an assumption and cannot be proved (that is why he “postulated” that the speed of light is a constant). It is nice in that we need not worry about how we are moving relative to “a preferred frame of reference” however, we can still always do all our physics in “a preferred frame of reference” if we wish (that is, in fact, the central issue of relativity itself).

Originally Posted by modest

Defining tau loosely as what clocks measure and x as what a ruler measures and the metric where c=1 and y & z are omitted we might plot something like:

S is not moving in x while S' is. The red lines are light emitted from S and detected at S'. Taking things slowly, I'll just ask one question: what is the change in tau between the detection events for S'? Is there enough information (as I've said nothing about time) to answer this question?

Your diagram is fine except for one very important issue: all three entities being referred to are momentum quantized in the tau direction (even the photon which just happens to have a tau momentum of zero) thus their position in the tau direction has an uncertainty of infinity. It is thus an error to presume that their path (and thus their interactions) can be explicitly represented in your diagram you have displayed. There is nothing wrong with the coordinate system you have laid out; the problem is that you have to very very careful in deducing the positions where interactions can occur.

Time which I define to be an interaction parameter (things can interact if they are in the same place at the same time) is not a measurable thing but rather a hypothesized parameter used to divide the future from the past (something which can not be defined except at the point of interaction). Since both interacting elements positions in the tau direction have an uncertainty of infinity, so does that point of interaction.

The only factor which we have to offset the difficulty of establishing when and where an interaction can occur is the fact of my fundamental equation which is a wave equation with a velocity of v_?: i.e., the distance between interactions is explicitly v_?t where t is the time change since the previous interactions. For convenience, if we ignoring the momentum quantization and examining only the vectors which show the actual direction of the momentum we need to talk in terms of interactions themselves. We can start with the assumption that S and S' interacted at the origin of your coordinate system. This a good reason to show the vectors for the momentum of S and S' as originating there and establishes t=0 for both entities.

Now let us describe the phenomena you are attempting to show in your diagram. The next interaction of significance occurs after a delay of one unit of distance in the coordinate system (v_?t=1): after waiting one unit of time (or one unit of tau as measured on his clock: i.e., he defines time so that c=unity) S emits a photon towards S'. Then, after waiting another unit of time (essentially identical to the first period) S emits a second photon towards S'. The difficult issue is to establish exactly the position in your diagram where those two photons interact with S'. Those interaction points are very definitely not at the end of the red lines you show.

Interaction can only occur when the length of the path of both S' and the photons (plus their delay on S) are exactly the same. Since you have shown S' to be at the angle of 45 degrees, that point is easy to calculate (actually it is not difficult for any angle but this one I can do in my head). The point where the first photon interacts with S' (in the rest coordinate system) will be when x+1 (essentially the age of the photon) is equal to x divided by the cosine of 45 degrees which is or

.

Which is, of course, the point at which S' is at the point x=2.4155 (remember, both the photon and S' are smeared out in the tau direction). Since S' is moving at an angle of 45 degrees with respect to S and their clocks agreed at the origin the clock on S' will read exactly 2.4155 at the moment of receipt of the photon (assuming S' also defines time such that c=unity).

The second photon will be intercepted at a distance where x+2 is equal to or

.

Thus an observer on S' will actually see the period of the clock on S (which is being used to time the photons being emitted) as having a period of 2.4155 times the period of his clock. Now all you have to do is figure out the Doppler effect the S' observer attaches to that timing (essentially, the delay he attributes to the fact that S is moving away from him).

You really need to follow the second part of my opening post on this thread. The details of this kind of calculations are worked out in detail.

I hope I have cleared up the significant issues here. Looking forward to hearing from you again.

Have fun -- Dick

[Bombadil]

After looking at this some I suspect that I may be considering a couple of things incorrectly. Firstly what exactly the transformation of the fundamental equation that moves it to a new reference frame is. I have been considering this to be any terms that can be added to the fundamental equation so that it is no longer valid. This clearly is not what the transformations that we are interested in are, but rather it seems that what transformations it is that we are interested in is the addition of mass or momentum operators to the fundamental equation.

There is one other issue that I have been having that is, how do we know that the Schrödinger equation tells us anything about the fundamental equation. That is, how do we know that the V(x) term wouldn’t be so complex or in a particular form so that we can no longer use Newtonian mechanics as an approximation to the fundamental equation.

Actually I think that this issue has already been brought up although I didn’t fully realize it or how you where solving it. Simply put it is that since the equation is scale invariant we can look at it on any scale and due to all interactions taking place due to a Dirac delta function, which has only a single point that it is not zero on, this allows us to look at the Schrödinger equation on a scale in which the V(x) function vanishes. Clearly on this scale the approximations, except perhaps the last approximation used to derive the Schrödinger equation, can be justified. From what I can tell the last approximation can be justified if we consider the rest frame of the object of interest.

In this way we can derive the Schrödinger equation and in so doing show that Newtonian mechanics is an approximation to the fundamental equation when looked at on some scale.

Originally Posted by Doctordick

I am sorry Bombadil, but I very much get the impression that some very important aspects of my presentation are just missing their mark. It seems to me that you are just attacking the problem from the wrong direction. I suspect there are two issues in play here. First, I suspect that your understanding of mathematics does not include much experience solving difficult differential equations. The single most important issue there is that no general solution to a many body problem has ever been found. The validity of my fundamental equation can not be judged through its solutions because those solutions simply are not available to us. Its validity rests entirely on my deduction and nothing else.

This would be correct it is also a topic that I am trying to start going into.

Originally Posted by Doctordick

If you followed my deduction of the fundamental equation, you would understand that it is no more than a proof that any explanation of anything can be interpreted in a way which obeys that equation. That is, any ontological basis may be translated into a set of points in that Euclidean space I have set up. As Anssi has realized, what we are really talking about is a general epistemological construct consistent with that hypothetical ontological basis. Persistence is the central issue of any epistemological construct. Those points which make up a given present (defined to be new knowledge added to the past, “what we knew or thought we knew” ) are simply presumed to be a new distribution of the previous present. Each time slice is presumed to consist of exactly the same elements which made up the previous slice (indicated by the use of the same index i ); however, the presumed persistence says that they existed between those time slices. This is the central issue behind the dual identification: identification via the index “i” with the further numerical label x_i being plotted. That continuation which presumes existence between “presents” yields an epistemological construct which can model absolutely any explanation which can be conceived.

Then the question is vary much given an arbitrary set of elements (the ontological basis), arbitrary in that any particular element is identical so that any differences between elements is part of the explanation and not a property of the elements themselves. How is it that someone can explain such a set of points, that is, how can someone obtain expectations about how the elements will change given only the points.

What we are in fact doing is mapping such a set of points onto a Euclidean space and using a evolutionary parameter t to ask how might we explain how the system changes with t. But this change is itself part of the explanation and a consequence of new information becoming available and in order for us to conclude what the change is we must correspond elements at one value of the parameter t with elements at another value of t (that is they are considered the same element) and in so doing we conclude that the same elements existed at every point corresponding to a value of t.

Originally Posted by Doctordick

That any conceivable explanation can be so interpreted is the central issue; not what that explanation is to the person who dreamt it up. When you attempt to give me your explanation of anything, I make an attempt to understand what you are telling me. If that explanation is flaw-free (and I would certainly presume it is or I wouldn't bother trying to understand it as trying to understand a flawed explanation is clearly a waste of time) then your communication of your explanation can be interpreted in such a way that it obeys my equation. That is the first step! What you must remember is that your world view includes the meanings of the words you use and the mechanism you use to convey those words (sounds or electronic signals or even your own senses).

So whether or not a flaw free explanation satisfies the fundamental equation is not the issue but rather the issue is that there exists a isomorphism between the explanation and a solution to the fundamental equation. That is, there is a mapping that preserves the result satisfying the fundamental equation.

Originally Posted by Doctordick

Your world view is the whole magillah. I likewise possess a world view and my interpretations of the communications you put forth are just another piece of my world view. There exists no evidence at all that there is any “real” correlation between your explanation (your method of keeping track of your expectations) and my explanation of what I think I know. What I know of “other people” is no more than the explanation I have managed to construct in my own mind (my mind itself being such a construction). We are each perceiving the others view through our own solution to the problem; our own personal explanation of our experiences.

The real question is how such a world view is constructed as there is nothing but arbitrary information to base it on even the way that we map the information before forming a world view must be part of the world view.

So what we must do is first realize that it is arbitrary information that we are dealing with then find a arbitrary method of mapping the information in such a way that we can analyze are world view and realize that it can be interpreted in such a way that it satisfies the fundamental equation?

Originally Posted by Doctordick

Again, you seem to have the horse on the wrong side of the cart. Any flaw-free explanation of anything can be interpreted as a solution to that fundamental equation (which is only valid in the rest frame of the universe). It isn't a question of “keeping the fundamental equation valid”, it is a question of so interpreting their explanations.

That is in order to use their explanations we must be able to interpret the explanation in such a way that it obeys the constraints put down by the fundamental equation. What we must consider is that that explanation is in its rest frame because it is simply not a valid explanation anywhere else and we are not in its rest frame.

Originally Posted by Doctordick

Tell me, does your world view include the possibility of two inertial frames moving with respect to one another? And does your world view include the possibility that an object originally in one frame can be moved to the other: i.e., can acceleration exist?

Certainly acceleration can exist I suspect that more of the problem here is why acceleration moves from one frame to a another how I am understanding this is that after an object has accelerated to a new reference frame in order for use to still use an explanation of the object in its rest frame we must consider that the momentum operators are no longer the same for the object in both explanations, that is our rest frame and its rest frame are no longer the same.

Now my question is what kind of number is the momentum operator that is added as it appears to be just a imaginary number that is needed for the object that is no longer in our rest frame. But wouldn’t an arbitrary complex number also be considered a new reference frame? Would acceleration still move it from one reference frame to the other or will such a reference frame even exist?

It may be that I am just trying to consider modifications that don’t or cannot exist in the fundamental equation.

Originally Posted by Doctordick

The fundamental equation is valid only in the rest frame of the universe. That does not require a unique frame for two reasons; first I defined “time” to be what we know and “the present” to be “a change in what we know”; it follows that “what we know” is continually changing and thus it is entirely possible that the “rest frame of the universe” may change. And secondly, whenever an attempt to explain any specific phenomena is undertaken, great quantities of information concerning the universe are commonly ignored (we work out the problem in a mental environment which clearly presumes a “universe” consisting of considerably less than what is defined to be “The Universe”).

In a sense the question here is, are we explanting the universe or is the universe the explanation. In the former we have no defense for saying if we have a valid explanation. Furthermore, we have no way to know if there is any kind of mapping between our explanation and the universe that we are explaining as we will have elements in our explanation to make it a valid explanation that need not be part of the universe and there is no way to know what the rest frame is as we don‘t know everything about the universe. In the latter case clearly the explanation has a rest frame even if it will move as new information becomes available to us either from realizing that the explanation is not valid or from new information that the explanation is based on becoming available to us. Furthermore any element that is part of a flaw free explanation that we are using is clearly part of the universe in that the universe would be inconsistent without it, which is not possible.

[Doctordick]

Originally Posted by Bombadil

After looking at this some I suspect that I may be considering a couple of things incorrectly. Firstly what exactly the transformation of the fundamental equation that moves it to a new reference frame is. I have been considering this to be any terms that can be added to the fundamental equation so that it is no longer valid. This clearly is not what the transformations that we are interested in are, but rather it seems that what transformations it is that we are interested in is the addition of mass or momentum operators to the fundamental equation.

I am not sure of exactly what you mean by “we are interested in”. We are interested in any transformation which can be defined and exactly how the defined transformation should be performed and what the meaning of the transformed solution is (that depends very much on exactly what kind of transformation one is talking about).

Originally Posted by Bombadil

There is one other issue that I have been having that is, how do we know that the Schrödinger equation tells us anything about the fundamental equation. That is, how do we know that the V(x) term wouldn’t be so complex or in a particular form so that we can no longer use Newtonian mechanics as an approximation to the fundamental equation.

If you examine the deduction of my fundamental equation, you will discover that a very important step in that deduction is the proof that, no matter what patterns the valid elements may have, there always exists a set of hypothesized elements such that the rule will constrain the valid elements to exactly those required patterns. When one makes the approximations required to deduce Schrödinger's equation (doing all the required integration), that self same rule ends up being a function of “x”. Thus the meaning of the original proof is simply that, under the approximations made, there always exists some function of x which will require the behavior of any specific element to obey Schrödinger's equation where V(x) is that function. Is it possible that V(x) could be so complex that we can no longer use Newtonian mechanics? That depends on what you mean by “use Newtonian mechanics”. If you mean, “so complex that we can not solve the problem”; sure, there are a lot of Newtonian problems so complex that solution has eluded the scientific community for centuries. But can that be taken as evidence that Newtonian mechanics is false (false in the sense that even if the approximations used are valid, Newtonian mechanics is still false)? I think not.

Originally Posted by Bombadil

Actually I think that this issue has already been brought up although I didn’t fully realize it or how you where solving it. Simply put it is that since the equation is scale invariant we can look at it on any scale and due to all interactions taking place due to a Dirac delta function, which has only a single point that it is not zero on, this allows us to look at the Schrödinger equation on a scale in which the V(x) function vanishes. Clearly on this scale the approximations, except perhaps the last approximation used to derive the Schrödinger equation, can be justified. From what I can tell the last approximation can be justified if we consider the rest frame of the object of interest.

It seems to me that you are confusing two very different issues here. Deriving the Schrödinger equation and showing that Newtonian mechanics is an approximation to the fundamental equation has nothing to do with any scale issues. Objects are defined to be collections of elements which remain in a coherent structure over a sufficiently long time to be thought of as individual entities. You should understand that one of the major approximations necessary to be made is that the energy of the entities must be approximately given by . That means that the kinetic energy (the energy of motion) must be small compared to : i.e., the elements going to make up that object cannot have net relativistic velocities with respect to the rest frame of the object. This is a fundamental constraint on Schrödinger's equation. That further means that V(x) cannot be so large to generate relativistic Newtonian velocities. The net result is that the collection of elements going to make up objects (such as my mirror assembly) cannot have relativistic velocities relative to one another. It follows that the directions of the individual elements making up the objects are all on essentially parallel paths, moving at v_?. Any deviation from those parallel paths must be small.

Originally Posted by Bombadil

Then the question is vary much given an arbitrary set of elements (the ontological basis), arbitrary in that any particular element is identical so that any differences between elements is part of the explanation and not a property of the elements themselves. How is it that someone can explain such a set of points, that is, how can someone obtain expectations about how the elements will change given only the points.

I think I will go over to Anssi's position on that. We are talking about an epistemological construct to explain a collection of elements which we know nothing about. We have a collection of elements associated with the index t_i. It is the moment we presume persistence (that "element i" in a collection at t_k is the same element as "element i" in a second collection at t_q) that we need to attach a new numerical label x_i in order to assure that these are still individual labels (in order to keep the fact that persistence is a presumption) which can be associated in any manner. This step starts us down that deduction of my fundamental equation.

Originally Posted by Bombadil

What we are in fact doing is mapping such a set of points onto a Euclidean space and using a evolutionary parameter t to ask how might we explain how the system changes with t. But this change is itself part of the explanation and a consequence of new information becoming available and in order for us to conclude what the change is we must correspond elements at one value of the parameter t with elements at another value of t (that is they are considered the same element) and in so doing we conclude that the same elements existed at every point corresponding to a value of t.

I get the impression that you are trying to confuse yourself. There are three steps involved here and you need to understand each of those steps before proceeding to the next. First there is the deduction of my equation (which has to do with explaining an arbitrary past; that is why my first step is to define time). Second, is the proof that Schrödinger's equation is an approximation to that equation. And, third, is the demonstration that the picture requires the same relativistic transformations as does Maxwell's equation. Mixing and mushing with these three different issues is a procedure just crying to confuse you.

I really think that what you are trying to do is to achieve epiphany; trying to get your brain (that source of squirrel thought) to give you solution you don't have to think about.

Most of what you say seems to be so “off the wall” that I don't have the interest to go down those paths. I have discovered a very good reason why our view of the world obeys the laws of physics; I have not discovered a way of creating a world view. As I have said many times, actually solving my equation is beyond possibility (it is that proverbial many body problem). Logical thought is insufficient to the job; only “squirrel thought” (which is beyond logical examination and thus can not be proved to be without flaw) is actually capable of providing even a rough solution. But we can talk about rules that the explanation must obey! And that is the very essence of science.

Actually finding solutions is another problem entirely and I will eventually talk about such things (as I believe there is a simple solution to AI); however, I will not approach that issue until I have communicated my deductions in their entirety.

Have fun -- Dick

[AnssiH]

It is quite late when writing this, but I just wanted to give a quick sign of life here. I have read through the OP and my first reaction was that it seems to make perfect sense, and appears to reach - at least in my mind - quite expected conclusions. Many times, I would have expected that the relationships between isotropic C <-> simultaneity <-> geometry should be clear to everyone at least to the extent of being able to see how changing one definition (or call them postulates) affects the others, but I guess I've been proven wrong on that one many times :I

I also skimmed the responses and indeed seems like most of the reactions are based on little bit poor understanding of where the fundamental equation came from... That's a bit unfortunate but I guess it suffices that people then take that result on faith at first... :I

Anyway, as was the case with Schrödinger, I should still walk through the math in detail, to get an exactly proper view. And once again I will need help with that, so I'll try to get around to ask some questions...

But for now have to hit the sack,
-Anssi