08-04-2008
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 Understanding  Sponsor | Some subtle aspects of relativity. Will, I am sorry for being unable to present my thoughts in a clear concise manner but I apparently have a somewhat strange way of looking at things. No one seems to comprehend that what I have done is to set up a logical structure designed to provide a representation of any and all epistemological constructs such that they are guaranteed to be flaw free with regard to what is known (what is known being undefined). Everyone presumes I am putting forth a theory of some sort. This is not a theory; it is a logical structure designed to provide a factual guarantee that all expectations expressed in that form are factually flaw free. Surprisingly, the constraint that the epistemological construct be flaw free turns out to have a rather simple representation: the expectations from any flaw free epistemological construct are given by solutions of my fundamental equation: i.e., the probability that a set of ontological elements will be part of the universe of possibilities is given by the squared magnitude of  . That is a fact, not a conjecture! If one were to follow my proof carefully, they would discover the truth of that statement. But no one takes the trouble to do such a thing. I am instead confronted with two classes of people, those who cannot follow my proof because the lack the education in formal logic and mathematics and those who, though they have the education to do so, refuse to examine that proof because they “full well know that it can not possibly be correct”. Well, life is tough all over.Nonetheless, I will attempt to answer the complaints I received from Erasmus00 on my presentation of relativity. At his suggestion I am starting a new thread devoted to clearing up some subtle issues which concern him. The following are my answers to some of his complaints. Quote:
If you doubt that assertion, consider the “plotting of the evolution of primates”. We can do this on a piece of paper, assigning a specific point on the paper to represent a specific primate (where, for the fun of it, we can put drawings of the specific primate being referred to). We can then draw lines between various points which specify the evolution of those primates. I have, in fact, seen just such drawings in many books discussing the issue of evolution, yet no effort is put forth on the idea that such a plot implies a “measure”. Oh, the geometric mechanism of the presentation may have a measure but one can not presume that measure carries over to the plot. A “measure” of the ontological elements being represented by these numerical references must be established in the epistemological construct being represented: i.e., it is possible that some measure might be defined which can be represented by the measure of the geometry, but this is certainly not a necessity. I have defined time, but not the measure of time. I have defined position (as using those numerical references as a set of coordinates in that x,tau space) but I have not defined the measure of that position. I have defined Energy, Momentum and Mass; as specific differential terms of that fundamental equation. And, oh yes, I have also defined one's expectations in terms of the solution of that equation. Unless I have missed something here, I haven't defined anything else! Now one might be tempted to say that I have defined these measures by identifying the Schroedinger equation as an approximation to my equation. But have I? Aren't these “measures”, used by modern physics, defined elsewhere? I don't think these measures are defined by the Schroedinger equation itself at all; they are defined by other arguments and are then presumed to be the correct measures to be used in the Schroedinger equation. Until your epistemological construct defines those measures, they are free variables of the presentation. This leads to some interesting observations, some of which I will lay out for you at the end of this post. Meanwhile, I will return to your complaints: Quote:
To reiterate, it is presumed that we have a specific valid solution to a problem which is expressed in a general relativistically correct representation of reality (using a specific Einsteinian “space-time” representation). We can use a parameterized representation of the paths of every entity involved (having also included a hypothetical clock attached to each and every entity). This leads to five algebraic expressions for values associated with every point in every path of every entity in that specific Einsteinian plot. Einstein's picture only uses four of those for the geometric representation and the fifth becomes a measure of path length (Einstein's invariant interval or “proper time”: i.e., the reading on the clocks themselves). We have here the (specific; correct; valid; unquestioned) solution to a specific problem expressed in a parametric form. All I am doing is re-plotting exactly the same numerical values, which were plotted in the original Einsteinian space time geometry, but in a different geometry. This is no more than an alternate plot of exactly the same information. I plot those paths (which constitute the correct valid solution to the given problem) given by the parametric expressions in a four dimensional geometry consisting of the coordinates x,y,z and tau exactly as given by the explicit parametric expressions yielding the known correct solution. By the way, tau is a real number as used here; I use tau, the time representation of the invariant interval, as the parameter because, in Einstein's picture, the invariant interval along the path of any entity is always imaginary when expressed in spacial terms. That leaves me with the fifth parametric expression associated with every point in every path,  .Now think about what this variable expresses. It is time in the representation which was used by whoever it was that correctly solved that general relativistic problem, and found that specific; correct; valid; unquestioned solution. This surface in his Einsteinian representation represents simultaneity from his perspective. Time has exactly the old fashioned meaning: i.e., things can interact when they exist at the same place and time (forces at a distance can be seen as virtual entities which, through exchange, interact with the primary entities when the entities being exchanged are at the same place and time as those primary entities). This is a concept entirely consistent with the Newtonian perspective. Newton used this variable “time” as a dynamic parameter of mechanical evolution of the structure being examined. Under the assumption that one could set all clocks to agree, Newton represented dynamic evolution in space time diagrams setting space and time orthogonal to one another. Einstein continued this representation in spite of the fact that he knew full well that one could not set all clocks to agree. What I think Einstein missed was the fact that time could still be used as a parameter of the dynamic evolution of his structure (as that evolution is very dependent upon the actual path being taken by each specific entity making up any structure). In view of that fact, how about we use this fifth parameter  as a parameter of evolution just as Newton did (and, I might comment, just as it is used in quantum mechanics). Our parameterized representation of the correct valid solution to our problem assigns a value of t to every point of every path of every entity. Note that this value continually increases along the paths specified in our geometry. Would it not be convenient that this parameter be path length in our geometry? Can we conceive of a geometry where t might be at least proportional to our path length? Does it not seem reasonable to match the relationship between the five variables already expressed in the Einsteinian picture (which we know to be the physically “correct” solution? How about we just rearrange the terms in his expression,  into  implying exactly the same relationship? O'migod, that's the path length in a Euclidean geometry!  Who would have thunk it! Boy, it sure makes for a convenient geometry to consider doesn't it.  Quote:
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Since tau, one of the coordinates of this geometry (a coordinate which, by the way, is exactly what is read on clocks attached to the entities) has no bearing upon the whether or not an interaction can take place it should be clear that, in this geometry, we need some kind of mechanism to project out the differences in the tau coordinate as they bear upon interactions. An excellent mechanism comes to mind: i.e., the uncertainty principal. If the value of this coordinate has an infinite uncertainty (i.e., it is projected out as not a necessary part of our world view) then the momentum in that direction can have zero uncertainty (it can be a quantized variable). And what quantized variable do you think comes to my mind? Well from doing calculations of half lives on unstable particles it becomes quite clear to me that the uncertainty principal relates the uncertainty in rest mass to the uncertainty in tau in exactly the way the uncertainty in position is related to uncertainty in momentum in modern quantum mechanics. Add to this the fact that, for massless entities, the magnitude of momentum is essentially the magnitude of energy (exactly as the magnitude of rest mass relates to energy) and I simply can not comprehend the total refusal to relate rest mass to the momentum of an entity in the tau direction (except that do do so is inconvenient ot Einstein's picture). Look at the similarities. Momentum can be converted into energy; but only when the conversion conserves momentum (a body with momentum cannot covert that momentum into energy without interacting with another body). It's a simple kinematic thing. Likewise mass by itself with nothing to interact with cannot convert that mass into energy because of exactly the same kinds of kinematic constraints. People fail to see the possibility of such a perspective because they all work in laboratories made of mass quantized entities with equipment they use to record these phenomena built entirely of mass quantized entities. So who is hiding what? I have a thought experiment you really need to perform. Suppose, for the fun of it, that I am an individual from a technologically advanced society and I meet with you to show you a couple of devices we have invented. I can't show you why it works the way it does because I, personally, don't know the science behind it; but I do know exactly what it does. The first device looks exactly like what you would see as an old fashion analog pocket watch. It has a dial with three hands which show hours, minutes and seconds, and has a knurled stem at the top which would appear to be for setting and/or winding the watch. But I tell you it is not a watch; it is a one way time machine. When the stem is turned it will move the holder (and the holder only) into the future. When the stem is not turned, the reading on the time machine will read exactly the correct time (we won't worry about relativistic effects here, just assume that, for practical purposes, we live in a Newtonian universe). When the stem is turned, the reading on the face can be advanced. When the reading is advanced, the holder will be moved to exactly the time indicated on the face. The reverse is not possible. It is my understanding that one can not move to the past because doing so would cause paradoxes, but moving to the future will cause no such problems. The question is, if I operate my time machine, what do you see? If you think about it a little, you should realize that, as I turn the stem, I move to whatever time is indicated on the face: i.e., I don't disappear and then reappear at the new time, I instead move through each and every time indicated on the dial. If you look at the face of the device while I am turning the stem, you will simply see the correct time as, whatever time you are at, I am there too (the second hand will appear to advance just as it did when I wasn't touching the stem). You will see me standing very still with my hand on the stem. If I advance the dial one hour while I take one breath (during the breath I turn the minute hand entirely around the face), you will see that breath as taking the entire hour. If my pulse were sixty beats a minute, you could perhaps detect my heart as beating once or twice during that hour (depending of course on how fast I personally am turning the stem). We won't worry about other effects; you could push me but I don't think either of us would like the results. My second device is a toy we make for our children. It appears to be a standard baseball but it is not. It contains exactly the same time machine which I just demonstrated for you; however, it has no stem. Within the ball is a second device which, via internal dynamic effects enables it to know exactly where it is (remember, for practical effects of this thought experiment, we live in a Newtonian universe). When it is moved, the time machine (it and the ball within which it is contained) is advanced in time proportional to the distance it is moved. It is advanced exactly one second for every foot it is moved. Such a ball will display some rather interesting dynamic effects. (For the sake of simplicity, we won't consider rotation; the system is not designed to be rotated as rotation brings up some very complex effects.) Consider two children ten feet apart playing catch with such a ball. From the children's perspective, how long does the ball take to cross the room? Suppose you replace the children with professional baseball pitchers? Then try firing it out of a canon. If you cannot figure out the logical consequences let me know and I will explain (and justify) the results. Another thing you might look at is tying a string to the ball and swinging it is a circle. I think you will find the consequences are quite interesting. Now to a portion of the observations which arise from the measure issue I talked about earlier. My fundamental equation was derived from the necessity of shift symmetry. There is another symmetry inherent in idea of using arbitrary numerical references to the undefined ontological elements on which the flaw free epistemological construct is to be built. That is the existence of scale symmetry: if a given epistemological construct can be deduced from a certain set of numerical labels then the same epistemological construct must be perfectly consistent with those same numbers multiplied by some arbitrary constant. If our expectations are to be given by  as a function of those references (those numbers) then the solution must be scale invariant. Note that, in the original derivation, my fundamental equation is valid only in a frame of reference where the sum of the differentials vanish: however, I show this is not a serious issue because any is easily transformed to a frame where the differentials do not vanish.However, this constraint on a valid frame still leads to one very significant conundrum. If we have a portion of the universe which can be considered as totally independent of another portion and, if the differentials of the two portions do not vanish in the same frame of reference, the resultant fundamental equations can not be asserted to be valid in all three of the possible reference frames. It turns out that this problem is easily solved. If you look at my fundamental equation, is is (sans the Dirac delta function) a simple many body wave equation in four dimensions with a wave velocity of 1/K. The problem is actually identical to problem Maxwell's equation presented to the physics Community. It was solved by what is essentially a scale transformation related to the two different reference frames and exactly the same methods may be used here (in order for all three reference frames to see the same fundamental equation as valid, they must all see it as describing an expanding sphere). This presents a simple algebraic problem which is quite easy to solve. If you need me to do this; let me know and I will show the explicit solution. The most important part of the solution is what is commonly referred to as Lorentz-Fitzgerald contraction. There must be exactly that scale transformation between the two frames (if the two portions of the universe can be considered as totally independent). If they are not totally independent, then the fundamental equation cannot be applied to them separately: i.e., they can not be handled as if they are independent. Seems quite reasonable to me. Also, please notice that the actual “measure” here is still determined elsewhere by some method within the epistemological construct. Notice further that this method, whatever it happens to be is determined independently in each of the three frames (if it isn't then the two portions referred to are not totally independent). My arguments above are only setting a required scale relationship between these portions required by the validity of my fundamental equation. Notice that, in my representation, time is a mere parameter characterizing the evolution of the system: i.e., 1/K is a constant but totally arbitrary factor. In order to relate this to what physicists call time, it is necessary to design a clock in my representation. You can find a specific design of an ideal clock in the physicsforum thread, posts #64 and #66 (again the post is a bit long and required two parts. I apologize for the diagrams being url references and not images. For convenience, I will post the relevant images here: A picture of the ideal clock.  A tau,y cut at the midpoint of the oscillator perpendicular to the x,z plane.  An identical moving clock.  Vector representation of the clock  Analysis of the embedded geometry  Note that, in that presentation, I use “c” as the evolution velocity. Essentially the presentation goes through exactly the same if you use 1/K. The apparent speed of light is actually the ratio of the units used to define tau and the units used to define x,y and z (these are set by the methods used to define them in your “valid” epistemological construct). As I said, the value of 1/K is actually totally arbitrary and though clocks may seem to measure time, the actual “time” (the evolution parameter) is an unmeasurable variable. The apparent velocity of light is set by the methods used to measure x,y,z and tau. It is the assumption that tau along the path of an object is the same as the evolution parameter which yields our standard result of “c”. Note that the real issue in this analysis is that there exists no way to guarantee that your frame of reference is the frame of reference where the differentials vanish (which, by the way, would define a rest simultaneous frame). This is a tad different from Einstein's statement that the physics is independent of that frame of reference (which, I would also comment, we know full well is false). If you doubt that assertion, consider the microwave background radiation from the supposed big bang. So my approach allows one to define a unique frame of reference (in fact, it is valid only in the frame where the sum over those differentials vanish) which simply takes care of the problems inherent in non local collapse of the wave function and some of the other difficulties between relativity and quantum mechanics. Another strange and interesting phenomena arises. Suppose we change the sign of the “space” variables. Since the sum of the differential for the whole of the universe must vanish (or my fundamental equation is invalid), this can make no change in the fundamental equation. If the ontological elements invented to defend the epistemological construct yield a non zero contribution from the Dirac delta functions (which I am convinced is a distinct possibility), the same is not true of t. If the sign of t is changed, the whole equation can be returned to the initial form by multiplying through by minus one except for the fact that the Dirac delta function then changes sign, as the Dirac delta function is defined to be positive even when the arguments change sign. Any place the integrals involved in the transformation to the Schroedinger equation produced an attractive potential, they will now produce a repulsive potential. This fact makes for some other rather important consequences. Have fun -- Dick Last edited by Tormod; 08-05-2008 at 03:47 AM. Reason: Math tag problem | |||||
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08-05-2008
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| Understanding Sponsor | An article on GR and QM Well, I have just read an interesting article in July's “Scientific American”. My complaint with Einstein's theory of relativity is that he mishandles the issue of time and that this is the very issue which has been blocking their attempts to cast general relativity into quantum mechanics. Well, it seems that some European physicists have discovered a subtle trick around that shortcoming. I wouldn't be surprised to hear that they manage to accomplish the task of casting GR into QM, at least they are dealing with exactly the problem in Einstein's theory. I found a couple of the things they say to be very revealing. Quote:
I do have one complaint with one comment in their article Quote:
At any rate, they get around the difficulty with time by making differential elements of their space time agree with the direction of time. This at least inserts an evolutionary aspect to their computer analysis. But it also leads them to the idea of “atoms of space time” (which I suppose are regions where one need not worry about being careful with your definition of time. But it does look like a trick which will work. Have fun -- Dick | |||
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08-08-2008
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 Creating   | Re: Some subtle aspects of relativity. Forgive me for playing catch-up. I have a sincere desire to understand your results Dr. D. It's sounds like you advocate a 5D Euclidean geometry over Minkowski's: Quote:
Secondly, it would help me if you could summarize what t and tau are meant to represent here. I have a feeling you intend them meaning something quite different than I'm used to. Actually, if you used the above to describe the motion of a photon and a massive particle that would be very helpful. Is tau zero for the photon and not zero for the not photon? ~modest ----------------  | ||
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08-09-2008
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| Understanding Sponsor | Re: Some subtle aspects of relativity. Hi modest, it was a pleasure to read your post as it seems to display an honest interest in understanding what I am saying. Quote:
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Suppose both the photon and the massive particle were being sent from Earth to Alpha Centauri (which I will take to be exactly four light years away). For the sake of this discussion, I will presume the massive particle is moving (from the conventional perspective) at a velocity of ten percent the speed of light (I just pulled that out of my hat). Now, the frame of reference I intend to use is a rest frame with respect to Alpha Centauri and Earth. So, in order to make things easy, let us define the “x” axis as being the line from the Earth to Alpha Centauri where Earth is taken to be at zero. To quote my opening post to this thread: Quote:
Since, in my four dimensional frame, tau is what a clock attached to the entity under discussion would read, the photon (who's “invariant interval” along this path is zero) would travel parallel to the “x” axis (the trip does not change its tau value). The massive particle, on the other hand would appear to be moving at ten percent the speed of light so the actual direction of its movement would would have to have a tau component (tau, the clock attached to that entity would have a non zero reading by the time it got to Alpha Centauri). But hey, I'm not there; so suppose I had previously told my partner, now at Alpha Centauri, to return both entities to me at the same velocities and the same momentum with which he receives them (I will presume the time lag for him to accomplish this is zero for all practical purposes. When they get back, I will have enough information to describe their apparent paths. (If I look only at the one way trip, I have to make assumptions which I can not prove.) So let us look at the photon first. It has made a round trip of distance eight light years, so t (its evolution parameter, time in Einstein's picture; in that static frame defined by the Earth and Alpha Centauri) has changed by eight years. The photon is now at the position x=0, y=0, z=0 and tau=0 but t has changed by eight years. I personally have been sitting in my chair on Earth at the position x=0, y=0, z=0 and some tau position. Since my “evolution parameter”,t, my change in position in this four dimensional Euclidean space is given by ct, my tau position must have changed by eight light years (proportional to what the clock attached to me reads). Since the photon and I have exactly the same x,y,z and t we can interact: i.e., the reading on those clocks attached to us or the photon (which yields tau) has nothing to do with our being able to interact. So we will see the photon as going from Earth to Alpha Centauri and back in eight years. What about the massive particle? Well, we have already said that it appears to be going at ten percent the speed of light. That being the case, when it gets back, we will have seen it as taking eighty years: i.e., we will have moved in the tau direction eighty light years. The massive particle is also back to x=0, y=0, z=0 and tau= some value (again remember that tau has nothing to do with our ability to interact) and the path length it has traveled must be eighty light years long. Being a massive particle, we know it's change in tau position is not zero nor is it eighty light years, it has traveled a total of eighty light years in some diagonal direction (forty years out and forty years back) where  (again, its path length being given by ct). Solve that for tau and one has  years. So an ideal clock attached to the massive particle will read 79.6 years for the round trip. Note that, in Einstein's picture, the massive particles “clock” runs slow by a factor  or exactly 79.6 years for the round trip.The above analysis is essentially the analysis I was trying to get Erasmus00 to perform when I gave him the thought experiment below. Quote:
As I have said, all we need is a mechanism to project out the tau dimension and the results become absolutely identical to standard relativity. Quantize the momentum in the tau direction and “wallah” the uncertainty principal performs the projection and the two pictures give exactly the same results for any conceivable circumstance, Since the picture is of quantized massless entities in a four dimensional Euclidean universe, it turns out that all exchange forces (even those mediated by massive exchange particles) are ruled by exactly the same factors demanded by Maxwell's equation in three dimensions (i.e., photon exchange) so one also obtains exactly the same Lorentz-Fitzgerald contraction for any stable structure concievable. So it is just a different way of looking at exactly the same thing; however, it has some very powerful advantages over Einstein's picture. First of all, time has become a parameter of the dynamics, not a dimension of the geometry (we are back to Newton's use of time as an evolution parameter) a perspective which is one hundred percent compatible with quantum mechanics from the get go. Secondly, we are dealing with a Euclidean universe where every entity travels at exactly the same speed. This has some important subtle consequences. According to established authority, Einstein proved that "a reduction of gravitational theory to geodesic motion in an appropriate geometry could be carried out only in the four-dimensional space-time continuum of Einstein's relativity theory". If that statement were actually true then he certainly has strong support that his picture is worth the effort (I don't think anyone would refer to GR as a trivial intellectual exercise); but, the real question is: is it true? Maupertuis is credited with the proof no such transformation existed in a Euclidean universe; however, that proof revolved around the fact that different initial velocities yielded different trajectories: i.e., different geodesics. In the picture above, which is totally in conformance with all conventional experiments, this difficulty does not exist as “different velocities” do not exist. General Relativistic transformations yielding gravitational geodesics are relatively easy to deduce in this picture and once again, they are entirely consistent with quantum mechanics from the get go. Last, but not least, my fundamental equation (which is deduced entirely from fundamental definitions and symmetry principals) results in exactly the picture given. What more can one ask? I hope you found that presentation clear. If you have any questions you know how to reach me. Have fun -- Dick Last edited by Doctordick; 08-13-2008 at 01:18 PM. Reason: left out a "t" on the LaTex tag "sqrt" | |||||||
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08-11-2008
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 Thinking | Re: Some subtle aspects of relativity. Quote:
 is a measure of total distance that has been traveled in time t . That is, we always travel tc distance where dx dy and dz are the infinitesimal change along that axis in a three dimensional plane and  is the distance traveled along the  axis which is also experienced as time.I’m not sure but the statement that is what a clock will measure still has not been proven?Quote:
coordinate of an object, or that no mater what the coordinate is that the object having it will always act like it is at the same coordinate as the object it is interacting with?Also, corresponded to mass so does this mean that there is no uncertainty in the mass of an object?Also, I’m not quite sure what you mean by Quantize the movement in the dimension?Quote:
If I understand this correctly it is the second one that is correct. That is, we want a function that both sides of the fundamental equation can be multiplied by, so that no matter what the sum of the differentials sum to, we get the same equation. It seems that due to shift symmetry that such a function can’t be a function of the variables. But how do we know that such a function is a constant and is not a function of the differentials? Quote:
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08-13-2008
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| Understanding Sponsor | Re: Some subtle aspects of relativity. Quote:
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In essence the problem arises because of the fact that there exists no mechanism to prove you are in a frame where the velocity of light is the same in both directions. This is exactly the problem brought up my Maxwell's equations and the null result of the Michelson-Morley experiments; the conundrum which lead to the solution proposed by Einstein (actually it is the Lorentz-Fitzgerald contraction which solves the problem; the issue Einstein explained was, “why the Lorentz-Fitzgerald contraction was universally necessary”). I show that scale symmetry together with my fundamental equation demands that Lorentz-Fitzgerald contraction is universally necessary. Quote:
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Notice that what the standard relativistic picture sees as "time distortion" in the moving object just doesn't exist in my picture because I regard time as an "unmeasurable" variable. Go look at my ideal clock in that earlier post; so long as acceleration is not included, it measures change in tau exactly (just as does an ideal clock in Einstein's relativity). If one goes to GR, life gets a little more complicated because no ideal clock can be designed with no physical extent; however, the issue is still solved in a very simple manner. I notice that you have not commented on my geometric proof. I assume you now understand the proof but there are a few important aspects of that proof to be pointed out; hope you haven't decided there is nothing more to be said. Have fun -- Dick Last edited by Doctordick; 08-20-2008 at 01:19 PM. Reason: Error correction | |||||||||
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08-19-2008
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| Thinking | Re: Some subtle aspects of relativity. Quote:
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Now I’m wondering if this has any connection with the effect that the  and  operators have when on there own in the fundamental equation.Quote:
Would I be correct in understanding that the equation that you are using is arrived at by modifying an equation from special relativity and you have simply rearranged it into a more convenient form for what you are doing with it? | ||||
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08-19-2008
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| Creating | Re: Some subtle aspects of relativity. Because the initial post is quite long, I'm attempting to comment things I think get to the heart of my objections rather than discuss all the ideas presented- if you feel I've missed something crucial, please highlight it for me. Quote:
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