Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: gamburch on 06/10/2007 13:57:33
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With Special Relativity all observers see surrounding space as stationary with respect to them. In other systems, for example, a sound source moving through air, a disturbance takes place with respect to the surrounding medium.
From a purely epistemological view Special Relativity is a problem since cause and effect would seem to teach that a disturbance from an object imbedded in a medium would be independent of motion of the object. Because this is not true for Special Relativity, conventional wisdom has been that the concept of a medium must be discarded. It is hard to see, however, how this rather draconian view solves the underlying problem; the classical analogy being something about babies and bath-water. Perhaps there is another way.
Consider a Euclidean four-space with a universal time parameter. Let us define an aether in the space that has elastic and inertial properties so that it makes sense to consider waves in the medium. When an object in the aether causes disturbance, the resulting waves travel with respect to the aether so that we have a situation much like acoustics; but, in four dimensions.
In this four-space let us conceive of a particle (as opposed to the object of the previous paragraph) as a point moving on a path in the four-space. The particle’s size in the three-space perpendicular to its direction of travel is assumed to be small. The path can be in any direction in four-space and, for Special Relativity, need not be curved. The particle travels along this path at the speed of wave propagation in the aether with time determining its position along the path. Since particles traveling more or less in the same direction at nearly the same time can be put together to make observers (all observers are assumed to be collections of particles), we shall consider that all observers are moving at the same rate as a particle, and this rate is the same as signal propagation in the aether.
Since observers communicate with each other with signals traveling at the same rate as their speed with respect to the aether, we must examine the effects of motion of each observer with respect to the aether and each other. Observers following paths in different directions of limited angle with respect to the each other appear to be moving with respect to each other. Since the aether is isotropic and all observers are moving at the same speed with respect to the aether, we should expect each to see the same situation as any other since only their direction of travel is different and the aether is assumed isotropic. This property matches Special Relativity.
Furthermore, since each observer is moving at the same speed as his means of communication in the four-space, the coordinate in his direction of motion is annihilated so that he observes a three-space perpendicular to his direction of travel. This three-space, with its fourth coordinate obscured by being in the direction of travel of the observer, can rotate in four-space to change its direction of motion with respect to other observers. By these means observers see the space of Special Relativity.
My question is this. Is this model suitable to explain Special Relativity? If not, why not?
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Science usually tries to reduce things. This approach is pretty fruitful most of the time. So why to make a model with an extra factor in it? After all - they are ALL models, aren't they?
You would have to expand this idea of yours and to back it up with some maths that would predict things to behave the way they do.
Without some more consolidation it can't go much further than a 'what if' sort of thing.
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Thanks sophiecentaur. As you may have guessed I have written a whole paper about this subject, but its about 16 pages long. Since it remains classical its math is classical too; as in Morse and Feshbach, for example. I'll copy the whole thing to you if you promise to read it and give me feedback.
I do introduce a new factor, that is, a four dimensional space. It's a simple one though, being flat and with a universal time. What is different is the concept the space is viewed by a traveling observer. This gives the space the appearance of a Minkowski space to all observers.
In the paper I show this simple concept gives quantitative explanations for Special and General Relativity, among other things.
Thanks again for your thoughts.
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I will do my best to read it, gamburch.
Can't promise to understand it, tho'.
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My question is this. Is this model suitable to explain Special Relativity?
I believe your explanation is very close to correct. One thing, however: If you look at the Einsteinian equations for relations between the space time of observers moving at speed v in the X direction with respect to each other, which are:
X' = (X - vT)/sqrt(1 - (v/c)^2)
Y' = Y
Z' = Z
T' = (T - (v/c^2)X)/sqrt(1 - (v/c)^2)
you will note the term sqrt(1 - (v/c)^2) popping up frequently. If that looks somewhat Pythagorean, it is, and from this can be derived the "4-distance" between two events, in space time, which has the property that it is constant for all observers. And the "4 distance" is
sqrt([delta X]^2 + [delta Y]^2 + [delta Z]^2 - [c * delta T]^2)
This is the Pythagorean theorem in 4 dimensions with one peculiar twist: The term involving the time enteres not by addition but by subtraction. This means that the 4 dimensional space in question is not Euclidian, but something somewhat different. We must be aware of this when talking about particle paths through such a space; they do not relate the way they would if the space were fully Euclidian.
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I have tried to send a diagram but failed. The following is a description that goes with the diagram I couldn't send. Please note that the little square box was theta in the original, but came out as a little square box in transmission. Let me now describe the diagram. It has two lines, with one vertical and the other inclined to and intersecting the first at the angle theta, or little square box. These two lines with the vertical called A and the second B are the paths of the particles in four-space. A horizontal line is drawn through the point of intersection. The paths have points on them equidistant from the point of intersection with each labeled cdt. The label cdt is the distance traveled by each observer along his world line after the intersection. Another horizontal line is drawn on the diagram above the first horizontal line and through the cdt line on B's path. The distance on this second horizontal line to the path of A is labeled vdt where v is the speed of B as measured=ed by A. Please note the projection of B between the intersection and cdt is cSQRT(1-(v/c)2).
Here is the description of the diagram.
Only a slightly more complex situation arises when we consider that observer B is moving relative to A. By moving relative to A, we mean his direction of travel in four-space is different than that of A. If the angle between their two paths is , A will see B as moving relative to him at the speed v, where v equals c sin, in the three-space perpendicular to his direction of travel. In this case we see that tan = v/(c(1 – (v/c)2)1/2) since sin = v/c. These formulas are most easily verified by noting we are in the frame of A, and, since B is moving relative to A, the length of travel along the path of B during the time interval dt is cdt. The projection back on the path of A by this segment of B’s path is dt’(1 –(v/c)2)1/2. Thus the aether theory yields a simple geometric interpretation of the magnitude of u, the relativistic velocity. It is simply tan, where is the angle between the directions of travel of A and B in four-space. It is to be noted if we observe A from B we get the same result, but with respect to a new three-space perpendicular to B’s path.
I hope all this is clear. Too bad we don't have a blackboard.
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Oops, I forgot to mention that A sees the path of B as cdt'SQRT(1-(v/c)2) thus A sees dt' = dt/cdt'SQRT(1-(v/c)2). This is the same as Specoal Relativity.
Sorry for the carelessness!
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Oops again. Now taking a deep breath.
dt' = dt/(1-(v/c)2)1/2
Also note that I'm learning how to do superscripts