Science Forums 2

[Doctordick]

Sorry about being so slow to answer. At 3:30 AM Saturday March 28 we got a telephone call that my wife's mother's house had been struck by lightning and was burning. At four o'clock we were packed and headed to the gulf coast. We had intended to be there for a couple of days but ended up staying two weeks dealing with the insurance and arranging for a place for her to stay until the house was rebuilt. Believe me, cleaning up after a major fire is no simple matter.

Originally Posted by Bombadil

Then c, that is the speed of light, is only a limiting speed when the objects can be considered separately, when they can’t be considered separately c is no longer a limiting factor?

You seem to miss the central issue here. I have “defined” the past to be what you know; the the future to be what you do not know and the present to be a specific change in what you know. I then introduced the tau axis for the simple purpose of allowing the undefined data (the past) to be representable by a set of points in a Euclidean space. The parameter “t” is then no more than a reference parameter referring to a specific “present”. Through symmetry arguments I showed that any function capable of producing your expectations (your explanation of that past) would have to obey my equation so long as the momentum of the entire universe was zero in that Euclidean reference space (momentum being defined in my presentation).

Now, I have shown Schrödinger's equation to be an excellent approximation to my equation so long as the velocity of objects (also defined in my presentation) are small with respect to “c” and Schrödinger's equation has been studied extensively for many many years. Anyone competent in physics would recognize my fundamental equation as an n body equation of interacting point elements lacking mass (analogous to a wave equation with quantized interactions).

It follows that the equation results in an undefined speed (undefined because the parameter “t” is not a measurable element) for “non-interacting” elements. Thus it is that any “object” is most definitely limited to travel at less than that speed (after integrating out the dependence on tau all that is left is the apparent velocity orthogonal to tau). When the elements cannot be considered separately then the collection certainly is limited to be less than or equal to c (equal to c when every element is moving orthogonal to tau).

Originally Posted by Bombadil

So only when a object can be considered to be separate from any other object of interest can we consider the Dirac delta function to have no effect so that we can consider an expanding sphere of the probability wave for the object?

I am afraid it is a little worse than that. Not only must it be separate from any other object (the argument of the Dirac delta function cannot vanish for any other element: i.e., for any i) but you must know the exact position of the element we are talking about (it is known to be at zero in both frames when t=0 by definition of the problem we are examining)

Originally Posted by Bombadil

I don’t understand what the relevance of the energy associated with the momentum having to be positive is, but will the energy have to be positive due to energy being associated with the derivative to t, which due to it being defined as nothing more then a evolution parameter must be positive.

As I said, the equation is being related to the n body equation of interacting point elements lacking mass (the common physical meaning attached to such an equation). In such a representation, momentum in the positive x direction is taken to imply exactly the same energy and as does the same momentum in the negative x direction. In exactly the same vein, when I set momentum in the tau direction to be mass, the energy associated with positive mass (momentum in the positive tau direction) would be exactly the same as the energy associated with negative mass (momentum in the negative tau direction). In fact, energy of an element is, in my picture, no more or less than the magnitude of the momentum of that entity the same as one would expect in a universe consisting entirely of photons.

Originally Posted by Bombadil

Will this define a measure along the t axis seeing as it is just an evolution parameter? Or will it define t only if we have defined the value of .

There is no “t axis”; “t” is a simple parameter identified with a change in our knowledge. Defining “t” and defining are opposite sides of the same coin.

Originally Posted by Bombadil

So then, can movement in any other direction be dealt with simply by considering the additional distance that the oscillator will have to move in the direction of movement?

Yes, it is no more than a problem in analytical geometry and exactly the same answer will be obtained.

Originally Posted by Bombadil

So is the time dilation due to space dilating while distance for the moving frame is still defined in the same way although it has been scaled for an observer not in its rest frame.

Time does not “dilate”; neither does space “dilate”. The “apparent dilation” is entirely due to the mechanisms we use to establish our measures. Our explanation of the universe needs to be internally self consistent; that, and that alone, is the fundamental “?cause?” of the relativistic transformations.

Originally Posted by Bombadil

Do we have to use the inverse transform here because we are moving in the opposite direction as to what we assumed to be transforming to in the first place?

Here I get the definite impression that you simply don't follow what I am talking about. The whole thing is the issue of observing physical phenomena with measures defined in a specific frame. If we look at Jones' measurement of a specific phenomena we have to transform our measures to his measure. If we look at a specific measurement performed by Jones and how that measurement looks in our frame, we use the inverse of that same transformation.

You have to think these things out carefully in detail. The idea that space and time change “physically” is little more than a rule of thumb for performing transformations between numerical results of performing experiments from different frames of reference. What actually happens has nothing to do with your frame of reference. It is the internal consistency of your explanation (which is almost always based on some frame of reference) which leads to these transformations.

Originally Posted by Bombadil

So then this is due to both observers using the assumption that the speed of the oscillator that their clock uses has a constant speed.

Not really; it is the assumption that the speed of the oscillator that their clock uses is the same in all directions which generates the problems. It arises directly from the fact that there exists no self consistent way of defining simultaneity except when the distance between the events of interest is zero; essentially the concept “time” is meaningful only at the location of the entity defining it.

As I have said many times, if “existence at the same time” is what defines interactions, then “time is not a measurable variable”. If, on the other hand, “time is what clocks measure” is the definition of time, then time has nothing to do with whether or not things can interact (think about the twin paradox). Physicists problems arise because they use two conflicting definitions of time as if they are equivalent (they can only do this by defining what is called simultaneity, a concept which requires a preferred frame of reference).

Have fun -- Dick