Science Forums 2

[Bombadil]

Originally Posted by Doctordick

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).

So then t is nothing more then a way of telling if two or more elements can interact and is not an axis that is moved along. That is elements can interact if they try to occupy the same location at the same value of t.

Also didn’t you at the same time require mass to sum to zero in order for the fundamental equation to be valid which would also mean that the total energy must be zero. In both of these cases is a positive value the only possible value resulting in all elements having a zero mass and momentum? The energy must of course then be zero in order for equality to hold.

Originally Posted by Doctordick

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).

But wouldn’t even an element that is not interacting with other elements have to have interacted with other elements in order to be known which implies that at some point it had a defined speed and that if an element interacts at some future time that its speed can be defined during the time that it wasn’t interacting or does it only have a defined speed while it is interacting with other elements?

Either way if I’m understanding this right during the time that an element has an undefined speed (that is it is not interacting with any other elements) it can’t travel a distance that would suggest that it traveled faster then c during the time that its speed was undefined.

Originally Posted by Doctordick

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.

So the momentum associated with an element traveling in the positive direction is the same as that which is associated with an element traveling in the negative direction and weather the derivative is positive or negative has no effect on the value of the momentum?

Also the mass sums to zero in fact all elements have zero mass so that the momentum is the only source of energy in the equation. I have to wonder at this point how this fits with what we normally call mass and how it relates to what you have defined as mass? I wonder because if no element has mass then it seems that no object that is constructed of elements can have mass but nonzero mass is commonly used in Newtonian physics (in fact I can’t think of what you would do which would use a zero mass) and you have shown that Newtonian physics is an approximation to the fundamental equation so how are these related?

Originally Posted by Doctordick

Again, as all velocities along our displacement vectors are v_?, d₁+d₂=S. It follows that, from the perspective of our rest frame, this is exactly or, solving for S,

.

Here, are you still using the definition for the value of sine in the above equation, I think that you are? If so I’m not quite sure how you come to the choice of theta, I think how you do is that S is the total distance that the object has traveled which is the same as the distance that the oscillator has traveled which could be wrote out as while the y axis is the distance that the object has traveled do to its velocity which can be wrote out as using these we arrive at the same value of as you have previously defined. But is the proper thing to use here or should t be used. I think that as measured by the rest observer is the proper thing to use here although I think that this is equivalent to the value of t.

Originally Posted by Doctordick

During this time the observer will have moved a distance of . He however will call this distance (based upon his personal measurements of length and his perception of what he has measured) and will assume that the clock has receded from him by that distance. Since, as far as he is concerned, his standard clock is correctly measuring time, he will read the elapsed time between the received signals as . He will therefore see the clock as receding from him at a rate given by

and everyone agrees as to the relative velocities. I need to point out that, as these two observers do not agree about either their distance measurements nor their time measurements one should find this agreement with regard to relative velocities somewhat surprising (it is not really a trivial issue).

Here I’m not sure I understand your use of instead of as this seems to be how distance is scaled for a moving observer. Unless this is the transformation used to find the length of the observer in the rest frame in which place we would find the distance that the observer would measure between him and the clock by multiplying the distance in the rest frame by .

Also, do you mean that the speed that the observer measures for the speed that the clock is receding from him is the same as what his speed moving away from the clock is measured to be in the rest frame?