Tuesday, March 17, 2015

Why Can’t Anything Move Faster than the Speed of Light?

Special relativity postulates that the speed of light, c, is constant and frame of reference independent. We also learned that c is the speed limit of the universe. The explanation given is that the mass of an accelerated object approaches infinity as it approaches the speed of light, thus an infinite amount of energy would be required to accelerate even the smallest particle to c . Moving faster than the speed of light would violate causality according to Einstein.

Quantum-geometry dynamics agrees that the speed of light is the maximum speed of any object. The difference is that the constancy of the speed of light is not a postulate of QGD, but a consequence of the structure of space and matter. The maximum possible speed of an object is imbedded in QGD’s definition of speed; itself derived from its axiom set (see Introduction to Quantum-Geometry Dynamics).

According to QGD, all particles and structures, including particles we consider fundamental, are made of preon{{s}^{\left( + \right)}} bound by gravitational interactions which at their scale are immensely greater than gravity (see derivation of gravitational interaction in An Axiomatic Approach to Physics). Also, preon{{s}^{\left( + \right)}} are kinetic particles whose momentum is fundamental. We represent the momentum vector of a preo{{n}^{\left( + \right)}} by \vec{c} and its momentum as the magnitude of its momentum vector or \left\| {\vec{c}} \right\| . Preon{{s}^{\left( + \right)}} are also the fundamental particle of matter and according to QGD are the fundamental units of mass. The mass of a particle or structure is then simply equal to the number of preon{{s}^{\left( + \right)}} it contains.

The momentum of preon{{s}^{\left( + \right)}} is fundamental and is thus the same whether it is free or bound. The trajectories of bound preon{{s}^{\left( + \right)}}are contained within a particle or structure, that is, the orientations of their momentum vectors may change but never their magnitudes which correspond to their momentums.

From the above, the momentum of a particle or structure is simply the magnitude of the vector resulting from the sum of the momentum vectors of their component preon{{s}^{\left( + \right)}}. That is: \displaystyle \left\| {{{\vec{P}}}_{a}} \right\|=\left\| \sum\limits_{i=1}^{{{m}_{a}}}{{{{\vec{c}}}_{i}}} \right\| where {{\vec{P}}_{a}} is resultant vector or momentum vector of a particle or structure a and {{m}_{a}} is its mass which as we have explained is the number of preon{{s}^{\left( + \right)}}in a .

From this we can define speed simply the ratio of the momentum of particle or structure over its mass. That is: \displaystyle {{v}_{a}}=\frac{\left\| \sum\limits_{i=1}^{{{m}_{a}}}{{{{\vec{c}}}_{i}}} \right\|}{{{m}_{a}}}. Let us take a bit of time to consider this definition of speed.

One of the first things we may notice is that it makes no use of the relational concept we call time.

It is also an intrinsic property of a and is entirely independent of frame of reference. Because speed is an intrinsic property, it may also be understood as absolute and independent of the speed of the source.

Using this definition of speed, we find that the maximum possible speed of a occurs when its momentum is at its maximum. The maximum momentum of a is when all momentums vectors of its component preon{{s}^{\left( + \right)}} move in the same direction. It this case, we have the maximum possible speed is \displaystyle {{v}_{a}}=\frac{\left\| \sum\limits_{i=1}^{{{m}_{a}}}{{{{\vec{c}}}_{i}}} \right\|}{{{m}_{a}}}=\frac{\sum\limits_{i=1}^{{{m}_{a}}}{\left\| {{{\vec{c}}}_{i}} \right\|}}{{{m}_{a}}}=\frac{{{m}_{a}}\left\| {\vec{c}} \right\|}{{{m}_{a}}}=c which as we have seen to the fundamental momentum of a preo{{n}^{\left( + \right)}}. It is not surprising then that when applying the definition speed to a single preo{{n}^{\left( + \right)}} we find {{v}_{{{p}^{\left( + \right)}}}}=\frac{\left\| {\vec{c}} \right\|}{1}=c. Therefore, the speed of a preo{{n}^{\left( + \right)}}is numerically equivalent to its momentum.

We can thus assume that, if QGD’s prediction that photons are made of preon{{s}^{\left( + \right)}}, their momentum vectors must point in the same direction and thus the speed of a photon \gamma is \displaystyle {{v}_{\gamma }}=\frac{{{m}_{\gamma }}\left\| {\vec{c}} \right\|}{{{m}_{\gamma }}}=c. It follows the speed of light and the maximum speed of a particle or structure are one and the same quantity and is equal to c.

It is worth noting here that according to QGD the energy of a particle or structure is given by {{E}_{a}}=\sum\limits_{i=1}^{{{m}_{a}}}{\left\| {{{\vec{c}}}_{i}} \right\|}={{m}_{a}}c . It follows that for particles such as photons that move at the speed of light, \left\| {{{\vec{P}}}_{a}} \right\|={{E}_{a}}, that is, their momentum and their energy are numerically equivalent.

From the above explanation we understand that nothing can move faster than light because nothing can move faster than its component preon{{s}^{\left( + \right)}}  , but then why don’t preon{{s}^{\left( + \right)}}  move faster or slower? Since faster or slower preon{{s}^{\left( + \right)}}  would mean a higher or lower speed limit, what sets their speed to exactly c ?

According to QGD, aside from preon{{s}^{\left( + \right)}}  , there exist only one other type of fundamental particles. QGD predicts that space is discrete and made by fundamental particles we will call preon{{s}^{\left( - \right)}}  . Preon{{s}^{\left( + \right)}}  , the fundamental unit of matter, travel through space by leaping from preo{{n}^{\left( - \right)}}  to preo{{n}^{\left( - \right)}}  . The leap between two preon{{s}^{\left( - \right)}}  is the fundamental unit of displacement or fundamental unit of distance. So the speed of a preo{{n}^{\left( + \right)}}  is fundamental and corresponds to the speed at which it makes a preonic leap. A preo{{n}^{\left( + \right)}}  can only move by one leap at the time so the speed at which it moves is imposed by the discrete structure of space itself and that speed so happens to be c .

This is explained in detail in Introduction to Quantum-Geometry Dynamics.

Suggested reading:

Locality, Certainty and Simultaneity under Instantaneous Interactions

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