Zero And Special Relativity
A Limit At The Speed Of Light?
In Einstein's 1905 papers, along the way to deriving E=mc2,
he uses the Lorentz Factor in a variety
of different cases. This term is as important in Special Relativity as the
better-known mc2 part of the equations. It describes the
relationship between moving bodies. v is velocity and c is the speed of
light.
The Lorentz factor contains both Type 1 and Type 2 infinities:
Infinity Type 1 is v2
/ c2 in that we can make v as close to c as we like, in
infinitesimally small increments.
We can also vary v to be infinitesimally close to 0 as we like, but we
will ignore this as it does not lead to a Type 2 infinity.
Infinity Type 2 is
when v=c then 1 / sqrt(1 - (v2 / c2)) = 1/0.
Type 2 infinity is never generated when zero is viewed as { } because
zero is treated as null or "nothing" and the division is
"incomplete".
When we view zero as null, then in contrast to the conventional view,
when v=c the result of 1 / sqrt(1 - v2 / c2) is
null, not infinity. This has implications only exactly at velocity
v=c.
"Velocities greater than that of light have -- no possibility of
existence."
When Einstein made his famous prediction[2]
it was based on the acceleration of an object from rest toward the speed
of light governed by the following equations, which include the Lorentz
Factor:
Einstein understood this to show ever-increasing energy approaching the
speed of light and infinite energy at the speed of light. So
when v=c:
W = mc2 * infinity
There are some problems with this interpretation:
(a) If v=c is outside the scope of the equation then this becomes mc2
* null.
(b) Photons do not accelerate to the speed of light; they
travel at the speed of light - the speed of light is constant.
Dealing with this in the same context as an accelerating object is
misleading. We are dealing with two separate classes of objects –
those travelling at the speed of light and those that aren't.
(c) Einstein's interpretation actually shows that nothing can travel
at the speed of light, using the Lorentz Factor in this form.
This led to the prediction that photons must be mass-less, else they
would require infinite energy to travel. This prediction has had to be
tweaked and twisted in order to maintain the illusion that if it had
mass it would require infinite energy.
(d) The equation does not permit for v > c, not just because of
infinities, but because it requires the square root of a negative number
– i.e. an "imaginary number". This may be overcome by changing
the equation, but illustrates that the Lorentz Factor is into
"uncharted territories". This "no go zone" actually
begins at v = c although it is not immediately obvious until v > c.
This is not to say that the speed of light is not a limit, but it
cannot be for the reasons Einstein stated.
Einstein and Infinity
Einstein's views on zero, infinity and division by zero were a product
of his education and his times, which were dominated by Euclidean Geometry
and Newtonian physics. I.e. 1/0 = Infinity and Infinity-1 = Infinity.
From Discover
Magazine "The Master's Mistakes"
http://discovermagazine.com/2004/sep/the-masters-mistakes/
'To Einstein, infinity was no answer at all - it was a failure...
... To Einstein, a statistical probability was even less acceptable than
the infinities of a singularity. A physics that could not predict
individual events was no physics at all, he said. It was, at best,
guesswork...'
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