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A colleague questioned an assumption of mine in a recent paper. The assumption was that in the limit as v->c, the result is that t = L/c. This leads to the commonly discussed idea that light experiences zero proper time, and zero proper distance. (by the way, is this a commonly held perspective?) My paper is the first in a series, reasoning that light experiences no passage of time (or space) as it travels, yet due to the "Simultaneity principle", it always arrives at a point L/c into the future from when it was emitted. This value, L/c, is what I'm trying to verify here.

I would like to present my reasoning here as to why that mathematical result is true, and not simply a hand-waving assumption. Your feedback would be helpful. I will start by calculating the value for t' in the limit as v->c. I will then invert the idea to show that t = L/c.

(By the way, I understand and sympathize with many people's feeling that the question of what life is like from the perspective of a photon is a ridiculous question. I agree, mostly, in that it involves undefined quantities and is something that cannot be experienced, or even described, in human terms. This is fundamental. In my current work, however, I find it very instructive in illuminating the nature of light to ask the question "how does light 'experience' the universe?", because the undefined quantities involved lead to some very interesting possible conclusions. So there is my apology...)

Setup: Imagine event A is the emission of a photon from the surface of the sun. Event B is the absorption of that photon by a solar panel on a satellite orbiting Earth.

1) t' = gamma ( t - xv/c^2 )

the unprimed frame represents the sun/satellite system. The prime frame represents time as experienced by a photon (I know...just bear with me, and confirm that my mathematics is correct).

2) in the mathematical limit as v->c, gamma increases without bounds, but we also find that the term in parentheses ( t - xv/c^2 ) goes to zero. this is because t = x/v is the time taken for the light beam to pass between event A and event B (as measured by a satellite-bound observer). So this can be written as ( x/v - xv/c^2 )

3) in the limit as v->c, we can write it as:

x/c * ( 1/beta - beta )

as mentioned, this goes to zero in the limit as beta->1.

4) we can now rewrite the original equation as:

t' = t * (x/c) * ( 1/beta - beta) / ( sqrt( 1-beta^2 ))

5) we can therefore graph this quantity to understand its behavior as v->c. I have graphed t' as a function of beta. (see the attachment). Indeed, t' not only approaches zero as v->c, it HITS zero as v=c, and the point seems to be a well-defined limit. As far as I can see, there is nothing in this mathematical result which prohibits the interpretation that light experiences zero proper time.

That concludes the first step, showing that the value for proper time in the limit as v->c is zero.

If there are no problems with that, I then want to invert the problem.

1) if t'->0 as v->c, then we can use our original equation

t' = gamma ( t - xv/c^2 )

to write:

0/(infinity) = ( t - xv/c^2 ) as v->c

(?right?)

2) obviously, if this is correct, in this case:

t = xv/c^2 has to be true, to make the equation work.

3) finally, plugging in v->c (which is our requirement), this equation approaches:

t = xc/c^2

t = x/c

(or t = L/c)

This result is important, because in the first of my papers I present the perspective that if light indeed experiences zero proper time and zero proper space, the simultaneity effect essentially dictates that each particle of light will always arrive t = L/c into the future from any inertial systems perspective. We cannot truthfully say that light moves from its own perspective (since it has no 'experience' of Time and space), but from an inertial system's perspective it does move, as a result of the simultaneity effect, much like the strings of yarn in the elevator from a previous post. good example!

The point is that light moves through time and space, not because it's experiencing motion, but because reality is refreshed, like a TV screen, according to the simultaneity principle, at exactly the ratio t = L/c. the result is the apparent traveling of a photon at that rate.

This is a very shortened description of the paper. this simple new perspective on light has many possible interesting and profound consequences, which I point out in the papers.

(you can contact me if you want to read the original papers...www.SkyNelson.com)

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# Relativity equation - calculating the algebraic limit

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