Taedeor I

Logically, time cannot pause completely.

But how about, we slow it down?

Friendly note, don't take this seriously. I'm not qualified for hoc stercore.

Similar to how Einstein worked out time dilation with light clocks and the postulate that light always travels at a consistent speed c, perhaps we can use light to create a scenario in which time seemingly has that the clock of the observer apparently speed up with respect to observers.

Say there are clocks A and B and there are observers there, observers A and B. The goal of the scenario is to have A appear faster than B to B.

I'm making this up as I go along.

Let's set up some limitations. In B's perspective, A must never appear to be faster than light. Violates relativity (especially in the sense that would require infinite energy plus some more and we can't get infinite energy since infinity itself isn't a value per se, but rather a door you can't ever get to).

Another one, energy cannot be created or destroyed. Felt like I had to address this for myself before going forward.

Also, light travels at c and only c.

In a light clock, one tick is when a photon reflects from the top mirror to the bottom one. Here's a light clock right below this:

The diagram on the left shows what a light clock tick would appear to an observer, in this case, B. On the right, that's what A's light clock looks like to A.

The first thing that may come up to someone's mind if the goal was to shorten each tick would be to decrease height h. However, length contraction only works along the axis of motion (according to my understanding) so we cannot decrease h by length contraction since the clock moves along the x axis, or sideways. Not upwards or downwards.

Although, I guess that kind of clock would be interesting...

Hold on.

So if the light clock moved on the axis light traveled on...

I dunno. Too much thinking at the moment.

Anyways, let's quantify (make it into numbers and crap) a tick on the light clock.

d = rt
d/r = t

2h/c = t

That's for the diagram on the right. On the left, let's say that the distance between ticks is L, and the distance the photon travels is D, not d. Totally different.

(L/2)^2 + h^2 = (D/2)^2
(L^2)/4 + (4h^2)/4 = (D^2)/4
L^2 + 4h^2 = D^2

d = rt

sqrt(L^2 + 4h^2) = ct'
sqrt(L^2 + 4h^2)/c = t'

Honestly maybe I should take a special relativity approach. I don't wanna create a gravity field every time I slow time down, I mean, sounds very dangerous. Then again, gravity is perceived as weak because the gravitons escape into higher dimensions, maybe I could use that...

sqrt(L^2 + 4h^2)/c = t'
2h/c = t

4h^2 and L^2 + 4h^2
L^2 was added when the light clock moved, since L was the distance between tick events...

Wait. L is also a value in the left diagram, just as zero... Oh. It seems I've wasted my time here.

WAIT A GURDARN MOMENT MOTHERHECKERS!

WHAT IF... L WAS IMAGINARY?

t' would logically decrease since imaginary numbers squared make negative numbers... Oh, oh yes. It's like subtracting candy from a baby!

Y'know, I've thought of this before but with a different (and personally more childish) approach. I took the time dilation formula, where t' = t/sqrt(1 - (v/c)^2), and made it out so t' is lower than t. The quantity v (velocity) ended up as imaginary. I thought of making time imaginary, but then again, I also thought of distance as imaginary at some point. But how?

Well looks like progress has been made.

But there's the question, how can L be imaginary?

Don't take this seriously.