Calculating different time frames

[Sorcerer]

Well i think. This is enough discussion for this topic. Clearly, this question is beyond relativity. So if i have to solve it, i would have to make a new branch of physics with completely different ideas from einstein’s relativity. And i cannot creat this branch.

No. What was done was I solved for v using the time dilation equation. That IS special relativity (and a simplified version at that).To reiterate, here is time dilation solved for v. Plug in values for t and t₀ and see what you get. Here t₀ is the moving clock.

$$v = c \sqrt{ 1 - \frac{t_0^2}{t^2}}$$
I already worked out every step to get to v starting with the time dilation equation. The reason the speed is imaginary when you make the moving clock tick faster is because THAT IS IMPOSSIBLE in special relativity. The moving clock will always tick slower.Edit- I used delta t’s instead of just t and t’ because I like thinking in terms of elapsed intervals of time, but it doesn’t matter since the equations are linear. t, delta t, dt, doesn’t matter. Same result. Moving clocks tick slower.

Edit 2- Oh wait I see what your saying. Yes, a moving clock ticking faster is “beyond” special relativity, in the same way that an apple falling upwards is beyond general relativity (and Newton). Your scenario is simply not possible according to physics as we know it. It requires a speed that is imaginary (a number multiplied by the square root of negative one).

 

[Sorcerer]

Anyway, setting aside the fact that your opening post was an impossible scenario (the moving clock ticking 100 times faster than your local at rest clock- again, moving clocks tick SLOWER not faster), if you flip your numbers so that your clock reads 100 seconds in the interval and the moving clock reads 1 second, you SHOULD be getting a speed very close to c, as I believe two or three people have been pointing out.

That is what time dilation is, and it is more pronounced the faster v is. Or, you can solve for v and say this: the faster v is, the greater difference between t and t’ (with the moving clock seconds t’ < t always).The algebra was worked out step by step earlier, so that should no longer be a confusion. The only issue now is that you originally stated an impossible situation (the moving clock ticking faster than your local at rest clock). And as I’ve said a few times, if you just swap your numbers you get a POSSIBLE situation, and v turns out to be the reasonable value it should be: nearly but less than the speed of light.

 

[PeterDonis]

there is not a very large difference b/w V* and V. But the difference in the Dilation factor is too big. This is the abnormality that i am getting.

It's not an abnormality, it's an obvious consequence of the fact that the formula for time dilation is not linear in velocity. If you think that's an "abnormality", you need to go back and review basic math.

Suppose time for the moving person is normal. But time for the stationary person has slowed down. Its the opposite of time dilation

We can't suppose this because it contradicts relativity, i.e., it contradicts the actual laws of physics that have been measured very precisely in thousands of experiments.

When you do that the speed is imaginary, as I just showed.

"Imaginary" here means "meaningless". There is no such thing.

Clearly, this question is beyond relativity.

No, it isn't. You are just imagining a problem that does not actually exist.

 

[PeterDonis]

The OP question has been answered. Thread closed.