Time Travel Equation for Case B

[Shubh Goel]

TL;DR Summary

Assuming travelling at speed of light is possible.
If i leave earth at the speed of light, two things will happen:
A. On observing earth, i will see that time has
freezed on it and if i go faster then I will
observe time going backwards.
B. For those on earth, as the observers see
me, they will see me traveling at speed of light
but there will be a time difference in which
they see me and one in which i am. I will have
already done what they see.

For case B-
Conditions:
1. The observer was observing since the time they were in contact.
2. There are only 2 directions for motion: back and forward.
3. Relative velocity is not equal to zero.
4. Bodies are moving away from each other
Time difference = t
Relative velocity = v
Distance between position of source of the beam of light the observer is seeing and the observer= x
C= speed of light
The equation comes out to be T=vx/c^2

 

[vanhees71]

Travelling at the speed of light is impossible for any massive object. For any massive object it makes sense to define a relative velocity which by definition is the velocity of the one body in the (instantaneous) rest frame of the other.

Since a massless particle has no rest frame, it doesn't make sense to define a relative velocity among two massless particles.

The relative velocity of a massless particle and a massive one is again the velocity of the massless particle in the (instantaneous) restframe of the massive one, and its magnitude is always $c$.

 

[Shubh Goel]

The first line of post is assuming attaining speed of light is possible and if we just assume that there is no phenomenon of increasing mass with increase in speed, is the theory still valid? I just want to clarify that its not some serious equation. It's just for an ideal world. Can you tell if the equation will be valid in that case?

 

[weirdoguy]

The first line of post is assuming attaining speed of light is possible

But you've been already told, that it's impossible according to our laws of physics. So we have no basis to discuss it.

if we just assume that there is no phenomenon of increasing mass with increase in speed

Mass is usually defined in a way that it is constant, independent of speed, so we don't have to additionally assume it .

 

[Ibix]

The first line of post is assuming attaining speed of light is possible and if we just assume that there is no phenomenon of increasing mass with increase in speed, is the theory still valid? I just want to clarify that its not some serious equation. It's just for an ideal world. Can you tell if the equation will be valid in that case?

You have two options: non-relativistic physics and relativistic physics. In the former you may describe traveling at the speed of light, but there are no effects on time and the entire approach is wrong above small fractions of lightspeed anyway. In the latter you cannot describe the experience of traveling at the speed of light, full stop. This is not an engineering problem that we might one day overcome - it's something that is directly forbidden by relativity. Any attempt to describe "what you would experience if you were traveling at the speed of light" necessarily involves self-contradiction somewhere and is therefore nonsense.

There is no "ideal world" in which you can travel at the speed of light. 99.999999%, yes, if you want, although the technology to do it isn't available. But not the actual speed of light.

 

[Dale]

@Shubh Goel as you have been informed we cannot have a discussion about relativity assuming something with mass can travel at c in an inertial frame. There are two options:

1) I can close the thread since we cannot discuss the question you want to ask

2) You can choose to discuss a close alternative where the massive object is moving at slightly less than c in some inertial frame

Please let us know your preference.

 

[Shubh Goel]

@Shubh Goel as you have been informed we cannot have a discussion about relativity assuming something with mass can travel at c in an inertial frame. There are two options:

1) I can close the thread since we cannot discuss the question you want to ask

2) You can choose to discuss a close alternative where the massive object is moving at slightly less than c in some inertial frame

Please let us know your preference.

I will prefer option 2 please

 

[Shubh Goel]

If we move close to speed of light, will the equation work?

 

[Ibix]

If we move close to speed of light, will the equation work?

Since you give no derivation it is difficult to tell. Your interpretation is odd, though. There is always a delay before someone sees an action you have takenn and even if you are stationary with respect to me and just one meter away, it takes light informing me of something you did about 3ns to reach me. Most relativistic maths assumes you've corrected for this delay. No time travel comes out of this at any speed.

Post the derivation of your formula (you will probably want to read the LaTeX Guide linked below the reply box so that your maths is readable) and we can see what you've done.

 

[Shubh Goel]

Since you give no derivation it is difficult to tell. Your interpretation is odd, though. There is always a delay before someone sees an action you have takenn and even if you are stationary with respect to me and just one meter away, it takes light informing me of something you did about 3ns to reach me. Most relativistic maths assumes you've corrected for this delay. No time travel comes out of this at any speed.

Post the derivation of your formula (you will probably want to read the LaTeX Guide linked below the reply box so that your maths is readable) and we can see what you've done.

 

[Shubh Goel]

My equation was wrong. Sorry for wasting your time guys. Can someone tell me what is the correct equation for relation between relative time for object traveling at high velocities.

 

[Ibix]

My equation was wrong. Sorry for wasting your time guys. Can someone tell me what is the correct equation for relation between relative time for object traveling at high velocities.

Remember that this is relativity theory - and here "relativity" means that you can always regard yourself as being stationary. So there isn't a formula for anything "travelling at high velocity" because there's no absolute meaning to that phrase. However, someone may be moving at high velocity relative to some other object. In that case, both will measure the other's clock ticking once for every $(1-v^2/c^2)^{-1/2}$ ticks of their own clock. (If this seems contradictory, then you need to look up the relativity of simultaneity). As I noted in your (now locked) other thread earlier, this formula assumes that the two objects correct for the changing light travel time due to the changing distance between them. If they do not do that, they will (literally) see the other's clock tick once every $\sqrt{(c+v)/(c-v)}$ ticks of their own clock (here $v$ is positive if they are moving apart, and I am assuming no tangential motion).

 

[Shubh Goel]

Thank you! I understood parts of it but i guess i got to study relativity from scratch.

 

[Ibix]

Be very careful with online sources for learning - there's a lot of nonsense out there. My usual recommendation for a book is Taylor and Wheeler's Spacetime Physics, the first chapter of which is free online if you want to have a look. @PeroK always recommends Morin's Special Relativity For The Enthusiastic Beginner. And former mentor here @bcrowell wrote a couple of texts which are free to download from here (proper text on Special Relativity) and here (non-mathematical introduction to relativity that's fairly honest about what you can understand without maths). I gather that Khan Academy's stuff is pretty good if you prefer videos, but I've never watched their relativity courses.

 

[PeroK]

The first chapter of Morin's book is available here:

https://scholar.harvard.edu/files/david-morin/files/relativity_chap_1.pdf

 

[jedishrfu]

OPenStax.org free physics books have chapters on Special Relativity:

Here's one chapter from their College Physics AP book:

https://openstax.org/books/college-physics-ap-courses/pages/28-1-einsteins-postulates

They also have a non-calculus version called College Physics and a series of 3 books called University Physics for freshman college courses. Each should also have chapters on Special Relativity with different depth levels.