# B Traveling backwards through time: clarification please

#### MikeeMiracle

Summary
I am looking for some clarification for was is meant by "if you could travel faster than light you go travel backards in time." It seems to be a pop sci-fi reference.
I am 99.99% sure I am correct but would like some clarification from the other members here. I occasionally read that "if you could travel faster than light you go travel backards in time." This statement does not make sense to me and seems to be a misinterpritation of reality.

I will provide an example, let's say I throw a ball to my left and then instantaneously (FTL) travel several miles away with a telescope and look at myself. As far as I am concerned I would see myself start to throw the ball to my left. This is not time travel per se, it is just a delayed image of what has happened due to the time it takes for the light to travel from my previous spot to where i threw the ball to the spot where I ended up after instantaneous moving away to see myself.

True time travel would allow me to remain at the same location and I could concievably then decide to instead throw the ball right instead of left, thus I have "changed" the present if you like and create a paradox. As far as I am aware this is not theoreticaly possible, is that correct?

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#### Orodruin

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and then instantaneously
The crux is here, in the word "instantaneously". If something teleports instantaneously in one frame, then there is another frame where this means that the object appears at the new position before it disappears at the original position. There is also a frame where the object disappears and then it takes some time before it reappears at the new position. This is all due to the relativity of simultaneity. Regardless, if this type of FTL travel were possible, then it would be possible to arrange for having something sent back in time (as in "reappearing in the past light-cone of the disappearance event") by repeating the process in a particular manner.

#### MikeeMiracle

Does that mean I could merely "see" the present in the past of the light cone or actually influence events in the past light cone, I guess that is the question.

#### kent davidge

Does that mean I could merely "see" the present in the past of the light cone or actually influence events in the past light cone, I guess that is the question.
The events causally connected to you, that is, the events that you influenced in the past or that you can influence in the future are all "time-like" separated from your current location "now", which means that those in the future will remain in the future in any frame, whereas those in the past will remain in the past in any frame, all of that relative to their "now".

#### Heikki Tuuri

This was discussed at Physics Forums a month ago. Nobody found a good link to literature.

If you can do faster-than-light travel at any speed relative to any inertial coordinate frame, then you can travel to your causal past. That is easy to show.

If you can only travel faster than light relative to a single inertial frame, you cannot travel back in time relative to that frame. You cannot travel to your causal past.

#### Orodruin

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Does that mean I could merely "see" the present in the past of the light cone or actually influence events in the past light cone, I guess that is the question.
You would be able to affect things in your past light cone.

#### Orodruin

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If you can only travel faster than light relative to a single inertial frame, you cannot travel back in time relative to that frame. You cannot travel to your causal past.
... which would break the assumption of no frame being special.

#### MikeeMiracle

Ok, it still seems terribly counter intuative that I could influence past events in the light cone but I accept the answer. For example, it's easy to comprehend acceleration in a spacial dimension, but I guess here we are talking about accelerating faster than light purely in the temporal dimension.

#### Orodruin

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but I guess here we are talking about accelerating faster than light purely in the temporal dimension.
Nobody has mentioned any form of acceleration. Light does not accelerate. It is unclear what you mean by your statement.

#### confusedhome

The main problem as I see it is where the math shows the point of Time not existing at all between past and present, or the speed of light for that matter.

#### MikeeMiracle

I assume you must accelerate/travel faster than light to go back in time, what direction are you travelling in?

#### Ibix

I assume you must accelerate/travel faster than light to go back in time, what direction are you travelling in?
That's the bit you can't do. It's impossible to describe you reaching lightspeed, let alone passing it. That's why the paradoxical results of exceeding light speed don't bother us. The question of what happens can never come up (outside the pub, anyway).

#### MikeeMiracle

My original questioned asked if the statement "if you could travel faster than light you go travel backwards in time" was a true statement or not. After being told I could influence my past light cone I assued that meant it was possible, at least theorietically / mathematically.

#### phyzguy

Ok, it still seems terribly counter intuative that I could influence past events in the light cone but I accept the answer. For example, it's easy to comprehend acceleration in a spacial dimension, but I guess here we are talking about accelerating faster than light purely in the temporal dimension.
As @Heikki Tuuri said, if you can travel FTL in any frame, you can show that you can travel to your causal past. I made the attached space-time diagram to show how you would go about it.

#### Ibix

After being told I could influence my past light cone I assued that meant it was possible, at least theorietically / mathematically.
If you can travel faster than light then you can affect events in your past lightcone and generate paradoxes (unless one restricts faster than light travel to finite speed in a chosen frame, or some such thing).

However, accelerating to the speed of light is impossible - we cannot describe you doing it. So the paradoxes that would arise if you could do something you can't do, don't bother us.

Ideas that permit faster than light travel (e.g. the Alcubierre warp drive discussion to which @Heikki Tuuri refers) may allow such causal paradoxes. But they don't bother us either because they simply change "you can't travel faster than light" from a blanket statement to a specific one - "you can't get the exotic matter you'd need to travel faster than light".

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#### Janus

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My original questioned asked if the statement "if you could travel faster than light you go travel backwards in time" was a true statement or not. After being told I could influence my past light cone I assued that meant it was possible, at least theorietically / mathematically.
Let's put it this way, "IF" you could travel faster than c, then our present understanding of the universe predicts that you could travel back to your own past.
This means one of three things :
1. FTL is just simply not allowed in our universe.
2. The predictions based on our understanding are wrong.
Of the 3, the last one is the least likely.

#### jbriggs444

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Of the 3, the last one is the least likely.
The Novikov self-consistency principle suggests that causality paradoxes do not arise. i.e. That any universe involving close timelike loops (such as unrestricted FTL travel could allow) must still be globally self-consistent.

#### Mister T

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If you can do faster-than-light travel at any speed relative to any inertial coordinate frame, then you can travel to your causal past. That is easy to show.
Actually, it's impossible to show. I suspect what you mean is that you can use the equations of special relativity to show it. But those equations are built on a foundation that contradicts your premise!

The foundation of special relativity is that light speed is invariant. You start out stating "if you do faster-than-light". That violates the foundation that light speed is invariant. Therefore whatever conclusions you draw are bound to be incorrect.

#### Nugatory

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The Novikov self-consistency principle suggests that causality paradoxes do not arise. i.e. That any universe involving close timelike loops (such as unrestricted FTL travel could allow) must still be globally self-consistent.
We have to distinguish two cases here. There are curved spacetimes that are solutions if the EFE and contain closed timelike curves; this is the situation that the Novikov was considering.
However, in this thread we are working with a flat spacetime in which there are no closed timelike curves; any closed curve in flat spacetime must necessarily be spacelike somewhere, as are for example the FTL signal paths in the tachyonic antitelephone. It is unclear to me that Novikov’s thinking applies here.

#### phyzguy

I always loved the Star Trek TNG episode "Cause and Effect", where the Enterprise gets caught in a closed timelike loop. Of course, in order to make a story out of it, they have to find a way to break out, but it's an interesting episode nonetheless.

#### PeterDonis

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It is unclear to me that Novikov’s thinking applies here.
I don't see why it wouldn't. A closed curve in spacetime that has spacelike segments would still be just as amenable to applying a self-consistency criterion.

#### Orodruin

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However, in this thread we are working with a flat spacetime in which there are no closed timelike curves
Small correction: We are working in Minkowski space. There are flat spacetimes that contain CTCs, the most prominent example being $\mathbb S_1 \times \mathbb R$ with the circle being timelike.

#### Heikki Tuuri

If there is a closed timelike curve in a spacetime and some matter travels along that curve, it may be impossible to find initial conditions such that realistic matter returns to the exact same state after a cycle.

https://en.wikipedia.org/wiki/Gödel_metric

General relativity does allow closed timelike curves. The best known example is the Gödel metric.

It is not known if general relativity has any dynamic solutions at all with realistic matter. If there are closed timelike curves, finding a realistic solution looks even harder.

The matter in the Gödel metric is non-interacting dust of an infinitesimal grain size and a smooth distribution. It is not realistic matter.

#### PeterDonis

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It is not known if general relativity has any dynamic solutions at all with realistic matter.
I'm not sure what you mean by this. FRW spacetimes are precisely such solutions. They don't have CTCs, but your statement here does not appear to be restricted to spacetimes with CTCs.

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