FTL and causality (split from What do you want science to now?)

[Yllanes]

Split from this thread.

Maybe I'll understand better if I rephrase my example... and someone can embellish it. A beam of light leaves Earth in 2006, to arrive at a star 5 light years away, in 2011. I use an unknown method to arrive at the star in 2010. What can I do that would violate causality?

Causality is determined by the light cone. Events inside the light cone are causally related to its centre. Events outside the cone are not. The boundaries of the cone are the worldlines of a light ray. If you can break these boundaries (travel faster than light) you can break causality.

The spacetime interval is defined as s² = x² - c²t². s² is the same for all inertial observers. If s² < 0, the temporal separation is greater than the spatial separation, so the events can be causally related. That is, if t_A < t_B, then A can be the cause of B. If I shoot you, moments later you die. This happens in this order for every observer, no one sees you dying before I shoot. Causality is not relative.

If tachyons (particles travelling faster than light) existed, this would change. Check, for example, the section on tachyons here.

Another way of looking at this is noticing that a particle travelling faster than light in one reference frame R can be travelling backwards in time in another reference frame R'. In other words, FTL travel = time travel. And it is obvious that time travel implies several paradoxes and contradictions. To see this, consider the following figure:

The axes in black (red) represent R (R'). R' is a reference frame moving with some velocity parallel to the x axis relative to R, so its axes appear slanted. The grey line is the worldline of a light ray. Notice how it bisects both frames. The green line represents the worldline of a tachyon. As you can see, it takes less time for the tachyon (in R) to cover the same distance as the light ray. Simultaneous events in R are those living on the same horizontal line. Simultaneous events in R' are those living on a line parallel to the axis x', such as the dotted red line.

Consider now that the origin is event A, with coordinates (0,0) in both systems. The point of intersection between the green line and the dotted line is event B. This event has positive time in R, but negative time in R'. So the tachyon is travelling back in time in R'.

And now for something completely different:

But what about redshift? Photons change their wavelength and frequency.

This is different. Doppler shift does not mean that photons change their frequency during their travel, it just means that different observers will measure different frequencies. With the oscillation of neutrinos, the same particle that starts its voyage as an electronic neutrino may arrive at Earth as a tau neutrino. The same observer sees the same particle change.

 

[TobiasTheViking]

that went right over my head..

I usually think that i'm not totally "MTV generation", and that i actually can comprehend stuff, and, you know, like, have original thoughts of my own.

With the above sentence, and my inability to comprehend the OP i guess i have to reconsider what i think about myself.


Any chance you could explain it in a simpler way.

Like, give an example of how the case above with arriving in 2010 causes a a causality problem.

 

[ponderingturtle]

that went right over my head..

I usually think that i'm not totally "MTV generation", and that i actually can comprehend stuff, and, you know, like, have original thoughts of my own.

With the above sentence, and my inability to comprehend the OP i guess i have to reconsider what i think about myself.


Any chance you could explain it in a simpler way.

Like, give an example of how the case above with arriving in 2010 causes a a causality problem.

It is not that arriving in 2010 causes the problem it is that from some observers you will get there in 2004 and they could concievably send you a message that would reach you before you leave. From your point of view it would be arriving in 2010, but that is not something anyone else can agree on.

 

[Yllanes]

Any chance you could explain it in a simpler way.

Like, give an example of how the case above with arriving in 2010 causes a a causality problem.

OK. If you can get to the star faster than light would, you can also get back before you departed.

It's like the example I gave on the other thread about Lincoln's assassination. For a spaceship travelling through a distant galaxy, the American Civil War may still be happening, because the line of simultaneity for that spaceship is slanted, as in the red reference frame in the OP.

Suppose you can get to that spaceship instantaneously (or in one second as measured from Earth). Then the Civil War would be a contemporary event for you in your new reference frame. If you can get back in another second (as measured from that galaxy), you could arrive in the middle of Gettysburg, having departed in 2006. I'll draw a little diagram for that trip and get back in a moment...

 

[TobiasTheViking]

I'm still not sure i get it.. Besides for the dotted line and the light ray line i don't get any of the other lines(and they are only descriped as being a colour, sorry, i don't know which one of them are green).

 

[TobiasTheViking]

also, i don't undestand why that dotted line doesn't go through 0,0(even if the dotted line is a tachyon)

 

[TobiasTheViking]

OK. If you can get to the star faster than light would, you can also get back before you departed.

It's like the example I gave on the other thread about Lincoln's assassination. For a spaceship travelling through a distant galaxy, the American Civil War may still be happening. Suppose you can get to that spaceship instanteneously (or in one second as measured from Earth). Then the Civil War would be a contemporary event for you in your new reference frame. If you can get back in another second (as measured from that galaxy), you could arrive in the middle of Gettysburg, having departed in 2006.

I can't see how that could happen unless one changes reference frames.. But then again, any acceleration is, afaik, changing reference frames.

I have no problem with jumping 1000 light years away in one second and then looking back through a telescope and see what happened to earth 1000 years ago, i can't see that as a problem.

That is simply a byproduct of the light having spend 1000 years to travel to where you are now.

Then to do FTL travel one would have to calculate "where would that planet be now, considering the picture we have is 1000 years old", then one jumps to that place, and see the earth as it is.


Hm, i guess the only problem i can see with that is that from what i am saying there would have to be some correct/primary/better/real reference point.

But it doesn't seem unlikely to me that some theory could be made where FTL is possible because of certain limitations on which transitions between reference frames are allowed..

Then again, that is probably just because i don't know enough about the area

Hope i'm not saying very retarded borderline 9/11denier stuff

 

[sphenisc]

Going from the vertical line clockwise

1) The y axis of the R frame of reference which is marked t (time) , it's black.

2) The y axis of the R' frame of reference which refers to its own t' (time) , it's red.

3) A light ray in grey.

4) The x axis of the R' frame of reference which refers to distance, it's red.

5) A line parallel to the x axis of the R' frame, but occurring 'earlier' in the R' frame of reference ( it crosses the R' y axis lower down), it's a dotted red line.

6) A tachyon line in green.

7) The x axis of the R frame of reference which refers to distance, it's black.

Hope that helps.

 

[TobiasTheViking]

Well, ok, now i can read it, still don't get it. Why are there two R'? what is the dotted line?

 

[Anacoluthon64]

A major difficulty in understanding is to be found in the "strangeness" of, or unfamiliarity with, the general class of affine transforms, i.e. rectilinear coordinate systems where the "independent" axes are not required to be orthogonal. In the extreme case where a body moves at the speed of light c, the two axes are collinear.

ETA: The red coordinate axes (inertial frame R') are the result of a mapping to the black axes (inertial frame R), but note that inhabitants of both R and R' would each insist that their own coordinate system is orthogonal, but the others' is not.

'Luthon64

 

[TobiasTheViking]

Consider now that the origin is event A, with coordinates (0,0) in both systems. The point of intersection between the green line and the dotted line is event B. This event has positive time in R, but negative time in R'. So the tachyon is travelling back in time in R'.

Ehm, i don't see how it would be negative in R'

 

[Jimbo07]

Consider now that the origin is event A, with coordinates (0,0) in both systems. The point of intersection between the green line and the dotted line is event B. This event has positive time in R, but negative time in R'. So the tachyon is travelling back in time in R'.

Ehm, i don't see how it would be negative in R'

What Yllanes should have done was put a big red dot where the green line and the red dashed line cross. Event A happens at position 0 on the x axis and event B happens at the dot's position, b, on the x axis. Now, take that dot, and trace the red dashed line back to the R' axis and you will see that it's below (and parallel to) the x' axis.

So, the dot is located:
R: at b > 0, t > 0
R': at b' > 0 not equal to b > 0, t' < 0

 

[sphenisc]

Consider now that the origin is event A, with coordinates (0,0) in both systems. The point of intersection between the green line and the dotted line is event B. This event has positive time in R, but negative time in R'. So the tachyon is travelling back in time in R'.

Ehm, i don't see how it would be negative in R'

Look where the tachyon crosses the parallel red lines.
The tachyon crosses the dotted red line just 'above' where the x is. This is the earlier time point on the R' y-axis. Then look at the solid red line running parallel to the dotted one. The tachyon crosses this at the origin. This is a later time point ob the R' y axis. Thus the tachyon can be interpreted as having gone from a later time point to an earlier one - i.e. backwards in time.

 

[grayman]

I had a tachyon observation explained to me this way, sorry I can't provide an illustration, perhaps someone more computer literate will supply the diagram:

An observer would see the tachyon travelling in one direction (a) with another running parallel (b), as another (c) seems to converge and destroy (a). Imagine the letter Z. (a) at the top of the Z, (b) at the bottom, and (c) as the diagonal line.

If the timeline is seen as moving laft to right, it would appear that (a), (b), and (c) all start at the same time, with (b) and (c) starting from the same point until (c) meets (a) and obliterates both.

However, what the observer is witnessing is (a) traveling along until it reaces a speed faster than light, at which point it is travelling back in time (b), to a point where it drops to sub-light speed and contiues on its way (c). The observer sees three tachyons when it is actually the same one.

My head hurts now.

 

[Yllanes]

Well, ok, now i can read it, still don't get it. Why are there two R'? what is the dotted line?

There is an R (reference frame for an observer on Earth) and an R' (reference frame for an observer moving with some speed relative to us). I forgot to label the axes in R'...

Ehm, i don't see how it would be negative in R'

This is because I didn't explain it and I somehow assumed that everyone is supposed to know about spacetime diagrams... Sorry.

The important things are:

• Two events simultaneous in a reference frame are not necessarily simultaneous in another reference frame.
• If the frames are represented in a spacetime diagram, to get the time for an event you trace a line parallel to the x axis and see where this line intercepts the t axis.
• For R, a line parallel to the x axis is horizontal.
• For R', a line parallel to the x' axis is slanted.
• So, to get the time of event B in R, you trace a horizontal line and see where it intercepts the t axis, as we do normally with cartesian axes.
• To get the time of event B in R', you trace a line parallel to the x' axis and read the point of intersection in the t' axis. This is the dotted line. We see that the point of intersection is on the negative half of the t' axis. So the time for B in R' is negative.

I did draw two big points named A and B, but it seems I didn't save the picture after doing it...

Hope i'm not saying very retarded borderline 9/11denier stuff

Not at all... The OP was aimed at people who already knew something about SR and spacetime diagrams. In retrospect, that was a silly choice, because someone who can understand that post probably already knows why FTL => breaking causality.

I have no problem with jumping 1000 light years away in one second and then looking back through a telescope and see what happened to earth 1000 years ago, i can't see that as a problem.

This is different to what I am saying. If I am in the spaceship, which is moving at a speed v<c relative to the Earth, then the Civil War may be happening right now for me. If I am in the spaceship and at rest with respect to Earth, the Civil War would not be contemporary, 2006 would. Simultaneity is determined by the relative velocity, not by relative position. Even if the Civil War is contemporary, I wouldn't see it by looking through a telescope, I would see Earth at a much earlier time.

The trip is as follows: I look into a galaxy 65 million light years away from Earth and see nothing, because I'm seeing what was there millions of years ago. However, I somehow know that there will be a spaceship in that spot a second from now. So I make my FTL jump and arrive there. I look back into Earth and see an asteroid killing the dinosaurs. This is reasonable, because it took me alsmot no time to get there, but the galaxy is 65 million light years away, so I would see Earth as it was 65 million years ago. Now I make my FTL jump back to Earth. Do I arrive 2 seconds after I left? To answer that we need to consider two scenarios:

• The spaceship is at rest with respect to Earth. Then my reference frame will not be slanted, my concept of simultaneity will be the same as the one they have on Earth and I will get back two seconds after I left.
• The spaceship is moving with respect to Earth. Then my reference frame will be slanted and my concept of simultaneity changed. Depending on the velocity of the ship, I may very well calculate (not see) as simultaneous the time of the battle of Gettysburg. So now, if I make my jump, I would arrive at that battle.

 

[Yoink]

Not that I'm a physicist or anything, but wasn't the definitive work on this question done in the 1978 film Superman? Substitute "flying by unknown means to a distant star" with "flying by same unknown means very very fast around the earth." At a certain point you start to clock back through time--allowing you to rescue Lois Lane and making every other Superman-involved plot supremely pointless from then on.

 

[ponderingturtle]

Hm, i guess the only problem i can see with that is that from what i am saying there would have to be some correct/primary/better/real reference point.

THe saying is this

Things can go faster than light
Things can not go back in time
All inertial reference frames are equal

Pick 2.

 

[toddjh]

A related question that I haven't yet seen answered in terms I can understand:

What's wrong with violating causality? So a future cause can affect a past event...so what? Sure, that would be counterintuitive and bizarre in terms of everyday human experience, but so are a lot of aspects of modern science.

Is there a good reason to believe such a thing would be impossible, or even unphysical? Does it violate any laws of physics, per se?

 

[ponderingturtle]

A related question that I haven't yet seen answered in terms I can understand:

What's wrong with violating causality? So a future cause can affect a past event...so what? Sure, that would be counterintuitive and bizarre in terms of everyday human experience, but so are a lot of aspects of modern science.

Is there a good reason to believe such a thing would be impossible, or even unphysical? Does it violate any laws of physics, per se?

Ok you set out on your trip in 2000 arive at your destination 20 LY away in 2005 and your ship promptly crashes. Now the passing space ship traveling under the speed of light see this and sees that you are also still at home as you have not left yet and tells you not to go.

So you don't go.

Now you have an invalid observation from the spaceship, it saw you there and crash.

The point is that it is not counter intuitive or bizar, it leads to logical contradictions and would remove any predictability from the universe.

 

[TobiasTheViking]

To all you guys who replied, thanks, i'm sorry to say i still don't get the diagram, maybe i'm just unable to understand it(there is a lot of stuff i just can't comprehend, i need to learn stuff in a very up->down way instead of the normal down->up way).

The important things are:

• Two events simultaneous in a reference frame are not necessarily simultaneous in another reference frame.

Totally follow you on that one point

Not at all... The OP was aimed at people who already knew something about SR and spacetime diagrams. In retrospect, that was a silly choice, because someone who can understand that post probably already knows why FTL => breaking causality.

I actually do know quite a bit about SR(or think i do ). I've listened to a lot of the stuff from The Teaching Company and seen a lot of PBS shows and stuff. And while they have done a great deal for me in regard to the reference frame stuff, they either didn't properly(or it has just slipped from my mind since then) explain why FTL would be time travel.

The only aspect i don't get, that i know off anyways, is how FTL would be time travel. And i am sorry to once again say that i just don't comprehend the diagram above.

This is different to what I am saying. If I am in the spaceship, which is moving at a speed v<c relative to the Earth, then the Civil War may be happening right now for me. If I am in the spaceship and at rest with respect to Earth, the Civil War would not be contemporary, 2006 would. Simultaneity is determined by the relative velocity, not by relative position. Even if the Civil War is contemporary, I wouldn't see it by looking through a telescope, I would see Earth at a much earlier time.

The trip is as follows: I look into a galaxy 65 million light years away from Earth and see nothing, because I'm seeing what was there millions of years ago. However, I somehow know that there will be a spaceship in that spot a second from now. So I make my FTL jump and arrive there. I look back into Earth and see an asteroid killing the dinosaurs. This is reasonable, because it took me alsmot no time to get there, but the galaxy is 65 million light years away, so I would see Earth as it was 65 million years ago. Now I make my FTL jump back to Earth. Do I arrive 2 seconds after I left? To answer that we need to consider two scenarios:

• The spaceship is at rest with respect to Earth. Then my reference frame will not be slanted, my concept of simultaneity will be the same as the one they have on Earth and I will get back two seconds after I left.
• The spaceship is moving with respect to Earth. Then my reference frame will be slanted and my concept of simultaneity changed. Depending on the velocity of the ship, I may very well calculate (not see) as simultaneous the time of the battle of Gettysburg. So now, if I make my jump, I would arrive at that battle.

And the part i fail to understand is why it isn't the first option.

I can see that from a specific reference frame(which you might reach by FTL) one might be able to observe the battle of Gettysburg. I fail to see why watching that from the other reference frame(which would have a time delay) would involve you traveling to the scene at Gettysburg if you initiated the FTL.

I can't comprehend how FTL can do anything other than either get you there NOW(though i do see that there is a problem about when NOW is in the different reference frames).
Or why you don't get there NOW+<some time that is less than the time it would take light to travel there>.


If you people give up on me that is aok, but i have, by now, given up on the diagram. I just can't comprehend it.