# The Alice and Bob example of the FTL violates causality

1. Apr 2, 2015

### L.E.N

As many, I wondered why FTL communication has problems with causality. Went over many posts here in PF, and wasn't satisfied. And then I read this explanation, by Richard Baker:

http://www.theculture.org/rich/sharpblue/archives/000089.html

His explanation is a bit more clear, but there's something I still don't understand:

1) Alice is positioned at P, and sends an FTL massage (for example "Hi Bob, planet Zoton is right in front of me") to Bob, who is positioned at Q.

2) Bob transmits an answer ("OK, now push the red button") to Carol, who is also at Q (what's carol's use in the explanation, by the way? Didn't get it), and Carol transmits the answer to Dave at position R.

3) Dave then transmits the answer to Alice... who is also at position R??? How can she be at P and R at (almost) the same time? Didn't she just transmitted the instantaneous FTL massage 10 seconds ago from position P? Is it the same Alice at all? If not, when did she get replicated? Or... Are Dave and Carol even in the same universe as Alice and Bob? WHAT'S GOING ON???

2. Apr 2, 2015

### Orodruin

Staff Emeritus
In Alice's frame, the events R and P are at the same point in space, but R occurs before P. The point is that Carol is transmitting a message to Dave at FTL in their common rest frame. The point of Dave and Carol is simply to single out a different inertial frame, for which a FTL communication corresponds to sending a signal back in time in the rest frame of Alice and Bob. Since Bob and Carol is at the same event Q when Bob receives the signal, he can just tell Carol this and she can send the FTL signal (in their system) to Dave. Dave is at the event R together with Alice so he can just tell her he received the signal, but for Alice, this event occurs before P, the event where Alice sent the first signal.

3. Apr 2, 2015

### rootone

Alice is not in two places at the same time.
Alice at P is in one frame of reference and at R she is in another.
Same Alice, but at a different place and time.

4. Apr 2, 2015

### wabbit

I wonder why it is better to complicate things to such an extent with Alice, Bob, Dave, Caroll, a red button and whatnot... To each his own but for me while the FTL-change frame-negative time argument is (deceptively ? ) easy, the whole crowd there just confuses me thoroughly.

5. Apr 2, 2015

### Orodruin

Staff Emeritus
In all frames, Alice will be at P and R at some time. The point is that in Alice's rest frame, P is simultaneous with Q, while in Carol's rest frame, R is simultaneous with Q. This is just relativity of simultaneity.

6. Apr 2, 2015

### Orodruin

Staff Emeritus
I agree, but it seems some need the full construction of a loop and seem to think changing coordinates is cheating.

7. Apr 2, 2015

### wabbit

That seems to relate to what I was alluding to with "deceptively easy", perhaps changing coordinates is a kind of cheap trick for those like me who are both lazy and mathematically inclined, but there might be some more understanding gained from the effort of going through the whole concrete setup, red button and all.

8. Apr 2, 2015

### Orodruin

Staff Emeritus
I think that once you have the argument, it is quite trivial to construct the loop, you can simply send two signals back in time, one from Alice to Bob and a reply from Bob to Alice.

9. Apr 2, 2015

### L.E.N

1) Since everyone in the example uses instant massaging, the whole thing took less than, say 20 seconds max, and the distance between P, Q, and R, although not mentioned, is probably (and let's say it is) in the billions of kilometers. And the whole mess began only after Alice (after a very long voyage) reached P (which I decided to call Planet Zoton).

2) So, from a 5 year old POV (thanks Groucho), There are two Alice.

Please explain the 5 year old, in view of these distances and the 20 seconds time, how it is only one Alice.

10. Apr 2, 2015

### Orodruin

Staff Emeritus
The main thing to realise is that simultaneity is not a well defined concept in relativity. What is an instantaneous message in one frame is a message that travels back in time in another. The two different Alices you are thinking about are the same Alice, but at different events along Alice's history.

11. Apr 2, 2015

### rootone

Thanks for clarifying Orodruin.
Alice is always in Alice's frame of reference, but at some point in her history that is simultaneous with P, and later it is simultaneous with Q.
Leaving aside the speed of light for a moment to make my point,
If I phone my wife to say I expect to be home in 20 minutes, and then I arrive on time, this mean only that 20 minutes have passed.
The me that arrives on time is not a different person to the one who phoned earlier.

Last edited: Apr 2, 2015
12. Apr 2, 2015

### L.E.N

Weird, I thought that understanding order of events (inc' simultaneity) was one of the main reasons that motivated Einstein to form his theory. At least from what I read about it (I think I read it here: http://www.einstein-online.info/home-eo?set_language=en ). But OK, I think I'm starting to get it. Lets enhance the experiment:

Dave, besides having an FTL ansible, also has an FTL jump-wherever spaceship. He can travel almost instantly to every point in the diagram. So, if he takes Alice from point R and jumps near Zoton (point P), will he have two Alices now at point P?

13. Apr 2, 2015

### Orodruin

Staff Emeritus
No, if he takes Alice with him, Alice will not continue existing in the same place.

Let us do the following instead, which only involves one person and is time travel rather than just sending a message back (the idea is the same).

Alice can make instant FTL jumps to anywhere as well as accelerate to any velocity < c once she has done so.
After experiencing event R, she waits around for some time until she reaches event P. She then makes an FTL jump from event P to event Q, which is simultaneous with P in her rest frame. Once at Q, she accelerates instantly to a frame where Q is no longer simultaneous with P, but instead simultaneous with R. Since Q and R are simultaneous in this frame, she can make an FTL jump to R, where she will meet herself from the past.

When it comes to "sending a message", just think of "Alice" as "the message".

14. Apr 2, 2015

### L.E.N

Hmmmm. I'm trying to make the order of events of the experiment you suggested:

1) Alice starts at R (say it's some big rock floating in space).

2) Alice accelerates to planet Zoton (P) (not instantly, you didn't say instantly, so it took her time, say a few hours) from the rock R, which continues to float away. Obviously, there is no more Alice in R (which floats away), or where R had been, before Alice accelerated from it. After all, a few hours had passed.

3) After Alice finally reaches Zoton, she FTL jumps instantly from Zoton (P) to the spaceship Queena (Q) which moves at the same speed as Zoton (P).
Time for All points (and whatever time it is) continues to pass by of course, and all points continue to move in space.

4) Alice takes control of Queena and instantly accelerates it to match the speed of R. Yes? Still R and Q are no longer in their original position, everything is moving, and the same hours that passed for R, have also passed for Q (in its new speed), if they are to correlate. Right?

5) Once Alice see the speed is correct (say it takes her 3 seconds to notice and decide, meaning more time and space travelled), she jumps to R, hoping to meet herself. But wait, which R? R the rock that floated away from its original location, moving at great speed (and is now at a location where Alice had never been), or R the initial point where the rock was, where Alice accelerated away from the it a few hours ago (due to her regular non-FTL voyage to P) ?

If I understand correctly, when Alice jumps from Q to R in your experiment (say R the initial position) she did travel back in time, but didn't meet herself. She only met the place she was a few hours ago. The "other" Alice is right now at P, preparing to FTL jump to Q. Yes?

If I understand correctly, even if the experiment was FTL jump from R to P to Q to R (and this whole jump voyage would take 4 seconds), Alice still would miss herself in R, because of the need to match the speed of point Q to that of point R... My brain needs an oxygen tank.

15. Apr 2, 2015

### L.E.N

Look at Figure 5 in Richard's explanation:
http://www.theculture.org/rich/sharpblue/archives/000089.html

Say Alice has an FTL comm connection to Dave, and she calls him and say "Hi Dave, I'm in front of planet Zoton (P), you should see the view!"
Dave answers in his FTL comm: "What are you talking about?? If you're at Zoton (P), then who's that right next to me, at R????"

If to rely on Richard baker:
Figure 3. "By itself, this single use of the ansible doesn’t create a causality violation... Even if Bob re-transmits with his [FTL] ansible, Alice receives the reply just a little after she sent out her signal. The problems arise when we bring another inertial frame into play."
Seems logical to me. FTL massages might travel instantly, but it takes humans some time to type or speak.

16. Apr 2, 2015

### aabottom

I'm with wabbit. The words, characters, and equipment, make it HARDER to understand. Special Relativity is quite simple mathematically. Give me the equations and I can understand it.

I recently read Einstein's book, Relativity. He makes it sound so easy, and it is. (Special Rel that is. Not so much General Rel.)

17. Apr 3, 2015

### Orodruin

Staff Emeritus
No, Alice does not need to accelerate. In Alice's initial rest frame, R and P are at the same point in space. What you seem to be missing is that each event (R, P, Q) are points in spacetime, i.e., they describe not only a location but also a time. The vertical direction in the diagrams you see is the time direction. Therefore, if two events have the same x-coordinate, they happen at the same spatial point (in Alice's rest frame).

18. Apr 3, 2015

### L.E.N

Yes, and yet, something in the explanation still bothers me:

Since every participant has speed, their position changes with time. Even if everyone was "stationary", space still moves around them, meaning, their position still changes with time. But you know what, let's stick exactly to the diagram. Figure 5, what is the order of events? Everytime I try to put down the order of events, I get a mess.

1) Alice meets Dave at R.
2) At the same time Alice meets Dave, Carol meets Bob (by Carol's POV... Bob's POV is that Carol is nowhere near him).

What now?

3) Alice stays at R, and time moves on, until R becomes P.
4) Dave's X value changes, meaning his position changes, along with his time.
5) Alice at P. It's the same place as R, but after, say 1 hour. Dave is out of her light cone. And Bob finally meets Carol by his POV, but wait, how come Carol is still there? She has the same speed as Dave, shouldn't her X,Y values be different? Her position should be somewhere in Bob's future light cone when Alice "arrives" to P, no?

6) Mess.... I'm sure the problem is not with the theory, but with the explanation. I think animation would explain better than pictures.
Actually I think the problem is with me. If I remember correctly, a major point of SR theory, is that observers with different speeds might have differences on agreeing on order of events. In cases like that, every POV will be true only to the POV's observer, not all other observers. There is no single POV, no single order of events that is right for all and agreed by all, in cases like that. So even animate explanation won't help. Right?

19. Apr 3, 2015

### wabbit

This sounds ambiguous. You mean "according to Alice, she meets Dave at the same time Carol meets Bob, but according to Bob, those two events do not happen at the same time", right ?

Yes, this is a key point. You cannot say "At the time something happens" without specifying whose time you are referring to. Events happening at the same time from Alice's viewpoint, happen at different times from Bob's viewpoint.

Last edited: Apr 3, 2015
20. Apr 3, 2015

### rootone

Einstein originally described the story using just two people, the concept of reference frames, and the axiom of the fixed speed of light.
It's not that hard to understand.
Now we are beginning to talk about four people , some additional apparatus, things travelling faster than light, and some kind of concept of an absolute spacetime which isn't relative to anything else.
I think I'll stick with the original plot.