Talk:Special Relativity/Faster than light signals, causality and Special Relativity

This article ends by saying:

Notice that the violation of causality would actually be quite limited and would only apply to "space-like" separated events,

That's not true. It's actually neither limited, nor applying only to spacelike separated events. The separation of A and B is spacelike, but the separation of B and C is timelike. So causation is violated between two events with a timelike separation, too. Furthermore, it points out that a round-trip message from the earth to the moon would only let you communicate 1 second into the past. But if you bounced the message back and forth N times, then you could communicate N seconds into the past. So you could communicate arbitrarily far into your own past. That kind of causality violation is not very limited!

Finally, it suggests that all this is somehow related to quantum entanglement or EPR type experiments. It really isn't. They aren't related at all, though that's a common misconception. It would be better to delete that speculation.

Simply because Jane sees or calculates Bill’s time as being behind hers, doesn’t mean it actually is. For example, we see galaxies as they look in cosmic time 12.8 billion years (with us at 13.8 billion years). But if we transmitted information “instantly,” it wouldn’t arrive at that galaxy in the year 12.8 billion, it would arrive in year 13.8 billion. And if an alien replied “instantly” to us, he would say, “Yes, it is the year 13.8 billion here.” I see no violation of causality possible in such communication, neither we nor the alien have any means of seeing any further into the future than the year 13.8 billion, nor anyway to communicate to the past before 13.8 billion years.
 * This argument sounds flawed. Please feel free to correct me.  This is written in the spirit of devil's advocacy; it you point out an error in my reasoning I will appreciate it.

To use the graphics on that page, Look at the figure showing a red arrow from Jane to Bill, and then from Bill to Bertha.

Putting in example numbers, let’s say that Jane left Bill in the year 2000 traveling at gamma=2, v=.866c, towards Bertha’s planet 4.4 light years away. Bill and Bertha share a reference frame, so time moves at one speed, so when Jane left, it looked to Bill like Bertha had a clock reading 1995.6, but because he knows about the speed of light, he “knows” Bertha’s year is really 2000 just then.

Jane arrives at Bertha’s planet in the year 2000 + 4.4/.866 = 2005, local time. Jane’s time experience was just half that, or 2.5 years. She calculates that Bill’s clock ran slow at half speed again, so she calculates that Bill is in the year 2001.25.

She then sends an instant message to Bill in 2001.25, who sends it on to Bertha in 2001.25, and Bertha gains foreknowledge.



The flaw I see is that Jane only calculates Bill’s time as 2001.25, it is not really 2001.25. Bill and Bertha’s planet are both in the year 2005, that is Bill’s real time. After all, if Jane turned around, she would suddenly say, “Oh, Ben is in the year 2008.75!” And then Jane would zoom home at the same speed to find that Bill has aged 10 years to her 5. Jane’s calculation shows that dramatic 7.5 years of aging just because she turned around (that’s the complication of the twin astronaut paradox when approached in this fashion).

In other words, Jane’s calculation of Bill’s time is her personal estimate and not reality. As mentioned, changing direction changes her personal estimate. The reality is that every location in the universe has a calculable cosmic time (years since the big bang) and there is no way that even at instantaneous travel, can any message be sent to an earlier time on the cosmic time scale. We can see the past, but we can’t communicate with it.