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I recently read a sci-fi book, where some (very few) people can communicate telepathically, which happens to be instantaneous.

So, every spaceship has a crew member who telepathically communicates with his/her partner on Earth.

Would this lead to a cause/effect paradox? How and why?

More about the book, in case anyone is interested:

Heinlein: Time for the Stars - The book is narrated by Tom, a young man, who discovered he can telepathically communicate with his twin brother Pat. At age 16, they are hired as special communicators by Long Range Foundation. Tom leaves on a spaceship, while Pat stays on earth, and the pair serves as a communication link between Earth and the spaceship.

The rocket accelerates towards almost light speed. As the speed increases, the twins find it increasingly hard to communicate, because of time dilation. Back on Earth, Pat gets married, and has a daughter, while Tom is still a teenager...

ADDED: One thing that makes this different from generic FTL communication is that each pair of communicators started on Earth. Most are twin brothers/sisters, and there is also a set of triplets, where one stays on Earth, and the other two leave with two different spaceships into two different directions.

So the only way to make sense of this is to say that there is some distinguished frame of reference whose simultaneity dominates. For instance, perhaps some bond forms between Tom and Pat while they are both on Earth, and this bond is formed specifically in reference to the Earth's frame of reference. When Tom goes off into space, the bond retains this frame of reference. It's "set" on Earth's frame of reference, regardless of what Tom and Pat do.

There is definitely a special bond between each pair of communicators. They are either twins, or two people who spent a lot of time together to develop telepathic communication.

As the whole project originated on Earth, all these communicator bonds are "set" on Earth's frame of reference (whatever that means...)

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    $\begingroup$ Yes, FTL communication can lead to effects happening before causes in some frame. We already have a few good questions about it here. FWIW, Heinlein had to bend the rules of relativity to make that book work. But I liked it anyway when I read it decades ago. :) I re-read it a year or so ago, and still enjoyed it. $\endgroup$
    – PM 2Ring
    Commented Jun 18, 2019 at 19:41
  • $\begingroup$ See en.wikipedia.org/wiki/Relativity_of_simultaneity Especially the green on black animated diagram near the top of the page. $\endgroup$
    – PM 2Ring
    Commented Jun 18, 2019 at 19:47
  • $\begingroup$ FTL communication would not break physics - little or none of the formalism would have to be changed. It would however falsify the "block universe" interpretation of SR - we would then be left only with a Lorentzian interpretation still standing. $\endgroup$
    – Steve
    Commented Jun 19, 2019 at 0:40
  • $\begingroup$ Why do people think telepathy is instantaneous? $\endgroup$
    – Natsfan
    Commented Jun 20, 2019 at 21:16

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In special relativity, there is no objective meaning of "simultaneous". People in different frame of references disagree as to what is "simultaneous". So the only way to make sense of this is to say that there is some distinguished frame of reference whose simultaneity dominates. For instance, perhaps some bond forms between Tom and Pat while they are both on Earth, and this bond is formed specifically in reference to the Earth's frame of reference. When Tom goes off into space, the bond retains this frame of reference. It's "set" on Earth's frame of reference, regardless of what Tom and Pat do.

This wouldn't violate the basic rules of relativity, but it would violate some principles that scientists generally accept. For instance, there's something called the Causality Ordering Principle, that says that if A causes B, then A will be before B in all frames of reference. In the situation you present, however, Tom can communicate something to Pat, and thus Pat knowing something can be caused by Tom communicating that, and yet there will be frames of reference in which Pat knowing it comes before Tom communicating it. And if there is another set of twins that have their bond "set" in that other frame of reference, then you could relay messages between those four people in such a way that someone could get a message from their own future (e.g. old Pat could send a message to his younger self).

One possible interpretation is that the twins are actually communicating with someone in another universe. So if Pat talks to his younger self, he is simply talking to someone in another universe that happens to be exactly like he was in his past.

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    $\begingroup$ Note that you do get paradoxes if you have two different privileged frames of reference: your example suggests that maybe Tom and Pat could have an Earth-frame-of-reference whereas maybe Alice and Bob having met on Proxima b might have a Proxima b frame-of-reference. This leads to a problem where an event E happens, Tom, in E's future-light-cone, sends info about the event to Pat outside of that light-cone. Pat happens to be near Alice and tells her, and she can relay it to Bob, but when Bob is in E's past-light-cone. $\endgroup$
    – CR Drost
    Commented Jun 18, 2019 at 20:20
  • $\begingroup$ Besides Tom and Pat, there are other pairs and other spaceships. However, they all started on Earth at some point. $\endgroup$
    – Granny Aching
    Commented Jun 20, 2019 at 16:36
  • $\begingroup$ @CRDrost : a frame of reference does not exist in any real sense. Nor does a light cone. We live in a world of space and motion. The map is not the territory. It doesn't matter how you move, or how a message moves, you are never going to turn back time, because time is merely a cumulative measure of motion. There is nothing you can do to undo that motion. $\endgroup$
    – John Duffield
    Commented Jun 20, 2019 at 21:35
  • $\begingroup$ @CRDrost Yes, I discussed that in the last sentence of my second paragraph. $\endgroup$
    – Acccumulation
    Commented Jun 20, 2019 at 22:36
  • $\begingroup$ @JohnDuffield You're the one making the map versus territory error. "Light cone" refers to a real part of the universe. The thing it refers to really exists. The phrase itself is arguably "map" rather than "territory", but that's true of every single other utterance in the English language. Your comment, like your answer, is nonsensical. You seem to be either unwilling or unable to string together a coherent point. $\endgroup$
    – Acccumulation
    Commented Jun 20, 2019 at 22:41
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Suppose you had a telepathic phone that could call anywhere in the universe right now. You call your friend in the Andromeda galaxy to say hello. He says, "Hey, stay on the line, I am going to call you back on my other line" (also with instant telepathic connection).

Well, the Andromeda galaxy is moving towards us at 300 km/s (0.001$c$), so when he calls you back from 2 million light years away, he is now talking to the Earth 2000 years in our future.

And now so are you.

In summary: Right now in the Andromeda galaxy, "right now" on Earth is somewhere around 4019 AD.

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I'm pretty sure that instant communication would give us evidence that relativity is kind of wrong.

Relativity is compatible with all the evidence we have now. Instant communication would give us evidence that we can't get now. Evidence that relativity says will not exist.

I don't know what new physics we'd get that replaced relativity and incorporated the new evidence. It would be compatible with relativity about everything that relativity now correctly predicts.

Maybe that's a bad way to say it. Maybe we would simply get new interpretations of relativity, and the interpretations that are incompatible with the reality of simultaneity would be discarded.

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Would possibility of instant communication break physics?

No. Not at all.

I recently read a sci-fi book, where some (very few) people can communicate telepathically, which happens to be instantaneous. So, every spaceship has a crew member who telepathically communicates with his/her partner on Earth. Would this lead to a cause/effect paradox? How and why?

No it wouldn't. That's a myth based on misunderstanding. Unfortunately such myths tend to get popularized, and eventually taken as gospel truth by the paying public. The way to appreciate this is to use Einstein's operational definition of time: time is that which a clock measures. A clock is a device that features some regular cyclical "local" motion, that's all. Then it displays an accumulated version of this on the clock face. There is nothing you can do to make this accumulated measure of motion reduce. There is no message you can send, and there is no way you can move to "turn back time". In similar vein there is no message you can send and no way you can move to make cause precede effect. It might affect the way you see things, but it doesn't change those things one iota.

Moreover, it doesn't matter whether the clock is close to you, or some distance away. Don't be seduced by expressions such as "in my frame of reference", because in the context of special relativity, your frame of reference is little more than your state of motion. And don't be seduced by the Andromeda paradox. Changing your state of motion doesn't affect Andromeda one bit. Remember that this "paradox" came from Roger Penrose, the guy who gave us the parallel antiverse. Take it with a pinch of salt. And don't forget that the CMBR serves as an "absolute" reference frame of sorts. See this question. Everybody can gauge their motion through the universe using the CMBR dipole anisotropy, and everybody can work out that the universe is circa 13.8 billion years old.

It's like what Steve said in his comment. FTL communication wouldn't break physics, but it would falsify the block universe interpretation of SR. It would also clear up some of the "woo" that tends to gain popularity when it shouldn't.

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  • $\begingroup$ I wouldn't be so quick to dismiss something Penrose said. He is a highly decorated mathematical physicist who shared the Wolf Prize in Physics in 1988 with Steven Hawking. None of this means he is always right but he deserves more credit than "the guy who gave us parallel universe". $\endgroup$
    – Natsfan
    Commented Jun 20, 2019 at 21:13
  • $\begingroup$ @jmh: I've looked into special and general relativity at length, and find myself thinking that some of the things Penrose said don't square with what Einstein said. Do you seriously think turning round and walking the other way has any affect on the Andromeda galaxy? Or that you can jump into a black hole and come out in a parallel universe? Even though the black hole mass increases by the 100kg mass of you and your spacesuit? Penrose and Hawking got their Wolf prize for singularity theorems, but I'm afraid to say there are some issues there. Ask a question about it and I'll elaborate. $\endgroup$
    – John Duffield
    Commented Jun 20, 2019 at 21:30
  • $\begingroup$ i said his awards did make him right in those cases. i wasn't implying he was correct just that he has amazing intellectual prowess and his musings should at least be heard. $\endgroup$
    – Natsfan
    Commented Jun 20, 2019 at 21:38
  • $\begingroup$ jmh : noted. Ask about the singularity theorems and I'll try to demonstrate why I think the way that I do. There are some misconceptions in gravitational physics. $\endgroup$
    – John Duffield
    Commented Jun 20, 2019 at 21:46
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    $\begingroup$ Penrose never claimed that turning around has an "affect" [sic] on the Andromeda galaxy. And given that you got that wrong, I'm skeptical that you're characterizing his views on black holes correctly. $\endgroup$
    – Acccumulation
    Commented Jun 20, 2019 at 22:36

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