paradoxes if instantaneous signals

koolmodee

Would there be paradoxes arrise if information could pass instantaneously? If there where no limit how fast things can move.

I know that in SR when faster then light travel is allowed, the casual order differ for different observers.

Are there paradoxes in the classical Galilean space-time view, which allows instantaneous signals, as well?

Or are speed limits only necessary in SR and GR?

thanks

granpa

it would just mean that there would be one simultaneous 'now' for everyone .a preferred frame. nothing else would change.

Fredrik

Yes. Alice sends a message: "Hello. I'm just testing my tachyon message device". Now there's an inertial frame in which the message was received before it was sent. If the recipient, Bob, is stationary in that frame, he can send a reply: "Please destroy your tachyon message device immediately. Your tachon beam hit your sister in the head and killed her". Alice receives the message before she sent the original message and decides to trust Bob, so she destroys her device right away, and is never able to send the original message.

Note that in this thought experiment, we don't consider the fact that each signal takes a while to detect. Detection isn't instantaneous. This is actually a loophole in the argument above. It is possible to send certain signals faster than c. If the shortest possible time to decode the signal is long enough, Bob can't send the reply soon enough to cause a paradox.

Instantaneous messages aren't a problem in a Galilean spacetime, because simultaneity isn't an issue.

The speed limit is a part of the definition of those theories.

bernhard.rothenstein

I think that Galileo's relativity is Einstein's one, when c goes to infinity even is many consider that it is Einstein's one at very low speeds.

RandallB

Correct - no time paradox created.

Fredrik

Why do you guys think so? I'm pretty sure you're wrong. (See #3).

Edit: OK, I think I get it. You interpreted the question as "What would happen if we let the invariant speed of special relativity go to infinity?" while I interpreted it as "What would be the consequences if we could send messages at speeds much higher than the invariant speed of special relativity?".

Maybe the OP can explain what the question was about.

RandallB

No just instantaneously information transfer nothing travels no change to SR, exxcept that we will be able to find which frame should be considered preferred.

koolmodee

So we can say a Galilean universe is a logically coherent, free of paradoxes universe but one which happens not to be the universe we live in. Can we?

Fredrik

That just isn't true. It would be true if there's a particle that moves at infinite speed in one particular frame, but no tachyons and no particles that move at infinite speed in any other frames, but that's definitely not what the question was about.

If it's possible to send messages at arbitrary speeds (and detect the signals in a short enough time), there will be paradoxes, as I explained in #3. If you google for it, you can probably find a site or an article that explains what I said in #3 with a spacetime diagram, or you can just make one yourself.

Yes, and we can say the same thing about Minkowski space without tachyons. (The universe we live in doesn't have a flat geometry).

granpa

if in one frame event 1 instantly communicates across space and causes event 2 then in other frames event2 may indeed APPEAR to occur before event1 but there is no way event2 could causally interact with event1 (for instance, to prevent it from occurring). therefore no paradox.

MeJennifer

I agree.

Events in spacetime which would have instant information transfer are not points but lines or even hyperplanes.

No paradoxes except for "paradoxes" in planes of simultaneity. But planes of simultaneity are not physical they are just coordinate charts.

Note that, not worked out sufficiently in modern theories IMHO, GR already has a non-local flavor. For instance try to define the EM tensor for a point.

JesseM

But they are coordinate charts which have a specific relevance to physics, namely that all physical phenomena which obey relativity must obey Lorentz-invariant equations which are the same in each inertial frame (and Lorentz-invariance is understood as a physical symmetry of the laws of nature, just like translation invariance and CPT symmetry). So if you want to have "instantaneous" communication, that means either that this instantaneous communication obeys the postulates of relativity and therefore allows communication backwards in time (a violation of 'causality' in physics terminology), or it means that there is a preferred definition of simultaneity and hence the laws governing instantaneous communication are not Lorentz-invariant and violate the first postulate of SR. As someone once said, "FTL, relativity, causality: you can only pick two".

Fredrik

This is wrong. If the recipient (Bob) is stationary in a such a frame, he receives the message before it was sent, and if there's no lower bound on the time it takes him to detect the signal, read the message and write the reply, and no upper bound on the speed with which he can send the reply, then he can send a reply to Alice that both of them will agree arrives before the original message was sent.

granpa

I figured somebody would say something like that. in such a universe there would be a single simultaneous 'now' for everbody. a single preferred frame.

events on board a rocket would be out of synch but they would be able to detect that and it wouldnt lead to any paradox's.

its no different from aether theory or any other theory that has a preferred frame. (a 'real' now)

atyy

I think there is no required speed limit for everything in a Galilean universe, but there is a speed limit for light, because of Olber's paradox.

Newtonian gravity travels instantaneously, so it would be required that something travels faster than light?

Fredrik

I have presented the argument for paradoxes. You haven't pointed out any flaws in it, and you haven't presented any arguments for your claim. Why would there be a preferred frame, and which one would that be?

granpa

well. set a single clock to send out a signal instantaneously telling everyone what time it is and that would be the preferred 'now'.