Paradoxes if instantaneous signals

[koolmodee]

Would there be paradoxes arise 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]

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

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.

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

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

Or are speed limits only necessary in SR and GR?

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

 

[bernhard.rothenstein]

Would there be paradoxes arise 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

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]

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

Correct - no time paradox created.

 

[Fredrik]

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

Correct - no time paradox created.

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]

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?".

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]

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.

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.

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?

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]

No just instantaneously information transfer nothing travels no change to SR...

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]

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

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]

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.

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 wouldn't lead to any paradox's.

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

 

[atyy]

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?

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 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 wouldn't lead to any paradox's.

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

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'.

 

[Fredrik]

Only to an observer at rest in that frame. To someone who isn't, the "instantaneous" signal isn't instantaneous. The message arrives either before or after it was sent, depending on the observer's velocity.

To get your conclusion, you have to assume that everyone agrees which transmissions are instantaneous, but there's nothing in the original question that justifies that assumption.

 

[granpa]

To someone who isn't, the "instantaneous" signal isn't instantaneous.

...there's nothing in the original question that justifies that assumption.

an instantaneous signal was the only assumption.

 

[Fredrik]

Then your conclusion is just wrong, because of what I said in #18. Anyone else can also send out a signal that's instantaneous in their rest frame, and that defines another preferred "now". So all the frames are "preferred", not just one.

 

[JesseM]

I think Fredrik is talking about the question of what instantaneous signalling would mean in the context of relativity, whereas granpa is imagining a model where relativity proves wrong because there's a preferred definition of simultaneity which determines the behavior of instantaneous signals. Like I said earlier, "FTL, relativity, causality: choose only two". Fredrik is talking about a situation where we discard causality but keep the other two, granpa is talking about a situation where we discard relativity but keep the other two.

 

[granpa]

a preferred frame is no different from any other frame. why would it change or do away with relativity?

 

[JesseM]

a preferred frame is no different from any other frame. why would it change or do away with relativity?

Because the first postulate of relativity says that all fundamental laws of physics must work the same way in every inertial frame. One way of thinking about this is to say that if you have different experimenters in windowless ships moving inertially, if they both perform the same experiment they're guaranteed to get the same result according to relativity, so there's no way either of them can determine their speed relative to any preferred absolute rest frame. If there were such a thing as an instantaneous signalling device, and it had a preferred frame, then an experimenter in a windowless ship at rest in this frame would get a different result with this device than an experimenter in a windowless ship moving relative to this frame, and both could determine their speed relative to the preferred frame. Thus, if such a device existed it would prove relativity incorrect.

 

[granpa]

well that's taking a broader view of relativity than I prefer. to me relativity is simply that moving objects shrink, become time dilated and experience loss of simultaneity.

 

[JesseM]

well that taking a broader view of relativity than I prefer. to me relativity is simply that moving objects shrink become time dilated and experience loss of simultaneity.

Your definition is different from the one used by all physicists--Einstein's two postulates are always seen as essential to the definition of relativity. Also, what do you mean by "experience loss of simultaneity"? Relativistic simultaneity is just a convention about how to synchronize clocks, there's nothing stopping you from synchronizing them in a different way. The physical argument for using this convention is precisely the fact that the laws of physics will be the same in different frames if you adopt this convention, while they won't be if you adopt some other simultaneity convention.

 

[matheinste]

Hello granpa

Quote:-from 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.----

Question:- from Fredrik

---Why would there be a preferred frame, and which one would that be? ---

Exactly what i asked in response to the same statement in a previous thread but never received a committed answer.

Matheinste.

 

[RandallB]

I have presented the argument for paradoxes. You haven't pointed out any flaws in it,

Several have pointed it out you chose to ignore it. Instant messages don’t travel in a frame; they do not have a speed.

You cannot assume something far away but not moving in your common Ref Frame will receive an instant message it at the same Clock Time as you sent it because you have already agreed to the simultaneity rules right. You could calculate the correct time that instant massage would arrive by using the correct preferred frame. But again you have agreed to abide by simultaneity rules (I am right about that I hope), Thus you don’t know what frame is preferred and therefore don’t know when that instant message will arrive there.

BUT once and only when you get your instant message system working (good luck with that) we will immediately be able to use it to define which of the many reference frames is in fact preferred to use with SR.

Any other claims require ignoring simultaneity and are of no use here. So if you’re not respecting simultaneity try the philosophy forum.

 

[JesseM]

Several have pointed it out you chose to ignore it. Instant messages don’t travel in a frame; they do not have a speed.

You could say the speed was infinite in that frame (using the assumption that speed = distance/time, in the limit as the time goes to zero the speed goes to infinity). In any case, you don't have to worry about the speed, you can just worry about the time between the signal being sent at one location and the signal being received at another. If it is possible to send a signal such that the event of it being sent and the event of it being received are simultaneous in one frame, then assuming there is a nonzero spatial separation between the events in this frame, the simultaneity rules of relativity guarantee that there is another inertial frame where the event of the signal being received actually happens at an earlier time than the event of it being sent. And according to the first postulate of relativity, if there is one inertial frame where it is physically possible to send signals such that they will be received before they are sent, this must be possible in every inertial frame. Do you disagree with any of the above?

If not, consider a situation where you are traveling away from me inertially at some sublight speed, and I send you a signal such that the event of it being sent by me and the event of it being received by you are simultaneous in my frame, which means the event of it being received will happen before the event of it being sent in your frame. If you immediately send a reply such that the event of it being sent by you and the event of it being received by me are simultaneous in your frame (which must be possible if it was possible in my frame, according to the first postulate), then the reply will be received before it was sent in my frame. By arranging the distances and the (sublight) speeds of my ship and your ship in the right way, it is possible for me to receive your reply before I sent the original message. I can illustrate this with a numerical example if you have doubts about this.

You cannot assume something far away but not moving in your common Ref Frame will receive an instant message it at the same Clock Time as you sent it because you have already agreed to the simultaneity rules right.

The whole point of an "instantaneous signal" is that it is received at the same time it is sent, otherwise it wouldn't be instantaneous. Of course, because of the simultaneity rules, a signal which travels instantaneously in one frame wouldn't travel instantaneously in all frames; in some frames it would seem to travel FTL but forward in time (for example, in my frame I might receive the signal 10 light years away from the position it was sent, but only 5 years after the time it was sent), in other frames it would actually be received before it was sent. But according to the first postulate of relativity, anything which is possible in one frame must be possible in all frames. Of course, you're free to imagine that the first postulate is actually incorrect when applied to instantaneous signalling, in which case you can avoid the problem of causality violations; but in this case, you are imagining that the theory of relativity is incorrect.

You could calculate the correct time that instant massage would arrive by using the correct preferred frame.

If there is a preferred frame for instantaneous signalling (i.e. if it is possible to build a device such that signals can be received at the same moment they are sent according to one frame's definition of simultaneity, but it is not possible to build a device such that signals can be received at the same moment they are sent according to any other frame's definition of simultaneity), then that means relativity is incorrect. If relativity is correct, all laws of physics must work the same way in every inertial frame, including the laws governing an instantaneous signal transmitter.

 

[Fredrik]

well that's taking a broader view of relativity than I prefer. to me relativity is simply that moving objects shrink, become time dilated and experience loss of simultaneity.

The special theory of relativity consists of a mathematical model (Minkowski space) and a set of postulates about what "mathematical things" in the model we actually measure when we perform experiments. Example: What a clock measures is the proper time along the curve that represents its motion. The complete list of such postulates is what defines special relativity.

That guarantees that there are no preferred frames. A theory with a preferred frame is not special relativity.

I have presented the argument for paradoxes. You haven't pointed out any flaws in it,

Several have pointed it out you chose to ignore it. Instant messages don’t travel in a frame; they do not have a speed.

You're clearly defining "instantaneous" in a way that contradicts special relativity. Normally, I would explain that in more detail, but JesseM did that very well, so I suggest you read his posts.

 

[granpa]

so that's what this thread is really about. a chance to beat up on aether theory. well count me out.