The logic of information travel.

[dydxforsn]

I was discussing with my E&M professor the idea of faster than light information exchange, which of course we found to be impossible, it didn't take much analysis of the simultaneity of events as seen by Einstein to realize that faster information travel than light would completely change the theory (making the beta term different if not making time completely invariant of location), a theory that many take for granted today (and how could somebody not, I find it the most interesting theory in science, simple, profound display of logic.)


My question is, what is the logic for faster than light information travel? What is the argument? I notice (seeing I don't read them) popular culture science magazines speak of quantum entanglement taking over fiberoptic lines and a handful of other nonsense and I just don't see why people think faster than light information travel is at all possible or conceivable.

 

[Phrak]

I was discussing with my E&M professor the idea of faster than light information exchange, which of course we found to be impossible, it didn't take much analysis of the simultaneity of events as seen by Einstein to realize that faster information travel than light would completely change the theory (making the beta term different if not making time completely invariant of location), a theory that many take for granted today (and how could somebody not, I find it the most interesting theory in science, simple, profound display of logic.)

Do you also understand that electromagnetic waves commonly travel faster than c? Light carries information. Can you explain this? As well, electron waves must necessarily exceed c.

 

[yuiop]

My question is, what is the logic for faster than light information travel? What is the argument? I notice (seeing I don't read them) popular culture science magazines speak of quantum entanglement taking over fiberoptic lines and a handful of other nonsense and I just don't see why people think faster than light information travel is at all possible or conceivable.

A lot depends on what you mean by "information" or "meaningful information". In SR everything with rest mass is constrained to travel at less than the speed of light and light that has zero rest mass and positive energy is constrained to travel at the speed of light. The fastest form of communication in SR is by way of photons which have energy. Some forms of apparent superluminal signalling such as swiping a laser beam across the surface of the moon, or a nearly parallel wave hitting a beach have in common that no mass or energy is transferred from A to B faster than the speed of light and it not possible for A to select what information he wants to send to B (or when), so it can not be used for transmitting meaningful information.

In quantum entanglement, one interpretation is that if a photon passes through a polariser, it entangled partner instantly re-orientates itself to the same orientation as its partner even if the two entangled particles are light years apart. It seems that at the quantum level, there is a connection between entangled particles that is indeed superluminal, but like other apparent superluminal signalling methods, there is no transfer of energy from A to B and no way to use the phenomena to transmit meaningful (non-random) information from A to B. There are alternative interpretations that try to get around the non-local (superluminal) behaviour of entangled particles, but these come at a price. The many worlds interpretation (MWI) requires that every time a decision is made or a particle travels through an analyser that the universe splits into a infinite number of parallel universes and some sort of super computer sorts these parallel universes into the correct corresponding universes with consistent histories in real time. So it all it takes to avoid the superluminal behaviour of quantum particles is the creation and sorting of an infinite number of infinite universes every plank time interval. Each of these infinite universes splits into a further infinite universes a moment later creating a super exponential increase in universes every second. Probably easier to accept that superluminal signalling is possible between entangled quantum particles and that this does not violate SR because no energy is transferred superluminally and no meaningful information can transferred superluminally. Yes, this does mean that there is no clear distinction between cause and effect in the connection between entangled quantum particles because the connection is spacelike.

So what is "meaningful information"? Well I am not sure how to define that, but I can give an example of meaningless information. Let us say Bob has a superluminal receiver which when switched on always reads out a random sequence of ones and zeros with an average of 50% 1s and 50% 0s. Alice who is light years away has a superluminal transmitter. Whenever it is switched on, whatever is transmitted is instantly received by Bob's superluminal receiver. Each 1 that is transmitted by Alice corresponds with a 1 arriving instantly at Bob's location and each 0 transmitted by Alice corresponds with a 0 arriving instantly at Bob's location. The catch is that Alice has no control over whether her transmitter transmits 1's or 0's so the information transmitted by her is meaningless in the sense that it is random. Bob can make no sense of the messages transmitted by Alice and does not even know if Alice's transmitter is switched on or not because either way, all Bob receives is a random sequence of 1's and 0's. It seems that quantum particles have "superluminal connections" that do not violate SR. It is very clever how nature works when you think about it.

 

[dydxforsn]

good post yuiop, but I have one question. With the photon example why exactly can't you just use a linear polarizer on one side of an entangled beam and communicate via the angles 0-180 degrees?


But yeah, I completely forgot about the distinction between meaningful and useless information. That explains the search.

 

[K^2]

Because whether the photon passes through linear polarizer is going to be random. All you are going to know is that if your photon passed through your polarizer, it did the same for the other guy. That's information, but it still doesn't let you encode useful information.

As a result, entanglement can be used in communication protocols for security or to carry quantum information across classical channels (quantum teleportation), but it cannot be used for FTL communication, since you are still relying on a secondary channel that is light-limited.

The only channel that seems to allow meaningful information to be communicated FTL is quantum tunneling, but it has many limitations. It does not violate causality locally, since the tunneling signal is not technically propagating through space, and global causality may be violated according to General Relativity anyways.

 

[yuiop]

good post yuiop, but I have one question. With the photon example why exactly can't you just use a linear polarizer on one side of an entangled beam and communicate via the angles 0-180 degrees?

Thanks. To try and answer your question let me describe a simple thought experiment and maybe you can tell me if it basically describes what you have in mind.

Let us say we have a source of vertically polarised entangled photons. Bob is close to the source with a polarising analyser on one beam and Alice is much further away and detects photons on the second entangled beam. Let us say this source consistently produces entangled photons at a rate of once per second. When the source has been switched on for a sufficient period, Alice starts to detect photons at a rate of once per second. Bob rotates his source to various positions and Alice continues to make positive detections at a rate of once per second. Obviously not very useful as a communication device because Alice does not have a polarising analyser in her beam. So let's give Alice an analyser that is orientated at 0 degrees (vertical) and she leaves it in that position. Now when Bob has his analyser orientated at 0 degrees (vertical) Alice will receive photons at a rate of once per second, but if Bob rotates his analyser to 90 degrees, Alice will instantly stop receiving photons. Bob and Alice now have a means to transmit information FTL. What has gone wrong? The trick was that the source emits entangled photons with a consistent vertical orientation, but it would seem such a source is forbidden by QM. In reality, the source can only emit photons with a random polarisation angle. Now Alice receives a random sequence of 1's or 0's and whatever angle Bob rotates his analyser to, Alice continues to receive a random sequence of 1's or 0's. (Here a 1 means a photon passed through a polariser and is detected while a 0 means no photon was detected in a one second interval.) It is only when Bob and Alice compare notes later by normal sub-luminal methods that they can detect that there is a correlation between their measurements. This means that Bob and Alice cannot exploit the super-luminal connection between the entangled particle to transmit meaningful FTL information to each other.

 

[JesseM]

it didn't take much analysis of the simultaneity of events as seen by Einstein to realize that faster information travel than light would completely change the theory (making the beta term different if not making time completely invariant of location),

Why do you think the beta term would have to change or time wouldn't be invariant of location? Even if FTL signal transmission were possible, inertial frames could still be constructed the same way with clocks synchronized by light signals. The real problem with FTL signals in SR is that they would also imply that signals could be sent backwards in time (i.e. you could send a message into your own past light cone), as discussed here.

 

[Naty1]

My question is, what is the logic for faster than light information travel?

There is none.


PHRAK

Do you also understand that electromagnetic waves commonly travel faster than c? Light carries information. Can you explain this?

You know better than that!

Only the phase velocity might exceed c with electromagnetic waves, as in a plasma, for example, but the inverse, the group velocity, is what carries information...so no information can be transmitted at superluminal velocities...

 

[dydxforsn]

nah, nvm Yuiop I was thinking macroscopic many photon light for some reason, I wasn't thinking. Yeah, it makes sense why the information is random for a single photon at a time (they just kind of randomly decide which orientation to take when confronted by a LP if I remember right, though I'm just a senior undergraduate and so the mechanism is beyond my scope). Thanks a lot for your time though!JesseM, it just seems to me that Einstein would use something other than light (that was faster) when discussing what he could perceive to be "simultaneous". I see what you're saying and I would say it like that if I were to write something scientific, but it's sort of the same thing (I think) to say your perception of simultaneity has changed and that you had a time travel experience. I dunno, the faster than light travel may not be speed invariant (different depending on the reference frame) and that starts a train of thought that is hard to think about and ponder the implications. If the faster than light speed was invariant of reference frame than it would mean beta would have to change right?

There's nothing special about light except that it's the fastest.

 

[Phrak]

There is none.

PHRAK

You know better than that!

Only the phase velocity might exceed c with electromagnetic waves, as in a plasma, for example, but the inverse, the group velocity, is what carries information...so no information can be transmitted at superluminal velocities...

OK, then we agree on item one. The phase velocity is the wave velocity. However it's not uncommon but common. Any interference will do it, it's the mode of transmission in waveguides that supports waves that are slices of interference waves. v_groupv_phase=c². Only planar light has a phase velocity of c. The generalization to other modes in vacuum is common here, and everywhere, but false.

But looking at the mass dilation equation and making wide generalizations, as I imagine the OP and his prof might be doing is not enough.

Next, the group velocity is not really the information velocity. See signal velocity.

 

[JesseM]

JesseM, it just seems to me that Einstein would use something other than light (that was faster) when discussing what he could perceive to be "simultaneous".

Not if he wanted all laws of physics, including the laws governing electromagnetism (Maxwell's laws in Einstein's time, or quantum electrodynamics in ours) to respect the "principle of relativity" which says they should obey the same equations in all inertial frames. These laws predict that electromagnetic waves (or photons) have an invariant speed of c, so you need a coordinate transformation which has the property that something moving at c in one frame also moves at c in every other frame. More generally, the equations of electromagnetism are "Lorentz-invariant", meaning that if you take the equations expressed in the coordinates of one frame and then apply the Lorentz transformation (which transforms coordinates in one inertial frame to coordinates in another inertial frame, assuming you're using inertial frames of the type Einstein suggested in his 1905 paper), you'll find that the equations look exactly the same when expressed in the coordinates of the second frame. The basic prediction of relativity is that all fundamental laws of physics are Lorentz-invariant like electromagnetism, and there's nothing inconsistent about the possibility that FTL particles could exist but the equations governing their behavior would still be Lorentz-invariant.

 

[dydxforsn]

The faster than light thing is an awful paradox and I guess it's debatable in which of many ways it would mess with the theory, so it's hard for me to choose the exact way to rebuttle. I can think of a few that would be hard to reconcile and would certainly make people feel uncomfortable. Namely, there would be a reference frame in the universe that would be a standard and if you found which frame had the greatest speed for this "thing" you would have found a preferred reference in the universe. I believe god created all reference frames equally heh (sometimes the first postulate simply states the equivalence of all reference frames, IE. you can't find a preferred frame)

On the topic of time travel though, I'm saying that you wouldn't think that was the past because of what you think is simultaneous. Heh, we're arguing two sides of a paradox that will go nowhere.

 

[Naty1]

PHRAK: "...Next, the group velocity is not really the information velocity. See signal velocity."

yea, there are unsualy situations...I'm not familiar with them but my understanding NONE can be used for information transmissions...

wikipedia: http://en.wikipedia.org/wiki/Signal_velocity

The signal velocity is the speed at which a wave carries information. It describes how quickly a message can be communicated (using any particular method) between two separated parties. Every signal velocity is always slower than (or equal to) the speed of a light pulse in a vacuum (by Special Relativity).

 

[Phrak]

PHRAK: "...Next, the group velocity is not really the information velocity. See signal velocity."

yea, there are unsualy situations...I'm not familiar with them but my understanding NONE can be used for information transmissions...

wikipedia: http://en.wikipedia.org/wiki/Signal_velocity

I suppose so. Maybe. But what is information? I keep trying to pin it down as a physically meaningful quantity but it keeps getting away.

 

[Naty1]

But what is information? I keep trying to pin it down as a physically meaningful quantity but it keeps getting away.

beats me...it is a slippery concept...the following ideas are as close as I have gotten...

(My own problem is that I still don't understand entropy. And I KNOW my professor in college has HIS trouble with it...)

Entropy is in fact a subset of information theory, but wiki treats it a bit differently here:

A key measure of information is known as entropy, which is usually expressed by the average number of bits needed for storage or communication. Entropy quantifies the uncertainty involved in predicting the value of a random variable. For example, specifying the outcome of a fair coin flip (two equally likely outcomes) provides less information (lower entropy) than specifying the outcome from a roll of a die (six equally likely outcomes).

There are other mathematical definitions for communication theory:

By definition, the amount of self-information contained in a probabilistic event depends only on the probability of that event: the smaller its probability, the larger the self-information associated with receiving the information that the event indeed occurred.

http://en.wikipedia.org/wiki/Information_content

I just checked Roger Penrose's monstrous book THE ROAD TO REALITY which seems to have some mathematics on just about everything...but only Schrodinger's Cat involving "information"..so maybe it's not "real" ??

 

[Phrak]

Researching 'physical information' would be a worthy persuit.

Apparently others don't have such a hard time with the meaning of physical information as I. Susskin and Hawking argue information loss and black holes. Their idea of information seems to be embodied by quantum numbers.

As I dimly recall, Shannon information entropy and thermodynamic entropy are not exactly the same thing but differ by a negative sign. The quantity called information entropy was named such after noticing its similarity to thermodynamic entropy. At one time I collected books on information theory but read very little. I think the best was by Robert B. Ash, "Information Theory." Shannon's work is very impressive, building an entire new science on four or five additional axioms--definitions really.

Shannon information theory is built on defining information in discrete units--a set of N discrete things. The simplest being bits; the set of two. Obviously, this is not the only way, where quantum computation is carried out with qbits.