[Petrochemicals (OP)]

As in the title, pretty simple, but Google is failing on definition.

[evan_au]

As far as we know, information cannot be transmitted faster than "c"=speed of light in a vacuum.

Although if there are some big masses in said vacuum, there can be more than one path that light can take between two points, and some paths will be faster than others...

[Origin]

I think that you could substitute the word 'signal' for 'information', if that helps.  Just for clarification the speed of light is represented by a small c not a capital C.

[Colin2B]

As in the title, pretty simple, but Google is failing on definition.

You could, as @Origin says, consider it to be the content of a signal, data, or something that changes your knowledge.
I assume you are thinking of this discussion  https://www.thenakedscientists.com/forum/index.php?topic=82864.msg651428#msg651428

In this case we have some knowledge of the system, that both polarisations will be the same, but we don’t know what state the polarisations were prepared in. The state of the polarisation is sent from A to B at the speed of light, but B still doesn’t know the state until it is measured at B. As soon as B measures the state his/her knowledge changes due to that information, but that information is local, it only travels from the measuring equipment to the person at B (at speed c).

[TommyJ]

As in the title, pretty simple, but Google is failing on definition.

You could, as @Origin says, consider it to be the content of a signal, data, or something that changes your knowledge.
I assume you are thinking of this discussion  https://www.thenakedscientists.com/forum/index.php?topic=82864.msg651428#msg651428

In this case we have some knowledge of the system, that both polarisations will be the same, but we don’t know what state the polarisations were prepared in. The state of the polarisation is sent from A to B at the speed of light, but B still doesn’t know the state until it is measured at B. As soon as B measures the state his/her knowledge changes due to that information, but that information is local, it only travels from the measuring equipment to the person at B (at speed c).

Wikipedia:

In Information theory one of the main measure is entropy.
Entropy quantifies the amount of uncertainty involved in the value of a random variable or the outcome of a random process.

From the related parallel thread link quote:
'It's just that the complex quantum state of the universe is unknowable, so if something (eg the spin of an electron) becomes entangled with the universe, the state of the electron also becomes unknowable.'

This is true for what I have been taught and used in communication field.
Irrespective to the transfer media or method it is still information (even meaningless till you discard it or decipher).

[Colin2B]

In Information theory one of the main measure is entropy.
Entropy quantifies the amount of uncertainty involved in the value of a random variable or the outcome of a random process.

From the related parallel thread link quote:
'It's just that the complex quantum state of the universe is unknowable, so if something (eg the spin of an electron) becomes entangled with the universe, the state of the electron also becomes unknowable.'

This is true for what I have been taught and used in communication field.
Irrespective to the transfer media or method it is still information (even meaningless till you discard it or decipher).

I agree with the principle of what you are saying. Could you expand your reply to explain to @Petrochemicals how it applies to the specific question he is asking.

 

[TommyJ]

Thank you, Colin2B and everybody here.
More science and comprehension on the subject.

Information theory is a part of mathematics and empirical science and a study of quantification (counting and measuring).
The question comes to the information transfer between at least two detectors.
It is closely bound to probability theory.

Example 1. Identifying the outcome of a fair coin flip (with two equally likely outcomes) provides less information than specifying the outcome from a roll of a die (with six equally likely outcomes).
These are examples of probability chance, but not yet information gained. Until a coin is flipped, there is no information outcome - you need to see the result, which cannot come faster than c.

Example 2. Let’s take an information delivery from the simplest system example of entangled particles. This gives better probability chances, but the principle is still the same. Until the state of one measured detector is transferred to another (not faster than c), there is no information transferred.

The experiment of a decaying particle of zero spin, which separates into two particles. Hence the total spin is zero, each new particle will have the same spin value but with opposite directions. We don’t know which direction each particle’s spin is, since it was not determined before separation.
.
What if you measure what each particle’s spin is (in the state of not determined before separation).

As the particles are entangled, there is a correlation between directions, but the correlation level is unknown: orthogonal (fully undetermined), opposite (fully correlated), and any middle state (with any probability of determination).

When you measure at least one of the spins, the system is still undetermined. Not on any side you know what correlation of two measurements would be. Until you send the measurement result from one side to another (not faster than c).

You only know the probability distribution of the ‘0 or 1’ state on the other side before transferring the measured state.

[Petrochemicals (OP)]

Thank you, Colin2B and everybody here.
More science and comprehension on the subject.

Information theory is a part of mathematics and empirical science and a study of quantification (counting and measuring).
The question comes to the information transfer between at least two detectors.
It is closely bound to probability theory.

Example 1. Identifying the outcome of a fair coin flip (with two equally likely outcomes) provides less information than specifying the outcome from a roll of a die (with six equally likely outcomes).
These are examples of probability chance, but not yet information gained. Until a coin is flipped, there is no information outcome - you need to see the result, which cannot come faster than c.

Example 2. Let’s take an information delivery from the simplest system example of entangled particles. This gives better probability chances, but the principle is still the same. Until the state of one measured detector is transferred to another (not faster than c), there is no information transferred.

The experiment of a decaying particle of zero spin, which separates into two particles. Hence the total spin is zero, each new particle will have the same spin value but with opposite directions. We don’t know which direction each particle’s spin is, since it was not determined before separation.
.
What if you measure what each particle’s spin is (in the state of not determined before separation).

As the particles are entangled, there is a correlation between directions, but the correlation level is unknown: orthogonal (fully undetermined), opposite (fully correlated), and any middle state (with any probability of determination).

When you measure at least one of the spins, the system is still undetermined. Not on any side you know what correlation of two measurements would be. Until you send the measurement result from one side to another (not faster than c).

You only know the probability distribution of the ‘0 or 1’ state on the other side before transferring the measured state.

But the actual seperation of the particles Is I believe the information speed limit start point. If you seperated the particles from each other at c, that would be the limiting speed would it not ? Similarly rather than sending the signal of the particles state at C, you could travel at C to the particles to determine their state? This would not violate the relevant rules.  But from the entangled particles  do have to be seperated and moved within the confines of lightspeed limitations.

If the above is true information can be treated just like lightspeed and is of no real importance.

[TommyJ]

But the actual seperation of the particles Is I believe the information speed limit start point. If you seperated the particles from each other at c, that would be the limiting speed would it not ?

Separation is not sending information, this is explanation of how the most correlated 2 detectors can be achieved.

Similarly rather than sending the signal of the particles state at C, you could travel at C to the particles to determine their state? This would not violate the relevant rules.  But from the entangled particles  do have to be seperated and moved within the confines of lightspeed limitations.

Separation related to getting information for non-local system. Could you travel between particles with c?
The fastest way to send a bit of information is c. If your information requires more bits (a 'word'), it would be a bulk of information, each bit is sent by c.
Take a pair of mobile transmitter - receiver. Before decoding the received information, the receiver should get state of transmitter (bit rate, starting and ending sequence time). This state should be sent from transmitter to receiver additionally.
Simplest bit of information is knowledge, is it '1' or '0', and you cannot know this without additionally sent state (what is '1' and what is '0': left/right; green/blue, etc).

[Colin2B]

I suspect the length of the replies and the amount of information hasn’t helped to clarify.

But the actual seperation of the particles Is I believe the information speed limit start point. If you seperated the particles from each other at c, that would be the limiting speed would it not ?

yes, but you don’t know the information until you make the measurement, all you know is it could be one of 2 values and even that information had to be transferred at light speed or less.

Similarly rather than sending the signal of the particles state at C, you could travel at C to the particles to determine their state? This would not violate the relevant rules. 

correct

But from the entangled particles  do have to be seperated and moved within the confines of lightspeed limitations.

yes, no other way to do it.

If the above is true information can be treated just like lightspeed and is of no real importance.

Not sure why you say ”of no real importance”. The state of 0s and 1s in your computer can be of great importance, but is limited to light speed.

[evan_au]

the entangled particles  do have to be separated and moved within the confines of lightspeed limitations.

The entangled objects don't need to be electrons or protons, which are limited to travel at slower than c (as are you).
- It is possible to entangle massless photons, in which case they can travel at exactly c.

[TommyJ]

Not sure why you say ”of no real importance”. The state of 0s and 1s in your computer can be of great importance, but is limited to light speed.

And this is exactly what information is, otherwise you know only 50/50% of 'yes' or 'no', which is the worst case of being informed.

[Petrochemicals (OP)]

Not sure why you say ”of no real importance”. The state of 0s and 1s in your computer can be of great importance, but is limited to light speed.

It is of no importance due to the fact that the separation can only happen at maximum C, so essentially this idea of separation is limited by lightspeed due to the separation, so making a statement about information exchange is secondary to the separation. Basically information is governed by the light speed limit on movement by C anyway.

[TommyJ]

Basically information is governed by the light speed limit on movement by C anyway.

Information transfer.

[Colin2B]

Not sure why you say ”of no real importance”. The state of 0s and 1s in your computer can be of great importance, but is limited to light speed.

It is of no importance due to the fact that the separation can only happen at maximum C, so essentially this idea of separation is limited by lightspeed due to the separation, so making a statement about information exchange is secondary to the separation. Basically information is governed by the light speed limit on movement by C anyway.

I really do not understand what you are trying to say.

[chiralSPO]

Unfortunately, misinformation apparently travels instantaneously 

On a more serious note:

For all "non-quantum" systems, it should make sense that for any two systems to interact, there must be some signal or particle or wave or something that travels from one to the other. Since there are no particles, waves, or other signals that we know of that can travel faster than c, this sets a lower limit on how long it takes for one system to influence the other, based on how far away the are from each other.

Things get kind of (ok, really) counterintuitive when considering systems and phenomena that are ruled by quantum mechanics. Depending on what sort of information you are interested in, space may be completely irrelevant—but this also means that this information cannot be transferred.

For example: take the classic case of two entangled particles, in which we know that the spin of the whole system is 0, but both particles have a superposition of nonzero spin (i.e. one particle is 50% +1 / 50% –1 and the other is 50% –1 /50% +1). Based on this relationship, anyone who observes one of the particles collapses the superposition and makes one of the particles spine up, and the other spin down. knows that the other has precisely the opposite spin—no matter where it is. If I check the spin particle that is close to me, it takes non-zero amount of time based on the distance between me and that particle. If I see that it has a spin of +1, then I already (instantly) know that the other particle has a spin of –1, even if it is ten billion light years away (somehow). But here's the catch: no information has moved from the distant particle to the close one or to me (and vice versa). If an observer on the other side of the universe was observing the other particle, they would also see that the superposition had collapsed (and presumably would also see the same result? but I'm not entirely sure of that... for some things, multiple observers can get contradictory answers, and some things they must get the same). But neither observer would be able to send a signal to the other (each collapses their own particle when they observe it, so they cannot know if a collapse is due to their own observation or not).

[TommyJ]

Please note that entangled particles are an example of the simplest and best correlated system.
An example with coin or dice gives less chance of probability of guessing the system state (between 1 and 0).
Guess-information is instantaneous

[Halc]

Since there are no particles, waves, or other signals that we know of that can travel faster than c, this sets a lower limit on how long it takes for one system to influence the other

This assumes the principle of locality (PoL), something which has never been proven. There might be signals that we don't know of, such as those proposed by realist interpretations like Bohmian mechanics.
I hold to PoL myself, but it is merely a preference, not something that I can assert to be the case.

two entangled particles, in which we know that the spin of the whole system is 0, but both particles have a superposition of nonzero spin (i.e. one particle is 50% +1 / 50% –1 and the other is 50% –1 /50% +1). Based on this relationship, anyone who observes one of the particles collapses the superposition and makes one of the particles spin up, and the other spin down. knows that the other has precisely the opposite spin

This assumes the distant particle has an actual spin, even unmeasured. This assumes the principle of of counterfactual definiteness (PoCD). Bell's theorem showed that only one of PoL and PoCD can be true, so your statements cannot both be true.
So if I measure spin-up on my local particle, I simply know that were the far one to be measured, it would be spin down. But until it is measured, it has no known state. If it's a light year away, it would take a year for me to measure it. It having been measured by something else doesn't count as a measurement by me. Not yet at least.
So for instance in MWI/RQM (similar for purpose of this example), I might have just measured spin-up locally. The far particle measurement takes place well outside the light cones of my local measurement. Both spin up and spin down are measured, entangling the distant particle with the measurer in separate worlds, but relative to me, that distant particle along with the measuring device is in superposition of both states. Only when I measure the result of that distant action will the state of the far particle collapse into spin-down.

If I see that it has a spin of +1, then I already (instantly) know that the other particle has a spin of –1

You instantly know that when you measure the far particle, you will get spin -1. You don't know that it's that state before it is measured. See the difference?

If an observer on the other side of the universe was observing the other particle, they would also see that the superposition had collapsed

Can't see that. I could send a message if that were possible.  I have a bucket of entangled particles here and you have the other halves a light year away. I'm watching the world cup. If team A wins, I measure all the particles, collapsing them. If not, I leave them unmeasured.  The guy at the far end knows when the game is over. If he observes his bucket of particles no longer in superposition, he knows that A won, else he knows that B won. Message sent. That violates the limit of c on information transfer.
All the far guy can do is measure his particles, which just gives random results and tells him nothing about the game.

[Petrochemicals (OP)]

If an observer on the other side of the universe was observing the other particle, they would also see that the superposition had collapsed

Can't see that. I could send a message if that were possible.  I have a bucket of entangled particles here and you have the other halves a light year away. I'm watching the world cup. If team A wins, I measure all the particles, collapsing them. If not, I leave them unmeasured.  The guy at the far end knows when the game is over. If he observes his bucket of particles no longer in superposition, he knows that A won, else he knows that B won. Message sent. That violates the limit of c on information transfer.
All the far guy can do is measure his particles, which just gives random results and tells him nothing about the game.

But how did the guy at the other end of the universe get the particles? Did you send them to him or did he come to collect? Either way the the distant  person could have actually just made the journey to the information source as fast or faster than he could have with the entangled particles?

[Halc]

But how did the guy at the other end of the universe get the particles?

Probably brought them with him when he first went. He's only a light year away, not "at the other end of the universe". Maybe he left 40 years ago, so the particles would have needed to be prepared then.

Either way the the distant  person could have actually just made the journey to the information source as fast or faster than he could have with the entangled particles?

The information about the world cup (played yesterday) was not available when the particles were prepared 40 years ago.