Why quantum entanglement doesn't allow faster-than-light communication (2016)
forbes.com
forbes.com
Correlation which is not beyond classical is shaking up a shoebox with a pair of gloves in it, and having two people take the gloves far away from each other to then observe what hand they got. They then understand the hand the other has. There’s one bit of information here corresponding to which hand went to person A.
Entanglement is just this but “more.” You can’t communicate with a pair of gloves. Person A does not know when person B has realized person A knows what glove they have. Just the same, it does not matter who matters which of the two particles in a Bell pair first! Many quantum information theorists don’t even believe the wave function is “real” but just a mathematical tool for making predictions about measurement outcomes.
You should come at entanglement from this angle, because the main difference between the bell test and the pair of gloves is the state of the particles is undetermined before measurement, and the chosen measurements will result in different correlations between the measurement outcomes.
Example: Lets say you check if the glove is white or black, you see it is white. Then you check if the glove is half white/half black, or half black/half white, you see it is half white/half black. Then you check again if it is white or black, now it is black. That is how quantum gloves would work, but real gloves doesn't work that way.
You only get to check once, I think. The rest doesn't matter, supposedly.
Changing a particle like this by making repeated measurements is a standard example in undergrad quantum mechanics.
Edit: There is always a part of the particles state that you can't know, you know Heisenberg's indeterminacy principle, so if you measure position you now makes velocity undetermined, and then if you measure velocity now you make position undetermined, and then if you go back and try to measure position the particle will be in a new random spot.
So, it sounds exactly like a "gloves in a box" example, right?
I'm not trying to be cheeky, I'm just pointing out that the example really does sound analogous, as stated so far.
Then if you check number of fingers many times, you get the same result every time. But if you alternate checking fingers and color, you will get random results every time.
Edit: Not that I'm saying this is what original poster meant, just that this is the main difference between quantum particles and our macroscopic objects like gloves.
The odds of one scratch winning are of course 50%, and the odds of the other person winning are of course also 50%. The odds of both people winning are 25%, and both people losing also 25%.
The CHSH experiment suggests otherwise: that when one person loses the other person is less likely to also lose, such that the likelihood of both losing is only 15%. How can this happen? I haven't a clue. I'm not a theoretical physicist, and I haven't personally conducted this (~ $5,000) experiment. But it's a result that deeply bothers me.
If you build this system you can then scratch a whole lot of tickets. Each ticket has a 50% chance of a side having the prize, but as long as both parties are consistently scratching the same side of entangled pairs they will win more often than they lose, revealing whether or not they are in agreement. I have no idea how this could be true, but people keep running the experiment and keep getting similar results. And, it seems like this could result in faster than light communication, so there's probably a better ELI-5 out there.
That’s easy, even without quantum mechanics. All you need is to have a different distribution of lottery tickets. Print tickets such that, if one wins, the other is more likely to win, which you can do by having the number of winning spots per ticket be random and correlated. For example, there could be a 50% chance that neither ticket has a winning spot and a 50% chance that each ticket has one winning spot.
But you could imagine a pair of tickets with internal radios, such that, when you scratch one, it tells the other one, and together they simulate a general function where the joint probability of (win on ticket 1, win on ticket 2). If you set up the probabilities appropriately, then you can’t use the tickets to send a signal, and the result is referred to in the literature as “non-signaling boxes” (the magic tickets are the boxes).
Quantum mechanical entanglement can do something like this, except that the probability distributions you can generate with entanglement are a subset of the more general non-signaling boxes.
In order to refute this you need to get into the CHSH experiment's design, which doesn't use the raw detection rate but compares detections that should not have similar results. Imagine that both tickets have a prize on the right side, and both participants have agreed to always choose the left side. CHSH predicts that some of the time the prize will change sides: but, crucially, only from the losing side to the winning side, and only if the other ticket lost, and even if the tickets are revealed close enough in time that a signal could not propagate between them.
The conclusion of CHSH is that detections are correlated to the angle between the sensors, and not the angle between the sensors and the source.
This makes absolutely no sense. There is no such thing as a winning or losing side until it's been scratched, and even if the ticket were able to randomly switch from a loser to a winner, how would it ever know that the other ticket was also a loser? And if it's true that detection is correlated to the angle between detectors, it seems easy enough to build a statistical system around variable sensor angles that is able to communicate instantaneously.
I might not have interpreted everything you said, either. Internet forums aren't the best way to discuss deep problems.
Refute what? I'm pointing out that classical (non-quantum) scratch-off lottery tickets can have the property you described. This is only thematically related to the CHSH game, and I'm rather confused as to what you're trying to say.
The Wikipedia articles about the CHSH inequality are IMO quite bad. The conclusion of CHSH has approximately nothing to do with measurement angles. Here's what CHSH is saying, based on one formulation, which is IMO far, far nicer than Wikipedia's and makes the same point.
1. There's a game that two players could play (with the help of a neutral third party). The neutral third party picks random bits x and y, tells player A the value of x and tells player b the value of y. Each player then chooses a play (A's play is a and B's is b) according to whatever strategy they like, except that they can't communicate. They are allowed to communicate with each other beforehand, though. You can look at sites like this for more details about the game works: https://circles.math.ucla.edu/circles/lib/data/Handout-2987-...
2. If A and B are only allowed to choose random numbers (jointly before the game and separately once it starts) and do local calculation, then they cannot win with more than a certain probability. This is the CHSH inequality, and it's a statement about classical statistics.
3. If A and B are allowed to produce an entangled state before the game and each hold on to one part of the state, then they can make measurements on their parts once the game starts and use those measurements as part of a better strategy. This strategy wins with probability higher than the CHSH inequality allows.
No, if A always scratches the left, and B alternates between left and right, your classical trick of having some tickets with two winners and some with two losers won’t produce the correct win distributions for B’s choices.
The CHSH game is an attempt at explaining the experiment. The core of CHSH is a formula describing an expected distribution: `S = E(a, b) - E(a, b') + E(a', b) + E (a', b')`, where classical explanations can achieve an S with magnitude approaching 2. Experiments arriving at an S > 2 are said to support the quantum theory.
My proposal was intended to be independent of A and B’s strategy. As a fully worked-out example, suppose the tickets are printed like this:
With probability 42.5%: all positions win
With probability 42.5%: all positions lose
With probability 7.5%: Both of A’s options win and both of B’s options lose
With probability 7.5%: Both of A’s options lose and both of B’s options win.
This follows the rules of the game, and it has the following properties. A wins with probability 50% regardless of their strategy, as does B. And A and B get the same outcome 85% of the time.
For the CHSH inequality (following the pretty-bad Wikipedia article), each E term is the probability that A and B both win when they use the indicated strategies, which is 0.425. So S=0.85, which is well within the limit, as it should be since these are extremely boring classical tickets.
You are correct that many say this, but this is a constant source of frustration for me (a physicist who does believe the wave function is the only real thing). These physicists never seem to articulate what then is supposed to actually be “real” (under their definition) or what laws govern the “real” things as opposed to the wave function. Implicit seems to be that there is some kind of separate classical realm that obeys non quantum mechanical laws. Is this separate classical realm to be understood as a macroscopic limit of the quantum realm? But if so then the whole picture is circular since wavefunctions are supposed to be mere bookkeeping devices for classical things.
Or to put this more succinctly, if the wave function is a mere bookkeeping device, then bookkeeping for __what__?
(I should mention that yes I know about QBism and all that and my confusion is not for lack of talking to QBists about such things — I just can’t make heads or tails of what they tell me!)
Bookiping for things that happen so fast and at such a small scale that our current technological tools cannot fully capture data with enough precision and accuracy for us to make an good model of the underlying behaviour.
Imagine you put a spinning ball on top of a frozen lake on a windy day. You are going to observe the ball spin continously towards the same orientation until several gusts of wind make it spin the other way around, and this goes on and on for hours. From the measurements of the wind and current spin of the ball, you can make a model that accurately and precisely predicts the spin of the ball on the almost frictionless frozen lake.
Now imagine your spinning ball is extremely small you can't even see it or any "wind" with any tools that you currently have, but you can still measure its spin to a certain precision. Now imagine this "wind" is so strong and volatile that the tools you have sometimes takes a somewhat accurate physical snapshot of it and sometimes it just misses the gust. You take a look at the somewhat accurate measured spin and it seems to have changed without any reason, but it was just because your tooling is not accurate and precise enough to capture all the quantum gusts of wind that influence the quantum ball, so it looks like the ball is changing its spin randomly, whist in reality, we just can't precisely measure whatever is influencing the ball's spin with our current tooling. The influences are there, it's just that our tooling can't capture them precisely and accurately enough.
To combat that, we continously measure the ball's spin and we are able to figure out a pattern, not a precise one (because again, our tooling is not precise and accurate enough), but a pattern based on probability of the ball being in a specific spin state, we can even combine this with our inaccurate measurements of the quantum wind and further improve the accuracy of the probability. But never to a precise pattern, because our tooling sometimes misses certain wind states that it looks like the ball chagend spin randomly.
If we had tools that precisely and accurately measured the ball's spin and the quantum wind, we would be able to build a precise and accurate model of the spin based on those measurements. But we can't, although, we still want to make science around these inaccurate measurements, and probability based patterns are just enough for the science we want to make.
The wave function is just the result of our lack of precise and accurate measuring tools and measuring methods at this quantum scale. And for now, it's good enough for the science we want to do.
But even if you could make some baroque version of a model like this (with the position of one ball instantaneously reacting to other far away balls perhaps and some pilot waves) invoking it still wouldn’t answer my question about ontology. Implicit in this description seems to be the existence of a separate non-quantum realm (little balls that spin, jostled by “wind”). What are these balls supposed to be made of? If not atoms (since atoms are stable by virtue of quantum mechanics, which you seek to explain), then why don’t they suffer from ultraviolet catastrophes? Hopefully you see my point.
I'll read up the inequality experiment.
Decoherence is sort of analogous to air. It's so ubiquitous in your life that you don't really think about it, but you'd notice immediately if it was removed. Being steeped in air your whole life has twisted your physical intuitions. That's why Aristotle thought "objects come to rest" when actually objects move at constant speed unless acted upon by a force. Similarly, being steeped in decoherence has twisted your physical intuitions. Like thinking "adding more ways for something to happen must make it more likely" or "a particle's position is independent of its momentum" or "I can measure an object without affecting it". But actually different paths can interfere, and momentum is the Fourier transform of position, and measurements apply phase noise.
Decoherence is so ubiquitous that it's a huge challenge to engineer systems that suppress it. This is why quantum computers are so hard to make, and why quantum error correction has so much more overhead compared to classical error correction. Classical error correction only has to fix bit flips, and it can do so by making phase flips worse (which it does). Quantum error correction has to simultaneously fix bit flips and phase flips.
When two particles are entangled, rotating one around the X axis by an angle A and the other by an angle B and then measuring produces measurement results that agree with probability cos^2(A-B). Same as the probability of a photon with polarization angle A passing through a polarizing filter with angle B. Decohere the entanglement before the rotations, and the measurements will instead agree with probability cos^2(A)cos^2(B) + sin^2(A)sin^2(B). Note that cos^2(A-B) = cos^2(A)cos^2(B) + sin^2(A) sin^2(B) + 2 cos(A) cos(B) sin(A) sin(B), meaning decoherence is taking away the 2 cos(A) cos(B) sin(A) sin(B) interference term. That's the downgrade. That's what makes your best possible CHSH win rate drops from 85% to 75%. If entanglement allowed sending messages, the initial CHSH win rate would be 100% instead of 85%.
One hypothesis is that there is no spooky action. One particle was 'always' going to resolve one way, likewise with the other. Like inspecting 'heads' on one side of a coin 'forces' 'tails' onto the other side.
I accept that this coin-hypothesis has been disproved by people who actually know what they're talking about.
But to me, this implies that you should build your spooky FTL message by transmitting "Measured" rather than heads/tails:
Have an array of 8 particles at both locations. They represent measured/unmeasured rather than heads/tails. You got yourself a one-way single-use FTL byte.
For this to not work (which I'm sure it doesn't) you'd need to be unable to distinguish between a measured/unmeasured particle. To me this is equivalent of being unable to prove that there is anything spooky going on.
So how can you have it both ways? How can you theoretically know that something was sent when measurement itself would destroy any evidence of something being sent?
The classical idea is more like as follows: you have a guy Charles who makes two letters each with a card in that has written on it either number 0 or 1, and gives one letter to Alice and another to Bob. Now, "entanglement" here is that if Charles writes 0 in Alice's letter he writes the number 1 in Bob's, and vice versa. Alice and Bob are also aware of this. This means that even at a distance, if Alice opens her letters and sees a 0, she knows that Bob's has 1 in.
For a long time, Einstein and co. through the "EPR paradox" (Einstein-Podolsky-Rosen) thought that QM would be something like this, but we just didn't know how to access the actual letter "in transit" yet, which they called an "element of reality". They were wrong.
It turns out that Bell's theorem basically says that in this situation the correlation between the two letters would be less strong than quantum theory predicts for entangled states, so this cannot be the full explanation.
Bell's theorem says you either need to give up the idea that there is no "spooky action", or give up determinism (no true "element of reality" that really holds what's going on), or you can retain both if you let go of another concept called statistical independence.
> Have an array of 8 particles at both locations. They represent measured/unmeasured rather than heads/tails. You got yourself a one-way single-use FTL byte.
You can't have a quantum state where something is the superposition of measured and not measured, this violates a fundamental postulate of quantum mechanics: that measurement "chooses" one of the states in the measurement basis. I think you touch on that later, in that you can't tell via entanglement if a measurement took place elsewhere, which is partly why we can't experimentally demonstrate a non-local theory yet.
Basically, it isn't that some signal is transmitted, it's that if they are entangled the states of each system cannot be independently known. That is, like in the letters example I gave: it can be either 0 for Alice and 1 for Bob, or 0 for Alice and 1 for Bob. Now, the reason why information is not transmitted is the same: Bob didn't know what was in his letter before he measured it, so it's randomly symmetric between 0 and 1, there is no information transferred. It turns out that this kind of symmetry between the two states tells you nothing that can be used to transmit information.
Only 2 can hold at once and there's consensus to have 1. and 3., with that we lose the hidden variables. Instead, having 1. and 2. hold would be so interesting.
Either way, MWI is by far the most popular interpretation that is both local and realistic.
Can you not also say that the determinism includes the observer, aka superdeterminism (which is just determinism because that would surely be global).
> or you can retain both if you let go of another concept called statistical independence.
is superdeterminism
And then a measurement isn't just to land a die, but also to choose which axis to measure - ie ask the dice are you a 1 or a 6. The other die magically spins around to the same axis and gives the corresponding result.
But I'm not sure this analogy is satisfactory and explains the 'spookiness' either.
> a guy Charles who makes two letters
So Charles at least knows the information on the cards. Are you essentially saying that there's no way for Alice or Bob to distinguish that information from 'background noise'? If so, that is not a great analogy other than to illustrate a historical & incorrect perspective. Which may have been what you were doing and if so is fine.
> measurement "chooses" one of the states in the measurement basis
Okay, say you 'do some entanglement of multiple particles stored in two separate tubes' where you know there is some kind of pattern in the entanglement. Is the issue that there is no way to know how to find that pattern without possessing both 'tubes'?
Read the next part, I was discussing the idea thought of by Einstein that was dismissed by Bell's theorem.
> Okay, say you 'do some entanglement of multiple particles stored in two separate tubes' where you know there is some kind of pattern in the entanglement. Is the issue that there is no way to know how to find that pattern without possessing both 'tubes'?
I'm not sure what you mean by this, can you elaborate?
If you set up the first part of experiment, wherein you know certain particles are entangled, would it be possible for someone on one side of that entanglement to read a pattern from that side alone (if they 'knew where to look') which matched a pattern on the other side?
At this point, if my question even makes sense, we're only talking about a very impractical method of data storage... I'm just curious whether even that is possible.
Just to be a bit pedantic, as it can otherwise lead to some confusion: the measurement outcomes are always random.
If the particles are entangled, then it is the correlations that are not random.
Alice measures at angle X, gets value V1
Calls Bob on the phone, okay I measured angle X.
Bob measures at angle X, also gets value V1
Bob measures at angle Y, gets value V2.
Bob calls Alice back says, okay I measured angle Y.
Alice measures angle Y, also gets V2.
If each party acted independently they would randomly change the state on the other side and each party would get what appears to be random values.
A is sending entangled stuff to B and C.
B measures and gets a set of angles that tells them what C would be measuring
C changes what they are measuring.
(And just to rapidly get it out there, I fully expect that I'm merely misunderstanding something here.)
Edit: Also, to add, my understanding is that they are not "getting angles" per se, but would be seeing distributions. Which is why you would need more than 1 particle, as it were. So, you would say of the X I have recorded, 30% have been blue, 70% have been green. I suppose the concern is that you have no way of knowing when the "100%" mark is done until after classical communication, such that it is impossible to know what the final distribution you are measuring is? Effectively?
It's because measurements at B do not convey any information to C while the measurements are performed and vice versa. Unless B calls C to inform them of the choice of measurement setting, C will not know the measurement outcome at B's side. This is true even if they know that they share entangled states prior to prior to performing measurements.
> Edit: Also, to add, my understanding is that they are not "getting angles" per se, but would be seeing distributions. Which is why you would need more than 1 particle, as it were. So, you would say of the X I have recorded, 30% have been blue, 70% have been green. I suppose the concern is that you have no way of knowing when the "100%" mark is done until after classical communication, such that it is impossible to know what the final distribution you are measuring is? Effectively?
There has to be post processing of data where they drop the results of rounds where their measurement choices don't match. This is important because of what's called non commuting measurements. Measurements in one setting don't give us any information about measurement outcome in another setting. So effectively at one end, they have to record their measurement choice and corresponding outcomes of said measurement. And when comparing the data, the participants only have to keep the outcomes of rounds where the measurement choice is the same at both end
Framing I saw was more of a truth table like where B/C have known states they can be in that each lead to a known distribution of outcomes. It was not clear that the known distribution was only an observed distribution.
I'm not sure I'm understanding your percentages statement completely, but when the parties have entangled states, these inconsistencies will match on each side under the assumption that their measurement choice is the same.
> Framing I saw was more of a truth table like where B/C have known states they can be in that each lead to a known distribution of outcomes. It was not clear that the known distribution was only an observed distribution.
If the states are locally known to the parties, they'd still have to perform a statistical run of experiments as before. The choice of measurements would be key in distinguishing a classical from a quantum correlation
But how could they?
Charlie prepares a pair of entangled electrons and sends one each to Alice and Bob. Alice performs a spin measurement along some angle and, entirely randomly, gets either up or down as a result.
Alice and Bob decide on their measurement settings and measure a bunch of electrons using the same angle for each measurement. They can even agree in advance so they both know which angle the other will use.
After the run, Alice will have a bunch of measurement results which are roughly 50% up and 50% down. Bob too will have a bunch of measurement results which are roughly 50% up and 50% down. Assuming ideal detectors and such, there will be no discernible pattern to the ups and downs for either.
Only if the afterwards come together and compare their results pair for pair will they see the quantum correlations between the value in each pair. For some angles, they're more likely to be anti-correlated, and for some angles there doesn't seem to be any correlation.
That is, if they both used the same angle, the they'll find that each time Alice measured up then Bob measured down, and every time Alice measured down then Bob measured up. And if they used a similar but not equal angle, then it's more likely that when Alice measured up then Bob measured down, and vice versa.
And since they by now know that this experiment has been done before and the predictions of quantum mechanics hold, they can even predict this result. However what good does it do for Alice? After all, regardless of measurement settings Bob will measure a uniform 50/50 distribution of ups and downs.
If the answer really is that they have to wait for the end of the entire experiment, I think that settles it for me. Will think some more on it. (And again, as noted, I have not thought that hard on this. Even with my odd "would this work" you need some way to get entangled particles sent across stupid large distances. Which... already seems silly?)
Charlie doesn't see anything. He sends the electrons here and there. He's just produced the entangled electrons, he hasn't measured them. If he did he would destroy the entanglement and ruin the experiment (which is what secure quantum communication is about).
Unless he gets some reply (say a photon or electron sent by Bob), he doesn't know what either measure.
But if he does get a return particle then they're just communicating classically, so why not just pick up a phone?
Stated differently, the framing I saw was that the "spooky" action was somehow setting detector C to a specific setting would cause a different reading in detector B. And this was done in such a way that B could not know that C had changed. But, simply getting a new reading at B means that either A or C has changed, necessarily?
And again, going off old memory. Never my area of study, such that I assume I am misunderstanding. It is frustrating because most "pointing out my mistake" assumes I care about individual protons. I'm saying if we can agree to have A set to send with constant rate, then barring that getting broken, it seems you have a scheme whereby B and C can know what they are doing in aggregate.
That was the entire point of my initial post: there's no discernible difference in the actual individual measurement results regardless of detector settings.
The quantum correlations only show up if someone compares both measurements pair by pair. And to do so, regular communication must happen.
Many sources are very sloppy when it comes to phrasing this, so you're not alone in being confused. I too thought like you way back, thinking it could be used for communication.
I suppose all that is left in the intuition busting, is how the probabilities don't add up as expected?
Lets imagine electrons are objects in a program, then the "electron class" has a private field containing a seed value to a pseudo-random number generator (ie deterministic), and the two electrons are initialized with the same seed value.
Further imagine that performing a measurement of an electron amounts to taking the seed, generating a random number between 0 and 360 degrees (sample value), and then comparing that random number to the measurement angle. If the sample value and the measurement angle is closer than +/- 90 degrees we say the measurement result is up, otherwise down.
Alright, so, if we imagine that when Charlie prepared the electrons, he creates two "electron objects", and passes one to Alice and the other to Bob.
If Charlie prepares entangled electrons, he'll ensure both instances have the same seed value. If he wants to create regular non-entangled electrons, he'll make each have a random seed value.
For non-entangled electrons, Alice and Bob will not see any correlation if they later compare notes.
For entangled electrons, if Alice and Bob uses the same angle they must get the same result per definition[1]. And indeed one can find the correlation as a function of the difference in angle, and it's a linear function from perfect correlation if the angles are the same (zero difference) to zero correlation (perfect anti-correlation) when the angles are 180 degrees apart.
However on real, entangled electrons in the lab things are different. There you'll find that the correlation is higher than the linear function when the difference is smaller than 90 degrees, and less than the linear function when the difference is greater than 90 degrees[2].
Thus if we measure the entanglement at not just 0 and 90 degrees difference but also 45 degrees difference, we'll find that our lab measurements do not agree with our simulated measurements.
Hence we conclude that entangled electrons do not behave like small objects that were created with the same "hidden value", ie the seed value in my example.
That's the essence of Bell's theorem and the tests of it (at least according to my memory).
[1]: Note that measuring real entangled electrons Alice and Bob will get exactly the opposite result, they're perfectly anti-correlated, but this matters not for this explanation and not worrying about it will make the explanation easier.
[2]: IIRC it goes like cos(a/2)^2 or something along those lines, ie https://www.wolframalpha.com/input?i=plot+%7B1-abs%28x%2Fpi%...
I have not looked back at the book I read. I definitely remember it had examples that were not paired off. I'm assumingy memory is simply off.
Hidden variables, like my "electron objects", would give a linear relationship.
However what quantum mechanics predicts and what we measure in the lab is a non-linear relationship that for some angles yield stronger correlations. Hence the phrase "violating Bell's inequality".
After Bell people devised other inequalities for other experimental setups which also can be used to rule out local hidden variables. A popular example are the CHSH inequalities[1], which is easier to realize experimentally, and give a stronger disagreement with hidden variables.
I've never seen the particles not paired up, and I don't see how that would work.
The whole point is that according to quantum mechanics, the pair of entangled particles aren't two separate systems, but that they must be treated as having a single state.
> I accept that this coin-hypothesis has been disproved by people who actually know what they're talking about.
The quantum erasure experiment is to my mind the best example of the spooky action at a distance. The outcome of the particle pairs is measured after the entanglement occurs implying not just "spooky action at a distance" but also in time. https://www.youtube.com/watch?v=8ORLN_KwAgs
I believe that "nothing changes over there" implies not only no spooky action, but also no entanglement.
> using "action" suggests that something changes
By my understanding, the delayed part is important. It implies something did change as the state of the earlier entanglement will be different based on a measurement which occurs after the entangled state has been created. If this is correct, then there has been an "action" at a distance.
Though an alternative understanding could be that the state is set based on a future event which hasn't occurred yet. That would avoid needing an "action" to change the state after the entanglement event, but implies other things.
In four-dimensional space-time they 'travel' along a 0-length path; the correct formulation of Pythagoras' formula becomes "distance = t^2 - x^2 - y^2 - z^2".
Which would be an imaginary number for a spacelike path, yes, e.g. from one side of your table to the other. It's a useful imaginary number -- we call it 'length' -- but it doesn't correspond to a path that actually exists.
> t^2 - x^2 - y^2 - z^2
Off by a constant factor (c).
> distance = [above]
distance^2.
This is still not quite right since we're interested in how coordinate changes affect the spacetime interval. So take distance -> S, the spacetime interval instead of the Euclidean distance, and then sprinkle in the deltas: dS^2 = c dt^2 - dx^2 - dy^2 - dz^2. That is the Minkowski metric (the flat metric of special relativity) in Minkowski coordinates.
The right hand side can be positive (for a timelike spacetime interval), negative (for a spacelike spacetime interval), or zero (for a null spacetime interval). Massless particles, when not accelerated, travel on null spacetime intervals, as do other solutions of massless wave equations. Light is rarely accelerated. However a null interval does not mean no distance, it only means that there is an exact balance between the spacelike portion of the spacetime interval and the timelike portion of the spacetime interval. An object moving against the t and x coordinates at speed "c" will (choosing units for clarity) tick off one second along the t-axis for every light-second it travels along the x-axis. A timelike trajectory ticks off more than one second per light-second along the x-axis; and a spacelike trajectory ticks off fewer seconds per light-second along the x-axis.
So, with light always in inertial motion, and always moving at "c", the spacetime interval for an element of light (classical or quantum) will always be zero. That does not imply in any way that the element of light does not travel at all. Also it does not imply that if we split the spacetime interval into timelike and spacelike components, that we find that the photon experiences "no time".
The confusion arises frequently because the usual way one splits a timelike spacetime interval (e.g. for a massive particle) into its timelike and spacelike components is to use the proper time interval (and that leaves us with proper lengths). Proper time is a specific affine time which can be caluclated for non-null spacetime intervals, but not for null spacetime intervals. We can use a different affine time for those instead (leaving us with affine lengths that are not "proper lengths"). But even so there are changes in coordinates (e.g. (t=0,x=0)->(t=10,x=10); the photon is ten seconds older and ten light-seconds further away along x).
[Experts who already know about invariance under coordinate transformations etc. should also know not to pick too hard at that last sentence. The point is that if we do c \def = 1, then 1dt^2 - dx^2 = 0 for arbitrary photon displacements along x and this is true at least up to rescaling.]
Basically the results of two slits with particles combine into no pattern. If you retroactively keep track of which slit, and then only look at that slit, it makes a pattern.
If you have a single particle there is no local experiment that you can do to determine whether that is entangled to a particle somewhere else. You need to use both particles in the experiment in order to prove it one way or the other. Mathematically, this is due to the fact that the density function for one half of an entangled pair is the same as the maximally mixed state for one particle.
See CHSH[1] for an example of an experiment you can do if you have access to both particles and you want to show they are entangled.
This is true. There is no way to tell if a measurement you do happened on an entangled particle or on a "free" one.
You can only tell in retrospect, when you correlate results, which requires classical communication.
The key to understanding this is that _any_ interaction with anything counts as a "measurement" from the particles perspective.
I like to think that our simulation has a bandwidth compression algorithm that only decodes the state of a particle when it needs to calculate an interaction. Just like how your dungeon crawler doesn't spawn mobs until they are within interaction distance. But that's just fun head canon.
I can invent a story that the coin in my pocket has two sides, each of which is in a superposition of heads and tails.
If you disprove that by repeatedly looking at both sides and noting that they always end up different, then I can invent the story that the observed side tells the unobserved side what to become.
If you disprove that by separating the sides by a great distance before observing them both, I can invent the story that they coordinate instantaneously, ignoring the speed of light.
This comment chain is a prime example of the ways quantum mechanics are (mis)understood and how many of us struggle to fully reason out the implications of each piece of it. I hope we can all learn something.
If you block one slit and then shoot particles, then block the other slit and shoot particles, you end up with a completely different pattern than if you have both open at once.
This isn't difficult to understand, the only difficult part is people not wanting to believe it is true and trying to come up with classical explanations for quantum mechanics, even though we have hard proof that classical physics can't explain this.
The difficult part is that even though the particle went through both slits, it only ever ends up in a single spot at the end, that is the "wave function collapse", it was a wave that went through both slits, and then it collapses to a single point when we measure it at the end. That is still not well understood by anyone today.
"Measurement" is a terrible word we've been using, along with "observer".
What matters is information propagating from one system to another or, perhaps better, when the superposition has any external effect, then the superposition collapses and the system assumes a classical state.
If you measure one of the particles and look at the result, you then know what term of the quantum state you ended up in, so you know the probability distribution of the other particle's results.
Nature does not need to work according to what our brains consider reasonable, but the MWI getting rid of several very weird notions makes it very appealing, I won't lie...
There is a spooky world split that separates the entire universe instead of just having a spooky thing having to the particle. Some prefers having a small spooky thing over a large spooky thing.
But you don’t.
If I have the entangled version of the MEASURED byte and measure, only I know I’ve measured it. The corresponding MEASURED particles on your side still appear fuzzy to you because you haven’t measured them. If you measure them, they will reveal their state which correlates to mine BUT that doesn’t tell you if I have already measured my side of byte or not.
In effect, the heads/tail coin on your side is still spinning even after I have grabbed my side of the tail/head coin.
You may get HEAD as your result but that only tells you that I will get TAIL when I measure on my side, not that I have measured it already.
If you and I agree to measure at the same time, then I will know your state by determining mine but this is the same as knowing your state because I know how a two sided coin works, not FTL.
Like if I gave two people red balls without telling them what the colour is. One takes it out and sees it is red, the other now instantly has a red ball. But they were always red. So there is no actual interaction between the balls, they were just set up in a pre-defined matching state.
To our observations the balls are in a quantum state (the balls are wrapped in paper you can’t see through) but they always had a specific state. We just weren’t capable of determining that state because the interior is invisible to us. The interaction would always have produced that outcome, so it appears like they are communicating when in reality it would happen regardless.
Also Superdeterminism might allow for Local Hidden Variables.
What we usually call the speed of light is in fact the maximum speed of information propagation.
It is not about light, and you should think about quantum entanglement as a hidden variable, there is no magic there.
It could be nonlocal of course, but that would imply information moving faster than light again. Unless you count the entirety of MWI as "hidden variables", I guess?
What I am saying is that the hidden variable hypothesis is nonetheless a good mental model as a first approximation to reason about QE, say as a non-professional physicist.
People get confused, especially sci-fi authors, adding to the general confusion about anything touching Quantum Physics being almost magical/limitless or unexplainable. This is a lot more pedestrian in practice.
I very much doubt Ursula Le Guin thought we could build an ansible (FTL comms) any more than Larry Niven thinks the Teela Brown gene (heritable luck) is real.
It is a really tough topic to get an intuition for, though.
The main article attempts to explain why instantaneous “spooky action at a distance” is real, yet information can’t be relayed this way.
I'll show myself out
What I am saying is that, in my understanding, there is no action that can occur without a particle that acts, and since no particle can travel FTL, nothing can happen FTL.
In the case of Quantum entanglement, mustn't some particle travel from the first quantum thing to the entangled quantum thing in order to have an effect?
I believe that my understanding is flawed! I don't know how to get a clearer view though. Any advice?
It should be called the "speed of information."
If the sun somehow magically disappeared, we would continue to orbit that empty space for about 8 minutes.
I kind of assume this is incorrect because it seems like a simple explanation and explanations of this stuff tend to not be simple
I think it'd be cool to set up colonies on other planets, or hell, other solar systems, but the inability to communicate seems like a pretty hard blocker. I mean, even sticking to the solar system, will start taking six hours for the light to even reach earth from Pluto, assuming it can even have a direct path.
I don't know anything about physics, so I was hoping that the entanglement hypothesis might allow us to fix that, but clearly that wasn't the case. This makes me sad.
I'm just kind of hoping that physicists are all wrong, and that there turns out to be some fancy math that allows to do something faster than light. Not saying it's gonna happen that way, but a guy can dream.
Maybe entanglement is a much more 'immediately physical' phenomenon than 'spooky action at a distance'. Just guessing as a layman here: maybe entangled particles are just physically connected {along some higher dimension / some unknown process}.
Spinning together (effectively switching spaces constantly) such that they are always the same state. So the undetermined measurement stems from being unable to tell which particle specifically you have at the time of measurement.
The idea of a particle's spin being 1/2 feels tied to this idea - (that a 720 rotation happens: if a particle P1 spins 360 in space A, spins 360 in space B before returning to space A, maybe entanglement is P1 and P2 filling space A and B to 'full'?)
In other words - detector A may receive particle B or A depending on the particle's current orientation at measurement.
Weird thoughts. Take with a lot of salt.
I have always thought this might be a possibility - but wouldn't we be able to observe this somehow?
Is it actually possible this could happen and there's no way we could observe it?
Gravity distorts space-time - but it's observable.
For these particles to be connected still - wouldn't that be some disturbance in space-time?
Ruling out "it's magic", we can presume that everything in the universe is linked logically somehow, the link between the two entangled particles must exist and we just haven't been able to observe it yet.
So where did all our antimatter go… ?
Yes, this ties into this.
https://en.wikipedia.org/wiki/CPT_symmetry
Worse, the symmetries of the Standard Model are pretty complicated, especially when one goes from the local Lorentz or Poincaré symmetries x SU(3) x SU(2) x U(1) to the global continuous symmetries that capture https://en.wikipedia.org/wiki/Custodial_symmetry, (particlularly QCD) flavour symmetry, and scale symmetry. There are some further long-range approximate symmetries too, and those get worse with spacetime curvature. These all may have to be accounted for if one is time-reversing a region of the spacetime-filling fields of the Standard Model.
> So where did all our antimatter go?
Good question. Nobody can really tell you right now. Maybe there are galaxy clusters totally dominated by antimatter, maybe the antimatter is in a different Hubble volume, maybe it all annihilated into the cosmic microwave background and other ultra-low-energy relic fields (e.g. the cosmic (anti-)neutrino background) we haven't detected or discovered yet, maybe into primordial black holes, maybe in an extension of the Standard model to extremely high energies there isn't a matter-antimatter balance in the first place. One can write down an enormous number of different theories, and relax knowing that there is presently no evidence to favour or disfavour it, provided it's compatible with the experimental and astrophysical evidence we have today.
(I do like the idea, building on an idea arising from Wheeler's one-electron universe, that anti-electrons (in this case more than one) are screened within pion condensates ("maybe they're hiding in neutrons", vaguely), because that makes the symmetries even crazier, and particle physicists deserve that).
The only thing that is known is that the other entangled particle has opposite spin than what you register.
Then we could generate particles from each that can be potentially entangled to the original system as well. Can it work that way?
If we keep looking at one bit there's probably not much we can do. But when we start looking at entanglement of systems then maybe some we learn about some phenomenon that makes this possible.
Excuse my ignorance, I'm not even a physics major so I probably spewed meaninglessness but I'd love to learn more from replies!
Wake me up when the next "Expanse"-level sci-fi lands.
Although I read the book when it first came out, I have basically zero memory of it, so I don't recall if FTL communication is essential to the story. However, having just watched the first season of the Netflix season, I explicitly noticed that even though it mentions use of FTL communication, the story absolutely doesn't need it at any time. There's a local representative of the distant folk who is clearly trusted to make decisions, and could represent the distant folk for all communication purposes.
When Evans speaks with the San Ti/Trisolarians, he is talking to them via one of a pair of sophons - quantum entangled protons.
Whether this changes their chance of success is certainly debatable, but it definitely changes their behavior.
(0) note that AFAIR from reading book 1 just about a month ago, this is series-canon, not book-canon.
This is not a fact to begin with, and in the book their civilization was repeatedly wiped out.
> Secondly, the trisolarans are hyper-advanced. They turn individual protons into sapient robots and play with antimatter, therefore they can make a damn air conditioner. Manufacturing habitats to isolate them from the effects of their orbit would be easier than almost every single other thing they do in the entire series, including transporting their whole species across interstellar distances. Some of the things they do would be harder than keeping their planet in a stable orbit by force.
This is not the failure mode they’re concerned with.
You also seem to drastically overestimate their capabilities.
however you missed some explanatory details:
!!!SPOILERS BELOW!!!
the trisolarans specifically evolved to survive their chaotic orbit, by being able to completely "dry out" and wait in stasis for a safer time. this is based on how some worms and bacteria on earth have the ability to survive extreme conditions by similar protective stasis methods.
the trisolarans are very intelligent but their advancements are constrained by the need to rebuild the civilization at unpredictable intervals. this actually drives their technological innovation as they are existentially motivated to figure out how to predict the orbital intervals.
its also implied that the trisolarans did not think themselves very far advanced compared to humans, only that they had a few centuries head start on understanding the fundamental nature of physics. they conclude that all they need to do is sabotage our particle colliders to confound our ability to gain any more insight into subatomic mechanics to prevent us from achieving what they have
moving their civilization across interstellar space is far less difficult than it would be for humans mostly because the civilizations can be dehydrated and kept in storage, not needing supplies to live out the years in transit. even so it still takes incredible engineering and resource investment to achieve because the fleet must move semi-autonomously and reliably for centuries because FTL travel is beyond their ability.
it would be impossible to stabilize their orbit because the planet is being chaotically thrown between 3 large stars. they are also not just concerend with surviving the next "hot cycle" they had predicted true apocalypse for even their survivable species. IIRC the planet was doomed to eventually fall into one of the stars based on their predictions
not quite. they are aware that they are significantly ahead of humans, but have also observed human scientific and technological progress following an exponential curve, since we do not get our civilization(s) wiped out periodically.
they fear that we will easily catch up with them in 400 years unless they somehow intervene.
Every time a seemingly intelligent person takes the dark forest hypothesis seriously I am dismayed. The only answer to the dark forest is: FTL is impossible and we are presently incapable of detecting ourselves at a distance of 4 LY so there is a 0.0% chance of detecting anything beyond that.
You don't need to detect a civilisation. All you need to detect is a planet hospitable to whatever biology suits you.
That said, our detection tech improves relatively quickly and we might be able to directly image rocky planets before this century is over. It's safe to assume that, if there is someone curious enough to look for planets with biosignatures or technosignatures that has been perfecting their craft for thousands, or millions of years, by now they must be very good at that.
It's fun, but it's not an accurate prediction of our technological abilities.
But I do think it's worth suspending disbelief a bit to try and enjoy the other ideas presented. It's fiction for entertainment, not a serious warning to stop broadcasting signals out into the universe.
And then you are in segmentation fault hell.
Sun had to rewrite the entire JVM in 2003 with a new memory model, later adopted in C++11 (and still the current C++ memory model) which failed for C++ because this model only works well if you have a VM with GC.
C# is just a plain Java copy after Microsoft got sued for J++ in 1998.
All other languages have problems with concurrency and threads that make them unsuitable for anything really.
So again, Java is the ONLY language/VM you can use on the server and on the client you still want a combination of C(++) and Java for performance + ease of use (avoid segmentation fault hell that no person should suffer).
If you saw bad Java code then that is not the fault of Java.
FWIW, I'm also pretty sure this type of comment (and therefor my comment?) are against the rules, but I've been rate limited for like 90% of my time here because I don't use burners to get into fights so dafuq do I care.
Anyway, hope you have a Good Friday. If it makes you feel better, you're much lower on the crucifixion scale than the even providing it's name.
"While I'm on the topic of concurrency I should mention my far too brief chat with Doug Lea. He commented that multi-threaded Java these days far outperforms C, due to the memory management and a garbage collector. If I recall correctly he said "only 12 times faster than C means you haven't started optimizing"." - Martin Fowler