> 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.
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.
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.
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.
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?