In quantum mechanics two particles can be entangled in such a way that a measurement done on one will guarantee what the measured state of the other will be. But how does this jibe with special relativity setting limits on whether two events can be said to occur simultaneously or not? Can you have a situation in which two observers each perform a measurement on one of a pair of entangled particles, and each observer’s reference frame is such that he sees his measurement as having been done first? What if they randomly decide to perform incompatible measurements such as measuring a particle’s spin orthogonal to the other experimenter’s measurement?
As noted in the Wikipedia article on quantum entanglement, one possible explanation is due to the time dilation effect of Special Relativity. Since photons travel at the speed of light, from the photon’s “point of view” no time passes. So, still looking from the point of view of the photon, a measurement made on one of a pair of entangled photons at the present moment would determine the state of that member of the pair for the present and all of its past. This would instantaneously determine the quantum state of its entangled partner, since from its point of view as well, time is standing still.
The article notes that entangled particles which travel at speeds less than that of light (electrons and positrons, for example) can be explained by “corresponding logic”. I would have to think about that a good deal more, however.
Invoking Special Relativity is not the only possible explanation, however. A good deal of interest lies exploring the notion of hidden variables. In a nutshell, this speculates that the process(es) generating entangled particles produces some information about the total quantum state which is carried by each member of the pair in some fashion which we have not yet been able to detect.
Your phrase “each observer […] sees his experiment as having been done first” seems problematic when considered in light of the Special Theory. As far as I can tell, there is no way to decide which is correct or, conversely, whether both are correct.
Note: the Wikipedia article on quantum entanglement presents summaries of theories as to how the well-demonstrated phenomenon of quantum entanglement might be taking place. As seen by the two capsule summaries above, the notion of simultaneous events is not invoked, due to the Special Theory.
I am far from a physicist and my understanding is woefully inadequate but here is my 2 cents anyway.
I’m not sure where you are getting the concept of simultaneous from. As far as I understand simultaneous is not important to quantum entanglement. It doesn’t matter who measures the spin when just that spin measured in one direction tells the spin of the other particle when measured in the same direction.
This does not violate special relativity as no information can be passed faster than the speed of light due to the randomness of the measurements of spin (50% chance of up spin, 50% chance of down). The fact you are not able to control the initial setting of a spin means that you are not able to use the entanglement to transmit information.
A nice little video by Veritasium explaining this can be found here. My understanding is mostly based on this information.
What I’m asking is, if there is disagreement over which measurement was done first, then which measurement is “driving” the result?
The problem is essentially the same as the original EPR-paradox in non-relativistic quantum mechanics. In the original EPR paradox two incompatible observables (namely position and momentum) are measured simultaneously, in relativistic quantum mechanics, simultaneous is replaced with “spacelike separation” (i.e. the two observers making the measurements don’t necessarily agree on the order the measurements are made)
The answer depends very much on interpretation. For example Bell showed that for a certain class of hidden variables theory relativity must be violated by influences propagating faster than c. On the other hand a more conventional interpretation would be that the collapse of the wavefunction is not in itself a physical phenomena so the “incompleteness” shown by EPR represents a pitfall of interpreting it as physical.
Given that simultaniousness is a function of the observers frame of reference and not an absolute I’m not sure that the question even makes sense. Hopefully someone with actual knowledge will chime in.
Absolutely, and it’s been done. It doesn’t change anything.
Then the results of the two experiments will be completely uncorrelated. This is actually part of the core of Bell’s Inequality: If you only ever make compatible measurements, then the results will always exactly match, but that’s no big deal, because it’s really easy to get that from hidden variables. If you only ever make completely incompatible measurements, then the results will have no correlation at all, and that’s consistent with the same hidden variable theories. But if you make partially-compatible measurements, then the results will be somewhat but not entirely correlated, and the degree of correlation is impossible according to any conceivable hidden variable theory.
You’re right, simultaneity is dependent on the frame of reference of the observer, to be consistent with relativity neither measurement can decide the outcome of the other in a classical manner. On the other hand both measurements must correlate in a way that is consistent with quantum physics, so interpretation is key. You can take an unconventional route and interpret entanglement some relativity-violating hidden variables theory (then presumably relativity becomes an emergent theory and you may have to deal with preferred frames, etc) or you can take a more conventional route and interpret it in a manner consistent both with the principles of QM and SR, but at the expense of a definite local reality.
IANAP but it seems clear to me that there can be two observers in different inertial frames of reference that communicate with each other via radio about an observation they made and the timing can be such that they disagree about which observation was made first. And if we throw in the fact that the observation in question is half on entangled pair, that shouldn’t change anything. So, yes, they could disagree about which of them made the observation first. And since all inertial frames of reference are equally valid, you can’t really say that either of the measurements is “driving” the result.
This is kinda like the counter-intuitive aspects of the Schrodinger’s Cat thought experiment. If the cat is both alive and dead before we open the box, and then it’s dead after we open the box, then we feel guilty because it seems like the act of opening the box is what kills the cat. This idea messes with out concepts of cause and effect. On a similar note, we have this mental image of a scientist sitting in a lab next to a big blue button which is labeled “measure the entangled pair” and another scientist in another lab with a pair of lights on a panel, one red bulb labeled “the entangled pair has not be measured” and the other one a green bulb labeled “the entangle pair has been measured” and we imagine that the first scientist presses the blue button and it causes the lights on the other scientist’s panel to switch from red to green. But this is all fantasy, just like Schrodinger’s Cat is a fantasy.
Btw I have a book (though it is a bit too philosophically dense for my liking, so i can’t say I’ve read it all!) by Roland Omnes, who is sometimes credited with updating the Copenhagen interpretation, that covers the philosophical aspect of this situation.
What he says is essentially is that most of the time the state of a quantum system is not associated with that system having definite value for observable properties. The one exception is when a measurement made and the result of that measurement is a non-degenerate eigenvalue of the observable, i.e. the result of such experimental outcome gives you both a definite property and a definite state of the system.
In the case of two compatible and time-like separated measurements of entangled particles a long the lines described in the updated EPR-paradox, both observers performing the measurements can say what the result of the second measurement (because of the time-like separation there is no disagreement as to order of measurements) is before it is carried out as a) the measurements are compatible and b) they both have access to the result of the first measurement, which is a non-degenerate eigenvalue. If we alter it so that the measurements are space-like separated neither can say what the result of either measurement will be before it is carried out.
In the time-like case saying the outcome of the 2nd measurement is already determined seems prima facie sensible as knowing the result of the 1st measurement allows you to predict the result of the 2nd measurement; but in the space-like case saying the outcome of either measurement is determined before it takes place, whilst not logically-inconsistent, is empty of any value as no observer can know the result of either measurement before it is carried out. Omnes therefore describes the line of reasoning that either measurement determines the result of the other one as “reliable” (because it cannot be contradicted), but “not true” (as there exist are consistent logical frameworks where the outcomes are not determined before the measurements take place).
So as I said it is very much a matter of interpretation.
There are a few loopholes that are allowed when doing experiments with entanglement and some other aspects of quantum theories.
Many experiments that are reported, only succeed when allowing one or more of the loopholes. So they cannot be considered 100% reliable.
I am still unconvinced of the reality of quantum entanglement, as far as the idea that observing one particles state, instantly forces a particular state in the other, distant particle.
Too much of quantum theory contains inherent rules that refute the possibility of 100% proof of the experiments.
I know I will be scorned for such thoughts. But it is my gut feeling.
Which itself generates either an implicit paradox or implies a non-local connection.
It should be noted that both the causal nature of general relativity and the concept of “waveform collapse” are both assumptions that are necessary to make the theory work with consistency (in the former case) or used as a starting point for calculations (in the Copenhagen and some other interpretations) but neither has been demonstrated to be true in a general sense. It is entirely possible that causality in the normal sense does not hold at the level of quantum mechanics, and that waveform collapse is at most an epiphenomenon of some more fundamental behavior that resolves the interactions of fundamental particles, just as simulating an impact of a ball onto a wall as an instantaneous impulse with a coefficient of restitution factor will give answers that are approximately correct for the momentum transfer but fail to capture the actual material deformation and energy loss from heating and acoustic radiation of such an impact.
Stranger
This is a fascinating area and I can’t resist making a comment based on what has been posted here and the very minimal knowledge I have on this topic. I think it’s probably fair to offer the view that the simple and straightforward answer is that the simultaneity problem doesn’t exist because no mainstream view of quantum entanglement considers that either measurement ever “drives” the other. It would seem more appropriate to characterize entangled particles as simply having the quantum attributes of a single particle, but that no FTL communication occurs to accomplish this. Would others agree that that’s a fair statement?
Local hidden variables would seem like a viable way to accomplish this, but the Bell Theorem and the increasingly robust experiments showing violations of Bell’s inequalities seem to rule that out. The de Broglie-Bohm “pilot wave theory” as I understand it posits a kind of superdeterminism as the operative mechanism, which Bell himself thought improbable. As already said, the underlying mechanism – whatever that even means in the quantum world, because we can only understand it by analogy with the macroscopic world – seems to be a matter of interpretation.
It’s fascinating that quantum entanglement not only has applications in quantum computing but also, paradoxically, in communications and cryptography (see 4.2 Uses of Entanglement). Entanglement can’t ever transmit information faster than light, but paradoxically it might be able to increase the capacity of a conventional light-speed information channel!
That’s probably about as close as you’ll be able to get to an accurate statement, using non-mathematical language.
And the big contribution of entanglement to cryptography applications is that it lets you tell if a message has been tampered with, which helps to prevent man-in-the-middle attacks.
It’s actually fairly easy to understand the maths if you take a very simple case and look at it at a basic level. (Though html is not the best for writing equations
Let us say we have ‘particle a’ and we focus on a measurement on that particle which produces either the result of ‘1’ or ‘0’. The quantum state vector corresponding to a (definite) result of ‘1’ we shall label |1[sub]a[/sub]〉 and the corresponding state vector* for a measurement of ‘0’ we shall label |0[sub]a[/sub]〉.
Now in quantum mechanics you are always allowed to add (superpose) state vectors together to create new state vectors. The state vector corresponding to there being an equal chance of getting a result of either ‘1’ or ‘0’ would be:
|1[sub]a[/sub]〉 + |0[sub]a[/sub]〉
(I will omit the constants of normalization)
You can also multiply by vectors by complex numbers to create new state vectors and all possible states of the particle could be written in the form:
p|1[sub]a[/sub]〉 + q|0[sub]a[/sub]〉
Where p and q are complex numbers.
Now lets say we also have ‘particle b’ with similar properties, we could describe all possible states of particle b as having the form of:
r|1[sub]b[/sub]〉 + s|0[sub]b[/sub]〉
Where r and s are complex numbers.
Now what happens when we want to view ‘particle a’ and ‘particle b’ as part of the same quantum system? The answer is we ‘multiply’ the vectors together using something called the tensor product. Therefore all the state vectors of the combined system of two particles where the particles are in single particle states can be described as having the form:
(p|1[sub]a[/sub]〉 + q|0[sub]a[/sub]〉) ⨂ (r|1[sub]b[/sub]〉 + s|0[sub]b[/sub]〉) =
pr|1[sub]a[/sub]〉|1[sub]b[/sub]〉 + ps|1[sub]a[/sub]〉|0[sub]b[/sub]〉 + qr|0[sub]a[/sub]〉|1[sub]b[/sub]〉 + qs|0[sub]a[/sub]〉|0[sub]b[/sub]〉(equation 1)
Now just as before we can add state vectors (and multiply them by complex numbers) to get new state vectors. Interestingly we can add two state vectors of the form of equation to get a state vector not of the from of equation 1. In fact we see that ‘most’ (by a certain definition of ‘most’) allowable state vectors for the two-particle system are not of the form of equation 1. One such example would be:
|1[sub]a[/sub]〉|1[sub]b[/sub]〉+ |0[sub]a[/sub]〉|0[sub]b[/sub]〉
This describes the situation where there is an equal chance of measuring a ‘1’ or a ‘0’ for either particle, but measuring a ‘1’ on one particle guarantees a result of ‘1’ for a subsequent measurement of the other particle and similarly a result of ‘0’ on one particle guarantees a result of ‘0’ for a subsequent measurement of the other particle.
So entanglement are multi-particle states that can’t be ‘factorized’ into single particle states.
*NB there is a certain redundancy in the description of quantum states by state vectors as some vectors represent the same quantum state.
Or in other words we might often talk about a superposition of states when referring to an observable such as spin a long the x-axis and what we mean is that the state of the particle is such that it does not have a definite value for this observable. Entanglement is when a multi-particle system is in a superposition of states, such that the particles in it do not have definite single particle (pure) states.
Thank you for the informative responsive which I want to read in detail.
Just as side note, indeed HTML has its issues. I’ve quoted the first part above just as I see it, but you probably see it differently. In the line “… The quantum state vector corresponding to a (definite) result of ‘1’ we shall label |1[sub]a[/sub]? and the corresponding state vector* for a measurement of ‘0’ we shall label |0[sub]a[/sub]?” the characters I’ve replaced with red question marks appear to me as unknown characters with HTML unicode hex value 3009, which turns out to be a right angle bracket (> in my browser config) so I take this to be the ket notation for quantum state vectors. Now that I’ve deciphered the hieroglyphic resulting from our apparently incompatible browser settings, let me contemplate it. And thank you again for the insights. 
nm – it’s the Firefox browser on just one computer, all the others and my tablet show your symbols just fine – probably some simple browser setting I need to change.
That 〉 (“ket”?) character is definitely a weird one. It’s not the the same code as any normal > or similar character. The character even seems to include an expanse of empty white space to its right. That is, in a text such as “|1a〉)” the apparent blank space just before the right parenthesis is actually part of the 〉 character.
Batang!!
No, that’s not a Japanese war cry, it’s a TTF font that for some reason wasn’t present on the (Windows XP) computer in question. It’s a font that contains, among many other things, mathematical notations including a large right angle bracket which is a different character than an ordinary “>”.
So it wasn’t a browser setting problem. When I installed the Batang font from another XP machine, it fixed the problem. There may well be other unicode fonts that fix it just as well.
So extra thanks to Asympotically fat for not only enlightening me on the math of entanglement, but also upgrading the font library on one of my computers.