Is this possible? Or is this more like the logical fallacy of “irresistible force vs. immovable object” where the superlative nature of both simply can’t be true?
Quantum Entanglement, I think: means that if two particles interact - say collide and go shooting off in opposite directions - then they remain “probability fields” until one is measured by location or speed. At that point, instantaneously, both particles assume the proper relative measures, i.e., the second particle behaves in the way it must if the first particle registers the measurement. They “sync up” instantaneously, regardless of distance.
???
If so, to take this to an absurdist extreme: what if BOTH particles were observed simultaneously but in different ways? i.e., speed for one and location for the other.
Is this simply not possible? Or would this cross the streams?
Entanglement means the particles have properties which are logically dependent on one another. An example is quantum spin: If you imagine electrons as tiny little balls which are spinning around their axes, they can be spinning “up” or spinning “down” (clockwise or counterclockwise) relative to your observing apparatus. Spin is related to angular momentum, which must be conserved: If the system as a whole had zero angular momentum before an event, it must have zero angular momentum after.
So, if a particle which wasn’t spinning emits electrons, which are always spinning, it must emit them in pairs, and it must emit them such that their spins cancel: One spinning up and one spinning down. Those electrons are entangled: If you measure one of them, and see it’s spinning up, you know the other must be spinning down. It’s logically forced by the conservation relationship.
The oddness comes from the basic idea, which has apparently been experimentally verified, that information about spin isn’t present in a system until it’s measured. Therefore, until the electron hits your detector, it has no defined spin: It could be either up or down, with a fifty-fifty probability on each. The electron doesn’t “secretly know” which it is. In the usual interpretation, observing the electron “Collapses the wavefunction” and, at that instant, it randomly falls into one state or the other.
The interesting part, therefore, is when you have entangled electrons separated by a great distance and observe one of them: By observing one, the states of both are now set in stone, because they’re entangled, but how did the other one know what the first one was measured to be? Isn’t this a massive violation of the light speed barrier to communication? Can I cheat at the stock market by sending information back in time? Is Warren Buffet a Time Lord?
Sadly, no. You’re not actually sending any information that way: Since the states of the particles are random, and the other electron behaves the same way even if its state is now constrained by your observation, you can’t know whether the distant electron has been observed, and you can only find out what the state of the distant electron is by observing the nearby one. The only way to know when the distant electron was observed is to ask the other observer, which you can only do using normal communications channels that obey the speed of light. Therefore, even if the particles are communicating over some faster-than-light channel, this isn’t a useful way to exploit that. No time travel for you.
I don’t know how that pair of properties would be entangled in the first place. I don’t know enough to say it’s impossible, but it doesn’t seem likely.
When you say the measurements “sync up” regardless of the distance means in relativistic terms that the measurements have a spacelike separation. (They are farther apart in space and close enough in time so that a light signal could not travel from the one measurement to the other before it was done. Any two events that have a spacelike separation occur simultaneously in some frame of reference (some observer traveling at a constant velocity). But there are other frames of reference in which observers say that measurement A occurred before measurement B and still others in which B occurred before A.
So the situation you describe happens in every one of these experiments.
The whole point of these experiment is somehow the particles “know” what the other is going to show while there is no way under relativity that that should be possible. One explanation for this was there was something hidden about the particles we could not see which was determining what the measurements would show when the entanglement was set up (and the particles were close together). This is the “hidden variables” explanation – the one that is obviously true by common sense to any non-physicist. Unfortunately experiments show that this explanation can’t be true.
I think it really helps to understand what the experiments look like. This is a clear but non-technical account of the nature of the Bell’s Theorem experiments, with no math beyond basic arithmetic:
On the one hand, it’s critical to get the point (as the OP does) that the data are not consistent with the more natural idea that entangled particles carry hidden states that are simply “revealed” at the point of detection.
On the other hand, it’s also important to realize that the sense of “spooky action at a distance” arises from an attempt to form a classical intuitive account of the correlated behavior of entangled particles under QM. But it does not really mean that one of the particles is “causing” the other particle to “change” (in a classical sense) instantaneously at the other end of the universe.
“Spooky action at a distance” should not be seen as a classical analogy that has useful explanatory power in thinking about how QM works. It should rather be seen as an indication that our classical intuition (and general common sense) simply doesn’t work when we encounter the weirdness of QM. What QM “really” means is, of course, a subject of decades-long unresolved debate on interpretation.
The GHZ experiment is in some ways clearer, and more paradoxical, than the usual paradox discussed with Bell’s theorem.
In the GHZ experiment, three entangled photons are created. Each can be asked the question “H or V?” or asked “L or R?” but cannot be asked both questions.
Rule 1) If all photons are asked the H/V question there will always be an odd number of H’s.
Rule 2) If only one photon is asked the H/V question and the other two asked L/R then, if the one is H, the other photons will mismatch (L-R or R-L); if it is V the other photons will match (L-L or R-R).
You perform the experiment as many times as you wish, and always see results conforming to these rules.
Now suppose you ask two H/V questions and one L/R question and get these results:
#1 #2 #3
H H -
- - L
(Paradoxes similar to the following arise with all other combinations as well.)
By Rule 1, you deduce #3 would have responded H had you asked it the H/V question. By Rule 2, you deduce photons #1 and #2 would have responded R had you asked them that question. That is, you “know” the “local hidden variables” would be
#1 #2 #3
H H (H)
(R) (R) L
But these three deduced values (R-R-H) contradict Rule 2 !
The simplest way to cope with this paradox is to imagine that the photons know what questions each others are asked, i.e. that information flows from the “future” measuring event backward to the entanglement.
This is in fact pretty much just a statement of the EPR paradox. The conventional answer is that it simply does not make logical sense within the context of quantum measurement theory to talk about two simultaneous measurements like this - it is logical contradiction. One measurement must precede the other, even if the time between them is arbitrarily small. There is no quantum state corresponding to the outcome of two simultaneous measurements of this sort.
What of course is interesting is that there is no logical contradiction in simultaneous measurements per se, as long as the observables are compatible, for example if we measured the position of both particles. What of course is even more interesting about the EPR paradox in particular is that the two measurements take can take place at spatially separated locations where they do not appear to interfere with each other.
Yes, the logical contradiction aspect is what I was suspecting with my “immovable vs. irresistible” analogy.
Your comment on there being “NO logical contradiction in simultaneous measurements, per se” is what bakes my noodle within that context.
Ah, Paradox, is there nothing you can’t confuse?
Thanks for the comments so far; ignorance feels like it is getting fought, if only chipping away at a better understanding of the central paradox of it all. Riemann your summary of why Spooky Action is, indeed, spooky, is helpful. And with the descriptions of the experiments, it is clear that they are entangled, but it is not clear that scenarios like the one I describe in the OP are adequate to capture what is happening at the quantum level.
Thank you for the link. I read it and I have some questions.
My first thought, reading the possibilities in the experiment, I came up with 50% before 5/9ths. I thought that the probability of any electron’s properties (Pn) would fall into 8 possibilities. If those are all equally likely (assumption) then, with detectors randomly in orientations 1, 2, or 3, the following would result:
Electron Random detector measurements Measure the same?
P1 P2 P3 1 & 2 1 & 3 2 & 3
G G G G G G G G G Y Y Y
G G R G G G R G R Y N N
G R G G R G G R G N Y N
G R R G R G R R R N N Y
R G G R G R G G G N N Y
R G R R G R R G R N Y N
R R G R R R G R G Y N N
R R R R R R R R R Y Y Y
50/50 - on average 4xSames & 4xDifferents
Oddly enough, I understood the 3x3 square showing the detector orientations and whether they would measure Same or Different. I’m just having a hard time reconciling the above with 5/9ths.
Also, you couldn’t make two measurements, separated by any distance, simultaneously…because Relativity kind of does away with simultaneity. There will be a valid frame of reference in which one happened before the other.
i.e., how would you communicate between the two experimental apparati that they are to start “now?” How do you contrive the simultaneity? Essentially, it can’t be done.
Does that work? You can violate Relativity by the “simultaneous” waveform collapse?
I think we’re talking about two different things; otherwise, you’ve just disproven Relativity.
I’m saying that you can’t make the measurement of an entangled particle-pair at two different places at “the same time.” Joe can’t measure the spin of particle A at the exact same time that Jack measures the spin of particle B. If they could, then this might imperil the entanglement concept, as the OP envisions.
You misunderstood the question slightly (no worries–I misunderstood the question when I first read it as well).
The question was on the specific case of a particle that flashes green for detector position 2 and red otherwise. There are 9 possibilities for the two detectors: 1-1, 1-2, 1-3, 2-1, 2-2, 2-3, 3-1, 3-2, and 3-3.
Clearly, 1-1, 2-2, and 3-3 always give the same answer, so that accounts for 3/9. The detectors will also give the same result for 1-3 and 3-1, though, since those are both red. That adds to 5/9 total.
Note that the final result does not depend on the assumption that the 8 initial “programs” are equally likely. What we know is that no matter what the distribution, the overall likelihood must fall between 5/9 and 1. It can’t be possibly be less than 5/9 (without violating an assumption) because none of the 8 possibilities can have results less than 5/9.
There’s no paradox involved, really. Think of the classical case where you have two envelopes, one with a red card, and the other with a green card in it. If you go to Titan, and I stay here on Earth, we both open our envelopes simultaneously, and either I see a red card—in which case, I know you see a green card instantaneously—or I see a green card—where again, I know you see a red card. Whether we make this observation simultaneously (in some frame of reference) does not influence this at all.
Now, quantum theory has an option that’s missing in the classical world, which is that you don’t just have either the case of me having a red, and you a green card, or me having the green and you having the red card, but also, arbitrary linear combinations of these possibilities. This is known as superposition—whenever a quantum property can assume different values, it can also assume values that, mathematically, are a sort of sum of these values (well, modulo certain restrictions known as superselection rules, which I won’t go into here). In such a case, it is impossible to attribute any property definitely to a physical system in such a superposition—all you can do is attribute probabilities that, upon measurement, either of the possible properties will be observed.
So really, all that entanglement is is correlation (the fact that whenever I know my card, I know yours, as well) plus superposition: either of the possible correlated cases manifests upon measurement with a given probability. Who measures first, or if the measurements are simultaneous, does not really matter.
Though I don’t really endorse that particular interpretation (or indeed, pretty much any of the interpretations on the market), it might be useful to think about this in the many-worlds picture: what happens upon measurement is simply that the observer realizes in which world they are—either in the world where your card is red, and mine is green, or the world in which mine is green, while yours is red. So if they measure simultaneously (again, within some given reference frame), they’ll simply both simultaneously find out in which world they are—and in fact, if you believe the branching-worlds picture, in one world, they’ll find out they’re in the you red-me green world, and in the other, they find out they’re in the you green-me red world.
Sure they can—that was in fact the original EPR-example: two entangled particles on which you either perform position or momentum measurements.
It still might be the case that there are hidden variables, however, if that’s so, then they must be able to influence one another instantaneously across arbitrary distances (see Bohmin mechanics).
I’m not sure I understand you correctly, but as far as I can see, there’s absolutely no problem with simultaneous measurements in quantum mechanics—and as OldGuy above points out, for measurements at spacelike separation, there always is a reference frame in which they are simultaneous.
There’s also the issue that Chronos alludes to (I think): when the wave function ‘collapses’ depends on where you put the cut between the observer and the observed; and since this is arbitrary (you can put it between the particle and the measuring device, the measuring device and the observer, or even the observer and their records), so is the precise timing of the collapse. In the end, there’s always a consistent story to tell, although which one that is might only be obvious after the fact.
For completeness, I should perhaps note that I’m simplifying here: in the quantum case, there are not simply two correlated properties in superposition, but many of them, corresponding to different measurement choices you might make. So, in the cards analogy, if there is the possibility of you having red/me having green or vice versa, there is also the possibility of me having yellow/you having blue (and the other way around), you having pink/me having violet, and so on. This corresponds to the fact that in whatever direction you might chose to measure, say, the spin value of a pair of spin-entangled particles, the other particle will be found having the opposing value (if the pair was created from a spinless original state). But it doesn’t really change matters.
In a relativistic context space and time are not separated but are a combined property called spacetime. An objects actual path through spacetime is called the worldline and the light cone represents all possible worldlines. The light cone is related to the speed of light but is more correctly thought of the speed of causality. While several things can exceed this speed of light they cannot have causal efficacy. Entanglement can be used for the correlation of random results, but it does not convey information.
As Half Man Half Wit pointed out. You have no control over the state of the earth card, and once you make a measurement you lose entanglement. You can infer the state of the titan card by noting that it must be complementary to the earth card.
Because there is no superluminal information being communicated this event does not violate GR. Observers within of an event’s light cone may not agree on the order of events let alone on the timing. Various factors like frame dragging, time dilation and the curvature of space time can change their perception of time.
The only way to have those events to appear tangent chronologically despite being distant spatially to an observer is to choose a reference frame that makes them so. Even if you choose that frame of reference; where the two actions appear to be simultaneous it does not mean that it would always appear to be so from the events perspective. Another issue is that the time and place of remote events are not fully defined until light from such an event is able to reach our traveler as described in the much simpler flat spacetime of Einstein’s Train.
The Gödel metric and other closed timelike curves describe events tangent in space but distant chronologically. This unsettled science and other theories like Loop quantum gravity, string theory or ??? will be needed.
Obviously I wrote this post a few months ago, so it is not that fresh in my mind, but in bog standard quantum theory a simultaneous measurement requires that there exists a joint eigenbasis for the set of operators representing the set of measurements. However the condition for the existence of a joint eigenbasis to exist for a set of operators is precisely that the set of operators commutes.
As you point out that when you bring relativity into the mix “simultaneous” can be replaced by"spacelike"in the above.
So for a set of simultaenous/spacelike measurements where the operators commute QM can describe such a situation with no contradiction, but when the operators don’t commute such a simultaneous set of measurements is nonsensical in QM.
Now there’s been a ton of stuff written on the subject and most would agree that this seemingly-paradoxical situation comes about from the assumption we can make arbitrarily precise measurements of ‘reality’ whenever we like.
Ah, I hadn’t interpreted the OP to intend to make different measurements on both particles (nor had I noticed that this is a zombie thread). However, even in that case, there’s no problem, since the two measurements are carried out on different subspaces of the joint Hilbert space, and thus, commute trivially, and the joint measurement operator is just the tensor product of the two local measurements.
