I thought they were entangled. What exactly is entangled in this situation, if not the electron and nucleus involved?
I think this analogy breaks down for true quantum systems. For example, it is possible to set up an experiment where the property to be measured is something like the polarisation direction of entangled photons, but where the axis of measurement is not determined in advance. For a single, predetermined axis of measurement, it would be possible to set up a predetermined correlation like the example with the pieces of paper mailed to London and New York. But if the measurement process is only determined at the end - after the papers have been sent through the mail - there's no way to maintain all the required correlations, unless there are some "hidden variables". But hidden variable theories have also been tested, and the evidence seems to rule them out, too.
Actually, let me flesh that out a little with an example to try to explain what I mean. Suppose that on your two pieces of paper the words "Up" and "Down" can be written, or alternatively "Left" and "Right". If one paper has "Up", you know the other is "Down". If one is "Left", the other must be "Right". The state of the envelopes is prepared and they are sent to London and New York. After they arrive, the receiver in London, say, makes a choice "I think I'll measure Left-Right, rather than Up-Down". Then he opens the envelope and, sure enough, sees "Right" written on his piece of paper. At this point, he can be sure that the New York receiver will open his envelope and see "Left". But, he could have chosen to measure Up-Down instead, in which case when he opened his envelope he could only see "Up" or "Down" written, with no possibility for "Left" or "Right". And the New York correlation would remain. Of course, in the classical world this experiment can't be done. But it can be done with photons or other quantum entitites.
That's ok. Text. But you have no sufficient means to know about pre existing entangled particles, so you have to create them and track them since beginning, infact you have to confine them to meaningfully utilise this entanglement property. Otherwise how do you foresee any use of this and how do confine or track a photon?
The problem is when maths is taken as reality, but actually it is not. A system can be in multiple possible states depending on certain other factors, the work of the maths or mathematicians is to give an expression about these possible states at any given instant depending on influencing factors.....that will be your psi function..uncertain about the state of system. Now once we observe the system and determine the reality that the system is in state A, and claim that the wave function is collapsed on observation is actually semantic nonsense. Science at its gullible absurdity. The system on our observation is not in state A, because wave function has collapsed or superposition eliminated, the entire set of influencing factors have done their job and actually the wave function or the state function becomes deterministic because on observation we know what we did not know while formulating the wave function. Take for example a building collapses and a man gets trapped in the rubble, there are three possible states depending on various complex analysis...dead, alive or hurt (I have just added hurt). Now we can mathematically create an expression which can give all three possible states depending on influencing factors. Once we observe then say the man is alive, that will be one particular set of influencing factors whose solution leads to alive. The wave function has not collapsed, it is just that we are equipped better information, our wave function becomes deterministic. It's quite likely that when we observe the man is in dead state, the post mortem may give a conclusion that an iron rod pierced through his heart, we knew this possibility while formulating but we were not sure whether this would have happened till we saw the man. So it is nonsense to claim that the man was simultaneously dead or alive or hurt, prior to observation. It's just that based on lack of information we could not have determined the actual state, and we made mathematical possibility analysis.
That's about Schrödinger's cat. The cat in reality can only be dead or alive irrespective of nature of wave function. Without knowing the influencing factors state at any given instant we cannot determine the actual state of cat so we have a probability function. But once we observe the probability function becomes a deterministic outcome. Well you can call it mathematical collapse but there is no reality in it. It cannot be stated that cat was alive or dead simultaneously.
The violation of Bell's Inequality contradicts that description. What Bell's violations indicate is that the system is not in a given single status merely unknown to us at any particular moment, which we simply discover by measuring it. The current best established explanation of this is that it is instead in a superposition of two or more states, and remains in that superposition until fixed in one status by an interaction with an environment that forces determination of it. That explanation agrees with observation and experiment. Repeated runs of that kind of setup will not violate Bell's Inequality - the different states are not entangled, no superposition exists, etc. Maybe the issue can be brought into focus by inverting that example - lets mail some slips of paper and describe what we would find if they were entangled as photons and such can be. We mark a few dozen slips of paper as follows: Each slip has three words on it, one each chosen by coin flip from the following pairs: down/up, left/right, back/forth. So a slip might have "down right back" on it, but never "down up back" - clear? Then Bell's Inequality gives us the following, as a logical truth and inescapable classical physical reality: the total count of slips with "down" but not "left" and slips with "left" but not "forth" (the sum of those two counts) is equal to or larger than the count of the single category "down" but not "forth". This will be absolutely true of every actual collection of physical slips you mark like that, guaranteed, in classical world. For example, you mark ten slips: dlb, drb, dlf, ulf, urb, urb, drf, ulb, drb, ulf. Your counts are: 3 + 2 = 5, and 3. Five is greater than three. To be convinced, draw three Venn diagrams of the intersection of the three sets d, l, and f, and shade the three areas described. You can see how it works, how it has to work (and of course it's been proven by formal logic as well, given very basic assumptions) Then you are ready to realize how strange the quantum world is. Because in our little play acting model here, we mail this envelope full of these slips to London: and three tellers each count a set, and when we add and compare their counts we find the inequality is violated. The number of slips with with "down" but not "forth" is greater than the total number of slips in the other two sets combined. Every time we do it, every different pile of slips we mark and mail. That is what the experiments and demonstrations performed and analyzed by dozens of physicists with all kinds of different setups in different labs all over the world have found, in quantum world.
This looks like an excellent post but have to admit I am not extracting as much meaning as I had hoped for. I seem to be missing something (IQ?). Are the quantum model slips (say 10) entangled? Or what?
That suffers the same problem. Are you not assigning a state to a property before the experiment starts? That doesn't happen, in QM particles, unless you make measurement on a particle, note it, and then make the exact same measurement again -- as in sending a beam of electrons through a Stern-Gerlach magnet, isolating the "Down" deflected electrons and sending them through the same magnet exactly as before.
I'd like to introduce, concept if you will, into this discussion: pseudo randomness VS "exact" randomness. We've always been told that when you make a measurement of a property of a QM particle with 2 states, it is 50% which of the 2 states you will measure, and it is what I'll call "exact randomness". I think that is pretty standard. Now, consider a person measuring the up/down state of an electron in a Stern-Gerlach magnet, and taking the beam of all "down" electrons. If s/he sent them through the same setup, they would all again measure down. Now consider s/he just doing the first measurement and not repeating it with the down electrons. S/He should have measured 50% up electrons and 50% down electrons. Unbeknownst to you, s/he feeds the "down" electrons into your input stream. Would that alter your measurement of the electrons? You had no knowledge that they were "down" electrons measured by the other person. Would you still measure 50% down and 50% up electrons, even though your input was seeded? It may seem like there is an easy answer: your outcome would be skewed by the input. But to me it seems that in nature, there are times when you would encounter a hidden process just like this, one that would seed your input skewed 1 way or another. So, if you still measured 50% up/down, then the measurement process would truly be random, and also be tied to 1 person. If not, then nature could possibly be pseudo random, and the randomness we see would only be due to good mixtures. At the level -- number of particles -- 10^70 (or is it 10^140), how could humans differentiate between true randomness and pseudo randomness?
Yes Of course Well, you have 2 drb and 2 ulf there. Is that intentional? I would have expected that, if you have 3 "slots" each of which can be filled in one of 2 ways, then there would be \(2^3=8\) possible configurations, whereas you have 10, which sort of makes your duplications unwise
000 001 010 011 100 101 110 111 Selecting any ?1? or 1?? or ??1 (a total of 4) gives (the expected by me) 2 of each of the others where 2+2=4. I don't see where we're going from there. Edit... If (for example) we added 111 to the above list we'd have 1?? occurs 5 times ?1? occurs 3 times ??1 occurs 3 times where 3+3>5
Let's go with complementary degrees of freedom, and forget about particles for a little. Spin-orbit coupling is entanglement of spin angular momentum with orbital angular momentum, and there are two 'particles'. Performing Bell state measurements is a bit problematic, the electron and nucleus aren't very far apart. Nonetheless, Bell state measurements aren't "required", or nobody could know entangled photons are produced by SPDC.
Sorry for being vague: I meant to illustrate my caveat about these macroscopic models of "entanglement" by describing what a quantum world batch of slips would act like - what one of these "model" illustrations would be acting like if it were set up to actually behave as an entangled system would behave, and not as as seesaw behaves or a classically correlated bunch of paper slips behaves. No, let's not. That particular example selected by coin flip, as specified. You have eight combinations, and ten slips - some duplications are inevitable (two is lower than the expected number). Imagine how many you'd have with a hundred slips. Bell's Inequality holds with any combination of slip markings, in classical world. If we mandate the system behave as in quantum world, with the slip markings standing for spin directions or the like, Bell's Inequality is - somehow - violated with any combination of slip markings. That is a fundamental difference.
There are complications - you have to measure the same axis: https://en.wikipedia.org/wiki/File:Sg-seq.svg An electron has more than one way of being up/down.
Classical status of cat around poison or man under rubble is independent of observation. Your slip example seems to explain the concept behind, but the concept does not fit into the slip count. Your original count statement holds good prior to dispatch and after receipt.
Let me ask few questions.... 1. Is it right to conclude in case of Schrodinger thought experiment of cat/poison/radioactive that the cat could have been simultaneously both alive or dead or even superposed condition of these two states? 2. Is it right to conclude in case of that man under rubble that he could be simultaneously dead or alive? 3. Is it not that in case of observation of (non destructive) the state of classical object does not change, simply because the interaction on account observation may not be able to change the object? 4. Is it not that in case of observation of the quantum particles (like electron or photon), the interaction during the observation changes the state not the act of observation per se? For example to observe an electron, the process may require collision of this electron with probing photon or other particles? 5. Let us say that probability function of a particle as derived from wave function is F(p1,p2,p3) where p1, p2 and p3 are variables. Now depending on the values of these Ps, the state of that particle/object would be fixed. What we are doing is observing the particle / object not the event associated with p1,p2&p3. That means without monitoring the object or without knowing p1,p2 and p3 we have no means to fix the state of object. So it is more a question of our inability to determine the status due to lack of information rather than any physical absurd happening like the cat was simultaneously dead or alive?
Your slip count example may be illustrative but does not fit. Why not give example of one such demonstration or lab experiment which confirm this.
My point was about the classical "models" of entanglement floating around the thread (and the world), in which cause/effect correlation is used to model entanglement. They seem to me more likely confusing than explanatory. I tried to illustrate that. Not according to the Bell's Inequality violations. The physical absurdity is ineradicable - you can pick from among a couple of different absurdities as your explanation, but you aren't going to find anything comfortable. The cat business, like the seesaw and other classical object models, seems to lead astray.
True. The cat scenario is bad push. You hinted at multiple lab experiments and demonstration...hopefully they do not lead astray...pl post at least one.
