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What would happen if for some reason quantum entanglement were suddenly turned off? By "turned off", let's say that every entangled state is immediately replaced with a separable (but still classically correlated) state, e.g. a Bell state $(|00\rangle+|11\rangle)/\sqrt2$ might be replaced with $(|00\rangle\langle 00|+|11\rangle\langle 11|)/2$. The laws of quantum mechanics still hold.

What effect would this have on my everyday life? Could I still get out of bed, have a shower, take the bus to work, etc.? I'm not interested in the effect it would have on physics experiments such as Bell nonlocality no longer being detectable. I am interested in my everyday life as a non-physicist.

I have seen this similar question and find the answers given rather unsatisfactory. I understand that this scenario doesn't really make sense, since if the laws of quantum mechanics still hold then there will necessarily be entanglement, e.g. solving the Schrodinger equation to find the ground state of helium. I don't think this should make it impossible to understand the essence of the question and give some insight into how entanglement affects everyday life (if indeed it does).

Edit: another way of understanding what I mean by this question is "what processes in my everyday life rely on entanglement?".

Antony
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    I suspect at least the chemical reactions would change a lot, which means... well... – peterh Jul 18 '16 at 02:01
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    You can't get rid of entanglement without getting rid of QM, in which case nothing would be here. The more visible effects are the existence of the classical world trough decoherence. I don't know what you mean by replacing states in the way you suggest. The first thing you write is a state, the second is an operator that maps a state to another state. They are not even mathematically the same thing (a vector is not the same thing as a square matrix). – CuriousOne Jul 18 '16 at 02:13
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    It's hard to parse what this question asks. Almost all quantum states are entangled, so "turning off entanglement" is tantamount to turning off quantum mechanics. And if you turn off quantum mechanics, matter isn't stable, magnets don't exist, nuclear reactions don't happen... basically, physics is woven too tightly together to just rip out a piece of it. It's like asking how your life would change if you removed the circulatory system. – knzhou Jul 18 '16 at 02:35
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    A good alternative question is "are there any processes in biology that require quantum coherence"? (I know nothing about this subject, but apparently photosynthesis might.) – knzhou Jul 18 '16 at 02:36
  • @CuriousOne: the first state vector implicitly refers to the corresponding density matrix $|\phi^+\rangle\langle\phi^+|$ where $|\phi^+\rangle=(|00\rangle+|11\rangle)/\sqrt2$. – Antony Jul 18 '16 at 03:53
  • @knzhou: as already noted, I'm aware that a strict interpretation of the question would imply the non-existence of quantum mechanics. Regardless, I think it should be possible to give some answers in the spirit of the question. Along your lines, an alternative way of phrasing it would be "are there any processes in my everyday life that require entanglement?" (note this is a stronger requirement than the one you suggest on quantum coherence). – Antony Jul 18 '16 at 03:58
  • Quantum states and the density matrix are two completely different things. I still don't know what you are asking. – CuriousOne Jul 18 '16 at 03:58
  • Quantum states and the density matrix are not two completely different things. The density matrix of a pure state $|\psi\rangle$ is given by $|\psi\rangle\langle\psi|$. – Antony Jul 18 '16 at 04:00
  • The density matrix doesn't express pure states. It expresses a statistical ensemble of mixed states. It does so by preserving both the structure of conventional statistics and quantum superposition, including the tensor product structure that causes entanglement. You can't eliminate an effect with the same mathematics that is used to express it. – CuriousOne Jul 18 '16 at 04:05
  • perhaps of interest http://physics.stackexchange.com/questions/80434/how-is-quantum-superposition-different-from-mixed-state –  Jul 18 '16 at 04:09
  • @CuriousOne: A density matrix certainly can be used to express a pure state, as above. A density matrix $\rho$ will be pure if and only if $\rho^2=\rho$. Being new here I'm not quite sure what the conventions on stackexchange are for digressions like this, but I feel that this is rather detracting from the original question and discussion... Please refer to a textbook on quantum mechanics instead of discussing it here. – Antony Jul 18 '16 at 04:12
  • OK, I think I am a bit slow today. :-) Are you suggesting to replace entangled states with classical "white ball/white ball drawn from urne" correlations? – CuriousOne Jul 18 '16 at 04:31
  • @CuriousOne: Yes, exactly. I included the example in the question to emphasise that classical correlations should still be allowed. In other words, in the CHSH experiment, the non-existence of entanglement does not mean that no correlations are possible; one can still obtain a value $S=2$ using classical correlations (compared to $S=2\sqrt2$ for quantum). Thus I am asking "what everyday processes require quantum entanglement rather than just classical correlation?". – Antony Jul 18 '16 at 04:36
  • Classical correlations will not be able to create atoms and molecules , there will be a continuum of an electron around a proton. – anna v Jul 18 '16 at 04:39
  • @annav: could you explain what you mean by that? Are you saying that classical correlations alone would contradict quantisation of energy? – Antony Jul 18 '16 at 04:45
  • So you are looking for examples like "Quantum Entanglement and Chemical Reactivity" M. Molina-Espíritu†, R. O. Esquivel†‡, S. López-Rosa*⊥‡, and J. S. Dehesa? – CuriousOne Jul 18 '16 at 04:45

4 Answers4

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The question assumes that quantum entanglement actually happens the way it has been described by quantum mathematics. Which may or may not be true. All is not set yet. Leaving that aside -

In any case, entanglement is not a law in itself, it is a phenomenon. It is a consequence of basic underlying laws at quantum level. For example, anti correlation of spin is a phenomenon caused by law of conservation of angular momentum. Then there is statistical correlation of spin. And there are other multiple entangled properties.

You can not take entanglement away without modifying those underlying laws. But then modifying the underlying laws will not affect only entanglement phenomena, it can impact pretty much everything in the universe.

In fact, There may be just one most fundamental law of the universe, and changing any laws may not be possible without changing the most fundamental law. Changing that law would change everything. As knzhou rightly said, "physics is woven too tightly together to just rip out a piece of it"

kpv
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  • Sorry, but I find this rather unsatisfactory. I think there should be more interesting responses than "if entanglement didn't exist then nothing would be possible". Let's say that the question was "how would my everyday life be different if gravity didn't exist?". I could say that gravity is just a consequence of the curvature of spacetime, and having no gravity would mean that all sorts of things wouldn't exist. Alternatively, I could say "if we turned off gravity on earth then everything would fly off the surface". It is this sort of more interesting answer that I am looking for. – Antony Jul 18 '16 at 05:08
  • @Antony: I gave an example - To turn off anti correlation (of spin) of entanglement phenomenon, you need to turn off the law of conservation of angular momentum. The effects of turning that law off are way too many to list. Then it is statistical correlation of spin, which may also be consequence of the same law. I am only taking about spin. There are other entangled properties that will require modifying other laws. – kpv Jul 18 '16 at 05:14
  • ok, but my question is specifically about the phenomenon of entanglement. As I wrote in the question, it can be interpreted as "what processes in my everyday life rely on entanglement?". It should be possible to answer that without resorting to "if entanglement didn't exist then angular momentum wouldn't be conserved, and that would have many consequences". Regardless of the fact that it's not physically consistent, it should be possible to imagine living everyday life in a world in which angular momentum is conserved but entanglement doesn't exist. What would be different? – Antony Jul 18 '16 at 05:23
  • @Antony "Regardless of the fact that it's not physically consistent" Please read about the principle of explosion. Once you assume a contradiction, every statement becomes true, so physics, mathematics, and logic itself stop having anything meaningful to say. –  Jul 18 '16 at 13:50
  • @ChrisWhite: thanks for the link. However, again, I don't see that this should prevent one from giving more interesting answers than "everything breaks down, your question doesn't make sense". I am looking for people to pinpoint specific processes that rely on quantum entanglement. As in my gravity analogy, one can easily give some examples (e.g. without gravity, I couldn't pour milk into my bowl of cereal). Of course, the consequence of not having gravity would lead to a similar "explosion", but that doesn't mean that it's impossible to give insight into the role it plays in my everyday life. – Antony Jul 18 '16 at 13:59
  • I am (extremely) sympathetic to the part of this answer that says you can't "turn off" entanglement without changing lots of physics, so that the question becomes impossible to answer until you specify what else you're changing. But it's not true that if you give up quantum entanglement, you've got to give up conservation of angular momentum. After all, Newtonian mechanics satisfies conservation of angular momentum and manages to do so without anything resembling quantum entanglement. – WillO Sep 29 '16 at 22:18
  • @WillO: "Newtonian mechanics satisfies conservation of angular momentum and manages to do so without anything resembling quantum entanglement" - It manages without "knowing" anti correlation, not without "it being there". Anti correlation is a consequence of conservation law and is also part of entanglement. If you do not know that, you should be sympathetic to yourself. – kpv Sep 30 '16 at 00:42
  • @kpv: I have no idea what your last comment is supposed to mean, but a counterexample is a counterexample, and Newtonian mechanics is very definitely a counterexample to the statement that conservation of angular momentum implies anything remotely resembling entanglement. – WillO Sep 30 '16 at 01:32
  • @WillO: "Anti correlation of spin" part of "Entanglement" is just one phenomena that follows conservation of angular momentum. So, the law itself does not require to list all phenomena, specially when it was not even known at that level in Newton's times. But to make this phenomena disappear, the underlying law has to disappear and that would change everything. For example we say what if rain water did not fall down - that would mean the gravity did not work on rain water - so it requires gravity to change, or dissappear causing much more havoc. – kpv Sep 30 '16 at 02:34
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I will turn my comment to an answer, in reality answering your statement in the comments:

Thus I am asking "what everyday processes require quantum entanglement rather than just classical correlation?"

Classical probabilistic analysis depends on classical dynamics, the emergence of entropy from statistical mechanics is a good example.

There have been and there continue to exist efforts to show that the quantum dynamics emerges from an underlying level of classical dynamics. A good example of this is Bohmian mechanics. It is able to give the same results as non relativistic quantum mechanics, i.e. bound quantized states. Afaik it fails in relativistic quantum mechanics.

In your question you are not proposing that the known particles are composite or have an underlying level of complexity that might lead to equations with emergent bound quantized states. Just having classical probabilities in place of quantum mechanical ones, which is what will happen if the QM phases are not there, will lead to continuum four vector states. The bound states have probability 1, which is not possible in classical probabilities for the same set up of particles, and the forces as we have found them. I cannot see how it could be contrived , unless with a substructure a la Bohm.

anna v
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Entanglement manifests via correlations. If you can get rid of entanglement while keeping those correlations, I guess nothing will change in your life.

So what is the question exactly? If it is, "do we know how to reduce quantum correlations to classical ones?" (ie. do we have a proper hidden variables theory), the answer is no (at this time, no such theory is convincing).

If it is, "does quantum mechanics still hold in the absence of entanglement?" then the answer is also no, contrary to what is assumed in the question. Entanglement is not a peripherical part of quantum mechanics, it is a deep aspect of it.

To the question "what processes in my everyday life rely on entanglement?", rephrased as per the above as "what processes in my everyday life rely on quantum correlations?", the answer is: all of them, because all physical processes are ultimately described by quantum mechanics, and I don't see what it would mean to accept quantum mechanics without accepting quantum correlations.

Still there is an interesting twist here: physics has progressed by the analysis and description of causal correlations. So all common physical processes, and naturally all classical ones, can be described without the need to introduce non-causal correlations, which is why it is hard to pinpoint a specific process directly requiring quantum correlations to be explained.

Stéphane Rollandin
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Entanglement is fundamental to our understanding of the behavior of matter. If you get rid of entanglement then matter must behave differently. Which would break the processes that keep your body working.

Actually, entanglement is so deep in quantum mechanics that it's not clear how you could remove it without just throwing out the whole theory. It's a bit like asking "How would my life be different without angular momentum?". And it's not like we can just go back to classical mechanics, because then electron orbits would decay.

So I guess I would describe your life under no-entanglement conditions as... short? Everyone everywhere dying in a fraction of a second because electron transport stopped working or something.

Craig Gidney
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  • Knowing that electron orbits do not decay, could we consider it like an ultimate proof of the entanglement instead of looking for it in the EPR-like experiments ? –  Jul 18 '16 at 17:42
  • @igael No, there could be other mechanisms or models that prevent decay. But they'll have more differences w.r.t. quantum mechanics than just "drop entanglement". I don't mean to imply that there is no other possible model, only that they have to differ more than you might expect. – Craig Gidney Jul 18 '16 at 18:24
  • @Antony According to some researcher, you may face the risk of destroying the spacetime. – XXDD Jul 19 '16 at 14:27