Nonlocality and Simplicity

I just read an article called “How quantum mechanics could be even weirder” in the Atlantic.

The article is actually relatively good in explaining some of how quantum mechanics actually works in terms that are appropriate to laymen.

Neglecting almost everything about ‘super-quantum,’ there is one particular element in this article which I feel somewhat compelled to respond to. It relates to the following passages

But in 1935, Einstein and two younger colleagues unwittingly stumbled upon what looks like the strangest quantum property of all, by showing that, according to quantum mechanics, two particles can be placed in a state in which making an observation on one of them immediately affects the state of the other—even if they’re allowed to travel light years apart before measuring one of them. Two such particles are said to be entangled, and this apparent instantaneous “action at a distance” is an example of quantum nonlocality.

Erwin Schrödinger, who invented the quantum wave function, discerned at once that what later became known as nonlocality is the central feature of quantum mechanics, the thing that makes it so different from classical physics. Yet it didn’t seem to make sense, which is why it vexed Einstein, who had shown conclusively in the theory of special relativity that no signal can travel faster than light. How, then, were entangled particles apparently able to do it?

This is outlining the appearance of entanglement. The way that it’s detailed here, the implication is that there’s a signal being broadcast between the entangled particles and that it breaks the limits of speed imposed by relativity. This is a real argument that is still going on, and not being an expert, I can’t claim that I’m at the level of the discussion. On the other hand, I feel fairly strongly that it can’t be considered a ‘communication.’ I’ll try to rationalize my stance below.

One thing that is very true is that if you think a bit about the scope of the topic and the simultaneous requirements of the physics in order to assure the validity of quantum mechanics, the entanglement phenomenon becomes less metaphysical overall.

Correcting several common misapprehensions of the physics shrinks the loopiness from gaga bat-shit Deepak Chopra down to real quantum size.

The first tripping stone is highlighted by Schrodinger’s Cat, as I’ve mentioned previously. In Schrodinger’s Cat, the way the thought experiment is most frequently constructed, the idea of quantum superposition is imposed on states of “Life” and “Death.” A quantum mechanical event creates a superposition of Life and Death that is not resolved until the box is opened and one state is discovered to dominate. This is flawed because Life and Death are not eigenstates! I’ve said it elsewhere and I’ll repeat it as many times as necessary. There are plenty of brain-dead people whose bodies are still alive. The surface of your skin is all dead, but the basement layer is alive. Your blood cells live three days, and then die… but you do not! Death and Life in the biological sense are very complicated states of being that require a huge number of parameters to define. This is in contrast with an eigenstate which literally is defined by requiring only one number to describe it, the eigenvalue. If you know the eigenvalue of a nondegenerate eigenstate, you know literally everything there is to know about the eigenstate –end of story! I won’t talk about degeneracy because that muddies the water without actually violating the point.

Quantum mechanical things are objects stripped down to such a degree of nakedness that they are simple in a very profound way. For a single quantum mechanical degree of freedom, if you have an eigenvalue to define it, there is nothing else to know about that state. One number tells you everything! For a half-spin magnetic moment, it can exist in exactly two possible eigenstates, either parallel or antiparallel. Those two states can be used together to describe everything that spin can ever do. By the nature of the object, you can’t find it in any other disposition, except parallel or antiparallel… it won’t wander off into some undefined other state because its entire reality is to be pointing in some direction with respect to an external magnetic field… meaning that it can only ever be found as some combination of the two basic eigenstates. There is not another state of being for it. There is no possible “comatose and brain-dead but still breathing” other state.

This is what it means to be simple. We humans do not live where we can ever witness things that are that simple.

The second great tripping stone people never quite seem to understand about quantum mechanics is exactly what it means to have the system ‘enclosed by a box’ prior to observation. In Schrodinger’s Cat, your intuition is lead to think that we’re talking about a paper box closed by packing tape and that the obstruction of our line of vision by the box lid is enough to constitute “closed.” This is not the case… quantum mechanical entities are a combination of so infinitesimal or so low in energy that an ‘observation’ literally usually means nothing more than bouncing a single corpuscle of light off of it. An upshot of this is that as far as the object is concerned, the ‘observer’ is not really different from the rest of the universe. ‘Closed’ in the sense of a quantum mechanical ‘box’ is the state where information is not being exchanged between the rest of the universe and our quantum mechanical system.

Now, that’s closed!

If a simple system which is so simple that it can’t occupy a huge menu of states is allowed to evolve where it is not in contact with the rest of the universe, can you expect to see anything in that system different from what’s already there? One single number is all that’s needed to define what the system is doing behind that closed door!

The third great tripping stone is decoherence. Decoherence is when the universe slips between the observer and the quantum system and talks to it behind our backs. Decoherence is why quantum computers are difficult to build out of entangled quantum states. So the universe fires a photon into or pulls a photon out of our quantum mechanical system, and suddenly the system doesn’t give the entangled answers we thought that it should anymore. Naturally: information moved around. That is what the universe does.

With these several realizations, while it may still not be very intuitive, the magic of entanglement is tempered by the limits of the observation. You will not find a way to argue that ‘people’ are entangled, for instance, because they lack this degree of utter simplicity and identicalness.

One example of an entangled state is a spin singlet state with angular momentum equal to zero. This is simply two spin one-half systems added together in such a way that their spins cancel each other out. Preparing the state gives you two spins that are not merely in superposition but are entangled together by the spin zero singlet. You could take these objects and separate them from one another and then examine them apart. If the universe has not caused the entanglement to decohere, these spins are so simple and identical that they can both only occupy expected eigenstates. They evolve in exactly the same manner since they are identical, but the overarching requirement –if decoherence has not taken place and scrambled things up– is that they must continue to be a net spin-zero state. Whatever else they do, they can’t migrate away from the prepared state behind closed doors simply because entropy here is meaningless. If information is not exchanged externally, any communication by photons between the members of the singlet can only ever still produce the spin singlet.

If you then take one of those spins and determine its eigenstate, you find that it is either the parallel or antiparallel state. Entanglement then requires the partner, separated from it no matter how far, to be in the opposite state. They can’t evolve away from that.

What makes this so brain bending is that the Schrodinger equation can tell you exactly how the entangled state evolves as long as the box remains unopened (that is that the universe has not traded information with the quantum mechanical degree of freedom). There is some point in time when you have a high probability of finding one spin ‘up’ while the other is ‘down,’ and the probability switches back and forth over time as the wave function evolves. When you make the observation to find that one spin is up, the probability distribution for the partner ceases to change and it always ends up being down. After you bounce a photon off of it, that’s it, it’s done… the probability distribution for the ‘down’ particle only ever ends up ‘down.’

This is what they mean by ‘non-locality.’ That you can separate the entangled states by a great distance and still see this effect of where one entangled spin ‘knows’ that the other has decided to be in a particular state. ‘Knowledge’ of the collapse of the state moves between the spins faster than light can travel, apparently.

From this arises heady ideas that maybe this can be the basis of a faster-than-light communication system: like you can tap out Morse code by flipping entangled spins like a light switch.

Still, what information are we asking for?

The fundamental problem is that when you make the entangled state, you can’t set a phase which can tell you  which partner starts out ‘up’ and which starts out ‘down.’ They are in a superposition of both states and the jig is up if you stop to see which is which. One is up and one is down in order to be the singlet state, but you can’t set which. You make a couplet that you can’t look at, by definition! The wave function evolves without there being any way of knowing. When you stop and look at them, you get one up and one down, but no way of being able to say “that one was supposed to be ‘up’ and the other ‘down.'”

You can argue that they started out exactly as they ended up on only a single trial. As I understand it, the only way to know about entanglement is literally by running the experiment enough times to know about the statistical distributions of the outcome, that ‘up’ and ‘down’ are correlated. If you’re separated by light years, one guy finds that his partner particle is ‘up’… he can’t know that the other guy looked at his particle three days ago to find ‘down’ and was expecting the answer in the other party’s hands to be ‘up.’ So much for flipping a spin like a switch and sending message! When was it that the identities of ‘up’ and ‘down’ were even picked?

But these things are very simple, uncomplicated things! If neither party does anything to disrupt the closed box you started out with, you can argue that the choice of which particle ends with which spin was decided before they were ever separated from one another and that they have no need after the separation to be anything but very identical and so simple that you can’t find them in anything but two possible states. No ‘communication’ was necessary and the outcome observed was preordained to be observed. You didn’t look and can’t look, so you can’t know if they always would have given the same answer that they ultimately give. If the universe bumps into them before you can look, you scream ‘decoherence’ and any information preserved from the initial entanglement becomes unknowable. Without many trials, how do you ever even know with one glance if the particles decohered before you could look, or if a particle was still in coherence? That’s the issue with simple things that are in a probability distribution. Once you build up statistics, you see evidence that spins are correlated to a degree that requires an answer like quantum entanglement, but it’s hard to look at them beforehand and know what state they’re in –nay: by definition, it’s impossible. The entangled state gives you no way of knowing which is up or down, and that’s the point!

As such, being unable to pick a starting phase and biasing that one guy has ‘up’ and the other ‘down,’ there is no way to transmit information by looking –or not– at set times.

Since I’m not an experimentalist that works with entangled states, there is some chance that I’ve misunderstood something. In the middle of writing this post, I trolled around looking for information about how entanglement is examined in the lab. As far as I could tell, the information about entanglement is based upon statistics for the correlation of entangled states with each other. The statistics ultimately tell the story.

I won’t say that it isn’t magical. But, I feel that once you know the reality, the wide-eyed extravagance of articles like the one that spawned this post seem ignorant. It’s hard not to crawl through the comments section screaming at people “No, no, no! Dear God, no!”

So then, to take the bull by the horns, I made an earlier statement that I should follow up on explicitly. Why doesn’t entanglement violate relativity? The conventional answer is that the information about knowing of the wave function collapse is useless! The guy who looked first can’t tell the guy holding the other particle that he can look now. Even if the particles know that the wavefunction has collapsed, the parties holding those particles can’t be sure whether or not the state collapsed or decohered. Since the collapse can’t carry information from one party to the other, it doesn’t break relativity. That’s the standard physicist party line.

My own personal feeling is that it’s actually a bit stiffer than that. Once the collapse occurs, the particles in hand seem as if they’ve _always_ made the choice you finally learn them to contain. They don’t talk: it’s just the concrete substrate of reality determined before they’re separated. The on-line world talks about this in two ways: either information can be written backward in time (yeah, they do actually say that) or reality is so deterministic as to eliminate all free will: as if that the experiment you chose to carry out is foreordained at the time when the spin singlet is created, meaning that the particles know what answer they’ll give before you know that you’ve been predestined to ask.

This is not necessarily a favored interpretation. People don’t like the idea that free will doesn’t exist. I personally am not sure why it matters: life and death aren’t eigenstates, so why must free will exist? Was it necessary that your mind choose to be associated with your anus or tied to a substrate in the form of your brain? How many fundamental things about your existence do you inherit by birth which you don’t control? Would it really matter in your life if someone told you that you weren’t actually choosing any of it when there’s no way at all to tell the difference from if you were? Does this mean that Physics says that it can’t predict for you what direction your life will go, but that your path was inevitable before you were born?

At some level one must simply shrug. What I’m suggesting is not a nihilistic stance or that people should just give up because they have no say… I’m suggesting that, beyond the scope of your own life and existence, you are not in a position to make any claims about your own importance in the grand scheme of the universe. The wrr and tick of reality is not in human hands.

If you wish to know more about entanglement, the EPR paradox and this stuff about non-locality and realism, I would recommend learning something about Bell’s inequality.

Edit 6-7-19:

A quick additional thought. The part of quantum mechanics from which Bell’s inequality is originally derived comes from the same lineage as the Heisenberg operator formalism and ultimately the Schrodinger equation; this form of quantum mechanics has the flaw in that it is pseudo classical where Schrodinger’s equation basically assumes that information passes around instantaneously since it’s non-relativistic. It’s important to be careful about claims of simultaneity, or suppositions that information travels faster than the speed of light in this background since Newtonian physics says essentially that information has no speed limit, which is actually wrong. This makes you wonder if we’re yet established to truly ask the right question.