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.


The Waste of Time That is the EmDrive

I stumbled over an article yesterday that I found again today in my newsfeed that finally causes me to be willing to spend time writing about something. The article is here.

This article is about a sketchy physics topic that the popular media loves itself something fierce. Namely, the EmDrive.

This device is supposed to be a form of engine that can drive spacecraft faster and more efficiently than current technology otherwise allows. The creator of the EmDrive loves to claim that the device can solve all the world’s ills, from the energy crisis and global warming to the drip under your sink. Never mind that the excessive claims should set everybody’s danger sense a-tingling, it is a device that has persisted past it’s creator’s obvious lack of background in the basic science of physics.

Here’s a description of how the EmDrive is supposed to work as quoted from the article:

How the EmDrive works

The EmDrive is the invention of British scientist Roger Shawyer, who proposed in 1999 that based on the theory of special relativity, electricity converted into microwaves and fired within a closed cone-shaped cavity causes the microwave particles to exert more force on the flat surface at the large end of the cone (i.e. there is less combined particle momentum at the narrow end due to a reduction in group particle velocity), thereby generating thrust.

The general idea here is that you’re injecting microwaves into a hollow cone and allowing them to bounce around. Because the cavity is asymmetrical, the argument goes, they end up breaking symmetry on the pressure they’re exerting and push the cone only in one direction.

In a way, the set-up is almost an exact duplicate of the thought experiment that Einstein used to come up with the equation of E=mc^2, but beyond that, this is actually a flagrant violation of conservation of momentum. You can think about it this way: a guy standing inside a train car pushes against the wall of the train car… no matter what the shape of the inside of the car, the guy walking around never moves the center of mass of himself with the car –even if the car will actually move slightly as he walks back and forth, if the axles of the car and the rails are frictionless. The only way the car can continue to move is if the guy goes running along the car and jumps out the end, thus enabling his center of mass to be decoupled from the car… if he were to keep running, the center of mass of his system and the car would remain at rest, while he and the car must both be moving in order to conserve the net zero momentum they started with as a system. The analogy breaks down because the guy standing on the ground would be able to exert force to stop running. As Christopher Nolan wrote in Interstellar: the only way to go somewhere in space is to leave something behind. As a physicist’s aside, one has to put in a train car analogy at least once in this discussion because Einstein loved trains during his explanations of special relativity (I’m convinced that this is part of why Sheldon Cooper loves trains).

Breaking conservation of momentum is a pathological, ‘do not pass go’ fault that should immediately consign this whole EmDrive concept to the dumpster the same way Avagadro’s number kills Homeopathy. Despite that, the creator of the EmDrive has a ready response:

However, Shawyer claims that following fundamental physics involving the theory of special relativity, the EmDrive does in fact preserve the law of conservation of momentum and energy.

The author’s recourse is “Don’t worry about it, it’s hidden in special relativity!” Having dealt with special relativity and being aware that Einstein used this very thought experiment to prove E=mc^2, I can assure you that violating conservation of momentum is still completely fatal to an argument. Special Relativity isn’t exactly an impassable mountain that breaks conservation rules the way General Relativity does.

Despite all of that, various labs around the world have built EmDrives to test the idea. In the end, this is sort of like continuing to test whether or not autism is caused by vaccination, but okay, fine.

To everyone’s surprise, some of these labs, including Eagle Labs at NASA, have reported tiny tiny thrust. Something smaller than micronewtons IIRC, but still thrust.

And, of course, the cranks go wild! Here it is, the reactionless Cannae drive that will take us to Alpha Centuari by 2035 and Vulcan by 2150.

Now, the fact is that while these labs have reported thrust, we don’t know exactly why it did. Sure, it did, but we need a theory that sits within physics that explains why it did. Rest assured, the reasons given by the drive’s creator are completely bogus, so new explanations are needed. Is it Casimir vacuum pressure? Is it warped spacetime? Is it Calvin’s Universal Transmogrifier? We need to figure it out.

The Finnish physicist in the IBTimes is remarkably conciliatory even if his tacitly favorably worded response is actually just another huge nail into the EmDrive’s already well-built coffin. Here is this physicist’s explanation:

“The EmDrive is an engine like any other engine. It takes in fuel and produces exhaust. The fuel side is easy for everyone to grasp – microwaves are being fed in. The trouble is, we don’t see anything coming out, which is why people think it doesn’t work,” Annila told IBTimes UK.

“So how could something come out that you can’t detect? Well, the photons bounce back and forth inside the metal cavity, and some of them end up going together in the same direction with the same speed, but they are 180 degrees out of phase. Invariably, when travelling together in this out-of-phase configuration, they cancel each other’s electromagnetic field out completely.

“That’s the same as water waves travelling together so that the crest of one wave is exactly at the trough of the other and cancelling each other out. The water does not go away, it’s still there, in the same way the pairs of photons are still there and carrying momentum even though you can’t see them as light.

“If you don’t have electromagnetic properties on the waves as they have cancelled each other out, then they don’t reflect from the cavity walls anymore. Instead they leak out of the cavity. So we have an exhaust – the photons are leaking out pair-wise.”

Whatever else I might think about everything here, this is actually not a bad explanation. Photons have the quality where they can be superpositioned: if you pick two photons headed in the same direction, of the same polarization, with their E-fields 180 degrees out of phase, the Poynting’s vector still exists, allowing them to still carry momentum, but their field oscillations will cancel out. If they are introduced pair-wise in this manner, there’s not a reason to think that they can interact with matter any longer and they could simply slip straight through the confinement of the drive and off into empty space. So, the thrust from the drive would then be generated by the physical asymmetry of the cone allowing photons to pair up and escape easily in one direction, but not in another.

As a slight aside, I think I disagree with the Finnish physicist’s usage of water waves in the example above. The reason is that macroscopic waves in water are not discrete the way photons are. By effecting the continuum of material in water, the displacement of the wave crest from its resting state is what contains the energy of the wave: for small displacements, the momentum is perpendicular to the direction of travel. By adding a second oscillation 180 degrees out of phase, you completely cancel out the energy of the wave… and no wave remains after the fact. I’ve been thinking and I continue to think about whether or not the same is true with photons. I don’t think that it is mainly because photons are quantum mechanical particles and they have a quality of being discrete objects in the sense of their particle-wave duality. Photons contain linear momentum parallel to their direction of travel, while a water wave does not (the momentum is perpendicular to its direction of travel), and two photons caught traveling in the same direction must conserve momentum, regardless of their phase.

Now, I am granting here that there’s a physical explanation for why thrust is being generated, but we’ve slipped into explicable physics. If you stop and think about what we’re talking about, all we’re talking about is a very specialized form of microwave antenna. If you want thrust from momentum carried away by emitted microwaves, this process of pairing up photons so that they become invisible to the walls of the device (and sensors behind the device) is sort of beside the point. Granted, it would not torch anything behind it, this device is not the most efficient way to produce photons in the form of thrust. A flashlight or a laser would be much more efficient at converting power into thrust by doing essentially the same thing.

You could presumbly do an experiment like this one with a lasing cavity using optical light. I would partially-silver the surface of one mirror with a coating that is about a quarter wavelength thick before you hit the actual mirror. It’d be technically challenging since you’re talking about 1/4 micron thicknesses that are the tolerance of the lasing mode, but that’s something that can be attempted. Provided you stay at a condition of optical gain in the cavity modes (not all the photons are canceling) you should be able to test whether the recoil of the laser body due to the emitted radiation is the same as the recoil at the laser light spot. You could probably just set it up as an interferometer with adjustable arms and forget the coating. Again, this would depend on polarizing the emitted light.

Just thinking about it, I can imagine several more ways to test this in an optical setting. Some of them could be quite cheap to do.

Point is that there’s nothing magic about this.

Again, the problem with the EmDrive is that it’s exploiting physics to not do the most efficient thing it could do at its supposed task. If you start tabulating the amounts of power needed to generate thrust that is appreciable by these methods, you’re going to start tripping over conservation of energy somewhere. This not being magical, the amounts of energy needed to do anything are also not magical and will turn into eyepopping numbers when you start demanding that the thrusts the engine can produce are big enough to move masses humans might want to move with it.

I’ve been quite generous here. This is supposing that the explanation the Finnish physicist has supplied is useful over the other potential sources of noise in the experiment –the micronewtons or nanonewtons Eagle labs reported is so tiny that somebody’s breath could have been hitting the side of the experiment.

Scaling this thing up in force is crazily hopeful and would require you to jettison basically the whole design and go with something that does better what this device is actually doing. At some point, it will be time to forget about this EmDrive and relegate it to the wide-eyed, hopeful crankery that it is.