Please Note: These comments are not directed at Dr. Kaku. I am quite sure that he is amply aware of the issues raised here. The need for this commentary arises because, in the video, Dr. Kaku speaks about the situation in an informal way. This is a good approach for popularizing the subject, for introducing students to the subject, and for providing quick background information so that one can move on to a more germane point. Dr. Kaku's remarks, however, can also serve as a springboard for those who would like to become aware of the differences between an informal treatment and a more exact approach, or between a popular treatment and one that goes into greater depth. This second option is the goal of this commentary. This commentary, however, is only a further step in a longer process. Those who are more advanced would probably benefit from a discussion that is even more precise.
One of the first points Dr. Kaku makes is that, while Einstein may have had a problem with quantum mechanics, he was "wrong," and "we do this every day." Hmmm...It is important to realize that, just because someone says they 'do something everyday' does not mean that they understand what they are doing. One can, for instance, drive a car all around, and never know anything more about a car than a handful of things about the keys, the doors, the windows, the mirrors, the steering wheel, the gas tank, the seat belts, the radio, and the trunk. However detailed this knowledge may be, it would not enable one to build a car, or even to diagnose an engine problem. For the purposes of a daily commute, of course, this limited knowledge is sufficient, and, in general, it is not really a problem. We would, however, become rather alarmed if we discovered that our mechanic didn't know any more about a car than these same rudimentary facts.
The reason Einstein was troubled by quantum mechanics was that scientists did not really understand what was happening in certain circumstances. Instead, they were simply being taken for a ride by equations which were accurately predicting things that were so weird that Einstein called them "spooky." The role of a scientist is to understand what nature is doing (the word 'science' comes from a Latin word meaning 'knowing', and the intention behind the name was that the modern 'scientist' was out to one-up the ancient philosophers, who, so the story went, had speculations but no real certainty about the workings of nature because they lacked the experimental method of science), so, for a scientist to be comfortable in a state of ignorance is about as alarming as having a car mechanic who hasn't got a clue as to what happens under the hood.
Dr. Kaku's 'don't worry, we do this all the time' approach is akin to (and, perhaps, an outgrowth of) the approach advocated by Dr. Feynman many years earlier in video 1. There Dr. Feynman strongly advised his student not to even try to understand quantum mechanics, but just to nod along to his lecture, and learn to appreciate and work with the quirks of nature, as you might learn to sing a song in a language you don't understand. David Mermin summarized this type of approach with the catchy line, "Shut up and calculate!" On this view, the whole matter boils down to knowing how to work with the equations--nobody knows what they mean, but we know how to add and subtract, and do algebra and calculus, so everything works out. This would be like having a mechanic who knows how to fix every individual part, but who doesn't have a clue as to what contribution each part makes to the drivablity of the car. Such a mechanic, then, might declare you car to be equally undrivable whether it had a cracked head gasket or a burnt out light in the glove compartment.
Many generations of students have been educated in this mode, and some may not even be aware of the true nature of the problem--the math works and the rest is just a philosophical problem (and, to them, philosophy is just a pile of BS, for that was the word on the street in the 20th century). Dr. Kaku, however, makes a helpful transition to highlighting this problem with the introduction of the image of an umbilical cord. As he points out, however, there are unfortunate problems with this image when you try to apply it to particles on different sides of the galaxy. The most immediate problem would be how you'd get around the apparent contradiction involved in saying that quanta are 1) sub-atomic particles and 2) that they have 'umbilical cords' which can extend for millions of miles--I mean, they are either very small or they are not. But let us skirt that issue by saying that the umbilical cords are exceedingly thin (sub-atomic in their breadth, if not in their length). Next we have the problem of instantaneous communication between the distant particles. One might think, on the basis of experience with ropes, wires and thread, that a tug on one end instantly produces motion on the other end, but in reality, the motion transfers along the line at a velocity which cannot exceed the speed of light--and, if it goes too fast, the line will simply snap. One way to think about it is like a chain of people holding hands--if the person on one end moves, pulling the others with him, the line either breaks or it takes time before the person on the far end is required to move. The 'umbilical cord' model is still constrained by the restriction to speeds below that of the velocity of light and so does not provide us with the solution we need.
Dr. Kaku's description of the physical circumstances stops more or less at the state of affairs as they were known in 1935 when Einstein first discovered the problem. The situation became significantly more complicated in the early 1960s (about the time Feynman gave the lecture in video 1) when John Bell hit upon an argument which physicist Henry Stapp has called, "The most profound discovery in science." In order to get at the core of Bell's discovery, we have to make one addition to Dr. Kaku's presentation. The correlation between the separated particles is not a mater of certainty but a matter of probability--that is, there is a chance that the relation which Dr. Kaku describes will occur, and a chance that it won't (Dr. Kaku may be indicating this when he says later in the video that the connection between the particles is "random," but this is not clear). The odds are given by the equations of quantum mechanics (and experiments bear out the fact that the equations give the right result). What Bell pointed out--and proved mathematically, beyond the shadow of a doubt--was that the probability equation provided by quantum mechanics violated the very rules of probability theory!
Einstein had thought that something had be left out or overlooked when quantum mechanics had been formulated. Bell's argument showed that, no matter what you added in, it wouldn't make a difference, because it was mathematically impossible to get a probabilistic system to behave in the way that quanta behaved. This meant that it was impossible to construct a model which would behave in the same way as the quanta, and so impossible to figure out what they were doing.
One might be tempted to attribute some kind of awareness to quanta (Dr. Kaku speaks in these terms), but the awareness would have to violate the constraints of relativity theory, and extend not only to 1) what a given particle's partner was up to, but to 2) what all other particles had been doing and 3) to the equation provided by quantum mechanics. These three conditions would have to obtain because the probability rate is determined not only on a case-by-case basis, but also cumulatively, so that, if there's a 20 percent chance that a certain outcome will obtain, the quanta have to 'know' that the target value is 20 percent and they have to 'know' how close the quanta in their test group are to hitting that target. Consequently, the problem is not only 'spooky action at a distance' but spooky collaboration over all space and time--I mean, how do you spell 'vast right-wing conspiracy?'
Those physicists who bothered to look up from their equations and formulae over the past 80 years quickly came to notice that, if quantum mechanics was right (and all evidence indicated that it was), then the theory of relativity (which was also supported by all kinds of evidence) was wrong, or vice versa. The way to tiptoe around this problem was to set up an imaginary divide between the rules which applied to sub-atomic particles and those which applied to bigger, 'everyday' or 'macroscopic' objects. On the macroscopic side, the rules of relativity held, on the quantum side, they apparently didn't. Thus, physicists and philosophers could speak of 'quantum non-locality', which is a more precise way of talking about a certain kind of magic which, they maintained, was restricted to quantum interactions. (Of course, buying into this line of thinking meant ignoring systems like that of Schrödinger's cat which showed that this imaginary divide can easily be crossed, but let's just keep quiet about that.)
The word 'non-locality' provides a more precise way to speak about magic because there are at least two distinct kinds of magic: 1) the magic practiced by professional magicians--which is actually a combination of science and various forms of deception--and 2) the magic of supernatural beings (which is what the professional magicians are trying to imitate or convince their audience of). Non-locality would correspond to the second type of magic, except that the scientists would not like to admit the existence of any supernatural beings who'd be operating behind the scenes--and, indeed, it'd have to be a rather odd group of drunken leprechauns at work if there was, because they'd have to have nothing better to do than mess around with quantum objects in such a mathematically precise way.
So this is what the most profound discovery of the entire history of science was boiling down to: magic--real magic, not trickery--was a scientific fact, supported by both mathematics and experiment. This is what was upsetting Einstein (even though, at his time, the issue was something that could only be glimpsed or guessed at, whereas, for the past 30 years it has been a certainty), but Einstein was quietly dismissed at the time as an old-fashioned fuddy-duddy, a guy who wasn't 'with it' enough to keep up with the new generation, ya know. He simply wasn't 'feeling it,' if you dig: Daddio had to pop into a new groove and swing if he was going to keep up with these cats, 'cause the wind was now coming out of the south, and the mumbo-jumbo of New Orleans was getting set to call the tune.
A generation of rebels, tired of all the heartless rules and dried-up reasons of the past (or just caught up in an existential crisis--maybe for real, or maybe just because it was the trendy thing to do), didn't need physicists to tell them that the world didn't play by humanly intelligible rules, but it sure didn't hurt their zeitgeist to have that be the case. If your teacher could turn you on to being an unthinking zombie who knew how to play with equations, and you could get paid for that--well, groovy! Pass me some of that, and--here--you try it: everybody's doing it.
Another fifty years later, and--man!--we're still sure that Einstein was wrong. Why? Because we do it all the time...
Well, here's some new news brother: Einstein wasn't all that wrong. There was something fishy going on, but it wasn't magic, and it wasn't the fault of quantum mechanics, nor was it the fault of the theory of relativity. The culprit? Probability theory. You see, Bell found a discrepancy between probability theory and quantum mechanics, and he and everyone else assumed that nothing could be wrong with probability theory, and so they put the blame on the wrong suspect. It turns out, however, that all that math and all those experiments were telling us that we needed to expand probability theory, so that's what I did (by the grace of God).
You can read the formal presentation in the professional journal where it was originally published, The Mathematical Scientist, or enjoy a more playful presentation in a sequel to The Fog, namely The Fall Of The Magi which features a conversation between Dr. Splitter, Bubbles, and Simon Sempel, and includes guest appearances by Perry Fuseos, whom you might know from The Second Existence Debate: The Beginning and The Middle. Whichever way you go, you'll end up knowing more than Einstein, and, if that doesn't impress your friends, well then, you need new friends.