" . . . there is another conservation law standing in the way of progress -- the law of conservation of angular momentum -- spin. "
-- Robert L. Forward
So what is spin, i.e. angular momentum in the quantum realm, as exhibited for example by an electron or proton? Well, the first image that comes to mind, as it did to the physicists investigating the phenomenon in the 1920's is that of a rapidly rotating electron or proton (the only particles known at the time.) This picture at least provides a simple mental image for those still nostalgic for the old Bohr solar-system model of the atom. There is this electron "planet" orbiting a "proton" sun (let's stick with the hydrogen atom, please) and both are "rotating" about their mutual axis just like the planet earth and the sun spin about theirs. It is a pleasing picture, cute in a way, but it is wrong. Worse, it is unhelpful. The fact that it is so wrong brings us to one of the immediate problems in thinking about the quantum world, the world of "micro-physics," and we might as well get it out of the way. As the great physicist Pauli noticed almost at once, if you calculate the "rotation" velocity of an electron, assuming it is behavior like a rotating planet, it turns out to be faster-than-light. This is presuming the electron is an extended body of some sort, not a point particle, which is in fact how most physicists think about it. Faster-than-light is a big no-no and as every physicist will tell you a calculation that yields such is giving a strong indication that the initial picture is wildly in error. No way to get around it. Moreover, if we think of an electron as a spinning ball, how the heck does it hold together given the enormous electrodynamic forces that must be coursing through it?
There are some things, given the current state of our knowledge, it is best not to go there -- at least so current wisdom tells us. Though some activity is taking place that can be measured in quantum terms that resembles what in the macro-world we would call "angular momentum" (it is a conserved something after all), try as best as you can to put the rotating mini-planet image out of your mind -- forever.
Now, I don't mean to suggest that pictures as such are a bad thing. That is the way we learn to interact with our environment and it is far from clear to me that a blind physicist or mathematician would be an any advantage in thinking about the quantum world as compared to his sighted compatriot. Moreover, using mental pictures to guide experiments, thought or otherwise, has been a key skill for physicists, e.g. Einstein, and you can't go wrong as a physicist when following Einstein. But the fact of the matter is that the quantum realm is best understood in terms of abstractions, symmetries in particular which have been all the rage since Noether's pioneering work. So if we think of "spin" in terms of a symmetry what do we learn?
". . . while spinning is mathematically similar to rotation, it is unlike any rotation that we can ever perceive with our senses." -- Charis Anastopoulos [PoW]
"Even if the symmetries of a physical system are the only thing we know about it, we can still understand many aspects of its structure." [PoW]. And that is the key to grasping the quantum world. The rotations and translations of [Minkowsky flat] spacetime together form what is called the Poincare symmetry. What this means is that once we have confirmed the presence of this symmetry, "we can decompose any system with a given symmetry into smaller systems that still possess the symmetry. We then decompose these smaller systems into yet smaller ones possessing the symmetry." [PoW, page 139.] And so on, until we arrive at the fundamental or irreducible systems. These components describe the motion of free (i.e. no external forces) particles.
In the end, the analysis reveals two numbers which describe these free particles. The first number describes the particles rest mass. The second describes something that resembles "intrinsic spinning. It is therefore called spin." [PoW, page 140].
This is a marvelous result and is as solid as you can get in the quantum realm. But unfortunately, and this point cannot be emphasized enough, it falls apart in General Relativity. As the great physicist John Wheeler (1911 -- 2008) was to discover, there is no way to incorporate "spin" into General Relativity except in very special circumstance. This was a big disappointment to him because he was hoping to develop a kind of ("already", as he referred to it) unified field theory just using topology in GR. but because the flat Minkowsky spacetime completely breaks down in GR (recall the "fields upon fields" description means good-bye to the spacetime backdrop), so does the beautiful Poincare symmetry. And that means notions of conservation of mass and angular momentum become much more dicey and difficult to deal with.
I'm not sure what Emmy Noether would have made of this but I suspect she would not have been altogether happy with this development. Nor would a classical physicist. But for those of us seeking the spin drive to the stars, this "unfortunate" development, offers hope towards that end.
[to be continued].
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