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Not only does this avoid unfair rudeness, it might be that what you said could have been more clear. Sabine,I agree with you that it's not fair to ask a physicist to explain something in layman terms and then expect the explanation to be fully correct, that there are certain critical steps that require intensive mathematics. "particles that have to be rotated twice to return to the same initial state" occupy non-orientable surfaces? {\displaystyle \chi ={1 \over {\sqrt {5}}}{\begin{bmatrix}1\\2\\\end{bmatrix}}} Now, we simply square this value to obtain the probability of the particle being found in a spin up state: P The way I see it what we are really talking about it pretty clear: we are trying to explain the results of experiments, and the results of experiments in quantum mechanics are pretty odd.

“Virtual Think Tanks: Physicists Who Blog” APSNEWS 25(9) 3 (2016) [October 2016] Sabine “Bee” Hossenfelder” Backreaction“occasionally offers unadulterated opinions” When everybody thinks the same thoughts, nobody thinks at all.

Ian, do you mean that QM needs some sort of substrate to live in?

But there must be something in reality that we're talking about, even if we have to resort to pointing to indirect effects in the macroscopic world.Again, I'm concerned that much of modern physics, including quantum mechanics, has become nothing more than a signaling game for analytical people. .

In any case, I get the strong impression you're not interested in my opinion to begin with, you just want to urgently voice your opinion that you think something must be wrong with what I explained (if you allow the word). https://en.wikipedia.org/w/index.php?title=Eigenspinor&oldid=958014196, Creative Commons Attribution-ShareAlike License. The conserved angular momentum is the combination of orbital & spin AMs. That's where this analogy ends. Sabine, That's what I was asking, if particle spin is a calculation and not a physical one; i.e it doesn't spin like a top or the earth on it's axis.

no corresponding (single valued) spherical harmonic function to represent the amplitude for

Shayne,As I said, mathematics *is* the explanation.

The simplest and most illuminating example of eigenspinors is for a single spin 1/2 particle.

Neither, for that matter, did I ever say that math will remain the best explanation (indeed I have extensively argued that this is a naive position to hold). I wondered if spin could be observed in between states due to the example of the toy car around the track analogy. "That would be akin to fingerspelling in American Sign Language (ASL). spin one-half. {\displaystyle S_{z}} Best,B. Best,B. The problem with this is that it's damned hard to draw. And in any case, it works very badly as an illustration. {\displaystyle S_{y}} Bee;"If readers get away thinking they can follow a verbal argument, they’re left to wonder why physicists use all that math to begin with.

Strictly speaking, they are not vectors at all, but in fact spinors. Louis,No, a spin 1/2 particle doesn't spin like a top or the Earth on its axis because these wouldn't have spin 1/2.

When you use mathematics, it's just to have a high fidelity link between the causes and effects you're talking about; it's not the explanation itself, it's a tool of precision.Mathematics can be an explanation -- of mathematics.

a particle to be at some position.

I suppose there is a good mathematical reason for that convention! And that this thing has some undiscovered properties from which QM emerges?Best,J.

. Protons and and neutrons are also spin 1/2, observed in kind.

I believe I read that one needs two complex numbers to describe the particle`s wavefunction in terms of spin, thus two rotations (SU2) are needed to return to the identical state. {\displaystyle \chi _{+}} , χ

You can indeed obtain the transformation behavior of spinors from that of gamma matrices, but that merely moves the task to figuring out how the gamma matrices transform under rotations. Submitted comments will only appear after manual approval, which can take up to 24 hours. "I agree with you that it's not fair to ask a physicist to explain something in layman terms and then expect the explanation to be fully correct, that there are certain critical steps that require intensive mathematics.
It's another thing in reality which bears some isomorphism to the original thing.

Whatever you do, there's some part of the ring's surface which you don't see. richard. I understand much of QM is mathematical probability of an observable state.

@Uncle Al,the Moebius is of no importance, the car round trip on it is chiral and spin 1/2.J.

Sabine,"It is trivially possible to express math in any language you want, basically by reading it out.

Or we might say that you have *described* what you think the situation is, but you haven't *explained* (and likewise regarding Sabine's earlier response to me). It then follows:[(1+ cos(a))G_1 + sin(a)G_2]A = 0So that (cos(a/2)G_1 + sin(a/2)G_2)A=0Which means A must transform by half an angle to match the half angle transformation of the object it multiplies.



"when they move around a lot then things are hot." Kaleberg, In answering my question by embellishing what Sabine said in her article I'm inferring the answer to my question is; the rotation is mathematical and not a physically observable one. Thanks Sabine, that is the best explanation of spin 1/2 I've come across in the 35 years since I first came across it in a popular science book as a teenager. Physical helices are chiral. What does it even mean for something that doesn't have a location to have a velocity or to accelerate? . "Almost all cases where you can use some 'real world' example for what's actually a math equation will fail.

[

It's commonly said but what people and probably yourself included are referring to is the common instinctual process in which regular usage of a thing - anything - will see a degree of support emerge in instinct for use of that thing.



You calculate the spin by asking 'How would the particle behave if it was rotated?' It may seem unsatisfyingly abstract, but it's the best answer we have.The other bad analogy that I was going to bring up goes like this: this is like trying to figure out what's really going on in a computer program that you use. , with z component of angular momentum Well, you could ask, which direction is "vertical" when it comes to a spin 1/2 particle? How's about the Dirac belt trick to illustrate the 720 degree rotation thing? Seeing only one possible way to encapsulate the information of empirical experience leads people to think that the way they're looking at is itself the information.The mathematical description is often the most precise explanation we have, but using that as an excuse to refuse to show one's hand and simply lay bare what the mathematics is referring to is a deep failing. I'm concerned that modern physics has moved away from engineering and switched to something much more similar to chess (i.e., a fascinating game for smart people).

In fact I'm basically writing a whole book about how that is a fallacious attitude.

The lack of symmetry is worrying me but if I am correct then why have the last 2 series as they are then identical which is also worrying me.

You can actively perform the operation I was referring to in a merely mathematical sense. You can actively perform the operation I was referring to in a merely mathematical sense. For example, we could liken the power balance in a relationship to a seesaw: when one party's power increases the other's decreases. S Kaleberg, Louis,Not sure what you mean. Cup is rotated by 720 degrees in order to return to original position. spin up

Is a mathematical Möbius band chiral?

and that's the purpose of theory - to make experimentally testable predictions.

The equation is a language act, not a thing to behold as the ultimate piece of data. As an enzymologist I have an appreciation of the power of maths but never having gone beyond the absolute basics of calculus and matrix algebra I cannot follow the technical arguments. Shayne, Sabine,OK, right now mathematics "is" the explanation. For a spin 1/2 particle, there are only two possible eigenstates of spin: spin up, and spin down. "I'm not well-versed on that topic, so I'll let others deal with that.


Have I found a typo? Well, orbital ("classical") angular momentum by itself is not conserved. buy the-damned-book to see how this works Do the damned experiment to see how everything works.

So if the spin is 1 you turn by 2*Pi, ie once, if the spin is 1/2, you turn by 4*Pi and turn twice, if the spin is 2, you turn by Pi, which is half round. How about isotropic vector language?http://www.sjsu.edu/faculty/watkins/spinor.htm. Best,B. A model I consider simple is two interlocked gears, one twice the diameter of the other.

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