Michel:
As you will have noted, I admitted in my wording that I was hypothesising and referring to a self-measured electron spin. I know that these do not correspond to lab measurements. To me, a measurement is the recording of an event, and then that event can be used to infer some change in state. For example an electron gives off a photon. That photon is somehow recorded (ie the event) and an inference is made, such as an electron has emitted that photon. It adds detail to the inference if the photon is given off in controlled conditions such as in a controlled magnetic field. And that you have directed a beam of electrons at that magnetic field. For example it adds to the inference if the electron can be recorded as an up or a down depending on where it lands on a photographic plate or CCD or whatever. So I concede that the only known is the event (a photon is given off) and the rest is inference. And I also concede that none of that physical measurement can occur within an infinitesimal R3 box travelling with the electron.
Joy:
Joy wrote:
So far so good, provided we understand that the "rotation" of the "electron" is meaningful only with respect to the R^3 box. Thus your following statement is not true:Ben6993 wrote:
Yet I still like to think of the electron having its own chirality, or call it a self-observed constant spin state determined by its structure.
How can you say anything about the rotation of the electron without any reference to the R^3 box you have put around it? You cannot. Therefore you should not think of an electron as having its own chirality. I think your picture of electron is corrupted by too much exposure to the quantum mechanical picture of the electron spin.
"So far so good," .... that line is fine and encouraging!
However, I do not follow your logic for the other lines.
I will have another try. This time with reference to your hidden variables, say -1 for the electron and +1 for its paired partner. Before I go further I should say that I have always thought of the LH or RH chirality belonging to the electron as its hidden variable. I think that Fred asked you if you had ideas about what the hdden variables were and you replied, if my memory is correct, that you were working on it.
If an electron has a hidden variable -1 rather than a +1, that is compatible with a chirality, say Left Handed rather than Right Handed. If the value stays constant during time of flight then that variable value is conserved during the time of flight, and stays a constant in your geometric algebra calculations. Ie if the electron is LH it stays LH and that is a property of that electron irrespective of its S3 environment.
In my terms, I envisage the LH electron as a different structure to the RH electron, so it has to be conserved during time of flight. It can only change structure at an interaction. I can imagine a demon travelling in the infinitesimal box with the electron. Though I prefer to use a guardian angel, and to personify the electron. The angel keeps telling the electron, yes you are still LH. Although the infinitesimal R3 boxes keep changing during the flight, the angel keeps reassuring the electron that it is still LH. In my view the electron is worried unnecessarily as its chiral LH-ness is in its structure, despite what any distant observers might imagine.
Now what one calls the hidden variable other than a hidden variable is not well founded. You are still working on it.
A complication is that of LH and RH helicity, which is not what I mean here. That does depend on the observer as well as the particle.
An additional point is that I liked your reply in a nearby thread about having optimism wrt mathematics. I agree entirely. Maths is essential for physics, however complicated the maths needs to be, and what you and Jay are doing is terrific. And that is irrespective of whether you are correct or incorrect.