What is wrong with the proof below? Theorem: The current theory of the Weak Interaction is wrong. A W- and W+ do not exist. Proof: Assume a W- exists. Then theory/experiment shows it should decay to an electron and electron antineutrino. Then (by conservation of angular momentum): se + sn = sw so 1/2 + sn = 1 so sn = 1/2. But a pi-minus also exists and decays to the same two particles, in which case: se + sn = sp so 1/2 + sn = 0 so sn = -1/2. This contradiction proves a W- does not exist (since the other assumption is proven true). Similar reasoning goes for a W+. QED. From: Willem F Esterhuyse Email: talanum1yahoo.com
Ah, I see your problem. While spin is often expressed as a positive number, what is meant is that the absolute value of the spin is that number. In other words, a spin-1/2 particle either has spin +1/2 or -1/2. Read for example the top two paragraphs here: https://chem.libretexts.org/Bookshe...Electronic_Configurations/Spin_Quantum_Number
I was computing with intrinsic angular momentum (the size of the vector) not the spin of the electron in an atom.
In order to invalidate my proof you would have to prove the electron is always produced in spin down state.
No. "Up" and "down" only have meaning in an environment that is not symmetrical, for instance in the presence of a magnetic field due to something else. If you have an electron or a neutrino on its own in free space, there is nothing to define which direction is up or down for it to orientate itself with or against. In interactions involving more than one entity with angular momentum, one can speak of up and down relative to the other entities involved, because they define an up and down direction against which the orientation of the one under consideration can be defined. But that is all it means.
I don't see how that changes anything? You still need to throw in the missing minus sign. No, you got that the wrong way around: the burden of proof in this case is on you, because the Standard Model of particle physics is the null hypothesis here. Please provide evidence that the electron isn't "always produced in spin down state".
If in free space an electron cannot have +/- 1/2 spin, just 1/2, then my proof stands. Wikipedia says electron spin is: +1/2. Anyway choosing a spin 1/2 in one formula, and in the next formula -1/2 is inconsistent, isn't it? If experiment says it exist, it does not neccesarily - it could be a phantom since the experiment is set up with the mathematics built in.
The intrinsic spin is a represented by a quantum number, s. As such it can, for different types of QM entity, have either integer or half integer +ve values only. The projection of s, along an axis defined by something external to the QM entity, is something else. It represents the alignment of the spin direction with respect to a defined external axis. Look up "space quantisation". When one speaks of an election having a spin of +1/2 or -1/2 it is always in relation to something external; another particle, an external field. This projection is designated not by s but by m(s) or S(z) or something, to show it is different. S and m(s) or S(z) are not the same thing. Read the para here on "spin projection quantum number": https://en.wikipedia.org/wiki/Spin_(physics)#Direction
So my proof stands. In this case the experiments must show something else and must be looked at again.
The error is in your assumption, that electron spin is 1/2 so it must always point in the same direction. Or something like that. Which is not supported in any way by experiments; the thing about physics is it doesn't matter what your theory says, if it doesn't agree with experiments then it's just wrong.
I see you've missed (the point of) my post. Please follow the link in post #2 again, and (re-?)read those first few lines to clear up your confusion.
As both Arfa and NotEinstein have pointed out, and as I have told you explicitly myself, you are muddling up the intrinsic spin with the projections of that spin along an externally defined axis (when there is one). It is the projections that can take +ve or -ve values, because the sign denotes orientation in space relative to an axis of some kind. The spin itself is just a value with no particular direction, so it makes no sense to say it is +ve or -ve. Think about what -ve spin means. It just means spinning in the opposite direction. Opposite to what? See what I mean? It's nonsense. If you get +ve or -ve values in these equations of yours what is means is the orientation of the spins of the various particles relative to one another. The spin of an electron, for example, is 1/2. It can only be "up" or down" (i.e. +ve or -ve) relative to some defined spatial axis. This can be due to another electron, or to its own orbital angular momentum, or to the spin of the nucleus, or to an external field.
Yes, exchemist. The original computation sums intrinsic angular momentum, i.e. the value the particle has. The assumption is proven wrong by the contradiction. It cannot be more clear cut. The experiments must have been biased.
You seem to be rather obtuse about this. Yes the π⁻ ,which is a spin zero boson, can (so I learn from Wiki) decay into two spin 1/2 particles, an electron and an electron antineutrino. All that means is that, at the moment of decay, their spins are in opposite directions relative to one another. Both are s=1/2 particles. When W⁻ decays, you get exactly same except that, at the moment of decay, both spins are parallel to one another. But both are still spin 1/2 fermions. I repeat, it is meaningless to say that a particle has an intrinsic spin of "-1/2". Minus with respect to what? In other words, spinning in the opposite direction to what?
Just as clear cut as the link I posted, but apparently, you appear to have trouble understanding its content? All of them? You do know that this is something even undergraduates test all the time. Are you claiming ALL of them are "in on it", or are being lied to or something?
No. I have it now: the error is that the two spin values are not a contradiction. The antineutrino can have spin 1/2 or spin -1/2 relative to the electron spin axis. So I may reluctantly have to accept the Weak Force although neutron decay can happen by the Strong Force.
I'm glad you (finally) read my link, and have corrected the error in your thinking. Happy to have helped!Please Register or Log in to view the hidden image!
