7/6/2023 0 Comments Tau lepton mass![]() ![]() In other words when I loosely refer to wave-particle duality, my confusion is mostly about why light, electrons, or whatever, come in little blips of waves, and why Planck’s constant isn’t just zero. I struggle to imagine a discrete wavepacket which preserves its volume integral of psi star psi over time while mingling with all the other wavefunctions out there. ![]() ![]() But the observables of the electron are not the same as the wavefunction, nor is the only relevant visual property of a classical particle that it exists at a single point in space the fact that particles are discrete, and “atomic” in the Greek sense, is what I find so hard to reconcile with their wave nature. Yes, the closest its wavefunction can be to a classical point particle is a very tight Gaussian in space whose momentum has a high degree of uncertainty. Yes, electrons are described by wavefunctions which evolve under Schrodinger’s equation. It’s a perspective worth trying on in a poetic sense, but yeah, if the math doesn’t fit the data, then it’s not physics.Īs far as your comments about wave-particle duality, I disagree. Yeah to be clear, I was only putting it forward as a very, very loose visual analogy. The classical state would be a sharp point in phase space which would be the momentum and position of the particle at time t). The closest thing it can be to a classical particle is being a Gaussian wave packet (which minimizes the uncertainty principles, ie you get a blob of width and height Δx and Δp in phase space centred around some point. The state of an electron is always described by a wave function. This however was achieved by quantum mechanics around 100 years ago. It's a term used early on when people couldn't reconcile the two types of behaviours. What you suggest has absolutely no basis.Īlso wave particle duality isn't a fundamental principle of quantum mechanics. It's what actual mathematical models accurately describe reality. Physics isn't what we like to imagine things as. It's worth pointing out that this is basically entirely crackpot. Knots, vortices, or some strange cousin thereof seem visually compelling because they can be loose while still preserving their characteristics, and when tightened to a point can be localized here or there but not everywhere with equal probability. Is there a way to work the Dirac equation and some spinor magic to get a rigorous sense of how a tau particle or muon can decay into an electron? Specifically, is there any property other than mass that these particles differ from each other in, and does this hint at any kind of underlying structure that might apply more generally to this whole three generations of matter situation? I’d love to learn some math to supplement and inform this intuitive view. Not saying that in a literal sense, but just in the sense that electrons are things which seem to have a certain intrinsic tangledness or vortexness to them. The way I imagine this intuitively is something along the lines of Lord Kelvin’s old knots-in-the-ether picture. Do you know where I can read more about how this decay via weak interaction works? I understand that electrons don’t decay on their own since they have charge, and no lower mass negatively charged particle to decay into (but bring a positron around and you can make photons since the net charge becomes zero). ![]()
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