- #31
EugeneBird
- 4
- 0
When you finish measuring the location of particle, it certainly looks like a particle - you have found something at one position in space. When you wait a bit and then measure its position again, it is still a particle. No question about it - it is a particle. When you then do this several times, and reflect on what mathematics would describe where you are finding the particle each time, you (actually physicists 100 years ago) discover it looks like a wave spread out from the particle, around any obstacles, and the probability that you find the particle in a certain place is related to the amplitude of that wave.
The formula for a wave looks like d2y/dx2 = y, but it turns out the wave that is guiding the particle has a factor of "i" (the square root of negative one). To figure out the shape of the wave, you have to know about the forces acting on the particle (the "Hamiltonian") and use that to solve the Schrödinger equation. When you solve the Schrödinger equation for the "wavefunction", and you try to measure the momentum of the particle according to the Rules of Quantum Mechanics, you might be surprised to find the solution describes a wave. I think the technical way to say it is that the eigenvalues of momentum (possible values the particle's momentum might take) are frequencies of a wave.
So there are some aspects of particles that are wavelike in their nature. What if you could look at an electron - would it look fuzzy and spread out like a wave, or would you never be able to see it because it would be a little point no matter how hard you looked at it? Well, as far as they've gotten, it does look just like a point ... but it is probably made up of smaller things (some think little open vibrating strings). We probably won't be able to make light waves of a high-enough frequency to see the details of an electron in our lifetime, and QM and Relativity famously disagree on how the parts of something that tiny would look and behave. String theory's math bases the behavior on the math of ordinary string (massive point particles connected by massless spring-like forces). Electrons do seem to be spinning all the time, though, because they have magnetic fields, and one can think of these fields being cause by the electrical charge of the electron spinning around some axis. I think most experts would correct me and say that the spinning might not be real - but according to famous theoretical physicist Leonard Susskind in a Stanford lecture I saw, it could be that they are extended, spinning objects.
The formula for a wave looks like d2y/dx2 = y, but it turns out the wave that is guiding the particle has a factor of "i" (the square root of negative one). To figure out the shape of the wave, you have to know about the forces acting on the particle (the "Hamiltonian") and use that to solve the Schrödinger equation. When you solve the Schrödinger equation for the "wavefunction", and you try to measure the momentum of the particle according to the Rules of Quantum Mechanics, you might be surprised to find the solution describes a wave. I think the technical way to say it is that the eigenvalues of momentum (possible values the particle's momentum might take) are frequencies of a wave.
So there are some aspects of particles that are wavelike in their nature. What if you could look at an electron - would it look fuzzy and spread out like a wave, or would you never be able to see it because it would be a little point no matter how hard you looked at it? Well, as far as they've gotten, it does look just like a point ... but it is probably made up of smaller things (some think little open vibrating strings). We probably won't be able to make light waves of a high-enough frequency to see the details of an electron in our lifetime, and QM and Relativity famously disagree on how the parts of something that tiny would look and behave. String theory's math bases the behavior on the math of ordinary string (massive point particles connected by massless spring-like forces). Electrons do seem to be spinning all the time, though, because they have magnetic fields, and one can think of these fields being cause by the electrical charge of the electron spinning around some axis. I think most experts would correct me and say that the spinning might not be real - but according to famous theoretical physicist Leonard Susskind in a Stanford lecture I saw, it could be that they are extended, spinning objects.