This discussion has been very helpful, so thanks a lot! I suppose I always thought that the microscopic states that became entangled with the measurement apparatus had to be pure eigenstates. I suppose this doesn't have to be the case with a more coarse measurement? When we consider something...
Okay, that all makes sense. So we can think of the fields position and momentum degrees of freedom as being entangled without classical measurement device (whatever that may be) in such a way that when we make an observation, we can infer that the field has collapsed, not into a pure position or...
Looking at your first example, wouldn't we say that when the photon is emitted, the photon and hydrogen atom state are entangled so that by measuring the photon energy we can reliably infer the energy of the hydrogen atom? Or, with the S-G example, that the silver atom's position degree of...
Building on my previous reply. I suppose we can think of the image as a series of both coarse position and momentum measurements, and what you're saying about the coarse position measurements not disturbing the classical trajectories makes sense if the states are not collapsing into pure...
Gotchya. So am I correct in assuming the image can be broken up in a series of position measurements? Or should it be thought of as a series of momentum measurements?
I suppose I'm still somewhat confused, but I think we're getting somewhere. Going back to the image above, I'm wondering how we break the image up into measurements where collapse is taking place. Can we break up each track into equally time spaced blips and all such collections of blips...
Thanks for the reply! Hmm okay, so they're in an eigenstate of the momentum operator when the measurement is performed, but then what do we make of the particle tracks such as those seen in the image below:
It seems as if a series of very precise position measurements has been performed on the...
I'm not sure this really answers my questions. I understand the idea of computing amplitudes by performing time evolution on a state resembling incoming free particles and projecting on an outgoing state of (possibly different) free particles, but when a measurement has been performed, what...
How do we map experimental measurements of quantum fields, such as those seen in accelerators, to the theory's mathematical formalism? When we see images of particle tracks produced in accelerators such as the LHC, I think it's safe to say a measurement (or series of measurements) has been...
Are you saying that we're deeming the states that are not symmetric or antisymmetric as non-physical and throwing them away? Is that why we look for a symmetric and antisymmetric basis in the first place?
Also, I'm not sure what types of symmetry are present in the basis states for ##c_1\bar...
PeroK, what exactly do you mean by:
How can we show this?
In this case I believe a two-component isospinor is used to represent each quark state (u, d, s), with underlying symmetry group SU(2). Does that mean in this case that the matrices which transform states in the product space of the...
PeroK, look at sections 8.3-4. The top two bullet points are contained in an asterisk note on the bottom of pg. 293. As, for the third bullet, this seems to be a crucial part of the argument made in problem 8.22, although I don't quite understand what Griffith's is getting at here.
Hello,
I'm trying to make sense of some of the group theoretic discussion found in Griffith's Introduction to Elementary Particles. I have had a fair amount of exposure to elementary group theory, but no representation theory, and have some specific questions related to this which refer to the...