----- Original Message ----- From: "Warren Ockrassa" <[EMAIL PROTECTED]> To: "Killer Bs Discussion" <[email protected]> Sent: Friday, March 11, 2005 2:17 PM Subject: Re: quantum darwin?
> On Mar 7, 2005, at 10:02 PM, Dan Minette wrote: > > [those are some good refs, Dan -- I need some time to digest them > though. ;) ] > > > This is getting close to the time where the introduction of a bit of > > formalism might be helpful. I think I can do it without going too deep > > into the math. > > That's probably good. It has been lo many a moon since I've cracked > calculus in any depth. > > > But, first let me ask you a question. Are you familiar with > > eigenstates > > and superpositions? For example, if you measure the spin in the x > > direction, the spin in the y (which is orthogonal to x) is a > > superposition > > of up and down. |s> = ( |+> + |->)/sqrt(2). Is that something you've > > seen > > and feel comfortable with discussions that assume that you know it? > > Not quite yet. Is there anything even approximating a usable metaphor, > or something out of more classical physics I could assimilate more > readily? The problem with metaphors from classical physics is that they ignore the reasons why the change to QM had to be made. Instead, I think one needs to wade in and actually consider the data as they are. In other words, one has to at least be willing to "shut up and calculate." and table any questions about how things could actually be that way. The best place to start, I think, is spin. My old foundations of QM teacher said that spin was probably the most QMish of all the aspects of QM. So, lets consider a spin 1/2 particle: the electron. Spin is intrinsic angular momentum. It cannot be the real "spinning" of the electron without the surface of the electron going faster than the speed of light. So, here we have one new feature already....intrinsic angular momentum without any observable motion. In any given direction, a measurement of the spin of the electron gives either +1/2 or -1/2. If one measures the spin of the electron as up in a given direction, and then remeasures it at an angle 2x from the original direction, one gets up again cos(x)^2 of the time and down sin(x)^2 of the time. For example, if one measures at 180 degrees, x=90 degrees, cos(x)^2 =0 and sin(x)^2=1. This makes sense, because at 180 degrees, one should always get down. If one measures at 90 degrees, x=45 degrees. At that angle, cos(x)^2=.5, sin(x)^2=.5....which also makes sense. To get this, the wave function is given as sin(x)*|d> + cos(x)*|u> ...a superposition of two eigenstates: |d> (spin down) and |u> (spin up). The wavefunction itself is not an observable, we only observe the eigenstates. When this was first developed, Einstein accepted that the formalism worked, but he thought that the indeterminacy inherent in this formalism would eventually be replaced by a more deterministic physics. Attempts to develop this has been labeled "hidden variable" theories, because they assume that there are more classical variables that we don't see yet underlying QM. But, I want to make sure that this step in the formalism is accepted first. If this doesn't make sense, I need to clarify it before going on. (Lurkers are encouraged to unlurk and ask questions if they need clarification.) Dan M. _______________________________________________ http://www.mccmedia.com/mailman/listinfo/brin-l
