lew@ihlpa.ATT.COM (Lew Mammel, Jr.) (08/10/87)
I've been dabbling in some literature lately and since Karl Popper is mentioned so frequently ( on the net and elsewhere ) I thought I'd be in for some good stuff when I started his Quantum_Theory_and_the_Schism_in_Physics which was written some years ago but only recently published, according to the prefatory material. It starts off interestingly enough with a personal view of the emerging philosophical problems in QM from the thirties through the fifties. Popper name drops a bit and rather coyly suggests he may have been influential in the highest circles of thinking (i.e. Einstein, Bohr, et. al.) even though he was just a camp follower, as it were. He states that he anticipated the Einstein-Podolsky-Rosen paradox with a version of his own, which was however fundamentally flawed - a misfortune which Popper freely confesses to, but seems not to have learned from. I say this because of his suggestion in this work of yet another experiment designed to flush out the error of the Copenhagen Interpretation, or the Popper version thereof. I posted Popper's proposal as described in his book two days ago. Briefly, it is an attempt to cause dispersion in the measurements of one particle's position by localizing another particle which is correlated with it through an earlier interaction. The way Popper describes it, he seems to be claiming that it would be a way to transmit a faster-than-light signal, since one could modulate the dispersion of a series of measurements at one location by adjusting the width of a slit at another location. I'm flabbergasted that someone so evidently prestigious could be left so far behind in his understanding of the most elementary rules of QM analysis. In the first place, the Copenhagen Interpretation is not a splinter theory of QM, but just ( of course ) an interpretation. So when Popper says that his experiment would disprove the Copenhagen Interpretation, he's really saying that it would disprove QM. The thoughtful student can have confidence from the start that Popper is all wet. But instead of rejecting Popper's proposal on a priori grounds, we may attempt to isolate the particular error of reasoning. I think that it lies in the failure to adequately consider the initial two-particle state. Briefly stated, Popper fails to consider the uncertainty relation between the position and momentum of the center of mass of the interacting particles. This is easy to to do, I think, because usually most of the analysis is done within the center-of-mass system and the system itself is regarded as an uninteresting free particle. When you start talking about the particles' positions w.r.t. the laboratory frame, though, you'd better not forget about the motion of the center of mass. Consider the usual coordinate transformation: r = ( r1 - r2 )/2 R = ( r1 + r2 )/2 A 2-particle state, |A>, has wave-functions, <r1, r2|A> and <r, R|A> in the two coordinate systems. We usually separate the Hamiltonian in the latter system to get: <r,R|A> = <r|Ar><R|AR> In other words, we consider the 2-particle state to be the tensor product of the center-of-mass single particle state, |AR>, and the reduced mass single particle state, |Ar>. What Popper is doing is implicitly assuming that: <R|AR> = delta( R ) ( dirac delta function ) This is what allows the inference of one particle's position from the other's. Note though, that this implies infinite uncertainty in the momentum of the center of mass, so we lose the ability to correlate the trajectories of the independent particles. This is what I think Popper is basically overlooking. Lew Mammel, Jr.