# Which interpretation best explains the classical limit?

Trying decide, apropos that famous Feynman quote, whether there is a 'real problem' with quantum physics. My own rather inexpert view is that if there is, the it's something to do with the classical limit. (The measurement problem being an interesting special case of this.)

In particular because this is a substantive and indeed experimental problem. Although you wouldn't normally think that when I pick up a tennis ball and throw it across the room that this constitutes experimental refutation of quantum mechanics, I think that unless the phenomena has been adequately explained within the framework of quantum physics then that is just what it is.

There might be such an explanation of course I just don't know what it is. On the face of it though it must be quite challenging reconciling such different descriptions of the world. Although on the other hand I suppose this is not so strange, we're familiar with the idea that the system can be explained by different laws depending on what the observables are, e.g thermodynamics is the appropriate theory if the observable is temperature and pressure and so on. This is sometimes called "emergence" although that may refer to something more specific. Anyway in the instance of me throwing a tennis ball I suppose the relevant observable is something like the center of mass motion and we some explanation for why such macroscopic observables like this obey classical physics.

I'm also interested especially in comparing how Bohmian mechanics and the many worlds interpretation deal with this question. It's been argued that it's an important virtue of Bohm's theory that the classical limit question is straight-forward, since the classical position variables are in from the start and go all the way down so to speak. Whereas in the MWI, an otherwise quite similar interpretation, the quantum state comes all the way up. I have difficulty understanding how the quantum state of the whole universe gets sliced up in our perceptions into the classical world we observe.

Any thoughts?

## Answers and Replies

Ehrenfest's theorem gives you back Newton's laws and the usual classical equations for momentum and energy and so on. These predict the motion of a tennis ball pretty well.

Ehrenfest's theorem gives you back Newton's laws and the usual classical equations for momentum and energy and so on. These predict the motion of a tennis ball pretty well.

The Ehrenfest's theorem works only when the support of the wave function is localized on a macroscopic level. Unfortunately the wave function has a stubbon tendency to spread. Thus for example, by applying the Ehrenfest's theorem to a particle which crosses a beam splitter we obtain a very strange trajectory, that mediates the transmitted and the reflected trajectories. Not to mention what happen when also the detectors behind the transmitted and reflected beams are taken into account...

The question of how a large mass particle, like an ideal tennis ball, behaves is goverened adequetly by Ehrenfest's theorem. Spreading of a wavepacket is essentially nil (for a Gaussian wavepacket I think there's a factor (h/m)^2 can't remember offhand, it's in Merzbacher). If you want to talk about light then naturally it won't work because you are dealing with an inherently quantum phenomenon.

My understanding of what the OP was implying, only his second paragraph, was that quantum mechanics doesn't predict the trajectories of large particles, like tennis balls. However in this case Ehrenfest works, you get Newtons equations and the usual laws of projectile motion.

Demystifier
Science Advisor
Gold Member
All interpretations give the correct classical limit.
Nevertheless, even those who do not like the Bohmian interpretation cannot disagree that in this interpretation the derivation of the classical limit is the most direct.
(Or can they?)