What would happen if the uncertainty principle was false?

[haael]

We have the uncertainty principle. How would our world be different, if someone measured position and momentum of a particle with 100% accuracy? Would some other laws of physics be violated, too?

I mean - what laws of physics depend on uncertainty?

It is clear to me, that the whole wavefunction approach would be false. But what else? Something about entropy? Would double-slit experiment be still possible?

 

[billbray]

I'm just a student, but, as far as I know, every process in the universe that we know of relies on the uncertainty principle. there would be none of the four forces, no matter - everything would not exist; the universe woud still be chaos.

 

[haael]

there would be none of the four forces

Right. Out current description of interaction relies heavily on the uncertainty. But I doubt that anything wouldn't exist. Classical physics doesn't have uncertainty and it does exist happily, with some inconsistency with experiment - there is no double-slit pattern, there are different predictions on entropy etc. And there is the ultraviolet catastrophe, but as said, interactions require uncertainty.

My question is - how much of quantum world can we drag into classical physics without introducing uncertainty of momentum and position?

 

[SpectraCat]

Right. Out current description of interaction relies heavily on the uncertainty. But I doubt that anything wouldn't exist. Classical physics doesn't have uncertainty and it does exist happily, with some inconsistency with experiment - there is no double-slit pattern, there are different predictions on entropy etc. And there is the ultraviolet catastrophe, but as said, interactions require uncertainty.

My question is - how much of quantum world can we drag into classical physics without introducing uncertainty of momentum and position?

Classical mechanics can be formulated in terms of position and momentum variables. Classically, if we know the positions and momenta of a set of particles at any time point, all future and past configurations of that system can be predicted.

When we get to the quantum level, the position and momentum are replaced by operators, however those operators don't commute, and so we immediately get the uncertainty principle. Furthermore, we expect based on the Bohr correspondence principle that all classical systems evolve smoothly out of quantum systems with increasing quantum numbers (and dimensions and masses).

My point is that the HUP is intertwined with the physics of our reality as such a fundamental level that it is basically meaningless *from a physical point of view* to speculate how things would be different without it. On the other hand, mathematically it is quite clear how to deal with this .. we do it in stat mech all the time. For any expression involving hbar, you can get the classical approximation by taking the limit of the expression as hbar goes to zero. Or equivalently you can just take [x,p]=0 and see what happens. I guess you will get garbage .. just look at the Ehrenfest theorem, by which the classical laws of motion are expressed as averages of QM operators, using the Heisenberg equation of motion. None of that works out if [x,p]=0.