Show more

The truly wild thing is that we can understand the need for these basic revisions in our understanding of the world with just a bit of early college level mathematics.

Show thread

Surprisingly, the answer appears to be no. We can certainly imagine theories underneath QM which have more in common with Classical Mechanics. But all such theories appear to require a huge metaphysical revision - we must give up locality or admit retro-causality or accept the existence of many worlds or accept that our own world is a sort of illusion caused by the dynamics of the "real" world, which is a big wave function.

Show thread

So the question naturally arises: is Quantum Mechanics like a coin flip. In other words, can we imagine that some complicated hidden theory is operating underneath the Quantum Mechanical, probabilistic description, which recovers all the elements of our classical world.

Show thread

But if we have a super computer and a very careful account of the initial conditions of the coin flip and a good model of the coin's material distribution, and the hardness of the surface it strikes and so on, we can imagine getting arbitrarily close to predicting the outcome with 100% confidence.

Show thread

Its easy to imagine something like this. The actual dynamics of flipping a coin are extremely complicated, but if we confine ourselves to the question of what side a flipped coin will land on, then we can ignore all the petty physical details and recover a surprising powerful theory: the chance of getting heads (or tails) on a fair coin is 50% regardless of all the details of each individual throw.

Show thread

In other words, we imagine that quantum mechanics is just a statistical theory which describes some unknown but classical system.

Show thread

The most natural impulse here, if we want to hang onto the notion that such classical ideas like position and momentum and energy really do exist, is to imagine that Quantum Mechanics is not a complete theory.

Show thread

Last time we noticed that unlike classical mechanics, where a direct analogy between elements of the theory and elements of reality exists, in QM we only predict the probability distribution of elements of classical reality in QM.

Show thread

I guess I'll try out threading this time to see if it makes this all easier to follow.

Show thread

Let's continue thinking about how Quantum Mechanics challenges interpretation.

So we can immediately understand why eg Einstein had a problem with thinking QM was a fundamental theory. It doesn't talk about aspects of the universe directly, just about probabilities of measuring those aspects.

So in classical mechanics you take a state of a plumb bob as a pair of numbers (x,y) and you evolve them forward in time. Your predictions are of the form "at time t, x will be X". In quantum mechanics your predictions are of the form "At time t the probability of x being between Xa and Xb is P".

So the nice thing is the first weird thing about quantum mechanics isn't hard to understand at all: Quantum Mechanics doesn't contain things which map directly onto aspects of physical reality. Instead, it just lets you calculate the probability of observing aspects of physical reality within some range of interest.

While its true that because of nonlinear dynamics we expect every model to eventually deviate from the real system it describes, I'm pretty sure that for classical mechanics if we are comfortable with looking only a small time into the future and we make a few other moderate assumptions we can always in principle find a model which is close enough to reality that we can interpret the elements of the model as representing aspects of reality.

The interpretation of this model is straightforward: to the extent that the assumptions we made are in accord with the real world, the position of the point mass predicted by our physics is meant to represent the position of the bob. That is, if at t =10 s we calculate that the bob will be at some x,y position, then we expect that the _real_ bob will be at that position precisely to the degree with which we captured the system in question in our model.

This bears some elaboration. Think of a real, physical pendulum. Subject to some error associated with the elasticity of the line and the friction with the air, we can describe such a pendulum using a model where a point mass is constrained to move on a circle of radius equal to the length of the bob, and is subject to a uniform force (gravity) pulling downward.

Show more
Mastodon

Server run by the main developers of the project 🐘 It is not focused on any particular niche interest - everyone is welcome as long as you follow our code of conduct!