Today I want to switch from interpretations of quantum mechanics to extensions of quantum

mechanics.

So far we have discussed interpretations in the sense that maybe you imagine some underlying

microscopic picture, but the goal is always to construct something that is completely

compatible with all the predictions of quantum mechanics as far as you can achieve that.

And today we want to switch to extensions of quantum mechanics which means theories that

in some way or another go beyond quantum mechanics, so they make different predictions.

Right away I have to say the following.

There is no experimental evidence so far that would compel us to go beyond quantum mechanics.

Everything is consistent with quantum mechanics as far as we can tell and also all the consistent

theories that are being developed, for example for quantum gravity.

They do not contradict usual quantum mechanics.

They are based in some way or another on usual quantum mechanics.

So the hope nevertheless could be that if you are constructing some theory that goes

beyond quantum mechanics then maybe by looking at it you can learn something also about the

interpretation of quantum mechanics.

Certainly we have had such cases for example when one went from Galileo transformations

to Lorentz transformations from the usual classical mechanics to relativistic mechanics

that was an extension because it contained the old theory as a limiting case, but it

introduced a new parameter which was the speed of light.

And then it gave rise to predictions such as energy-mass equivalence, so at least you

learned something new about some aspect of mass from this extension.

And of course there was the switch from classical mechanics, Newtonian mechanics to quantum

mechanics itself.

But it turns out apparently to be surprisingly hard to come up with any theory that really

goes conceptually beyond quantum mechanics and still goes to quantum mechanics in the

appropriate limits.

And so what I am going to talk about are just attempts of modifying quantum mechanics a

little bit, mostly attempts that try to get rid of this what some people consider embarrassing

possibility of macroscopic superpositions like Schrödinger-Katz states.

And it turns out that these extensions usually can be formulated formally within the formalism

of quantum mechanics.

And mostly they just postulate some extra fundamental universal decoherence mechanism

that should always be present and is not derived from the usual physical interactions that

we know.

But still in the end you'll write down some master equation for your density matrix for

example.

Okay.

So this chapter then is about extensions of quantum mechanics.

And as I said I picked those that have some relation to these interpretation questions,

decoherence and so on.

I also have to say right away that I guess for none of these extensions people have really

checked all the possible theoretical consequences.

So it could very well be that instead of having to do an experiment to check whether they

are true or not you could also somehow derive a mathematical contradiction at some point

if you were to take these theories really serious.

Okay so let me start with a rather generic approach which is therefore quite popular

whenever you want to propose experiments to test whether there are any such deviations

from usual quantum mechanics.

And this approach basically just says oh assume there is some universal fundamental extra