Is the Totalitarian Principle Essential for Grasping Infinite Potential?

[spaghetti3451]

The totalitarian principle states that 'every process that is not forbidden must occur'.

Isn't this principle self-obvious? After all, a process that is not forbidden can, by definition, occur.
But, I think I am missing a layer of meaning implied by this statement. If that is so, would you please clarify my confusion?

 

[Simon Bridge]

There is a difference between "can occur" and "must occur".
Consider the process where you eat pickled earthworms for lunch.
It is not forbidden by any natural law that you eat pickled earthworms for lunch - did it happen?

 

[spaghetti3451]

I see your point.

I think this is not a fundamental physical principle, but only a guide to the discovery of physical principles. Isn't that right? I say that because it lacks the features of any physical principle - no physical quantities are stated, no equations are mentioned, etc.

 

[kurros]

That is mostly true, but I believe that there is also motivation based on effective field theory. Lagrangian terms that are not forbidden by symmetries etc. have a habit of being radiatively generated in the low energy limit of generic higher energy theories; or something like that, I'd have to go look it up...

 

[collinsmark]

A better phrasing of the Totalitarian Principle, by Murray Gell-Mann, is "Everything not forbidden is compulsory." There is a subtle difference between saying "is compulsory" and "must occur." They're only equivalent if you're thinking along the lines of the many worlds interpretation of quantum mechanics. And even then, the outcomes don't necessarily occur in the same "world" (so to speak).

The Totalitarian Principle comes about when utilizing Richard Feynman's sum over paths (also called, sum over histories) which involves Feynman's path integrals.

Before Feynman (and Wiener and Dirac), wavefunctions were traditionally calculated by modeling the energy potential, V, and then solving the second order, partial, differential equation called Schrödinger equation, of which there is a relativistic version. This can be a real bear if V is complicated.

The sum over paths approach is equivalent, yet in many situations is much more manageable.

One might rephrase the Totalitarian Principle to say, "When calculating the wavefunction using sum over paths, anything that is possible, even remotely possible, must be included as part of the path integral."

One final distinction is that "anything that is possible" is not the same thing as "anything that is imaginable." It's true that anything possible, even if it is extremely unlikely, must be included in the sum over paths, path integral. But there must be at least a remote possibility. And just because one can imagine something, doesn't necessarily mean it's possible.

 

[Simon Bridge]

"When calculating the wavefunction using sum over paths, anything that is possible, even remotely possible, must be included as part of the path integral."

Beat me to it - that's the next step. Cheers :)