Is probability a fundamental aspect of quantum mechanics?

[Hurkyl]

I do not recognize anything in these notions attributed to me that resembles my actual thoughts, can you clarify what distinctions you are making here?

As my premise is that the act of reasoning about 'reality' involves writing down a game, following the rules of the game, and interpreting the result in 'reality' -- especially with the notion that doing a good job of it involves coming up with a sufficiently detailed and accurate rule-set so that we don't have to make up additional rules as we go along -- at least superficially fits into your description of "finding the laws that govern nature".

I think willing to chalk things up to natural language simply being rather poor at conveying nuances of topics like this, and I'm reading different emphasis from the words than you're writing than the emphasis you intended to put into them.

 

[Ken G]

As my premise is that the act of reasoning about 'reality' involves writing down a game, following the rules of the game, and interpreting the result in 'reality' -- especially with the notion that doing a good job of it involves coming up with a sufficiently detailed and accurate rule-set so that we don't have to make up additional rules as we go along -- at least superficially fits into your description of "finding the laws that govern nature".

Sure, your way of interpreting the phrase "finding the laws that govern nature" can be a valid interpretation of that phrase, but it certainly isn't the standard one, nor is it the one I aimed my critique at. I have no objection to how you are interpreting it, that is quite demonstrably what we do. But people who hold that nature herself does actually follow laws, and that's the reason it works for us to look for laws, are using the standard meaning of that phrase-- which is that laws are actually part of nature, not something held up to nature as a kind of template or game. They hold that when nature decides what to do, she first says to herself (in effect), "now what do the laws say I must do here." That is what I am talking about, and pointing out pitfalls in. I'm not saying nature does or does not do that, for I have no idea what nature does, I'm saying that it is not in the best interests of physics to frame it in those terms-- at least not when we are probing it as deeply as we can (it's fine when we are speaking colloquially). Your terms, on the other hand, are much more careful, and I would agree are just exactly what we are doing-- and demonstrably so.

I think willing to chalk things up to natural language simply being rather poor at conveying nuances of topics like this, and I'm reading different emphasis from the words than you're writing than the emphasis you intended to put into them.

Yes, communication is the hardest thing, but if we iterate the process I'm sure we will succeed!

 

[Jano L.]

Bhobba,

I am afraid Ballentine does not derive Hamilton's principle at pages you gave. It would be great to discuss this further, but perhaps it is good to move to another thread. I made one here:

https://www.physicsforums.com/showthread.php?p=3937361#post3937361

Jano

 

[yoda jedi]

I am eager to see the derivation of classical mechanics.

and the inverse, quantum mechanics from classical physics.

Schrodinger equation may be derived
from Hamilton-Jacobi equation.
.

 

[Jano L.]

It may be guessed but hardly derived. The Schroedinger equation was constructed with classical mechanics and wave theory in mind, but is new and does not follow from classical mechanics.

 

[yoda jedi]

"The Schrödinger equation is shown to be equivalent to the classical Hamilton-Jacobi equation of motion plus the equation of continuity familiar in classical fluid dynamics and classical electrodynamics, with an additional term added to the potential energy called the quantum potential that is responsible for quantum effects"

"Any time-dependent solution of Schrodinger equation may be always correlated to
a solution of Hamilton equations or to a statistical combination of their solutions"

 

[juzzy]

Well, I have come back to this thread after a few days away and am amazed by the number of posts. From this very intelligent debate (which may be slightly over my head at times), I shall conclude that the statement 'we don't know' was a legitimate one to make. I came seeking an answer and have come away more confused than when I started, which is true of every new thing I learn in quantum mechanics. However, my gut feeling is that the universe is fundamentally probabilistic. By fundamental I mean the point at which our ability to compute breaks down. What is beyond there? Who knows?