11 Jan '10 23:06>
I think that this might be the best article I've ever read in my life. And I'm serious!
http://arxiv.org/PS_cache/quant-ph/pdf/0310/0310035v1.pdf
http://arxiv.org/PS_cache/quant-ph/pdf/0310/0310035v1.pdf
Originally posted by PalynkaLet me try a form of an answer.
Why care whether it violates the postulates of Euclidean geometry?
Originally posted by adam warlockI still don't see it.
Let me try a form of an answer.
Everybody knows that no mathematical entity exists in the real world exactly as we define them to be. The real point of discussion is if they do exist in a world outside our own and who put them there (if we think that the answer is that do they exist in an independent way).
But if you've read the original artic ...[text shortened]... argument given by Meyer is totally ridiculous.
The valid option is the second one.
Originally posted by Palynka1 - Normal Quantum Mechanics is constructed in an Euclidean space
I still don't see it.
A circle intercepting a line is something that doesn't really exist in the physical world. Does it? I don't even know what a line is in the physical world! Something 1-dimensional... Does that exist?
If not, then what's the big deal that Euclidean geometry isn't the best possible construct to describe quantum-mechanics (especiall ...[text shortened]...
I'm not saying Meyer is correct, but it seems to me that the counter-argument is silly.
Originally posted by adam warlockI really, really, really, really doubt that Meyer didn't know his suggestion wasn't contradicting Euclidean properties. If he didn't, then he shouldn't be talking about topological properties.
1 - Normal Quantum Mechanics is constructed in an Euclidean space
2 - A theorem is proven in Normal Quantum Mechanics
3 - Someone gives an argument that contradicts euclidean properties
Conclusion: That argument isn't to be applied in normal Quantum Mechanics. As simple as that. And Meyer applied that argument in normal Quantum Mechanics.
What I y!" Scrap that! I'm just saying: "yes the theory is right" and get done with it)
Originally posted by PalynkaMan you really are not getting this. It has nothing to do with physics it has all to do with logic.
I really, really, really, really doubt that Meyer didn't know his suggestion wasn't contradicting Euclidean properties. If he didn't, then he shouldn't be talking about topological properties.
My points about these constructs not existing in reality, is just to illustrate that it to me it doesn't seem shocking at all that Euclidean properties are n ve to be wrong? Of course not.
So again, the argument by itself seems...silly to me.
Originally posted by adam warlockIn short, the implication is that Meyer believes Euclidean geometry is not the best geometry to describe quantum mechanics. So?
Imagine that I start to work on the context of spheric geometry and get some really nice theorem A.
Then some guy, let us call him Tom, comes along with an argument that disproves A. And says that my "theorem" isn't a theorem at all.
Some other guy, let us call him Dick, analyzes his argument and realizes that by a consistent analysis of his argu ...[text shortened]... se of spheric geometry. What Tom did was to prove a theorem in a different kind of geometry.
Originally posted by PalynkaIn short, the implication is that Meyer believes Euclidean geometry is not the best geometry to describe quantum mechanics. So?
In short, the implication is that Meyer believes Euclidean geometry is not the best geometry to describe quantum mechanics. So?
Contemporary quantum mechanics is an approximate description of reality at a quantum level. Today, you say Euclidean geometry is used. That's cool. But I still haven't seen a single argument why in the future we cannot say that ...[text shortened]... ular reason why that corollary is an impossibility, I don't see how he disproved anything.
Originally posted by adam warlockThe way I see it, he first disproved the theorem based on finite precision measurement and ONLY THEN suggested an framework where the theorem also doesn't apply.
[b]In short, the implication is that Meyer believes Euclidean geometry is not the best geometry to describe quantum mechanics. So?
You haven't understood. Nor Meyer's article, nor Peres one... 😞 By the way have you read Meyer's one?
Read this again:
imagine that I came to you and said "Palynka you got it all wrong! The sum of the inner ang ith the assumption of a euclidean space. Simple, straight logic.[/b]