Originally posted by Palynka
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.
Man you really are not getting this. It has nothing to do with physics it has all to do with logic.
I'll try with a different example.
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 argument one can deduce a property that is a contradiction in the context of spheric geometry.
What this tell us is that what Tom actually did wasn't disproving my theorem since my theorem holds in the case of spheric geometry. What Tom did was to prove a theorem in a different kind of geometry.
Or in another way: imagine that I came to you and said "Palynka you got it all wrong! The sum of the inner angles of a triangle are always less than pi (obviously that having the high pedigree that we have we measure angles in radians, not degrees)!" I think your answer would be something like: "No, no it depends on your set of assumptions. Ypu can't say that I'm wrong since we are working based on different assumptions. What you can argue is about the applicability of my results based on my assumptions and the applications of your results on the set of your assumptions."
Now let us get back to our case. What Meyers did was exactly that. He thought that he had disprove a very deep theorem on quantum mechanics. But he didn't do that because that theorem is proved in the context of normal QM and normal QM is euclidean.
Since Meyer's argument is valid in the context of a non Euclidean geometry is point is mute.
I'm not saying, neither is Peres, that the right form of QM is euclidean what Peres showed is that Meyer's argument isn't in the domain of application of QM. And so can't really disprove nothing that is in the context of normal QM.
I really, really, really, really doubt that Meyer didn't know his suggestion wasn't contradicting Euclidean properties.
It's quite possible that he did. After all, his article was published so that means that it passed the peer review process. And that the means that the reviewer didn't get it. Once the paper got out some people started quoting it as being a great paper, so obviously they didn't get it too.
The point that Peres makes is really a subtle one. And that's why I find this article to be the best I've read.
These kind of things happens all the time in science. I'm not talking about frauds, I'm talking about real mistakes. I've done my share, and I've seen other people's mistakes too.
As a side note: von Neumann also got it wrong on this area. He also published a paper that was later found to be wrong.
So if von Neumann made a mistake I think it is highly possible that Meyer made a mistake.
I can imagine how hard it must have been for people to accept that time was relative to the observer and that we had to use a non-Euclidean space to represent this new concept of spacetime.
Yes it was hard! It was so hard that Einstein disliked it with a passion at first and only got to like it when he found it impossible to construct GR without the concept of space-time continuum whose geometry isn't euclidean.
Contrary to what most people think the idea of space-time doesn't come from Einstein. It comes from Minkowskii and at first Einstein was very much against it.
All physics had been Euclidean up until then! (correct me if I'm wrong)
This is mostly right so i won't even correct you I'll just add a little bit. People had used non-euclidean geometry in physics and math (and separating these two sciences before the 19th-20th century doesn't make much sense really) but they used it with a different mindset. They pretty much used in the context of specific problems but never with the notion that the geometry of the Universe might not be Euclidean (the being basically Gauss and Riemann that said that only experience could say what was the geometry of the Universe). For instance the geometry used in astronomy is spheric and it has been for a long time, but people saw that as being just a tool for solving a problem not as being a real contender for the geometry of the Universe.
A good book on this is this one: http://www.amazon.com/Poetry-Universe-Mathematical-Exploration-Cosmos/dp/0385474296
If you are in Portugal you can get in the subway stations bookstores by a very nice price (The portuguese title is A poesia do Universo).