I haven't been in the forum in ages so I thought I'd say hi (not that anyone rembers me )

 

I got into a discussion about the BT paradox and I was wondering what would happen if we converted the paradox from Euclidean space to Minkowski space.

 

Ideas?

erm...what's the BT paradox?

-Uncool-

I got into a discussion about the BT paradox and I was wondering what would happen if we converted the paradox from Euclidean space to Minkowski space.

 

Ideas?

From a mathematical standpoint' date=' I think that Minkowski space shares enough properties of Euclidean 4-space for the Banach-Tarski 'paradox' ([i']It's not a paradox, it's just goes against one's intuition.[/i]) to still hold. I believe that you can still create sets that are not Lebesgue measurable in Minkowski space as well, and aside from the Axiom of Choice, this is all one needs to make Banach-Tarski 'work'.

 

Physically, I don't believe that non- Lebesgue measurable subset of a physical object is possible, so in 'real life Minkowski space', Banach-Tarski wouldn't work.

 

erm...what's the BT paradox?

-Uncool-

The Banach-Tarski 'Paradox'. A very nice introduction (i.e.' date=' not too mathematically detailed[/i']) to Banach-Tarski is located here: http://www.kuro5hin.org/story/2003/5/23/134430/275

However I think we are talking about involving 'real life Minkowski space' we still have to take into acount that the idea of a mathematical so if Minkowski space was to be described as continous. Don't we have the same properties of Euclidean space and so we could infer that the BT paradox can still be taken forward?

However I think we are talking about involving 'real life Minkowski space' we still have to take into acount that the idea of a mathematical[/b'] so if Minkowski space was to be described as continous.

You have to be able to create a non-Lebesgue measurable subset of the object of interest, and for physical objects, this is not possible, since they are composed of atoms. From a Banach-Tarski perspective, it doesn't matter if the space shares all the properties of Euclidean space, if the objects that inhabit that space cannot be divided into non-Lebsegue measurable subsets.

if Minkowski space was to be described as continous

 

There is much debate over describing Minknowski space as either continous or discrete because there is no identities to describe it so the hope of ever dividing space is still possible under the lack of knowledge of Minknowski space so far.