infinitiies in relativity

[Jacques]

Hi

General and special relativity have some problem with some infinit solution.

I was thinking (I am prety sure some else thaught of that) why not use some mathematic that admit infinity as a solution ? I am specialy thinking of projective geometry.

Maybe by admitting infinit solution we are not stuck there, and can go further in our understanding of black hole.

Can we extend Lorentz transform to work at c ?

[Mr Skeptic]

No. Infinity is not a number. If you end up with a final answer of infinity, then you can't do anything with it anymore (unlike if your answer is an equation that results in infinity, in which case it can be divided or subtracted from another similar equation and potentially get answers). Basically, if 1/infinity = 0 and 5/infinity = 0, then you can't get either of them back by infinity * 0 = ???, like you could with normal numbers.

[michel123456]

No. Infinity is not a number. If you end up with a final answer of infinity, then you can't do anything with it anymore (unlike if your answer is an equation that results in infinity, in which case it can be divided or subtracted from another similar equation and potentially get answers). Basically, if 1/infinity = 0 and 5/infinity = 0, then you can't get either of them back by infinity * 0 = ???, like you could with normal numbers.

 

just thinking: that is because you have only one zero.

same thinking: you could have a several number of infinities, or an infinity of infinities, declaring that infinity1 is different from infinity2, and so on, all problem will vanish. As if you looked to infinity in all directions: these are all different infinities. Why do we have to reduce everything to only one infinity? and by extent, to one zero? It is just a problem of mathematical convention that do not permit the existence of different zero's and infinities. After more thinking, there must be several infinities in mathematics.

 

----------------------------

Let's try.

If we replace infinity by any other symbol, we have:

 

[math] \frac{A}{B}= C [/math]

and

[math] \frac{D}{B}= E [/math]

where [math] {B} [/math] is any number, including infinity

It is not difficult to see that if [math] {A}\neq {D} [/math] then [math] {C}\neq {E} [/math]

So IF [math] \frac{A}{\infty}= zero [/math] & [math] \frac{D}{\infty}= zero' [/math] then zero and zero' are different.

 

OR

[math] \frac{A}{\infty}= zero [/math] is incorrect.

 

Did I miss something?

Edited December 8, 2010 by michel123456

[ajb]

Can we extend Lorentz transform to work at c ?

 

You want to find some compact analogue of the Lorentz group...

 

I have no idea if this can be done. If you feel brave have a shot at it.

[Jacques]

No. Infinity is not a number. If you end up with a final answer of infinity, then you can't do anything with it anymore (unlike if your answer is an equation that results in infinity, in which case it can be divided or subtracted from another similar equation and potentially get answers). Basically, if 1/infinity = 0 and 5/infinity = 0, then you can't get either of them back by infinity * 0 = ???, like you could with normal numbers.

That is true. If we use regular math.

But,

if 1/infinity = 0/1 and 5/infinity= 0/5 then

infinity * 0/1 = 1 and infinity * 0/5 = 5

Some kind of "rational numbers" that flip spacetime dimension. Numerator becomming a denominator and visversa.

May be wath I just wrote here is pure scrap, I am not a mathematitian , but I know that some math can cope with infinity (projective geometry projective space) and I thaught that it might be useful for physic.

Edited December 8, 2010 by Jacques

[Mr Skeptic]

That is true. If we use regular math.

But,

if 1/infinity = 0/1 and 5/infinity= 0/5 then

infinity * 0/1 = 1 and infinity * 0/5 = 5

Some kind of "rational numbers" that flip spacetime dimension. Numerator becomming a denominator and visversa.

May be wath I just wrote here is pure scrap, I am not a mathematitian , but I know that some math can cope with infinity (projective geometry projective space) and I thaught that it might be useful for physic.

 

Sorry, zero does not get any smaller by dividing it. Perhaps if you go with the concept of infinitesimals (very very close to zero but not quite).