Arcadian Functor

occasional meanderings in physics' brave new world

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Marni D. Sheppeard

Monday, April 30, 2007

Sparring Sparling IV

Since comments on blogs float like corks on the sea, I will bookmark here the interesting remarks of Matti Pitkanen and Carl Brannen on the Abell cluster A586, which is a particularly spherical galaxy cluster. The authors of this recent paper find that, for A586, the ratio of kinetic energy density to potential energy density is $-0.76 \pm 0.05$. This is quite different to the value of $-0.5$ expected from the usual virial theorem.

Ignoring interpretations involving the Dark Force, Carl pointed out that the actual value of $-0.75$ was precisely three times the expected value. This may be explained by a higher value for the speed of light, which fits nicely into the preon particle physics, but the actual value of $c$ is not really relevant.

Kinetic energy goes as $v^2 = v_{1}^{2} + v_{2}^{2} + v_{3}^{2}$ for a 3-vector $v$. Thus for the three speeds of light, forming a 3-vector $(c_1, c_2, c_3)$, the kinetic energies will add. But if we ignore the three speeds, and substitute instead a value which is the length of $(c_1, c_1, c_1)$, then we would have $c = \sqrt{3} c_1$. In the first instance the kinetic energy goes as $\frac{v^2}{c_{1}^{2}}$, while in the second it goes as $\frac{1}{3} \frac{v^2}{c_{1}^{2}}$. This is why kinetic energy at small cosmological scales is incorrectly defined by a factor of 3. Of course, at small scales this doesn't matter.

This links the mass generators of M theory, which obey the tripled Pauli statistics, to the three time coordinates.

4 Comments:

Blogger Javier said...

Excuse me for the slight off-topic. Might be it is a F.A.Q. but I still haven´t found an answer.

I see you are using MathML in your bllogspot blog. If i do copy & pste of the mathml code of some of your formulae and I publish it in my own blog (also in blogspot) it is not rightly represented.

So the question is, which is the trick for getting MathMl working on blogspot? Till now I was using LaTeX with an external server, but I find it awkfull because of the obvious reason that the server could dissapear in any moment.

About your blog I can´t say too much, technical algebraic geometry (as math people study it) is something I plain to study soon, but till then I find many of your entries very hard to understand. Obviously that´s myfault and not yours.

April 30, 2007 3:48 PM  
Blogger Kea said...

Hi Javier. Thanks to somebody called Gebar, I use the Uni of Nottingham server, which is pasted into the Blogger template. It is available from:

http://www.maths.nottingham.ac.uk/personal/drw/LaTeXMathML.js

April 30, 2007 3:53 PM  
Blogger Kea said...

Note to the reader: the frequency of complaints about my flawed reasoning is increasing at a rate that suggests a dedication to my blog that is surprising in a respectable person.

April 30, 2007 5:58 PM  
Blogger Matti Pitkanen said...

Kea,

I wrote a little posting about the notion fundamental length inspired by the comments about light velocities. Just the usual debunking of string theories plus unashamed self-promotion;-).

Cheers,
Matti

April 30, 2007 6:09 PM  

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