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Maxwell distribution

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Hi all! According to the Maxwell distribution for gas molleculas, the density of probability of that mollecula has |v| velocity is as follows:
  
F(|v|) = 4*PI*v^2*(m/(2*PI*k*T))^1.5*exp(-m*v^2/(2*k*T));

or simply:

F(|v|) = a*v^2*exp(-A*v^2);
  
That means, that for some temperatures, the probability of velocity, that is more than light velocity ( v > c ), IS NOT ZERO! But it''s against theory of relativity! Is there any "relativity-friendly" Maxwell distribution? And if yes, what does it look like? Thanks in advance, Brennende Komet

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Hey BrennendeKomet,

Can you put your question in the context of game development?

Graham Rhodes
Senior Scientist
Applied Research Associates, Inc.

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learn what the theory of relativity is (completely) and you will know why it is called Relativ ity. It is Relative. That is why you are able have molecules traveling faster than a light wave or photon.
Using relativity in this case just means that you can''t measure it (unless you use a water tank or so forth) because you can''t see the damn thing. Maxemillians equation still works for this in theory. In practice my guess is that the molecules wouldn''t like those temperatures very much at all.

My two cents.



Beer - the love catalyst
good ol'' homepage

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quote:

Can you put your question in the context of game development?



Sure... i was designing a realistic (i hope so ) engine for a spaceship simulation, and i wanted to determine the velocities of rushing-out moleculas. In fact, now i use their mean velocity, but what if it is big, comparable with 'c'? (goto->my_question)


quote:

learn what the theory of relativity is (completely) and you will know why it is called Relativ ity. It is Relative. That is why you are able have molecules traveling faster than a light wave or photon.


You probably mean some other relativity... I mean "Einstein's theory of relativity" - where IT'S ASSUMED THAT THE LIGHT VELOCITY 'c' IS MAXIMAL, and only masless bodies can move with 'c', and IN ANY REFERENCE FRAME the body, with positive mass, moves with velocity THAT IS LESS THEN 'c'. That is for moleculas too.


quote:

In practice my guess is that the molecules wouldn't like those temperatures very much at all.


... here probably you-re right, because at high temperatures the gas can transform into plasma, and there Maxwell distribution can be 'disturbed', i guess...

So... any other suggestions?

Edited by - BrennendeKomet on February 2, 2002 9:19:21 AM

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There is a great missconception about the theory of relativity:

Particles CAN travel faster than lightspeed, if they have no mass (or a mass so small that the laws of physics doesnt apply or take a new meaning. Meaning that there might be new forces at hand when mass reaches close to zero.)

For particles (molecules) their speeds are determined by their mass, not only by max''s probabitlities. If you use energies instead of velocities your calculations will be correct.

/Time is never on your side. It doesnt have sides.

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BrennendeKomet,

The problem you face is that Maxwell''s velocity distribution is a Classical Theory based on Newtonian Mechanics. If you want a relativistic formula, you need to rederive it... or go and get a book on Statistical Mechanics. Any decent book on quantum mechanics should also have it... unfortunately I''m at home and not in my office, so I cannot just look it up for you... try a web search.

Timkin

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quote from Hull:

----------------------------------------------------------
Particles CAN travel faster than lightspeed, if they have no mass (or a mass so small that the laws of physics doesnt apply or take a new meaning. Meaning that there might be new forces at hand when mass reaches close to zero.)
----------------------------------------------------------

OK, but what about tachyons, they move faster than the speed of light and they have mass...

The more energy you put into them the slower they go. They move asymptotic to the speed of light. Just like the normal particles, but then from the other side!~

It is a nice discussion, but it may have nothing to do with games at all.

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Bose-Einstein statistics and Fermi-Dirac statistics are the quantum statistics that work where the classical statistics don''t work. Look them up.

quote:
There is a great missconception about the theory of relativity:

Particles CAN travel faster than lightspeed, if they have no mass (or a mass so small that the laws of physics doesnt apply or take a new meaning. Meaning that there might be new forces at hand when mass reaches close to zero.)


This is not correct.

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