/sci/ - Science & Math

>I know temperature is a measure of the average kinetic energy of particles.

Correct.

>So if all particles were moving at the speed of light then this would be the maximum?

Correct, but that would be infinity.

>But would that not mean they have infinite mass, causing black holes?

That's just bullshit, gravitational mass is not influenced by speed. Stop clinging to the retarded concept of mass including a gamma factor, it's wrong and misleading.

Maybe yes, maybe no:

http://en.wikipedia.org/wiki/Absolute_hot

Current physics breaks down at Planck temperature.

hmm assuming you took all the energy in the universe and focussed it on one particle that would be the hottest possible, of course that is obviously impossible

>>2474835
E=MC^2???

>That's just bullshit, gravitational mass is not influenced by speed. Stop clinging to the retarded concept of mass including a gamma factor, it's wrong and misleading.

I'm not OP, but it's been awhile since I took modern physics. The concept of relativistic mass comes from the relativistic momentum relationship, right? So are we supposed to consider the gamma paired with v instead of the mass in that equation?

>>2474873
You mean <span class="math">p = \gamma m v[/spoiler]?

That's how relativistic 3-momentum is defined. You had better not thing of the gamma factor as paired with anything.

I suggest you try to learn relativity in Minkowski space, it's much more elegant and much less likely to lead to misunderstandings.

>>2474873
The only reason you would want to "pair" the gamma factor with anything is so that your "new" laws can look like your "old" laws. While this is good for "coming up" with a new theory, it isn't a clever way to get a thorough understanding of special relativity. Special relativity is essentially different from non-relativistic classical mechanics, and should be taught with that in mind.

>>2474835
don't be a fucking idiot, if gravitational mass wasn't affected by speed then gravity would seem weaker as speed increased, the only way to keep gravitational forces apparently constant despite speed is to say gravitational mass increases at exactly the same rate as inertial mass, so that while the force increases the effect is equal.

your fucking stupid hypothesis would have to imply that gravitational and inertial mass and different, which is not the case

>>2474931
>if gravitational mass wasn't affected by speed then gravity would seem weaker as speed increased

What the fuck are you basing this on? My guess is you don't know shit about physics.

>your fucking stupid hypothesis would have to imply that gravitational and inertial mass and different, which is not the case

Gravitational mass and rest mass are the same. Your fucking stupid idea of defining inertial mass as including a gamma factor makes them different.

Now let people who actually know physics do the talking.

>>2474894
>>2474905

So then the common concept of mass is incorrect in terms of special relativity? This means any mass "increase" is really an energy increase because of the mass-energy equivalence?

>>2474943
do you think forces on an object effect the same results without respect to the speed of the object?

>>2474828
No one knows if there even is one. Particles which have mass can't be accelerated to the speed of light, because it would essentially require an indefinitely large amount of energy. The Planck temperature, which is around 1.4 × 10^32 K is conjectured a possible highest temperature, but all that's known at the moment is that our current models can't describe it due to the strength of gravitational interactions at this temperature.

>>2474956
Mass doesn't change.

Energy changes, not because E = mc², but because E = gamma m c². E = mc² is true only for a particle at rest.

>>2474960

No. Because F = ma is not true in special relativity. If you want it to still be true, inserting a gamma factor in front of m is not enough. You have to use a tensor.

And that's retarded, since using 4-vectors is much more elegant.

>>2474975
so what you're saying is that gravitational mass remains constant but does not exert the same effect as velocity changes?

>>2474851
So Planck temperature is pretty much what I said. At maximum temperature all articles moving at the speed of light, so they will become infinity more massive, creating black holes. There is no quantum theory of gravity so we don't know what the fuck goes on then.

Correct me if I’m wrong.

>>2474956
I'm afraid my knowledge of relativity is somewhat lacking, but I believe that from a hamiltonian point of view, you pretty much just put mass equal to energy. But beware that in this case, "energy" refers to the system's Hamiltonian.


Anyhow, what we think of as the mass in non-relativistic mechanics is the rest-mass in relaticistic mechanics, and that is the only mass that you have to worry about. The rest-mass is independent of coordinate system, therefore it is beneficial to use exactly that quantity instead of something else.

>>2474975
Erh, it holds in special relativity that <span class="math">F=\frac{d}{dt} \gamma m v[/spoiler].

>>2474990

Alright, thanks, interesting stuff.

>>2474985
Gravitational mass does not change. The way forces are felt changes according to velocity.

Gravity does not act as a force, but as a change in the metric tensor of the space. Newtonian gravitation has no place in a relativistic formalism, that's what prompted Einstein to develop General Relativity.

>>2474987
You're right about there being no fully developed theory of quantum gravity. I said nothing about black holes. It's impossible for anything with mass to travel at the speed of light.

>>2474835
>That's just bullshit, gravitational mass is not influenced by speed. Stop clinging to the retarded concept of mass including a gamma factor, it's wrong and misleading.

But in General relativity the strength of gravity is based on the energy-momentum tensor, meaning gravity would be affected by a particles "kinetic energy" as a higher energy implies that the momentum would be higher, and that means that gravity would be stronger.

>>2474996
Yes, but that's not F = ma, because of <span class="math">\dot \gamma[/spoiler].

once I heard it was 9999º.

>>2475015
am i being trolled

>>2475007
so what you're saying is the way that gravity interacts with an object changes based on the velocity?

>>2475014
True, but you don't need a tensor (of order two) to write down the equivalent equation, <span class="math">F=m(\dot \gamma v + \gamma a[/spoiler]

>>2475024
The "way" gravity acts is the same always.

>>2475025
But if you want to define a "mass" to write it in the form F = ma, m needs to be a tensor.

>>2475024
No, I'm saying exactly the opposite. Ask >>2475010, he obviously knows more about GR than I do.

Somebody here said that the max temperature was -0 Kelvin or something. I can't remember why.

>>2475033
that's interesting. so as speed increases, we should perceive the same results between two sources of gravity?

>>2475036
>The system can then be characterised as having a negative temperature. A substance with a negative temperature is not colder than absolute zero, but rather it is hotter than infinite temperature. As Kittel and Kroemer (p. 462) put it, "The temperature scale from cold to hot runs:

+0 K, . . . , +300 K, . . . , +∞ K, −∞ K, . . . , −300 K, . . . , −0 K."

>>2475052
It should however be mentioned how a system with a negative temperature is not in a proper state of thermal equilibrium, since its ground state is less populated than its excited states (think of a laser).

>>2475037
I said nothing about that. The "way" gravity acts is given by
<div class="math">\frac{d^2 x^\alpha}{ds^2} = - \Gamma ^\alpha _{\beta \gamma (x) \frac{dx^\beta}{ds}\frac{dx^\gamma}{ds}.</div>
I don't know what exactly you mean by going fast, do you mean relative to the source bending timespace?

>>2475091
<div class="math">\frac{d^2 x^\alpha}{ds^2} = - \Gamma ^\alpha _{\beta \gamma} (x) \frac{dx^\beta}{ds}\frac{dx^\gamma}{ds}.</div>

>>2474828
Temperature is average kinetic energy. Let's use hydrogen as it's the smallest atom and ignore relativity. the mass of 1 hydrogen atom is roughly 1/(6.022*10^23) grams, and has the velocity of 3*10^8.

That means v^2 = 9*10^16 so KE = 3/4 *10^-7but this is in grams, and we want kilograms for SI units joules so divide by 1,000 and get
3/4 ^10^-10 joules = (3/2)*1.3806503 × 10^-23 *T
Which gives you a max temperature of (1/(2*1.38))*10^13 K per amu. or 3.6*10^12 Kelvin per amu.

Now this is ignoring relativity, if you used the correct formula for velocity (which takes into account relativity) then the answer would obviously be infinity.