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Absolute Hot

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Re: Absolute Hot

#51

Post by wodenokoto »

teh_klev wrote: post #46
calhoun137 wrote: post #27

This is an amazing video by vsauce called How Hot Can It Get and which deals with the same concepts. I very highly recommend it for everyone. https://youtu.be/4fuHzC9aTik

Thanks for that, I hadnt' bumped into that channel before. After watching this one I watched the one on how to count past infinity....mind suitably blown :) https://www.youtube.com/watch?v=SrU9YDoXE88

If we are posting great V-sauce videos, "Which way is down" is the best explanation of the relationship between space-time and gravity I have come across.

https://youtu.be/Xc4xYacTu-E

Re: Absolute Hot

#52

Post by mirimir »

badosu wrote: post #33
louisswiss wrote: post #26

Earlier quoted context omitted.

Does that mean it doesn't take more energy to accelerate an electron to the speed of light than a tennis ball?

No hadron can achieve the speed of light. See: Ek=mc^2/√(1−(v/c)^2)−mc^2 For v As v->c it does not matter as much, the lorentz factor is much more significant, the mass operates just as a base multiplier and sum factor. As v->c, x->0 where Ek~1/x, i.e. tending to infinity with a division by zero when v=c. In conclusion, the speed is the relevant factor instead of mass when near speed of light, regardless of the objec…

Another perspective is that the object's effective mass is going exponential as v->c. I mean, that's why we say "rest mass", right?

Re: Absolute Hot

#53

Post by dTal »

OscarCunningham wrote: post #25
sampo wrote: post #24

Earlier quoted context omitted.

So +0K is the lowest low, and -0K is the highest high.

Right. In many contexts it makes more sense to use 1/T. Then there's no discontinuity and as things get hotter you decrease smoothly from positive, through 0, to negative.

1/0 seems like a pretty major discontinuity.

Re: Absolute Hot

#54

Post by pdonis »

dandare wrote: post #10

Question: is the analogy of thermal energy as particles flying around and bouncing into each other just analogy? At what temperature would the particles fly at the speed of light? > Above about 10^32K, particle energies become so large that gravitational forces between them would become as strong as other fundamental forces according to current theories. I see, the gravitation would become a problem even before the s…

> At what temperature would the particles fly at the speed of light?

Never. More precisely, never for particles of ordinary matter that have nonzero rest mass. Relativistic effects change the dependence of temperature on velocity (more precisely, the dependence of kinetic energy on velocity), so that kinetic energy/temperature increases without bound as the speed of light is approached.

For a "gas" of photons, particles of light, the particles always move at the speed of light, because they have zero rest mass. But photons can have any kinetic energy, so a photon gas can have any finite temperature.

Re: Absolute Hot

#55

Post by chowells »

dTal wrote: post #53
OscarCunningham wrote: post #25

Earlier quoted context omitted.

Right. In many contexts it makes more sense to use 1/T. Then there's no discontinuity and as things get hotter you decrease smoothly from positive, through 0, to negative.

1/0 seems like a pretty major discontinuity.

There's no discontinuity at 0. It's a limit point that is unreachable, as far as we know. That's why 1/T is a better measure. It makes it obvious that +0k is the unreachable limit of "adding a quantum of energy results in an infinite increase in entropy". (-0k is the unreachable limit of "adding a quantum of energy results in an infinite decrease in entropy".)

Re: Absolute Hot

#56

Post by Phrodo_00 »

sp332 wrote: post #12
dandare wrote: post #10

Question: is the analogy of thermal energy as particles flying around and bouncing into each other just analogy? At what temperature would the particles fly at the speed of light? > Above about 10^32K, particle energies become so large that gravitational forces between them would become as strong as other fundamental forces according to current theories. I see, the gravitation would become a problem even before the s…

You can't accelerate anything to the speed of light without an infinite amount of energy. It just takes more and more energy to get closer to that speed. https://en.wikipedia.org/wiki/Speed_of_light#/media/File:Lor...

> You can't accelerate anything to the speed of light

You can't accelerate anything _with mass_ to the speed of light. Although I guess that stuff with no mass already travels at the speed of light, so you wouldn't need to accelerate it.

Re: Absolute Hot

#57

Post by evincarofautumn »

OscarCunningham wrote: post #25
sampo wrote: post #24

Earlier quoted context omitted.

So +0K is the lowest low, and -0K is the highest high.

Right. In many contexts it makes more sense to use 1/T. Then there's no discontinuity and as things get hotter you decrease smoothly from positive, through 0, to negative.

I remember when I first learned about absolute zero, ages ago, and thought “if it’s unreachable, it must be like an asymptote…but that would mean we’re measuring temperature ‘upside-down’…”

Much later, I learned about that very thing (1/T, “thermodynamic beta”) while wikiwalking after hearing about the concept of negative temperature. Then I fell into a rabbit-hole wondering if we also measure speed upside-down in that way, since you can’t accelerate to light-speed. And indeed, when you’re talking about relativistic effects, units of time per distance can be more illustrative sometimes than our intuition of distance per time.

Re: Absolute Hot

#59

Post by wnoise »

Unfortunately, this a terrible name, concept, and even article.

The vast majority of it is directly from a pop-science NOVA episode and not actually well-backed.

There are reasonable bounds you can place on energy density where we expect current physical theories to stop making sense.

But energy density is not the same as temperature. It is true that for things like ideal gases, temperature is roughly "energy per degree-of-freedom", which is an energy density of sorts, but that's not fundamentally what temperature is.

Temperature is nothing more than a specific measure of how energy will flow due to entropic effects. In the right systems, this can be arbitrarily high without a high energy density. (In fact, elsewhere on this very post, people have pointed out "negative temperatures" where the temperatures become "hotter than infinity", they "wrap around" to negative.)

Re: Absolute Hot

#60

Post by adrianratnapala »

jdmichal wrote: post #17
caf wrote: post #14

Earlier quoted context omitted.

There's no finite level of kinetic energy at which the speed of an object exceeds c.

I believe you mean, "There's no finite level of kinetic energy at which the speed of an object equals c." Exceeding c is, of course, not known to be possible at all, even with infinite energy.

Except for massless particles, which do go at the speed of light. And that's important: photons etc. are part of the thermal soup just like every thing else.
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