Hacker News Reader

Comment by andrepd | Hacker News Reader

> Temperature is not infinite [...] There is finite space and time. Finite speed.

There's no theoretical limit for temperature, and we believe spacetime could be infinite even though the observable universe is not. Nevertheless this is a very silly argument. If it's finite but absurdly high it's good enough for the purpose.

View on HN

If the energy density in a fixed volume of space gets too high it collapses into a black hole. That seems to suggest that there is a kind of limit to temperature.

I'm a complete noob in this area, but that doesn't mean that temperature has reached it's limit does it? The black hole can carry on getting more dense and hotter.

No, the black hole can't get more dense. If you put more energy into it it gets bigger.

Schwartzchild radius is directly proportional to mass, so (if I understand correctly) it's if the energy density of a surface area rather than of a volume is too high.

Only if it's concentrated. Otherwise the entire universe would have collapsed into blackholes during the big bang. You need an energy gradient for gravity to work like that.

Yes, there is a theoretical limit for temperature.

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

For all intents and purposes, however, it is preposterously enormous.

That's not a limit for how hot temperature can get, just a limit at which existing theories break down.

No, there's not. Read what you posted more carefully. Planck temperature is the scale at which gravitation becomes as important as other forces, and thus without a working theory of quantum gravity we can't predict what happens at that scale.

https://en.wikipedia.org/wiki/Planck_temperature

Planck length, Planck time and Planck temperature are not the minimal/maximal values for these quantities that "could exist". It is the boundary of the regime that our current theories can describe.

> There's no theoretical limit for temperature

I suppose when the particles reach lightspeed?

The archtype of temperature is a black body radiator. Classically, you make a block of metal (ceramic, whatever), with a spherical cavity and drill a small hole into the cavity. Then you draw a vacuum and heat the cavity, point a scope at the hole, and measure the spectrum of ligh tcoming out. In this circumstance, there is no mass that limits the energy: you are measuring the temperature of a black, empty vacuum; thus there is no upper limit.

> Then you draw a vacuum and heat the cavity

What are you heating if it's a vacuum? How can you heat nothing?

You're measuring radiative heat, which indeed exists for most of its time in nothing. I guess that the idea of GP is that you could make the heating block arbitrarily big (say, size of the universe) and have it dump all its radiative heat into that cavity.

I see. Thanks.

The difficulty here is people don't often specify if they mean heat in the form of kinetic energy or radiation.

Much like how people say things like "releasing energy" without specifying the form of energy.

When you heat something, you have to add energy to it. Mass and energy are equivalent; both warp spacetime. You will, in fact, reach a temperature where your block of metal collapses.

I was simply trying to explain to my P that temperature is not dependent on the speed of a massive particle.

OK, but arbitrarily high temperatures necessitate arbitrarily high mass-energy densities, and the latter won't happen without a gravitational collapse.

I'm sorry, but this is a complete misapprehension of "black body" radiation and your experiment is nonsensical. "Black body" refers to an object that absorbs all incoming radiation, and nothing to do with the "a black, empty vacuum". The spectrum of such an object therefore is entirely radiative (no reflection) and depends only on its temperature. As a sibling points out, a vacuum cannot be heated - there is nothing to heat - and does not have an emission spectrum. Your experiment would simply measure the spectrum of the bottom of the hole you drilled.

I see that I am mistaken: The temperature is a function of the particles energy, not its speed. The energy at light speed is infinite, so that doesn't really pose a temperature limit.

There does however seem to be an quite widely assumed maximum temperature: the Planck temperature of about 1.417×10^32 Kelvin.

Reply on news.ycombinator.com