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Absolute Hot

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Re: Absolute Hot

#71

Post by snowwrestler »

wnoise wrote: post #70
snowwrestler wrote: post #69

Earlier quoted context omitted.

If the temperature wraps around to negative, doesn't that imply a maximum value at the wrap point? Do we know the temperature value at which it wraps to negative? Is it literally "infinity Kelvin?"

Yes, the wrap point is literally infinity, wrapping to negative infinity. https://en.wikipedia.org/wiki/Negative_temperature is not terrible, for an overview, though the disclaimer is just annoying at this level. For thinking about this point, it's much easier to talk about "thermodynamic beta" (sometimes called "coolness" or "coldness") which is just 1/T = partial S/partial E. The behavior of a spin system that admi…

Thanks!

Re: Absolute Hot

#72

Post by trentlott »

drostie wrote: post #32
komali2 wrote: post #21

Earlier quoted context omitted.

Right, this was how I was taught about temperature, and I'm just realizing now it probably isn't the best analogy... Like, do particles shot through a particle accelerator have a super high temperature? They're moving awfully fast! Or does it have to be "vibration," in which case, "vibrating" relative to what?

It's technically not 100% defined. See my comment below for more details about degrees of freedom and energy. Suppose you have a system with 100 degrees of freedom and 2 units of energy, spread out as (0.01, 0.01, ..., 0.01, 1.01). A bunch of its energy is in one of those hundred degrees of freedom. You can assign it two different temperatures: the temperature 0.01, which would describe how energy will right now flow…

> there is a family of systems of "negative temperature" which become less uncertain as you add more energy to them . . .

I'm no physicist, just a chemist. What are they?

Re: Absolute Hot

#73

Post by trentlott »

badosu wrote: post #66
mirimir wrote: post #52

Earlier quoted context omitted.

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?

Since E=mc^2 -> m=E/c^2. For a moving object you could then m=(Er+Ek)/c^2, which creates the impression that the mass is variable (as the term Ek is zero when at rest and increasing with velocity), giving rise to the terms 'rest mass' and 'relativistic mass' respectively for the rest energy and total energy equations. This interpretation is somewhat outdated but the terminology rest mass maintains its legacy. One cou…

So how does 'invisible' kinetic energy (say, that of a ball traveling on the planet) change its mass?

If we cancelled out that movement (relative to the Milky Way), does the mass change?

Is how much do the various relative movements affect our mass, and would it be possible to pull tem apart? (Solar System, Relative to galactic center, other galaxies, etc)

Re: Absolute Hot

#74

Post by wnoise »

evincarofautumn wrote: post #57
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.

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 th…

For speed we don't measure it "upside down", no. But there is another transformation: "rapidity", which does add linearly (at least for one spatial dimension) and goes to infinity when velocity goes to c.

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

Re: Absolute Hot

#76

Post by badosu »

trentlott wrote: post #73
badosu wrote: post #66

Earlier quoted context omitted.

Since E=mc^2 -> m=E/c^2. For a moving object you could then m=(Er+Ek)/c^2, which creates the impression that the mass is variable (as the term Ek is zero when at rest and increasing with velocity), giving rise to the terms 'rest mass' and 'relativistic mass' respectively for the rest energy and total energy equations. This interpretation is somewhat outdated but the terminology rest mass maintains its legacy. One cou…

So how does 'invisible' kinetic energy (say, that of a ball traveling on the planet) change its mass? If we cancelled out that movement (relative to the Milky Way), does the mass change? Is how much do the various relative movements affect our mass, and would it be possible to pull tem apart? (Solar System, Relative to galactic center, other galaxies, etc)

I am not sure, I am not a physicist.

What I understand is that the contemporary conception is that the mass does not change.

I just presented the argument for a notion of rest mass and relative mass.

Re: Absolute Hot

#77

Post by evincarofautumn »

wnoise wrote: post #74
evincarofautumn wrote: post #57

Earlier quoted context omitted.

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 th…

For speed we don't measure it "upside down", no. But there is another transformation: "rapidity", which does add linearly (at least for one spatial dimension) and goes to infinity when velocity goes to c. https://en.wikipedia.org/wiki/Rapidity

Well no, I just meant that sometimes working in inverse units makes things easier to understand than the “intuitive” units you use in daily life. “Time per distance” helped me personally get a better intuitive sense of time dilation and length contraction. I hadn’t heard of rapidity before, but it’s really interesting, and makes sense after some musing—thanks!

Re: Absolute Hot

#78

Post by drostie »

trentlott wrote: post #72
drostie wrote: post #32

Earlier quoted context omitted.

It's technically not 100% defined. See my comment below for more details about degrees of freedom and energy. Suppose you have a system with 100 degrees of freedom and 2 units of energy, spread out as (0.01, 0.01, ..., 0.01, 1.01). A bunch of its energy is in one of those hundred degrees of freedom. You can assign it two different temperatures: the temperature 0.01, which would describe how energy will right now flow…

> there is a family of systems of "negative temperature" which become less uncertain as you add more energy to them . . . I'm no physicist, just a chemist. What are they?

I mean it's not just one system, but the idea is what I just said.

The classical example is if you have a bunch of magnetic moments in a magnetic field and they do not interact with each other: then stuffing energy into the system requires aligning them against the magnetic field, and this makes the state more ordered. The problem is that these moments are generally in thermal contact with some apparatus that keeps them in place or vibrational degrees of freedom of their centers of mass or so. But you can get this thing to happen in magnetic resonance setups.

Negative temperature states pop up in a lot of strange places, the two that I know more closely are that lasing has this property of "as I dump more energy into the system I get more bosons in the lasing state" and Onsager in 1949 published a little article called “Statistical Hydrodynamics” which sort of went viral for the time, it points out that there is a way to view the instability of turbulent systems as due to negative temperature regimes of the vortices in those systems.

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