
Absolute Hot - johnny313
https://en.wikipedia.org/wiki/Absolute_hot
======
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.)

~~~
snowwrestler
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?"

~~~
wnoise
Yes, the wrap point is literally infinity, wrapping to negative infinity.

[https://en.wikipedia.org/wiki/Negative_temperature](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 admits negative temperatures
can be described smoothly in terms of beta -- hotter systems have beta that is
lower, and zero is not particularly special.

Now, any real system is coupled to the rest of the environment, so can't be in
equilibrium at a negative temperature, as it would continuously leak heat
until it cooled down enough to have some positive temperature. But if its
internal equilibration proceeds much faster, then it's still useful to talk
about its temperature as a quasi-equilibrium case.

~~~
snowwrestler
Thanks!

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dandare
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 speed.

~~~
sp332
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...](https://en.wikipedia.org/wiki/Speed_of_light#/media/File:Lorentz_factor.svg)

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

~~~
badosu
No hadron can achieve the speed of light. See:

Ek=mc^2/√(1−(v/c)^2)−mc^2

For v<<c you have significant discrepancies on the energy required to
accelerate to a specific speed with regard to mass. I.E. Newton: Ek=(mv^2)/2

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 object being an electron or the mount
Everest.

Of course, assuming the equation holds ;-)

~~~
mirimir
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?

~~~
badosu
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 could refer to it as the `(proper |invariant
|intrinsic )?mass` instead.

The variable mass issue is then 'solved' by 'refactoring' the equation to use
momentum where mass is coupled with velocity, over which the complexity of the
lorentz factor is engulfed.

~~~
trentlott
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)

~~~
badosu
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.

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ssivark
Ooh boy, quantum mechanics is _fun_ :-)

Think of the quantum vacuum as having a large number of degrees of freedom
waiting to get excited by energy -- like a fleet of unused AWS instances in a
system with very effective load balancing. The moment the load (roughly,
energy) on the running instances (particle present in the system aka "quanta")
increases beyond the threshold for creating a new one (aka rest mass of a new
particle), a new instance is spontaneously created. Heating the system is akin
to increasing the load on your system, and new instances will keep getting
spun up.

Is there a limit on how many such particle instances can be created? If we
neglect gravity, no -- you can just keep adding instances/quanta and never run
out. (and how much ever energy you dump in, the system's temperature will not
increase beyond the Hagedorn limit [2])

But if you stop ignoring gravity, the gravitational attraction between the
spun up instances will keep increasing as you spin up more of them, eventually
forming a black hole at some point (because you cannot squeeze in more than a
certain amount of information in a given volume [1]). This is roughly where
you wave your hands and and come up with heuristic explanations using Planck
length, Planck mass, etc.

That's the limit of current understanding. Any refinement to this story would
be a massive breakthrough!

PS: A relatively sobering (nonetheless exciting) possibility is that much
before gravitational effects become important, your "effective field theory"
proves insufficient to model the system, and you are led to a "more
fundamental" model.

[1]: [http://scholarpedia.org/article/Bekenstein-
Hawking_entropy](http://scholarpedia.org/article/Bekenstein-Hawking_entropy)

[2]: A technical explanation of the Hagedorn limit: At finite temperature, the
occupation probability of states is exponentially decaying with energy (i.e.
energy divided by temperature gives the log-probability) [3]. But, if the
degeneracy of high-energy states grows exponentially, then that could
entropically compensate for the exponential decay of the occupation
probability, to have more occupation at higher energies than lower energies!
The transition point in this tradeoff is the Hagedorn limit. That is why,
additional energy is more likely to create new particles/states than simply
increase the per-particle energy of the existing ones.

[3]:
[https://en.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann_stat...](https://en.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann_statistics)

------
Jun8
Good answer from Physics SE on why there's no upper limit to temperature:
[https://physics.stackexchange.com/questions/1775/why-is-
ther...](https://physics.stackexchange.com/questions/1775/why-is-there-no-
absolute-maximum-temperature)

~~~
klodolph
Would also add to this that ideas about what "temperature" means change when
you are switching between equilibrium and nonequilibrium thermodynamics. In
nonequilibrium thermodynamics a bunch of your equations go out the window,
like the Boltzmann distribution, and all of the rules built on top of that
which are many.

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OscarCunningham
See also:
[https://en.wikipedia.org/wiki/Negative_temperature](https://en.wikipedia.org/wiki/Negative_temperature)

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

~~~
OscarCunningham
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.

~~~
evincarofautumn
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.

~~~
wnoise
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](https://en.wikipedia.org/wiki/Rapidity)

~~~
evincarofautumn
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!

------
bovermyer
A temperature so hot that we have to invent a new quantum theory before we can
figure out what physics would be like at that level? Yikes.

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shaded-enmity
Hmm, at school we were taught that the maximum temperature is such that
wavelength of the emitted black-body radiation would equal Planck length, is
this rationale no longer sound?

~~~
wnoise
It was never sound.

Black-body radiation describes the distribution of power emitted at given
wavelengths or frequencies emitted by an ideal black body.

1\. Distributions don't have one wavelength. There is a "peak" wavelength at
which most power-per-wavelength is emitted, but there is still power emitted
at all wavelengths no matter what temperature something is.

2\. There is not sufficient reason to believe that the Planck length is a
limit on the wavelength of light. This would break Lorentz symmetry.

3\. Most things aren't ideal black bodies, but still have temperatures. Even
if very hot objects couldn't emit light of Planck length, they can still
couple to the environment and emit heat in other ways.

------
calhoun137
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](https://youtu.be/4fuHzC9aTik)

~~~
teh_klev
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](https://www.youtube.com/watch?v=SrU9YDoXE88)

~~~
wodenokoto
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](https://youtu.be/Xc4xYacTu-E)

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nategri
If you like this, you might enjoy:
[https://en.wikipedia.org/wiki/Negative_temperature](https://en.wikipedia.org/wiki/Negative_temperature)

------
MrEfficiency
Planks Constant really changed my understanding of what the universe is made
of.

Our physics and understanding of matter seems to be relevant under very
specific conditions.

The moment we can make technology that can impact the smallest of sizes(if
this is even possible), we might get an answer for what the universe is. Or
maybe it would turn out to be "42" and it still wouldnt make sense.

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hinkley
Wouldn't fusion trigger at much, much lower temperatures?

We are talking about the theoretical limit of temperature, but what is the
_practical_ limit? There's a point beyond which heating hydrogen just gets you
helium and more heat, but heating anything heavier than iron gets you
something colder than the inputs.

~~~
sigi45
Isn't fusion a reaction which has to happen? I would think that at that energy
level there are no more elements which are able to form.

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mustardo
This video is probably the best explanation
[https://www.youtube.com/watch?v=oHyctwgE6m4](https://www.youtube.com/watch?v=oHyctwgE6m4)

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RichardCA
I have a really simple question.

Has anyone ever done an experiment to confirm that SR comes into play at
ultra-high temperatures?

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kazinator
Note how T stands for temperature, so we can use the symbols NIL for absolute
zero and T for absolute hot.

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rocks
What is "simple english" below languages? Never seen this before.

~~~
dfxm12
It's been around for nearly 15 years. It's geared towards younger folks, folks
with learning disabilities that might make it hard for them to read and people
who are learning English as a second language.

[https://simple.wikipedia.org/wiki/Simple_English_Wikipedia](https://simple.wikipedia.org/wiki/Simple_English_Wikipedia)

~~~
Koshkin
Incidentally, for many readers of Wikipedia it may be not the language _per
se_ that is difficult to understand, so it would have been nice if there
existed simpler versions of articles that otherwise may not be accessible to a
lay person.

~~~
extragood
Sometimes I don't care about the theory or equations related to a topic, and
just want the gist of it quickly.

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hnryjmes
or, how my Pixel XL feels in my hand after about 10 minutes of use

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SurrealSoul
Looks like they found a way to measure my mix tape

~~~
Bjartr
If this were reddit I would've upvoted you, but this kind of cleverness
should, if it constitutes the whole post, should be left to reddit.

Now, should this thread ultimately hehehe a discussion on the virtues and
approaches to creating mixtapes it would be another thing, but at this point
in time I'm not seeing this as a positive contribution to discussion. That is
why I downvoted your genuinely amusing comment.

~~~
probably_wrong
Not that I disagree with you, but I should point out that it's a reference to
the video "Absolute hot" of the YouTube channel "Casually explained".

~~~
Bjartr
Personally, I don't think that changes what constitutes a good discussion
contribution on HN.

There's plenty of discussion here going into the details of the physics and
the semantics at hand. We don't have to lower the bar for the discussion just
because the topic under discussion was presented in a simple way.

