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Is There Such a Thing As Absolute Hot?
AlpineR writes "Is there an opposite to absolute zero? An article from PBS's NOVA online explains several theories of the maximum possible temperature. Maybe it's the Planck temperature, 10^32 K, beyond which the known laws of physics break down. Or maybe just 10^30 K, the limit of some versions of string theory. If space is actually 11-dimensional then the maximum temperature could even be as low as 10^17 K, attainable by the Large Hadron Collider. Or maybe infinite temperature wraps around to negative temperature and absolute hot is the same as absolute cold."
That's what you get for writing a universe in C.
I am trolling
I would have never thought there was a speed limit for the universe before I read Einstein's special theory of relativity. Anything is possible.
"Maybe this world is another planet's hell"
Aldous Huxley
> "Or maybe infinite temperature wraps around to negative temperature and absolute hot is the same as absolute cold."
Or maybe the universe is a snake eating its own tail!
Or maybe monkeys will fly out of my butt.
Yes, and it's my wife's sister. I love the holidays!
But the answer is much, much simpler.
42.
McDonald's coffee?
Margaret Thatcher. Covered in whipped cream. (apologies to anyone who was planning to close their eyes in the near future)
If you haven't made a developer cry, you've wasted a day.
Black holes are garbage collection.
I have to wonder about the definition of temperature at such high energies. I would think it would be difficult to envisage a situation where you have anything resembling a Maxwell-Boltsman distribution at 10^33 K, so just what is meant with temperature in this case?
Temperature is directly related to the velocity of the atoms in a gas or plasma. Since the speed of light cannot be exceeded then there must be a maximum temperature.
DUH!
While it may well be that there is a maximum "energy density" for a particular space, it would not really be a true opposite to absolute zero. Absolute zero represents complete cessation of motion... a true opposite would be infinite motion (obviously not infinite velocity). Also, it seems quite possible that whatever upper limit exists at one particular time in one particular space may differ from another... either varying as the universe ages, with whatever gravitational field may exist locally, or at the very least in different universes that may exist. As such, while absolute zero is just that... absolute (in that no heat is no heat under all conceivable reference points), "absolute heat" almost certainly does not uniformly exist. I suppose another way to say is that if you plug absolute zero in as the value in a mathematical calculation, you will always get the same result, but there is no one value "absolute heat" corresponding, which can closely approach actually existing in our universe.
There is a news reader in France named Melissa that would qualify as "Absolute Hot" //sorry, I thought this was Fark
Absolute zero is when all atomic motion ceases, right? The effective speed limit of the universe is the speed of light, so I'd assume absolute hot would be when when the atoms are traveling near or at the speed of light. Because mass cannot actually reach the speed of light, nothing can actually reach the absolute hot.
Or is that super mega crazy talk?
like this.
"Is there such a thing as absolute hot?"
1. Turn on a burner on the stove. Turn it up as high as it will go.
2. Wait 5 minutes for the burner to warm up.
3. Place the palm of your hand on the burner.
4. You tell me.
I haven't followed that link, and neither should anyone else. Probably another MyMiniCity spam game.
Don't thank God, thank a doctor!
Once we figure what absolute hot is, McDonalds will begin serving their coffee at that temperature.
Seems to me there would have to be an absolute hot. Absolute zero, ferinstance, is the temperature at which all molecular motion stops. Nothing moves at absolute zero. Heat would, then, be a function of how fast the molecules are moving in a given substance, right?
Given that the universe has an effective speed limit ( C: it's not just a good idea, it's the law), it seems to me that for a given substance, there has to be an upper limit of how hot it can get solely because the molecules within it aren't allowed to vibrate any faster. (I'm not certain that the function of vibration speed to heat isn't substance dependent-- it may be.)
However, given that the idea of an absolute hot is apparently not agreed upon by physicists, I am probably missing something important in my layman's analysis of the situation.
-F
The opening sentence of the article kind of ruined it for me as a science article because of the use of such a ridiculously archaic unit. I can understand the stubbornly conservative US population rejecting these new-fangled SI units, but I would've thought the scientific community, and the scientific media, would have more sense. Didn't you guys trash a Mars probe because of some idiot using PSI when he should've been using Pascals?
If we can put a man on the moon, why can't we shoot people for Apollo-related non-sequiturs?
The saddest poem
but I know about women.
I found the line of thought intriguing, until it said "negative temperature". The whole point of "absolute zero" is that there _are_ no negative temperatures.
Please correct me if I got my facts wrong.
we should switch the scale of hotness: accept Carmen Electra as 1 unit of hotness as measured in the year 2000. Also accept that 2 Carmen Electras is twice as hot as 1 Carmen Electra. As the number of Carmen Electras approaches infinity, their total combined hotness approaches some saturation limit, after which it is no longer possible to determine whether hotness of N x Carmen Electra is greater than hotness of (N+1) x Carmen Electra, which breaks down the laws of mathematics and thus the laws of physics by making N=N+1.
I must add that Chuck Norris can kick Carmen Electra's ass even at the hotness limit.
You can't handle the truth.
Temperature is basically the average kinetic energy of the particles, and kinetic energy is half the mass times velocity squared, when things start to get very hot, the particles would eventually start getting up to relativistic speeds.
This has lead some people to suggest that the cosmic speed limit (the speed of light) imposes a cosmic temperature limit - but that's NOT the case.
As things start to move closer and closer to the speed of light, relativity says that their mass increases (as seen from the perspective of an outside observer). Whilst there is a cosmic speed limit - as you approach it, your mass increases without limit. Since unlimited mass and finite velocity means unlimited kinetic energy, relativity does not impose a cosmic temperature limit.
If there is a cosmic temperature limit, it's caused by something else.
www.sjbaker.org
That would absolutely bend my brain - a thermal equivalent of a Smith Chart.
At that temperature any water would be denatured, so it would be a "dry heat".
I read this as:
Our physics breaks down at very high and very low "temperatures". They must be similar! What if you go to Infinity +1!? You must be back where you started!
We currently measure temperature as the kinetic energy contained within the molecules of a substance, correct? Following this, the more energy you put into those molecules... the higher the temperature. If that temperature suddenly dropped to absolute zero, where did the energy go? Did we just condense into matter? Did we just break the second? Is it simply that our definition of "temperature" breaks down with the rest of our physics at those energies? Or will the matter behave as we might expect it to, and just continue to increase in temperature as you add energy. This article felt like some wild speculation mixed with some physics concepts without any real reasoning to the question. I get it wrong somewhere?
I'll believe in corporations having personhood when Texas executes one... - advocate_one
Absolute zero is a non-existent state. Well, no. It exists, but it cannot be attained ever. It requires matter to not exist. That is a bit difficult to do.
Both absolute zero and t'other way are those lines that approach a number but never reach it (like how x/2 never equals zero but gets really close). Things also change physically as something nears AZ and t'other way.
More informations can be provided if so desired.
I have research that I can provide if desired. Also home experiments. Some fun ones with your microwave to simulate extreme temperature conditions.
It's 42 bits.
My 10 year old son asked the same question a couple of weeks ago. I replied that perhaps it relates to the fastest that the molecules in a substance can jiggle, presumably tending towards the speed of light?
And indeed the fucktard got modded down! hah!
Aaaaaaaayyyyyyyyyyyyyyeeeeeeeeeeeeeee!!!!!
Obviously the poster hasn't seen Monica Bellucci in Malèna!
That's hot....
Umm... Heidi Klum?
It must have been something you assimilated. . . .
"Who the fuck knows?"
The temperatures on Pluto are much cooler then 0F, but are still above absolute zero K. 0K is not something that changes, Wikipedia's Pluto Article
But no one has tied relativity to quantum mechanics yet. Therefore those speed limits only apply to a narrow vision of the universe.
Sorry but Special Relativity and Quantum Mechanics are very well integrated: it was first done by Dirac in ~1932 and led to the prediction of anti-matter which was discovered a few years later with the positron (anti-electron). The Dirac (along with the Klein-Gordon and Proca) equations form the underpinnings of Quantum Field Theory which is what we use in particle physics to describe all the fundamental particles of nature (that we know of) and how they interact (except via gravity). This has Lorentz invariance built into it and is a complete union of QM and SR.
What is harder is to unify QM and GR. This has not been successfully done yet. You can create a quantized gravitational field relatively easily but the problem is that you have to specify a maximum energy scale in order to normalize it (in 3+1D at least). This is bad because there is no justification for a maximum energy scale once you include gravity where the physics will change. Hence either the theory is wrong or there is something else at some really high energy. In either case you cannot use it to make meaningful predictions and so we say we have no valid way, yet, to unify QM nd GR.
Some people are working toward reaching absolute zero.
This guy, however, he is working toward absolute stupid.
...isn't temperature basically a measurement of motion, as many posts have pointed out? If that is true, and absolute zero is the point at which motion completely ceases (which to me says that the universe as a whole would have to reach absolute zero in order for any single part of it to actually reach such a temperature), then, essentially, temperature is just a numerical description of a process. If it is just a description, then absolute zero describes ~motion and any other temperature (no matter how minutely different than absolute zero) describes motion, so it seems to me that the opposite of absolute zero is logically any non-zero temperature. But then again, do we have any really good idea of what exactly motion is, I mean it seems to me that Einstein's theory of relativity shows that motion is a subjective matter, such that motion is only really measured as a differential, and thus that temperature is only really measured as a differential. If that is true, then absolute zero (and probably any kind of absolute hot (is hot==~zero???)), are only useful when comparing one situation to another, and are thus only theoretical tools used to describe extrema of any kind of function regarding temperatures, and there real values wouldn't have many practical uses. But, I clearly have no idea what I'm talking about, so I'll just accuse this thread of being a shameless plug for some new spicy liquor with a hopelessly simple ad-campaign in it's near future.
This allows God to be real, unless declared integer. (See fortune cookie for details.)
It's a small world and it smells funny; I'd buy another if it wasn't for the money; Take back what I paid (SoM)
Temperature is directly related to the velocity of the atoms in a gas or plasma.
No - it is directly related to the kinetic energy of the atoms in a gas and the electrons and ions/nuclei in a plasma (there are no atoms in a plasma). In classical physics this is 0.5mv^2 but this is just the low energy approximation of the true KE which is "ymc^2-mc^2" where y=gamma=1/sqrt(1-v^2/c^2). As you can see this has no upper bound.
Now I have to tape them open.
What is heat and how is it measured?
You have two components: degree and flux. If we consider radiant heat and we make the assumption that a pure vaccuum can have any amount of radiant flux per unit volume (or area, depending on how you measure it), then there is no limit on the amount of flux. (Yes, I realize that is a circular argument.) There is no guarantee that you can have infinite flux in a vaccuum though. Who says the universe is linear in that respect? For instance, radiant energy at any frequency has wave/particle duality. There is a limit to how many particles we can have in a given volume. Therefore there may well be a limit to how much flux you can have in a certain volume of empty space if we limit frequency/wavelength.
The degree of heat is usually expressed in terms of frequency/wavelength. The question then becomes: Is there a minimum wavelength? If space is quantified then there may well be a minimum wavelength. That would set a limit on the maximum energy that any particle can have.
That used to be reversed.
I'm half asleep right now, but are you certain you're not mixing up heat and temperature? The two are not the same, and I could easily see heat increasing without limit but temperature increasing relativistically to a finite value.
It's a small world and it smells funny; I'd buy another if it wasn't for the money; Take back what I paid (SoM)
I think calculation of the Hagedorn temperature at 10^30 K should be taken with a massive grain of salt. String theory has an adjustable parameter, which is the length scale on which the extra dimensions are curled up. Since string theory is supposed to be a model of quantum gravity, and there is only one fundamental length scale in quantum gravity -- the Planck scale -- the general assumption is that if string theory is right, that length scale should be the Planck scale. Converting that length to a temperature, you get the Planck temperature, 10^32 K. If there's a maximum temperature that's 100 times less than that, then that unitless factor of 1/100 has to come from some model-dependent calculation, and the NOVA article carefully notes that it's just this one guy's model that gives 1/100. I think all we can reasonably say at this stage is that if there is any natural scale beyond the scales that have been explored with current particle physics observations, we can only guess that it's the Planck scale, which corresponds to the Planck temperature.
The article doesn't explain very well why there should be any maximum temperature scale, but it's not really that hard to understand. There are model-independent, fairly plausible reasons for believing that there is a limit on the amount of information that a given amount of space can contain. If spacetime was really continuous rather than discrete, then it could contain an infinite amount of information in any volume, so it's reasonable to conclude that spacetime must be discrete. (Lee Smolin's Three Roads to Quantum Gravity spells out this argument in a lot more detail.) If spacetime is discrete, then the only reasonable distance scale for the minimum distance is the Planck scale. That means that a particle can't have a wavelength less than the Planck scale, and therefore it can't have an energy greater than the Planck energy. That means that a gas can't get hotter than the temperature at which every particle has an energy equal to the Planck energy, and that's the Planck temperature.
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"Is There Such a Thing As Absolute Hot?"
Yes, its a very, very spicy vodka.
Understanding is a three edged sword. - Ambassador Kosh Naranek, Babylon 5
It's clear who learned to spell from TV.
you had me at #!
this thread is useless without pics.
An Infiniti is a car, and it will wrap around almost anything into which the driver rams it.
Absolute stupid on THIS planet.
At the big bang (so far as we know) all of the energy (=mass) was concentrated in the same place at the same time. To be any hotter than that would require more energy than exists in the universe.
--- These are not words: wierd, genious, rediculous
This is probably redundant but Ihaven't read all the way down.
Temperature is a measure (the logarithm of, in fact) of the number of available energy states that the particles in question can populate. Absolute zero simply means the ensemble has only one available energy state. This in no way means there is zero energy or zero motion. Atoms will still exist at absolute zero -- unless there's some newfangle theory I missed that claims cold electrons will just fall from their P-zero orbitals.
https://app.box.com/WitthoftResume Code: https://github.com/cellocgw
Unless the spin of the constitute particles of the atom is an integer, where at very low temperatures they should collapse into a Bose-Einstein condensate.
Temperature does not measure the latent energy, chemical energy, etc., though heat does get absorbed and released by those.
Just an ignorant question from somebody who hasn't opened his physics-books in a while:
If absolute zero is when particles stop their brownian motion, what is the reference-frame of that measurement? If 'd measure the motion and energy of an atom in a lab here on earth, and get it to 'stop' relative to my instruments, i'd be measureing absolute zero, right? But couldn;t earth's motion through the universe be interpreted as a 'unilateral brownian motion', which would mean that the atom actually does have at least some energy left in it?
sorry if i'm overlooking something obvious, but this question really intrigues me...
At the top right of the article there is a picture of the Sun, and its caption claims that the Sun's core is about 10^17 degrees. This is about 10 orders of magnitude out, whether you're talking Kelvin, Celsius or Fahrenheit! It's more like 1.6×10^7 K, which supports sustained hydrogen fusion. Any hotter and the Sun would blow itself apart.
Three rights make a left. Freedom of speech, freedom of the press, freedom of assembly.
I thought that temperature was directly proportional to the speed that the electron travels around the atom. Since no matter can travel faster than the speed of light then there may be maximum temperature. Then again I may be wrong again but doesn't the small nuclear force hold the electron in orbit around the atom. Could the electron travel so fast that it reaches an escape velocity?
"absolute zero only applies to our planet... try pluto for example... the temperatures there are a lot cooler than 0K..."
This does not bode well for you.
So... Running really, really, *really* fast is a _bad_ idea for dieting?
Heat is motion energy in a particle. I assume that motion is limited to no more than the speed of light, and that as the vibration approaches the speed of light that relativistic effects would become apparent.
Even if positive infinity wraps around negative infinity (most mathematicians don't agree but there is a minority that thinks that way), this doesn't mean absolute hot means absolute cold, because absolute cold is zero, not negative infinity.
http://www.gnu.org/fun/jokes/eternal-flame.html
I was taught assembler
in my second year of school.
It's kinda like construction work --
with a toothpick for a tool.
So when I made my senior year,
I threw my code away,
And learned the way to program
that I still prefer today.
Now, some folks on the Internet
put their faith in C++.
They swear that it's so powerful,
it's what God used for us.
And maybe it lets mortals dredge
their objects from the C.
But I think that explains
why only God can make a tree.
For God wrote in Lisp code
When he filled the leaves with green.
The fractal flowers and recursive roots:
The most lovely hack I've seen.
And when I ponder snowflakes,
never finding two the same,
I know God likes a language
with its own four-letter name.
Now, I've used a SUN under Unix,
so I've seen what C can hold.
I've surfed for Perls, found what Fortran's for,
Got that Java stuff down cold.
Though the chance that I'd write COBOL code
is a SNOBOL's chance in Hell.
And I basically hate hieroglyphs,
so I won't use APL.
Now, God must know all these languages,
and a few I haven't named.
But the Lord made sure, when each sparrow falls,
that its flesh will be reclaimed.
And the Lord could not count grains of sand
with a 32-bit word.
Who knows where we would go to
if Lisp weren't what he preferred?
And God wrote in Lisp code
Every creature great and small.
Don't search the disk drive for man.c,
When the listing's on the wall.
And when I watch the lightning burn
Unbelievers to a crisp,
I know God had six days to work,
So he wrote it all in Lisp.
Yes, God had a deadline.
So he wrote it all in Lisp.
Is there such a thing as absolute hot?
Yes, she sits in the next cubical.
Someone, think of the hot grits guy!
This reminds me of a question posed in Middle School during our discussion of absolute cold.
So... is there an absolute... toasty?
Ah, the sound of 30 7th graders sputtering with laughter.
Mmm... toasty.
Is it possible that Slashdot could stop republishing stupid stories that have already made the rounds twice on digg and reddit? You're better than this, Slashdot.
I could see that as you heat something up, it will give off lots of blackbody radiation. At a certain point, there may be a practical limit to putting more energy in than is being lost due to the radiation, but I don't see this as a theoretical limit.
JET Program: see Japan, meet intere
Did anybody else read the last bit as "Large Hardon Collider"?
http://www.mathies.com/blog/jessica_bielsm.jpg
Absolute zero has a definition based on the behavior of particles and their interaction.
It is that they have no vibrations, and that they're completely coupled.
Absolute hot should have a similar definition as a target.
As an opposite to absolute zero, it would be that particles cannot be made to vibrate more, and that they are completely uncoupled. Uncoupling requires they not interact with each other, which means they don't "feel" the 4 forces, even after those have unified, supposedly at the Plank temperature. If they still feel the unified forces at 10^32 K, the uncoupling from the unified forces (Force? U-force?) may be greater than the Plank temperature.
Finding a way to measure something that's completely uncoupled without coupling a measurement device to it is going to be a trick, in the real sense. Measuring absolute zero is a trick of taking things very near 0 K and using lasers to control their vibration such that they appear to be closer to 0 K. And in one case I seem to recall to be less than 0 K, evidence that's it's truly a trick. I don't recall anyone getting anything to behave exactly like 0 K except as being in a range around it which the measuring device was unable to resolve well enough to prove the behavior as having absolutely no vibration.
"I may be synthetic, but I'm not stupid." -- Bishop 341-B
she should be the basis for any measurement of hot
Jessica Alba
Margaret Thatcher. Covered in whipped cream
The developers aren't the only ones you've made cry today. How do I get that horrible picture out of my tortured barin? You fiend! Did you learn that awful technique in your CIA "special rendition" class?
mcgrew's razor: Never attribute to stupidity that which can be explained by greedy self-interest
It's wrong to say that temperature is defined by the kinetic energy of molecules, and such a definition is incompatible with systems having a negative temperature (many systems can be arranged to have a negative temperature, but of course none have T = 0). In truth temperature is defined as: 1/T = (change in entropy)/(change in energy) or in words, temperature is inversely proportional to the rate of change of entropy with respect to energy.
All "hot" really means is that the molecules are moving fast.
The maximum temperature would probably be whatever the heck it would be if the molecules were moving at the speed of light.
http://video.google.com/videoplay?docid=4540330056185734698
Turns out Newton's laws *are* wrong. They just aren't wrong *enough* for it to make much of a difference to us when you're talking about for example, day-to-day human activities, most of which involve speeds much lower than the speed of light. For calculating speeds of airplanes and automobiles, Newton's laws are reasonable approximations -- but they are indeed wrong according to the world of relativity.
Since particles shouldn't be able to move faster than light, and temperature is simply a measure of the vibration of particles, wouldn't the maximum possible temperature be the temperature at which the molecules are moving at the speed of light? Perhaps the limit is lower, but I can't see any way there could not be a limit.
I remember my professor talking about "temperature" in my thermodynamics course. He said something about temperature not being the fundamental quantity, it's some sort of (potential?) energy (u), and 1/u is what we call temperature. So as we see temperature go up, u is actually going down, and when it reaches zero and below, temperature actually gets infinite and wraps around to be negative. I don't remember the specifics, as I have a tendency to sleep through class, and my textbook is thousands of miles away atm.
Yes.
Angela Jolene is absolutely hot.
The real Sig captains the Northwestern. This one captains
Of course there is, and her name is Angelina Jolie... :)
-- Ed Carp, N7EKG erc@pobox.com PGP KeyID: 0x0BD32C9B What I'm up to: http://intuitives.mine.nu
What paradox? You're describing two inherently different things:
1) A black hole, which does not release particles (hawking radiation aside) 2) An object that is releasing particles behind and in front of it due to relativistic effects. Just google search "relativistic mass black hole". The very first link is a university FAQ debunking "very fast particle = black hole". http://www.google.com/search?hl=en&safe=off&q=relativistic+mass+black+hole&btnG=Search
So, if there is a speed limit, there must be a heat limit as well.
Patents Drive Free Software as Hurricanes Drive Construction Industry
Duh
Negative temperature is far more interesting. A Pauli paramagnet with negative temperature gives energy to anything that is above absolute zero, no matter how hot.
I think I already experienced that. Habenero Nachos. Not eating them. Just wait a couple of hours.
You're talking about Jessica Alba, right?
Absolute hot is how I like my pizza
supposing absolute hot exists
what would happen if something reached absolute hot?
For a second there I thought this was about vodka.
Sounds like someone believes in temperature wraparound.
Twitter supports and protects racists - by smearing their critics with the "Hate Speech" label.
The concept of negative temperature has been around for quite a while:
From http://en.wikipedia.org/wiki/Negative_temperature
In physics, certain systems can achieve negative temperatures; that is, their thermodynamic temperature can be of a negative quantity. Negative temperatures can be expressed as negative numbers on the kelvin scale.
Temperatures that are expressed as negative numbers on the familiar Celsius or Fahrenheit scales are simply colder than the zero points of those scales. By contrast, a system with a truly negative temperature is not colder than absolute zero; in fact, temperatures colder than absolute zero are impossible. Rather, a system with a negative temperature is hotter than the same system with an infinite temperature.
The answer isn't a number, but rather another answer (which could perhaps be expressed as a number). Light.
It doesn't seem to make sense at first, but the heat is defined by the speed of the particles in the matter. These particles cannot exceed the speed of light. The max temperature then by definition is light, which is the limit that the particle energy and speed could approach.
I am not a physicist, but this just seems to be common sense.
Tibbon
tibbon.com
Is there really such thing as particles that don't move? At absolute Zero, are there really little atoms sitting absolutely still, with electrons or whatnot frozen in place? Do atoms and particles and reality really still exist after all energy has left the building?
For those of you who read A Brief History of Time by a one Mr. Stephen Hawking... You will know that the earth simply rests on the back of a giant tortoise and that tortoise is on a tortoise and so is that one, all the way down!
I'm sick of following my dreams. I'm just going to ask where they're goin' and hook up with 'em later.
When reading this article and the comments below, the whole thing reminded me of knurd and Orakh.
When one reaches both sides, strange things happen and the results are strange.
Luggage survived the experience...
: )
Clausius definition of entropy:
dS=dQ/T
Q is the heat content (in units of energy) of the system, S is the entropy (the logarithm of the number of states available to the system) and T (or kT with constant included) is temperature (defined in units of energy).
S increases rapidly at low temperature. As things get hotter (increasing T) the entropy changes less and less as additional heat Q is applied. At infinite temperature S would approach some finite fixed value.
Generally by adding to Q you make more states available to a system. Atoms can suddenly twist, jerk, lose electrons, shine in X-ray light, etc. Ice can change state to water, or water can change state to steam. As you apply heat (Q) to a system the temperature T stalls when it reaches these points, since dS is so large. Melting and boiling both increase the disorder. As long as the system has a rising number of states to explore as it gets hotter, entropy keeps going up.
If there are only a finite number of states to explore, then you can actually reach a point where you pass maximum entropy and actually start to decrease the entropy of a system by adding more energy to it- if there are fewer available states at that energy. T switches from positive to negative infinity. As more energy is pumped in, the system is dominated by fewer and fewer high energy states. That's how a laser works; technically a population inversion has to be created in a laser where more atoms in a crystal are in an excited state than the corresponding ground state. If at least half of them aren't in the excited state the light won't make it out of the crystal. As you pump the laser past 50% the number of available states goes down (approaching a limit not reached in practicality where all atoms are in the excited state). So the concept of negative temperature would be useful for describing that system, in terms of those particular transitions.
So basically it's zero -> positive infinity/negative infinity -> -0 or "absolute hot" which is approaching a single most energetic state available. This is similar to absolute zero which approaches a single least energetic ground state. Except it's approaching zero from the other direction- it's more like "absolute minus zero".
No, no ! In dot code (a form of Morse code without the dashes). The slash is used to escape - thought everybody knew.
How many beans make five, anyhow ?
Would it really matter ?
How many beans make five, anyhow ?
. . .
(and no, the cat's not got my tongue)
Om
It's an interesting premise, but not worth pursuing to wits' end.
You can chase absolute morality too, as long as you apply it to your own culture or, at a stretch, the human race.
Absolute hot/cold is only relevant our own physics.
Of course, before Relativism, "our physics" meant something completely different again.
Some people have mentioned that relativity does not impose a maximum temperature, since although it has a maximum particle speed, kinetic energy and therefore temperature is infinite.
However, when you bring thermodynamics into it, things become more complicated.
Thermodynamics is derived from the statistical behavior of large collections of particles. The thermodynamic laws are derived from the partition function, which is a sum of the form exp(-beta E), where beta ~ 1/T is inverse temperature and E is the energy of a state of the system. The sum is over all the possible states.
In some systems, the number of states increases exponentially with energy, so the sum eventually diverges even though each term is an exponentially decaying function. The temperature at which this happens is the Hagedorn temperature mentioned in TFA. You can think of this situation as "entropy winning over energy", as the number of states determines the system's entropy.
In particular, in relativistic quantum field theory, relativity requires that it be possible to create particles matter-antimatter pairs if you put enough energy in the system.
One thing that can happen in some relativistic systems (though it doesn't have to happen) is that when you put enough energy into a system, it mostly goes into creating new particles instead of making existing particles go faster. Thus, the Hagedorn temperature: as you reach it, all the energy you're putting in to heat the system goes into particle production, and nothing goes into raising their temperature. (This is not the only way in which a system can have a Hagedorn limit, nor do all relativistic systems have this limit, but it can happen.)
TFA implies that this limit only exists in string theory. But it exists in other theories as well. For instance, quantum chromodynamics, the theory of the strong nuclear force, has a Hagedorn limit. But in QCD, it is thought that it's not a true maximum temperature. Rather, the divergence of the partition function there signals the presence of a phase transition, from quarks confined in hadrons to a free quark-gluon plasma. Perhaps in string gas cosmology it's a true limit; I don't know much about that.
If the entropy increases even faster than exponentially, you can get weird situations like negative heat capacities, i.e., where adding more energy to a system lowers its temperature! There, you actually take kinetic energy from existing particles and put it into particle creation, creating so many new particles that the overall temperature of the system decreases.
Incidentally, the beta factor mentioned above in the partition function explains another point in TFA, about negative temperatures. In statistical thermodynamics, you can see that the key parameter is not temperature T, but inverse temperature beta ~ 1/T. As you increase temperature towards infinity, beta decreases to towards zero from above, so hotter temperatures correspond to smaller betas. You can imagine how a negative beta, then, corresponds to an even hotter temperature than any positive beta. In other words, negative temperatures are hotter than positive temperatures. As beta is decreased smoothly through zero from above, temperature increases to positive infinity, jumps discontinuously to negative infinity, and then approaches zero temperature from the other side. The hottest temperature, then, is -0 K — or rather, the limit as you approach 0 K from below, instead of above (which is a different limit from the perspective of the more fundamental parameter beta).
For a little more about the Hagedorn temperature, read this historical essay and this paper (section 2). Wikipedia has a good discussion of negative temperature.
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I don't know about you guys, but my head hurts.
Sudo would let me be God, temporarily. /proc/kcore would force me to reverse-engineer quite a bit before even attempting to make a modification, and I'd be as likely to gain godlike powers as I'd be to crash the entire Universe.
Don't thank God, thank a doctor!
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As proposed here:
Ultimate HOT + COLD Answer!
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- aqk
F U
I thought the amount of randomness counted for the temperature of a system. Speed cannot be the sole factor.
So I would have guessed something like speed * entropy = temp.