Can pressure be negative?

[Ziggurat]

Quantum physics formally assumes infinitely positive or negative temperatures in descriptions of spin system undergoing population inversion from the ground state to a higher energy state by excitation with electromagnetic radiation. The temperature function in these systems exhibits a singularity, meaning the temperature tends to positive infinity, before discontinuously switching to negative infinity.[3] However, this applies only to specific degrees of freedom in the system, while others would have normal temperature dependency. If equipartitioning were possible, such formalisms ignore the fact that the spin system would be destroyed by the decomposition of ordinary matter before infinite temperature could be reached uniformly in the sample.

C. Kittel, H. Kroemer (1980). Thermal Physics (2 ed.). W. H. Freeman Company. ISBN 0-7167-1088-9.

Turns out the quote isn't even from Kittel and Kroemer, but from Wikipedia. The quote references Kittel and Kromer, but it's not from Kittel and Kromer. Taking an actual quote from Kittel and Kromer, Appendix E, page 460 (no web link - I'm transcribing this by hand from the book on my shelf), which covers negative temperatures:

The concept of negative temperature is physically meaningful for a system that satisfies the following restrictions: (a) There must be a finite upper limit to the spectrum of energy states, for otherwise a system at a negative temperature would have infinite energy....

In other words, for such a system, we do NOT have infinite energy. Continuing (page 461):

(b) The system must be in internal thermal equilibrium.
...
(c)The states that are at negative temperature must be isolated and inaccessible to those states of the body that are at a positive temperature.

Most systems don't meet these restrictions, but some do. Since we can satisfy these requirements in real, physically realizable and tested systems, negative temperatures are quite real. Now that we've established negative temperatures, what do Kittel and Kromer have to say about infinite temperatures? From page 462:

The temperature scale from cold to hot runs +0 K,..., +300 K,..., +∞ K, -∞K,..., -300 K,..., -0K. Note that if a system at -300 K is brought into thermal contact with an identical system at 300 K, the final equilibrium temperature is not 0 K, but is ±∞ K

So we cannot have negative temperatures without infinite temperatures. And we have negative temperatures. Therefore we have infinite temperatures. According to the source you dishonestly claimed was the source of your quote.

 

[Ziggurat]

When we talk about temperature being infinite, we are talking about the temperature as it is mathematically defined, not as it is physically measured.

This is not correct. The temperature, as measured, is indeed infinite. You just need to keep in mind what it means to measure temperature, and be careful about how you do it for a negative-temperature system.

Every single thermometer that exists measures temperature by measuring something else, some other state variable which has an established temperature dependence. So an alcohol thermometer measures the volume of the alcohol, a bimetalic strip measures an angle of deflection, a thermocouple measures a voltage, etc.

But that's not all: most thermometers actually measure their own temperature, not the temperature of another system. When the thermometer is in thermal equilibrium with another system, we know (from the definition of temperature) that the temperature of the thermometer itself will match the temperature of the other system, but that point is quite important. That's why you cannot measure a negative or infinite temperature with, say, a mercury thermometer: the thermometer itself doesn't support such temperatures, so if it reaches thermal equilibrium with the system we're trying to measure, that thermal equilibrium will necessarily be positive finite temperature.

So how do you measure negative or infinite temperatures? Well, you do it the same way you determine the temperature of the thermometer itself: you measure something else about the system itself, and you relate that to temperature. That's all any temperature measurement is to begin with, so if we're not comfortable doing that, then we're not comfortable with temperature at all. So what's the appropriate something else? In the example I gave, it's simply the magnetization. If the magnetization is in the opposite direction to the applied field, the temperature is negative. If the magnetization is zero, the temperature is infinite. That's rather easy to physically measure.

 

[Calrid]

Just reading the backposts. The irony here is great.
Yes, the irony here is great.

Originally Posted by Calrid View Post
Yeah for the most part what they have said is true however the fog descends when they resort to describing maths limits or infinities as experimental reality. The limits of integrals aren't called limits for a laugh they are the limit to which numbers approach, in the same way infinities in physics are as said evidence of a mistake and usually denote that the equation is not 100% accurate but is accurate within its limits (hence renormalisation) although tbh we have no idea if its a pictoral representation anyway and the equations are inductive not deductive.
A definite integral's limits of integration are just the endpoints of an interval. The fundamental theorem of calculus says

\[ \int_a^b dF = F(b) - F(a) \]

You've gotten that wrong before, and were corrected. You ignored that correction. Getting freshman calculus wrong and continuing to get it wrong is not the best way to establish your credibility.

Originally Posted by Calrid View Post
Some anonymous nobody no matter how highly educated they are (or claim to be). is not going to be all that reliable.
Originally Posted by Calrid View Post
An important and valuable lesson for me is not to trust anyone's credentials, especially when they spend much of their time attacking other peoples and don't seem to have formed any sensible conclusions on particular issues.
Originally Posted by Calrid View Post
That is after all what distinguishes good science from crackpots. Integrity and openness and a willingness to learn. I will learn but I will not blindly accept nonsense from people.
Yes, the irony here is great.

Originally Posted by Calrid View Post
Which is ironic as the subject is being studied less and less and physics departments are shutting all of the place in my country. Our university lost ours and the professors were either layed off or merged with the maths department. Which is tragic really. Means I can't study this locally and have to go through the OU, or travel all the way to Southampton to get on a course, which is just too expensive to do anyway £9000; I guess I'll have to go sell my cow if I want to climb that beanstalk? *********** Tories.
I'm sorry to hear of your country's misfortune and its tragic consequences for your university. I feel special sorrow for your cow.

Physics is still being taught at my current university, at the universities I attended as a student, and throughout my country. Calculus also.

Are you a native English speaker? No seriously because clearly the context there makes it obvious what sort of concept I am talking about, infinity is not a number (well outside of some hypothetical guff about sets, but who cares about that)? The first time you said this I ignored it as I was referring to infinity as a limit, not x=1,2..10 as limits. I would respect you a hell of a lot more if you weren't being unctious and sucking up to this guy as well. Your point is trite and semantic, that's why I don't accept it in context.

Last time I checked by most definitions infinity is unbounded and asymptotic. It does not bound a finite quantity by definition it shows us a limit to which some value could approach if infinity was its limiter, which is what I was on about. At infinity things may converge but it is a limit for a very good reason, nothing physical can achieve it without the laws of physics being broken.

Pity they don't teach reading comprehension and the fundamental nature of context at your University, really isn't it. When you write out a Taylor-Maclaurin series do you actually write out all the infinite steps, or assume it is accurate by axiom? The difference is key.

Was reading Chromer on high temperature mechanics, infinite temperatures and their dependance on negative kelvin temperatures.

One question does that mean that its actually physically possible to measure something as having infinite heat or temperature? That seems paradoxical to me? Or is it just a theoretical limit of the calculus within which temperatures may exhibit finite temperatures.

A quick google turned up absolute hot, which is AKA the planck temperature or the temperature at the big bang, so this would seem to contradict an actual measurable infinity.

Am I getting unnecessarilly confused as I always assumed infinity was a purely mathematical concept, not a physical reality? For example in kind of the same way 0k is not achievable infinite k is not achievable in experiment.

Infinite temperature (or negative temperature) is something that can only be achieved for a system with a finite number of discrete energy levels, and a finite number of particles populating those levels. In that case, infinite temperature is characterized by case where all of the levels, from lowest to highest, have populations that are equal within small statistical fluctuations. If you create a population inversion in such a system (as in a laser), then the system can be said to have negative temperature by the same definition.

However it is important to realize that these are highly-specific cases which can only be achieved with the input of more energy than comes out, so everything is consistent with the 2nd law (and 3rd law) of thermodynamics. In the broader sense of "how hot can I get this arbitrary sample of bulk matter", infinite temperature is fundamentally unobtainable, as is negative absolute temperature.

http://www.physicsforums.com/showthread.php?t=499474

This is a forum that actually has some scientific credibility, unlike this one which just seems to be a load of blind leading the blind people from the impression I have got.

If no one on the above forum sees fit to accept the reality of infinite temperature in experiment, why the hell do you all accept it so readily.

So lets end the dance once and for all and you put your money where your mouth is. Accept the Calrid Challenge and win your $1 million, post on that thread that physical infinities can be measured, ie temperature in materials that show an infinite temperature, or conversely you can just keep posting your opinion like anyone cares? Take it to the judge.

Either way if you don't post now, and get an answer from an acceptable third party, I am just going to declare you a crackpot. And everyone on this forum should take note you don't have the guts to put your money where your mouth is and have your views confirmed by real experts not people who imagine they are.

And yes a resort to authority is valid before this guy says it isn't again. This is not philosophy, science is reliant on authority (and experiment therein). Otherwise no one would believe anything. Don't quote maths at me show me an experiment that has claimed to measure anything infinite in a thermal sense except as a peculiarity of maths.

Will you people stop perpetuating scientific myths. You should know damn well better not to misrepresent maths as reality because you never learnt the difference, maths is an approximation, it is useful to understand the difference between infinite limits and actual physical reality. The science section is not a skeptical section, it's a bunch of credulous people, believing any guff some self styled expert claims just because he was right in the past.

Learn what experimental science actually is, not what you believe it is. There is a difference between theory and practice in this case.

After 2 months of being misinformed and misrepresented by frauds I am tired of repeating the facts only for people to then misrepresent that too. Yes infinity is a concept not a numerical and bounded quantity (with the exception of the universe). No infinite temperature cannot be achieved physically, as you've now been told by two separate experts, and two separate and reliable links. Get over yourselves, just accept this guy can be wrong.

These people are all telling you this and yet you continue to maintain the lie in the face of real scientists.

 

[Ziggurat]

Oh goodie, looks who's back!

At infinity things may converge but it is a limit for a very good reason, nothing physical can achieve it without the laws of physics being broken.

This is trivially false. Sol's example of the slope of a surface is a perfect illustration of how a physical quantity can become infinite without anything strange happening.

http://www.physicsforums.com/showthread.php?t=499474

This is a forum that actually has some scientific credibility, unlike this one which just seems to be a load of blind leading the blind people from the impression I have got.

Oh lookie, SpectraCat's response is pretty much the same thing I said!

If no one on this forum sees fit to accept the reality of infinite temperature in experiment, why the hell do you all accept it so readily.

Small problem: somebody on that board did accept the reality of infinite temperature. Which makes you a liar.

So lets end the dance once and for all and you put your money where your mouth is. Accept the Calrid Challenge and win your $1 million

Since you obviously don't have $1 million, you're just revealing yourself to be a liar in yet one more way. I have no interest in playing by the conditions set by a liar.

And yes a resort to authority is valid before this guy says it isn't again.

Then let's appeal to Kittel and Kroemer. I gave you the relevant quotes. They back up what I said. Yet you still haven't come to terms with them.

This is not philosophy, science is reliant on authority

No, actually, it's not reliant on authority. But even if it were, you'd still be just as wrong.

Don't quote maths at me show me an experiment that has claimed to measure anything infinite accept as a peculiarity of maths.

You can't discard the math. The math is the definition of temperature.

But then, you still haven't figured out what temperature is.

Learn what science actually is, not what you believe it is.

After 2 months of being misinformed and misrepresented by frauds I am tired of repeating the facts only for people to then misrepresent that too. Yes infinity is a concept not a numerical and bounded quantity (with the exception of the universe). No infinite temperature cannot be achieved physically, as you've now been told by two separate experts, and two separate and reliable links. Get over yourselves, just accept this guy can be wrong.

The only established expert presented so far is Kittel and Kroemer, and they disagree with you. As for your physicsforums friends, well, I've got no idea who they are. Drakkith seemed to agree with you about infinite temperature but provided no justification. SpectraCat disagreed with you and agreed with Kittel and Kroemer. He tried to futher explain the concept to you, but clearly the effort did not succeed.

The fact of the matter is that you still don't even know what temperature is. All of your mistakes originate here. You will never figure this out until you learn what temperature is, and you cannot learn what temperature is until you learn the math behind its definition. And yes, you CANNOT define temperature without the math.

 

[Calrid]

Oh goodie, looks who's back!



This is trivially false. Sol's example of the slope of a surface is a perfect illustration of how a physical quantity can become infinite without anything strange happening.



Oh lookie, SpectraCat's response is pretty much the same thing I said!



Small problem: somebody on that board did accept the reality of infinite temperature. Which makes you a liar.



Since you obviously don't have $1 million, you're just revealing yourself to be a liar in yet one more way. I have no interest in playing by the conditions set by a liar.



Then let's appeal to Kittel and Kroemer. I gave you the relevant quotes. They back up what I said. Yet you still haven't come to terms with them.



No, actually, it's not reliant on authority. But even if it were, you'd still be just as wrong.



You can't discard the math. The math is the definition of temperature.

But then, you still haven't figured out what temperature is.







The only established expert presented so far is Kittel and Kroemer, and they disagree with you. As for your physicsforums friends, well, I've got no idea who they are. Drakkith seemed to agree with you about infinite temperature but provided no justification. SpectraCat disagreed with you and agreed with Kittel and Kroemer. He tried to futher explain the concept to you, but clearly the effort did not succeed.

The fact of the matter is that you still don't even know what temperature is. All of your mistakes originate here. You will never figure this out until you learn what temperature is, and you cannot learn what temperature is until you learn the math behind its definition. And yes, you CANNOT define temperature without the math.

Edited by LashL: 

Removed breach.

I know what temperature is its not the definition I disagree with its your bemusing ideas that claim that the states of matter reflect maths in real experiment.

Edited by LashL: 

Removed breach.

Kroemer does not make any claim about experiment, the quote is moot, it only refers to calculus. No such experimental paper is provided, nor could it ever be. It is not experiment it is a text about the maths involved.
Anyone who works in the field or who has worked in the field beyond PhD level is an accepted expert. These people do, take it up with them.

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[Ziggurat]

Edited by LashL: 

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My claim is that Kittel and Kroemer are correct. It's strange that you think claiming a standard physics textbook is correct requires any kind of courage. It's also strange that you still haven't figured out that SpectraCat agreed with me.

I know what temperature is

I don't think you do. If you did, you'd recognize that the claim that infinite temperature requires infinite energy is wrong, which is what you've said before. And the only person to actually back you up on that forum made the same mistake.

Edited by LashL: 

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And yet, I'm not the one lying about what people in other forums are saying.

You know it and you are too scared to take it to anyone but those on this forum, because you know they would tell you in experiment no such thing is achievable.

Why would I be scared of that happening when it already DIDN'T for you?

Hell they have told you, and yet you cannot accept reality.

"They"? Who is this "they"? You've got ONE guy who disagreed with you, and he made the same mistake you did. And you've got someone else who disagreed with you and agreed with me. What's the reality? Again, I'll defer to Kittel and Kroemer.

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I don't need to. The claim has already been put somewhere that matters by Kittel and Kroemer.

Physicsforums is moderated by both experimental and theoretical scientists in the field and experts in the mathematical field. It is highly regarded as the finest source of physics information on the web, and the largest group of experts on any forum on this subject.

So maybe you should pay attention to SpectraCat.

Edited by LashL: 

Removed quote of moderated content and response to same.

Kroemer does not make any claim about experiment

Yes, actually, they do. And it's Kittel and Kroemer. Two authors.

the quote is moot, it only refers to calculus.

No, it refers to the definition of temperature. How can the definition of temperature be moot to a conversation about temperature?

No such experimental paper is provided, nor could it ever be.

Not true. Three experimental papers are referenced: Phys. Rev. 81, 279 (1951), Phys. Rev. 106, 160 (1957), and Phys. Rev. 109, 1441 (1958). Do you even have access to the Kittel and Kroemer book? Or are you just guessing about its contents?

 

[Perpetual Student]

I thought this was settled weeks ago.

 

[Ziggurat]

I thought this was settled weeks ago.

No. Calrid never figured it out or gave up, he simply got suspended for a month. And now the suspension has been lifted, so he's back. We'll see how long he lasts this time. My guess is he won't last the week.

I'm not registered at Physics Forums, but I think he's Schrodinator over there. That name appears with a strike through, which suggests to me that he might have been banned there too.

 

[Tubbythin]

I'm not registered at Physics Forums, but I think he's Schrodinator over there. That name appears with a strike through, which suggests to me that he might have been banned there too.

Just noticed he is almost Dirac backwards.

 

[Calrid]

Removed entire post as it was nothing but breaches of Rule 12 and Rule 0.

Replying to this modbox in thread will be off topic  Posted By: LashL

 

[Ziggurat]

Oh, and by the way, I think that Calrid does not in fact have access to a copy of Kittel and Kroemer. In that Physics Forum thread he linked to, he used a wikipedia quote which references K&K, but the quote isn't from K&K. He made that same error in this thread, but evidently repeated it even though I pointed out that it's not from K&K.

 

[Calrid]

Cut out the personal attacks and name calling.

Replying to this modbox in thread will be off topic  Posted By: LashL

 

[Ziggurat]

So what I am saying is wrong because I am banned?

No. You're banned because you can't behave yourself.

But that's not why you're wrong. You're wrong because you refuse to learn. You couldn't even figure out that SpectraCat was agreeing with me and with Kittel & Kroemer, and pointing out that you were wrong. Hell, you haven't even bothered to learn what temperature is, or why we define it the way that we do.

 

[Ziggurat]

Come on where are your balls?

I see you're trying to prove me right about not lasting the week.

I have the book

Then why did you quote from Wikipedia and attribute it to the book, rather than actually quote from the book?

The fact is if those papers ever made the claim such things actually exist, they would of never been published

Nonsense. Negative temperatures require the existence of infinite temperatures. It would, in fact, be a MORE extraordinary claim to say that negative temperatures can exist without infinite temperatures. That would require a discontinuous Beta(E) function, and that would be quite remarkable indeed.

Furthermore, the experimental reality is quite simple. A paramagnet with magnetization opposite the field has negative temperature, and those papers demonstrated that such systems can be produced. A paramagnet with zero magnetization has infinite temperature. It would be amazing to claim that a paramagnet at negative temperatures (antiparallel magnetization) can cool down to positive temperatures (parallel magnetization) without passing through zero magnetization. It would be even more amazing to claim that negative-temperature paramagnets didn't cool down to positive temperatures. And the fact that a paramagnet with zero magnetization in a field has infinite temperature is a direct and unavoidable consequence of the standard definition of temperature.

But you haven't challenged the standard definition of temperature. In fact, you have not even indicated that you understand or even know what that standard definition is.

 

[W.D.Clinger]

Calrid has asked me some personal questions. I will answer his questions and ask some more general questions of him.

Are you a native English speaker?

Yes.

No seriously because...

Seriously.

I would respect you a hell of a lot more if you weren't being unctious and sucking up to this guy as well.

Seriously: Why should I (or anyone else) care whether you respect me (or anyone else)?

Pity they don't teach reading comprehension and the fundamental nature of context at your University, really isn't it. When you write out a Taylor-Maclaurin series do you actually write out all the infinite steps, or assume it is accurate by axiom? The difference is key.

Taylor's theorem is a theorem, not an axiom. Sometimes a Taylor series contains only a finite number of nonzero terms, in which case it would be fair to say I have written out the infinite series in full after I have written out those nonzero terms.

Either way if you don't post now, and get an answer from an acceptable third party, I am just going to declare you a crackpot.

Why should I (or anyone else) care whether you declare me (or anyone else) to be a crackpot?

After 2 months of being misinformed and misrepresented by frauds I am tired of repeating the facts only for people to then misrepresent that too.

...snip...

These people are all telling you this and yet you continue to maintain the lie in the face of real scientists.

Why should I (or anyone else) believe you can distinguish real scientists from frauds?

ETA: Alas, I will never learn the answers to those questions, because Calrid was banned about 5 minutes before I posed them.

 

[Ziggurat]

No. Calrid never figured it out or gave up, he simply got suspended for a month. And now the suspension has been lifted, so he's back. We'll see how long he lasts this time. My guess is he won't last the week.

Looks like I was overly generous. But it was an easy call.