h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Many moons ago, Jan^ and I had a most stimulating argument about the possibilities of temperatures below absolute zero. See: http://www.h2g2.com/forumframe.cgi?forum=19585&thread=19355
Jan^ went off to get a tame scientist to back up his argument. He never returned. Does that mean I won?

That depends what was your side of the argument?

You mean you didn't read the argument? Tsk!
Based on 'The Physics FAQ' (in particular 'Below Absolute Zero - What Does Negative Temperature Mean?'), I argued for the existence of negative absolute temperature. Where do you stand?

Negative temperatures don't make sense in the same way that negative speeds don't, I think...

26199

But negative velocities do (going backwards)

True enough, but I think that the comparison was attempting to be made that negative absolute temperature (which is a scalar, not a vector quantity) is as incredible as negative speed (also a scalar, not a vector quantity). This, I think, is inaccurate given the discussions put forth by Queezer and the Physics FAQ he referenced.

The concept of temperature below that of "absolute zero" is something I (being a chemical/nuclear engineer and not a condensed matter physicist) found fascinating, informative, enlightening, and a little confusing. Heh. The arguments put forth by Queezer and stemming from the excellent answers in the Physics FAQ, I have to say that I am convinced that the condition is indeed possible, even likely in certain circumstances. Admittedly, the definition of "temperature" is more complex than the one used by the lay person (how hot/cold it feels, or how much it raises/lowers the thermometer). But using the thermodynamic definition of temperature and the nature of thermodynamics in condensed matter physics, I have to say that I agree. Negative absolute temperature can exist, confusing as it may seem.

For you non-physicists out there (of which I am one), I have a bit of advice on how to wrap one's mind around this concept. It doesn't help to think of it in our "classical" sense of what temperature is, since we usually experience temperature on a macroscopic scale. To attempt to apply the things we know about our world by our own physical experiences to those of the atomic realm can be futile and confusing. In this case, unless you are REALLY keen on understanding the thermodynamic definition of temperature when one gets to the atomic level, I'd recommend you just take someone's word for it as there is really no simple way to explain it without using the mathematical definition of temperature (as the differential of entropy with respect to energy) and some hefty condensed matter physics theory. I know, nice advice, eh?

If you are keen to read this stuff, I recommend reading the article that Queezer referred to (http://math.ucr.edu/home/baez/physics/neg_temperature.html), but only if one has an interest in how physicists (and some engineers) think about temperature. That is, in terms of the entropy and energy of a system, which is the fundamental reason we feel heat and cold (really just an absence of heat). It doesn't make sense to think of material with negative absolute temperature as being "colder than cold", as heat can actually flow FROM that system to another system of a higher absolute temperature ... which, by our experience, would feel "hot" - even though it has a lower absolute temperature. Strange stuff, physics.


JD

You say negative speeds make no sense. But then again, the same was said about higher spatial dimensions, negative energy and God knows how many other accepted modern scientific principles.

As scientists we have to be open minded and accept that things may be possible even though we cannot see our way clear as to how.

/Mike

Negative speeds *don't* make any sense, simply because of the definition of speed. Speed is distance travelled divided by time taken. Distance travelled is always positive or zero, time taken is always positive or zero. Therefore speed is always positive or zero. Velocity, as The Cow pointed out, can be negative. Which is why I said 'speed'.

When it comes to the physical universe, there's pretty much always some degree of uncertainty. But when we're dealing with our own definitions of things, we stand a chance...

26199

Excellent, a convert! Thanks for your support!

From what I heard (last year's physics class) Absolute 0 is a a bit like the Speed of light. you can't reach it, you can get pretty close, but not all the way there. Another problem it would seem with negative temp. is that once you get to somewhere around 99.99% of absolute 0, the individualities of the electrons sort of collapse and then you have a mass that is composed of waveforms, and then they have wave particle duality etc. These substances are known as Boze-Einstein Condensates. Anyway, tell me what you think . . .

Yes and higher spatial dimensions don't make any sense either. Objects have length, breadth, width and duration. How can an object project in a direction other than that? But they can. In fact alot of current scientific principles, particularly the Grand Unification Theories, depend on their being 10 or even 26 spatial dimensions.

Time taken is always positive or zero? That's debatable. What if you ran time backward? Could that be a negative speed?

/Mike

I don't have any problem with multiple dimensions...

But time taken is still positive if you run time backwards, in the same way that a ruler's length is still positive if you turn it the other way around. You're measuring the distance between two points in time, and that can never be negative.

So I'm going to have to maintain that negative speed is meaningless

26199

You think? That is assuming that time is a scalar quantity. But when you start considering the direction of time, surely it become a vector?

/Mike

If three years of a Condensed Matter PhD has taught me anything, it is that theoreticians are best left to their own devices. It is like the old joke about the physicist who can predict the winner of every horse race, provided the horse is perfectly spherical and in a vacuum. The article mentioned only applies to a small, and extremely artificial system which none of us will ever be bothered by. I suggest you just forget all about it.
As to never getting to absolute zero, that is the point, that to make something cold, you have to remove it's heat energy. Once you are down to milli-Kelvin (is that like a little Victorian? ) temperatures, this can only be achieved by putting something colder in contact with your first object. Thus, as you don't have something at absolute zero to start with, you can't put it into contact with your first object, to cool that to absolute zero. Does that make sense?
Also, on negative time, yup time is a vector, it can be negative. While physicists can't run time backwards, theoretical particle physicists will tell you what would happen if they could. Disturbingly, things do not always happen the same (but backwards) as you would expect. This is why I dropped particle physics like a rabid tiger.

Munchkin (you caught him just before a discusion on the behaviour of electrons at 45mK, which explains a lot)

Mike writes:
"Yes and higher spatial dimensions don't make any sense either. Objects have length, breadth, width and duration.
How can an object project in a direction other than that? But they can. In fact alot of current scientific principles,
particularly the Grand Unification Theories, depend on their being 10 or even 26 spatial dimensions. "

I don't think it's accurate to compare the concepts of higher dimensions with the concept of speed. See below.

Mike also says:
"Time taken is always positive or zero? That's debatable. What if you ran time backward? Could that be a negative
speed?"

Not using the mathematical and engineering definition of speed. Speed is defined to be the absolute value of the scalar componont of a velocity in a given direction. Where as velocity is defined purely based on the rate of change in position (relative to something else) over time, speed is a simplified version of velocity intended for certain conventions necessary for engineering gauges and such. You car reads speed. You can drive forwards or backwards and you speedometer will register a positive quantity of speed as you do. It's the same reason why driving in reverse will not remove miles from your odometer. At least, modern cars. It doesn't matter which direction YOU are pointed when you move ... for computing speed, the given direction of movement is always taken as positive regardless of the change of that direction (that is what is meant by the 'scalar component of the velocity vector' - direction changes are irrelevant and the direction of the rate of change of position is always taken as positive). The concept of running time backwards is similarly irrelevant to the overall concept of speed. I would suppose that theoretically anything is possible, but speed, as it is defined and used in practical applications, simply assumes the standard convention that time always moves forward. Here on Earth, the cases that this does not happen are, at last count, not very many at all. None, in fact, unless something new's popped up on the "Paradox Periodical" board that I missed. And, since everyone lives on Earth at the moment (or at least, with a few hundred thousand miles) it seems logical to assume that time will continue to march forward (for the time being, heh) and that speed will indeed remain positive.

I don't understand how time could be a vector quantity, as Mike suggests later. However, even if it were, the same logic applies. Speed is a conventionally defined quantity based on the absolute value of the scalar portion of a velocity in a given direction. If time were a vector (which implies time can have multiple directions to travel in - can anyone imagine what time going sideways would mean?), a whole lot of equations would have to be re-done, and would become needlessly complex. Why needlessly? Because everything we've done so far with time having just one degree of freedom has worked quite well. I hereby refer all further discussion on this to strict adherence to the KISS** principle applied frequently and with great success in engineering (nothing to do with the rock band).

The concept of negative speed is not comparable to the ideas of other dimensions existing or not existing because speed is, very simply, an easy and practicable way of thinking about velocity without all that tedious mucking about with direction and other dimensions and what have you. When one thinks about higher dimensions, one is by definition mucking about with other dimensions and what have you. Which is all well and good, of course, but it means absolutely zilch to any given police officer who wishes to cite you for exceeding the speed limit on a given road. Don't even try to argue with them about time conventions, instantaneous derivatives, reflectivities, quantum effects, and what have you. They don't have much of a sense of humor when it comes to matters of deep physics, trust me on this.

So you see, likening the two concepts just doesn't make sense. As an engineer who works closely with physicists (some of whom are of the theoretical type), this sort of thing is quite frequently a source of mutual amusement and good-natured ribbing. I frequently find myself chuckling at their crazy concepts while they frequently seem to shake their heads in bemusement at my seeming inability to imagine the 'simplest' abstract concepts and constructs. It usually drives everyone else mad, but that's another point of view entirely. I think I've beaten this topic to death now. Heh.


JD

**KISS = "keep it simple, stupid" ... it's a very common acronym around here. No offense intended to those that wish to make things complicated.

Speed is only a scalar quantity because distance travelled is a scalar and time is scalar. If time was a vector, then speed must also be a vector - but a different vector to velocity.

Time can travel both forward and backward... as demonstrated by particles such as tachyons which travel backward through time. Time travelling sideways is frequently interpreted as travelling through parallel universes.

Thing is, time CAN move in more than one direction, so must be a vector!

/Mike

Oh, and I know there isn't really any comparisson between higher dimensions and negative speeds. I was simply pointing out that they're both nonsensical ideas.. but one happens to be true. Why not the other?

That clears it up thanks.

Ah, isoentropic cooling again. Systems of higher absolute temperature have less dimensions than those of lower.

Its all down to degrees of freedom in the Boltzman equation.

Anyway, speed = | v | by definition. A modulus cannot be negative, again by definition. That is what was refered to when "taking the scalar component" was bandied about. Magnitude is always positve, direction isn't.

Also, I can visualise (in some way) up to 4D. Maths can go up to infinite D. It makes as much sense as anything else. The models, in fact, are simpler in higher dimensional space and we have reason to believe that although we only have freedom in 3 integer dimensions, and movement in 4, there are either 11 or 26 dimensions of spacetime.

Just because you can't see it, doesn't mean its not there.

So s = | v | hmm? Well then I say that definition is wrong.. because I insist on time being a vector.

It is not unknown for new principles to throw out old definitions. As I mentioned elsewhere recently.. Newtonian Gravity F = GMm/r^2 is wrong. It's close, but it's wrong. Einstien proved that and came up with his own, more accurate version based on spacetime curvature.

By definition, s = d/t where d is distance travelled and t is time. Any vector multiplied by a scalar results in a vector. If time is a vector (for it has both direction and magnitude) and distance is scalar then speed must be vector.

This is no more or less acceptable than the idea of negative energy, which just in recent years has become an accepted idea - principally associated with exotic matter found around wormholes.

/Mike

Time *is* a vector in maths... physics is taking longer because to accept this because it requires throwing out causality, no small thing.