## Cooling To Absolute Zero Mathematically Outlawed After a Century (newscientist.com) 210

After more than 100 years of debate -- which at one point even elicited interest from Albert Einstein and Max Planck, physicists have finally offered up mathematical proof of the third law of thermodynamics, which states that a temperature of absolute zero cannot be physically achieved because it's impossible for the entropy (or disorder) of a system to hit zero. While scientists have long suspected that there's an intrinsic 'speed limit' on the act of cooling in our Universe that prevents us from ever achieving absolute zero (0 Kelvin, -273.15 C, or -459.67 F), this is the strongest evidence yet that our current laws of physics hold true when it comes to the lowest possible temperature. From a report on NewScientist:

*Now Jonathan Oppenheim and Lluis Masanes at University College London have mathematically derived the unattainability principle and placed limits on how fast a system can cool, creating a general proof of the third law. "In computer science, people ask this question all the time: how long does it take to perform a computation?" says Oppenheim. "Just as a computing machine performs a computation, a cooling machine cools a system." So, he and Masanes asked how long it takes to get cold. Cooling can be thought of as a series of steps: heat is removed from the system and dumped into the surrounding environment again and again, and each time the system gets colder. How cold depends on how much work can be done to remove the heat and the size of the reservoir for dumping it. By applying mathematical techniques from quantum information theory, they proved that no real system will ever reach 0 kelvin: it would take an infinite number of steps. Getting close to absolute zero is possible, though, and Masanes and Oppenheim quantified the steps of cooling, setting speed limits for how cold a given system can get in finite time.*
## Wow (Score:5, Funny)

Thats really cool!

## Re:Wow (Score:5, Funny)

Thats really cool!

Not as cool as it theoretically could be.

## Re: (Score:3, Funny)

You're lucky, I couldn't quite finish reading it...

## Zeno's Paradox (Score:5, Insightful)

## Re:Zeno's Paradox (Score:4, Insightful)

Isn't this just Zeno's paradox applied to really good fridges?

It would be if each additional half-distance traveled required more work and more time than was expended to travel the first half.

## Re: (Score:2)

It would be if each additional half-distance traveled required more work and more time than was expended to travel the first half.

Then how do you travel half of the Plank length?

## Re: (Score:2)

It would be if each additional half-distance traveled required more work and more time than was expended to travel the first half.

Then how do you travel half of the Plank length?

You don't. When you're within a Planck length, your atoms are already interacting with the atoms of the target, i.e. you're already touching. Any further movement isn't movement toward the target, it's into it.

## Re: (Score:2)

So then in effect, if you're one Planck length unit away, then moving half of the distance means you're there. Would that also be the same as saying if we're one Planck temperature unit away from zero entropy, then the next step, no matter how small, would be absolute zero? And if so, doesn't that mean we can reach absolute zero?

## Re: (Score:2)

So then in effect, if you're one Planck length unit away, then moving half of the distance means you're there.

No, if you're one Planck length away, you're

alreadythere.## Re: (Score:2)

Ok what about two then?

## Re: (Score:2)

Ok what about two then?

How about 10^20? 10^20 Planck lengths is the diameter of a proton. The atoms are interacting chemically and/or bouncing off one another long before you're even that close.

## Re:Zeno's Paradox (Score:4, Interesting)

In real life as far as movement goes you're never actually trying to get to an exact point. For one thing, because of uncertainty in measurements you can't ever get to an _exact_ point. You can't even tell _exactly_ where something is. On top of that (literally in this case) objects take up space, even individual atoms, so if you move an object to a point it won't be exactly at that point, it will be overlapping that point to some degree. So no matter how precise you're trying to be you're always overshooting at least a little bit. Which means that even ignoring the problem of calculus Xeno's paradox has a hole in it. You're never trying to get exactly to a point, you're actually trying to get to a little past the point and just stopping once you're close enough/sufficiently overlapping. It's effectively the same as starting out trying to run twice the distance, getting halfway, and declaring yourself done.

The difference in this case is twofold, one: there's no "past the point" you can aim for. The whole idea of absolute zero is that it's the lowest you can go. Two: they seem to be saying that there is no quanta of temperature. You can never remove the last bit, you can only remove a portion of what is there.

Assuming that the second part is correct (i'll leave the proof or disproof of that to actual scientists =) the first part makes it impossible to ever arrive at actual zero.

## Re: (Score:2)

I'm pretty sure Zeno's paradox applies regardless of measurement precision. The problem is that, since you're assuming constant velocity, moving the first 50% takes 50% of the total time.. moving the next 25% takes 25% of the time and so forth. Basically you have two infinities "cancelling" each other out (which happens surprisingly/scarily often in physics!)

With the freezing, as I understand (and its well possible that I don't,) you remove 50% in one unit of time, then the next 25% in another equal unit

## Re: (Score:2)

## Re: (Score:2)

If you're at an exact point with no uncertainty, you can't know anything about your momentum. Since there's limits to momentum in the physical Universe, you can't be at an exact point with no uncertainty.

## Re: (Score:2)

## Re: (Score:2)

## Re: (Score:1)

That's was what people thought in the 5th century BC, but it turns out that you can actually reach 0 if the time taken by each step forms a convergent series.

## Re: (Score:2)

Like getting to the end of a race track cannot ever happen. To get to the end you first have to get 1/2 the way there. To get to the half way point, you first must get to the 1/4 point. To get there, you must first get to the 1/8 point. You have an infinite number of steps to get from the start to the end so there are always more steps between and you can never complete it. This is one of Zeno's Paradoxes and it is shown to be false basically because of calculus.

So saying you cannot complete an infinite n

## Re:Zeno's Paradox (Score:5, Informative)

Like getting to the end of a race track cannot ever happen. To get to the end you first have to get 1/2 the way there. To get to the half way point, you first must get to the 1/4 point. To get there, you must first get to the 1/8 point. You have an infinite number of steps to get from the start to the end so there are always more steps between and you can never complete it

This is one of Zeno's Paradoxes and it is shown to be false basically because of calculus.

"Basically because of calculus" is the most hand-wavy excuse. The REASON you can reach the end of a race track is that the time to complete 'each 1/2 step' converges to zero. What if we added some 'overhead' so the time per step didn't converge to zero... then what happens? Say we add the requirement that you stop for 0.1 seconds each time you traverse another "1/2 of the remainder", now how long will it take to cross the finish line?

Answer: You won't finish. Now it WILL take infinite time.

So saying you cannot complete an infinite number of steps in a finite amount of time is wrong!

If the iterations converge to requiring zero time to complete then maybe you can complete an infinite series of them in a finite amount of time. Otherwise... nope. Forget it.

## Re: (Score:3)

## Re:Zeno's Paradox (Score:5, Informative)

Actually, 0.999... *is* equal to 1.... in real life. They are simply two different ways of describing the exact same number.

I'll give you benefit of the doubt and assume that you are not somebody who thinks that they have a clear understanding of why they should be different and would ignore any proofs to the contrary, but here is one of probably a dozen proofs that should be readily understandable by anyone who knows how to compute the decimal expansion of a fraction.

Consider that the decimal expansion of 1/9 is 0.111.... repeating forever, and it is clear that if you multiply this decimal expansion of 1/9 by any one-digit number, there are no carryovers in the multiplication, so 0.111... multiplied by 9 would therefore equal 0.999... repeating forever, but we also know that 1/9 multiplied by 9 is 1, and thus 0.999... must be equal to 1... They look different, but they are actually the same. This is not simply the result of some series converging on the number 1, it literally is the exact same number. It is simply an alternative representation that arises out of the ways that we are permitted to describe numbers in mathematics.

## Re: (Score:3)

## Re: (Score:2)

There are several ways of proving 0.999... = 1. Two very easy ones:

1) If 1/3 is 0.333..., what is 1/3 * 3?

2) What is the difference between 1 and 0.999... ?

## Re: (Score:2)

Try to follow this:

1 / 3 = 0.333...

0.333... x 3 = 0.999...

(1 / 3) x 3 = 1

ergo 0.999... = 1

## Re: (Score:2)

## Re: (Score:2)

## Re: (Score:2)

You could get an object to absolute zero, you are unlikely to achieve by cooling but by forcing through stasis to cease to exist. Though of you cause it to cease to exist, has to ever really achieved absolute zero.

## Re: (Score:2)

Nice try but you pulled the V=5 completely out of your ass and it contradicts IV=4 since you defined I=0.9999999999....

## Re: (Score:2)

## Re: (Score:2)

## Re: (Score:2)

## Re: (Score:2)

but V = 5

is wrong. V is 4.

0.999... = I (I = 1)

IV = 4 (1*4 = 4) (V = 4)

V = 4/I (4 = 4/1)

V = IR (4 = 1 * R) (R = 4)

I = V/R (1 = 4/4)

V = 4R/V (4 = 4*4/4)

R = V^2/4 (4 = 4^2/4)

but V = 5 (WRONG, it was defined as 4 by the second line)

But "Mr.Z of the LotFC" points out "IV=4 & V=5 as Roman numerals (as is 0.999...=I)...the derivation appears to be a math pun of sorts."

## Re: (Score:2)

## Re: Zeno's Paradox (Score:2)

0.9999... Is

exactly1.## Re: (Score:2)

Not always [wikipedia.org].

Though you need to get into some pretty advanced math before you'd care about number systems where 0.999... != 1.

## Re: (Score:2)

In real life, I type 1 and that's it. On the other hand, I could type 0.9999999, continuing the sequence until my fingers got tired, and it still wouldn't be equal to 1. Mathematically, what I'd get if I typed an infinite number of 9s is simple and understandable, but that can't be represented in the real world without additional notation (such as an ellipsis).

## Re: (Score:2)

Which is why Heisenberg never wanted anyone to tell him the momentum of his car keys.

## Wrong! (Score:5, Funny)

## Re:Wrong! (Score:5, Interesting)

Nope.. .Still wrong.

As an atom spins it gives off infrared energy. The slower it spins, the less infrared energy it will give off also contracting in size.

Since EVERYTHING in the known universe gives off infrared energy, it is near impossible to shield infrared energy from reaching the atom and it is highly unlikely for it ever to reach absolute zero.

Absolute zero is the point that the atom will no longer spin. They are correct that absolute zero will never be attainable from an object of mass.

BUT...

The problem nobody talks about is that object of mass doesn't need to stay an object of mass. At absolute zero it will return to the energy that it was before it became mass, AND absolute zero is attained because photons do not give off heat.

But then again, it is no longer mass., so who cares?

Nathan

## Re: (Score:3)

I don't think so. If it has energy, then that energy can be transferred, and heat is the transfer of energy. Absolute zero is an energy-less state....

## Re: (Score:2)

I don't think so. If it has energy, then that energy can be transferred, and heat is the transfer of energy. Absolute zero is an energy-less state....

I think that's sort of the point, you can't have a energy-less atom. Otherwise the electrons would merge with the protons and you end up with neutrons. You could take a lone neutron and declare it at absolute zero compared to the rest of the universe, but that would be trivial. I'm sure trying to cool a hypothetical neutronium substance would also have difficulties. You can say that heat just deals with systems but the system will be the sumation of the energy of the system will be at least that of one atom

## Re: (Score:1)

The only problem I have with your proposal is that you seem to be suggesting that the possession of some amount of temperature (enthalpy) by an atom is an intrinsic requirement to maintain the atom's existence.

I don't know of any mechanism that makes that possible, but regardless of the mechanism, would you expect this process to be symmetric? If so then to turn energy into matter (the reverse of what you wrote) then the process has to take place at a location with zero temperature, or, that once the atom h

## Re: (Score:3)

The only problem I have with your proposal is that you seem to be suggesting that the possession of some amount of temperature (enthalpy) by an atom is an intrinsic requirement to maintain the atom's existence.

I think that is the core question that's raised. What is an atom?

I guess as a prediction "matter decays into energy at absolute zero" could be either right or wrong, but for me it belongs in the same category as "black holes are wormholes to other universes".

What energy? I'd think you have to entirely remove all energy from a closed system in order to reach absolute zero - no energy, no matter.

## Re: (Score:2)

Something doesn't seen right here. Isn't energy quantized? If so, then an inability to get to absolute zero (quantum state zero) means that quantum state number one is the lowest possible energy level. Wouldn't quantum state number one then be absolute zero?

What prohibits something from being at quantum state zero? If two things at quantum state #1 interact, might not one of them subsequently be at state zero and the other at state 2?

Does temperature actually have a meaning in the context of single atoms?

Th

## Re: (Score:2)

Energy

statesare quantized, yes. And there is a lowest state for any particular particle which, as far as anybody knows, you cannot drop below while still remaining that particle. For example if an electron gets dropped into energy state "0", its effectively joined the nucleus and one of your protons becomes a neutron -- its a gross oversimplification but basically that's what happens to form neutron stars.Free energy on the other hand is not quantized (or at least our best models don't show it to be suc

## For the humour impaired.... (Score:2)

JOKE!.## Exactly the sort of burdensome regulations (Score:5, Funny)

## Re:No, THE COLDEST (Score:1)

Cooling American to absolute zero will be the coldest, it will be so cold, because a lot of people are saying that global warming is a hoax. The Chinese have absolute zero, and they're very unfair to us.

We're going to make America Cool again!

## Re: (Score:2)

Does this mean I can get a HUGE government discount on an Air Conditioner?

If we all buy one, we can export all our extra heat overseas... fix the trade inbalance, and create more Jobs here... I'm thinking A/C repairman...

It's gonna be great!

## Re: (Score:2)

our new president was elected to repeal. We're going to make America Cool again!

We're tired of being cool.

signed,The Dakotas.

## "Lisa, get in here!" (Score:5, Funny)

"In this house we obey the laws of thermodynamics!"

## Re: (Score:2)

## Would? (Score:2)

Now that has me wondering about the singularity in a black hole. And now my brain hearts a little as so many things seem to conflict with all of this.

## Re:Would? (Score:5, Informative)

Would this also be a property of time? That you can't reach absolute zero because doing so, would be akin to stopping time, if only for that specific single point in space?Now that has me wondering about the singularity in a black hole. And now my brain hearts a little as so many things seem to conflict with all of this.

Read Hawking's "A Brief History of Time" - it's from the 80's but he deals with this and related concepts elegantly. Time never gets to zero - as soon as you try you're back to where you started. cf. Alice's Adventures.

I think the proof in this case is a bit different, though. If a system had zero energy, you couldn't even interact with it (i.e. observe it). And there's the quantum noise of everything in the universe; it probably isn't possible to stop the soup without removing space from the universe, and fields will always be interacting with matter no matter how hard a scientist wishes otherwise.

Unless we develop technology to create voids in the universe or to exclude fields we're going to have vibrating matter.

## Re: (Score:2)

Unless we develop technology to create voids in the universe or to exclude fields we're going to have vibrating matter.

My observations have led me to conclude that vibrating matter has a tendency to fill voids in quite interesting ways.

## Re: (Score:2)

I was pondering a similar thought myself. If the universe continues its expansion outpacing the speed of light, shouldn't it eventually be possible for a particle of two atoms to to be the only existent particle within its visible universe. Whatever heat it had at the beginning I would expect it to lose to radiative cooling over time. Since there wouldn't be any other particles in the observable universe there shouldn't be anything to heat our particle by radiating back at it.

## Re: (Score:1)

This is a great line of Thinking. I suggest "Leonard Susskind's Modern Physics course concentrating on Classical Mechanics".. In a different talk (Leonard Susskind on The World As Hologram) he describes the bet he "won" with Steven Hawking about information being persevered in black holes.

I'm going to wing it here so bear with me

We know the first 3 laws of physics as newtons laws of motion. There is another more fundamental law called the "Zero" law that describes entropy. The entropy of a a particle contai

## Properties of matter and energy (Score:2)

I don't think you need to bring time into it. Just think about the absolutes of matter.

On the one hand, there is absolute zero.

On the other hand, there is the speed of light.

These are measured as different properties (temperature vs velocity), but they are the two opposite infinite states of matter.

Absolute zero would mean the complete absence of energy. Light speed means matter has transformed into energy.

So by definition, when we're talking about matter, we're talking about the stuff that exists between t

## Re: (Score:2)

Sort of, but you've described it in a bit of a misleading way. Anything that moves at c is indeed massless, and we can usually take "matter" to mean any particles that have rest mass >0.

The tricky part is that word "transformed." You can't transform matter into energy just by increasing its speed. You have to annihilate it somehow and some of the products of that annihilation will be in the form of light-speed photons (and for a very very brief time if you do it right, gluon jets, which I believe also

## Re:Would? (Score:4, Interesting)

If you cooled it to absolute 0 you would know the velocity is rpecisely 0. That is a violation of Heisenberg's uncertainty principle.

## Never been to Canada (Score:5, Funny)

in the winter, pretty sure it's colder than that.

## Re: (Score:2)

in the winter, pretty sure it's colder than that.

It's the wind chill factor... (grin)

## Re: (Score:2)

So... if it's not quite absolute zero, but it's high humidity... does it "feel" colder than absolute zero? ;D

## Re: (Score:2)

North Pole, Alaska.

Where the weather forecaster accurately predicts when Hell will freeze over.

## Computing? (Score:2)

"In the car industry, people ask this question all the time: how fast does the vehicle accelerate?" says Oppenheim. "Just as a computing machine performs a computation, a car can take you to the mall."

No, still doesn't make any sense...

## Physicists are such bastards (Score:3)

Blah blah blah...you can't go faster than light.

Blah blah blah...you can't cool to absolute zero.

I'll bet a politician would tell me I could do either one of those if it would my vote. Why can't physicists respect my desires like the nice men in suits do?

## Re: (Score:2)

If a politician went faster than light would she break her election promises before she got elected?

## Reminds me of this engineering joke: (Score:5, Funny)

Reminds me of this engineering joke:

A mathematician, a physicist, and an engineer were asked to review this mathematical problem. In a high school gym, all the girls in the class were lined up against one wall, and all the boys against the opposite wall. Then, every ten seconds, they walked toward each other until they were half the previous distance apart. The mathematician, physicist, and engineer were asked, “When will the girls and boys meet?”

The mathematician said, “Never.”

The physicist said, “In an infinite amount of time.”

The engineer said, “Well... in about two minutes, they'll be close enough for all practical purposes.”

## Re: (Score:2)

Shouldn't it be the mathematician who answers “In an infinite amount of time.”, and the physicist who answers "never"?

The mathematician may not care, but the physicist "knows" about the eventual entropy death of the universe, which, happening in finite time, will ensure it's actually never going to happen.

## Re: (Score:2)

## not as definitive as it may sound (Score:2)

Before quantum mechanics was discovered, people could prove mathematically that no object could jump or tunnel out of a potential well; it was physically impossible. Now we know that this is quite possible since the "laws" of classical mechanics can be violated under certain conditions.

It's no different with quantum mechanics. Well, that's not quite true: it is actually a little different. Before quantum mechanics was discovered, many physicists believed classical mechanics to be complete. But for quantum m

## Re: (Score:2)

Sort of. Under QM, we may already know the theory is incomplete but at the same time, the parts we know well are far more constrained than anything classical physicists could have dreamed of prior to the introduction to QM.

For example, it would be extremely unlikely for any new or competing theory to work around the uncertainty principle and have any hope of being correct. Classical physicists thought they knew it all because they were only thinking about the things they could see. In modern QM, we have

## Re: (Score:2)

It's trivial to construct theories that "work around the uncertainty principle" and are compatible with all existing observations.

And the same is true for all the fundamental

## Re: (Score:2)

In which case you'd have no problem sketching one out.

## Re: (Score:2)

Indeed, I don't.

## Re: (Score:2)

Would you care to share?

## So... (Score:2)

even if it wasn't impossible to cool something to absolute zero, wouldn't it be an essentially useless thing to do because once you do anything with it, it would generate some amount of heat so immediately raise its temperature slightly anyway?

(I'm imagining the passing of current on a supercooled wire or computing on a supercooled cpu)

## Re: (Score:2)

## Re: (Score:2)

There's a big difference between impossible in practice (which lots of things are) and impossible even in theory. The latter is a much much stricter rule and can be used as a basis for other related theories to build upon since we can say for sure that its not just us failing to be clever enough.

## Two things (Score:2, Interesting)

One: I think you mean "ruled out" rather than "outlawed." That implies some sort of change in the legality rather than a revealing of a "legality" (which is a somewhat obtuse way of looking at this since science is a system of attempting to describe reality rather than an attempt to describe some sort of human invention or behavior) that already existed.

Two: This has an interesting implication for our universe, I think. It's possible that the entropy eventually reaches 0 in the universe as a whole (since th

## Re: (Score:1)

"Outlawed" is a reasonable word. Nobody breaks the laws of physics and lives to tell about it.

Remember: guns don't kill people; physics kills people.

## Does this mean (Score:2)

that anyone cooling anything to absolute zero will be put into Markov chains?

## entropy != disorder (Score:2)

The T-s diagram is quite precise and is used by a few gas turbine designers

## infinite number of steps isn't a deal breaker. (Score:2)

## Re: (Score:2)

There are. But simply counting 1,2,3,... is not one such series.

## Asymptotic? (Score:2)

--

.nosig

## Universal Heat Death? (Score:2)

"a temperature of absolute zero cannot be physically achieved because it's impossible for the entropy (or disorder) of a system to hit zero"

Would that then not imply that our universe is incapable of experiencing heat death?

## Re: (Score:2)

"Heath death" is somewhat of a misnomer. Entropy does not go away; it's when the entropy of the universe can no longer increase, due to the universe being at perfect equilibrium under the Third Law. There will still be temperature, and mater; individual particles flying around and never touching (no protons, though; they have long since decayed). We consider this to be an extreme low-energy state, not a complete lack of energy.

Disclaimer: I'm not a scientist. I just get bored and read stuff.

## Re: (Score:3)

## Re: (Score:2)

Would that then not imply that our universe is incapable of experiencing heat death?

Heat death is when there is no practical work to be extracted. This means that temperatures are the same and heat transfer can't take place. To get there we do heat transfer. Note the word transfer. Heat transfers from warm to cold bring both of them closer together.

The universe is already at 5K we can achieve temperatures colder than that in a lab. Any energy i.e. stars only add heat to this background. We may not every achieve absolute zero but we will eventually reach the heat death of the universe, and

## Outlawed (Score:2)

"Outlawed"

I do not think that word means what you think that word means.

Proven impossible, proven unattainable, sure...but it wasn't "outlawed".

I mean, if it was then why not just

repeal that lawand cool stuff to absolute zero?## Unintended Consequence (Score:2)

If you outlaw absolute zero, only outlaws will have absolute zero.

## Not again (Score:2)

Cooling To Absolute Zero Mathematically OutlawedIs there no end to what Trump will mandate with an executive order???

I'm sure that even now protests are forming around every liquid nitrogen tank in the country.

## Re: (Score:2)

I would argue that "where/when" there is no space, the temperature is absolute zero.

## Re: (Score:2)

"Where there is no space" doesn't sound meaningful to me.

## Isn't there a simple proof? (Score:2)

I am not a physicist, so I may be wrong, but I always thought that absolute zero is theoretically impossible. The temperature is a measure of random energy per degree of freedom. By Heisenberg principle delta_x * delta_p = h/2pi. So you have to get delta_p = 0 for absolute zero or delta_x = infinity.

The best you can get in lab by cooling atoms is to create a Bose Einstein condensate in which all the atoms acts as a single coherent wave. This can reduce random KE significantly. For particle of size of hydrog

## not quite true (Score:2)

a physical system, perhaps, cannot reach complete entropy. but a purely mathematical system can.

## They're all wrong (Score:2)

## Solution (Score:2)

Just calculate 0Â kelvin to a temperature we can actually achieve. Nevermind the physics that comes with it. Bah, details!