
Hitting Absolute Zero Has Been Declared Mathematically Impossible - djsumdog
https://www.sciencealert.com/after-a-century-of-debate-cooling-to-absolute-zero-has-been-declared-mathematically-impossible
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qntty
There's no such thing as "mathematically impossible" in the physical world. If
it's impossibility is evident in a mathematical model, that's still physical
impossibility.

~~~
simonh
I agree completely. How about mathematically proven to be physically
impossible?

~~~
SilasX
It should be "mathematically proven to physically impossible under _this
model_ /these assumptions".

Every math-based prediction about the real world will be based on two parts:

1) The world behaves like this model [up to our measurement accuracy].

2) The model implies this prediction.

Their claim would only be speaking to 2) -- that, under the model, you cannot
reach absolute zero. The model can still be wrong.

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thehardsphere
I am not a mathematician and I did not read the actual paper, so forgive me if
I beclown myself with this question.

Isn't this a nothingburger? How would you hit absolute zero anyway when the
minimum joint uncertainty of any given particle's position and momentum must
be greater than Planck's constant / 2?

~~~
timthelion
It seems to me that uncertainty is more uncertain a theorum to base your
beliefs about the universe on than entropy.

~~~
thehardsphere
True perhaps, but we're relatively certain about uncertainty.

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lutusp
> Hitting Absolute Zero Has Been Declared Mathematically Impossible

Wait ... wait ... this isn't about mathematics, it's about a mathematical
model of physics, of reality. The title is both confusing and confused. Also,
if something is mathematically impossible, declaring it so means nothing
(because mathematical truths don't rely on human authority).

There's an interesting scientific finding behind the title, but the title is a
disaster.

In any case, there's a simple heat-energy-transfer equation that can be used
to show that achieving absolute zero isn't possible for the simplest of
reasons:

    
    
        Q(t) = Δq * e^(-t * f)
    
        Q(t) = temperature at time t
        Δq = initial temperature difference
        f = a rate-of-heat-transfer factor
        t = time, seconds
        e = base of natural logarithms, equal to lim n -> ∞, (1+1/n)^n (2.171828....)
    

If you plot the temperature given by Q(t) over time (the temperature of one
body being heated or cooled by another), you see that the temperature never
gets to zero, because the rate of heat transfer depends on the remaining
temperature difference, and as that difference approaches zero, so does the
rate -- and neither becomes zero.

It's simple mathematics, but its meaning is located in reality, in physics. If
that were not true, another mathematical relationship could be substituted. So
it's not mathematically impossible, it's physically impossible. This kind of
mathematics describes reality, it doesn't substitute for it.

~~~
andrepd
Where does this expression come from? Proving this is the point.

~~~
lutusp
The equation I posted is the solution to a differential equation that
expresses the idea that a rate of change depends on the difference between two
quantities -- temperature, voltage and so forth. It is a very common solution
in physics, describing the rate at which water moves between connected
reservoirs, gas moves between connected tanks, current moves between connected
circuits in electronics, and many other physical systems.

More here:
[http://arachnoid.com/sage/differential1.html](http://arachnoid.com/sage/differential1.html)

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AdamN
I'm kind of confused. For example, if you have a glass sphere and then you
take all of the atoms out of the sphere so that it's a complete vacuum, isn't
that some sort of absolute zero? Or does that not count since you need at
least one particle to 'have' the temperature (i.e. a measurement of thermal
energy)?

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hughes
A perfect vacuum still displays activity in the form of "vacuum energy" \- a
counterintuitive property of the universe where particles apparently blink
into existence for a short duration in otherwise empty space.

[https://en.wikipedia.org/wiki/Vacuum_energy](https://en.wikipedia.org/wiki/Vacuum_energy)

~~~
ScottBurson
Right -- it's probably more accurate to say that a perfect vacuum has no
temperature than to say it's at absolute zero.

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Phemist
I'm a total layman to this stuff, but from my understanding isn't thinking
about temperature in terms of linear scales (Fahrenheit, Celsius, Kelvin)
fairly misleading for understanding how hard it is to "hit" absolute zero.
Wouldnt describing temperature as a logarithmic scale make it much more
obvious, from a layman's perspective, that absolute zero is impossible to
"hit". Ie, negative infinity degrees of "temperature"?

~~~
x1798DE
I've heard arguments to this effect, that absolute zero is more obviously
impossible when you think in terms of Thermodynamic beta - which is standard
physics notation for 1/(k_B __* T) and appears in many places including in
statistical mechanics.[1]

That also makes it more clear that while reaching 0 (i.e. infinite Beta) is
impossible, negative temperatures _are_ possible (this occurs in processes
that undergo a state inversion like in a laser / maser). [2]

[1]
[https://en.wikipedia.org/wiki/Thermodynamic_beta](https://en.wikipedia.org/wiki/Thermodynamic_beta)

[2]
[https://en.wikipedia.org/wiki/Negative_temperature](https://en.wikipedia.org/wiki/Negative_temperature)

~~~
Phemist
Interesting! Thanks, great answers (both this post and your response to its
sibling post)

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pmontra
Cool (pun intended) but somebody maybe remembers from three years ago that
it's possible to go below absolute zero. And it's hotter than positive
temperature there. An explanation at
[http://physicscentral.com/explore/action/negative-
temperatur...](http://physicscentral.com/explore/action/negative-
temperature.cfm)

~~~
scribu
tl;dr: The negative values described in that article are possible because a
broader definition is used:

> In statistical mechanics and thermodynamics, temperature is defined as
> follows:

> 1/temperature = change in entropy/change in energy

> This definition of temperature can go from positive infinity to negative
> infinity.

For context, the more common definition for absolute temperature is the
average kinetic energy of the particles in the system, which of course can't
be negative.

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madamelic
Can anyone explain why it took 100 years to 'prove' this?

Like a really basic proof is:

\- It takes an infinite amount of time and resources to remove energy to reach
absolute zero

\- You can't reach infinity

\- Therefore reaching absolute zero is impossible.

What deeper knowledge am I missing?

~~~
dragonwriter
> It takes an infinite amount of time and resources to remove energy to reach
> absolute zero

Since particles not at absolute zero have finite energy, this point is non-
trivial and proving this point was actually the focus. (Tangentially, I think
this has been a common and strong intuition, and suggested by extrapolation
from empirical evidence, that you could asymptotically approach but not reach
absolute zero because it would be progressively harder as you got closer. But
there's a difference between that and a mathematical proof grounded in
assumptions that are well-accepted.)

Yes, if you have this as a known truth, you're basically done.

~~~
madamelic
Ah! Thanks for the clarification.

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idlewords
You learn why reaching absolute zero is impossible in an introductory
thermodynamics class, but apparently this is a more rigorous proof.

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phkahler
So if entropy must increase, and temperatures must fall but can't reach
zero... Does that imply the universe must keep expanding?

~~~
contravariant
There's no rule that temperatures must fall. In fact there are rules that
temperature can't simply fall without moving energy somewhere else.

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SellerOfDollars
But my mom (and other assorted guardians and authority figures) told me
anything's possible.

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I_am_neo
So "if", and this is a big if, we did cool a sample to absolute zero by some
yet to be discovered process, it's total energy should shrink to nothing and
as so the sample should shrink to nothing and disappear?

~~~
idlewords
No. Quantum issues aside, a system at absolute zero would still have energy in
the form of its mass. You can think of mass as 'frozen' energy.

Note that in some systems it's possible to have negative temperatures, which
are "hotter" than infinite temperatures. See
[https://en.wikipedia.org/wiki/Negative_temperature](https://en.wikipedia.org/wiki/Negative_temperature)

Thermodynamics is cool!

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Splendor
> "It's the speed of cooling."

Maybe I missed it but did the article actually define this "speed of cooling"?

~~~
lutusp
The "speed of cooling" is a layman's way of describing the rate of temperature
change. For two connected masses at different temperatures, that rate is
described like this:

    
    
        Q(t) = Δq * e^(-t * f)
    
        Q(t) = temperature a time t
        Δq = initial temperature difference
        t = time, seconds
        f = heat transfer efficiency factor
        e = base of natural logarithms (2.71828...)
    

If you plot this equation
([http://i.imgur.com/DiZsY0G.png](http://i.imgur.com/DiZsY0G.png)), you
realize that the rate of cooling depends on the remaining temperature
difference, and as the difference declines, so does the rate. This means both
the temperature difference, and the rate, can never become zero.

The linked article addresses some more deep reasons why one can never achieve
absolute zero, but this well-known and conventional (i.e. non-quantum)
equation is a sufficient reason.

~~~
Splendor
Thank you!

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theincredulousk
The fact that it is technically possible to reach temperatures lower than
absolute zero because of quirks in the math really makes this "declaration"
less than meaningless to me.

Math is a description of the physical universe not a definition. As another
commented, what is mathematically possible and impossible is entirely our own
invention.

~~~
axlprose
> _what is mathematically possible and impossible is entirely our own
> invention_

That's actually quite a controversial statement that many professional
mathematicians might beg to differ with.

Viewing mathematical results and axioms as being totally invented, opens the
possibility of being able to just will contradictory proofs into existence,
and that is simply not the case in practice. Mathematics might be more for
description than definition, but what it's describing isn't usually the
physical world, it's the logical limitations of certain principles. And if
these principles are found to be reflected in some aspect of the "real world",
then the corresponding mathematics becomes applicable. But you can't just pick
any arbitrary axioms/principles and have them automatically be mathematically
coherent either, so again we're limited in the maths that we can "invent".

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jddm
link to original work:
[http://dx.doi.org/10.1038/ncomms14538](http://dx.doi.org/10.1038/ncomms14538)

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agumonkey
Or maybe possible but unobservable ?

