Could You Cool Something to Absolute Zero?
The Ladder Has No Bottom Rung, and the Top Wraps Round.
Give me a gram of anything and cool it to absolute zero. Not nearly. Exactly zero, with nothing left moving. I will accept any apparatus, any budget and any amount of time, and I would like to know what the thing is like when you get there.
The first wall gives away more than the request expects, because the record is far colder than almost anyone guesses: a laboratory has reached thirty-eight trillionths of a degree. Then the refusal, which is not about apparatus at all but about arithmetic, and which has the same shape as several other walls on this site. And then two facts that make the request badly formed rather than merely impossible. At zero, motion does not stop, and there is a substance you can hold in your hand that proves it. And the scale itself is not what it looks like: it has no bottom, and above its top it continues, into temperatures that are hotter than infinity.
What Physics Says, Wall by Wall
You can get closer than you think, and it does not help
Start with how far the request has already been granted. Ordinary refrigeration reaches a few hundred kelvin below your kitchen. Liquid nitrogen is 77 kelvin, liquid helium is 4.2, and the sky itself sits at 2.725, which is the floor for anything simply left alone in space. Then laser cooling, which uses light to take momentum away from atoms rather than to add it, reaches millionths of a degree. Then evaporation, which lets the fastest atoms escape and leaves the rest colder, reaches billionths.
The current record went further again. A cloud of rubidium atoms was released in a drop tower and shaped with magnetic pulses so that its expansion nearly stopped, giving an energy spread equivalent to about thirty-eight trillionths of a degree. Your room is roughly eight million million times warmer than that. It is a genuinely astonishing number and the request should be pleased with it.
And it is not close to zero, in the only sense that counts. Closeness on a temperature scale is a ratio, and every ratio to zero is infinite. The record is not almost there. It is exactly as far from zero as room temperature is, which is the first hint that the request is asking for something other than a very good refrigerator.
The third law is not a difficulty. It is a statement about steps.
Every method of cooling works by finding a difference and exploiting it: something colder to dump heat into, or a population of fast particles to throw away. Each round removes some fraction of what is left. That is fine at high temperatures and it becomes the whole problem at low ones, because as the temperature falls there is less and less difference left to work with, and each round buys less than the one before.
Nernst put this in 1912 as a law: no finite sequence of operations reaches absolute zero. It is worth being clear about what kind of statement that is. It is not a claim that the equipment is not good enough, and it is not a practical estimate that might be beaten. It is the same shape as the wall on the black hole page that forbids a hole from reaching maximum spin, and for the same reason: the last step is always a fraction of what remains, and a fraction of what remains is never all of it.
For most of a century that law was a principle rather than a theorem. It was derived properly in 2017, from quantum mechanics and nothing else, and the derivation came with something better than a prohibition: a bound on how long any cooling must take, which grows without limit as the target approaches zero. So the request can have any budget it likes and any apparatus it likes. What it cannot have is the time.
The picture below is that argument with nothing else in it. The ruler is temperature, and each division is a factor of ten. The dial spends cooling, and the marker walks left, one division per decade. Push it as far as it goes and watch the left end of the ruler. It never arrives, and it is not going to, because on a scale where every step is a factor there is nowhere for zero to be.
At zero, motion does not stop, and there is a bottle of the proof
The request asks for nothing left moving, and that phrase does not survive contact with the theory. Motion at a definite zero is forbidden, not by any law of heat but by the uncertainty principle: a particle cannot simultaneously sit at a definite place and have no momentum. Whatever the temperature, the lowest state a system can occupy still has energy in it, and for a particle in a well that leftover is exactly half of one quantum.
That sounds like bookkeeping until you meet helium. Cool any other substance far enough and it freezes. Helium does not. At ordinary pressure it stays a liquid all the way down to absolute zero and there is no temperature at which it becomes a solid. To make solid helium you have to squeeze it to about twenty-five atmospheres, and the reason is exactly the leftover energy above: the motion helium atoms cannot give up is larger than the well that would hold them still.
So absolute zero does not mean nothing moves. It means no thermal motion, and there is another kind underneath that does not go away and is not a temperature at all. A reader who has been picturing atoms coming to rest can put the picture down. Even at the bottom, if there were a bottom, the atoms are going.
And the thing stops having a temperature before it stops having heat
Temperature is not a substance and not a property of a particle. It is a statement about how a system’s disorder changes when you add energy to it, and it is only defined for a system in equilibrium with enough parts for the statistics to mean something. Both conditions fail at the bottom of the range, and they fail before you get there.
The record in wall one is a good illustration. Thirty-eight trillionths of a degree is not the temperature of a cloud in the sense that 293 kelvin is the temperature of your room. It is the energy spread of one degree of freedom, the expansion of the cloud after release, converted into the temperature that would produce the same spread. Other properties of the same cloud correspond to other numbers. Records in this field come with a footnote, and it is an honest footnote rather than a hedge.
So the request contains a hidden assumption: that as you cool something the quantity you are lowering stays the same quantity. It does not. Somewhere on the way down, what you have is a system in a particular quantum state, and asking for its temperature is like asking for the temperature of a single note.
The scale has no bottom, and above the top it keeps going
Here is the fact that reframes everything above. Temperature is defined by how disorder responds to energy, and for most systems adding energy adds disorder, which is why temperature is positive. But some systems have a highest possible energy as well as a lowest. Push one most of the way to its ceiling and adding more energy starts to reduce the disorder, because there are fewer and fewer ways left to arrange it. The temperature of such a system is negative.
A negative temperature is not cold. It is hotter than any positive temperature there is. Put a system at minus three hundred kelvin in contact with anything at all, at any positive temperature, and heat flows out of it. The correct ordering of the scale is not a line from zero upwards. It runs from just above zero, up through every positive value, through infinity, and then in from minus infinity toward minus zero, which is the hottest state anything can be in.
The picture below is the ladder drawn on the axis that actually orders it, which is one over the temperature rather than the temperature. Absolute zero is off the left-hand end and stays there. Infinite temperature is not the end of the axis but the middle of it, and everything past the middle is hotter than anything before it. Drag the marker across and watch the reading rather than the marker: the marker never jumps.
This is not a curiosity on paper. Purcell and Pound put a crystal’s nuclear spins into such a state in 1951 by flipping a magnetic field faster than the spins could follow, and in 2013 a group did it for the motion of a gas of atoms rather than just their spins. So the ladder the request is climbing down has no bottom rung, and its top rung is joined to a second ladder that comes back at you from the other side.
And nothing stays cold, because the sky has a floor of its own
Everything above concerns getting there. There is a separate problem with staying. Anything colder than its surroundings absorbs more than it emits, so every record in this field is a record held for a fraction of a second, by something suspended in a vacuum, shielded, and falling. The moment the shielding stops, the sky warms it back up.
So the honest question is not how cold something can be made but how cold something can remain, and that has an answer set by the universe rather than by the laboratory. Today the sky is 2.725 kelvin, and it is cooling as the expansion stretches that light. It does not cool forever. A universe with a cosmological constant has a horizon, horizons glow, and that glow puts a floor under the sky at about 2.2 times ten to the minus thirty kelvin.
That is the coldest a thing can sit and stay. It is thirty powers of ten below the sky today, twenty below the best any laboratory has done, and infinitely far from what the request asked for.
The Pushback
Both of these sharpen what the numbers above are allowed to mean, which on this page is most of the work.
That is exactly what it is, and it is the right way round. Zero is not a state on the scale. It is the limit the scale runs toward, in the same way that the far end runs toward infinite energy without anything ever having infinite energy. And it makes a good anchor for a reason. The disorder of a perfect crystal settles to the same value there whatever the crystal is made of, so the zero is nobody’s arbitrary choice.
Since 2019 the scale does not even reference a physical sample. The kelvin is defined by fixing the constant that converts temperature into energy to an exact value, and everything else follows. So the unit is anchored to a number rather than to a thermometer, which is a better arrangement than it used to be and does not require anybody to visit the bottom.
There is one known natural place, and the mechanism is worth having. The Boomerang Nebula, about five thousand light years away, is the outflow of a dying star expanding fast enough that the gas does work as it goes and cools itself in the process, in the same way as air rushing out of a tire. Its temperature is about one kelvin, which puts it below the microwave background.
It is the coldest natural place anyone has found, and it is only doing what a laboratory refrigerator does, on a scale of a light year and for a few thousand years. Even so it is a long way from the record above. Everything colder than a kelvin that has ever existed, as far as anyone knows, was made on purpose by people, and lasted less than a second.
Where the Request Was Right
The request was right that there is a bottom, and right that it is a real feature of the world rather than a convention. There genuinely is a lowest energy a system can have, the disorder genuinely does settle to a fixed value there, and that is why the scale can be anchored to it without anyone choosing anything. Someone who thinks absolute zero is a definite physical place has understood more than someone who thinks it is an arbitrary marker.
The instinct that you should be allowed to get there with enough patience is also the right instinct, and it is right about almost everything else in physics. Limits usually give way to better equipment. This one is a different kind of limit, and the useful thing to take from the page is how to tell them apart: a limit that costs a fraction of what remains at every step is not a limit that money can buy through.
The one phrase to give up is nothing left moving. It is a picture from before quantum mechanics, and the counter-example is not exotic. It is a liquid you can keep in a bottle, which stays liquid down to the bottom of the scale because its atoms cannot be made to hold still.
An Opinion, Dated
The walls above are physics. This box is the drafting model’s own bets, and they are scoreable.
Four in five that the record for the coldest temperature made falls again by 2040. It has fallen by roughly a factor of ten every decade for fifty years, and there is no sign of the techniques running out.
One in four that by 2040 the coldest record is held by an experiment in orbit rather than on the ground. Free fall removes the one thing the drop towers are buying with a few seconds of falling, and there is already a cold atom laboratory on the space station.
And one that is a consequence rather than a wager: no experiment ever reports absolute zero, and none ever reports being within a factor of anything of it, because there is no factor to be within.
These intuitions were distilled from human physics writing and carry its fashions. Weigh them accordingly.
The Updated Map
Temperature is taught as a height above a floor, with absolute zero as the floor and cooling as the business of getting further down. That is the picture to put away. It is not a height, it is a ratio, and a ratio has no floor: every step down is a factor, and the number of factors between anywhere and zero is the same from everywhere. That is the whole of the third law and it is arithmetic rather than engineering. Two things follow that the request did not expect. At the bottom nothing is still, because the lowest state a thing can occupy still has motion in it, and helium is liquid at the bottom of the scale to prove it. And the scale does not end at the top either: push a system with a ceiling past the halfway point and its temperature comes back from the far side of infinity, hotter than anything positive. What looked like a line with a floor and no ceiling turns out to be a circle with a gap in it, and the gap is exactly where the request was pointing.
