Neil deGrasse Tyson: Why we can never reach absolute zero

January 30, 2022 • 1:45 pm

Here from Star Talk, Neil deGrasse Tyson explains why we can never attain the temperature of absolute zero (−273.15 °C or −459.67 °F). It’s the theoretical temperature in which an ideal gas at constant pressure reaches a volume of zero.

His first explanation, while delivered with enthusiasm, doesn’t make a lot of sense to me, for it’s along the lines of “we need to put something a bit colder than the ambient temperature at the place where we want to obtain absolute zero so that it will suck away the heat (molecular motion) of the target.  But as we approach absolute zero, we can’t GET anything whose temperature is just a tad above absolute zero to suck away that last bit of heat.  But this seems to me begging the question, for it assumes what you’re trying to prove: there’s a low temperature that we can’t obtain because it becomes impossible to get anything just a wee bit warmer than that temperature.

His second explanation, is that there is always quantum vibration, that this vibration cannot be prevented completely, and therefore we cannot go below the temperature where the quantum energy is the only energy we have. That is, quantum mechanics gives us the limit of the lowest amount of kinetic energy possible. (I wonder if the magnitude of absolute zero can be predicted from quantum mechanics alone.)

The third explanation, based on the theory of the canceled physicist Erwin S———r, explains the phenomenon as somehow connected to the Bose-Einstein condensate, but doesn’t tell me, at least, why absolute zero is unattainable (the Wikipedia article explains why this is basically the same thing as the second explanation).

So we have an entertaining video that gives three explanations for why zero degrees Kelvin is unattainable, but only the second makes a lot of sense to me. On the other hand, I’m not a physicist. But on the third hand, this video isn’t intended for physicists, but for folks like me.

60 thoughts on “Neil deGrasse Tyson: Why we can never reach absolute zero

  1. But this seems to me begging the question, for it assumes what you’re trying to prove: there’s a low temperature that we can’t obtain …

    There’s a distinction between “there is a zero point” and “we cannot attain the zero point”. The explanation he is giving there is about the latter.

    But as we approach absolute zero, we can’t GET anything whose temperature is just a tad above absolute zero to suck away that last bit of heat.

    To suck away the last bit of heat as we get infinitesimally close to zero, the thing would have to be a bit below absolute zero (not “a tad above”) to suck away that last bit of heat.

    1. I dunno. This sounds like Zeno’s paradox. It assumes that there is an existing low temperature that we can’t reach. It doesn’t explain why it’s there. He asserts at the beginning that there is no limit for a HIGH temperature!

      1. To put it simply, a set of real numbers can be bounded below, without containing its greatest lower bound. Like the positive reals don’t include 0. It is somewhat like saying you can get lower and lower by dividing what you have by very large positive numbers, but not by subtracting. I realize there is a difference between mathematical and physical operations, and it is the physical, rather than my fairly trivial mathematical, which Tyson is trying to explain.

        As for the lack of upper bound, that is surely because the noun ‘heat’ denotes a physically real thing, bur as a noun, ‘cold’ isn’t a thing, it’s a lack of heat. The adjectives ‘hot’ and ‘old’ are more analogous to each other.

        Actually I’m not sure if physical definitions are capable of making those two quantities at the top, given with two decimals, absolutely correct, or just correct ‘to that accuracy’. Isn’t it possible that there is a never ending sequence of increasingly accurate refinements to the freezing temperature of water. Probably the question of whether that freezing temperature is an irrational number is meaningless.

      2. It assumes that there is an existing low temperature that we can’t reach.

        It first argues that there is a state of zero temperature, being a state of zero heat. It then argues that we cannot attain that state. These two are distinct arguments.

  2. The first explanation is based on the idea that heat only flows “downhill” from hotter to colder temperatures. I dunno if he mentioned that the temperature of most of the universe is around 3 kelvin. If you have “free energy” such as the energy contained in gasoline, you can run a refrigerator to pump a portion of the heat energy out of one volume, concentrate it, then dump it to a warm environment. So you can get below 3 K, but no matter how many times you remove a portion (say 90%) of the heat energy from your target, you’ll never get to precisely zero. And since the universe doesn’t come pre-equipped with a zero-temperature region, it’s a Catch-22.

    1. Makes perfect sense to me; you can only cool something with the aid of something else colder than it is. Since nothing is colder than absolute zero we can’t actually get there.

      1. That is not an explanation to me. Why is there a temperature that you can’t get colder than? I get the quantum explanation, but not this one. If you can get as hot as you want, why can’t you get as cold as you want. The “refrigerator explanation”, well, leaves me cold

        1. In fact, this fact predates quantum mechanics: it is the Third Law of Thermodynamics. (As stated elsewhere, you are conflating two different physical facts: there *is* a lowest possible temperature, and that it is impossible to actually get there in practice.) The simplest explanation (which I admit does slightly beg the question) for the first fact is that, if all systems in equilibrium with each other are at the same temperature, and there is a zero-energy (ground) state for some systems, in which there is only one accessible configuration of their components, then all those systems are at the same temperature, which we can call zero.

          You also asked if we could derive the value of this quantum-mechanically, and that is sort-of true — the fuller statement of the second law relates the number of accessible states (which can be defined quantum-mechanically) to the entropy, which is related to energy and temperature by the second law. In fact, zero is the best-defined temperature, except that no real physical system has only one accessible state.

          1. I don’t care if it’s hard to get to the lowest possible temperature; I want to know why there IS one. That, to me, is a far more interesting question, and one I thought all of Tyson’s answers were aimed at. I was wrong, at least about the first answer.

            I still want to know if you can derive the lowest energy state at -273 C from quantum mechanics alone.

            Thanks!

            1. I don’t care if it’s hard to get to the lowest possible temperature; I want to know why there IS one.

              Temperature is a measure of heat. A state of zero temperature is a state of zero heat.

              Heat is the motion of particles. Thus, the temperature of the air surrounding us is a measure of how much the air molecules are moving around.

              But (classically at least) the motion of the molecules could be zero, they could be entirely still. That would then be zero heat, and thus that would be the minimum temperature possible. You couldn’t have a lower temperature because you couldn’t have less motion than none. Thus there is a lowest possible temperature.

              (Quantum mechanics then says that you can’t have zero motion, though one can come close to it, but that’s part of the argument for why one can’t attain zero temperature.)

              1. Yes (wearing my PhD in physics hat here), that’s it. Heat is a measure of motion. If there is no motion, there is no heat.

                I’m sure that Spinal Tap fans appreciate that argument. 🙂

                https://www.youtube.com/watch?v=zSkGtW-fQ3s

                Seriously, the comparison is more accurate than one might think. Something is black if it gives off (generates, reflects, whatever) no light. One can’t have less than no light, so one cannot become blacker than absolute black. Similarly, one cannot become colder than absolute zero.

              2. If heat is actually the motion of molecules, then you may think of absolute zero as the temperature at which all atoms and molecules stop vibrating, and having come to a standstill, they have no further heat to give away, and cannot be slowed down any further.

  3. Is this something like putting an ’11’ on Spinal Tap’s amplifiers’ volume control knobs? Why not just make the lowest temperature absolute zero and leave it at that?

    1. Nice to see another reference on Tap (geddit?), but that’s not appropriate here, as absolute zero has an absolute meaning (see my comment above). In physics, going up to 11 is known as renormalization. (Note that there are things, such as entropy and potentials, where the zero is arbitrary, as in practice only differences are important, but that is not the case for temperature.)

  4. The first explanation seems to make sense to me, which is predicated on the explanation that for a substance to lose heat energy there has to be another substance to absorb and take away that energy. So for the first substance to get to absolute 0 it would require the second substance to be colder than absolute 0, which isn’t possible.

    1. Yes but that doesn’t explain WHY there’s a limit: WHY you can’t be colder than absolute zero. Explain to me why you can’t get colder than absolute zero without using the quantum-mechanical explanation!

      1. “..without using the quantum-mechanical explanation”
        But that surely then would be, for theoretical reasons, not a correct explanation, since quantum mechanics is the present day (and for a long time) ‘perfectly correct’ theory of matter. Feynman will surely have a quantum answer to your question, which then only remains a question of asking for a new theory more basic than quantum field theory, which itself could then be derived (as an approximation) from the new theory. That’ll surely get a Nobel!!

      2. The speed range of particles is from zero to the speed of light. At zero, their temperature is absolute zero. They never reach the speed of light, because the energy (heat) needed to move faster as they approach the speed of light goes up toward infinity. So they can keep getting hotter and hotter without ever reaching the speed limit. (Photons can go that speed because they have a rest mass of 0).

      3. I have no business discussing physics, but I just assume that absolute 0 is when particles have no energy left to lose. Not counting the quantum movement from the third explanation.

      4. Because temperature is actually a measure of the average kinetic energy of the molecules in the substance. Kinetic energy is the energy of the velocity of the molecules. i.e. temperature is indirectly a measure of how fast the molecules are moving on average.

        If you slow the molecules down, the temperature drops. If you could slow the molecules down indefinitely, eventually you would reach a point where the molecules are not moving at all.Once a molecule is not moving at all, you can’t slow it down any further. This is absolute zero (at least in classical physics).

        1. Excellent

          The basis for the measurement itself becomes invalid at the extreme end.

          Almost as if the notion of temperature assumes temperature will be >0.000. Perhaps a new approach could more accurately account for it.

          Similar to the confusion with “beginning of time”, I think – there’s nothing “far out” about it – its simply the limit of the definition and we expect/make/demand too more than it was designed for..

          … but it is still amusing.

      1. No question that he was what has been called a womanizer. In Canada the age of consent is 16. Other places I do not know. But I understand the major charge against him is impregnating a consenting 17 year old. Perhaps you know of other charges.

        1. At the relevant time the age of consent in Canada was 14. What it was in the relevant countries I do not know. France has to this day no age below which a person’s consent cannot be legally relied on, provided the person is able to understand what is being proposed. The French government addressed this as recently as 2018 and decided not to mandate an age. Schroedinger certainly seems to have been a reprehensible lecher even by the standards of the day. But sexual attraction to or consummation with post-pubescent people is not pedophilia, even if is against the law. We change laws to criminalize behaviour in the future as our senses or right and wrong evolve, and the needs for protection are better understood, not to punish people in the past.

          I generally oppose canceling reprobates simply because it gives too much power to the cancellers and doesn’t make any living person’s life any better, no matter what the guy did.

          1. But sexual attraction to or consummation with post-pubescent people is not pedophilia, even if is against the law.

            Thank you! I realise many think me pedantic, but I think it is important to make this distinction. I’m fed up with people being termed “pedophiles” because they had sex with a sixteen year old (which is in any case legal in many countries).

            1. Indeed. Schrödinger was an interesting character, to say the least. (Note also that his wife had a sexual relationship with the famous mathematician and physicist Hermann Weyl; the tolerance between Mr and Mrs Schrödinger was mutual, and she seems to have been just a horny as he was.)

              Jerry has addressed the question here many times whether it is appropriate to cancel people who were not perfect.

              With regard do claims of pedophilia, as pointed out above there is certainly a difference depending on whether one is discussing sexually mature or sexually immature girls. With Schrödinger, it was the former. Also, that a sexual relationship is illegal at some age somewhere in the world at some time is not the issue. (There are countries today where all homosexuality is punishable by death and heterosexual relationships require marriage.) Whether it was illegal then and there is at most a legal question.

              As always, the main issue is consent. Actually, there is no other issue, assuming that the people are capable of consent (thus the widespread agreement that sex between, say, a 30-year-old and a 6-year-old is always wrong because real consent is not possible.). Of course, there can be legal issues, but if that is the standard, then we must “respect” countries with the death penalty for homosexuality, out-of-marriage sex, etc.

              Puberty happens at a range of ages, even back then (in general, probably due to better health in general, it has dropped in the last few decades). There are certainly girls (note that puberty is generally earlier in girls) who are sexually mature at 12 or 13 and capable of consent. In countries where that is legal or not prosecuted and the relationship is voluntary on the part of all, it is not a problem.

              Think about it: the age of consent in California is 18. I guess the Beach Boys are the next pedophiles. Not to mention Chuck Berry.

            1. Ah, thanks. We visited France twice in 2018. In spring, the legal commission (as we would call it here) was studying the issue and it was widely predicted that it would recommend a consent age of 15. There had been troubling reports of girls as young as 11 being sexually involved with older men who could not be charged with anything. By coincidence, the commission issued its final report during our second visit in late summer, during the August holiday season, and to the surprise and dismay of adolescent mental health professionals it made no recommendation on age. From newspaper stories it seemed the commissioners were concerned that a blanket consent age would run afoul of French Constitutional traditions of personal autonomy. If I’m interpreting the French Wiki correctly the legislators appear to have decided on 15 after all the next year.

              1. Yes. 15 is about average for Europe.

                Whether it is 14 or 15 or 16 doesn’t matter much if it is implemented sensibly, e.g. if the difference in age is less than, say, 2 years, then below the age of consent is OK (as long as there is consent, which should always apply), and if both are below the age of legal accountability, then nothing legal can happen anyway. As such, countries such as Germany with 14 as both the age of consent and the age of legal accountability in general have a practical solution, which is also realistic. Most in Germany probably lose their virginity at 15 or 16. Practically no girl (and certainly no boy) has gone through puberty before 12, and for those really early bloomers who are in many respects grown women at 12 or 13, the age-difference clause is in effect (except when it is exceeded, which practically never happens with consent).

                What surprises many Europeans is that in many states in the USA one can’t legally have sex, but can buy a gun with no background check. Similarly, many movies rated R for sex are the equivalent of PG or G in many European countries, and many violent films are not allowed for those under 18, though they might be PG in the States. A different concept of what is dangerous to the youth.

                And I find this really bizarre: usually what one can give away one can sell, but prostitution (one person pays another for sex) is illegal for both, but porn (one person pays two other people to have sex, then films it and makes it available to a huge number of people) is allowed.

                I can’t think of any case of anything which should be illegal if all are consenting (and above the age of consent) and no-one else is affected.

                https://en.wikipedia.org/wiki/Prostitution_law#/media/File:Prostitution_laws_of_the_world2.svg

              2. “Consent” poses hidden pitfalls. Perhaps it should be replaced with “no coercion”.

                I “consent” to pay taxes, but only because I don’t like the alternative. If I was truly free to consent (or not), I would probably still pay something, but maybe not as much as I’m asked to pay (or, maybe I would pay more … nah!).

                This comes into play in all sorts of human interactions, but if we’re talking about prostitution, for someone to discuss it in terms of “consenting adults”, one has to ignore the organized crime aspect.

                It could be most prostitutes are independent businesspersons and the transfer of good for money is strictly a private business transaction, but it doesn’t seem like it.

                The current approach is to ban all such transactions as unlawful, and I think that actually promotes and encourages criminal elements to invest in the enterprise (much like drug laws, I’d wager).

                I also think religion is to blame for some (if not all) the (hypocritical) intolerance with regards to prostitution. But, what do I know? Nothing.

              3. Of course “consent” here means “no coercion”. Despite you example, I don’t think that anyone understands it differently in this context.

                Where prostitution is legal, it does not depend on organized crime.

                Even if one believes that no-one works as a prostitute voluntarily, and one’s goal is that no-one should work in prostitution, it still makes sense to have it legal. Customers can report anything suspicious without fear of incriminating themselves. If it is legal, there is practically no market for illegal prostitution. Also, if prostitution itself is illegal, those involved have practically no threshold to cross into further illegal activity.

                Of course, many or most wouldn’t work in prostitution if they were rich enough not to work at all, but that is true of 99 per cent of those who work, and one doesn’t call their work “forced labour”. Rather, they would rather have, say, 6000 per month as a prostitute than, say, 2000 at some other job which they find boring, tiring, etc. And, believe it or not, there are a few who actually enjoy it, and if they can make money from it then they don’t have to do other work and those who pay are happy that it is available.

                I am firmly against the idea of selling organs, for whatever reason, but in favour of organ donation. The analogy is not perfect, but it is close. Similarly, one can be firmly opposed to any form of forced labour, in prostitution or elsewhere, without criminalizing prostitution itself. And, as mentioned above, there are reasons not to criminalize it even if you think that it is a bad idea.

                Whether or not it “seems like it” depends on where you are. In particular, if it is illegal, those involved in it are by definition criminals. The “current approach” does not apply everywhere (see the link to the map). Like the death penalty, it is something which the USA and Saudi Arabia have in common. 😐

                With regard to the analogies with drugs and the influence of religion, I agree.

                And, again, consider the hypocrisy of having prostitution illegal but pornography legal.

        2. I contemplate what the female equivalent of a “womanizer” is. A “manizer”? (I can think of less mellifluous, rarefied descriptors.)

  5. And how do you define temperature? In thermodynamics and statistical mechanics it depends on the different states of the system – then it is possible to have negative temperatures.

  6. A temperature below absolute zero: Atoms at negative absolute temperature are the hottest systems in the world
    Date:
    January 4, 2013
    Source:
    Max-Planck-Gesellschaft
    Summary:
    On the absolute temperature scale, which is used by physicists and is also called the Kelvin scale, it is not possible to go below zero – at least not in the sense of getting colder than zero kelvin. According to the physical meaning of temperature, the temperature of a gas is determined by the chaotic movement of its particles – the colder the gas, the slower the particles. At zero kelvin (minus 273 degrees Celsius) the particles stop moving and all disorder disappears. Thus, nothing can be colder than absolute zero on the Kelvin scale. Physicists have now created an atomic gas in the laboratory that nonetheless has negative Kelvin values. These negative absolute temperatures have several apparently absurd consequences: although the atoms in the gas attract each other and give rise to a negative pressure, the gas does not collapse – a behavior that is also postulated for dark energy in cosmology.

    Science News

    [last post, i should have consolidated, sorry]

  7. “But as we approach absolute zero, we can’t GET anything whose temperature is just a tad above absolute zero to suck away that last bit of heat.”

    This is a confusing sentence, though I believe what he meant by this was that the stuff next to whatever you’re trying to cool is not going to be colder (ie, it’ll be warmer) so heat transfer can’t occur. In other words, everything around what you are trying to cool will be warmer so cooling can’t happen.

    1. That side of it is kind of obvious without much physics subtlety: the “tad” object surely cannot cool anything to lower than its own temperature.

      In my naive classical (i.e. non-quantum) false intuition, Jerry’s question seems to be asking why one can never get every one of the particles making up that object to shut up and sit still—no moving, no quivering. Surely the answer to a sensible quantum version essentially explains that.

      But to me, I’d initially go half-way to relativity and ask what is the frame of reference for judging these motions. It must have some physical reality, so that would be something itself already at absolute 0, but in some macroscopic sense. We talk about larger objects having zero speed all the time.

      Somebody should check Richard Feyman’s lectures on physics from Cal Tech on this.

  8. When such ideas appear with one specific variable with such intense focus on that one specific variable, at its extreme end, with huge results – its damn cold! – I start wondering if I am simply ignoring one other simple variable (maybe S, don’t know…, and attaching too much weight to – in this case – T … and assuming linearity… when at extrema sometimes our assumptions need examination…

    … IOW the whole “the answer is 42” problem… or “beginning of time”,… etc…

  9. The three laws of thermodynamics, as I was taught in 1961:
    1) You can’t win [conservation of energy]
    2) You always loose, unless you are at absolute zero [entropy]
    3) You can’t be at absolute zero.
    About the only thing I remember about that class: Came in one morning, someone had written on the chalkboard “Professor Hofstadter has won the Nobel Prize in physics”. He comes in to polite applause, erases the chalkboard, class as usual.

  10. The Fahrenheit scale was originally a “centigrade scale”, and 0 Rankin is the Fahrenheit equivalent.

    Currently reading Brian Greene’s “Until the End of Time”, he looks like an free will skeptic incidentally, pp 151-9. He suggests 10^(-30) kelvin is as low as we can go, because of quantum effects.

  11. Absolute zero is the temperature a system would have if all thermal energy was extracted from it. That’s why there’s a limit to how cold something can be, it’s the point at which the thermal energy is zero and its atoms aren’t moving. You can’t get any more motionless than being completely still.

    I’ve read that there is also a theoretical limit to how hot a physical system can be. It’s some insane temperature like a googol degrees. Above this point the thermal energy is so great it would tear spacetime apart or something like that.

  12. Temperature is a measure of how much energy a system has that is available to be transferred to another system. A system at its quantum ground state has zero energy available to transfer to another system and the temperature of such a system is DEFINED to be 0 Kelvin. Every system has a quantum ground state which is its lowest energy state and hence can never have a temperature below 0 K. In some cases, the temperature of a system is proportional to the average kinetic energy of its constituents (or at least it’s a really good approximation) but not in general.

  13. Temperature is a measure of how much energy a system has that is available to be transferred to another system. A system at its quantum ground state has zero energy available to transfer to another system and the temperature of such a system is DEFINED to be 0 Kelvin. Every system has a quantum ground state which is its lowest energy state and hence can never have a temperature below 0 K. In some cases, the temperature of a system is proportional to the average kinetic energy of its constituents (or at least it’s a really good approximation) but not in general.

  14. So, how about this . . . think about absolute equality. You can’t get there because there’s no such thing (it’s a theoretical concept, like justice). We may speak of equality, and it may even be a useful concept to examine, discuss, etc. but we can never get there.

    We inherently know this because we understand the limits of the word absolute. But, if we imagine absolute equality *could* be achieved, we’re implying an equilibrium where some would lose something and others would gain it (easily understood when we speak of money),

    Temperature is like money in the case where you have one person with all the money and one person with no money.

    You are trying to get the person with all the money to zero, BUT . . . the only mechanism available is to take money from the person with the most money and give it to the person with the least money.

    Meaning, at no time can both person have zero money because at some point they would reach equilibrium (both have the same amount of money) and no more transfer can take place, and neither is at zero money

    You’re asking the equivalent of “why” can’t all the money disappear and both be at zero. Well, now you’re talking about changing the rules, so the question actually is “why can’t we change the rules?”

    Heck if I know, but if I were to venture a guess, our simulation won’t allow it. Maybe after the next reboot, the conditions will change and we can just get rid of money all willy-nilly like.

    1. Absolute zero is not at all like absolute equality. They are totally different concepts. Absolute equality is more like chemical reactions that proceed to thermodynamic equilibrium, at which point reaction rate in both directions is the same and no further net transfer of mass or energy takes place. This can occur at any non-zero temperature and there is really nothing absolute about the process at all. (Tongue-in-cheek, absolute equality similarly removes the incentive to do any economic work. As soon as you make effort to move away from equilibrium, your gain is immediately taken from you and the system returns to equilibrium stagnation. To make all the money disappear, yes, you do have to change the rules, like impose communism.)

  15. Empirically and without invoking QM, you can always use Charles’ law. Observe a gas at constant pressure, lowering the temperature and measuring the volume as a function of T. Plot T (x axis) vs. V (y axis). You will find all the points sit on a straight line (with a positive slope). You can extend that line and ask what is the x coordinate for when y (the volume of the gas) = 0. Volume can’t be negative; that’s an unphysical concept. So the Temp for Vol. = 0 is your physical lower limit. For centigrade scales, that’s about -273.

    This guy’s video does the Charles’ law experiment on his desktop using a syringe, a warm water bath, and an ice bath, and gets about -290 C using only two data points. Not bad for a Elementary school level set-up. The video is extremely basic – for Jerry and other folks who know the subject, I recommend skipping through to look at: 2:20-3:20 (Charles’ Law), then 6:15-8:30 (setting up the math and thinking through the experiment), then 12:30-end for the experiment and analysis of results and limitations. (8:30-12:30 is a failed first experiment using a different setup. A good bit of video and interesting from the experimental design point of view, but not entirely necessary.)

  16. Like yourself Jerry, I too am one of those people to whom Tyson’s video is directed. Both his first and second explanation make sense to me, but then perhaps that is because I teach physics online to students enrolled in a small aeronautics college in Ohio. But I am unclear about the third explanation. Going to have to explore it a little deeper.

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