# Is quantum mechanics applicable to only small things?

There was a fill-in-the-blank question in my university test. It was something like:

Quantum mechanics deals with ____

I wrote "everything" and my lecturer gave me no marks. He was expecting something like "small", "nano" or something. I tried to convince him that quantum mechanics deals with everything in the universe and its effects are obvious only in smaller things. But he was so certain that quantum mechanics if applied on big things will give incorrect results. So, am I wrong? Won't quantum mechanics work on bigger things?

• Relevant: youtu.be/pktWhH6m_DM – More Anonymous Jul 23 '20 at 8:16
• @MoreAnonymous Thanks! – Rahul R Jul 23 '20 at 8:40
• Ooooooh, philosophy! :-) . In all seriousness, whoever wrote that question should be fired for basic incompetence. – Carl Witthoft Jul 23 '20 at 13:15
• @CarlWitthoft :) It was a question in an internal test. Not a semester exam question. I thought it was a trick question at first and that everyone would write "microscopic" or "nano" and he would surprise us by saying quantum mechanics works on every object. I was wrong... ( He was just a guest lecturer. Anyway he shouldn't have put such a controversial question) – Rahul R Jul 23 '20 at 13:25
• I've removed a number of comments that were attempting to answer the question and/or responses to them. Commenters, please keep in mind that comments should be used for suggesting improvements and requesting clarification on the question, not for answering. – David Z Jul 23 '20 at 22:14

The relationship between quantum and classical descriptions is somewhat tricky, unlike the relationship between the relativity and the classical mechanics. Classical mechanics can be simply thought of as the limiting form of the relativity at small velocities. Thinking of macroscopic objects, as if they were quantum objects with very short de Broglie wave lengths and therefore having low quantum uncertainty, is however not satisfactory. For one, these objects usually consist of many small objects interacting among themselves and with their surroundings, so one cannot avoid discussing decoherence/dephasing and adopting some kind of statistical physics description. Secondly, measurement is an essential element of quantum theory, which implies a microscopic (small) object coming in contact with a macroscopic one (a big thing), which may generate some logical paradoxes.

All this complexity does not negate the fact that macroscopic object are also quantum objects, although describing them with quantum laws is by far more difficult than applying these laws to atoms and molecules. Nevertheless, it is an active field of research. The examples that come to mind are:

• nanomechanical systems - these can be C60 molecules or carbon nanotubes containing thousands of atoms or similar size nanorods made of other materials that exhibits quantum behavior. These object are still microscopic, but far bigger than what is usually seen as quantum.
• macromolecules, such as proteins or DNA - there have been claims that the exhibit quantum behavior, tunneling through each other. My evidence might be anecdotal, but there is research in this direction. Still, these are studied.
• everything related to superconductivity, superfluidity - this may happen at visible scales, although at very low temperatures.
• Comments are not for extended discussion; this conversation has been moved to chat. – Chris Jul 25 '20 at 23:19
• @Chris thanks for the link to the chat - otherwise it is hard to find. – Vadim Jul 26 '20 at 12:09

An example of (very) big things that need quantum mechanics to be properly described is black holes.

• This is not about quantum mechanics being sufficient. It is about being necessary. – ɪdɪət strəʊlə Jul 23 '20 at 20:03
• Isn't the black whole actually too small? – akostadinov Jul 23 '20 at 21:20
• @akostadinov Not once you take the event horizon into account, which is where the quantum interactions are taking place to produce Hawking radiation. – nick012000 Jul 24 '20 at 2:25
• @uhoh Compared to the scale the OP's teacher seemed to be talking about this is still very big :) – ɪdɪət strəʊlə Jul 24 '20 at 5:53
• And neutron stars. – Peter Mortensen Jul 24 '20 at 13:30

Everything in the universe is such a broad word.

One thing that QM does not deal with is for example gravity. There are attempts to apply QM on gravity, but they are not successful so far and as it stands, QM cannot be applied here.

There is also problem with applying QM to everything at once. QM is quite problematic when it comes to explaining measurement. The standard formulation of QM introduces special agent to deal with it. So you need something outside of your QM system to act as this agent, which contradicts your attempt to apply QM on everything.

You may say, that QM should apply to everything as it is according to our understanding most fundamental theory we have, but that does not mean it does. Existence of quantum gravity might look promising, but we do not know yet. The measurement problem is however quite different and there is less hope it will be solved withing the framework of QM. It can be dodged as long as you retain some external agent - which is the strategy physicists adopted - but as long as you want to include everything there arises a problem. I think (I heard Lee Smolin to talk about it somewhere) research in quantum cosmology faces just this problem.

Edit

I would like to explain better the use of my word "agent". The problem is, that somewhere in the transition from QM to classical, the system must make choice about its state. The problem is QM does not define when does this happens, only how does this happens. It is up to the physicist to know when to apply the collapse during calculation, QM itself does not dictate this. The collapse itself is integral part of the QM, but when it happens is not. This missing knowledge that is left upon the physicist making the calculation makes QM not self contained and therefore it cannot be applied on "everything" in this sense. The choice must be made outside of its realm.

But of course this is based on standard formulation of QM I was taught. I do not follow research on this topic, so if there is more knowledge about this problematic, I would be glad to be corrected and read more about this. However, I remember from book by Sabin Hossenfelder "Lost in Math" that measurement problem is still huge hole in QM.

• Comments are not for extended discussion; this conversation has been moved to chat. – tpg2114 Jul 25 '20 at 16:02

Is Quantum Mechanics applicable to only small things?

No. It's applicable to things which can be described by quantum numbers such as - spin, parity, magnetic moment, charm, x-charge, helicity and others. Also such objects are subject to measurement of entanglement degree if any. And to them applies uncertainty principle and wavefunction. Usual boundary helping to consider such objects are De Broglie wavelength. For QM objects De Broglie wavelength must be much greater than Plank length : $$\lambda_B ={\frac {h}{mv}} \gg L_{Plank}$$ For example for human of 70 kg mass, taking unit speed, gives De Broglie wavelength on the order of Plank length, so certaintly QM effects on walking human can be safely discarded.

Above given equation can be rewritten in terms of object volume :

$$\lambda_B ={\frac {h}{\rho~V~v}}$$

This gives insight that De Broglie wavelength can be comparable between objects of high-density/low-volume AND low-density/high-volume. Latter corresponds to Bose-Einsten Condensate,- a specific ultracold gas type where all gas particles are entangled together and because of that whole gas cloud acts like "one big quantum particle". I.e. BEC gas cloud is a macroscopic quantum mechanical object to whom all QM rules apply.

• What do you mean by QM objects? Are you saying that there are other objects which do not follow QM? I believe that every object can be treated by QM. Its just that CM is more easy in most daily life cases and its just an approximation of QM when the wavelength is smaller than plank length. – Rahul R Jul 23 '20 at 9:36
• It's objects to whom quantum mechanics is applicable. I've explained in my post applicability rule. Of course not all objects are under consideration of quantum mechanics rules as well as not all objects are under special relativity rules (those with speed $v \ll c$), etc. mean technically you can apply any law as you with to any set of physical objects, but it's not much use of it, if it can be described by classic physics equivalently – Agnius Vasiliauskas Jul 23 '20 at 9:42
• Can you give some examples for objects which do not follow QM that can be explained with Classical Mechanics? – Rahul R Jul 23 '20 at 9:44
• Every tool has it's own uses - right ? You are not bashing nail with an axe, but use a hammer instead, right ? The same applied to theoretical physics foundations also. You use some physics model, where it is most useful/applicable. – Agnius Vasiliauskas Jul 23 '20 at 9:52
• Thanks for clearing the misunderstanding. I got what you meant. So can we all agree on the fact that QM can explain everything that CM can? – Rahul R Jul 23 '20 at 9:53

You are right in your understanding. Your professor is wrong. As mentioned earlier by others, quantum mechanics is applicable to the macroscopic regime too, but how to interpret the equations is something non-trivial and active research is pursued by many in this direction. Always remember, classical objects are quantum objects too.

If you are interested in knowing more, one such research area is called as macroscopic quantum mechanics (not something pioneered by Dr Carlo Rovelli, but by Dr Ravi Gomatam). Some of his papers are freely available from his ResearchGate account.

Or to get started, just go through his presentation here.

Your lecturer is wrong. Quantum mechanics would give accurate predictions when applied to macroscopic objects. The idea that quantum mechanics doesn't apply to macroscopic objects doesn't make any sense. Quantum mechanics explains the behaviour and interactions of atoms, and objects are made of atoms, so either quantum mechanics explains the behaviour of macroscopic objects, or it is false. The reason we don't see quantum interference for objects like human beings, pens etc has nothing to do with quantum mechanics not applying to those objects. Rather, quantum mechanics explains that when information is copied out of a system during an interference experiment interference is suppressed:

https://arxiv.org/abs/quant-ph/0703160

Since information about the location of large objects spreads into the environment on timescales that are a lot smaller than the timescales over which we see those systems evolve, those systems don't undergo interference.

Quantum mechanics deals with isolated things.

This would be my preferred answer to the question. Baring some very speculative stuff relating to gravity the reason we don't see quantum mechanical effects in everyday life is not because the things around us are big, but because they are messy.

Quantum mechanics is (to my mind) first and foremost a probability theory - one can think of it as stating that probabilities don't work quite classically (they can cancel out for example). When working with probabilities it is completely normal to update ones assumptions when the information available changes, "well given that you have played that card the chance of me drawing it is now...". Every time a quantum object interacts with the air particles around it it "gives the game away" at least partly, it tells the air molecules where it is when it hits them.

That information "leaking out" means that you have (in principle) access to a lot of constraints on where exactly the beachball is, lots of air molecules got hit. Once enough information is out their to determine its location then its location is not longer probabilistic. (In the sense that, after you draw the 2 of Clubs it is no longer probabilistic.) Once the beach balls location is fully determined then we no longer need a a probability theory: so goodbye quantum mechanics - no longer needed.

Consequences:

• The fundamental difference between the quantum computers in development and the computer you are using at the moment is that in a quantum computer the data is kept isolated from the rest of the universe throughout the calculation. So it can do quantum-ness.

• At least in principle, from the theory as-is, the universe itself (the entire thing taken together) works in a quantum manner, because their is nowhere else for information to leak out too. This highlights an interesting subtlety: classical physics arises from considering only part of a quantum system. As far as we know if you could somehow consider the whole system (not just the beachball but also every air molecule and photon it disturbs) quantum physics would re-emerge.

• "At least in principle, from the theory as-is, the universe itself (the entire thing taken together) works in a quantum manner"- So the whole universe works in quantum manner. So why should you specify "isolated"? As everything (the universe) is isolated, you could just say "everything", right? – Rahul R Jul 24 '20 at 17:25
• Saying "everything" is misleading because you might think that means "every individual thing". Individual things (people, cats beachballs) behave classically if they are in good contact with the rest of the world. "Behaving classically" does not mean that Quantum mechanics cannot be used to describe them - it means quantum mechanics is not NEEDED to describe them. You could say "everything, but not every thing". Its kind of silly though as that would be taking the model far beyond the realm in which is has been established. – Dast Jul 29 '20 at 11:32

Quantum mechanics (QM) doesn't deal with "everything". Otherwise it would be called The Theory Of Everything.

The most important obstacle is that QM doesn't deal with gravity. And since gravity becomes really relevant at large scales (with the exception of the Planck length) then there is some truth to your lecturer's judgement.

• Re "with the exception of the Planck length": Do you mean below the Planck length (or at scales below the Planck length)? – Peter Mortensen Jul 24 '20 at 13:38
• @PeterMortensen I"m not the expert in the field, but AFAIK it is believed that gravity becomes relevant at the Planck length. Unlikely that below Planck length things are meaningful. – freakish Jul 24 '20 at 14:41

No. People often tend to get the wrong idea. Quantum mechanics can be applied to any situation ( finding the maximum height reached by a ball or calculate the charge of electron). I assume, you think only Newtonian mechanics applies to macro objects. But Newtonian mechanics is just an approximation for quantum mechanics. Even NASA uses the good old Newtonian physics. :D

Might be that when the professor was telling you the answer he was expecting in lecture, you weren't paying attention, and now you're just looking for justification. Sure QM describes rules at the most foundational level of our comprehension, but those rules are most useful when applied to a certain problem domain, and the macro world isn't usually part of that (black holes aside). Though I would argue that "small" is a very simplistic answer - perhaps the most simplistic answer your professor would accept, where perhaps more specific answers would be preferred, not less specific ones.

How big do things need to become? Quantum mechanics describe the energy levels of atoms in plasma and molecules. That's what allows us to observe and deduce the consistency and history of the universe. It's what allowed astrophyscists to stipulate the existence of dark matter and energy, and it is quantum mechanics that will deliver the theories allowing us to eventually do away with them again and derive more exact descriptions both what happens in astrophysics as well as in gas kinetics.

Modern chemistry is unthinkable without the orbital models of quantum mechanics, and chemical processes happen in large plants. It doesn't stop being based on quantum mechanics just because you add large-scale statistics on top: the individual bond energies and electron interactions don't stop governing what happens just because it happens at scale.

The question is ambiguous!

Quantum mechanics deals with...

can mean two different things:

The science of quantum mechanics deals with...

or

The physics researched by the science of quantum mechanics deals with...

or equivalent

Quantum mechanical processes deal with...

It's fair to say that a scientist typically deals with microscopic things. So the teacher was right for this interpretation.

Of course, you were also right based on the other interpretation.

You are asking "Won't quantum mechanics work on bigger things?", and the answer is a big yes it does work.

One of the most fascinating examples is quantum entanglement, and the fact that it has been experimentally proven to exist between objects visible with the naked eye.

Quantum entanglement has been demonstrated experimentally with photons,[10][11][12][13][14][15][16] neutrinos,[17] electrons,[18][19] molecules as large as buckyballs,[20][21] and even small diamonds.[22][23]

https://en.wikipedia.org/wiki/Quantum_entanglement

Contrary to popular belief, quantum entanglement can apply to objects much larger then elementary particles.

The researchers led by Prof. Mika Sillanpää at Aalto University in Finland entangled two individual vibrating drumheads made from metallic aluminum. Each drumhead had a diameter the size of a human hair, making it huge by quantum standards.

https://www.zmescience.com/science/quantum-entanglement-large-object-43242/

• Why the downvote? – Árpád Szendrei Jul 26 '20 at 21:07