# Is quantum mechanics applicable to only small things?

Physics Asked by Rahul R on July 24, 2020

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?

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.

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.

Answered by Bob on July 24, 2020

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.

Answered by freakish on July 24, 2020

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 there is 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. 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.

Answered by Ashwin Balaji on July 24, 2020

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.

Answered by alanf on July 24, 2020

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.

Answered by Umaxo on July 24, 2020

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

Answered by ɪdɪət strəʊlə on July 24, 2020

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.

Answered by Agnius Vasiliauskas on July 24, 2020

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