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First of all I beg your forgiveness as I am not a physicist and the question I am going to ask may sound silly.

I am aware that beyond a certain threshold in the hierarchy of building blocks of matter (electrons, atoms, etc.) the 'standard' laws of physics (e.g. Newtonian physics) do not apply and we enter a totally different environment where the so called quantum mechanics apply.

  • Where is this threshold located in relation to types of particles?
  • Are there any other similar thresholds in physics indicating completely new environments? If yes, what are they? (other than classical mechanics, quantum mechanics, ...maybe string theory?).
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    $\begingroup$ Here's a related question with some answers you may find interesting. Which is the biggest object which can interfere with itself? $\endgroup$ – BMS Sep 11 '14 at 23:31
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    $\begingroup$ @BMS Can't help but notice that the answers in the question you linked to does not include Neutron stars, which are quite big. $\endgroup$ – Aron Sep 12 '14 at 4:06
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No other thresholds comparable to quantum-classical are known, nor is there any reason known at present to suspect them.

The precise threshold between quantum and classical physics is actually rather simply: it is ignorance (quantum) vs knowledge (classical).

More precisely, regardless of the sizes or masses or scales involved, quantum rules always apply when there is absolutely no trace of information anywhere in the universe about what is happening. In such cases of true and absolute ignorance, the hidden entity will in a strange and probabilistic way attempt to explore every possible history left open to that is compatible with the laws of physics and the "envelope of ignorance" that the rest of the universe sees for the system.

The result of this exploration of all options available is called the integral of all possible histories, and it is the direct source of all the wavelike and probabilistic behavior that we find so odd in quantum mechanics. For example, a single particle begins to look like a wave because within its envelope of ignorance it is forced (it's not an option ) to explore an infinite number of smoothly similar and nearby paths.

In contrast, once any information leaves about what is going on leaves the system and irreversibly becomes part of the outside universe, that aspect of the entity ceases to follow quantum rules and becomes part of classical physics, which allows only one possible future to be explored at a time.

The main reason why no other quantum-classical thresholds seem likely is that the above rules are really just different aspects of the same phenomena. That is, information is by definition the loss of the quantum default of unbounded exploration of all open options, forcing some part of the universe to become specific, real, and historical. Without this deep and essentially tautological relationship between between quantum generality and classical specificity, concepts such as history and information would cease to have meaning. After all, a universe in which all things are happening at once is in the end no different from a universe in which nothing ever happened at all.

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    $\begingroup$ In my opionion, the challenges in combining quantum theory with general relativity quite strongly suggest that there will be other thresholds, where string theory or something else will be needed. Also even at present, relativistic-classical is a comparable boundary to quantum-classical. $\endgroup$ – jpa Sep 12 '14 at 6:27
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    $\begingroup$ @jpa, your point about the interaction of GR and QM is an excellent one. The earliest deep dive I know of on this was by the amazing Dirac in his oddly overlooked Lectures on Quantum Mechanics; see e.g. Lecture 3, pp. 44-67, "Quantization on Curved Surfaces." His argument is that curved space is simply incompatible with quantum behavior, implying that a strongly curved space limits such behaviors to unusually fine-grained regions of space. I find Dirac's persuasive case, but that is also why I don't think GR is anything more than just a downward scale modifier on the QM threshold. $\endgroup$ – Terry Bollinger Sep 12 '14 at 13:05
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    $\begingroup$ @TerryBollinger, your answer, sir, just blows my mind. Brilliant! Let me ask a couple of questions as I am not 100% clear about the informational aspect of this. So let't say, we have a 'pocket' in timespace with absolute entropy (which you call "ignorance envelope"). Then some invisible hand, say you, will force particles to stop lingering and explore all posible histories. But what is that'invisible hand' which forces them to explore? Is it a property/function of: that state of ignaronace/total entropy, of each separate particle in the envelope or of the timespace itself? $\endgroup$ – Jess Parker Sep 14 '14 at 16:25
  • $\begingroup$ The two main sources opacity are: low energy (coldness, including radiation-free vacuum environments); and a lack of available transition options due to quantization effects at low mass-energies. Cold e.g. enables superconductors, superfluids, and Bose condensates to form human-scale quantum regions where all particles participate in a single wave function. Quantization blindness enables super light electrons to form stable wave functions (orbitals) even in the presence of vast, info-rich thermal energy. Their lack of low-energy transition opportunities leaves them no "memory to see that info. $\endgroup$ – Terry Bollinger Sep 14 '14 at 16:57
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Newtonian physics is generally a good approximation in a problem as long as any significant differences in the action involved in the problem are much larger than Planck's constant (if not, quantum mechanics will be needed), the speeds involved in the problem are much less than the speed of light (if not, special relativity will be needed), and as long as the Schwarzschild radius of any gravitating object in the problem is much smaller than the object's radius (if not, general relativity will be needed). In addition, if a problem meets the criteria for needing both quantum mechanics and special relativity, then quantum field theory is needed.

Quantum mechanics is generally adequate for analyzing the electrons within atoms, but quantum field theory is generally needed for any other kind of subatomic particles.

The above are really just rules of thumb. For example, macroscopic quantum phenomena exist, in which quantum phenomena are apparent at a macroscopic scale.

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    $\begingroup$ This is technically correct, but I wonder if OP will take anything away from it. Not being a physicist, references to action may not be helpful. Can OP weigh in here? $\endgroup$ – DanielSank Sep 12 '14 at 6:26
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    $\begingroup$ Yes, this answer is quite clear and intelligible for me. Thank you. $\endgroup$ – Jess Parker Sep 14 '14 at 12:35
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The answer depends on the thermodynamic temperature of the environment of these objects, the interaction strength with which they couple to this environment and their lifetime.

The spatially largest and consequently longest lived observed quantum effects, that I am aware of, are interference fringes of light that came from galaxies that are millions of lightyears away. The reason why these photons didn't suffer from decoherence is because they are very long lived (photon lifetime is infinite in the theory) and the universe is both very cold and only thinly populated with atoms which could scatter these photons. As a result, the light that was emitted so long ago is still coherent and will show the exact same interference terms that one would expect from a light source just a few feet away in the laboratory.

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Well, technically, both newtonian physics, relativity and QM work in tandem, all the time. However, some of the abstractions break down - for example, when you're dealing with an electron in isolation, it behaves well in accord with newtonian physics. The same way, even if that electron moves at half the speed of light, from the POV of the electron, it sill behaves classically. The interactions are the interesting part, and that's where the perceived "limits" lie.

Now, even you, as a macroscopic object, are subject to quantum physics. However, the classical approximation is by far close enough to the reality, that adding QM to the equation doesn't really change much. Think about it just like with e.g. the EM charge of an atom - no atom is truly neutral. It's just that the tiny electro-magnetic is easily lost in the tons of other interactions the atom and its constituent parts undergo - in this case, simple thermal effects are much stronger in magnitude than the moment.

One interesting "limit" for QM I've read about can be summarized as this: quantum mechanical effects are important when the physical delimitation of the "particle" is significantly bigger than the wave-length of that "particle". So for example, individual electrons will tend to behave less classically in EM interactions, because most of the EM charge of the electron is concentrated in a radius significantly smaller than the wave-length of the electron. On the other hand, your body is much larger than the wave-length of your body as a whole, so you as a whole tend to behave rather classically, even though your constituent parts don't. Taking a CPU as an example, every single transistor is dependent on quantum physics (quantum tunelling in particular) to work, but the processor as a whole does not display non-classical behaviour - in fact, even the transistor itself, as a black box, does not behave "quantumly".

Of course, all of this depends on accepting the quantum reality to be the more fundamental, or "closer to the territory" than newtonian physics. This may or may not be so, and there's a lot of debate on the specifics, as well as the major points (see the various interpretations of quantum physics, for example).

(Disclaimer: I am not an expert on the subject, and I don't have any special education in quantum physics.)

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It's not the kind of particle. It's the action. In QM there is a thing called the path integral. This adds together every possible path with a phase factor, the exponential of i (the square root of -1) times the action. The action is given through the Lagrangian, which is what gets you the usual least action principle for classical mechanics. The classical path is the least action path. Every other path is added on with this complex number multiplying it, effectively meaning its phase is shifted by this amount. The total of all these paths gives the probability for what the particle will do.

So you can ignore the quantum effects when the classical path dominates the behavior of the system. The usual way this happens is when there are many particles, so that the non-classical paths wind up averaging to very nearly zero. This is because the exponential function changes very rapidly with changing argument. So when there are many particles, it changes much more rapidly. The only path where all the particles will tend to add up will be the classical path, and the others will tend to line up randomly relative to each other, and so tend to wash out.

Note: Tend to, not do so absolutely . There are several well known macroscopic systems that can show quantum phenomena. For example, there is a photo-multiplier tube, which in principle can be made to detect a single photon, and so convert it to a macroscopic human-eye-visible thing. Also, there are some crystal structures that can be made to detect single phonon states, especially at cryogenic temperatures. And MRI shows some distinctly QM phenomena. I think there are some others, but I mis-remember them just now.

The classical limit is important because it means that QM will recover all the results of classical physics. It still retains, for example, the least action principle for large masses made up of large numbers of particles.

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The key threshold is https://en.wikipedia.org/wiki/Quantum_decoherence#Loss_of_interference_and_the_transition_from_quantum_to_classical_probabilities Essentially above this limit, parts of the system receive thermodynamic information from other parts, acting as observers, breaking the coherence and causing irreversible entropy change https://phys.org/news/2013-03-decoherence-quantum.html

Increasing the decoherence limit is a key preoccupation of quantum computing. https://hackernoon.com/decoherence-quantum-computers-greatest-obstacle-67c74ae962b6 And error correction can compensate for some information loss https://en.wikipedia.org/wiki/Quantum_computing#Quantum_decoherence

There are special circumstances when quantum behaviours can manifest at larger scales. https://en.wikipedia.org/wiki/Macroscopic_quantum_phenomena There is an interesting case of creating a quantum superposition of something (just) visible with the naked eye https://physicsworld.com/a/quantum-effect-spotted-in-a-visible-object/

Edited to add:

Are there any other similar thresholds in physics?

This is a bit vague. What does it mean to be 'like' the quantum decoherence threshold? But I think an affirmative answer can be ventured.

Essentially you have more complex equations with multiple terms in the quantum world, that reduce to simpler equations in the classical world. A lot of this is to do with the size and energies of information carriers like photons, and thermal vibration states, but it's not a hard and fast boundary.

We also have more complex equations from general relativity, which simplify at lower velocities and energies, and masses. These behaviours manifest that time is a dimension along with space.

There are other heuristic divisions, based on the scale of action of the different fundamental forces,where they dominate and other forces can be neglected.

It is proposed as you suggest, that another set of behaviours will be found at lower scales and shorter times, the planck scale. This may be where additional dimensions manifest, which unify quantum behaviors which are all time reversible, with expected quantum behaviours of time and space. The realm of superstrinv theory, or quantum loop gravity, or something else.

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