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Suppose that quantum mechanics (or QFT), like Newtonian physics and other past theories, turns out to have a limited domain of applicability, beyond which it is replaced by a deeper theory.

What is your best guess as to what physical parameter will delimit the boundary between quantum mechanics and its successor? Is it a length scale, an energy or energy density, a number of degrees of freedom, or something else?

Radical idea that there might be a new fundamental constant analogous to Planck scale /energy/length where some new theory might take over. What would you look for to observe this?

Is this a large scale problem, or small scale problem?

If QM breaks down it could be at high energies at small scales (high energy density)

What about intermediate / mesoscopic scale?

Can you abandon the wave function (non-ontic?) and build up a new theory that is consistent.

Is QM the problem? We haven’t seen any solid experimental evidence for QFT/QM breaking down?

Future  Ligo / optomechanical experiments to test QM with macroscopic systems, Superconducting experiments currently test in mesoscopic regime.

Could action be a relevant constant in a theory that underlies QM and gravity. Could Planck constant be something that is fixed or something that is emergent. If these things are emergent then length isn’t fundamental but emergent.

Planck Area (in 2 dimensions), in fractional quantum hall effect area of magnetic flux constant, or some Planck surface in higher dimensions.

What regime would we have to go to to see QM/QFT break down? LHC (high energy), LIGO, optomechanics, etc haven’t observed anything.

Does anyone really expect it to break down? So far it has survived every experiment thrown at it.

Perhaps quantum foundations and interpretations is a more interesting direction than what breaks down.

Combination of length scale and energy scale at different limits

Quantum mechanics has been a very successful theory that describes several natural phenomena that can be tested experimentally. This proves up to some extent the validity of quantum mechanics. Until today, most of the challenges that quantum mechanics faces are mostly leaned towards the different interpretations of the concepts of the theory. As a mathematical theory, quantum mechanics is consistent and makes predictions that are experimentally verifiable. With this one can argue that quantum mechanics has no successor theory. However there is no guarantee the there is broader theory that reduces to quantum mechanics. In fact, recent works on String Field Theory suggest that the 'rules' of quantum mechanics  can be derived from physical processes between extended degrees of freedom. However, this does not constitute a bigger theory containing quantum mechanics, but an equivalent formulation. Furthermore, there has been works addressing the fate of quantum mechanics under certain deformations that shows that quantum mechanics is a very robust theory.  In summary, quantum mechanics is a robust theory that as a mathematical framework is very strong, but there is still an active debate on what the right interpretation of it is. The outcome of such debate will probably shed light on the domain of applicability of the theory and the so-called physical parameter that will delimit the boundary between quantum mechanics and its successor (if there is any).

It is known QFT breaks down at a very high-energy scale. Planck scale is definitely beyond QFT’s applicability. At such a scale, quantum gravity effects sit in and it is not clear how to define basic quantities like the number of degrees of freedom and energy density. In another scenario, if a system involves many particles, huge quantum gravity effects may also take place and such system is not well understand.

May be the formulism of QFT needs to be changed. As advocated by Nathan Seiberg, the local Lagrangian formulism with gauge groups may be not the ultimate language to describe quantum physics. On one hand side, we see Seiberg duality, which indicates the gauge symmetry is not fundamental at UV scale. On the other hand, many theories, which do not have a Lagrangian description, can be calculated in the S-matrix approach.

To answer this question we should look at areas that unitarity is breaking.

Obvious scale could be planck mass (Quantum gravity scale).

another candidate would be dark energy scale.

Maybe the question is wrong. We should ask what would be the physical  quantity that we have not probed well and could potentially leads to new physics.  For quantum mechanics it was the action, for special relativity it was the speed.  What would be the physical quantity that leads to the new physics (beyond QM)?

We currently know that physics breaks at low energy (dark energy) and high  energy (QG).

it is probably not a length scale.

Degrees of freedom

Isn’t what we need to explain measure ment problem – how qm goes to classical 

Need something past the Copenhagen interpretation “difficult problem”

Is there evidence that we need a successor? Length scale is the planck scale?

Black holes?

Dark energy – doesn’t make sense from the classical  point of view – most of the universe can’t interact – classical part can’t

Multiverse – regions out of causal contact

We know that the speed of light is something we can compare velocities to in order to determine if special relativity is applicable. Similarly, the (reduced) Planck constant is something we compare the action to in order to determine if quantum mechanics is applicable. A natural guess for the scale of a more fundamental theory such as quantum gravity is the Planck scale. The number of degrees of freedom doesn’t seem to be relevant. However, it might be that “the question is wrong”; a boundary between regimes is not actually applicable here. It’s not as simple as a cutoff at the Planck scale. Physics seems to be nonlinear in a sense, so if something breaks down on one scale, it’s going to affect all scales. For example, in inflation quantum fluctuations can have large-scale classical consequences.

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