Photons, electrons are subatomic particles to which the wave-particle duality applies. Protons are heavier quantum objects and posses quantum tunneling which is a wave character.

What is the upper limit in size or mass after which quantum effects (wave-particle duality) no longer hold?

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    $\begingroup$ "quantum effects" hold no matter how big the object is. After all, QM is a better representation of Nature than CM. $\endgroup$ May 6, 2016 at 15:48
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    $\begingroup$ Wave-particle duality is an old confusing term from the times of pre-relativistic quantum mechanics that hasn't been necessary since 1929, when Mott correctly explained the emergence of particle behavior from wave equations. Today we study matter and radiation as part of one and the same wave phenomenon. Neither can exist without the other and we have developed a theory that describes both using similar types of wave equations. That larger chunks of matter show mostly particle like behavior is because of their short decoherence length, which makes the underlying wave behavior hard to observe. $\endgroup$
    – CuriousOne
    May 6, 2016 at 19:31
  • $\begingroup$ If you're talking about observables, the semi-classical and classical limit is observed at magnitudes larger than the de Broglie wavelength of the particle in non-relativistic settings, where $\lambda = \frac{2\pi\hbar}{p}$ and $p$ is the momentum of the particle. This is the regime where classical effects often overtake quantum effects, but like others have said, this is far more nuanced than just 'a particle of this size/mass will be a particle or a wave' since the separation is only artificial and is an approximation. $\endgroup$ May 6, 2016 at 23:52
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    $\begingroup$ LIGO's 40 kg mirrors are treated as quantum objects in order to observe sub attometer motion. $\endgroup$
    – JEB
    Jul 19, 2019 at 0:00

1 Answer 1


Quantum interference experiments have been done even by using large molecules, such as the C-60 fullerene; although there is no such thing as a 'limit', as quantum effects hold good for all objects, as it is already pointed out in the comments.

  • $\begingroup$ does that mean that even large molecules if fired on a double-slit wall will result in wave pattern ? $\endgroup$
    – M.ghorab
    May 6, 2016 at 20:08
  • $\begingroup$ Yes, although the gratings required to actually observe the interference pattern experimentally are much more complex than that. $\endgroup$
    – Harsha
    May 7, 2016 at 10:11

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