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I’m perfectly aware about the wave-particle duality of nature and therefore the difficulties of claiming what behaving like a particle is. This question is not about this very profound behavior of fundamental particles, thus, hereby I try to explain what I mean with that in present context. Here, an object behaves like a particle if when left free a) to interact with a screen it mostly produce a single small dot; b) if passing through a cloud chamber it leaves a clear path.

A good example of particle-like behavior is an electron in a cathode rays tube or a high energy electromagnetic photon. Obviously as was experimentally demonstrated, if a double-slit is had along the way of the objects a broad interference pattern will appear. This situation would account -as per current definition- as not being left free to interact.

The counter example would be an electromagnetic object at the radio wave-length. These objects will mostly behave as waves rather than photons.

Now, as a personal observation, it seems that almost all massive objects (electrons, protons, neutrons, etc.) tend to behave like particles in a broad range of energies (from rest to very high energies) with the same happening to almost all high-energy massless objects (mainly electromagnetic objects). It seems to me, that behaving as a particle is somehow associated to the objects energy (small mass=huge energy). So my questions are:

  1. Is the above observation true as a rule of thumb? If true, what are the exceptions to this, for example, a massive object or high energy massless objects that don’t follow the above rule, including gravitational waves or any other objects. Strange theoretical objects will be welcome.
  2. Is there a clear equation that gives a smooth transition between wave-like to particle-like behaviors as energy increases?

PS2: I found (this)1 and (this)2 questions here on the site. However, they are not what I’m looking for.

J. Manuel
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    In quantum mechanically modelled particles the "wave" is a probability wave many uinteractions have to be added in order to see a wave behavior. see https://www.sps.ch/artikel/progresses/wave-particle-duality-of-light-for-the-classroom-13/ . For photons this is true for all energies, from far infrared to high gamma in mainstream physics standard model. – anna v Apr 21 '22 at 13:25
  • This might not necessarily answer your question, but for me I was able to rationalize your first question as not always true. Light waves in space bend around objects (think how light curves around a planet). Light is high energy and massless, but it behaves as a particle in this context in that it is affected by gravity. The light wave started with a straight trajectory, but it curved around the planet. Comets, asteroids, satellites, etc. also get pulled by a planet's gravity, even if it started on a straight trajectory, and these have comparatively huge mass and relatively small energy [...] – Vanessa Riggz Apr 21 '22 at 15:35
  • ctd [...] : "compared to light." – SuperCiocia Apr 22 '22 at 05:03
  • The particle-like properties of radio waves are apparent in the Planck spectrum of the cosmic microwave background. – John Doty Apr 22 '22 at 14:34
  • @JohnDoty. At a very deep level, wave-particle behaviour is the rule, I don't deny that. However, radiowaves, mostly behaves just as the name implies, as waves... – J. Manuel Apr 25 '22 at 14:03
  • Maybe you could elaborate about what you mean by 'left free'. I do not understand why the double-slit would not leave the particle free, while a cloud chamber would leave it free. Both slits and chamber are which-path detectors, so why the difference? – Stéphane Rollandin Apr 27 '22 at 09:37
  • @StéphaneRollandin. I believe that the whole story about “wave-particle” duality of nature is due to the fact that somehow we all have an intuition of what it means being (behaving as) a wave and being (behaving as) a particle. As I said, I admit it is very hard to define behaving as a particle, and don’t want to move the focus of this question into that definition. At this point I will have to appeal into that intuition and waiting for an answer for: why high energy objects, unless otherwise specified, are treated as particles. – J. Manuel Apr 27 '22 at 10:32

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