I was watching this simulation of two quantum wave packets colliding in a box:


The wave function gets arbitrarily delocalized as time goes on until you have almost an equal probability of finding the two particles anywhere in the box. This would mean that the particles are "everywhere" in the box and the place where they would "appear" upon measurement would be almost random.

Do real particles traveling in interstellar space without interacting much at all with anything get smeared out in this way? If so how we can form images of extremely far away objects? It seems as if any photon emitted from a star would be extremely delocalized by the time the wave packet reaches earth, even if it has an initially well defined direction and position when emitted. The probability of finding it at any given point on the expanding "sphere of influence" of the wave packet would be extremely small.

Also, how most of the particles in our "real" world seem to be always very localized? I mean, my body doesn't dissolve as time goes on. I can imagine these reasons of why this happens in practice:

  • Because interactions between individual particles with large systems maintains them localized. Those interactions would be more similar to "measurements" than the interaction seen on the simulation and so their wave functions would be continuously collapsing.

  • Most of my particles are "locked" into a kind of potential from which they can't escape like the one on the simulation.

  • A combination of both.

Which one is correct, is there another explanation?



Yes they do. When a particle is finally measured, its wave function collapses to a point in the detector. This "collapse of the wave function" is a fundamental aspect of quantum theory and is highly nonlocal. Photons have been observed being bent round opposite sides of a black hole, in what is called gravitational lensing, with the wave function interfering with itself when it reaches Earth, in a kind of cosmic-scale Young's slits diffraction experiment. Such a photon wave may have expanded across billions of lightyears since it left its parent star, but vanishes in an un-mesaurably short moment when it hits a digital camera. Bing! Gone, just like that.

How come it manages to find our camera at all in all that vast waste of emptiness? Because there are many billions times billions of photon waves pouring out from that star and being lensed around that black hole. A few will make it to the camera, but which few is down to pure chance. That chance is described by the quantum wave function.

The reason our Earthly matter seems so localized is because its waves (called de Broglie waves) spread only slowly and very soon hit their neighbours. But in fact you can perform the Young's slits diffraction experiment on electrons, with care even on buckyballs, and they will behave like waves.

It is all so mindboggling that some physicists try to develop theories in which a real particle is somehow steered by "hidden variables" and the wave function is just an expression of our ignorance as to what those variable are. But all the quantum weirdness does not then go away, it must remain inherent in those hidden variables, which rather dampens the point of the exercise.

It was Hamlet to whom Shakespeare gave to say, "There are more things in Heaven and Earth ... than are dreamed of in your philosophy." I sometimes think this was the first historical expression of quantum physics.

  • $\begingroup$ So it seems as if energy and localization of a wave packet in the state space (position/ velocity) are correlated, more energetic particles are more localized. Could that be interpreted as space somehow emerging from high energy phenomena/particles? would it make sense to speak about something like euclidean space at all in a universe that only contains photons? $\endgroup$
    – AoiCode
    May 16 '20 at 13:43
  • 1
    $\begingroup$ Not really: high-energy gamma ray photons are no more localized after 10 billion years than low-energy radio photons. Massive particles are is subject to other influences, such as the Higgs field, which change their game considerably. In quantum physics, almost nothing intuitive is correct. Also one of the few things we know about space is that it is not Euclidean. Most places are locally Euclidean, but there are exceptions and globally it is closed in a way which we have yet to fathom. $\endgroup$ May 16 '20 at 18:31

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