3 ms·

No, I mean it will be evenly spread out in all directions and not have any location where it is dense.

scotty79 7y ago
I don't see what you are saying in the description of Erhenfest theorem. They are saying: "For general systems, if the wave function is highly concentrated around a point [... the thing different between classical and quantum ...] will be almost the same, since both will be approximately equal to [...]. In that case, the expected position and expected momentum will approximately follow the classical trajectories, at least for as long as the wave function remains localized in position."
- kgwgk 7y ago
  > at least for as long as the wave function remains localized in position." The problem is that, as he said, “the wave function would also thin out until it is smoothed out over the entire universe”.
  - scotty79 7y ago
    Is this then consequence of Schrodinger equation? How fast does that happen? Would the photon from remote galaxy be significantly spread out? How can we know it is not? Is the effect you are talking about the one described here: https://en.m.wikipedia.org/wiki/Free_particle https://en.m.wikipedia.org/wiki/Free_particle in section "Spread of a wave packet"?
    - kgwgk 7y ago
      See also https://en.m.wikipedia.org/wiki/Wave_packet#Gaussian_wave_packets_in_quantum_mechanics https://en.m.wikipedia.org/wiki/Wave_packet#Gaussian_wave_pa... “For example, if an electron wave packet is initially localized in a region of atomic dimensions (i.e., 10−10 m) then the width of the packet doubles in about 10−16 s. Clearly, particle wave packets spread out very rapidly indeed (in free space): For instance, after 1 ms, the width will have grown to about a kilometer.” “Note that a very narrow initial wave packet instantly becomes infinitely wide, but with a phase which is more rapidly oscillatory at large values of x. This might seem strange — the solution goes from being localized at one point to being "everywhere" at all later times, but it is a reflection of the enormous momentum uncertainty of a localized particle, as explained above.”
      - scotty79 7y ago
        I see but what about particles that are not that precisely localised and don't have such extreme uncertainity of momentum? It's very logical that a particle that might have any momentum quicky spreads out to be smoothly everywhere. Particle with not that precise position and not that uncertain momentum should stay fairly comapct for large amount of time.
        kgwgk 7y ago
        What does “fairly compact” mean if not “precisely localised”? If the wave function is not localized it doesn’t make much sense to talk about a particle in the first place.
        scotty79 7y ago
        "Fairly compact" as in precission that we can achieve, instead of perfect precission and mathematical consequence of quickly spreading over entire universe. I think it never makes much sense to talk about a particle. In the wave particle duality, the particle part doesn't have many arguments for it. You can understand and calculate everything using waves. Just not macroscopic kind of waves but waves that have few peculiar qualities that macroscopic waves don't have. Any way... Thank you for indulging my ramblings about the things I barely grasp. :-)
        kgwgk 7y ago
        You can get some intuitive understanding of “the wave” as something in space only when you have one single particle. But as soon as you have two interacting particles what you have is a single wave function which is a (complex) function of six parameters (three coordinates for each particle). Add more particles - and their spins - and pretty soon you cannot “understand” anything at all from the wavefunction on its own.

I don't see what you are saying in the description of Erhenfest theorem. They are saying: "For general systems, if the wave function is highly concentrated around a point [... the thing different between classical and quantum ...] will be almost the same, since both will be approximately equal to [...]. In that case, the expected position and expected momentum will approximately follow the classical trajectories, at least for as long as the wave function remains localized in position."

kgwgk 7y ago
> at least for as long as the wave function remains localized in position." The problem is that, as he said, “the wave function would also thin out until it is smoothed out over the entire universe”.
- scotty79 7y ago
  Is this then consequence of Schrodinger equation? How fast does that happen? Would the photon from remote galaxy be significantly spread out? How can we know it is not? Is the effect you are talking about the one described here: https://en.m.wikipedia.org/wiki/Free_particle https://en.m.wikipedia.org/wiki/Free_particle in section "Spread of a wave packet"?
  - kgwgk 7y ago
    See also https://en.m.wikipedia.org/wiki/Wave_packet#Gaussian_wave_packets_in_quantum_mechanics https://en.m.wikipedia.org/wiki/Wave_packet#Gaussian_wave_pa... “For example, if an electron wave packet is initially localized in a region of atomic dimensions (i.e., 10−10 m) then the width of the packet doubles in about 10−16 s. Clearly, particle wave packets spread out very rapidly indeed (in free space): For instance, after 1 ms, the width will have grown to about a kilometer.” “Note that a very narrow initial wave packet instantly becomes infinitely wide, but with a phase which is more rapidly oscillatory at large values of x. This might seem strange — the solution goes from being localized at one point to being "everywhere" at all later times, but it is a reflection of the enormous momentum uncertainty of a localized particle, as explained above.”
    - scotty79 7y ago
      I see but what about particles that are not that precisely localised and don't have such extreme uncertainity of momentum? It's very logical that a particle that might have any momentum quicky spreads out to be smoothly everywhere. Particle with not that precise position and not that uncertain momentum should stay fairly comapct for large amount of time.
      - kgwgk 7y ago
        What does “fairly compact” mean if not “precisely localised”? If the wave function is not localized it doesn’t make much sense to talk about a particle in the first place.
        scotty79 7y ago
        "Fairly compact" as in precission that we can achieve, instead of perfect precission and mathematical consequence of quickly spreading over entire universe. I think it never makes much sense to talk about a particle. In the wave particle duality, the particle part doesn't have many arguments for it. You can understand and calculate everything using waves. Just not macroscopic kind of waves but waves that have few peculiar qualities that macroscopic waves don't have. Any way... Thank you for indulging my ramblings about the things I barely grasp. :-)
        kgwgk 7y ago
        You can get some intuitive understanding of “the wave” as something in space only when you have one single particle. But as soon as you have two interacting particles what you have is a single wave function which is a (complex) function of six parameters (three coordinates for each particle). Add more particles - and their spins - and pretty soon you cannot “understand” anything at all from the wavefunction on its own.