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Does uncertainty of position of particles make substances continuous?

  1. Apr 23, 2014 #1
    Ever since learning about atoms and molecules as a child I have envisioned substances (air, water, metal, etc) as being composed of discrete individual atoms and molecules. Today it occurred to me that might be an oversimplification, especially for gasses in which molecules are free to move around.

    An electron being fired through a double slit setup goes through one slit or the other only when you look at it. When you don't it's position is in superposition between the 2.
    A molecule may be a discrete object with a specific position when you look at it and study it, but when it is one anonymous molecule of O2 in room full of air it's position becomes a superposition of all possible positions. In this case the range of possible positions would become much larger then the size of any 1 molecule or the distance between them, thus blurring the substance into something continuous and homogeneous.

    I'm not sure what that would mean though. I am at a loss to think of any experiment which would demonstrate a continuous and homogeneous nature of a gas. Any experiment capable of distinguishing individual molecules would collapse the superposition and result in individual molecules being observed.

    Has this idea of substance homogeneity due to quantum superposition been explored? If so, what was the result?
  2. jcsd
  3. Apr 23, 2014 #2


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    Actually solidity has nothing to do with those things. Electrons etc (collectively called fermions) are not little solid balls. They are, as far as we can tell today, point like objects in the sense they have a position that can be measured. What keeps them apart and gives things solidity is the Pauli exclusion principe.

  4. Apr 23, 2014 #3


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    "Continuous and homogeneous" is a polite fiction used in the macroscopic description of liquids, solids, and gasses. As you look closer and closer it falls apart. This was obvious even in Newton's time - as Newton pointed out.
  5. Apr 23, 2014 #4
    The reason why matter appear to be continuous at macroscopic scales is simply because there's so many atoms and your senses are very bad at resolving so many such smalls things. However, if you zoom in enough, for example using a scanning tunneling microscope, you can easily resolve each individual atom in the materials.
  6. Apr 23, 2014 #5


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    To put it a bit differently: The macroscopical (in most cases classical) behavior of interacting many-body systems consisting of a large number of particles comes from some "coarse-graining procedure", i.e., you are not interested in the detailed inner workings on the level of single atoms or molecules but only about pretty rough macroscopically relevant "macroscopic bulk observables". This leads to an effective (often classical) theory for the motion of these macroscopic observables.

    To describe the motion of a base ball you are in 0th approximation only interested in the motion of its center of mass, and this can be described by a classical Newtonian equation of motion, including the gravitational force of the earth on the ball and air resistance. Maybe, then you realize, it's a bit to rough a model to understand the trajectory of the ball and you want to include also rotations (spin) of the ball, treating it as a classical rigid body, taking into account the Magnus effect, etc. As you see, even on the classical level the necessary sophistication of your approach depends on how accurate you want to resolve the behavior of the object in question, and the first task is to find the right "relevant degrees of freedom" which you have to describe to reach your accuracy goal and which are the "marginal degrees of freedom" you "integrate over".

    This is the case also at the level of quantum theory. E.g., in the Stern-Gerlach experiment you can describe the motion of the atom's center of mass in the magnetic field pretty well by classical equations but have to treat the spin and the associated magnetic moment quantum mechanically.
  7. Apr 23, 2014 #6
    I am aware that large numbers of small particles can create the macroscopic illusion of homogeneaty. That was not the point of my thought. I'll try again.

    If we model a gas as a large number of classical particles then we have specific places where the particles are and we have spaces between them. Even when we don't know exactly where every molecule of gas is, we suppose that each actually does have a position, thus on very small scales the gas is non homogenious. This has been my understanding for years and is what I am now questioning.

    Atoms are not classical particles, they are quantum particles. Therefore they do not have well defined positions unless their positions are measured. Since we generally do not measure the positions of each atom in a macroscopic mass of gas it should follow that each atom of gas exists in a superposition of all possible positions. If the range of that superposition is larger then the distance between atoms then, at tiny scales, the gas is not compsed of atoms and gaps but rather as a continuous probability field.

    The double slit experiment demonstrates that quantum particles behave differently depending on wether or not they're measured. In principal, would a gas behave differently if you tracked the positions of each atom, thereby forcing them to behave more like classical objects and less like quantum particles?
  8. Apr 23, 2014 #7


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    No, the double slit experiment and similar experiments demonstrate that quantum particles won't remain in superposition if they interact with the stuff around them (All measurements involve some degree of interaction, and that's what ends the superposition; conversely experiments that demonstrate superposition are tricky because of the need to isolate the subject particles from the environment around them). As the molecules in a gas are continuously interacting with one another, it's not possible to maintain them in a state of position superposition for any extended time.

    You are describing the ideal gas of classical statistical mechanics. It's a very good approximation to the behavior of real gases, quantum effects and all, under a very wide range of conditions.
  9. Apr 23, 2014 #8
    Do the particles not interact with the barrier that the slits are cut in? I thought the reason that interacting with the barrier did not destroy the interference was because that interaction left no way of tracking the particle.

    Or, take the case of thin film interference of light. The interference is, as I understand it, a result of quantum superposition between the wave function reflected from the 2 surfaces. How is the reflection not a form of interaction? Reflection necessarily involves a transfer of momentum between the light and the reflective surface so in this case the surface actually experiences a physical effect from the interaction.
  10. Apr 23, 2014 #9


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    No this is incorrect. You're harkening back to the conceptually flawed wave-mechanics model. The wave-function of each single-particle non-interacting (or rather, weakly interacting) particle of the gas is not representing the gas particle itself in configuration space. The gas particle is not "smeared out" as you seem to be thinking. The wave-function of the particle is not a physical wave propagating in configuration space exhibiting some delocalized nature of the particle.

    Have you seen the concept of the density of states in statistical mechanics, particularly with regards to Bose-Einstein or Fermi-Dirac distributions?
  11. Apr 23, 2014 #10
    I'm with you in this as how could the momentum change without an interaction with the barrier? I would understand though it needs to be a reversible interaction to obtain interference.
  12. Apr 23, 2014 #11


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    Sure, some particles interact with the barrier. But most of those never make it to the screen.

    The barrier itself has nothing to do with the interference effect. Interference disappears when you (could) know which way the particle goes. That can be accomplished a variety of ways, some which involve a polarizer instead of a barrier. For example: parallel polarizers allow interference, while crossed polarizers inhibit interference.
  13. Apr 23, 2014 #12
    The quantum nature of the particles that make up a gas does indeed have important consequences under some circumstances. These consequences are worked out using a quantum version of statistical mechanics. It turns out that quantum effects are negligible unless the gas is cold enough.

    You are close to an important idea in quantum statistical mechanics. Quantum effects become important in a gas when the gas is cold enough that the thermal de Broglie wavelength is comparable to or larger than the distance between atoms. An extreme example is that when a gas of bosons has a thermal de Broglie wavelength that is large enough compared to the interatomic spacing, a Bose-Einstein condensate forms.
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