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Help with superposition

  1. Mar 5, 2006 #1
    I'm doing a writing "experiment" with a character that is aware of his existence as a drawing in a world created from my imagination.

    He is asking me why he is the only one that exists in his world.

    My answer is that he isn't the only one, but rather the only one who has appeared (it is in comic strip form) thus far. What I'm trying to get at is that there's an infinite amount of possible characters that neither of us know about, and it's only until I draw them into the strip that an individual character would lose the property of existing and not existing, by being observed.

    There's an obvious parallel to the concept of superposition, but at the same time I don't think referencing schrodingers cat or the double slit experiment would be appropriate. Those two are practical for explaining the quantum world, but what I'm trying to explain to the character is almost more philosophical in nature than scientific.

    So what I'm wondering is, if anybody knows of any non-scientific texts that explore superposition or related concepts.

    Oh, and the strip is here if anybody is interested.

    Thanks in advance. It would be nice if I could get this idea across without it being too dry for the reader.
  2. jcsd
  3. Mar 5, 2006 #2
    Schroedinger's Cat (SC) and the double slit experiment don't *explain* the quantum world. SC is an illustration of the measurement problem in QM, the inadequacy of the Copenhagen Interpretation, and the absurdity of talking about cats as being simultaneously alive and dead.

    The double slit experiment with photons, electrons, etc. is an unsolved mystery. That is, there is no qualitative understanding of how it happens. The same for quantum entanglement.

    The quantum world, if you take that to refer to a realm of nature underlying instrumental results, remains unexplained --- even though the experimental phenomena which resist qualitative understanding in terms of some deeper explanation can be reproduced and quantitatively accounted for.

    The superposition principle (the principle of linear superposition) might be phrased as: overlapping waves algebraically add to produce a resultant wave. Another way of saying it is: if two or more travelling waves are moving through a medium, then the resultant wave is found by adding together the displacements of the individual waves point by point. Another way might be: when several effects occur simultaneously, their net effect is the sum of the individual effects.

    For example, if there are a couple of waves moving along a rope stretched between two locations, and you describe the displacements of the the rope for each wave as y1(x,t) and y2(x,t), then the displacement, y'(x,t), where and when they overlap will be
    y'(x,t) = y1(x,t) + y2(x,t).

    You can demonstrate the superposition principle in your sink or bathtub. If you do this you'll also notice that the waves can pass through each other without being destroyed or even altered. That is, overlapping waves don't alter the travel of each other.

    In QM, the basic equation of motion is the Schroedinger wave equation. It's linear and homogenous. Consequently, the superposition principle holds --- which means that if psi1(x,t), psi2(x,t), ... psin(x,t) are solutions of the Schroedinger equation, then the linear combination of these functions, psi = C1psi1(x,t) + C2psi2(x,t) + ... + Cnpsin(x,t) , is also a solution.

    Here's the way Bohm, in his 1950 text "Quantum Theory" (page 174), puts it:

    "A basic idea in any wave theory is that if psi1 and psi2 are possible wave functions, then any linear combination apsi1 + apsi2, where a and b are arbitrary constants, is also a possible wave function. This statement is known as the hypothesis of linear superposition. It is necessary to assume some such hypothesis to explain interference and the production of wave packets. For example, in optics interference patterns are often predicted with the aid of Huygens' principle, which describes the wave intensity at any point as being determined by the linear superposition of waves starting from all possible points in a previous wave front. Whether this is the only hypothesis that can possibly explain interference is not known. It is, however, the simplest one that will do so, and it has been successful in explaining electromagnetic and acoustical interference phenomena. We tentatively extend this postulate to electron waves also. In fact, we have already done so without discussing the fact that it is a postulate in making up wave packets and in describing electron diffraction experiments in a manner analogous to the way that diffraction of light is treated. The great success of this interpretation then justifies its further application to a more general set of problems."
    Last edited: Mar 5, 2006
  4. Mar 5, 2006 #3
    great post sherlock, wow

    and haha i just read the comic strip, quite funny and interesting
    Last edited: Mar 5, 2006
  5. Mar 5, 2006 #4
    Ah, forgive my careless use of words. "Explain" is probably the last thing I should have said.

    What I mean rather is that SC and the double slit experiment, while useful as references to introduce the concept of superposition and the measurement problem, don't seem like suitable references for what it is I'm trying to explain to the fictional character (and the reader). They explain the same concept (or at least a similar one) but my goal isn't to introduce the reader to quantum weirdness, it's to introduce the reader to the idea of multiple characters that exist and don't exist.

    And that's where the problem lies, It's a bit tough to describe the concept in one's own words without sounding nuts. I was hoping maybe somebody knew of some other (non-scientific) texts on the issue that I could read up on. I have a solid grasp on the whole thing, but I find myself struggling to get the idea across to others.

    thanks =)
  6. Mar 5, 2006 #5
    The "idea of multiple characters that exist and don't exist" doesn't have anything to do with quantum theory, or superposition, as far as I'm aware.

    Characters that simultaneously exist and don't exist is just a contradiction in terms --- unless you further clarify/qualify what you're talking about. For example, you could say that a set of characters exist as rough ideas in your imagination, but don't exist as renderings in your comic strip yet. That is, these imagined but not yet drawn characters exist as potential future companions for your, currently, solitary character.

    This sort of existence as potentiality is akin to what is meant when Schroedinger's Cat is referred to as being in a superposition of alive and dead. That is, livecat + deadcat is simply a statement of the two possible (and equally probable in this case) outcomes of the experiment
  7. Mar 6, 2006 #6
    I know it sounds stupid but bear with me on this. I know that it "doesn't have anything to do" with superposition or quantum theory but there really does seem to be a connection:

    The cat that is dead as well as alive until it is observed. (yes i'm aware that it's just a thought experiment, but it still seems relevant)

    The particles of light go through both slits, each slit, and neither slits until they are observed.

    An infinite number of characters will both be presented to the reader and also will never be seen by the reader until a character is actually drawn, at which point that character loses the "weirdness" of existing (eventually coming into the strip) and not existing (never coming into the strip).

    It's more than a contradiction of terms, and more than just existing in my mind vs existing in the strip. I'm talking about existing outside of my conceptualizing anything at all.

    I know it's a bit of a stretch and a jump to move from superposition to this, but I wouldn't say they're entirely unrelated. I mean in quantum physics itself there's definately no connection, that goes without saying. My strip is in no way meant to explore anything remotely scientific, but I still see a relation on perhaps a theoretical level.

    The trouble I think is that I'm trying to relate something like quanta with something like a thought, or a potential existance. They don't exactly mesh up but I still can't help but think that these experiments have practical uses as experiments or explanations outside of physics.

    Of course, I'm very open to the chance that I'm barking up the wrong tree entirely and should be looking elsewhere, like some belief in multiple realities or something. In which case, I'd greatly appreciate being pointed in the right direction.
    Last edited: Mar 6, 2006
  8. Mar 6, 2006 #7
    Last edited: Mar 6, 2006
  9. Mar 6, 2006 #8


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    I would like to point out that there is a fundamental difference between the superposition principle in quantum theory, and the superposition principle in linear, classical field theories.
    In a linear, classical field theory, the physical object is a field, described by a function over 3-space (x time if you want to), f(x,y,z), which obeys a (set of) linear partial differential equation(s). This means that, if f(x,y,z) is a solution, and g(x,y,z) is a solution, then h = a f + b g is also a solution of the equations and as such, a different classical state. It is sufficient for the physics of the situation to be slightly different, and the linear partial differential equations turn into non-linear equations, and the property of linear superposition doesn't hold anymore. Nevertheless, there will still be an entire set of solutions {f,g,h,...} that describe different classical states of the system. This can happen, for instance, when there are strong fields and non-linear materials.
    Mind you that the superposition only holds in the case we're talking about fields, and in case that the equations turn out to be linear partial differential equations.

    If we were to talk about a system of point particles, for instance, we would have, say, 3 particles, a muon, an electron and a proton, the muon at point P, the electron at point Q and the proton at point R, represented by the triplet of space points {P,Q,R} it would be a stretch of imagination to talk about the superposition of the states {P1,Q1,R1} and {P2, Q2, R2}. So the classical superposition principle doesn't seem to apply to point particles, but only to fields (and even then, only when the system of equations is linear). For instance, does it make sense to talk about a superposition principle in the classical mechanics of the solar system ?

    Quantum theory, on the other hand, has DEEP INSIDE ITS POSTULATES, a fundamental postulate which is called "the superposition principle". It says that if a system can be found in |state1> and in |state2>, then it can also be found in a |state1> + b |state2>.
    The quantum state of our 3 particles at classical positions {P,Q,R} corresponds to a quantum state |P,Q,R>.

    As such, the thing that seemed totally unthinkable in classical physics, is postulated to be true in quantum theory:
    the state a |P1,Q1,R1> + b |P2,Q2,R2> is another physical state of the 3-particle system. We say that the classical state {P1,Q1,R1} occurs with amplitude a, and the classical state {P2,Q2,R2} occurs with amplitude b, in the said state. It doesn't involve any specific "linear" dynamics of the 3 particles or anything. No matter what the interactions of the particles, this superposition principle holds.

    In as much as the linearity of the wave equations in classical field theory (which was the origin of a classical superposition principle) is just an approximation to a specific dynamics of a specific system (electrodynamics, for instance, is NOT linear due to the coupling between charge and fields), in as much, the superposition principle in quantum theory is BUILD IN DEEP DOWN IN THE FORMALISM and has nothing per se to do with the specific dynamics, or even with the number of degrees of freedom, of the system under study.
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