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Quantum physics in three sentences?

  1. Nov 8, 2011 #1
    Ok, not all of quantum physics. Mainly just the Double Slit Experiment or Wavefunctions in general.

    You only have 3 sentences to teach either one (or both) to an idiot (not me) and they can't be run on sentences either.

    This also has to be a math free explanation.

    It's not so much a challenge of simplifying the ideas to their most succinct states as it is choosing what is important to know and what you don't really need to know.

    Kindof like the desert island deal. If you could only take three facts about quantum physics with you, what would they be?
     
  2. jcsd
  3. Nov 8, 2011 #2

    tom.stoer

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    Let's try something more general:

    In quantum mechanics a 'realistic' description using entities (like particle trajectories with well-defined position and momentum) known from our everyday's experience is no longer applicable and becomes wrong. Instead one has to refer to an abstract mathematical formalism from which the classical world does 'emerge' in some situations, but which shows genuine (and weird) quantum behavior in other situations (double slit, entangled particles a la EPR / Bell). A typical example for the genuine quantum behavior of 'quantum objects' (which are neither particle nor wave) is the double slit experiment where the abstract formalism tells us that one single, indivisible entity like an electron sniffs out all possible classical trajectories simultaneously, i.e. 'walks through both slits' simultaneously, interferes with itself and shows partially destructive interference.
     
  4. Nov 8, 2011 #3

    Demystifier

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    1. Wave function is a complex function of the space position x and time t.
    2. A linear combination of physical wave functions is a physical wave function itself.
    3. The squared absolute value of the wave function is the probability density for a particle to be found at the position x at time t.
     
  5. Nov 8, 2011 #4

    dextercioby

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    A small ammendment to point 2. <Within a coherent subspace of the physical Hilbert space, a linear combination of physical wave functions is a physical wave function itself>.
     
  6. Nov 8, 2011 #5

    Ken G

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    The quantum mechanics of wave functions and the double-slit experiment involves the union of that which we used to think were as different as night and day: the discrete and the continuous-- particle and wave. The union is accomplished by the quantization, in bundles of the Planck constant, of a dynamical quantity known as action. This quantization allows us to associate with any particle momentum a wavelength, which is a property of waves, and with any wave period a quantum of energy, which is a property of particles. These associations allow us to treat what we used to think of as disjoint wave and particle properties as two aspects of the same animal, like the trunk and the tail of a single elephant-- they allow us to recognize, rather belatedly, why particles and waves were always the same thing in different clothes.
     
  7. Nov 8, 2011 #6
    1. The state of any physical system is represented by a vector in an infinite dimensional complex space, with each component representing a particular state the system can be in.

    2. The state vector of any physical system evolves according to Shrödinger's equation.

    3. A measurement on a physical quantity (energy, momentum, position, spin, etc.), represented by Hermitian operators, yields one of its eigenvalues, with the probability of that value being given by the square of the projection of the state vector on the given eigenvector.

    (sorry, a math free explanation is not possible)
     
  8. Nov 8, 2011 #7

    Demystifier

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    What is a coherent subspace?
     
  9. Nov 8, 2011 #8

    dextercioby

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    The Hilbert space of states, assumed infinite dimensional and separable, is generally decomposed into a direct othrogonal sum of closed subspaces, each corresponding to discrete spectral values of the operators describing the so-called <superselection rules>. For example charge in case of a Dirac equation/field. The linear superposition between an eigenfunction with positive charge (positron) and negative charge (electron) makes no sense physically, so that a quantum state with electrons and positrons is not described by a linear combination, but by a tensor product.

    An eigenspace of an operator providing a superselection rule which corresponds to an eigenvalue of that operator is called a coherent subspace. It is a separable Hilbert space in its rights, if endowed with the scalar product inherited from the full space. Linear combinations of vectors only within the same (sub)space make sense (example above), not between vectors from different subspaces, corresponding to different eigenvalues.

    This is off the top of my head. As far as I remember, I think the introductory chapter from Streater & Wightman has a story on this. Also Galindo & Pascual's text on QM, or Fonda & Ghirardi's text on symmetries of quantum systems.

    Needless to say, in case superselections rules are missing, the whole Hilbert space is a coherent subspace (quanta of the KG field, or spinless Galilean particle).
     
    Last edited: Nov 8, 2011
  10. Nov 8, 2011 #9

    Demystifier

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    Thanks dextercioby. I have an offtopic comment, but I will open a new thread on it.
     
  11. Nov 8, 2011 #10

    DevilsAvocado

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    Caveat: QM works mathematically, everybody agrees on that. However, when you start to talk and describe what 'happens', you always run into the 'dilemma' of interpretations, and my guess is that some will have scathing comments on my 'talk' below ;). Nevertheless, as of today no interpretation is proven better than any other...


    Quantum Mechanics for Dummies
    • Quantum mechanics describes the very small microscopic world, where things behave differently from what we are used to in the macroscopic world of 'classical' objects.

    • One famous example is the Double-slit experiment, which demonstrates that matter and energy can display characteristics of both waves and particles.

    • Waves in quantum mechanics are fundamental and described mathematically by the wavefunction and the Schrödinger equation, which results in some uncertainty when calculating the exact outcome for one single particle, the outcome is therefore probabilistic in its nature.
     
  12. Nov 8, 2011 #11
    I would say that DevilsAvocado is the best 3 sentences so far (I will not attempt writing 3 sentences because I cannot top it). The others are good though.

    If I could add one thing it would be that quantum mechanics approximates very well to classical mechanics when considering large systems, e.g. QM agrees with Newton's Laws and GR when you apply QM on a macroscopic and large scale.

    I would also like to say that it is just a theory and is not necessarily the "truth"... maybe we will find a better theory in the future which is more generalized than QM. But it is the best theory we have as of now...
     
  13. Nov 8, 2011 #12
    1. Quantum Mechanics is an attempt to predict the outcomes of experiments on systems so small that our intuitive notions of particle, wave, position, momentum and even space and time might not be applicable.

    2. Several different properties of a quantum system may be measured but it is never possible to simultaneously measure all of them.

    3. Depending on the preparation of the quantum system some of its properties may be predicted with certainty but, in general, the predictions of the outcomes of measurements are probabilistic but have tremendous experimental confirmation.

    Not perfect but it is non-mathematical.
     
  14. Nov 8, 2011 #13

    DevilsAvocado

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  15. Nov 9, 2011 #14

    mysearch

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    By way of ‘gentle’ debate, rather than argument, just over a generation ago, Feynman suggested that nobody understood QM and now we appear to aspire to explain some of its central concepts to ‘an idiot’ in just 3 sound-bites. Clearly, there is hope for me :uhh: yet, although Heisenberg had a go at summarising the double slit experiment and the wave function collapse in just 1 sentence:
    “The path of a particle comes into existence only when we observe it."​
    I also like the summary in post #10, but possibly the :devil: is in the detail, if not in the avocado, as per bullet 3:
    People might also like to review the following thread ‘https://www.physicsforums.com/showthread.php?t=541962"’, which wasn’t restricted to 3 sentences, as a yardstick as to whether any consensus was reached on its definition, let alone its interpretation. For example, do quantum waves have any physical existence?
     
    Last edited by a moderator: Apr 26, 2017
  16. Nov 9, 2011 #15

    dextercioby

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    According to the standard formalism of QM, there's no more distinction between particles and waves, as these 2 concepts, as I said before, actually pertain to classical physics, namely the mechanics of point particles and waves (including electromagnetism). So <quantum waves> as a concept does not exist.
    The fundamental concepts of QM are: (quantum) system, states and observables of a system and virtual statistical ensembles. The rest is essentially mathematics.
     
  17. Nov 9, 2011 #16

    DevilsAvocado

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    Cool, I love "one-liners", less is more. In 1935 Erwin Schrödinger published http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=1737068" defining the term "entanglement":
    "I would not call [entanglement] one but rather the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought."

    :biggrin:
     
    Last edited by a moderator: Apr 26, 2017
  18. Nov 9, 2011 #17

    DevilsAvocado

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    Agreed, but if you’re going to tell 'an idiot' that the "QM world" does not exist, I suspect this 'idiot' would 'object' in some way:
    – Okay... I dunno... but... why should I spend my time on something that doesn’t exist...??? :uhh:​

    This is of course more 'contemporary' and closer to the 'truth' than post #10. I don’t know how to get around this 'problem of language'... I get a slight feeling that the 'contemporary abstraction' of QM is so abstract, that when 'an idiot' tries to make a figurative picture in his head... he’s immediate lost.

    This is from "Quantum Mechanics - A Modern Development", by Leslie E. Ballentine:
    Postulate 1a. To each dynamical variable there is a Hermitian operator whose eigenvalues are the possible values of the dynamical variable.

    Postulate 2a. To each state there corresponds a unique state operator, which must be Hermitian, nonnegative, and of unit trace.

    I have an idea what Ballentine is talking about, but do I get a deeper conceptual understanding from this? Well, unless I read the book, and understand the math, I’m afraid the answer is No...

    I’m not trying to raise an 'argument' here, I’m just curious. What’s your answer, if 'an idiot' asks:

    – Okay, "virtual statistical ensembles" sounds cool, but in case I’m not an idiot, we have single electrons in this Double-slit experiment, and afaict, we could have eons between each, so where’s your "ensemble" then??

    http://www.youtube.com/watch?v=FCoiyhC30bc&hd=1
    https://www.youtube.com/watch?v=FCoiyhC30bc ​
     
  19. Nov 9, 2011 #18

    Cthugha

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    I somewhat do not get your point. If you perform such a double slit experiment it does not matter whether you perform one measurement with 12876 (non-interacting) electrons or 12876 measurements with one electron. Both experiments are basically giving the same ensemble.


    For my take at the question of the begin of this topic, let me cite Neil David Mermin:
    "My complete answer to the late 19th century question "what is electrodynamics trying to tell us?" would simply be this: Fields in empty space have physical reality; the medium that supports them does not.
    Having thus removed the mystery from electrodynamics, let me immediately do the same for quantum mechanics: Correlations have physical reality; that which they correlate, does not."
     
  20. Nov 9, 2011 #19

    Ken G

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    I like Mermin's quote, but to correct it a little, all we can really say is that we do not yet have any reason to attribute reality to either the medium of the electromagnetic fields, or what is being correlated in quantum mechanics. That is not quite the same as being to assert that either are unreal, these are only 100 year-old theories! So what we are noticing is, physics is a process of assigning reality as needed, and in the mean time, we must adopt a stance of complete agnosticism-- or repeat the errors of our predecessors. Thus I view the various interpretations that attempt to assign reality to what is being correlated as "peeks" into a potential next theory, rather than as being able to say anything about reality currently. Mermin seems to adopt the ensemble interpretation, which is like saying "thou shalt adopt no interpretation until its time." That's a fine approach, but many physicists like to attempt a "sneak peek" all the same.
     
  21. Nov 9, 2011 #20

    Ken G

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    Yes, this is asking "what can we really know about a single particle". If the answer given by the ensemble interpretation is "nothing", this is formally correct, but seems a bit unsatisfying. Physics has never really been about knowing things, there was always some small chance that the whole experiment could blow up in our face. We are seeking effective knowledge in physics, not absolute knowledge. We are perfectly happy with idealizations, we call that "knowledge" in physics all the time! This causes considerable consternation to mathematicians, who seem to have a much more exacting definition of what it means to "know."
     
  22. Nov 9, 2011 #21

    - relationships transcend time and space....;)
    - just because something is small (photon) does not mean it cannot teach us big things about life/reality/universe
    - don't ever assume you know it all
     
  23. Nov 10, 2011 #22

    mysearch

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    Without wishing to divert the thread from the OP too much, I was hoping that somebody might be able to help me better understand a fundamental issue that confuses me about quantum mechanics (QM). In many ways, the following comment seems to summarise the accepted position of QM:
    The position of Einstein and Bohr can be used to characterise 2 different ‘philosophical’ stances regarding QM. Bohr’s position is said to be represented by the Copenhagen Interpretation and would appear to broadly align to the comment above. As such, the role/ability of science to describe the universe in terms of an objective reality appears to be in doubt or, at least, beyond the remit of QM. While accepting the role of mathematical models is a critical ‘tool’ of modern science, one of my questions is:

    Does theoretical physics deny the existence of a physical objective reality?

    I am quite new to QM and have only reviewed the key developments in QM up to the 1930’s. As far as I can see Compton affirm Einstein’s idea about light photons having a particle-like nature, which deBroglie then extended to electrons having a wave-like nature, such that the whole wave-particle duality debate re-emerged. Later, Schrodinger developed a wave solution, which although still rooted in classical wave mechanics appears to have a number of key changes. First, the switch to the complex [Euler) form allowed him to create a solution that used the 1st differential with respect to time, while also replacing the concept of amplitude with the symbol [Psi]. In this 1st differential form, he was then able to directly substitute the dispersive relationship between [k] and [w] and replace these terms with equivalent energy and momentum expressions rooted in deBroglie hypothesis. Based on classical wave mechanics, the square of the amplitude would correspond to energy, but Max Born later interpreted this concept as a probability density of finding a particle in a certain location in space. Paul Dirac then completes the mathematical transformation of the original wave equation by correlating it to relativistic energy, but in the process has to introduce 4x4 matrices, which also appear to require complex numbers in order to represent quantum spin.

    So does this mathematical transformation in itself exclude the possibility of objective reality or does it simply remain agnostic on the issue?

    Returning to a specific point raised in the comment above, which I am not arguing against, simply trying to better understand:
    If the quantum wave has no objective existence, then I don’t understand why quantum wave mechanics produces valid results. It would seem that at some level it is able predict the outcome of a physical process involving energy and momentum, which semantically we refer to as particles, even though it appears we cannot define their ‘substance’ other than in terms of a wave, which QM appears to state has no objective existence. Would really appreciate any deeper insights from knowledgeable members or pointers to other references rather than 1-line sound-bites. Thanks
     
    Last edited: Nov 10, 2011
  24. Nov 10, 2011 #23

    Ken G

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    My opinion here, and I believe this is something Bohr would have agreed with, is that physics is moot on the issue of existence of objective reality, but it has encountered some fundamental difficulties in accessing the concept. The concept of objective reality pre-existed anything we would recognize as modern physics, so we should probably say that physics was invented to answer questions about the objective reality concept. And in true Douglas Adams-esque fashion, we have now discovered that perhaps we never really understood the question we were asking physics to answer. Now that quantum mechanics has given its answer, we are faced with the challenge of figuring out what the question was supposed to be. That is essentially the role of interpretations of quantum mechanics, but they have succeeded too well-- they produce multiple versions of the question that quantum mechanics answers!
    Here are two other ramifications of the first-order form to consider: it means we only need the initial wave amplitude, not also its time derivative, to predict the evolution, but this comes at the cost of requiring amplitudes to be complex. So the wave function contains all the information needed, we don't need to augment it with information about how it is changing, but even real-valued wave functions evolve into complex-valued ones. Note this is really a huge shift-- one of the main philosophical stances of classical physics is that when you don't do anything to a system, it keeps doing what it was doing before. But in quantum mechanics, systems can change in fundamental ways even when you leave them alone. The second price we pay for this feature is indeterminacy-- the system must acquire some concept of indeterminacy (with respect to some observable) to undergo a fundamental change (in that observable) without something being done to the system.

    I would say neither-- it doesn't exclude what it cannot access, but it is not completely agnostic either-- it says, in effect, "I am not programmed to respond in that area", and since physics was invented as our program for generating such a response, it exposes some fundamental problems with the question we thought we were answering in the first place. The concept of objective reality has been seen to be a very useful notion that encounters fundamental limits that we may never be able to get around. That doesn't mean it doesn't exist, but it does mean that it might as well not exist, for all we get to know about it. But perhaps we simply need to adjust our expectations, to change the questions we are trying to answer, and we will be able to see this as a feature of physics, rather than a bug.
    I think you have reversed the logic that should apply to the issue of existence of objective reality. You seem to suggest that physics can only work to the degree that the concept of objective reality can give it meaning, but I would say that the concept of objective reality can only work to the degree that physics can give it meaning. All that has happened is we have discovered what seems to be a fundamental limit in the latter.
     
  25. Nov 10, 2011 #24

    mysearch

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    Ken, many thanks for some very interesting and useful insights. Again, my comments are primarily to help me better understand current thinking.
    I agree that the idea of objective reality is a very basic assumption, which quantum mechanics makes us question in more detail. Clearly, all human perception is subjective and limited by our physiology, but we are now talking about a far more fundamental concept, i.e. does objective reality cease to have any meaning at the quantum level. If quantum mechanics can only describe the evolution of a system from A to B in terms of a mathematical model, then I guess the question appears to be whether we accept it at face value or continue to question why it works?
    Fair point, although it seemed to me that the issue of matter wave dispersion within the quantum model leads to the more far reaching implications. When considering a ‘particle’ in isolation, e.g. a free electron, quantum wave mechanics seems to suggest that its associated quantum wave amplitude, i.e. its probability density, will quickly disperse over an expanding region of space and hence the subsequent need for some sort of wave function collapse. As far as I can see this concept is based on the idea that the wave packet is a superposition of quantum waves propagating with different velocities. Does quantum mechanics, as a mathematic model, provide any rationalisation of these waves or is it simply happy to accept the answers provided?
    While we might possibly spiral into an argument concerning the validity of any conclusion based on the verification of its premise; as a gross simplification, quantum mechanics appears to be a valid premise in that it can verify that a system starts at A and ends at B, but seems ambiguous about the process between A and B. While this has practical benefits, it not clear to me that physicists should be content to accept this situation, even though they may or may not (?) have any better ideas at this time. However, this may just be a personal bias!
    I agree, this does seem to be a cause of much debate. However, if an objective reality does exist, then it exists independently of any description of physics. Likewise, whether our physics has reach a fundamental limit might also be debated. Again, appreciate the helping hand.
     
  26. Nov 10, 2011 #25

    DevilsAvocado

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    Exactly, that’s my point, though I suspect that an "Ensemble Interpretation'ist" would argue around this...
     
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