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Thread: quantum quandary?

  1. #1
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    Default quantum quandary?

    i am having trouble unerstanding the basic quantum property reguarding particle wave duality. now they say particles exist as waves untill they are measured. this is suposed to be confusing but it seems pretty obvious to me that when you mess with something it will react therefore chainging its properties. in which case you *cannot measure both the location and speed acurately simotaniously. i think i am missing out in something because it seems prety clear. on that note would it be better to say that a particle acts as a wave untill it interacts with something because using the word measure is a bit misleading.

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    Default Re: quantum quandary?

    Quote Originally Posted by Gera Vassilenko View Post
    i am having trouble unerstanding the basic quantum property reguarding particle wave duality. now they say particles exist as waves untill they are measured. this is suposed to be confusing but it seems pretty obvious to me that when you mess with something it will react therefore chainging its properties. in which case you *cannot measure both the location and speed acurately simotaniously. i think i am missing out in something because it seems prety clear. on that note would it be better to say that a particle acts as a wave untill it interacts with something because using the word measure is a bit misleading.
    Yeah, I think that Quantum Mechanics is not very well explained in class and definitely not on most internet sites, even though there are exceptions. As it turns out, whether you see waves or particles depends a lot on the experiment that is done. It helps to consider the experiments that actually led to the development of QM.

    1. The Photon = In Thomas Young´s Experiment, light was sent through double slits and produced a wave pattern. However, the Albert Einstein´s Photoelectric effect indicates that light behaves like a particle. So you really need need a theory that incorporates both views (wave and particle) to be a complete theory for the photon. (BTW, there is a video on YouTube that shows how you can have fun with the photoelectric effect.)

    2. The Electron = Robert Millikan´s Oil Drop Experiment showed that the electron was a particle. (A simpler explanation is with this YouTube video.) However, the Davidson-Germer Experiment showed that the electron also was a wave. Thus, again, a complete theory must account for both the wave and particle nature of the electron.

    3. The Atom = John Dalton summarized something that all chemists had already observed in his atom theory of chemicals, thus establishing the particle nature of atoms. His idea of atoms eventually led Lothar Meyer and Dmitri Mendeleev to come up with the periodic table of elements (an interactive one is here). However, Otto Stern and Walter Gerlach demonstrated that even neutral atoms follow wave principles and discovered the spin characteristic of atoms. (A simpler explanation of the Stern-Gerlach experiment is available on YouTube.) Once again, a complete theory must account for both the wave and particle natures of the atom.

    It was Louis deBoglie that formalized that any particle in motion must have a wave associated with it that obeys the relation where and h=Planck´s constant, and momentum and the wave vector where with wavelength. This even works for the photon, since the relation has been experimentally verified (which also proves that even though photons have energy and momentum, they have no mass).

    Today, as a result of one of the four axioms of QM, the operators are substituted for the variables in particle theory in the following way (source = »Modern Physics And Quantum Mechanics« by Prof Elmer Anderson; ISBN=0-7216-1220-2; copyright 1971 by WS Saunders Company; page 149):

    In the position domain (along x-axis):






    In the momentum domain (along x-axis):






    This ensures that you have both particles and waves embedded into one theory that explains all behavior of particles (including photons). The theory has held up very well under all experiments. There are things QM does not explain, but the things it does explain, it explains very well. It should be noted that in QM, E is invariant between the position and momentum domains (cf above). So energy is perhaps the most important quantity in QM.

    I´ve skipped a lot of detail of QM, but I hope to have elucidated wave-particle duality a bit and hope this helps.
    Last edited by kg4pae; 08-01-2015 at 01:14 PM.
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  3. #3
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    Default Background Discussion

    "Light has no mass"... until it hits something....

    Come to think of it, you can't even see light until it hits you in the eyeball ....

    .... and what then?


    The first equation you have to really, really understand (after Newton and Maxwell) is:



    and its corresponding expression in terms of sines and cosines..
    (keeping in mind the unit circle in the complex plane)

    (e.g.: what happens if Px = Et - and why physically (not just mathematically) ?

    Hint: Be REAL careful how you conceptualize "x" and "t"...

    Then apply the Schroedinger equation with its operator interpretation (what does it really mean to take 1st and 2nd derivatives?) ... and then finally spin (+/-) and the Special Theory of Relativity (i.e., include the Pauli/Dirac matrices....)

    (you'll need to understand the Lorentz transform and Force)

    Then the "left hand rule" (parity violation) for the Weak Force
    And finally, the add the y and z dimensions for quarks and qluons....

    Then when you've accounted for all the parameters in the Higgs bozon mechanism, you'll finally be able to calculate the radius of the LHC from first principles....

    (BTW, you'll also need to understand dot ("inner") and cross ("outer") products of vectors)...

    The context for the Schroedinger equation is linear systems, where a system is characterized by "operators" (partial derivatives") operating on an input (the l.h.s. wave), which produces an output (the r.h.s. wave), where the inner parameters of the wave function are brought to the front (as multipliers) by the differentiation process to get the output. So the approach used by Schroedinger applies Fourier analysis to describe the physical relationships of the system under consideration. (Heisenberg uses linear algebra - matrices - for an equivalent approach, using periodic functions as bases for a vector space)

    That said, here's a link to a .pdf as a first take on the Non-Relativistic wave for QM (the input to the operator function that describes the system, which is expressed in partial derivatives):

    Non Relativistic QM Wave

    I describe the relativistic approach I take in the following posts, which will be eventually added to the document (this is all a work in progress, and subject to editing/correction)
    Last edited by BuleriaChk; 08-05-2015 at 09:22 AM.
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    Default Relativistic Quantum Mechanics

    The problem with QM is that to really get at what is going on, one has to understand linear system theory (convolution, impulse response, Green's functions, Dirac delta functions) which are difficult enough in signal processing and analysis, and much harder when physics involving energy and momentum are concerned.

    Basically, a Green's function G(x,s) is a function that when operated on my a linear function L (e.g. a derivative) produces a Dirac delta function which at all points except where x=s, in that case = 1:

    LG(x,s) =

    In QM, G(x,s) is the normalized wave, which is equal to one if all perturbations are accounted for....

    That is, if LG'(x,s) =tex]\delta(x-s)[/tex]

    then G(x,s) = (1/k)G'(x,s)

    In physics, relativisically, the 1/k corresponds to 1/E where E is the total energy of the system (as one constant).

    Then one introduces a structure into E, which further deconstructs G into which internal parameters (degrees of freedom) in G' are being operated on by L (so brought out in front of G' as invariants).

    This implies the system can be characterized as a Fourier expansion as a set of resonances; taking the inverse Fourier transform on the impulse (the Dirac delta funcdtion) gives the system response.

    Even more complicated is that the delta function is a "distribution" - with its area (energy) equal to one - e.g. a Gaussian - which extends to infinity, and so strictly speaking has to be terminated for conservation of energy.

    ================================================== ==

    I dunno about you, but it has been really hard for me to wrap my head around this (and I still don't grok it completely yet), and I only began understand it after I took a signal processing and analysis course in the EE department at UCSB.

    ==============================================

    Now take another look at the deBroglie wave equation:



    If we are covariant (and we are; see below), then in the "coordinate" system,
    we have xv = xc and tc as invariants, xc = ctc , and






    Substituting x = xc in the equation, we have:



    Where P' is now the relativistic momentum, and "space" is no longer an explicit part of the equation. (so neither is coordinate "time" in the "coordinate frame" interpretation.)



    See Relativistic Energy Derivation on my site for a discussion of how covariance, contra-variance fits into Einstein's supposed application of "coordinate frames" to STR (NOT relativistic quantum mechanics as discussed here. by deconstructing v/c into its "coordinate elements" x and t)*

    Then P' and E are both "action creation" rates (to be dimensionally consistent with h), and the "t's" are scaling factors on the actions with tc an invariant. (but not in the Lagrangian action L = T(m,v) - V(x) of classical physics - think about why not), where T is the kinetic energy and V is the potential energy. The "times" then configure the actions for the "momentum" action (which is a "v" dependent energy) and the "Energy" action





    Also, understand that

    is an equation for the "action" equating the energy of an ejected electron to the photon that ejected it from the surface, without mentioning anything about the surface.

    This means that "c" and "v" are to be understood as to "action" (mass) creation rates, and t (and t') refer to mass creation times for a single system ("cycle") of the wave equation. (xc is the unperturbed mass of such a single photon/electron)

    (next post - the significance of tc vs. t in the wave equation; a change in context (a "mistake") and a few remaining steps

    So context is everything, and one has to stop thinking in terms of Newton / Maxwell / and Cartesian "coordinates" and refer the analysis to energy/momentum at a single field "point" (the origin) (anywhere/ anywhen) (x,t) in "space time". (I usually change the parameter variables to (X,T) in energy-momentum space.

    *But Einstein is correct in his reference to "inertial frame".... it is the "coordinate frame" concept that is misleading. (GTR is an attempt to resolve the issue, by interpreting as a density in flat space time, and then curving "space-time" to represent changes in the density ("mass" acceleration) as representing gravity, which runs into difficulty by declaring c to be a global (universal) constant, instead of the humbler declaration as merely constant on the earth's surface (the environment in which we live and do our experiments. That said, first things (STR) first; GTR is a topic for a whole 'nother thread)
    Last edited by BuleriaChk; 08-06-2015 at 11:08 AM.
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    Default Re: Background Discussion

    One can thus express the mass of an electron relative to the mass of an equivalent photon by v/c, where v < c; and intrinsic property that is second order (energy), and expresses the fact that electrons "move" slower than photons when characterized by relativity, with E0 = Etc the "Rest Energy" of the electron, so the difference (originally (Px-Et)) is modelled in this context, and only depends on tv. (I derived this, but it will detract from the current focus:

    Most quantum mechanical contexts are not relativistic, and in this case Px=Et for so the wave equation is unity relativistically. (tv=tc)

    The next important concept to understand is that the Schroedinger equation is basically the (x,t,m,v) analog of the impulse-response model of signal processing; a "signal" has no mass and depends on time and amplitude, and one convolves an input with a system to get an output, with the system response given by a unit impulse input (a "Dirac delta function"), which has an "area" of unity (in physics, area is analogous to energy as a cross product).

    One can define a system based on amplitude parameters and convolve it with an input also based on amplitude parameters (times delta functions), and get a system output. For signal processing, system, input, and output can be continuous functions, and the Schroedinger equation for physics in terms of continuous functions in space, time, kinetic and potential energy (referred to h - which refers it to photo-electrons in a medium described by V(x) is its analogue in QM.

    Note that the system is contra-variant - decreasing wavelength is characterized by an increase in momentum-energy as contrasted with the relativistic covariance above, where mass increases with "wavelength" (X=CT), since increasing a relativistic "ruler" in space-time is equivalent to increasing the mass of a particle it describes, and VT' is a perturbation (for VT' positive definite) increases the total mass of the system, and thus its total energy.

    Relativistically, the analogue of the Schroedinger equation is the Green's function of quantum field theory, and the output is an energy distribution of particles (normalized to a unity input/output "probability" distribution. (for example, a Gaussian is often used as an input to model a Green's function)...

    So it gets pretty complicated (especially after you add in Pauli and Dirac), but it is doable, and one becomes aware of how symmetries are used to get quantifiable results of actual experiments.

    For many classical problems, one divides the wave equation into space and time separable functions, and works in either mass "space" (e.g. group theory, crystals) or energy "time" (e.g., particle physics with invariant masses). However in many contexts, these ideas are mixtures (Fermi levels, effective masses in semiconductor physics; charge variations in plasma physics; space distributions in particle physics.

    In particular, don't feel there is something obvious you're missing because you're confused - physics at this level becomes very complicated very fast, and many people have been working on their individual chunks of physics for a long period of time. My particular interest has been at the fundamental level, but I have also been involved in some of the above areas of interest in my career (such as it was...


    Bottom line; again, try to be aware of context at all times (e.g., "potential well", "particle interaction", semiconductor current through a potential gradient, phonon vibration of a crystal etc., etc., etc;, etc.). What process is being modeled, and how does it differ from other possible processes? And especially, what are the approximations being made in the model (because one has to make approximations if one is considering more than one particle or universe....

    I'll clean up the relativistic context I referred to in my first post and provide a .pdf to it if I get time, but there are many more areas of application for quantum theory then the relativistic foundation for "quantum field theory" in my previous posts in this thread ... like others, I am trying to provide road signs based on my own limited experience....
    Last edited by BuleriaChk; 08-05-2015 at 09:15 AM.
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    Default Re: Relativistic Quantum Mechanics

    Here is the rest of the analysis, which shows the relation of relativity to the "coordinate" (non-relativistic) interpretation of the wave equation. (Note: this derivation is my own, but it makes sense to me. I will be adding the .pdf version of this to my website shortly and providing a link in a separate thread shortly)

    Recapping from the last post, we have:



    where



    Now we realize that "t" iin the Energy term ambiguous, since it could be either tc or tv; we can now set that t = tc (which is the "period" of the system as a whole)

    so the equation becomes:



    and we set



    But



    so that





    The result is:



    where P is the classical momentum.

    Since the “time” components are now .



    For the final term, we use the “momentum” model of the first, and set

    ,

    since xc is an invariant, so that



    which is the rest energy independent of v.

    Since is an invariant, it need not appear on the l.h.s., so:



    that is,



    which is the difference between the perturbed energy (as a function of v) and the rest energy E.
    (One might be concerned that v=c implies an imaginary component under the radical, but this is resolved when the equivalent contravariant formulation is taken under consideration in the Lorentz transform in the complex plane (I.e., xv = xc since covariant mutiplied by contravariant = 1 - neither parameter is a function of v in that case).

























    Last edited by BuleriaChk; 08-05-2015 at 09:14 AM.
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    Default Non Relativistic Quantum Mechanics

    I just added a link that describes my take on the non relativistic approach to QM to a previous post:

    Non-relativistic QM
    Last edited by BuleriaChk; 08-05-2015 at 09:23 AM.
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  8. #8
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    Default Re: quantum quandary?

    My take on it is that there are two viewpoints ... 1) Classical 2) Quantum.

    When you observe something you are making a Classical observation of a Quantum system. Stuff gets lost in translation. ( Collapse of the wave function ). Basically, you are forcing the system to provide you with an answer, so you get an answer. This is all just a limitation of a classical translation of a quantum world.

    It is better just to look at the quantum world in its terms. For example an electron exists in a cloud. The electron exists in all of its super positioned states simultaneously.

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    Default Re: quantum quandary?

    Quote Originally Posted by tom View Post
    My take on it is that there are two viewpoints ... 1) Classical 2) Quantum.

    When you observe something you are making a Classical observation of a Quantum system. Stuff gets lost in translation. ( Collapse of the wave function ). Basically, you are forcing the system to provide you with an answer, so you get an answer. This is all just a limitation of a classical translation of a quantum world.

    It is better just to look at the quantum world in its terms. For example an electron exists in a cloud. The electron exists in all of its super positioned states simultaneously.
    Why not? Sounds ok to me. (well, except for the part about existence....

    (Did I really write all that stuff? I GOTTA stop doing that....)
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    The Relativistic Unit Circle 03/28/2017 07:40 AM PST
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