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Thread: The Paradox of Uncertainty Principle

  1. #1 The Paradox of Uncertainty Principle 
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    In quantum mechanics the uncertainty principle claims that position ‘x’ and momentum ‘p’ of an electron cannot be simultaneously known to high precision. The more precisely one property is known, the other can be known less.
    In Werner Heisenberg’s equation:
    dp dx >= h
    - where dp = change of momentum; dx =change of position; h =Planck’s constant, the energy quantum

    Heisenberg’s microscope

    Heisenberg originally illustrated his uncertainty principle by using animaginary microscope as a measuring device in which photons modifies the momentum and position of electrons, and as a consequence only one of it can bedetermined with high precision. This way ‘dp’ and ‘dx’ is caused by outer force, that is the equation depicts work with a limit as a consequence of quantized energy.
    F= dp/dt – where F is force and dt is the time of momentum change.
    So the work on electron caused by photons: W = dp/dt dx >= h

    However the classical equation of work has an inconsistency in this connection. In a peculiar way the unit of energy quantum (h) differs from the unit of energy (see: Planck constant – joule or joule second). Multiplying the left side by time, this inconsistency disappears, but at the same time ‘work’becomes mystical. The result remains correct until dt=1 but the equation ‘dp dx’ floats between work and power.

    (In his microscope presentation Heisenberg didn’t take into consideration that the resultant of the forces attacking particles can be zero, so it is possible to measure position and velocity without modifying momentum. So ‘h’ determine only the lowest energy limit of interaction, not the limit of observation.)

    The Copenhagen Interpretation

    Niels Bohr interpretedHeisenberg’s formula as the deviation of momentum and position independent fromouter force claiming that the probability distributions are fundamental and irreducible. According to this as one of the deviation nears zero the other must near infinite value to produce ’h’. Why should particles deviate without outer force became an unresolved riddle which divided leading physicists.
    (Bohr earlier developed a model of atom,in which electrons revolve in orbits around the atomic nucleus similar to the movement of planets around Sun. His model was attacked from many side, so making electron uncertain made his opponents uncertain too, saving his theory.)

    The paradox of Copenhageninterpretation

    The equation of momentum: p= mv
    - where p= momentum, m=mass, and v= speed of mass
    As v= dx/dt we can rewrite the equation as follows:
    p=m dx/dt

    It can be seen that momentum is derived from mass and velocity, so the precision of position is vital to the precision of momentum. (there is no momentum without position). However the Copenhagen interpretation claims that according to ‘uncertainty principle’ only one of them can be determined with high precision. This is the paradox of the Uncertainty principle.

    Many think that Heisenberg’s formula is related only to electrons. However as it isn’t contain any reference to electrons, its scope must be regarded as universal.

    While theoretical physicists are arguing for and against the probability of particles, the experimental physicists can determine the mass and velocity of particles by their momentum and positions without much ado. Giant particle colliders were built to accelerate and collide particles to research their components. Collisions need exact position and momentums of more particles at the same time.
    --

    I am opposing not a few special statements of quantum mechanics heldtoday, I am opposing as it were the whole of it, I am opposing its basic views that have been shaped 25 years ago, when Max Born put forward his probability interpretation, which was accepted by almost everybody…”
    ”I don't like it, and I'm sorry I everhad anything to do with it” - ErwinSchrödinger

    ”the actual quantitative physicists [are] wrong to consider a wave propagation without localization of the particle…” - Louis de Broglie


    “God doesn'tplay dice…”. - Albert Einstein

    The fog of ‘uncertainty’ hiding particles cannot be lifted almost in a hundredyears.
    In fact it became denser during that time.

    Sandor Fofai





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  3. #2  
    Moderator Moderator Markus Hanke's Avatar
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    This is the paradox of the Uncertainty principle.
    There is no paradox. Since momentum and position observables are Fourier transforms of one another, you cannot determine them both at the same time with arbitrary accuracy. This is basic mathematics. Same goes for other pairs of observables such as energy and time.

    the experimental physicists can determine the mass and velocity of particles by their momentum and positions without much ado.
    Reference just one repeatable, peer-reviewed and independently confirmed experiment for us where the HUP is violated.

    However the Copenhagen interpretation claims that according to ‘uncertainty principle’ only one of them can be determined with high precision.
    You forgot to mention the crucial bit - you cannot determine them both with arbitrary precision at the same time. Of course you can conduct two separate measurements, and determine both with arbitrary precision in each experiment.


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  4. #3  
    ▼▼ dn ʎɐʍ sıɥʇ ▼▼ RedPanda's Avatar
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    He posted the same stuff here: Physics Discussion Forum • View topic - Top 10 problems of theoretical physics

    A year later and he hasn't responded.

    I wouldn't waste any more time on it, Markus.
    SayBigWords.com/say/3FC

    "And, behold, I come quickly;" Revelation 22:12

    "Religions are like sausages. When you know how they are made, you no longer want them."
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  5. #4  
    Brassica oleracea Strange's Avatar
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    I don't think there is much point responding to this ignorant nonsense, however...

    Quote Originally Posted by Sandor Fofai View Post
    While theoretical physicists are arguing for and against the probability of particles, the experimental physicists can determine the mass and velocity of particles by their momentum and positions without much ado. Giant particle colliders were built to accelerate and collide particles to research their components. Collisions need exact position and momentums of more particles at the same time.
    These operate on large numbers of particles in bunches and so the can use the average position and momentum. Therefore they don't need to know both values precisely for any single particle.

    The rest is equally wrong.
    ei incumbit probatio qui dicit, non qui negat
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  6. #5  
    Brassica oleracea Strange's Avatar
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    Quote Originally Posted by RedPanda View Post
    A year later and he hasn't responded.
    He does seem the be the archetypal seagull poster.
    ei incumbit probatio qui dicit, non qui negat
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  7. #6  
    Moderator Moderator Markus Hanke's Avatar
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    The OP also appears to be forgetting that we are dealing with observables and probability wave functions here, not determinate scalar functions such as in classical mechanics.
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  8. #7  
    KJW
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    Quote Originally Posted by Sandor Fofai View Post
    The equation of momentum: p = mv
    This particular mistake is quite subtle. There are two kinds of momentum: kinetic and canonical. The kind that people are most familiar with is the above definition which is kinetic momentum. Canonical momentum is associated with Hamiltonian mechanics and is the kind of momentum referred to in the Heisenberg uncertainty relation. Interestingly, this distinction led to the Abraham-Minkowski controversy.
    There are no paradoxes in relativity, just people's misunderstandings of it.
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  9. #8  
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    Quote Originally Posted by KJW
    There are two kinds of momentum: kinetic and canonical.
    I am having trouble understanding what these terms refer to. What is "kinetic momentum"?

    Maybe by "canonical momentum" you something like the so-called second-quantization (sometimes called canonical quantization) which is [tex]p \mapsto -i\hbar \frac{\partial}{\partial x}[]/tex] (obviously an operator) and , also an operator. The latter is boring - the hat is just showing off, so we can forget it.

    The first is more subtle. Recall that in the very early days of QM that Neils Bohr postulated the allowable angular momenta for a (single) bound electron is ([tex]r/tex] being the "radius of the orbit" - an out-dated concept)

    Suppose, as de Broglie and Schrödinger (separately) did, that this constraint applies to the momentum of any un-bound sub-atomic particle, so that now one has to specify directional coordinate functions, and, for good measure transfer to the complex plane.

    This becomes where, as far as I can see, the sign is merely a convention (though I could be wrong).

    So it is often said that the HUP comes from the fact that, as operators, the QM momentum and position operators don't commute. Let's see this first.....

    Suppose an allowable function acting on the same space, call it - the "wave function".. Then by the product rule from elementary calculus gives us that

    which implies that

    .

    Or, quantum mechanically,

    How this leads mathematically to the HUP, I cannot see
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