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the curious case of uncertainty principle

November 12, 2011

Mohan, mdashf


Thursday
Bibhäv Paudel

hello sir, im a 12th grade student and im having trouble explaining the uncertainity of the velocity as in comes in the uncertainity principle by Heiseinberg , and what about speed of light , uncertainity in the measurement of the velocity of light , does this make sense ???

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there is

1. uncertainty relation between momentum and position which is basically a speed and position uncertainty hence depending on what uncertainty you have for position you get the uncertainty on time **and vice a versa**

2. in case of uncertainty between energy and time it is so in absense of relativity. In relativistic situations one can not define the position of photons (light) very sharply because they have zero mass and speed of light velocity. That means Energy-time uncertainty becomes a speed-time uncertainty for mass-less particles such as photons and momentum-time uncertainty for particles with mass such as electrons and mesons moving at very high speed (relativistic speeds).

SO for photons which are always relativistic when the “error” (actually uncertainty) in position is smaller than the wavelength you can determine the position of the photons to the accuracy of the wavelength, this is called ray-optics or wave-optics because we can define light rays as we can define a sharp position for the photons, ofcourse for small wavelengths.

But for small wavelengths that is very high freq. waves of light there is still an uncertainty between speed and time. The first case was speed and position now the 2nd case is speed and time. These two cases which in non-relativistic situation different cases are essentially the same thing for high energetic photons because there is a position and time in speed.

That just means if one (say position) is uncertain the other (time) has to be proportionately certain. eg if you take a picture with an intense source of light and the target of which you are taking the pic moves, it creates a fuzzy or smeared out impression. If you move your hand when pic is taken your hand’s image is funny, its smeared out. That is so, since there is speed = (distance, time) uncertainty, if one becomes sharply known the other becomes equally uncertain. In the picture usually the distance is what is uncertain since the time is already fixed. That means the image is not sharp but is fuzzy across a distance.

In summary for the relativistic quantum mechanics two separate uncertainty equations have become condensed into only one uncertainty relation, one between the distance and time.

[for photons momentum and energy are correlated, since photons are massless it still has a momentum because there is energy, so all uncertainty equations are valid in the scheme of theory but what is essentially playing is a consistent inter-relation among different physical quantities which become clear as per the situation.]

eg In a picture taken with a camera a moving train appears fuzzy and smeared out but stationary targets are depicted with better accuracy. That is the relative speed between the camera and the targets brings additional distance uncertainites into the image because the time is sharply known through the act of the taking the picture ..

10 Comments

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  1. November 13, 2011

    …”since photons are massless it still has momentum because there is energy”…

    Maybe you mean to say ….although photons are almost massless they still have momentum because they contain an equivalent quantity of energy….

    • Mohan #
      November 13, 2011

      I have 5 or 6 articles here that deal with the experimental situation of photons not having an absolute zero mass howsoever tiny (presently 10^-18 eV) But in theory even when the photons have absolute zero mass they always travel at speed of light, they never have a zero velociy, this means this default energy is also its momentum. This is special only for absolute-zero-mass particles hence there is no confusion. Photons being almost mass-less is the experimental situation which only tells you how much deviation you are seeing from an absolute-zero-mass theory.

      • Mohan #
        November 13, 2011

        check this reference: http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/relmom.html

        photons can not have a momentum if you think they have a zero mass, but they have a speed of light velocity which is a fraction of their wavelength and frequency, hence in this special case the energy = momentum in units of speed of light = 1. Consistent with theory nothing about the experimental situation of almost zero mass ..

        If you rely on Relativity only you would think photons have zero momentum since they have zero mass. But thats not the case. The answer comes from Quantum Mechanics, which tells photons are not only particles but waves. The wave nature is still prominent when the particle nature is not. A zero mass still means it has to propagate like a wave which means the group or phase velocity is a ratio of the frequency and wavelength. A wave’s energy is defined from it’s frequency and its momentum is defined from it’s wavelength which just means their ratio is the speed of light since it is a wave. But this also means a zero mass particle has certain wavelenth which is a measure of it’s momentum. Hence zero mass particles such as photons do have a momentum otherwise untenable from the definition of momentum. But that definition is for particles only not wave-particles. All notions of exclusive particles and exclusive waves were rejected by Quantum Mechanics. Basics.

  2. November 13, 2011

    According to Heisenberg’s uncertainty principle there must be some fluctuation/information or energy (= mass) anywhere at all times. From my own point of view rhis is true because time cannot be zero (or infinite for that matter). Therefore massless particles cannot possibly exist (singularities cannot either).

    • Mohan #
      November 14, 2011

      1. Information is not a physical variable. It’s an intelligent interpretation of physical variables. Information therefore is not fundamental. It’s an anthropic/intelligence parameter.

      2. maslessness is a consistent theoretical representation. Experimental mass of 10^-18 eV is consistent with this masslessness. If in future we discover another mass which is smaller in mass compared to photon’s experimental mass then theoretically that will pose a problem since any mass above this hypothetical mass is not absolute zero anymore, even theoretically, not just experimentally. Since we do not have such particles known we do not worry at present.

      3. a massless particle theory is consistent with a zero proper-time. Quantum Mechanical uncertainity of Heisenberg just states that there is a very small probability which anyway depends on the rest-mass of particles that the causality of zero-mass particles can be violated to a very small extent, the heavier the mass, the smaller that probability is. This you can say is the fluctuation, it does not exclude zero-mass or zero-proper time.

      4. In case of a hypothetical mass with lesser mass than photon is discovered theory will need to be changed because that particle will be superluminal compared to photons. But thats a problem Physicists of present are not grappling with, it is hypothetical to the present situation of theory. Presently neutrinos have been found to cross the photon’s speed barrier even with a mass which is billion x billion times heavier than photons, it is a different issue, it may or may not be true and we will find out.

      5. Experiment will eventually guide us towards a better understanding of Universe as will the impending theory. But there is at present no problem with zero mass, speed of light, zero proper-time as per Quantum Mechanics. Ofcourse Quantum Mechanics and other kinematical and dynamical theories established are not completely consistent with each other. WE are learning. eg Gravity is not unified with Quantum Mechanincs. Relativistic Quantum Mechanics is not completely consistent. That is the present state of knowledge. There might be other impending inconsistenicies which we are not completely sure of.

      6. Quantum Mechanics is a physical theory although philosophically and technically connected to ideas that have no basis. It is not a problem of Quantum Mechnaics because that is an established theory. The problem arises because of legitimate and illegitimate understandings. eg Complexities are legitimate understanding but metaphysics is illegitimate.

  3. November 15, 2011

    Ad 1.
    One of the definitions of information is the nature of particles and their natural properties.
    Ad 5.
    “But there is at present no problem with zero mass, speed of light, zero proper-time as per Quantum Mechanics.” My point is that I do have a problem with zero mass, constant speed of light and zero proper-time whether that’s QM-inherent or not.

    • Mohan #
      November 15, 2011

      reg 1. Information can be studied logically and also in physics but not as a fundamental variable like time or space. eg information content etc can be interpreted logically in thermodynamics or blackhole problem etc, but that is merely intellectual. It has physical meaning but no one has ever formulated it in terms of physics like one has eg formulated commutation relationship in quantum mechanics. WE merely say information is relayed or information is stored in physical system. Sometimes we have a clue that information must be consereved and some times we do not. But there has never been a way in fundamental physics to formulate information the same way momentum or energy or entropy is formulated, we merely associate information with these variables because in a complex system there is information.

      reg 2. when you say, you have a problem with zero mass and zero propertime, what do you mean. Let me first ask you your back ground. Are you a professional physicist?

  4. November 15, 2011

    Ad 1. Information as fundamental variable are your words, not mine. I have given you one definition of information (f.i. used by Leonard Susskind). Firthermore information plays an essential role in Eric Verlinde’s ideas about gravitation.
    Ad 2. My background does not matter. Arguments count. i don’t have a problem with the uncertainty principle like f.i. Gerard ‘t fHooft who is a determinist and therefore has a problem with QM to be continued in next comment)

  5. November 15, 2011

    I have a problem with QM because from my point of view the uncertainty principle is inconsistent with zero mass/zero time. I know that QM solves this problem by the “creation” of virtual particles, but I consider that creative bookkeeping. no science. In physics inconsistencies are the rule rather than the exception. Meanwhile the cosmological constant (based on virtual particles) has been brought into competition with dark something. This is not creative bookkeeping anymore but marketing. I know a lot of both.

  6. Mohan #
    November 15, 2011

    who cares what definition you give for information, it is not a fundamental physical variable and nobody has ever given such a fundamental equation in terms of information. Susskind and Gerard ‘t Hooft are Physicists who you have cited. You see background matters. Are you a Physicist, if you are not you will only make a comment that will reflect your depth of understanding, like you said inconsistencies are a rule in Physics. I know not a single Physicist out of 500 that I have met during my life that would say or think so, What arguments of yours are making a sense here? Even your website link isn’t working, are you a rule or exception? If you want to argue physics on such a screwed psyche, go find yourself another website another person. I have plenty of people discussing physics with me everyday, that do not have a background in Physics but nobody said Einstein’s theories are in general inconsistent as a rule, and its validity is an exception.

    This will be your last comment regarding imaginary tirade you have against Physics.

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