Uncertainty Principle Again.

Yesterday, an exciting discussion on a short Physics question turned somewhat argumentative (which is good as long as we are focusing on WHAT and not WHO, which is perhaps an ideal and difficult to reach at paradigm)

The question was very simple (and in my mind the answer is still simple) Although “Einstein; simpler things can’t be further simplified ” may or may not be valid in a situation where we are discussing  such a difficult concept as is “Quantum Mechanics”.

But in last 100 years despite “Feynman; it is safe to say no one understands quantum mechanics” has taken various hues and colors and we have seen in the big picture Feynman stands corrected, partly because there is always a new field of study or understanding opens up. But we can also say misunderstanding is not same as not understanding. Misunderstanding is a special form of understanding. A form where there is no understanding in a way there is some degree of understanding and some degree of not understanding gets mixed up. Not understanding (as in Nobody understands QM on a safer claim) on the other hand is a bit clearer on NOT. For Quantum Mechanics the latter is a time tested and more acceptable form of what we understand about Quantum Mechanics. Its partly to do with the elaborate linkage of one concept to another where using one principle incorrectly leads to incorrect application of another and gradually we end up screwing up not only Quantum Mechanics but also all valid forms of Classical Mechanics. eg Quantum Mechanics is a logical and consistent expansion of the ideas of Classical Mechanics. This is called as “requirement of consistency”. So for Classical Mechanics; Waves, and Classical Mechanics; Particles, to be consistent  we must have Quantum Mechanics in general and due to this wave-particle duality, Heisenberg’s Uncertainty Principle in particular.

If you are familiar, this is a blessing in disguise, because one can cleverly, if one is clear as to what one understands and what one does not (misunderstanding is the opposite, one is not clear as to what one understands and what one does not) one can pinpoint the answers; to better degree of accuracy. This is the power of Uncertainty Principle. It merely brings the “requirement of consistency” to even Classical Mechanics. As such there is nothing which is Classical Mechanics, nature does not define whats Classical Mechanics and Quantum Mechanics is a refinement of Classical Mechanics. This refinement is ordained because we bring in the quantum, which were mostly unknown before 1900-1925. Given this “requirement of consistency” despite how quirky affairs of understanding Physics can become, we have today understood far far more than we did in last century. As two quick examples, in fundamental understanding particle physics and in technological advancements all sorts of electronics and communication systems.

(exactly how atoms and molecules are  configured is one direction of understanding, exactly how their constituents are configured is another dimension of understanding of Quantum Mechanics. At the center lies an abstract concept, which keeps on producing more knowledge towards the inner; constituent side, nonetheless we also get better grasp and clarity of how the outer direction of understanding is possible; atoms, molecules and further up the scale, objects even towards cosmology. You may want to read Stephen Hawking’s explanation eg of how Uncertainty Principle explains Black-hole phenomena, namely Hawking Radiation. Black-holes are not quantum but classical objects, but the effects being quantum mechanical, correspond or move up the scale so that they are classical phenomena in how we can understand. Any radiation that escapes a black-hole can’t be explained by Classical Mechanics ideas, but we can detect such radiation and our detectors and black-holes are classical mechanics objects.)

So if you read the above (…) it should be fairly clear why (and how) Uncertainty Principle (UP) or any Quantum Mechanical understanding is applicable to Classical sized objects as well. These principles are at the base of our latest understanding and they are for this reason called as principles. Or, they would be called ” a fact of QM and not applicable on Classical Mechanics”. Some people (indeed as a matter of concern some who are teaching Physics) still believe, the latter; “UP: a fact of QM and not applicable on Classical Mechanics.”

First off therefore I will quote the question, ditto, so, we can grasp how exactly a bit more detail might elucidate the concepts better.

Here is the question, addressed to an elementary level of Physics Students whose conceptual integrity can’t be compromised, no matter where they want to apply their knowledge and skills, in a medical device, a satellite, an electronic gadget or in teaching a class.

* When a beam of light is used to determine the position of an object, the maximum accuracy is achieved if the light is  

A. Polarized         B. of longer wavelength           C. of shorter wavelength       D. of high intensity.

This question and its answer is perhaps to be found in a widely available course content, eg text books of Physics. In my understanding this is a very valid question. What it purports to convey is the “application/nature of light in determining eg size or distance of objects” as one example. In size one can think of a microscope, crystal diffraction patterns and atomic structure.  In distance one can think of X-ray sources, electromagnetic sources and various cosmological phenomena, where either a “regular lens telescope” is employed or even an electromagnetic-signal telescope is used (eg radio-wave telescopes array, here in Gauribidanur, I visited them in year, 2000). If this property of light as being a wave as well as a particle is not valid we would not be able to detect any electromagnetic waves. In another connection light is connected also to other subatomic particles which are linked via the uncertainty principle. Hence TV broadcasting via satellites would also be not understood if we are to reject the QM Uncertainty Principle. That would also mean all sorts of communication paradigm, GPS, electronics devices like mobiles and vidoe conferences they would all fail.

So to be noted; the above question talks about only properties of light. But inherently its connected to a wide variety of applications that has utility in modern day life.

(one therefore need not connect this question to a microscope and say microscope has classical sized objects and the uncertainty principle is not applicable. this was precisely the contention yesterday which led to some degree of arguments, with some teachers telling me how I don’t understand the uncertainty principle because they argued its not applicable to large objects. But I want to clarify certain misconceptions they are carrying, despite of the fact this question does not talk explicitly about large sized objects. The principle is just valid for all sized objects.)

So there was a counter argument from them about how light’s position and momentum uncertainty are not the large objects position accuracy and so on.

Okay so 3 things. 1. The principle 2. The Classical Objects. 3. The Quantum Objects.

1. Uncertainty Principle; Del X * Del P ~ h-cross. [the minimum uncertainty is in a regime of h-cross and not size of objects, h-cross is energy-time. Large objects do not affect this principle despite their size or distance because whats more prime in Physical Understanding is energy and time.] Connected with this is de-Broglie wave-particle relationship, which is a result of wave-particle duality hence, the uncertainty relationship is important in association with the de-Broglie relationship. The de-Broglie relationship is connecting how momentum (a particle concept) is connected to wavelength (therefore position with a given uncertainty, a wave concept). The relationship is lambda = h-cross/p. So having a wavelength light refers to an uncertainty in position, automatically. Given that we use light of a particular wavelength for any kind of study, detection, application; we will end up with a position inaccuracy. No matter what that application is, here; detection of position of the object. Very simple idea, the size of the object comes into the problem, not its energy. What comes is the energy, momentum and wavelength of the light. Given wavelength is eg 1 nm (1 nm = 10^-9 meters) the accuracy with which we can know the size or distance of objects (position in terms of physical variable) is 1 nano-meters. nm level signals are used eg in satellite communications. [It would be a very good problem to see why a GPS satellite registers ground distances to accuracy of say a feet. Hint; there are added degree of dimensions available, eg there are 24 satellites revolving around earth to give distance measurement on earth]

2. The object can be a large object, eg say something whose picture you are taking. But as explained above its not the energy of the object (or momentum) which is directly coming into the problem. That would be an added degree of concern if the object is moving with certain velocity, a reason why pictures are blurred. Because motion of objects introduces additional energy-time-momentum-position variables and their corresponding uncertainties. For the argument of the above problem one can imagine the large sized object, lets say a bird, is standing still on a tree while its picture is being taken. In that case if the wavelength of the light [few 100 nano meters = 1/10th of a micrometer] is used (eg in a digital-camera) the corresponding accuracy of the light will be less than micrometers. You can take a very sharp picture of the bird, which is lets say 6 inch long. But when you zoom in to a large degree, the inaccuracies will show up. [in this case how to see a micrometer level image? Is a computer sufficient to show us the uncertain edges of the pixels?] If the wavelength (here visible light) is so small, evidently by de-Broglie relationship, momentum or energy of such light is very large. But its not as large to disturb the feelings of the bird. The bird doesn’t have a problem with visible light, and such energy does not disturb its position or energy or any thing so to say. So while Quantum Mechanics is valid, we are accustomed to say this is a classical mechanics situation. To say QM is invalid is incorrect. To say QM is understood to be valid is a knowledgeable position.

If the wavelength of light** is large, then the energy is small, the intensity is small, what we call as feeble or dim light, in such situations evidently we can’t take a better detection of an object even if the object is large enough. Evidently again, Uncertainty Relation is valid, the size of the object does not influence the situation, unless, its moving at certain velocity, therefore certain energy.

(**light = visible light is always few 100 nano meters, but in general any electromagnetic waves are referred to as light, especially in Physics, where the optical properties are studied conceptually, this particular problem was purported to be imparted in a class of Ray Optics and Optical Instruments, Ray Optics is the situation when the wavelength is small, energy is large and the wave behaves like a “geometric straight line”, from that perspective also, this above question is important conceptual underpinning of the subject.)

3. The objects are quantum, eg subatomic particles, electrons, protons, cosmic ray particles, quarks etc.

Like in 2. above, there are two aspects therefore. A high energy (therefore high momentum, high frequency or low wavelength light or any radiation or any quantum particle such as a neutron in a nuclear reactor) wave (electromagnetic wave or light) will have a small wavelength, hence position can be measured accurately. But this is the problem of atom, its got such a small energy, which comes to the extent of h-cross, that a high enough energy of the detecting signal (high frequency or low wavelength) will sufficiently disturb the actual position of the quantum. This is called as “Observation affects reality”. Such a paradigm would have occurred for the bird if the bird were hit by a bullet or even a “Oh My God Particle”, the largest known energetic particle would change the location of the bird, disfigure it in the process and the particle would never come back and register in the camera. So we can’t take picture of a bird with a bullet. For the electrons and atoms, a very small energy can also disturb the configuration of the atom or electron orbit. hence a small energy, small frequency or a large wavelength is no good to measure position accuracy of the atom orbits without disturbing the original positions first. If we go for small energy to not disturb the actual energy of the atom, say, then the wavelength would be so large, the position of the atom would not be known, say by meters or kilometers. Then how can we say we have detected an atom?

Bohr took an atom’s orbit (for an electron) and made an “integer” number of wavelength of the electron. This is known as Bohr’s Quantization condition and is based on how an electron despite of being a particle also has a wavelength. Thus By such a wave-particle duality one knows the probabilistic or averaged out size of atoms, especially when they are not to be disturbed in any paryicular way. If we disturb them, the uncertainty relation is still valid. The uncertainty relation is a minimum amount of uncertainty one would make if one were to have no choice in deciding some other variables. But the actual uncertainties will always be more and more, due to various variables where we would have no choice to decide what exactly they could be. eg in NMR there could be energy and potential (voltage) fluctuations.

In all situations, conceptual, classical and quantum-objects the Uncertainty Principle is a far better judge than you and me. Its the work of generations of scientists.