Talk:Heisenberg's microscope

Bohr's Contribution

I recommend a new section be written called "Bohr's Contribution," which would discuss the following three points (comments welcome).

Bohr's Criticism

The introduction to this article (and a reference in the discussion) suggests that Bohr "criticized" the microscope argument. This is only partially correct. Bohr was critical of Heisenberg's interpretation of "uncertainty" as a mere "human inability" to know some things. So, he might have been critical of this aspect of Heisenberg's *interpretation* of the microscope. But Bohr clearly accepted the argument just fine -- see this p.583 of this 1928 Nature article, in which Bohr gives a rather more sophisticated version of the 1930 microscope argument given by Heisenberg. The main difference, from what I can tell, is that Bohr emphasizes the objective indeterminacy of momentum given a sharp position measurement, and vice versa -- he makes it clear that this is not a mere human ability to know something. Bwr6 20:58, 15 December 2010 (UTC)

Expression of the Uncertaintly Principle

As pointed out in the uncertainty principle article, Heisenberg's expression of this principle is not mathematically correct -- in this discussion, "change in momentum" $\Delta p_{x}$ should be replaced with "standard deviation of momentum" $\sigma _{p_{x}}$. However, I would suggest keeping the error in the "Heisenberg's Argument" section, since that section does give a literal expression of what Heisenberg said. However, in the 1928 Nature article], Bohr actually does give this correct expression in his discussion of the microscope. This alternative expression (and acknowledgement that it is correct) could be included in the discussion of Bohr. Bwr6 20:58, 15 December 2010 (UTC)

Historical Origin

Is it clear that Heisenberg invented the microscope argument and not Bohr? The first written instance of the microscope that I can find is in the above 1928 article by Bohr. All the expressions of it by Heisenberg that I've been able to find have been later. Some reference should be given here -- or, if none can be found, it should be acknowledged that it's not clear who invented the argument. Bwr6 20:58, 15 December 2010 (UTC)

copied from Basics of quantum mechanics talk:

Uncertainty principle and disturbance of position

I do not believe that the uncertainty principle teaches that the position is "disturbed" by measurement. I believe this is a throwback to the Heisenberg microscope thought experiment which is not a correct image of Uncertainty. I give a rather brutal debate on the Uncertainty Principle talk section because I'm battling strong supporters of the Heisenberg microscope. I do not mean to be unkind just strong in my arguments.

The Heisenberg microscope was a kind of reductio ad adsurdum argument, no? We start with the everyday view that says that electrons are little spheres circling the nucleus of some atom. We would like to know not only where it is, but where it is going and how fast it is headed there. So we can try to look at it with a microscope. The problem is that visible light has a large wavelength relative to the size of the electron, so we would not get a clear image. We would like a clearer image, so we try for gamma radiation. But one hit of gamma will give the electron the energy of ionization. So the second "frame in our movie" shows nothing because the electron is gone. If we back off on the energy, then we get more of an idea of momentum but we lose the exactness of

One of the things that most people seem to agree upon is that when a photon is absorbed by an electron then the electron changes its orbital or is ionized.P0M

Niels Bohr is actually said in some sources to have originated the thought experiment of a gamma-ray microscope which suggests that, since a microscope's light “disturbs” the motion of small objects under observation in an intractable way, exact simultaneous knowledge of the position and momentum of elementary particles is impossible. This thought experiment has repeatedly been deemed a poor proof of the uncertainty principle because

• 1. Heisenberg's microscope is stating that uncertainty is an error in measurement, when the uncertainty principle itself is not about there being an error in measurement due to the instrument or type of measuring procedure, but about there being a fundamental deviation between position and momentum of observables.

Please define "deviation." P0M

and

• 2. Heisenberg's microscope suffers from the same problematic assumptions about locality as Einstein's analysis of the EPR experiment.

Once this thought experiment has gotten you thinking about what you can really mean by "position" and by "momentum," then further thought exposes the problem of "location" to be deeper than everyday thought would lead one to believe. We assume that when Superboy leaves home moving so fast that nobody can see him and arrives at school a second later we would nonetheless have found his image on a sufficiently fast motion picture camera. He had a location whenever we might have opened the shutter of that incredibly rapid camera. In that sense of "location," I think you are right. When a photon or an electron is emitted in a double slit apparatus, we can know about it in two ways. (1) We fed the device enough juice to stimulate the emission of one particle. (2) Something showed up at an appropriate amount of time thereafter on the detection screen. We know nothing about position between those points in time. So if an electron in orbit is like a photon in passage, then it doesn't have a position in the sense we give "position" in everyday language. P0M 02:11, 3 January 2006 (UTC)

Thirdly, the uncertainty principle did not arise from observations of a single particle. The uncertainty principle arose from spectroscopy. In spectroscopy, no one is looking at subatomic particles through a microscope. In spectroscopy a single light source is illuminating an element. Therefore that single light source is disturbing all the particles to the same degree and the spectrum created is therefore all disturbed to the same degree so no particle is more or less disturbed than another. Yet, even in this case, Heisenberg is saying that there is still a deviation in measurement between position and momentum of a moving particle. This therefore cannot be due to a collision of a photon under a microscope, but is inherent in nature. Therefore, it is a fallacy to say that the act of measurement disturbs the particle. This is a leftover from the HM thought experiment. Nothing disturbs the particle. Heisenberg's uncertainty principle arose from inaccuracy in measurement where there was nothing to disturb the measurement. He saw this as not the fault of the spectroscope, but an inherent characteristic of the universe.--Voyajer 00:56, 3 January 2006 (UTC)

It's certainly true that the uncertainty principle did not arise from observations of single particles. A thought experiment is just that.

Spectroscopy can also be pursued by heating a sample of some material to incandescence. What one sees then are a few characteristic bright lines in the spectrum produced, and nothing in between. These characteristics were observed and used for a long time without there being any explanation for them. It turned out that these bright lines are related to the orbitals that are proper to the element under investigation, and the orbitals are in turn related to Planck's constant.

Shining a white light on a sample of a gas will result in the negative of the above situation, since certain wavelengths will be absorbed by the electrons in the gas, causing them to jump up a level rather than passing through to the observer.

So what in all of the above regarding spectroscopy has anything to do with uncertainty? The uncertainty in any measurement of atomic particles turns out to involve Planck's constant because the energy proper to any photon is a function of its frequency. Higher frequency gives clearer image but also delivers more energy to the thing you are trying to measure. P0M 02:11, 3 January 2006 (UTC)

Heisenberg derived the Uncertainty Principle from actual deviations in measurement using spectroscopy. He just didn't come up with it in a void. Sorry but you are about to get more than you asked for, but I find the different views on Heisenberg's microscope fascinating so I'm going to post them here (those I haven't posted to other talk). But first, the origin of the Uncertainty Principle is from measurements made in spectroscopy for matrix mechanics using in all probability the Fourier Transform Spectroscope invented in 1911.

Quote from origins of Uncertainty Principle:

"After Schrödinger showed the equivalence of the matrix and wave versions of quantum mechanics, and Born presented a statistical interpretation of the wave function, Jordan in Göttingen and Paul Dirac in Cambridge, England, created unified equations known as "transformation theory." These formed the basis of what is now regarded as quantum mechanics. The task then became a search for the physical meaning of these equations in actual situations showing the nature of physical objects in terms of waves or particles, or both. As Bohr later explained it, events in tiny atoms are subject to quantum mechanics, yet people deal with larger objects in the laboratory, where the "classical" physics of Newton prevails. What was needed was an "interpretation" of the Dirac-Jordan quantum equations that would allow physicists to connect observations in the everyday world of the laboratory with events and processes in the quantum world of the atom.

"Studying the papers of Dirac and Jordan, while in frequent correspondence with Wolfgang Pauli, Heisenberg discovered a problem in the way one could measure basic physical variables appearing in the equations. His analysis showed that uncertainties, or imprecisions, always turned up if one tried to measure the position and the momentum of a particle at the same time. (Similar uncertainties occurred when measuring the energy and the time variables of the particle simultaneously.) These uncertainties or imprecisions in the measurements were not the fault of the experimenter, said Heisenberg, they were inherent in quantum mechanics. Heisenberg presented his discovery and its consequences in a 14-page letter to Pauli in February 1927. The letter evolved into a published paper in which Heisenberg presented to the world for the first time what became known as the uncertainty principle."--[1]

"In 1927 Heisenberg tried to show the impossibility of quantum trajectory by the use of his microscope thought experiment. And in 1928 Bohr added that what can never be empirically decided should be left outside science for good. Yet Heisenberg's microscope thought experiment employed not quantum electrons but the arbitrary mixture of classical wave and particle presentations of it. And Bohr confused what is outside the domain of quantum mechanics with what is outside science at large -- a confusion known in the philosophical jargon as hypostatization. Clearly von Neumann tried to prove the impossibility of hidden variables in 1932 because he was not fully satisfied with Heisenberg's and Bohr's discussions. Yet hidden variables proved possible even if admittedly hideous. Meanwhile, heavy beam microscopes either had the Heisenberg-Bohr claim that we can never see atoms refuted, or shown it too vague for a proper debate. With this, much of the force of Bohr's thought experiments was gone." Quanta in Context, Joseph Agassi, Boston University, USA, and Tel-Aviv University, Israelin Einstein Symposion. Lecture Notes in Physics,Berlin: Springer, Vol. 100, 1979, pp. 180-203.

"Furthermore, Heisenberg's microscope is today seen as naive. It is based upon the idea that the wavelength of the probe in a scattering is the ultimate lower limit of resolution. Nuclear magnetic resonance imaging medical machines show that is false." Nature 242, 190–191 (1973)

"Readers are warned that Heisenberg's microscope experiment can be misleading. In particular, students should resist the temptation to believe that a particle can really have definite position and momentum, which, because of the clumsy nature of the observation, cannot be measured. In fact, there is no evidence for the existence of particles with definite position and momentum. This concept is an unobservable idealization or a figment of the imagination of classical physicists. Indeed, the Heisenberg uncertainty principle can be considered as a danger signal which tells us how far we can go in the using of the classical concepts of position and momentum without getting into trouble with reality." -A.C. Phillips

There is more, but then this talk section would be entirely too long.--Voyajer 02:40, 3 January 2006 (UTC)

Well, I can't resist one more:

Book:

"The Disappearance of Quantum Reality

"There the matter stood until Niels Bohr stepped in. While physicists such as Werner Heisenberg, Wolfgang Pauli, Erwin Schroedinger, and Max Born were working at the mathematical formulation of the new theory, Niels Bohr was thinking about what the theory actually meant. For this reason he summoned Heisenberg to Copenhagen and confronted him about the deeper significance of his "microscope experiment."

"Bohr argued that Heisenberg's explanation began by assuming the electron actually has a position and a speed and that the act of measuring one of these properties disturbs the other. In other words, Bohr claimed that Heisenberg was assuming the existence of a fixed underlying reality; that quantum objects possess properties-just like everyday objects in our own world-and that each act of observation interferes with one of these properties.

"He went on to argue that Heisenberg's very starting point was wrong in assuming that the electron has intrinsic properties. To say that an electron has a position and has a speed only makes sense in our large-scale world. Indeed, concepts like causality, spatial position, speed, and path only apply in the physics of the large scale. They cannot be imported into the world of the quantum.

"Bohr's argument was so forceful that he actually reduced Heisenberg to tears. Whereas Heisenberg had argued that the act of looking at the universe disturbs quantum properties, Bohr's position was far subtler. Every act of making a measurement, he said, is an act of interrogating the universe. The answer one receives to this interrogation depends on how the question is framed-that is, how the measurement is made. Rather than trying to unveil an underlying quantum property, the properties we observe are in a certain sense the product of the act of measurement itself. Ask a question one way and Nature has been framed into giving a certain answer. Pose the question in another way and the answer will be different. Rather than disturbing the universe, the answer to a quantum measurement is a form of co-creation between observer and observed.

"Take, for example, the path of a rocket in the large-scale world. You observe the rocket at point A. Now look away and a moment later glance back and see it at point B. Although you were not looking at the rocket as it sped between A and B, it still makes perfect sense to assume that the rocket was actually somewhere between the two points. You assume that at each instant of time it had a well-defined position and path through space irrespective of the fact that you were not looking at it!

"Things are different in the quantum world. An electron can also be observed at point A and then, later, at point B. But in the quantum case one cannot speak of it having a path from A to B, nor can one say that when it was not being observed it still had a speed and position." F. David Peat, FROM CERTAINTY TO UNCERTAINTY: THE STORY OF SCIENCE AND

IDEAS IN THE TWENTY-FIRST CENTURY, (Joseph Henry Press, 2002).

Here is Neils Bohr's take on things, from his 1949 "Discussion with Einstein." (Atomic Physics and Human Knowledge, p. 38f.

This phase of the development [of the observational problem] was, as is well known, initiated in 1927 by Heisenberg, who pointed out that the knowledge obtainable of the state of an atomic system will always involve a peculiar 'indeterminancy.' Thus, any measurement of the position of an electron by means of some device, like a microscope, making use of high-frequency rdiation, will, according to the fundamental relations (1) [E=hv and P =hσ ], be connected with a momentum exchange between the electron and the measuring agency, which is the greater the more accurate a position measurement is attempted. In comparing such considerations with the exigencies of the quantum-mechanical formalism, Heisenberg called attention to the fact that the commutation rule (2) [qp - pq = (-1)^-2 h/2π)] imposes a reciprocal limitation on the fixation of two conjugate variables, q and p, expressed by the relation

Δq×Δp≈h,

where Δq and Δp are suitably defined latitudes in the determination of these variables.

P0M 03:06, 3 January 2006 (UTC)

And from later in the same article:

As stressed in the lecture, an adequate tool for a complementary way of description is offered precisely by the quantum-mechanical formalism which represents a purely symbolic scheme permitting only predictions, on lines of the correspondence principle, as to results obtainable under conditions specified by means of classical concepts. It must her be remembered that even in the indeterminacy relation (3) we are dealing with an implication of the formalism which defies unambiguous expression in words suited to describe classical physical pictures. Thus, a sentence like 'we cannot know both the momentuum and the position of an atomic object' raises at once questions as to the physical reality of two such attributes of the object, which can be answered only by referring to the cnditions for the unambiguous use of space-time concepts, one the one hand, and dynamical conservational laws, on the other hand. While the combination of these concepts into a single picture of a causal chain of events is the essence of classical mechanics, room for regularities beyond the grasp of such a description is just afforded by the circumstance that the study of the complementary phenomena demands mutually exclusive experimental arrangements.

P0M 03:36, 3 January 2006 (UTC)

There are a couple of good examples in de Broglie's The Revolution in Physics, (check the index for uncertainty). I don't have the time to copy them over here. They indicate that there are more general ways to look at indeterminancy, ways that do not involve the same measurement contingencies that would occur in the microscope problem. P0M 04:00, 3 January 2006 (UTC)

Now I have found again what Heisenberg said in 1958. Somewhat surprisisngly, in view of what Voyajer has said, he still uses the microscope example, or, I should say, he uses a microscope example. Before I quote what he says, I think I should attempt to explicate something that I think may be a confusing factor. There are several sources of uncertainty regarding the position of an electron. One factor pertains to larger objects as well -- the experimenter has to judge pointers on scales, etc. The scales may not be perfect, the experimenter's vision may not be perfect. His judgment of a fractional position between two marks on a scale may not be so hot. The second kind of uncertainty is what Voyajer has been talking about, an uncertainty that is due to our imagining that if only we had a small enough needle we could pin an electron down or follow it along like a parent holding the hand of a child on a ferris wheel. But the "child" is more like an ill-defined, not really discrete, puff of water vapor. It doesn't have "a real position", it has whatever the fuzzy quantum domain equivalent is. The third kind of uncertainty involves exchanges of momentum that must occur in some measurement procedures. If we try to locate even the position of some macro objects by shining light on them, we can cause them to move. (I think the little windmill in a vacuum flask are called radiometers or something like that.) Whatever an electron is, if we keep zapping around with gamma photons we may eventually get a reflection, in which case we will know where the electron was at a certain time -- but it will be gone.

Physics and Philosophy, p. 47f.

Is the first step, the translation of the result of the observation into a probability function, possible? It is possible only if the uncertainty relation is fulfilled after the observation. The position of hte electron will be known with an accuracy given by the wave length of the γ-ray. The electron may have been practically at rest before the observation. But in the act of observation at least one light quantum of the γ-ray must have passed the microscope and must first have been deflected by the electron. Therefore, the electron has been pushed by the light quantum, it has changed its momentum and its velocity, and one can show that the uncertainty of this change is just big enough to guarantee the validity of the uncertainty relations. Therefore, there is no difficulty with the first step.

At the same time one can easily see that there is no way of observing the orbit of the electron around the nucleus. The second step shows a wave pocket moving not around the nucleus but away from the atom, because the first light quantum will have knocked the electron out from the atom. The momentum of light quantum of the γ-ray is much bigger than the original momentum of the electron if the wve length of the γ-ray is much smaller than the size of the atom. Therefore, the first light quantum is sufficient to knock the electron out of the atom and one can never observe more than one point in the orbit of the electron; therefore, there is no orbit in the ordinary sense....

Actually we need not speak of particles at all. For many experiments it is more convenient to speak of matter waves; for instance, of stationary matter waves around the atomic nucleus.

If it was not already clear, the mention of the possibility of describing the electron as a standing wave both makes it clear that the electron has no point location, and the fact that this "wave pocket" leaves orbit and becomes ionized makes it clear that the incoming gamma photon does something to the position and momentum of the electron. P0M 05:05, 3 January 2006 (UTC)

---

Okay, Patrick, don't get offended but I'm going to get black-and-white about this.

There is one, and only one, kind of uncertainty in the uncertainty principle.

True uncertainty is described here from article on the Uncertainty Principle: "Consider an experiment in which a particle is prepared in a definite state and two successive measurements are performed on the particle. The first one measures the particle's position and the second immediately after measures its momentum. Each time the experiment is performed, some value x is obtained for position and some value p is obtained for momentum. Depending upon the precision of the instrument taking the measurements, the measurements should be extremely close, however, they are usually off by a small fraction. If the experiments are repeated over and over and the results are plotted on a graph with a dot for every measurement, the graph will display a high density of dots for each measurement of position and another high density of dots for each measurement of momentum showing an inverse relation between the two measurements. However, the dots indicating each measurement will not all be plotted on top of each other because they would have to have infinite precision to be precise in each repeated experiment. In other words, there is an uncertainty in the outcome of the measurements. One might suggest that the instrument itself is flawed, but that with an infinitely accurate instrument, each measurement would indeed be infinitely precise. However, Heisenberg postulated in his principle that, even in theory, with a hypothetical infinitely precise instrument, that even in such a case, no infinitely precise measurement could be made of both the position and the momentum of observables at the same time and one must still provide for a dispersion, a standard deviation, a give-and-take (also called slop in engineering)."

• 1. What this means is that fundamentally in the universe there is a displacement between the position and momentum of a moving particle. It doesn't matter how you measure it, it exists. This and only this is uncertainty.
• 2. Uncertainty as a displacement is not caused by the instrument.
• 3. Uncertainty as a displacement is not the result of the measurement causing a disturbance.
• 4. Uncertainty as a displacement is not the result of a photon of any wavelength moving or "disturbing" the particle while measuring.
• 5. Uncertainty as a displacement is not caused by a collision between a photon (of any wavelength) colliding with the particle and disturbing it.
• 6. Quantum entanglement says that you can measure the position and momentum of an entangled particle by measuring one of its partners, therefore the partner particle being measured is not being pushed by a photon (of any wavelength whether a gamma ray from a microscope or visual light) because we are observing one partner particle in order to get the position and momentum of another partner particle, therefore, there is no disturbance to the partner particle not being measured, however, we know its momentum and location. Yet, even then without a disturbance of any kind, through measurement of other particles in an entangled state by measuring one particle in the state and therefore not "disturbing" the other particles, still, even then, there is an uncertainty or displacement between position and momentum.
• 7. So saying that uncertainty or displacement of position and momentum is caused by the photon of a microscope disturbing the position and momentum of a particle is absolutely dead wrong. (Can I be more clear?) Bohr said this to Heisenberg above. Bohr told Heisenberg that "your so-called Heisenberg microscope is stupid" in so many words as shown above from the book quotation because it means that there is some instrument error.
• 8. Uncertainty does not involve instrument error. Uncertainty exists even when in theory one has a hypothetical infinitely precise instrument and even if one isn't even measuring the particle in question but only its partner particle, even then, there is a displacement of measurement in a moving particle.
• 9. All books and textbooks that say that measuring a particle disturbs its position are dead wrong. They are relying on the Heisenberg microscope analogy which is dead wrong.
• 10. Heisenberg's microscope analogy was used mainly before 1935. After 1935 and the discovery by Einstein of quantum entanglement it became wrong to say that in a microscope, a photon could collide with the particle and disturb it. In quantum entanglement, one can measure a moving particle without looking at it directly.
• 11. The Heisenberg microscope analogy was trying to make uncertainty understandable. But it merely complicated uncertainty. It introduced the concept of a collision between a photon and the particle disturbing the particle. This is fundamentally wrong as Bohr told Heisenberg above. This is in effect saying that there is some error in the way things are measured that causes the Uncertainty Principle. There is not. Uncertainty still holds no matter how you measure it, no matter whatever indirect means you use that will not disturb the particle, the measurement is still displaced by the amount of the Uncertainty Principle.
• 12. Anyone that anyone quotes as saying uncertainty is caused by the disturbance of the particle by the measurement is dead wrong and does not understand the Uncertainty Principle EVEN Heisenberg as Bohr clearly showed above in his conversation with Heisenberg.
• 13. Uncertainty arose from data derived from measurements using spectroscopy. Heisenberg did not think the displacement of a moving particle being measured was the fault of the instrument but intrinsic to the universe. Therefore, as Bohr pointed out to Heisenberg, it was wrong to use an instrument model to try to prove the uncertainty principle because the analogy is false.
• 14. The website [2] describes the Heisenberg microscope and says, "Looking closer at this picture, modern physicists warn that it only hides an imaginary classical mechanical interaction one step deeper, in the collision between the photon and the electron. In fact Heisenberg's microscope, although it was a big help in developing and teaching the quantum theory, is not itself part of current understanding. The true quantum interaction, and the true uncertainty associated with it, cannot be demonstrated with any kind of picture that looks like everyday colliding objects. To get the actual result you must work through the formal mathematics that calculates probabilities for abstract quantum states. Clever experiments on such interactions are still being done today. So far the experiments all confirm Heisenberg's conviction that there is no "real" microscopic classical collision at the bottom."
• 15. "Readers are warned that Heisenberg's microscope experiment can be misleading. In particular, students should resist the temptation to believe that a particle can really have definite position and momentum, which, because of the clumsy nature of the observation [as Hiesenberg's microscope suggests that a microscope itself is just a clumsy way to measure things], cannot be measured. In fact, there is no evidence for the existence of particles with definite position and momentum. This concept is an unobservable idealization or a figment of the imagination of classical physicists. ..." -A.C. Phillips. In other words, you can't use Heisenberg's microscope and measure a moving particle and say, "Oops, if I just hadn't knocked that moving particle with a gamma ray photon, I'd know where it is this very minute." The uncertainty principle says you wouldn't know anyway. That's why Heisenberg's microscope is a horrible analogy. AND you can't say, "Well, if I just calculate the exact amount that a gamma ray photon will knock the moving particle, if I just know all there is to know about what a gamma ray photon will do to a particle, then I can just subtract out the amount of disturbance that the gamma ray caused and I will get the exact position of the moving particle before I disturbed it by measuring it with my Heisenberg microscope." NOPE. False. No way. Bad analogy. You can't ever know the position not even if you subtract out the result of hitting the particle with a gamma ray photon. In other words, the Heisenberg microscope analogy is wrong, wrong, wrong.
• 16. Many textbooks and authors misunderstand uncertainty due to the widespread use of the Heisenberg microscope analogy which is dead wrong. Quantum entanglement shows it is dead wrong. There is still uncertainty or displacement in the measurement no matter the method being used to measure. Even if there were such a measuring device as one that could measure a moving particle without using light or wavelengths, say a futuristic device that could measure a moving particle in some other fashion, still the Uncertainty Principle says that the measurement would show a displacement or uncertainty in position meaning a deviation between position and momentum even if no photon hits the particle.

17. Any book or textbook that says that the Uncertainty Principle "distorts" measurement is correct. Any book or textbook that says that the Uncertainty Principle "disturbs" measurement is incorrect. --Voyajer 21:25, 3 January 2006 (UTC)

This boils down to the definition of Uncertainty: "The position and the velocity of an object cannot both be measured exactly, at the same time, even in theory." If I can in theory visualize an instrument that can measure a moving particle without using a photon or wavelength to disturb it, then the uncertainty principle says even then, even in theory, I cannot overturn the uncertainty principle and will still get a deviation of measurement, a displacement, at the minimum of the uncertainty principle deviation of h-bar/2. The key words are "even in theory".--Voyajer 22:31, 3 January 2006 (UTC)

I'm not at all offended by your taking the time to explicate these matters. As I said above, there are at least three different things being called by the same name, and that is always a problematical situation. Two things seem important to me now. One is from a heuristic point of view: Since there is confusion, even among people who should not be confused, it is important for the beginning reader that the distinction between these three be made clearly at the very beginning. I have an idea of one way to make the consequences of quantum uncertainty clear even to the beginner, but I will hold off on that for the time being. The second important thing relates to "politics," i.e., to what one really has to deal with. You mentioned a stiff debate with editors on some discussion pages for other QM articles. Two Wikipedia policies are going to come into play. One is "neutral point of view." When there are several points of view on a subject, the encyclopedia writer may not say, e.g., "Mao's policy and plan for change in China was right. He was a veritable Abraham Lincoln to his people." Nor may one say, e.g., 'Chiang Kai-shek's continuation of the republican revolution would have ended the war with Japan quicker if the CCP had not interfered, and would have brought China out of its little dark ages period more quickly and humanely than ever the CCP could have done. Unfortunately, he was betrayed and reduced almost to insignificance." All the encyclopedia writer can do in the face of strong points of view is to say that Able, Baker, and Carter favor Mao, etc., etc. Dent, Fenton, and Garbo support Chiang, etc., etc. The other policy is "No original research." So you've got to be able to argue from authority, just to get the second point of view into the article. The artful way to achieve an objective account that still manages to make clear what the truth is would be to show the evolution of ideas, criticisms by people of stellar importance of the inconsistencies of lesser lights -- criticisms where they really nail them, and perhaps very nuanced explications by writers such as Messiah who mention "uncertainty of the first type, "uncertainty of the second kind," and "real uncertainty," start out from a position that brings in situations analogous to the Heisenbergs microscope situation and then cast it in light of the third kind of undertainty and thereafter continue to write about the third kind of uncertainty. P0M 01:22, 4 January 2006 (UTC)

• • You should understand that Messiah in saying "uncertainty of the first type" and "uncertainty of the second kind" and "real uncertainty" was not saying that Heisenberg's Uncertainty Principle could be divided into different types of uncertainty. Rather, Heisenberg's Uncertainty Principle can only be explained in one way. And Heisenberg's microscope is not the way. I have quoted several sources that show this very point, all of the highest caliber. However, I could quote hundreds more. I am a researcher and the best sources always say the same thing: Heisenberg's microscope is not a good analogy, presents a wrong viewpoint, and this was argued by Bohr. Messiah is speaking of something very, very, very different. I can't stress that enough. He was speaking about Immanual Kant's views of reality. There is what the universe is and there is what we say it is through our theories. When does a theory become the reality of the universe? When does "uncertainty" become real in this sense? This does not change the definition of the Uncertainty Principle which has only one definition as explained by Bohr to Heisenberg above. Messiah's work is merely a philosophical treatise on whether HUP is real in the Immanuel Kant sense.

Please relax. I am basically agreeing with you, and also to help you deal with any difficulty you may be having getting this matter straightened out in the course of editing other articles. Do you have access to Messiah's two volume Quantum Mechanics? He taught for several years at the French Atomic Energy Commission’s Center of Nuclear Studies at Saclay. He does not mention Kant. Amazon in Great Britain has a brief review of his book: " The books resulted from courses given at the Center of Nuclear Studies at Saclay during the 1950s, and they are esteemed for the clarity and coherence of their presentation." The ISBN is 0486409244. Vol. I, p 142 has some material that supports your position and may add the weight of authority if such is needed.

• • Major attacks on QM have come from Heisenberg's microscope such as Gong's essay. This is rebutted at http://physics.about.com/library/weekly/aa122202e.htm where a Cambridge physicist answers: "This misunderstanding is common, and is unfortunately made worse by the common use of the Gamma ray microscope thought experiment to motivate it to undergraduate students."

• • The Heisenberg microscope is ruthlessly destroyed by Henry Margenau and Leon Cohen. http://etext.lib.virginia.edu/cgi-local/DHI/dhi.cgi?id=dv2-65

Doubtless true. However, Margenau is not above exploring a similar situation and clarifying the components of such an experiment, much as Messiah does. See Robert Bruce Lindsay and Henry Margenau, Foundations of Physics, p. 420ff. I won't quote the entire thing, just enough to let you see that he is taking account of the effects of measurement. (N.B. To say that some meaurement difficulties involve quantum mechanical momentum interactions is not the same as saying that all quantum mechanical uncertainties are caused by momentum exchanges.) He goes on to give those effects of measurement their proper position in the context of general QM theory.

An inequality similar to (9.3-8) was first discovered by Heisenberg, and has been made the basis of a far-reaching and fruitful system of analogies, known as indeterminacy relations...Let it be required, for instance, to determine the coordinates and the momentum of an electron...The electron will, by virtue of the great momentum of short-wave-length radiation, experience a recoil which changes completely its initial state of motion and therefore precludes every possibility of determining it....Is the uncertainty attending the measurement of q conditioned by the destruction of the "state" through a measurement of p? ....In the foregoing statements we have placed the word state in quotation marks, fore clearly we were using the term in its classical sense. Quantum mechanically, coordinates and momentum of an electron do not define its state....Nevertheless it is possible to restate the matter using the correct definition of states in terms of ɸ functions. We shall then have to answer the question: will measurements change the state-function of the system? ....The answer cannot be derived from the postulates given so far, for we have not yet considered the manner in which ɸ functions change in time.....Later (Sec. 9.11) we shall learn how, in interactions where the energy operator involves the time, ɸ functions are modified in time. The answer to our query will then be in the affirmative: quantum mechanical states will change upon interaction with measuring devices.... (I'm leaving out quite a bit here.)....We therefore conclude that the scattering of measurements has its roots in a fact more fundamental than the destruction of states by interaction with measuring devices, namely, in the definition of states peculiar to quantum mechanics.

• • The destruction of Heisenberg's microscope has come way before me. Detractors use it to show uncertainty doesn't exist because it is such a weak argument and as I have quoted above many articles show Heisenberg's microscope is is not itself part of current understanding. This has been shown over and over again in many forms. My discussions on other talk pages especially with a quantum field physicist did not take long before it was agreed that it is not a part of current understanding. It is know accepted common knowledge among physicists that Heisenberg's microscope is not a correct model of HUP. This is found in several old journals such as ROYCHOUDHURI C 1978 FOUNDATIONS OF PHYSICS 8 (11-1): 845-849: "HEISENBERG MICROSCOPE - MISLEADING ILLUSTRATION". And it doesn't really need to spelt out again and again by me.

One approach would be to ignore the existence of this argument. Unfortunately, probably every high school student has heard some version of the general idea even though the term "Heisenberg's microscope" may never have been encountered. The other approach would be to do as Margenau et al. have done and show it for what it really is.

• • Bottom line: Who needs me to go on quoting reliable sources to believe me that Heisenberg's microscope is not a good analogy? Did everyone see below on "Absolute Zero"? Are there still people out there convinced that my arguments need reinforcing? Because I'm willing to go on debating this until the point is made. What is the point? The Uncertainty Principle is not about disturbing a particle. It exists when a particle is NOT disturbed. --Voyajer 01:50, 4 January 2006 (UTC)

I prefer to discuss rather than to debate. This discussion began with your statement: "I do not believe that the uncertainty principle teaches that the position is 'disturbed' by measurement." The uncertainty principle is just ΔpΔx ≥ h. It comes into play whenever there is a change of momentum or a change of position on the quantum scale. It has application to "cases where quantum mechanical states change upon interaction with measuring devices," and it also has application to "the definition of states peculiar to quantum mechanics." Heisenberg's microscope is not an analogy. It is a thought experiment. It appears, however, to function for many people as a red herring, leading them away from a deeper understanding of QM. It would also seem to serve as a straw man for some people interested in "defeating" QM. I think we should be open to discussing how to head off the objections of people who come to QM-related articles with at least the idea that "quantum mechanics means that measurements always distort what is being measured." I don't intend to find any more historical passages. We probably already have plenty of those. P0M 06:43, 4 January 2006 (UTC)

Distorting measurement and disturbing measurement are two different things. That is what I have been trying to say.--Voyajer 15:52, 4 January 2006 (UTC)

A thought experiment is "an imagined scenario. Our intuitions about the scenario may be incompatible, with what a theory claims about the scenario, forcing us to decide between the theory and our intuitions." A thought experiment example: If you lift a mountain it will take more force than if you lift a pebble. A mathematical equation: F=ma. Which is science? Certainty cavemen could have figured out that lifting a mountain even in thought would be harder than lifting a pebble. Did they have science then? Did they have Newton's laws of motion? Is a "thought experiment" in and of itself a scientific theory? What is science? The uncertainty principle has one formula, therefore, it has one scientific definition. The formula shows that measurement does not commute by h/2pi. There is a measurement error. (THIS IS NOT A DISTURBANCE, but a mathematical deviation in measurement i.e. a standard deviation.) The formula came years before Heisenberg's microscope. Which is science? The thought experiment or the formula? --15:52, 4 January 2006 (UTC)

Heisenberg "He attempted to explain this novel feature through a gedanken or thought experiment, which uses a hypothetical gamma-ray microscope to observe electrons. His original argument, however, is not part of our current understanding of the actual Uncertainty Principle, for it treats interactions between quantum objects somewhat unrealistically, analogous to mechanical collisions of classical particles."--theoretical physicist S Lakshmibala http://www.iisc.ernet.in/academy/resonance/Aug2004/pdf/Aug2004p46-56.pdf --Voyajer 16:28, 4 January 2006 (UTC)

Any book that says ΔpΔx ≥ h is wrong

The correct formula is ΔpΔx ≥ h-bar and where measurements are made once on each copy of an ensemble the formula is ΔpΔx ≥ h-bar/2. http://www.iisc.ernet.in/academy/resonance/Aug2004/pdf/Aug2004p46-56.pdf page 8 --Voyajer 16:28, 4 January 2006 (UTC)

Well, your link is broken, so I cannot really tell what it says...

Remember that $\hbar \geq \hbar /2$, and this implies no contradiction: It actually satisfies $\Delta x\Delta p\geq \hbar /2$. The Heisenberg microscope doesn't saturate the uncertainty, but it is completely legitimate to write $\Delta x\Delta p\approx \hbar$ since this satisfies the uncertainty relation.

Otherwise the excited harmonic oscillator would have the same problem! When it's in the energy state $E_{n}$, the position-momentum uncertainty relation is

$\Delta x\Delta p=\hbar \left(n+{\frac {1}{2}}\right)\geq \hbar /2$

for n>0. So if the Heisenberg microscope is wrong, then so is the quantized harmonic oscillator! —Pqnelson (talk) 19:33, 14 August 2012 (UTC)

Uncertainty Principle and Absolute Zero

"The temperature at which all classical molecular motion stops, equal to 0 Kelvin or -273.15° Celsius. However, quantum mechanically, molecules cannot cease all motion (as this would violate the Heisenberg uncertainty principle), so at 0 K they still vibrate with a certain small but nonzero energy known as the zero-point energy." http://scienceworld.wolfram.com/physics/AbsoluteZero.html

Okay, this is another example where Heisenberg's microscope does not apply. Is anyone measuring all the atoms in the universe at the same time so that a photon of light is hitting them so that they have an uncertainty of position and cannot reach absolute zero?

In other words, the Uncertainty Principle is applied to the universe even when no measurements are being taken. Therefore, no disturbance is being made to the measurements. The Uncertainty Principle is taken to be fundamental. It says that fundamentally no moving particle can ever have an exact position. Therefore, no moving particle can ever be said to stop its motion. Therefore, no atom can cease motion at absolute zero. This is without measurements being taken to "disturb" the particles. Therefore, Heisenberg's microscope is wrong.

Now, I want to mention this caveat. Heisenberg's Uncertainty Principle will in the near future be either proven or disproved. In creating BECs (Bose-Einstein Condensate) scientists are building better and better instruments to reach absolute zero. When they build one that reaches absolute zero, HUP will either be debunked or raised to the status of absolute law.--Voyajer 00:28, 4 January 2006 (UTC)

• "Heisenberg's microscope is. . . a misleading attempt to “explain” the concept behind a purely quantum mechanical theorem . . . " Chandrasekhar Roychoudhuri. Heisenberg’s microscope—a misleading illustration. Foundations of Physics, 8:845–849, 1978.

• ". . . the consideration of optical analogies — such as . . . Heisenberg’s gamma ray microscope, are mistaken. Indeed, the reasoning in these cases is fallacious because it employs propositions belonging to optics, not to quantum mechanics — e.g. the formula for the resolving power of a lens . . ." Mario Bunge. The interpretation of Heisenberg’s inequalities. In Heinrich Pfei®er, editor, Denken und Umdenken. Zu Werk und Wirkung von Werner Heisenberg, pages 146–156. R. Piper & Co. Verlag, M¨unchen Z¨urich, 1977.

• In their (Mara Beller and Arthur Fine.) Bohr’s response to EPR. (In Jan Faye and Henry Folse, editors, Niels Bohr and contemporary philosophy, pages 1–31. Kluwer, Dordrecht, 1994,) Beller and Fine convincingly show the difficulties one runs into if one tries to salvage the idea of disturbance causing the validity of the uncertainty relations. "The concept of disturbance, inaugurated in Heisenberg’s uncertainty paper, is an ill-fated and inconsistent one..." Mara Beller, Quantum Dialogue. The Making of a Revolution. University of Chicago Press, Chicago, 1999.

• The greatest most profound proof that uncertainty is not the result of a disturbance is from Einstein, himself, who inadvertently invented quantum entanglement for quantum mechanics. The idea of disturbance causing the uncertainties is not only incoherent, in 1935 it was also shown to be false, on the supposition that all disturbances propagate locally, in the famous EPR thought experiment. "Rosen , Einstein and Podolsky imagined two particles S and T that had spent some time in close interaction, so much so that they became thoroughly causally entangled: knowing the behavior of S would give complete information about the behavior of T, provided that the state of S could be measured without disturbing the state of T." No disturbance, yet measurement = uncertainty principle (is not equal to) Heisenberg microscope.

--Voyajer 04:47, 4 January 2006 (UTC)

In conclusion, Heisenberg's microscope was invented as allegory, not as a real interpretation of Uncertainty. It was a device subtlely trying to discredit Schroedinger's wave equation. It's use is not to define Uncertainty but to make it visual in an imaginary classical sense, but loses all real meaning of Uncertainty. The Uncertainty principle is defined by the formula. The formula came in the form of Matrix mechanics in 1925. In 1927, Heisenberg showed that matrix mechanics formulae describe the Uncertainty Principle. Matrix mechanics had been attacked by Schroedinger as being unable to visualize. Heisenberg countered with Heisenberg's microscope, but the analogy was not meant to be a real picture of the formula. The formula is real Uncertainty. Heisenberg's microscope is not. The formula is not about disturbance. The end.--Voyajer 04:53, 4 January 2006 (UTC)

Aaah, Patrick, I see why you won't budge. You wrote the article Heisenberg's microscope as if it is truly scientific and truly represents the Uncertainty Principle and is truly part of current understanding. It has been known to be incorrect since 1935 from a scientific standpoint. It is fine as far as metaphysics go. It is even good to look at to show Heisenberg's frame of mind when he wrote it since he was clearly trying to attack Schroedinger's wave mechanics. It is however not a scientific explanation of Uncertainty since it does not describe the formula. You should say so in your article perhaps quoting theoretical physicist, S Lakshmibala, at http://www.iisc.ernet.in/academy/resonance/Aug2004/pdf/Aug2004p46-56.pdf -- It is important not to be misleading in encyclopedia articles. It is important to show integrity. The Uncertainty Principle is about a distortion in measurement not about a disturbance in measurement.

You write in your Heisenberg microscope article: "The result of this thought experiment has been formalized as Heisenberg's Uncertainty Principle." Horrible, horrible. The Uncertainty Principle was not the result of some thought experiment. It was the result of mathematics. The formula came first. The thought experiment was "an after-thought". --Voyajer 16:40, 4 January 2006 (UTC)

Agreed. I had that part wrong. P0M 07:44, 5 January 2006 (UTC)

rework draft -- put it here so it won't get lost

Basing himself both on papers by Dirac and Jordan, on contacts with Wolfgang Pauli, Niels Bohr, and others, Heisenberg's first great contribution was the formulation of a theory of quantum mechanics that was expressed in matrix form, and his second great contribution was his indeterminacy or uncertainty principle. Heisenberg discovered that a natural limit on the certainty or precision of calculated results appeared whenever one attempted to deal with position and momentum of a particle at the same time or the energy and time of a particle at the same time. The limitations emerged from working through the equations, and were entirely apart from the kind of experimental error that theoretically could be reduced toward a limit of zero by improving measurement tools and procedures. (ab!=ba) The letter that Heisenberg wrote to Pauli in 1927 is the first known record of the communication of this finding to another person.

Two problems suggested themselves to Heisenberg: What did it really mean to speak of the position of a particle such as an electron? Were the uncertainties that emerged from the mathematics of the theory a kind of mathematical fluke that would find no support for their existence in the empirical world? Heisenberg worked the problem through in his mind and on paper. One way to determine the position and momentum of a particle would be to observe it with a microscope. When dealing with a sufficiently small particle, such as an electron, the higher the frequency of light one chose in the interest of pinpointing the location more closely, the more energy would be delivered to the particle, and knowledge of Planck's constant allows one to calculate the magnitude of this effect. So even on the assumption of a classical picture in which both the electron and the photons used to measure it were depicted as discrete entities, tiny hard spheres, the idea that a definite position could be known comes into question. This result "solidified in his mind the principle he had already derived without this analogy." (Aczel, 78) Heisenberg drafted his thought experiment paper in February of 1927. After Bohr read the paper, he wanted Heisenberg to rewrite it to avoid the inaccurate classical depiction of these entities, and to include the idea of complementarity between particles and waves, but Heisenberg responded only by adding a summary of Bohr's objections to his paper. (http://www.aip.org/history/heisenberg/p09.htm (midpage))

It seems clear that Heisenberg used his thought experiment as a way of introducing his ideas on indeterminacy. The problem is that it intentionally begins where his readers presumably will begin, with a classical picture. It shows them that on its own assumptions the classical picture will not work because while operating under those assumptions you cannot make sense of of the idea of known position and momentum. He uses Planck's constant to quantify the effect that measurement attempts would necessarily have. Making his thought experiment in this way may imply to some readers that the electron that was to come under investigation had a determinate position and momentum, and that after a measurement is attempted the original position and momentum is replaced by some other determinate position and momentum -- which is again unknown. But the thought experiment is intended to show that even if, for the sake of argument, we suppose that these particles have definite positions and momenta, those data cannot be learned by the means proposed in the experiment.

Forgot to sign. P0M 08:18, 5 January 2006 (UTC) Found citation.

Heisenberg vehemently objected at first to Bohr's views. Insisting on the primary use of particles and discontinuity, he refused Bohr's suggestion that he withdraw his paper, which was already in press. He did, however, append a paragraph alerting readers to Bohr's views and admitting the error regarding the resolution of the microscope. The battle with Bohr grew so intense in the early months of 1927 that Heisenberg reportedly burst into tears at one point, and even managed to wound Bohr with his sharp remarks. Obviously, there was much at stake for the 25-year-old.

http://www.aip.org/history/heisenberg/p09.htm

Very good. Nice research! Yes, this should be incorporated into the article. Impressive.--Voyajer 04:49, 8 January 2006 (UTC)

How is the telescope microscope being illuminated?

I just added a figure that followed what most figures seem to indicate, namely that the photons are arriving from the side. That figure is still on commons, as an earlier version of my new figure that indicates the illumination coming from below. I believe the proper illumination is from below because for small $\varepsilon$, the momentum imparted to the electron is small as per your formula,

$\Delta p_{x}\approx 2{\frac {h}{\lambda }}\sin \varepsilon /2.$

When I started this project I just wanted the microscope to look more like a microscope. Then I realized that adding wavefronts would be a nice touch because it is the diffraction of these wavefronts that yields the uncertainty in position. Now I suspect both wikipedia articles (this and Uncertainty principle have the direction of the incoming photon wrong.

Which ever way the incoming light is going, we need confirmation from experts. --guyvan52 (talk) 22:19, 15 February 2015 (UTC)

Here are two websites that have the microscope illuminated by light parallel to the optical axis:

1. http://faculty.gvsu.edu/majumdak/public_html/OnlineMaterials/ModPhys/QM/Duality.htm (see http://faculty.gvsu.edu/majumdak/public_html/OnlineMaterials/ModPhys/QM/Wave/microscope.gif )
2. http://brane-space.blogspot.com/2010/06/more-on-heisenberg-microscope-in.html (see http://1.bp.blogspot.com/_FkGV5soUkDY/TBabUeXbbmI/AAAAAAAAAjk/SdLtCcr8b0o/s1600/Hscope2.jpg )

--guyvan52 (talk) 22:53, 15 February 2015 (UTC)