GUS: It was 100 years ago in December 1925 that Heisenberg finally formulated his UNCERTAINTY PRINCIPLE... HE PUBLISHED IT IN 1927....

 

THEREAFTER:....

The same year that Heisenberg was awarded a Nobel Prize, 1933, also saw the rise to power of the National Socialist German Workers’ Party (Nazi Party). Nazi policies excluding “non-Aryans” or the politically “unreliable” from the civil service meant the dismissal or resignation of many professors and academics — including, for example, Born, Einstein, and Schrödinger and several of Heisenberg’s students and colleagues in Leipzig. Heisenberg’s response was mostly quiet interventions within the bureaucracy rather than overt public protest, guided by a hope that the Nazi regime or its most extreme manifestations would not last long.

Heisenberg also became the target of ideological attacks. A coterie of Nazi-affiliated physicists promoted the idea of a “German” or “Aryan” physics, opposed to a supposedly “Jewish” influence manifested in abstract mathematical approaches—above all, relativity and quantum theories. Johannes Stark, a leader of this movement, used his Nazi Party connections to assert influence over science funding and personnel decisions. Sommerfeld had long regarded Heisenberg as his eventual successor, and in 1937 Heisenberg received a call to join the University of Munich. Thereupon the official SS journal published an article signed by Stark that called Heisenberg a “white Jew” and the “Ossietzky of physics.” (German journalist and pacifist Carl von Ossietzky, winner of the 1935 Nobel Prize for Peace, had been imprisoned in 1931 for treason for his reporting of Germany’s secret rearmament efforts, given amnesty in 1932, and then rearrested and interned in a concentration camp by the Nazis in 1933.)

 

Heisenberg, relying on the acquaintance of his mother’s family with Heinrich Himmler’s family, sent a request to the SS chief to intervene on his behalf in acquiring the professorship in Munich. Himmler, after an investigation, decreed a compromise: Heisenberg would not succeed Sommerfeld in Munich, but he would be spared further personal attacks and (essentially) promised another prominent post in the future. Meanwhile, Stark and the Aryan physicists were for other reasons losing influence in the bureaucratic jungle of the Nazi state, particularly in the context of militarization. Amid this political turbulence, Heisenberg apparently never seriously contemplated leaving Germany, though he certainly received several offers of university appointments in the United States and elsewhere. Apparently, he was guided by a strong sense of personal duty to the profession and a national loyalty that (in his mind) transcended the particular politics of the regime.

In 1937 Heisenberg married Elisabeth Schumacher, the daughter of an economics professor, whom he had met at a concert. Twins were born the next year, the first of eventually seven children for the couple.

Heisenberg’s main focus of work in the late 1930s was high-energy cosmic rays, for which he proposed a theory of “explosion showers,” in which multiple particles were produced in a single process, in contrast to the “cascade” theory principally favoured by British and American physicists. Heisenberg also saw in cosmic-ray phenomena possible evidence for his idea of a minimum length marking a lower boundary of the domain of quantum mechanics.

World War II

The discovery of nuclear fission pushed the atomic nucleus into the centre of attention. After the German invasion of Poland in 1939, Heisenberg was drafted to work for the Army Weapons Bureau on the problem of nuclear energy. At first commuting between Leipzig and the Kaiser Wilhelm Institute (KWI) for Physics in Berlin and, after 1942, as director at the latter, Heisenberg took on a leading role in Germany’s nuclear research. Given the Nazi context, this role has been enormously controversial. Heisenberg’s research group was unsuccessful, of course, in producing a reactor or an atomic bomb. In explanation, some accounts have presented Heisenberg as simply incompetent; others, conversely, have suggested that he deliberately delayed or sabotaged the effort. It is clear in retrospect that there were indeed critical mistakes at several points in the research. Likewise, it is apparent that the German nuclear weapons project as a whole was not possessed of the same degree of enthusiasm that pervaded the Manhattan Project in the United States. However, factors outside Heisenberg’s direct control had a more substantive role in the outcome.

In contrast to the unified Anglo-American effort, the German project was bureaucratically fractured and cut off from international collaboration. Key materials were in short supply in Germany, to say nothing of the widespread dislocations caused by Allied bombing of the country’s transportation network. Moreover, the overall strategic perspective critically affected the prioritization or de-prioritization of nuclear bomb research. After a 1942 conference with Axis scientists, German minister for armaments and war production Albert Speerconcluded that reactor research should proceed but that any bomb was unlikely to be developed in time for use in the war. By way of confirmation, the official start of the Manhattan Project in the United States also occurred in 1942, and, even with its massive effort, it could not produce an atomic bomb before Germany’s surrender.

https://www.britannica.com/biography/Werner-Heisenberg/Heisenberg-and-the-Nazi-Party

 

 

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The 2025 International Year of Quantum Science and Technology (IYQ) recognizes 100 years since the initial development of quantum mechanics [WITH THE UNCERTAINTY PRINCIPLE AS ITS CENTREPIECE]. Join us in engaging with quantum science and technology and celebrating throughout the year!

Recognizing the importance of quantum science and the need for wider awareness of its past and future impact, dozens of national scientific societies gathered together to support marking 100 years of quantum mechanics with a U.N.-declared international year. 

On June 7, 2024, the United Nations proclaimed 2025 as the International Year of Quantum Science and Technology (IYQ). According to the proclamation, this year-long, worldwide initiative will “be observed through activities at all levels aimed at increasing public awareness of the importance of quantum science and applications.”

Anyone, anywhere can participate in IYQ by helping others to learn more about quantum on this centennial occasion, participating in or organizing an IYQ event, or simply taking the time to learn more about quantum science and technology.

https://quantum2025.org/

 

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The uncertainty principle is one of the most famous aspects of quantum mechanics. It has often been regarded as the most distinctive feature in which quantum mechanics differs from classical theories of the physical world. Roughly speaking, the uncertainty principle (for position and momentum) states that one cannot assign exact simultaneous values to the position and momentum of a physical system. Rather, these quantities can only be determined with some characteristic “uncertainties” that cannot become arbitrarily small simultaneously. But what is the exact meaning of this principle, and indeed, is it really a principle of quantum mechanics? (In his original work, Heisenberg only speaks of uncertainty relations.) And, in particular, what does it mean to say that a quantity is determined only up to some uncertainty? These are the main questions we will explore in the following, focusing on the views of Heisenberg and Bohr.

The notion of “uncertainty” occurs in several different meanings in the physical literature. It may refer to a lack of knowledge of a quantity by an observer, or to the experimental inaccuracy with which a quantity is measured, or to some ambiguity in the definition of a quantity, or to a statistical spread in an ensemble of similarly prepared systems. Also, several different names are used for such uncertainties: inaccuracy, spread, imprecision, indefiniteness, indeterminateness, indeterminacy, latitude, etc. As we shall see, even Heisenberg and Bohr did not decide on a single terminology for quantum mechanical uncertainties. Forestalling a discussion about which name is the most appropriate one in quantum mechanics, we use the name “uncertainty principle” simply because it is the most common one in the literature.

2. Heisenberg2.1 Heisenberg’s road to the uncertainty relations

Heisenberg introduced his famous relations in an article of 1927, entitled Ueber den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik. A (partial) translation of this title is: “On the anschaulich content of quantum theoretical kinematics and mechanics”. Here, the term anschaulich is particularly notable. Apparently, it is one of those German words that defy an unambiguous translation into other languages. Heisenberg’s title is translated as “On the physical content …” by Wheeler and Zurek (1983). His collected works (Heisenberg 1984) translate it as “On the perceptible content …”, while Cassidy’s biography of Heisenberg (Cassidy 1992), refers to the paper as “On the perceptual content …”. Literally, the closest translation of the term anschaulich is “visualizable”. But, as in most languages, words that make reference to vision are not always intended literally. Seeing is widely used as a metaphor for understanding, especially for immediate understanding. Hence, anschaulich also means “intelligible” or “intuitive”.[1]

Why was this issue of the Anschaulichkeit of quantum mechanics such a prominent concern to Heisenberg? This question has already been considered by a number of commentators (Jammer 1974; Miller 1982; de Regt 1997; Beller 1999). For the answer, it turns out, we must go back a little in time. In 1925 Heisenberg had developed the first coherent mathematical formalism for quantum theory (Heisenberg 1925). His leading idea was that only those quantities that are in principle observable should play a role in the theory, and that all attempts to form a picture of what goes on inside the atom should be avoided. In atomic physics the observational data were obtained from spectroscopy and associated with atomic transitions. Thus, Heisenberg was led to consider the “transition quantities” as the basic ingredients of the theory. Max Born, later that year, realized that the transition quantities obeyed the rules of matrix calculus, a branch of mathematics that was not so well-known then as it is now. In a famous series of papers Heisenberg, Born and Jordan developed this idea into the matrix mechanics version of quantum theory.

Formally, matrix mechanics remains close to classical mechanics. The central idea is that all physical quantities must be represented by infinite self-adjoint matrices (later identified with operators on a Hilbert space). It is postulated that the matrices Q">Q and P">P representing the canonical position and momentum variables of a particle satisfy the so-called canonical commutation rule

(1)QP−PQ=iℏ">QP−PQ=iℏ(1)

where ℏ=h/2π">ℏ=h/2π, h">h denotes Planck’s constant, and boldface type is used to represent matrices (or operators). The new theory scored spectacular empirical success by encompassing nearly all spectroscopic data known at the time, especially after the concept of the electron spin was included in the theoretical framework.

It came as a big surprise, therefore, when one year later, Erwin Schrödinger presented an alternative theory, that became known as wave mechanics. Schrödinger assumed that an electron in an atom could be represented as an oscillating charge cloud, evolving continuously in space and time according to a wave equation. The discrete frequencies in the atomic spectra were not due to discontinuous transitions (quantum jumps) as in matrix mechanics, but to a resonance phenomenon. Schrödinger also showed that the two theories were equivalent.[2]

Even so, the two approaches differed greatly in interpretation and spirit. Whereas Heisenberg eschewed the use of visualizable pictures, and accepted discontinuous transitions as a primitive notion, Schrödinger claimed as an advantage of his theory that it was anschaulich. In Schrödinger’s vocabulary, this meant that the theory represented the observational data by means of continuously evolving causal processes in space and time. He considered this condition of Anschaulichkeit to be an essential requirement on any acceptable physical theory. Schrödinger was not alone in appreciating this aspect of his theory. Many other leading physicists were attracted to wave mechanics for the same reason. For a while, in 1926, before it emerged that wave mechanics had serious problems of its own, Schrödinger’s approach seemed to gather more support in the physics community than matrix mechanics.

Understandably, Heisenberg was unhappy about this development. In a letter of 8 June 1926 to Pauli he confessed that “The more I think about the physical part of Schrödinger’s theory, the more disgusting I find it”, and: “What Schrödinger writes about the Anschaulichkeit of his theory, … I consider Mist” (Pauli 1979: 328). Again, this last German term is translated differently by various commentators: as “junk” (Miller 1982) “rubbish” (Beller 1999) “crap” (Cassidy 1992), “poppycock” (Bacciagaluppi & Valentini 2009) and perhaps more literally, as “bullshit” (Moore 1989; de Regt 1997). Nevertheless, in published writings, Heisenberg voiced a more balanced opinion. In a paper in Die Naturwissenschaften (1926) he summarized the peculiar situation that the simultaneous development of two competing theories had brought about. Although he argued that Schrödinger’s interpretation was untenable, he admitted that matrix mechanics did not provide the Anschaulichkeit which made wave mechanics so attractive. He concluded: 

to obtain a contradiction-free anschaulich interpretation, we still lack some essential feature in our image of the structure of matter. 

The purpose of his 1927 paper was to provide exactly this lacking feature.

2.2 Heisenberg’s argument

Let us now look at the argument that led Heisenberg to his uncertainty relations. He started by redefining the notion of Anschaulichkeit. Whereas Schrödinger associated this term with the provision of a causal space-time picture of the phenomena, Heisenberg, by contrast, declared:

We believe we have gained anschaulich understanding of a physical theory, if in all simple cases, we can grasp the experimental consequences qualitatively and see that the theory does not lead to any contradictions. Heisenberg 1927: 172)

His goal was, of course, to show that, in this new sense of the word, matrix mechanics could lay the same claim to Anschaulichkeit as wave mechanics.

To do this, he adopted an operational assumption: terms like “the position of a particle” have meaning only if one specifies a suitable experiment by which “the position of a particle” can be measured. We will call this assumption the “measurement=meaning principle”. In general, there is no lack of such experiments, even in the domain of atomic physics. However, experiments are never completely accurate. We should be prepared to accept, therefore, that in general the meaning of these quantities is also determined only up to some characteristic inaccuracy.

As an example, he considered the measurement of the position of an electron by a microscope. The accuracy of such a measurement is limited by the wave length of the light illuminating the electron. Thus, it is possible, in principle, to make such a position measurement as accurate as one wishes, by using light of a very short wave length, e.g., γ">γ-rays. But for γ">γ-rays, the Compton effect cannot be ignored: the interaction of the electron and the illuminating light should then be considered as a collision of at least one photon with the electron. In such a collision, the electron suffers a recoil which disturbs its momentum. Moreover, the shorter the wave length, the larger is this change in momentum. Thus, at the moment when the position of the particle is accurately known, Heisenberg argued, its momentum cannot be accurately known:

At the instant of time when the position is determined, that is, at the instant when the photon is scattered by the electron, the electron undergoes a discontinuous change in momentum. This change is the greater the smaller the wavelength of the light employed, i.e., the more exact the determination of the position. At the instant at which the position of the electron is known, its momentum therefore can be known only up to magnitudes which correspond to that discontinuous change; thus, the more precisely the position is determined, the less precisely the momentum is known, and conversely. (Heisenberg 1927: 174–5)

This is the first formulation of the uncertainty principle. In its present form it is an epistemological principle, since it limits what we can know about the electron. From “elementary formulae of the Compton effect” Heisenberg estimated the “imprecisions” to be of the order 

(2)δpδq∼h">δpδq∼h(2)

He continued: “In this circumstance we see the direct anschaulich content of the relation QP−PQ=iℏ">QP−PQ=iℏ.”

He went on to consider other experiments, designed to measure other physical quantities and obtained analogous relations for time and energy: 

(3)δtδE∼h">δtδE∼h(3)

and action J">J and angle w">w

(4)δwδJ∼h">δwδJ∼h(4)

which he saw as corresponding to the “well-known” relations

(5)tE−Et=iℏ or wJ−Jw=iℏ">tE−Et=iℏ or wJ−Jw=iℏ(5)

However, these generalisations are not as straightforward as Heisenberg suggested. In particular, the status of the time variable in his several illustrations of relation (3) is not at all clear (Hilgevoord 2005; see also Section 2.5).

Heisenberg summarized his findings in a general conclusion: all concepts used in classical mechanics are also well-defined in the realm of atomic processes. But, as a pure fact of experience (rein erfahrungsgemäß), experiments that serve to provide such a definition for one quantity are subject to particular indeterminacies, obeying relations (2)–(4) which prohibit them from providing a simultaneous definition of two canonically conjugate quantities. Note that in this formulation the emphasis has slightly shifted: he now speaks of a limit on the definition of concepts, i.e., not merely on what we can know, but what we can meaningfully say about a particle. Of course, this stronger formulation follows by application of the above measurement=meaning principle: if there are, as Heisenberg claims, no experiments that allow a simultaneous precise measurement of two conjugate quantities, then these quantities are also not simultaneously well-defined.

Heisenberg’s paper has an interesting “Addition in proof” mentioning critical remarks by Bohr, who saw the paper only after it had been sent to the publisher. Among other things, Bohr pointed out that in the microscope experiment it is not the change of the momentum of the electron that is important, but rather the circumstance that this change cannot be precisely determined in the same experiment. An improved version of the argument, responding to this objection, is given in Heisenberg’s Chicago lectures of 1930.

Here (Heisenberg 1930: 16), it is assumed that the electron is illuminated by light of wavelength λ">λand that the scattered light enters a microscope with aperture angle ε">ε. According to the laws of classical optics, the accuracy of the microscope depends on both the wave length and the aperture angle; Abbe’s criterium for its “resolving power”, i.e., the size of the smallest discernable details, gives 

(6)δq∼λsin⁡ε.">δq∼λsinε.(6)

On the other hand, the direction of a scattered photon, when it enters the microscope, is unknown within the angle ε">ε, rendering the momentum change of the electron uncertain by an amount 

(7)δp∼hsin⁡ελ">δp∼hsinελ(7)

leading again to the result (2).

Let us now analyse Heisenberg’s argument in more detail. Note that, even in this improved version, Heisenberg’s argument is incomplete. According to Heisenberg’s “measurement=meaning principle”, one must also specify, in the given context, what the meaning is of the phrase “momentum of the electron”, in order to make sense of the claim that this momentum is changed by the position measurement. A solution to this problem can again be found in the Chicago lectures (Heisenberg 1930: 15). Here, he assumes that initially the momentum of the electron is precisely known, e.g., it has been measured in a previous experiment with an inaccuracy δpi">δpi, which may be arbitrarily small. Then, its position is measured with inaccuracy δq">δq, and after this, its final momentum is measured with an inaccuracy δpf">δpf. All three measurements can be performed with arbitrary precision. Thus, the three quantities δpi,δq">δpi,δq, and δpf">δpf can be made as small as one wishes. If we assume further that the initial momentum has not changed until the position measurement, we can speak of a definite momentum until the time of the position measurement. Moreover we can give operational meaning to the idea that the momentum is changed during the position measurement: the outcome of the second momentum measurement (say pf">pf will generally differ from the initial value pi">pi. In fact, one can also show that this change is discontinuous, by varying the time between the three measurements.

Let us try to see, adopting this more elaborate set-up, if we can complete Heisenberg’s argument. We have now been able to give empirical meaning to the “change of momentum” of the electron, pf−pi">pf−pi. Heisenberg’s argument claims that the order of magnitude of this change is at least inversely proportional to the inaccuracy of the position measurement:

(8)|pf−pi|δq∼h">|pf−pi|δq∼h(8)

However, can we now draw the conclusion that the momentum is only imprecisely defined? Certainly not. Before the position measurement, its value was pi">pi, after the measurement it is pf">pf. One might, perhaps, claim that the value at the very instant of the position measurement is not yet defined, but we could simply settle this by a convention, e.g., we might assign the mean value (pi+pf)/2">(pi+pf)/2 to the momentum at this instant. But then, the momentum is precisely determined at all instants, and Heisenberg’s formulation of the uncertainty principle no longer follows. The above attempt of completing Heisenberg’s argument thus overshoots its mark.

A solution to this problem can again be found in the Chicago Lectures. Heisenberg admits that position and momentum can be known exactly. He writes:

If the velocity of the electron is at first known, and the position then exactly measured, the position of the electron for times previous to the position measurement may be calculated. For these past times, δpδq">δpδq is smaller than the usual bound. (Heisenberg 1930: 15)

Indeed, Heisenberg says: “the uncertainty relation does not hold for the past”.

Apparently, when Heisenberg refers to the uncertainty or imprecision of a quantity, he means that the value of this quantity cannot be given beforehand. In the sequence of measurements we have considered above, the uncertainty in the momentum after the measurement of position has occurred, refers to the idea that the value of the momentum is not fixed just before the final momentum measurement takes place. Once this measurement is performed, and reveals a value pf">pf, the uncertainty relation no longer holds; these values then belong to the past. Clearly, then, Heisenberg is concerned with unpredictability: the point is not that the momentum of a particle changes, due to a position measurement, but rather that it changes by an unpredictable amount. It is, however always possible to measure, and hence define, the size of this change in a subsequent measurement of the final momentum with arbitrary precision.

Although Heisenberg admits that we can consistently attribute values of momentum and position to an electron in the past, he sees little merit in such talk. He points out that these values can never be used as initial conditions in a prediction about the future behavior of the electron, or subjected to experimental verification. Whether or not we grant them physical reality is, as he puts it, a matter of personal taste. Heisenberg’s own taste is, of course, to deny their physical reality. For example, he writes, 

I believe that one can formulate the emergence of the classical “path” of a particle succinctly as follows: the “path” comes into being only because we observe it. (Heisenberg 1927: 185) 

Apparently, in his view, a measurement does not only serve to give meaning to a quantity, it createsa particular value for this quantity. This may be called the “measurement=creation” principle. It is an ontological principle, for it states what is physically real.

This then leads to the following picture. First we measure the momentum of the electron very accurately. By “measurement= meaning”, this entails that the term “the momentum of the particle” is now well-defined. Moreover, by the “measurement=creation” principle, we may say that this momentum is physically real. Next, the position is measured with inaccuracy δq">δq. At this instant, the position of the particle becomes well-defined and, again, one can regard this as a physically real attribute of the particle. However, the momentum has now changed by an amount that is unpredictable by an order of magnitude |pf−pi|∼h/δq">|pf−pi|∼h/δq. The meaning and validity of this claim can be verified by a subsequent momentum measurement.

The question is then what status we shall assign to the momentum of the electron just before its final measurement. Is it real? According to Heisenberg it is not. Before the final measurement, the best we can attribute to the electron is some unsharp, or fuzzy momentum. These terms are meant here in an ontological sense, characterizing a real attribute of the electron.

 

READ MORE: https://plato.stanford.edu/entries/qt-uncertainty/

 

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SEE ALSO: https://www.youtube.com/watch?v=c-Q5r3THR3M

 

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