Heisenberg’s uncertainty principle is a milestone of twentieth-century physics. We sketch the history that led to the formulation of the principle, and we recall the objections of Grete Hermann and Niels Bohr. Then we explain that there are in fact two uncertainty principles. One was published by Heisenberg in the Zeitschrift für Physik of March 1927 and subsequently targeted by Bohr and Hermann. The other one was introduced by Earle Kennard in the same journal a couple of months later. While Kennard’s principle remains untarnished, the principle of Heisenberg has recently been criticized in a way that is very different from the objections by Bohr and Hermann: there are reasons to believe that Heisenberg’s formula is not valid. Experimental results seem to support this claim.
Heisenberg’s uncertainty principle is a milestone of twentieth-century physics. We sketch the history that led to the formulation of the principle, and we recall the objections of Grete Hermann and Niels Bohr. Then we explain that there are in fact two uncertainty principles. One was published by Heisenberg in the Zeitschrift für Physik of March 1927 and subsequently targeted by Bohr and Hermann. The other one was introduced by Earle Kennard in the same journal a couple of months later. While Kennard’s principle remains untarnished, the principle of Heisenberg has recently been criticized in a way that is very different from the objections by Bohr and Hermann: there are reasons to believe that Heisenberg’s formula is not valid. Experimental results seem to support this claim.
Abstract How certain is Heisenberg’s uncertainty principle? Heisenberg’s uncertainty principle is at the heart of the orthodox or Copenhagen interpretation of quantum mechanics. We first sketch the history that led up to the formulation of the principle. Then we recall that there are in fact two uncertainty principles, both dating from 1927, one by Werner Heisenberg and one by Earle Kennard. Finally, we explain that recent work in physics gives reason to believe that the principle of Heisenberg is invalid, while that of Kennard still stands.
The uncertainty principle was first formulated by W. Heisenberg in the year 1927, which showed that certain physical values such as the position and the momentum of a particle, and also the time and the energy, cannot be specified with an arbitrary precision, something that was far from experiences in physics before the principle was discovered. In the same year, Kennard showed the same principle using a rigorous mathematical formalism, which has motivated further research of the principle in many different mathematical contexts. Using the fundamental results of Fourier analysis, and respecting the mathematical formalism of quantum mechanics, we present many different formulations of the uncertainty principle. We observe the principle for a single function – its qualitative, quantitative, operator and entropic formulations, for Gabor and wavelet systems of functions, and finally, generally for finite abelian groups, and more specifically for cyclic groups of prime order.
One of the various interpretations of quantum mechanics occupies a privileged position in the opinion of the majority of physicists. This is the Copenhagen view, which owes its fame and popularity not only to historical reasons but also to its simplicity and practical efficiency. As is well known, the Copenhagen outlook was elaborated collectively. Nevertheless, Niels Bohr's and W. Heisenberg's contributions should be singled out as particularly outstanding. This chapter describes two principles, which are in fact the two pillars on which Bohr's doctrine is built. These are: The working of measuring instruments must be accounted for in purely classical terms . Another one is quantum systems that should not even be thought of as possessing individual properties independently of the experimental arrangement. In the particular case of the pair of observables "position" and "momentum," the Heisenberg uncertainty relations can be considered as a generalization of the complementarity principle.
Of Werner Heisenberg's many contributions, two stand out. The first was matrix mechanics. It was the first form of what is called “the new quantum mechanics,” as compared to the “old quantum mechanics” of Bohr. Bohr's old quantum theory talked of electron orbits; these were themselves unmeasurable. Heisenberg found a way of putting what was measurable into a sort of table, called a matrix. He also recognized that measurement of the same properties, such as electron spin, could give different results. This led to his second great achievement, his uncertainty principle. Certain pairs of measurements, such as position and momentum, could not be simultaneously measured to any desired degree of accuracy. The more accurately measured the one, the less can be known about the other. This is not an experimental error. It is fundamental. Heisenberg is associated with another uncertainty: his role in attempting to build a German atomic bomb. What he actually did or did not do is still a matter of controversy.
Most of the physicians that I know are chary of Physics, especially the theory of elementary particles. Even if in Isaac Newton's mathematically precise universe, everything follows clear-cut laws and predictions are easy given appropriate starting conditions. Perhaps, however, physicians coping with this uncertainty will perhaps feel more in tune with Heisenberg's uncertainty law. Heisenberg (1901–76) described a theory of quantum mechanics, published in 1925, when he was only 23 years old. The uncertainty principle describes an imprecision in nature resulting in a limit to what we can know about the behaviour of quantum particles and, hence the smallest scales of nature. Heisenberg was awarded the Nobel Prize for Physics for 1932 for this theory and its application that resulted amongst other things the discovery of allotropic forms of hydrogen. His theory stated that we cannot always give an electron a position in space at a given time, nor follow it in its orbit, so that we cannot assume that the planetary orbits proposed by Niels Bohr exist. Mechanical quantities, such as position and velocity, should be represented, not by ordinary numbers, but by abstract mathematical structures called ‘matrices’ and he formulated his new theory in terms of matrix equations. The principle of uncertainty, says that the determination of the position and momentum of a mobile particle necessarily contains errors the product of which cannot be less than the quantum constant h and that, although these errors are negligible on the human scale, they cannot be ignored in studies. We cannot measure the position (x) and the momentum (p) of a particle with absolute precision. The more accurately we know one of these values, the less accurately we know the other. There are many ways of looking at this and in medicine we need to take account of uncertainty. Uncertainty in medicine can be resolved in many ways and can include Occam's razor. In medicine, all presenting symptoms in a patient may be explained by a few possible causes. In medicine, all presenting symptoms in a patient may be due to several disease and social processes at the same time. How can this be relevant to a working physician? The whole of medical practice has parallels with the certainties of Newton and Bohr. The object of a clinical consultation is to give a sign or complaint a diagnostic named description to be followed by a treatment regime which resolves the problem. Yet every physician knows and automatically models his understanding of a clinical problem perhaps unknowingly on a model based on Heisenberg's uncertainty principle. A core process, which is complicated by factors understood or not. The same principles are relevant to so many other features of life. There are certain fixed points in the diagnostic and clinical process. Gender, race, age, weight to height ratio, privileged and social life and intelligence. Some people age at different rates to their age cohort? Similarly, obesity does not always matter. The patient′s family history is another variable, complicated occasionally when the putative father with a family health trait may not be the actual father. The social story is a minefield, with the possibility of every phase of a person’s life being of relevance. A further element is how well the physician and the patient and their caring team relate. The clinical examination then gives a further array of data. From all of this comes a diagnosis which gives a pathway to a treatment schedule the ability of the patient to manage their treatment regime becomes important. There is a tendency that as soon as the diagnosis is made then the other elements fade away from the care plan, though of course it persists in the person's life. We are all consciously or unconsciously aware of the complex fabric of clinical care. It is intriguing to appreciate that other disciplines have been presented with the same multifactorial uncertainties. The era in Physics when Heisenberg introduced his view of nuclear physics was one when a precise physical model was being completed and gave certainty to a complex problem. His principle while obviously reintroducing uncertainty gave freedom of thinking and allowed further fruitful progress. We physicians do not enjoy uncertainty, and to have it formalized is uncomfortable. So we instinctively identify the major problem and treat that. By and large this is a useful process. It is however important to see this as a convenience. A convenience that may not always suit the patient. Applying the Heisenberg principles gives a broader view of a patient's concerns and problems and better care.
100±Δt Years of Quantum Uncertainty: From Origins to Modern Insights
Heisenberg's uncertainty principle is a cornerstone of quantum mechanics, marking a decisive departure from classical physics. Conceived almost a century ago through a thought experiment showing that measuring an electron's position inevitably disturbs its momentum, it began as a deceptively simple idea that sparked countless studies and grew into the rich research field it is today. This review traces its development into a spectrum of mathematical formulations -- known as uncertainty relations -- and explores their interconnections and wide-ranging applications. We highlight its central role in quantum metrology, where it underpins strategies for extracting information from quantum systems with ever-increasing precision, and its links to multiparameter estimation and squeezed states. This review, dedicated to the centenary of the uncertainty principle, reflects on how it has deepened our understanding of quantum theory and driven practical advances, and looks ahead to a century poised for further surprising and transformative discoveries.