How Heisenberg Discovered (Invented?) Uncertainty
He stumbled upon it, but didn’t know why it existed. His rival Schrödinger had to tell him.
Heisenberg was driving his car much too fast. A policeman stopped him and angrily asked: “Do you know how fast you were?” “No” replied Heisenberg, “but I know exactly where I am.”
This anecdote covers the essence of uncertainty in quantum physics: Either you exactly know the position of a particle, or its velocity, but never those two together. How did Heisenberg discover this important principle?
It was a consequence of matrix mechanics, invented by Heisenberg. Remember: The combination (“multiplication”) of two matrices is non-commutative, symbolically:
“A” and “B” are observables, or are they observed values? Nobody knew at the beginning of quantum mechanic’s development, nobody really knows today. Heisenberg admired Einstein’s philosophy, Einstein, when developing special relativity, committed himself to Mach’s philosophy: Physics has to do with observations or observable variables, not with “nature” or “reality”. So we stick to the term “observable”. The inequality means: There is a difference whether you first measure “A” and then “B”, or vice versa.
To derive an inequality in mathematics or physics is rather difficult and very complicated. Ludwig Boltzmann failed when he wanted to show that the entropy S at time t can never be smaller (i.e. must be equal to or larger) than that at time t=0: S(t)≥S(0). He couldn’t prove it, despite his brilliant use of probability and combinatorics. The mathematicians, especially Henri Poincaré, dismantled his calculations, which was unfair because entropy is about development over time, whereas time does not occur in mathematics. So we’ll stick to plain words and leave the mathematics to other articles.
What kind of uncertainty?
First question: What is the correct word for Heisenberg’s Principle? That’s no idle issue of linguistics, more of philosophy. Because there is a vast difference between the meaning of
- inaccuracy: a problem of measurement
- indeterminacy: pertaining to a theory
- vagueness: bad definition
- uncertainty: something inherent in nature.
Heisenberg, in his first publication, preferred the term “Ungenauigkeit”, which translates as “inaccuracy”. Hence the importance of measurements in the first interpretation of quantum mechanics, the “Copenhagen interpretation”.
Second question: What does Heisenberg’s principle mean? In his seminal work from 1927, “Über den anschaulichen Inhalt der quantenmechanischen Kinematik und Mechanik” (= “On the clear content of quantum theoretical kinematics and mechanics”):
Heisenberg gave four reasons for his principle — and all of them were wrong. Here they are:
(1) A problem of measurement. If you want to precisely determine the position of a falling ball, you have to take a snapshot in a very short time. But then you can’t determine the speed because for it you need two positions, i.e. a distance. Conversely: If you want to measure speed, you need two locations, the distance between which you divide by time. But then you are missing the exact position.
Solution: Heisenberg ignored the fact that two eminent scholars had already solved the problem in the 17th century: Leibniz with his “differentials” and Newton with his “fluxions”. They worked with infinitely small quantities, which they determined from finite quantities using limit procedures, thereby creating a whole new branch of mathematics, very important for physics: calculus.
(2) A problem of observation, the “gamma ray microscope”. If you look at a quantum system — a single electron, for example — you have to use a very good magnifying glass to be able to see it. Or better: a very good light source. Normal light is not enough for this; you need light with an extremely short wavelength, i.e. hard X-rays or even gamma rays. It would be illusory to believe that these high-energy rays would leave our harmless electron unharmed. They push it off the track, its location can no longer be determined exactly, neither its speed. Because of this disturbance, uncertainty arises.
This explanation is also wrong, and it was torn apart by his teacher and fatherly friend Niels Bohr before the article was published. Because the collision of two particles can be treated classically using Newton’s law of momentum, and Heisenberg knew that too. Besides, there is nothing in his inequality about an observer or even a microscope.
Mara Beller investigated the psychological background of quantum pioneers in her book “Quantum Dialogue. The Making of a Revolution”. Her thesis: Heisenberg wanted to avoid anything that had to do with waves. He was bothered by Schrödinger’s recently established “wave mechanics”, which thrilled all physicists and pushed his own matrix mechanics into the background. Hence his radiation microscope.
(3 Impossibility of exact predictions. In his article, Heisenberg says:
[The orbit of an electron] can only be calculated statistically, which can be seen as a consequence of the fundamental inaccuracy of the initial conditions.
Again, this has nothing to do with the fundamental indeterminacy of his inequality; rather, it is due to the deterministic chaos discovered by Poincaré.
Heisenberg further explains his ideas:
In the sharp formulation of the causal law: “If we know the present exactly, we can calculate the future.”, it is not the postscript but the premise that is wrong. In principle, we cannot get to know the present in all its determinants. Therefore, all perception is a selection from a multitude of possibilities and a limitation of what is possible in the future.
Indeed, but that’s because sometimes very tiny differences in initial conditions may lead to vast differences in position and velocity of particles after a short time, so you cannot calculate the future of the system exactly. As we said, this pertains to chaotic systems only. Atoms are not chaotic.
(4) The light microscope. Heisenberg compared his inequality with the one that describes the resolution of an ordinary light microscope. The resolution depends on the nature of the lens and of course on the wavelength of the light used: If it is larger than the object to be viewed, the latter can no longer be resolved (see argument 2).
The real reason
There is an explanation for uncertainty, and Heisenberg’s rival Schrödinger, of all people, provided it. If you regard a quantum object, like an electron, as the superposition of many waves — a wave packet — than uncertainty naturally appears.
Just take the two extreme cases:
(a) A monochromatic wave has one frequency only, hence one exact velocity, but no definite location. A wave theoretically fills the whole universe.
(b) A sharp impulse may be described by Dirac’s delta-function. It has a definite position, but consists of infinitely many waves, every one of them with a different frequency and velocity.
This explanation is recognized by Wikipedia, that states in its article about Heisenberg’s principle right at the beginning:
The Heisenberg uncertainty principle can be viewed as an expression of the wave character of matter.
But there are completely different interpretations, where there are no wave packets and the two aspects (particle — wave) are separated, without any necessity of uncertainty.
In the pilot-wave-interpretation of Louis de Broglie and David Bohm there is no need for uncertainty. Wikipedia is wrong when it writes:
The Heisenberg uncertainty principle results from the fact that a physical system is described in quantum mechanics using a wave function.
Actually, it’s not the wave function that matters, but rather its interpretation. If you take the psi-function as a wave packet, the statement is correct. If you take “psi” as the probability amplitude for a single particle, the statement is not true. If you take psi as a guiding wave (the pilot wave) for individual particles, the statement is certainly wrong.
But, and that’s a big BUT: Does Heisenberg’s uncertainty even exist? After all, every quantum physicist endorses it, counts on it, swears to it, uses it. Well, I own a book (in German) on quantum physics by Walter Weizel (“Physikalische Formelsammlung”) in which the entire mathematical formalism of quantum physics is presented and all the important theorems are derived. The term “uncertainty” doesn’t appear once, not in the “Register”, not in the main text. You are able to explain quantum physics without Heisenberg’s principle! The reason: It doesn’t exist.
No uncertainty?
That’s a strong statement, and we have to prove it. Science, as you know, depends on experiments, experience, reality. This is where it differs from religion. And experiment, experience and reality reveal this:
- In 1924, experiments by Bothe and Geiger as well as by Compton and Simon showed that electron orbits can be clearly determined. No uncertainty there.
- In 1929, the American physicist Edward Uhler Condon pointed out that the Heisenberg phenomenon does not apply to the vertical component of angular momentum. No uncertainty there.
- In 1998, the German physicist Gerhard Rempe at the University of Konstanz corrected a common opinion in textbooks about uncertainty: In the double-slit experiment, information about the path of a photon destroys the wave interference pattern. But this is not due to Heisenberg’s “vagueness”, but to entanglement. Note: Entangled particles have no uncertainty whatsoever!
- In 2011, Aephraim Steinberg at the Center for Quantum Information and Quantum Control at the Canadian University of Toronto succeeded in simultaneously and precisely determining the position and momentum of light particles (photons) using weak measurement in a double-slit experiment. With such a weak measurement, the particles remain nearly undisturbed — the observer’s influence becomes, on average, insignificant. Steinberg thereby refuted uncertainty and at the same time proved (by recording the trajectories of the particles) the pilot wave interpretation of de Broglie and Bohm.
Nobel Prize winner P.A.M. Dirac, who had discovered “fuzziness” before Heisenberg, expressed his doubts in 1963:
I think it is safe to assume that uncertainty relations in their current form will not survive the physics of the future.
The limits of Heisenberg’s uncertainty are limits of theory, not of nature.
The phenomenon is unscientific: Experimental experience has refuted it, and as a principle of knowledge it is not only useless, it even hinders progress because it dogmatically limits our knowledge. That’s actually happened:
- American physicist and Nobel Prize winner Charles Townes had difficulty developing the MASER (a microwave version of the LASER). He was advised against it because the way the device worked contradicted the Heisenberg’s principle. He did it anyway, and MASER and LASER have been violating this principle ever since.
- Egyptian chemist and Nobel Prize winner Ahmed Zewail had to overcome the doubts of his colleagues when studying chemical reactions in the femtosecond range. They told him: At these short times (one femtosecond = 10^-15 seconds = 1 quadrillionth of a second) there are huge inaccuracies in the energy, and the wave packet — important for determining the exact location — would soon dissipate. Such research would be doomed from the start — thanks to an untenable physical principle. Zewail did not allow himself to be deterred and won the Nobel prize, but had to publicly defend himself against the idolization of the Heisenberg phenomenon, which he did in an article in the renowned magazine NATURE in 2001. There he wrote:
The specter of quantum uncertainty could block our path to new discoveries.
Researchers of lesser character may have given up because the establishment (and potential funders) told them it was pointless to fight Heisenberg.
- The uncertainty disappears in another interpretation, the “transactional interpretation of quantum physics” (John Cramer 1980). There it is limited to an immeasurably small region that corresponds to the de Broglie wavelength.
As a principle, the Heisenberg phenomenon cannot predict anything except the failure of an effort. It does not provide any insight, it does not advance research, on the contrary, as we have seen. Then why insist on it? It is due to a postulate, or rather a dogma, in orthodox quantum physics that measurements can only determine the mean value of a quantity. Then the individual value is of course somehow indeterminate. But that doesn’t have to be the case. According to Bohm’s interpretation and Steinberg’s experiments, position and momentum (= velocity times mass) of each particle can be precisely calculated and determined. Without any vagueness, or whatever you call it.
This was an excerpt from my book „Das Rätsel der Quanten … und seine Lösung!“ Books on Demand, 2016
Werner Heisenberg: Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik. Zeitschrift für Physik. 43, Nr. 3, 1927, S. 172–198. In English: About the clear content of quantum theoretical kinematics and mechanics. Journal of Physics 43 (1927), 172–198
Ahmaed Zewail: The fog that was not. NATURE 412, July 19, 2000
Mara Beller: Quantum Dialogue. The Making of a Revolution. Univ. of Chicago Press 1993