Last week, I wrote an article titled “A short history of determinism”. In the article I argued that the universe was a determined entity. That is, an effect is always preceded by a connected cause. This assertion was inevitably challenged by questions about quantum mechanics.
There are many aspects of quantum mechanics and the uncertainty principle. One cannot hope to deal with all of them in one short essay. Therefore, in this short essay, I will only look at one of these interpretations. I wish to demonstrate that Heisenberg’s uncertainty principle does not in fact disprove the existence of a determined universe because it was based on the epistemological and ontological assumptions that are untenable.
The uncertainty principle states that “the more precisely the position of some sub- transitions particle is determined, the less precisely its momentum can be known, and vice versa”.
In 1925, Heisenberg developed his first ideas about quantum theory. His basic methodological assumptions were that only those quantities that are empirically observable should play a role in building any theory. Observational data about atoms was based on spectroscopy. Spectroscopy was associated with atomic transitions (An atomic transition is said to occur when an electron jumps from one energy level to another). Heisenberg considered that these transition quantities should form the building blocks of any atomic theory. Max Born discovered that these atomic transitions obeyed the rules of matrix calculus.
This mathematical model fitted almost perfectly with all empirical data at the time. The model meant that atomic transition quantities were discontinuous (called “quantum jumps” – that is, atomic transitions were indeterminate).
A year later, however, Erwin Schrodinger presented his theory of wave mechanics. He argued that an electron in an atom could be represented as an oscillating charged cloud. Not only did Schrodinger’s theory also fit perfectly with the empirical data it also argued that atomic transitions were not discontinuous quantum jumps but a resonance phenomenon. In other words, it posited a determined atomic world.
In response, in 1927 Heisenberg wrote his most famous paper that laid the foundation of the uncertainty principle. He began by arguing that in theory achieves “understanding” if it can grasp “experimental consequences qualitatively”. In other words, he argued the view that a concept only has meaning if it can be measured. If a concept cannot be empirically verified or measured it cannot be scientifically said to exist.
It is precisely this epistemological and ontological assumption that is problematic. This assumption has also been called “the measurement=meaning principle”. In other words, only phenomena that can be measured have any meaning.
Utilising this assumption, Heisenberg considered the measurement of the position of an electron by an electron microscope. The position of an electron is measured by illuminating it by using light of a very short wavelength. However, this brings about the Compton scattering. The photon of light collides with the electron. Owing to the collision the momentum of the electron is disturbed; the shorter the wavelength, the greater the disturbance. Thus, the very act of measuring the position of an electron disturbs its momentum. Heisenberg concludes “the more precisely the position is determined, the less precisely the momentum is known, and conversely”. Moreover, it is not just that the momentum of the electron changes but more importantly that it changes by an unpredictable amount. It is on the basis of this unpredictability that Heisenberg asserts the uncertainty principle.
However, Heisenberg accepts that the uncertainty principle does not apply to the past. It has been shown that both the position and momentum of an electron can be known precisely if the event we are talking about has already occurred.
That is assumed that in an experiment the momentum of an electron is precisely determined with a certain degree of inaccuracy (let’s call the inaccuracy ?Pi). Then its position is murder measured (which will displace the electron). This is measured with the inaccuracy ?Pq. After its displacement by the position measurement, its final momentum is measured once again. Let’s say it is measured with the inaccuracy ?Pf. The change in the momentum of the electron can now be measured by Pf – Pi. And the mean value of the momentum will be (Pi + Pf)/2. In this way the momentum is precisely determined at all incidents and Heisenberg’s formulation of the uncertainty principle no longer follows. Heisenberg accepts this and 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.” He concludes by stating “the uncertainty relation does not hold for the past”.
Hence, the argument can be broken into the following syllogism:
Premise 1) Theory must rest on that which can be observed and measured
Premise 2) No possible experiment will ever allow the simultaneous present measurement of the momentum and position of an electron
Conclusion: Since we cannot experimentally predict the future behaviour of the electron through, it can be stated that these concepts do not exist in the physical reality. In fact, we construct these concepts through our observation of them.
Most scientists have attempted to criticise Heisenberg’s second premise. For instance, Albert Einstein attempted to construct a thought experiment that in which the position and momentum of an electron could be predicted. However, in my opinion it is Heisenberg’s ontological principle, which is his first premise, needs to be challenged.
Heisenberg’s assumption takes empirical verification as the sole foundation of theory building. A method called induction. But it is only one of the methods of understanding the world. Deduction is the other.
In history we have seen many instances of philosophers and thinkers constructing deductive theories from logical premises about the laws of the universe. It was only sometimes centuries later that these deductive theories were finally empirically verified. Einstein himself first arrived at the theory of relativity from deductive logic (from a thought experiment). It was only decades later that his theory of relativity was empirically verified. How much poorer would be our scientific imagination if our knowledge of the natural world were restricted to only that we could currently observe.
(To be continued…)
Taimur Rahman is an academic, musician and socialist political activist from Pakistan. He teaches political science at the Lahore University of Management Sciences. He is the band leader and spokesperson for the political music band named Laal.