This is the equation of Heisenberg’s principle of indeterminism [1], also known as the uncertainty principle: ΔpΔx ≥ h/4π [2].
It asserts a fundamental limit to the accuracy with which the values for certain pairs of physical quantities of a particle, such as position, x, and momentum, p, can be predicted from initial conditions [3].
In other words, it is impossible to know the exact position and momentum of a quantum particle at the same time. The same happens to other pairs of conjugate variables, such as energy and time.
Furthermore, in his famous paper of 1927 about quantum kinematics and mechanics Heisenberg declared the failure of causality as follows [4]:
If one assumes that the interpretation of quantum mechanics is already correct in its essential points, it may be permissible to outline briefly its consequences of principle. We have not assumed that quantum theory — in opposition to classical theory — is an essentially statistical theory in the sense that only statistical conclusions can be drawn from precise initial data. The well-known experiments of Geiger and Bothe, for example, speak directly against such an assumption. Rather, in all cases in which relations exist in classical theory between quantities which are really all exactly measurable, the corresponding exact relations also hold in quantum theory (laws of conservation of momentum and energy). Even in classical mechanics we could never practically know the present exactly, vitiating Laplace’s demonBut what is wrong in the sharp formulation of the law of causality, “When we know the present precisely, we can predict the future,” it is not the conclusion but the assumption that is false. Even in principle we cannot know the present in all detail. For that reason everything observed is a selection from a plenitude of possibilities and a limitation on what is possible in the future. As the statistical character of quantum theory is so closely linked to the inexactness of all perceptions, one might be led to the presumption that behind the perceived statistical world there still hides a “real” world in which causality holds. But such speculations seem to us, to say it explicitly, fruitless and senseless. Physics ought to describe only the correlation of observations. One can express the true state of affairs better in this way: Because all experiments are subject to the laws of quantum mechanics, and therefore to equation [ΔpΔx ≥ h/4π], it follows that quantum mechanics establishes the final failure of causality.
Why Heisenberg Was Wrong
Bob Doyle, The Information Philosopher [5] and associate at the Department of Astronomy, Faculty of Arts and Sciences, at Harvard University [6] explains that the Heisenberg principle is an epistemological lack of information. But, it does not claim that the ontological precise position and momentum do not exist, only that we cannot know them, or, as Niels Bohr put it, that we cannot say anything about them.
The above means that cause and effect are, in fact, not broken at the quantum level, what happens is that the subjective observer cannot measure, record, or see it.
This means that even if the universe is fundamentally probabilistic [7], an interpretation this author shares, chains of cause and effect, indeed, continue to occur.
The opposite of indeterminism or uncertainty is determinism or certainty, not causality, therefore, indeterminism or uncertainty do not mean non causality. Furthermore, the fact that something cannot be determined or is uncertain by an observer does not mean that the underlying physical phenomena is not causal.
Causality means that an event mechanically and logically follows another as a consequence of it.
For example, once a position of a particle is determined, an observer may not be able to determine the next position; which is a mere prediction problem, not a problem of causality; but the next position will exist, whether observed or not, after the previous one occurred. That is causality.
Non causality, or a failure of causality would mean that once a position is determined the next one never occurs for no reason, or occurs before the previous one, which is impossible as time travel to the past is impossible.
Even if the next position or action is an actual end, collapse, or disappearance of the particle, due to quantum interactions or fusion of state with another particle, then that is a cause for the disappearance, after the previous event. Therefore, causality never failed.
It is just that in some links of the causality chain there may be a discontinuity of the information observed, or even a physical discontinuity where the next state does not follow close or adjacent to the previous one. But, the next step still happens as a consequence of the previous one.
As stated before, in the case of absorbed particles, it could be said that their cause and effect chain, and thus their existence has ended, but that does not, in itself, violate causality. It is just an end of a path.
In the case of initiation of particles, or spontaneous creation in the quantum vacuum [8], or when they are emitted when electrons jump to lower energy states [9], the same principle stands: It is a genesis, from which a chain of causality will start, until its eventual absorption. In which case, it follows the same reasoning as expressed for particle absorption. In other words, particle genesis is not a disruption of causality. It is just a start of a path.
If what Doyle wrote about an epistemological lack of information is correct, then indeterminacy is not a property of nature, but a problem of the observer.
If that is true, then causality is just fine.
References
[1] Uncertainty Principle – by Britannica: https://www.britannica.com/science/uncertainty-principle
[2] The Physical Content of Quantum Kinematics and Mechanics – by Werner Heisenberg (1927): http://etherplan.com/heisenberg-uncertainty.pdf
[3] Uncertainty principle – by Wikipedia: https://en.wikipedia.org/wiki/Uncertainty_principle
[4] Werner Heisenberg (1901-1976) – by Bob Doyle – The Information Philosopher – Associate, Department of Astronomy, Faculty of Arts and Sciences, Harvard University: https://www.informationphilosopher.com/solutions/scientists/heisenberg/
[5] The Information Philosopher – by Bob Doyle: https://www.informationphilosopher.com/
[6] Bob Doyle – The Information Philosopher – Associate, Department of Astronomy, Faculty of Arts and Sciences, Harvard University: https://scholar.harvard.edu/iphi/home
[7] Born rule – by Wikipedia: https://en.wikipedia.org/wiki/Born_rule
[8] Quantum vacuum state – by Wikipedia: https://en.wikipedia.org/wiki/Quantum_vacuum_state
[9] Atomic electron transition – by Wikipedia: https://en.wikipedia.org/wiki/Atomic_electron_transition
