It is often claimed that quantum mechanics or quantum phenomena disprove the principle of causality or at least cast doubt on whether it is a logically defensible axiom. Examples of quantum phenomena include radioactive decay, the Stern-Gerlach experiment, the double-slit experiments etc. Examples of people using quantum phenomena in such a type of an argument can be found here, here, here, here, and here etc. Olegt thinks the Stern-Gerlach experiment is an example whereby "classical logic is simply not equipped to deal with phenomena of this sort". That may be true, I don't know what olegt exactly means when he talks about “classical logic”. I just disagree that the principle of causality needs to be abandoned when it comes to quantum physics.
Below is a nice flash animation that let's you play around with it.
Set the flash animation up in the following manner.
Spin orientation: +z
Number of magnets: 3
Angle 1: 0
Angle 2: 90
Angle 3: 180
One can say that:
1) An electron with a spin Sz=+½ (spin pointing along the vertical axis) is prepared.
2) Magnet 1 or a magnet pointing in the positive direction of the Z-axis will always let electrons with spin Sz=+½ through the red (+) hole.
3) Magnet 2 or a magnet pointing in the negative direction of the X-axis will let electrons with spin Sz=+½ either through the red (+) or blue (-) hole in an indeterminate manner. The electrons coming out of magnet 2 will have Sx=±½.
4) Magnet 3 or a magnet pointing in the negative direction of the Z-axis will will let electrons with spin Sx=±½ either through the red (+) or blue (-) hole in an indeterminate manner. The electrons coming out of magnet 3 will have Sz=±½.
To state it differently:
1) An electron prepared in the initial state with Sz=+½ will have a determinate Sz value (+½) whenever it is measured if left undisturbed.
2) An electron prepared in the initial state with Sz=+½ will have an indeterminate Sx value (±½) before measurement.
3) An electron prepared in the initial state with Sz=+½ will have an indeterminate Sx value (±½) before measurement and a determinate Sx value after measurement. However, after the Sx measurement is made, the Sz value becomes indeterminate.
The question is what causes Sx to take on the specific value if Sx is indeterminate before measurement or before it passes through the magnet or when in fact it does pass through the magnet.
I will be approaching this from a Scholastic perspective and with that comes at least a rudimentary understanding of concepts such as prime matter, pure potentiality, substantial form, actuality, substance, accident, essence, cause per se, cause per accidens, causa in fieri, causa in esse, the four causes, the Scholastic view of change etc.
Some of it is summarized here:
Philosophy and Metaphysics Interlude 1: Matter
Philosophy and Metaphysics Interlude 2: Creation Ex Nihilo vs Change
Philosophy and Metaphysics Interlude 7: The Species Problem and a Scholastic Approach
Some Scholia on the Accidental Mode of Being
Some Scholia on Causality
I will highlight the important concepts here as they are related to the concept of an electron.
A) Inseparable vs separable accidents: Inseparable accidents “may be such that in the ordinary course of nature, and so far as its forces and laws are concerned, they are never found to be absent from their connatural substances”. Mass (e.g. 0.511MeV), charge (e.g. -1) and spin (e.g. ½) are inseparable accidents of an electron.
Separable accidents “may be such that they are sometimes present in their substances, and sometimes absent”. The kind of spin an electron has is an example e.g. Sx=- or Sz=+ or Sx=+ or the location of the electron is another.
B) Active and passive powers: Active powers derive from a substance’s form (e.g. charge or spin) and passive powers derive from the material component or prime matter of a substance.
C) The principle of Causality
The principle of causality has been stated differently (although essentially meaning the same thing) as:
- The existent being to which existence is not essential exists in virtue of some action external to it. (A Manual of Modern Scholastic Philosophy, p540):
- A being whose essence is not its existence necessarily demands for the explanation of its existence a cause which brought it into existence. Or The existence of a contingent being demands a cause. (A Manual of Modern Scholastic Philosophy, p375)
- Whatever happens has a cause ; Whatever begins to be has a cause ; Whatever is contingent has a cause ; Nothing occurs without a cause. (Ontology: or, The theory of being; an introduction to general metaphysics, p369)
- Cause and effect being correlative, to say that "Every effect has a cause" is to state a truism. The principle is usually stated thus : "Whatever happens (occurs, takes place, begins to be) has a cause";. The axiom Ex nihilo nihil fit is a negative statement of the same principle. And another statement of it, "Whatever is contingent (i.e. whatever does not contain in itself, in its own essence, the sufficient reason of its actual existence) has a cause" shows the connexion of the principle of causality with the principle of sufficient reason. Being that is necessary and self-existent has no cause. It is itself the reason of its own existence; whereas all contingent being is caused. The principle of causality is evidently a necessary principle in regard to contingent being, i.e. it is essentially involved in our very concept of contingent being. Nothing can happen without a cause: whatever happens has necessarily a cause, i.e. something which brings it about, which makes it happen, whether this cause be free (i.e. self-determining) or not, in its mode of action. (The Science of Logic: Conception, judgment and inference, p61)
- Every thing must have a sufficient reason why it is rather than is not, and why it is thus rather than otherwise : The only sufficient reason for a real change is efficient causality : Therefore every real change has an efficient cause (General Metaphysics, p319).
- Axioms such as the principle of Causality that “Whatever comes into being must have a cause”, and the principle of Contradiction that “It is impossible for a thing both to be and not to be at the same time”, together with all the truths of Mathematics possess this higher degree of necessity. (Principles of Logic, p238).
- Another way of saying it is “nothing can be reduced from potentiality except by something in a state of actuality” (Aquinas, a Beginner's guide, p65).
D) Infima and Essental species: The "infima species" is the lowest class that stands just above individuals i.e. below "infima species" there are no sub-classes but only individuals. The "definition" of a substance is something that describes the nature of the thing that is not only clear but distinct. The "definition" of a substance is described by the "essential species" predicable.
The "propria" (or property) predicable is related to an individual substance in a manner that describes something about the substance that necessarily follows from its essence or nature. An inseparable accident is "some quality which is found to belong invariably as a matter of fact to all the members of a class.
E) Prime matter is:
1) Is pure potentiality, "the something which can be transformed by an actualizing principle into anything which nature allows".
2) Is a wholly indeterminate substrate underlying change.
3) Itself does not undergo change.
4) Has no form.
5) Is the closest there is to nothingness without being nothingness.
6) Is a state of being without form, and since science deals with substances and all substances have a substantial form, this state is impossible to achieve experimentally.
7) Cannot actualize itself since it has no actuality, it is only actualized by something actual
Describing an electron in Scholastic terms
An electron prepared in the initial state with Sz=+½ can thus be described as follows in Scholastic terms (Figure 1).
A) All four electrons belong to the same essential species i.e. electron. Their propria are ½ spin, negative charge and mass (0.511MeV).
B) There are 4 different infima species of electrons and this is derived from their inseparable accidents. The 4 different infima species of electrons are:
1) An electron prepared in the initial state with Sz=+½ (Electron Sz+)
2) An electron prepared in the initial state with Sz=-½ (Electron Sz-)
3) An electron prepared in the initial state with Sx=+½ (Electron Sx+)
4) An electron prepared in the initial state with Sx=-½ (Electron Sx-)
C) An electron is a substance that is a composite of prime matter and substantial form. The electron has no substructure, it is simple.
So the apparent problem is to explain what causes an Electron Sz+ to change into an Electron Sx+ or Electron Sx- since there is no way to predict it.
Firstly, the principle of causality is not violated. Electron Sx+ or Electron Sx- can only be actualized from an Electron Sz+ by something else that is in a state of actuality, in this case the measuring apparatus Sx (Figure 2).
Electron Sz+ has potential being. In other words it can be an Electron Sx+ or Electron Sx-. Electron Sx+ or Electron Sx- are some of the final causes or natural ends of Sz+. Now it appears that these potentialities can only be actualized (by something else in a state of actuality) in an indeterminate fashion. In other words, we cannot predict which potentiality can be actualized before the act or effect or perfection. The question is then what is the cause of this indeterminacy. The simple answer is that electrons have no substructure, they are simple substances (not compound in the Scholastic sense) and thus has no proximate matter and only prime matter. So the reason for the indeterminacy is the material cause of electrons, prime matter. And as pointed out, prime matter just is the wholly indeterminate substrate underlying change and can be transformed by an actualizing principle into anything which nature allows. In this case nature allows it to be transformed into either Sx+ or Sx-.
To answer the question from a Scholastic view would, in my mind, be something as follows.
1) Electron Sx±½ is actualized from Electron Sz+ by something in a state of actuality (Principle of causality).
2) The cause of Sx's specific value is indeterminate but the reason is not. "To ask for the reason of any event or phenomenon, or of the nature or existence of any reality, is to demand an explanation of the latter ; it is to seek what accounts for the latter, what makes this intelligible to our minds. Whatever is a cause is therefore also a reason, but the latter notion is wider than the former" (Coffey1914, p357-359).
3) The reason for the indeterminacy, I would argue, is the material cause of the electron, its prime matter, which is wholly indeterminate and can be transformed by an actualizing principle into anything which nature allows. In this case nature allows it to be transformed into either Sx+ or Sx- in an indeterminate manner.
So I would argue there is no need to abandon the principle of causality when it comes to quantum physics and the Aristotelian concepts of prime matter and pure potentiality actually fit in quite nicely with the indeterminate nature of quantum physics.