تاريخ و تحقيق  HISTORY AND RESEARCH

According to Blackwell’s Dictionary of philosophy determinism means that every event must have a deterministic cause, i.e. a cause which ensures its occurrence (Mautner, 1996). Often determinism is used in the sense of predictability. But, these two are not the same. If causality holds and if one knows all the laws of nature and all initial conditions, then one can determine the future. But, it is possible that causality holds, but we might not be able to predict the future, due to our lack of knowledge about the laws of nature or the initial conditions. Causality is an onthological issue, whereas, predictability is an epistemological one.

Gradually causality was used in more restricted senses by physicists and finally the thesis that (i) there are universal laws and (ii) one can determine the future of any physical system by using these laws, was interpreted as determinism and was identified with causality.

This kind of determinism came under attack during the nineteenth century. Thus, Renouvier, e.g., disputed the strict validity of causality principle as a regulator of physical processes. Charles Peirce, American mathematician and physicist, gave chance a fundamental role in nature. In his view, the world is not strictly governed by Newtonian laws. It is also ruled by laws of chance. Boltzmann, Exner, Poincaré, etc. all disputed strict validity of determinism and speculated that the laws of nature are statistical in character.

Against these, some physicists (e.g. Planck, Nernst, etc.) refuted the statistical character of physical laws and attributed their use by humans to ignorance.

The first serious blow to causality came from Heisenberg’s uncertainty principle. Using a Gaussian wave packet to represent microphysical entities and finding its Fourier transform, Heisenberg obtained the following relation

Where (Δx) and (Δp)represent, respectively, the uncertainty in the measurement of coordinate x and its conjugate momentum p, and h is Planck’s constant (Wheeler, 1983, 62-84). Heisenberg’s interpretation of this relation was that we can not determine electron’s coordinate and momentum precisely at the same time. He gave an ontological interpretation to this relation, implying that it refutes causality. One could say that behind this statistical behavior there is a world governed by causal laws. But, Heisenberg emphatically denied this. In his words (Wheeler, 1983, 83):

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. … quantum mechanics establishes the final failure of causality.

Thus, in his view the uncertainty relations are not indicative of our ignorance of causal laws. Rather, they indicate the rule of chance in the atomic domain.

Some eminent physicists and philosophers welcomed Heisenberg’s interpretation of uncertainty relations. They thought that the indeterminism of atomic world solves the problem of human free will. Their argument was in the following form: Since psychological processes depend on physical processes which are indeterminate, so they too must be indeterminate. As Compton put it (Popper 1986):

It is no longer justifiable to use physical laws as evidence against human freedom.

and in Eddington’s words (Jammer 1973):

If the atom has indeterminancy, surely the human mind will have an equal indeterminancy; for we can scarcely accept a theory which makes out the mind to be more mechanistic than the atom.

But Einstein did not see any inconsistency between the rule of causality and human freedom (Benagen, 1993):

… you are troubled by the conflict between the purely causal outlook of Spinoza, and the outlook which aims at an active effort in the service of social justice. In my view, there is no real conflict here; for our mental tensions, indeed not only our passions, but also our drive to bring about a just social order, belong to the factors which, together with everything else, that take part in the causal nexus.

Bertrand Russell first (1927) welcomed the indeterminism of the atomic world (Russell 1989):

… the reason why physics has ceased to look for causes is that, in fact, there are no such things. The law of causality, I believe, like much that passes muster among philosophers, is a relic of a by gone age, surviving, like the monarchy, only because it is errorneously supposed to do no harm.

But later on he had doubts about indeterminism (Russell 1961):

… the reason why physics has ceased to look for causes is that, in fact, there are no such things. The law of causality, I believe, like much that passes muster among philosophers, is a relic of a by gone age, surviving, like the monarchy, only because it is errorneously supposed to do no harm.

But later on he had doubts about indeterminism (Russell 1961):

the new laws will be discovered which will abolish the supposed freedom of atom … It may seem as though, in the present chapter that I had been guilty of an inconsistency in arguing first against determinism and then against free will. But in fact both are absolute metaphysical doctrines, which go beyond what is scientifically ascertainable. The search for causal laws, as we saw, is the essence of science,and therefore, in a purely practical sense, the man of science must always assume determinism as a working hypothesis.

Dirac, too, first embraced indeterminism, but in 1970’s he talked of the possibility of the return to determinism (Holton 1980):

It seems clear that the present quantum mechanics is not in its final form. Some further changes will be needed, just about as drastic as the changes which one made in passing from Bohr’s orbits to quantum mechanics. Some day a new relativistic quantum mechanics will be discovered in which we don’t have these infinities occurring at all. It might very well be that the new quantum mechanics will have determinism in the way that Einstein wanted. This determinism will be introduced only at the expense of abandoning some other preconceptions which physicists now hold, and which it is not sensible to try to get at now. So under these conditions I think it is very likely, or at any rate quite possible, that in the long run Einstein will run out to be correct, even though for the time being, physicists have to accept the Bohr probability interpretation – especially if they have examinations in front of them.

K. Popper pointed out (in 1934) that Heisenberg had given a causal argument to dispense with causal descriptions (Popper 1980). Einstein was ready to accept quantum theory as a statistical theory in the sense of classical statistical mechanics. But he anticipated that this theory will be replaced by a causal theory (Born, I. 1971):

I cannot but confess that I attach only a transitory importance to this interpretation. I still believe in the possibility of a model of reality – that is to say, of a theory which represents things themselves and not merely the probability of their occurrence.

Another defense of causality was done by the French philosopher Lé on Brunschwicg, who pointed out that causality holds in the atomic domain and the indeterminancy noticed at the quantum level is an only an apparent one, resulting from the perturbation by the act of measurement. Johannes E. Heyde believed that the uncertainty relations are indicative of the impossibility of proving the rule of causality but not the possibility of proving the nonexistence of causality (Jammer 1974).

Physical Interpretations of Uncertainty Relations

There are two general kinds of interpretations for the uncertainty relations: statistical and non-statistical. This division corresponds to the fact that one may consider the wave function representing the state of a single system or an ensemble of systems.
(i) Non-statistical interpretations of Heisenberg relations

Here the wave function gives a complete description of a single system. This was the position of Heisenberg and most of his colleagues. There are several versions for this interpretation.

(a)One can not measure the position q and its conjugate momentum p with more precision than what the uncertainty relations admit. This is due to the fact that the measurement q disturbs particle’s momentum in an uncontrolable way. Thus, one cannot measure both of them precisely at the same time. This interpretation is rooted in Heisenberg’s 1927 paper and is the one used in most of the text books. It came under attack by Einstein, Podolsky and Rosen (EPR) in their celebrated 1935 paper. In the EPR thought experiment one may deduce a particle’s momentum without disturbing the particle (Einstein et al. 1935). In refuting EPR’s claim concerning the incompleteness of quantum mechanics, Bohr claimed that one can attribute a dynamical property to a system only in the context of a measurement (Bohr 1935).

(c) The uncertainty relations indicate our ignorance at the quantum level. Some of the proponents of this position believe that the uncertainty observed at quantum level is due to our ignorance about variables which are presently not accessible to us. In 1932 von Neumann argued that one cannot construct hidden variable theories which reproduce all predictions of quantum mechanics (Von Newmann 1955). But Bohm constructed such a theory in 1952 (Bohm 1952). This indicated that there were some loopholes in von Neumann’s argument. In 1964, Bell demonstrated that one of the assumptions of von Neumann was not compelling (Bell, 1966). In constructing his causal theory, Bohm had implicitly relaxed this assumption.

(ii) Statistical interpretations of the uncertainty relations

Here one assume that the wave function describes the behaviour of an ensemble of similarly prepared systems. These systems are similar in certain respects (in those respects that are quantum mechanically compatible). This is the interpretation favored by Einstein, Born, Popper and Blokhintsev. Einstein, in his 1948 contribution to Albert Einstein: philosopher-scientist, endorsed this interpretation (Schillp 1969):

One arrives at very implausible theoretical conceptions, if one attempts to maintain the thesis that the statistical quantum theory is in principle capable of producing a complete description of an individual system. On the other hand, those difficulties of theoretical interpretation disappear, if one views the quantum mechanical description as the description of ensembles of systems.

Fritz Bopp, German physicist, considers quantum mechanics an extension of classical statistical mechanics. In his view, particles have exact coordinates and momenta simultaneously (Popper 1982). L. Rosenfeld claims that Bohr believed that the wave function describes an ensemble of systems (Buckley et al. 1979, 28):

… there have been endless discussions among younger generations as to whether the wave function describes a single electron or an ensemble … For Bohr, there was never any question; it was obvious that we are talking of an ensemble. As soon as we introduce statistics, we are talking of an ensemble, because statistics is made just for that.

In Popper’s view, quantum mechanics is a statistical theory, because it tries to answer statistical questions (e.g. the intensity of spectroscopic lines). Thus, Heisenberg’s relations should be interpreted as “scatter relations” (Popper 1982, 53-60). These relations tell us that no state preparation can yield an ensemble of systems that are identical in every respect. A wave function represents an ensemble of similarity prepared systems but is silent about individual systems. The uncertainty relations do not tell us anything about the precision attainable in the measurements or the limits of our knowledge. They indicate the lower limit of the dispersion of the experimental results or the upper limit of the homogeneity of the quantum states. This dispersion is the result of state preparation and cannot be eliminated. He refers to Heisenberg’s relations as “the principle of statistical scatter”. Henry Margenau advocated this interpretation. He believed that one could measure conjugate variables simultaneously (Margenau 1961). Prugovecki, Russian physicist, who is a proponent of the statistical interpretation of quantum mechanics, believes that by introducing complex probability distributions into quantum mechanics, one may give statistical distributions for the simultaneous measurements of conjugate variables (Progoveki 1967).

Here we mention two important factors concerning the statistical interpretation of quantum mechanics:

  The statistical interpretation does not negate the existence of hidden variables. In fact, it encourages the search for such variables. Thus, in the statistical interpretation, determinism is not necessarily refuted.
  The statistical interpretation solves the EPR paradox. Einstein and Bohm were ready to accept the statistical interpretation of quantum mechanics, but both of them saw a fundamental deficiency in it. It neglects the fate of the individual system. In Bohm’s words (Buckley et al. 1979, 148):

Many people don’t fully and deeply realize that there is something missing. They are so used to doing statistical calculations, and saying that only statistics matters, that they do not notice that there is an actual, individual fact which is not accounted for.

Indeterminancy or Imprecision

Quantum physicists’ reception of irreducible chance in the atomic and sub-atomic world is based on two arguments:

(i) Even if there is a sub-quantum level in which determinism is ruling, there is no way that we can have access to it. Thus, it belongs to metaphysics and therefore is devoid of real empirical content.

(ii) John von Neumann’s refutation of hidden variable theories leaves no room for causal theories.

In refuting these arguments and Heisenberg’s interpretation of his uncertainty relations, we have the following comments.
  Uncertainty relations may have other interpretations than Heisenberg’s own interpretation (see e.g. Popper’s interpretation or Bohm’s interpretation)
  Von Neumann’s proof is not without loopholes, as Bell showed.
  Born explicitly admitted that his refutation of determinism had been a philosophical decision, rather than a physical one.
  The claim for the rule of chance in the atomic domain is based on the assumption of the completeness of quantum theory. This assumption, however, is very naive. Nobody is supposed to claim the end of physics.
  There is no convincing argument for the denial of a sub-quantum level, in which strict causality holds.
  The use of statistics for understanding nature is based on an a priori principle. In fact, the reliability of the law of large numbers is based on the rule of causality. Thus, some philosophers have stated that probability only makes sense in a lawful word. As Brunschwicz said (Bergman 1929):

The probability calculus is based on determinism.

  The appeal to indeterminancy for the explanation of human free will is not right. Because, even if we base decision making on physical processes, it is the result of the behavior of a macroscopic ensemble of particles not a single particle. Thus, even according to the standard view causality should hold. On the other hand, even though causality does not prove human freedom, it is not in consistent with and it even supports it. Because, without the applicability of causality how one can attribute any action to an agent.

  The principle of causality is a metaphysical principle. Thus, it can not be refuted empirically.
  The uncertainty relations do not prove that atomic object do not process exact coordinate and momentum. To reach Heisenberg conclusion, one has to add the extra assumption that only observable objects have reality.
  Some of the physicists who denied causality, were merely denying some of its archetypes, not the principle of causality itself. As Born put it (Born 1944, 3-4):

The statement, frequently made, that modern physics has given up causality is entirely unfounded. Modern physics, it is true, has given up or modified many traditional ideas, but it would cease to be a science if it had given up the search for the causes of phenomena.

Born adds that he has problem with the orthodox interpretation of causality (Born 1944, 101-102):

Can we be content with accepting chance, not cause, as the supreme law of the physical world? To this question I answer that not causality, properly understood, is eliminated, but only a traditional interpretation of it, consisting in its identification with determinism. I have taken pains to show that these two concepts are not identical. Causality in my definition is the postulate that one physical situation depends on the other, and causal research means the discovery of such dependence. This is still true in quantum physics, though the objects of observation for which a dependence is claimed are different. They are the probabilities of elementary events, not those single events.

Thus, we believe that there is no compelling evidence for interpreting Heisenberg’s relations as an indication of the rule of chance in the atomic and subatomic world, implying the failure of determinism in the microworld. Our present knowledge only permit us to interpret these relations as implying the presence of imprecision or lack of certainty in this domain. There is a strong possibility that in the future a causal theory of microworld would emerge. The resurgence of interest in 1990’s in Bohm’s theory and its extension to solve some problems in cosmology is indicative of the unhappiness of some eminent physicists with the standard quantum mechanics. As Gerard ’t Hooft, 1999’s Nobel Prize winner in physics, put it (’t Hooft 1997):

Much more reasonable is the suspicion that the statistical element in our predictions will eventually disappears completely as soon as we know exactly the complete theory of all forces, the Theory of Everything. This implies that our present description involves variable features and forces which we do not (yet) know or understand … Anyway, for me, the hidden variable hypotheses is still the best way to ease my conscience about quantum mechanics.

To assume that our lack of success in giving a causal description of the atomic phenomena is an evidence for the rule of chance in nature is harmful scientifically and is against the dictation of logic. Because the denial of determinism is only one of the interpretations of quantum mechanics, without being its only interpretation. As Mario Bunge put it (Bunge 1979):

Uncertainty in knowledge is far from being unequivocal sign of physical indeterminancy or haziness.

This uncertainty is simply an empirical uncertainty, and does not imply the failure of causality. It is good to stick to J. J. Thomson’s advice (Jaki 1992):

The immeasurable of today may be the measurable of tomorrow … it is dangerous to base philosophy on the assumption that what I know not can never be a knowledge.

What the Copenhagen interpretation does is that it makes an unwarranted jump from an epistemological proposition to an ontological one. As S. Jaki put it (Jaki 1989):

… the Copenhagen interpretation implies the fallacious inference from a purely operational to a strictly ontological proposition, namely, that an interaction that cannot be measured exactly cannot take place exactly.

The only thing we can logically say is that in one domain of science, our knowledge about causal laws is incomplete.

Causality in the Islamic Outlook

In the Islamic philosophy, the principle of causality is defined in the following way:

Every event requires a cause.

From this principle two corrolaries follow:

(i) Determinism. Every event has a sufficient cause, and with the presence of that cause, the event is present.

(ii) Uniformity of Nature. This means that similar causes entail similar effects. These corrolaries are inseparable from the principle of general causality, and any violation of them leads to the violation of the causality principle.

The validity of the principle of general causality is admitted in the Quran. Thus, e.g. the Quran talks frequently of the unchangeable patterns of God in the universe:

[Such has been] the course of God with respect to these who have gone before; and you shall not find any change in the course of God. (33: 62)

In the Quranic view, the cause of events in nature follow a certain measure, and every natural being has a definite and precise life span:

And there is not a thing but with Us are the treasures of it, and we do not send it down but in a definite measure (15: 21)

In the Quran, one finds many cases in which the role of certain intermediary causes in the occurrence of some events are mentioned:

And God has sent down water from the cloud and there with given life to the earth after its death (16: 55) And We sent down the winds fertilizing … (15: 22)

The existence of certain patterns in nature means the existence of natural laws, and this in turn means that the principle of causality is valid. This, however, does not imply that events are totally independent of God. Rather, it implies that everything is realized by God’s will, but through definite secondary causes. Here we cite one example:

As for the good land, its vegetation springs forth by the permission of its Lord, and [as for] that which is inferior [its herbage] comes forth but scantly … (7: 58)

This means that although God’s will is necessary for the growth of plants, the fertility of the land is also a condition. Some well-known Muslim theologians, particularly, of the Asharites School, used some verses of the Quran of the type

The commandment is wholly God’s … (7: 54)

and some verses that indicate the occurrence of miracles, to refute the rule of causality in the physical world, and they attributed the occurrence of every event to God’s will. In their view the connection between what is usually believed to be a cause and what is believed to be an effect is not a necessary connection. Thus, e.g., it is not fire which causes the cotton to burn, rather, it is God who makes the cotton to burn and if God does not want, the fire will not burn the cotton (Al-Ghazali 1997). These theologians thought that the admittance of secondary causes would result in denying God’s power.

In refuting the Asharites view, Muslim philosophers argued in the following way:

(i) The coincidence of two causes operating on a single object is impossible if the relation of the two causes is horizontal. But, in a vertical system of causes one can attribute every event to God, because He gives it existence. But the emanation takes place through definite means.

(ii) In the case material beings, what is commonly called “cause” is not the efficient cause. Rather, it is an intermediary or secondary cause which prepares the ground for God’s bounty. Mulla-Sadra explains Muslim philosopher’s view (Sadr al-Din Shirazi 1981):

Another group of philosophers and some elite among our Imamiah scholars say that objects vary in their acceptance of existence from the Origin. Some do not yield to existence unless another being precedes them, in the same way that accident should follow substance. Thus, the Creator, whose power is unlimited, grants the existence according to the possibilities through a particular order and in consideration of its various capabilities. Some come directly from Him, some through an intermediary or intermediaries. In the last form, nothing can come into existence unless its means and pre-requisites come into reality. God Himself is the Cause without a cause. Requirements for existence are not the result of deficiency in the Almighty’s power, but due to weakness in the receiver of emanation. How can one imagine any need or deficiency in the Creator, while means and ways are all originated from Him? Therefore, the Glorious God does not need any help in the creation of anything.

In the case of miracles, we find an apparent breakdown of the laws of nature. But, this does not mean that the law is not valid or that the law of causality is violated. Because it is possible to make one law ineffective by the help of another law of nature (e.g. neutralizing the effect of gravitational force by electromagnetic force). The problem is that we do not know all laws of the universe.

After the advent of quantum theory in physics and the acceptance of Heisenberg’s uncertainty principle as signifying the rule of chance in the microworld, some Muslim scholars have revived the forsaken theory of the Asharites, and they have appealed to quantum theory to support their claim (Hardy 1993).

But, in refuting these claims modern Muslim philosophers have argued in the following way (Mutahhari 1373 H.):

(i) The denial of the principle of causality in the microworld would mean defacing this principle in relation to the whole world, because causality holds the whole universe together. As Shabistari, the Persian mystic, put it:

If you remove a single piece out of its place the whole universe tumbles down

(ii)The generalization of the results of a limited number of experiments to general laws is only meaningful if the principle of causality holds. Planck elaborated on this view (Planck 1959):

Of course it may be said that the law of causality is only after all a hypothesis. If it be a hypothesis, it is not a hypothesis like most of the others, but it is a fundamental hypothesis because it is the postulate which is necessary to hive sense and meaning to the application of all hypothesis in scientific research. This is because any hypothesis which indicates a definite rule presupposes the validity of the principle of causation.

(iii)The impossibility of prediction in atomic domain results from our ignorance about the deterministic laws governing the microworld. This could be due to our lack of necessary experimental tools or due to the immeasurability of the effects of the observer on the experiment. (iv) The denial of the principle of causality amounts to the denial of reasoning. Because a proof is the cause of our accepting the desired result, and if the tie between the proof and the result were non-essential, the proof could not end in the result. In this case nothing would be the result of a proof and any proof might lead to any result. In short, science has to accept the principle of causality in order that its existence could be meaningful.

References

Al-Ghazali, A. M. 1997. The Incoherence of the Philosophers, Utah: Brigham Young University, 170

Bell. J. B. 1966. Reviews of Modern Physics, 38, 447.

Benagem, T. 1993. ’Struggle with Causality’, Science in Context, 6. 1, 306.

Bergman, H. 1929. ’The Controversy Concerning the Law of Causality in Contemporary Physics’, in Boston Studies in the Philosophy of Science, 13, 1974. Dordrecht: D Reidel, 426.

Bohm, D. 1952. Physical Review 85, 160 and 180.

Bohr, N. 1935. ’Can Quantum Mechanical Description of Reality be Considered Complete’, Physical Review, 48, 696-720.

Born, M. 1944. Natural Philosophy of Cause and Chance, Oxford: Oxford University Press, 3-4.

Born, I. (trans.) 1971. The Born Einstein Letters, London: Macmillan, 276.

Buckley, P. et al. (eds.). 1979. A Question of Physics, London: Routledge & Kegan Paul.

Bunge, M. 1979. Causality and Modern Science, New York: Dover, 328.

Einstein, A. et al. 1935. ’Can Quantum Mechanical Description of Reality be Considered Complete?’, Physical Review 47, 777-80.

Harding, K. 1993. ’Causality Then and Now: al-Ghazali and Quantum Theory’, American Journal of Islamic Social Sciences 1, 2, 165-177.

Holton, G. 1980. ’Einstein’s Scientific Program: The Formative Years’ in H. Woolf (ed.), Some Strangeness in Proportion, Mass.: Addison Wesley Pub. Co., 65.

Jaki, S. 1989. God and the Cosmologists, Edinburgh: Scottish Academic Press, 151

Jaki, S. 1992. The Relevance of Physics, Edinburgh: Scottish academic Press, 480.

Jammer, M. 1973. ’Indeterminancy in Physics’, in P. P. Winer (ed.), Dictionary of the History of Ideas, New York: Charles Scribner’s Sons, Vol. 2, 589.

Jammer, M. 1974. The Philosophy of Quantum Mechanics, New York: Wiley – Interscience, 77-78. Margenau, H. et al. 1961. ’Correlation between Measurements in Quantum Theory’, Progress in Theoretical Physics 26, 722-738.

Mautner, T. 1996. A Dictionary of Philosophy, Oxford: Blackwell Pub., 104.

Mutahhari, M. 1373 H. Majmue Athar (Collected Works in Persian), Tehran: Intesharat-e Sadra, Vol. 6, 686.

Planck, M. 1959. The New Sciences, USA: Meridian Books, 104

Popper, K. 1980. The Logic of Scientific Discovery, London: Hutchinson, 249.

Popper, K. 1982. Quantum Theory and the Schism in Physics, London: Hutchinson.

Popper, K. 1986. Objective Knowledge, Oxford: Oxford University Press, 218.

Progovecki, E. 1967. ’On a Theory of Measurement of Incompatible Observables in Quantum Mechanics’, Canadian Journal of Physics 45, 2173-2219.

Russell, B. 1961. Religion and Science, New York: Oxford University Press, 160-168.

Russell, B. 1989. Mysticism and Logic, London: Unwin Paperbacks, 173.

Sadra al-Din Shirazi, M. 1981. al-Hikmah al-Mutaaliyah fi al-Asfar al-Aghliyah al-Arbaah, Beirut: Dar Ihya al-Turath al-Arabi, Vol. 6, 371-372.

Schillp, A. (ed.). 1969. Albert Einstein: Philosopher-Scientist, La Salle, Ill.: Open Court, 671. ’t Hooft. G. 1997. In Search of the Ultimate Building Blocks, Cambridge: Cambridge University Press, 14-15.

von Newmann, J. 1955. Mathematical Foundations of Quantum Mechanics, trans. By R. T. Beyer, Princeton: Princeton University Press.

Wheeler, J. et al. 1983. Quantum Theory and Measurement, Princeton: Princeton University Press.

Original paper from Studies in Science and Theology (8/2001-2002, ESSSAT).