## Lecture 6: Relativity and Quantum Physics

### 6.1. Introduction

In the nineteenth century, it seemed to many that physics was essentially complete. Newton's laws of dynamics enabled the motions of the moon and the planets to be calculated precisely, and Maxwell's equations performed a similar function for electric and magnetic phenomena. A few things were still obscure, but doubtless they would soon be cleared up with little trouble.

There was no expectation that in a very few years around the turn of the century a series of fundamental discoveries would be made that decisively altered our understanding of the world. Becquerel discovered radioactivity, and this led to Rutherford's discovery of the nucleus of the atom and hence to nuclear physics. Einstein formulated his special theory of relativity that went beyond Newton and altered our conceptions of space and time. Planck discovered the quantum and this led in the nineteen twenties to the formulation of quantum mechanics. The era of classical physics was over and modern physics took its place.

Modern physics has changed the way we think about nature and about ourselves, and this has not been without its effects on theology. The result has been 'A radical questioning of such ideas as providence, moral freedom and responsibility, or the possibility of change under the influence of God' (from 'We Believe in God'. The Doctrine Commission of the General Synod of the Church of England, Church House Publishing, 1987).

What exactly is the nature of this influence of modern physics on theology? It is not possible to deduce any theological consequences from scientific theories, although the word implication is sometimes used in this context. Both by their nature and by their subject matter, scientific theories can have no theological implications. They can however suggest new ways of looking at things, can give us a deeper and wider view of the world, and this can lead us to look at our theology in a new way. Our ideas and concepts are stretched and developed by the need to describe the new physics, and these ideas and concepts may find application in theology. This happened when Aristotelian concepts of matter and form were used extensively in medieval theology; is there any counterpart today?

We will start by considering the impact of Einstein's relativity.

### 6.2. Einstein's theory of relativity.

The fundamental principle underlying the theory of relativity it that the laws of nature always have the same form for all observers. This follows from our belief that there are laws that describe, precisely and mathematically, the connections between causes and effects. This invariance of the laws of nature sometimes called the principle of covariance, or the principle of relativity. It says that the laws of nature are completely objective, and do not depend on who is looking at the phenomena or from what vantage point.

Einstein began by asking himself a very simple question: What would a light wave look like to someone who is travelling alongside it? It was known that a light wave is an electromagnetic wave that is described by Maxwell's equations, so he looked for a solution of these equations that describe a stationary light wave, and found that there is none. However we describe a light wave, it is always moving with the speed of light.

This led him to study very carefully the transformation equations that relate the spatio-temporal co-ordinates of events in one frame of reference to those in another frame moving with constant velocity with respect to the first. It had always been assumed to be obvious that these transformation equations are those due originally to Galileo. Furthermore, it was also considered obvious, according to the principle of relativity, that our description of phenomena should give the same result whichever reference frame we use. Einstein realised that Maxwell's equations do not satisfy this condition; they are not invariant under the Galilean transformation.

So he asked himself what the transformation would have to be to ensure that the light wave looks the same to all observers, whatever their relative velocities. This was already known to be the Lorentz transformation. He then asked what would be the consequences of assuming that the Lorentz transformation applied to all phenomena, not just to light waves, and found that this enabled him to explain many apparently anomalous results, such as that of the Michelson-Morley experiment.

Closer examination shows that the Lorentz transformation may be derived many different ways from apparently quite simple assumptions. It is, fundamentally, much more natural than the Galilean transformation. With suitable relativistic definitions, other physical quantities like energy and momentum also transform by the Lorentz transformation.

This has several consequences that are contrary to our normal intuitions. If we measure the velocity of light from a moving source, we get the same result as that from a stationary source. Velocities no longer add arithmetically. This is appreciable only for very high velocities, comparable to that of light. At lower velocities the Lorentz transformation reduces to the Galilean transformation, and that is why until then the effects due to the difference between the two transformations, called relativistic effects, had not been noticed.

The notion of simultaneous events is altered by relativity. Events that are simultaneous in one frame of reference are no longer always so in another; it depends on the relative velocity between the observer and the events.

The strangeness of all this took hold of the public imagination and soon people were saying that Einstein had shown that everything is relative. The then Archbishop of Canterbury, Randall Davidson, was told by Lord Haldane that "relativity was going to have a great effect on theology, and that it was his duty as head of the English Church to make himself acquainted with it". The Archbishop took this advice seriously, obtained several books on the subject, and tried to read them. He did not have much success in his attempts to understand relativity, and indeed was driven to a state of intellectual desperation. He therefore asked Einstein what effect relativity would have on religion, and was told: "None. Relativity is a purely scientific matter and has nothing to do with religion." So that was that.

The Archbishop comes out of this story rather well. In the first place he actually listened to what he was told, and went to the trouble of getting some books on relativity and trying to understand what it was all about. He made the usual assumption that any highly-educated arts man can in a few hours master any scientific subject, but soon realised his mistake. Then instead of forgetting about the whole matter, he asked a scientist for his advice, and chose a scientist who really knew about the subject. If only his example were followed today, we would be spared the acutely embarrassing spectacle of Churchmen and Churchwomen moralising on scientific and technical matters without having understood the first thing about them.

In spite of the Archbishop's example, the popularity of the theory of relativity among the general public, reinforced by the image of Einstein as the typical scientist, gave impetus to the idea that physics is relative, and thence that everything is relative. If Einstein had called his work the theory of invariance we would perhaps have been spared this nonsense.

### 3.3. Quantum Mechanics

The greatest change in our understanding of the world is due to the development of quantum mechanics. For many decades now it has proved itself to be an outstandingly successful theory. It is used by all atomic and nuclear physicists, and is the only known way of calculating what we want to know. And yet, despite this success, there is still continual controversy about its interpretation, symptomatic of a deep though confused recognition that all is not well. It shows once more that there are deep beliefs about the material world that underlie all our sciences, and that the price of neglecting them is not only conceptual confusion but harm to the progress of science itself.

Quantum mechanics was born at a time when physicists despaired of ever understanding the atomic world. It did not seem to be possible to understand the structure of the atom in terms of the particles and waves of classical physics. Bohr's model of the atom was remarkably successful in predicting the hydrogen spectrum, but at the price of assuming that between transitions the electrons remain in stable orbits. But how could this be, since Maxwell's equations show that an accelerated charge continually radiates, and so the electron must rapidly spiral into the nucleus? The anguish was very real. Pauli was so upset that he once said that he wished he had become a movie comedian instead of a physicist. It was with a sense of great relief that physicists heard of the work of Heisenberg and Schrodinger, who gave them a mathematical method for calculating the results of experiments. At last it was possible to move forward again, although there still remained the apparent contradiction between the classical electromagnetic theory and the new quantum mechanics. The distress was poignantly expressed by H.A. Lorentz, one of the greatest of the classical physicists, in 1924: "I lost the certitude that my scientific work was bringing me closer to objective truth, and I no longer know why I continue to live. I am only sorry not to have died five years ago, when everything appeared clear."

The formalism of quantum mechanics proved to be an exceedingly powerful tool; but what did it mean? How could one think about atomic processes in a physical way? It did not provide an answer to many obvious questions. Bohr and Heisenberg stilled these doubts by emphasising that what is important in physics is to have a way of calculating the results of experiments; all else is superfluous. According to Bohr, "physics is not about the world, it is about the way we think about the world." This was echoed by Heisenberg: "the laws of nature which we formulate mathematically in quantum theory no longer deal with the particles themselves but with our knowledge of the elementary particles". They further maintained that "quantum mechanics was the last, the final, the never-to-be-surpassed revolution in physics". Thus "physics has reached the end of the road; that a further breakthrough is no longer possible, although, of course. Much is still to be done by way of elaboration and application of the new quantum mechanics. This view was developed into what is now known as the Copenhagen Interpretation of quantum mechanics, which is to be found in practically every textbook, and is taught to all students. It may be noted that, as Stuart has observed, "Because the predictive success had been established before the Bohr-Heisenberg scheme was introduced, it cannot be that this success depends on that scheme: conversely, it follows that the predictive success of quantum mechanics does not constitute a test of the Bohr-Heisenberg scheme".

The main features of the Copenhagen interpretation are:

1. The completeness postulate that the wave function completely specifies what can be known about a quantum state.

2. The superposition principle that a quantum state represented by a linear superposition of allowable quantum states is itself an allowable quantum state.

3. The Heisenberg uncertainty principle.

4. The probability interpretation of the wave function.

5. The principle of inseparability that the object under investigation is inseparable from the experimental apparatus used to observe it.

6. The principle of complementarity.

7. The correspondence principle.

The first great success of quantum mechanics was Gamow's explanation of radioactive decay. He was able to show how the half-life depends on the energy, using the concept of tunnelling. The mathematics is so simple that we fail to notice the conceptual difficulties. We do not of course believe that the tunnels are real; we calculate the attenuation of the wave as it passes through the potential barrier. As soon as it emerges, it is a particle with a definite trajectory that we can see in a cloud chamber or detect with a counter. Yet how can the alpha-particle be first a wave and then a particle? Students who raise such questions are told to concentrate on the mathematics and not to waste their time on fruitless philosophical speculation.

Radioactive decay also raises problems about causality. According to the Copenhagen Interpretation, all nuclei of the same type are identical. All possible information that can be obtained from measurements is contained in the wavefunction, and this gives only the probability of decay per unit time. So why does a particle decay at one time and not at another? According to the Copenhagen Interpretation, there is no answer to this question, so there is a basic indeterminacy in quantum mechanics.

This is reinforced by Heisenberg's Uncertainty Principle, which is generally understood to say that the product of the uncertainties in the measurements of the position and the momentum of a particle is always greater than Planck's constant. Similar relations hold for other pairs of variable such as energy and time. The more accurately we measure one of these variables, the less accurate is the result of our measurement of the other variable. This is sometimes taken to mean that particles do not have a definite position and momentum. Heisenberg concluded that "since all experiments are subjected to the laws of quantum mechanics the invalidity of the law of causality is definitely proved by quantum mechanics."

The double slit experiment is used to demonstrate the paradoxical nature of the quantum world. With both slits open, we find interference. So the electron must be a wave when it passes through the slits, but then it becomes a particle again when it hits a definite point on the screen. It is natural to ask just what happens at the slits. If the electron is a wave, then does half the electron go through one slit and half through the other? If the electron is a particle, then it must pass through just one of the slits, so then why do we find an interference pattern and not just the superposition of two single-slit diffraction patterns? The interference depends on the presence of two slits, so how can the passage of the particle through one slit be affected by whether the other slit is open or not? A student who asks such questions is told that since there is no way of answering them experimentally (since the insertion of a detecting apparatus in one of the slits would destroy the interference pattern) they are meaningless and so must not be asked.

According to the Copenhagen Interpretation, the motion of the electron is described by its wavefunction and this contains all that can be known about it. When we make a measurement, the wavefunction collapses and the electron is found at a definite point on the screen. It is not made clear how we make the wavefunction collapse, or what physical process takes place when it does.

Until the advent of quantum mechanics, most physicists believed that we are investigating a real external objective world that exists independently of ourselves. Instinctively we still believe this, until we are asked about quantum mechanics, when most of us shift gear uneasily and start talking about the Copenhagen Interpretation. Most students accept this, as they are accustomed to believing anything they are told about physics, however paradoxical. There is however a more perceptive minority that is caused acute distress by what they are told to believe. In any other context, they would laugh it out of court, but since they are told these stories by their lecturers they cannot do this. It is not unknown for such students to abandon physics entirely.

There are several possible reactions to this situation. One can simply say that quantum mechanics provides us with the means to calculate everything we can measure, so what more do we want? The rest is just useless philosophical speculation that can be left to those who have nothing better to do with their time. To this one can reply that conceptual clarity is important in physics, as it can help us to see the way ahead to new discoveries. Furthermore, there is evidence that the present situation is actually impeding the progress of physics.

What then is the alternative? Can we make sense of the quantum world? Right from the beginning, Einstein refused to accept the Copenhagen Interpretation, and always believed that "the belief in an external world independent of the perceiving subject is the basis of all natural science." In a correspondence with Max Born, he declared: "You believe in the God who plays dice, and I in complete law and order in a world that objectively exists and which I, in a wildly speculative way, am trying to discover". He believed that quantum mechanics, successful though it undoubtedly is, constitutes just one step on the long road of our efforts to understand the world. The wavefunction tells us the average behaviour of an ensemble of systems, not all that we can know about a single system. Nature is much richer than we know and there is a microstructure still undiscovered whose average behaviour is what we measure and calculate by quantum mechanics. One day we may find ways of measuring these "hidden variables".

Einstein constructed several ingenious examples to demonstrate the incompleteness of quantum mechanics, but each time Bohr showed how quantum mechanics escapes from the net. Then von Neumann showed by very general arguments that there can be no hidden variables, and that seemed to destroy Einstein's view. However Bohm actually succeeded in constructing a hidden variable theory, and although it was generally considered to be of little practical use, its very existence showed that there is something wrong with von Neumann's proof. The flaw was found by Bell who realised that it only applies to a certain classes of hidden variable theories, but not to what are called stochastic hidden variable theories.

This provides the clue to the conceptual reformulation of quantum mechanics. It is essential to realise that there are no completely isolated physical systems. If there were, we could not study them. As it is, all physical systems are in continual interaction with their surroundings, and in particular are continually exposed to radiation from them. Thus we do not study isolated hydrogen atoms but ones bathed in a complete spectrum of electromagnetic radiation. This varies rapidly and irregularly both in frequency and amplitude, and although the exact way it does this is unknowable, we can calculate its statistical properties. This gives an extra term in the classical equation of motion of the hydrogen atom, yielding the Braffort-Marshall equation which may be solved to give the hydrogen spectrum. In this light, the Schrodinger equation is an ingenious formalism that implicitly takes into account the stochastic background radiation and enables the hydrogen spectrum to be calculated much more simply. This is called the stochastic interpretation of quantum mechanics.

Quantum mechanics thus refers not to each individual system but to the average behaviour of an ensemble of similar systems, and thus leaves open the possibility of attaining a detailed understanding of the behaviour of each individual system. The stochastic interpretation is a particular example of a wider class of interpretations that all share this property and are referred to as statistical interpretations. It should be noted that a critic of the Copenhagen Interpretation is not obliged to produce an alternative; indeed it is precisely the merit of such critiques that they leave open the details of the way to interpret quantum mechanics, and thus stimulate further work.

The stochastic interpretation can be applied to the other cases already mentioned. In the case of radioactive decay, the coupling between the nuclear and the radiation field perturbs the barrier so that its height fluctuates, thus allowing the particles of different energies to escape with the observed frequencies. A similar explanation makes it clear why particles are sometimes reflected by a potential barrier of lower energy than they have themselves.

The Heisenberg Uncertainty Principle refers to our measurements, not to the underlying realities, and it is unjustifiable to argue from our inability to measure exactly to a fundamental indeterminism. It is not even correct to say that measurements of the position and momentum cannot be made with greater accuracy than that specified by the Heisenberg Uncertainty Principle. This may be shown by considering single slit diffraction. We do indeed find out that as we vary the slit width (Ax) the spread of the diffraction pattern (hp) varies as well such that AxAp > h. It is however possible to measure the transverse momentum of each individual electron much more precisely. If we place a particle detector on the screen behind the slit we can determine the point of arrival of each electron, and hence we can calculate its transverse momentum with an accuracy much greater than that corresponding to the distribution as awhole. Thus while it remains true that we cannot predict the transverse momentum of the electron after it has passed through the slit, nevertheless subsequent measurements enable it to be determined to an accuracy much greater than specified by the Uncertainty Principle. Thus physics gives us no grounds for saying that the position and momentum of the electron are unknowable within the limits of the uncertainty principle, and still less that it does not have position and momentum.

In the double slit experiment, each electron is a particle whose trajectory takes it through one slit or the other. Its motion is influenced by whether the other slit is open or not through the stochastic field, which is influenced by the configuration of the slits. The wavefunction gives the probability distribution of the trajectories. The celebrated wave-particle duality is thus simply a category confusion. On the one hand we have particles moving along definite trajectories with definite momenta, and on the other we recognise that due to their interactions with the slits and with other matter and radiation these trajectories have a certain probability distribution calculable from Schrodinger's equation. The so-called wave nature of these particles is no more an intrinsic property than, for example, actuarial statements are intrinsic properties of a particular individual.

In all these experiments the quantum mechanical calculations are compared with the results of a large number or ensemble of measurements. The half-life of a radioactive decay can only be determined by measuring very many decay events, and the same applies to the interference pattern in the double slit experiment and the angular distribution in a scattering problem. The time of decay of a particular nucleus, or the point on the screen where one electron arrives, or the direction in which one particle is scattered, is of no scientific interest on its own. It is thus very natural to say with Einstein that quantum mechanics describes the behaviour of ensembles of similarly prepared systems, and gives only a partial account of the behaviour of each individual system. The very fact that quantum mechanics cannot tell us about the details of each individual system is a strong argument for supposing that it is an incomplete theory.

Since the wavefunction simply gives the probability of a system to be in a certain state the difficulties associated with the collapse of the wavefunction disappear. Probabilities are not material entities and so the very notion of collapsing is inapplicable.

Einstein's strongest argument for the incompleteness of quantum mechanics is given in his paper with Podolsky and Rosen. Bohr was only able to refute this by claiming that once two physical systems have interacted they always remain one system, however far apart they may subsequently move. This goes completely against the usual presuppositions of the physicist, besides violating special relativity. Although it was not possible actually to carry out the Einstein-Podolsky-Rosen experiment, a realisable version was proposed by Bell and carried out by Aspect and his collaborators. The results violated the Bell inequalities, and this is widely believed to support the Copenhagen Interpretation. However every derivation of the inequalities assume that when two successive measurements are made on a system, the result of the second measurement is not affected by the first. As this is contrary to quantum mechanics, it is not surprising that the Bell inequalities are violated.

Thus we see that adopting the statistical interpretation of quantum mechanics removes the conceptual paradoxes that plague the Copenhagen Interpretation. This by itself is a very great gain, but even more important it opens the way to further advances by showing the way to further research. It is clearly desirable to extend the calculations that explicitly take into account the stochastic background radiation. It is not yet clear how to obtain all the features of the hydrogen spectrum by solving the Braffort-Marshall equation, for example. At present there are few people working on such problems, mainly because of the prevailing belief in the Copenhagen Interpretation. If physics has indeed reached the end of the road as far as the quantum mechanical description of reality is concerned then there is no incentive, indeed there is a strong disincentive, to seek a deeper understanding, and this can discourage or block what might be fruitful lines of research. The futility of such work is so strongly believed among active scientists that to work in such areas is almost equivalent to professional suicide. At present, it is almost impossible to publish such work. It is conceivable that all efforts to go beyond quantum mechanics are doomed to failure, but there is no hope of finding this out if we never even try to go beyond it. It is certainly conceivable that at some stage the more detailed Formalism will give a prediction different from that of quantum mechanics, and then a real test would be possible. Should the result be positive, there is no doubt that the situation would change rapidly, and large numbers of physicists would rapidly start to explore the new field. It would not however imply that quantum mechanics is discredited, any more than Newtonian mechanics was discredited by the success of special relativity. It would mean that we had advanced one more step along Einstein's road. The vitally important need at present is not to hinder this progress.

There is good reason to suppose that the Copenhagen Interpretation already hinders research, by stifling questions that an innovative physicist naturally asks. A notable example occurred during the nineteen thirties, when Rutherford was trying to find the shell structure of the nucleus, following his successful work on the atom. He was however discouraged by Bohr who continually told him that the interior of the nucleus is a structureless soup and that it is thus meaningless to seek its structure. Rutherford's instinctive realism was gradually worn down by this, and eventually he gave up the search. We can now see that the experimental equipment available to Rutherford was not sufficiently precise to show the shell structure of the nucleus, but subsequently this was established beyond doubt.

This leads us to enquire about the philosophical basis of the Copenhagen Interpretation. Bohr was influenced by Hoffdung, and he and many of the founders of quantum mechanics worked in the intellectual climate of Machian sensationalism and the positivism of the Vienna circle. He did not state his position with philosophical precision, so there is much debate about his views. He appeared to take a positivistic view of the quantum world, while remaining a realist for the world of classical physics, a view that encounters difficulties about just where the boundary between them is to be drawn. It was thus very natural of them to admit only the results of measurements, and to say that all else is meaningless. Bohr was a very obscure writer, and in spite of many books on his philosophy, the judgement of Bell is that "nobody understands Bohr". Rather than trying to understand Bohr it is better, following Bohr himself, to try to understand nature.

Positivism is now widely abandoned in philosophical circles. Thus referring to logical positivism, Brian McGee asked A.J. Ayer: "But it must have had real defects. What do you now, in retrospect, think that the main ones were?" Ayer replied: "Well, I suppose the most important of the defects was that nearly all of it was false!' Unfortunately the news of the demise of positivism does not seem to have reached many members of the physics community.

On the statistical interpretation, the wavefunction gives the probability of the particle being in a certain place, so that there is no problem about the collapse of the wavefunction. The wavefunction gives our knowledge of the position of the particle. The Copenhagen Interpretation gives rise to serious difficulties, as shown by the story of Schrodinger's cat. Before we open the box, the cat is in a quantum mechanical superposition of states, one corresponding to it being alive and the other to its being dead. When I open the box, according to Copenhagen, I collapse the wavefunction, and at that time the cat becomes definitely either alive or dead. According to the statistical interpretation, the cat dies at a certain time whether we know about it or not, and when we open the box we find out what had already occurred. There is another consequence of the Copenhagen Interpretation that is less well-known. Suppose there is an observer outside the room that contains the box with the cat inside. If he cannot see into the room he does not know whether I have found the cat to be alive or dead, and so for him the wavefunction of the interior of the room contains both possibilities. It is only when he opens the door and looks into the box that his wavefunction collapses. Thus his wavefunction must be different from mine. I am the only person who can collapse my wavefunctions, and thus my science is unique to me. This solipsistic conclusion is radically opposed to the universal belief that scientists are all engaged on a common search to understand the same objective reality.

Working physicists have always used concepts that are not directly linked to measurements. Who, for example, has seen a quark or a black hole? This has been defended by J.J. Thomson: "I hold that if the introduction of a quantity promotes clearness of thought, then even if at the moment we have no means of determining it with precision, its introduction is not only legitimate but desirable. 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 knowledge."

Einstein himself in his early years was much influenced by Mach, but afterwards repudiated him in the strongest terms. He was not alone in opposing the Copenhagen Interpretation. In different ways, Planck, Schrodinger, Lande, Fermi and Dirac all spoke against it. Fermi early on expressed doubts about the validity of the Copenhagen Interpretation, criticising its tendency to "refrain from understanding things." This was echoed by Santos when he remarked that the Copenhagen interpretation hides rather than solves problems. Not long before he died Dirac said in a lecture that "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 are made in passing from Bohr's orbits to quantum mechanics . . . It might be that the new quantum mechanics will have determinism in the way that Einstein wanted. I think it is very likely, or at any rate quite possible, that in the long run Einstein will turn out to be correct, even though for the time being physicists will have to accept the Bohr probability interpretation -- especially if they have examinations in front of them." All these physicists bear witness to the radically unsatisfactory nature of the Copenhagen interpretation, and indeed its formal inconsistency has been demonstrated in detail by Stuart.

There is a very considerable body of research in the foundations of quantum theory that regards the Copenhagen interpretation with considerable reservation. For example, in the Epilogue to a Conference on "Open Questions on Quantum Physics" we read, with reference to the open questions in quantum mechanics "such an acknowledgement of unsolved conceptual problems in the foundations of microphysics is by contrast inadmissible within the purview of the stagnant philosophy of the Copenhagen Interpretation, which culminated in the absurd myth of the completeness of the quantum formalism". Thus "it therefore appears evident that a radical emancipation from the negative philosophy of the Copenhagen school is a necessary precondition if one is to look for a real solution of the main quantum paradoxes."

Physicists have not been slow in publicising the mysteries of the quantum world. These are fascinating enough, but the Copenhagen Interpretation has encouraged an even wider range of pseudo-mysteries. Some physicists, eagerly donning the mantle of the guru, have revelled in its paradoxes and have written many books on the wonders of the quantum world. Bohr led the way with his principle of complementarity, which played a useful heuristic role in the early days of quantum mechanics. He explained paradoxes like that of the double slit by saying that sometimes electrons are waves and sometimes particles, and that the two descriptions complement one another. One can thus look at phenomena in two ways, from the particle and wave viewpoints; these are contradictory but together they account for what we observe. He extended this idea far beyond physics, elaborating the idea that it is possible to have contradictory view of the same phenomena, each giving an important aspect of the truth. He applied it to free-will and determinism and enunciated the dictum that the opposite of a deep truth is another deep truth. This was naturally grist to the mills of those who try to bring peace to warring factions, and complementarity is now extensively used to reconcile irreconcilables in an atmosphere of confused goodwill.

Bohr's reply to the paper of Einstein, Podolsky and Rosen maintained that it two particles have ever interacted they remain ever after a single system. It has been suggested that the non-local interaction implied by this interpretation could be the basis of "an unstoppable and unjammable command-control-communication system at very high bit rates for use in submarine fleets." This is clearly a fantasy, since it is not possible to force a particle into a particular spin state.

Bohr, a great physicist and most lovable man, was led by his philosophical beliefs into elaborating a philosophy of quantum mechanics that is at variance with the belief in the reality of the material world that lies at the base of all scientific research. This was reinforced by the prevailing positivist climate among philosophers and came to be widely accepted. We can now see that this was a tragic mistake that is not only making it unnecessarily difficult for students to understand the quantum world, but is hindering the development of physics.

### 6.5. Conclusion

Modern physics has certainly altered the way we look at the material world, and has given us a more profound understanding of its structure. Many of the ideas associated with modern physics have taken on a life of their own, and have given rise to a wide variety of discussions in areas far removed from physics. It has been suggested that all is relative, that causality has been disproved, free-will vindicated and a way opened for the providence of God.

It is important to distinguish between the implications of modern physics, that is ideas that are its logical consequences, and ideas suggested by physics that are transported into another discipline; these should be validated by discussions within that discipline. As we have seen, it is very often a misunderstanding of a physical theory that is transported, and this makes it all the more necessary to analyse its validity in a new context. Even if it has been correctly understood, it must stand or fall on its own merits in its new context, and cannot appeal to physics for its justification.

There are several stages in scientific research that need to be carefully distinguished. First come the observations of the phenomena, followed by quantitative measurements. When many measurements have been made, it is often possible to identify certain regularities that can be economically described by a law. There are often several laws that describe different aspects of the phenomenon, and these may all be subsumed by a theory, from which the various laws can be deduced. The theory is not a deduction from the laws; it is a creation of the human mind, and as such it may be suggested by philosophical beliefs about the world or about how we find out about it.

The success of a theory is not a vindication of the philosophy that originally inspired it. There may well be other theories, based on other beliefs, that agree equally well with the experimental data. Furthermore, theories may be superseded by other theories that agree with a much wider set of data, as happened when Einstein's relativity superseded Newton's classical dynamics.

In other cases the same theory may be interpreted by several inconsistent philosophies, as quantum mechanics may be interpreted by realism and by positivism. It is thus not possible to deduce any philosophical conclusions from scientific theories.

This is not however to say that physics has no influence on philosophy. Ultimately the value of a philosophy that is used as the basis of science is shown by the results. If science flourishes, that is a good indication of the soundness of their underlying ideas: by their fruits you may know them.

What has been said of philosophy applies even more to theology. The deduction is not from the science to the theology but from the theology to the science. Indeed, as we have seen, modern science is based on Christian beliefs about the material world, and this is the only time in history that it has become a self-sustaining enterprise.

It is difficult to avoid the conclusion that all the discussions and books about theology and the new physics have yielded very little of value. Indeed it seems that the whole enterprise is fundamentally misconceived. One might then ask why there has been so much interest in the possibility of learning something from the new physics that is of great human significance.

The most plausible reason is the unquenchable desire for what is new. The latest scientific advances are so often written up by enthusiastic journalists who exaggerate their importance beyond all measure. You have only to pick up a few newspapers to find examples. What sells newspapers is sensation, horror, novelty, scandal and sex, and preferably a mixture of them all.

Why then do scientists so eagerly join the journalists in writing and lecturing about the wider implications of the latest discoveries? We all tend to think that our own speciality is of central importance and that its light should shine on all other human concerns. It is flattering for an expert in some arcane scientific speciality to be asked for his views on the future of mankind. He then finds that acting the guru is certainly more lucrative and less intellectually exhausting than scientific research.

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