Science and Transcendence: An Excerpt from Creative Tension
Limits of Language and Common Sense
We all are realists. If we were not, the surrounding world would soon destroy us. We must take seriously information given us by our senses. If, when crossing the street, we looked for extrasensory inspiration instead of watching the traffic lights, we would have been very quickly eliminated from this game. Poets and philosophers seem odd and impractical to others because abstract worlds of ideas divert their sight from earthly things. From our everyday contacts with the surrounding world (but also from many slips and bruises) our common sense is bornâ€”that is, the set of practical rules that tell us how to behave in order to minimize the damage the world could inflict upon us.
We like to quote science to justify our common sense. The scientific method is but a sharpening of our common sense. Experience constitutes the base of every science, and measuring instruments we use in our laboratories are â€œprolongationsâ€ of our senses. The world of technology, from the computer on my desk to artificial satellites, testifies to the ability of our common sense, which has so efficiently conquered the world of matter.
Such views, although flattering to our ears, are totally false. Widely spread imaginings concerning science do not match what science really is. Contemporary physics, this most advanced of all sciences, provides us an example fatally destroying these imaginings.
What could be more in agreement with our common sense than the fact that we cannot go back to our childhood? Time is irreversible. It flows irrevocably from the past to the future. However, this is not that obvious in physics. We know that to every elementary particle there corresponds an antiparticle. Such an antiparticle has the same mass as the corresponding particle but the opposite electric charge. When a particle collides with its antiparticle, they both change into energy. These are the experimental facts, but the first information about the existence of antiparticles came from theory. Since 1926 it has been known that the motion of an electron is described by the SchrÃ¶dinger equation. The discovery of this equation by SchrÃ¶dinger was a major breakthrough. Together with the works of Heisenberg, it has created the foundations of modern quantum mechanics. However, the SchrÃ¶dinger equation had a serious drawback: it did not take into account the laws of special relativity discovered by Einstein two decades earlier. Einsteinâ€™s theory is a physical theory of space and time. Although we can ignore it when dealing with the first approximation to the real world, if we want to be more precise in our investigation of the world we cannot avoid using a relativistic approach. The relativistic counterpart of SchrÃ¶dingerâ€™s equation was discovered by Dirac in 1928. It turned out that Diracâ€™s equation admitted two types of solutions. One of these types described well the elementary particles known at the time. The remaining solutions referred to similar particles but going back in time. How should this be understood? Dirac was audacious enough to claim that such particles really existed and coined the name â€œantiparticles.â€ This step was not an easy one. Our common sense had to be put upside down. To make this step easier, Dirac helped his imagination with the picture of the void with holes in it, and he interpreted these holes as antiparticles. It does not matter whether we would prefer holes in the void or time flowing backward; our common sense is jeopardized.
Let us consider another example. An atom emits two photons (quanta of light). They travel in two different directions, and, after a certain lapse of time, they are far away from each other (it does not matter how far; they can even be at two opposite edges of the Galaxy). Photons have the property called spin by physicists. It can be measured, and quantum mechanics teaches us that the results of the measurements can assume only two values. Let us denote them symbolically by +1 and â€“1. However, the situation is much more delicate than our inert language allows us to express. Strictly speaking, we cannot claim that an electron possesses the spin in such a manner as we say that Mr. Smith is tall or has twenty dollars in his pocket. When we are measuring the photonâ€™s spin, it behaves as if it were always there. In fact, before the act of measurement, the photon had no spin. Before the act of measurement, a probability existed that the act of measurement would yield, if performed, a given result with a given probability. Let us assume that we have performed the measurement obtaining the result +1. In such a case, on the strength of the laws of quantum mechanics, another photon acquires spin â€“1, even if it is at the other edge of the Galaxy. How does this photon instantaneously know about our measurement on the first photon and the result it yields?
This experiment was invented as a purely Gedanken experiment by Einstein, Podolsky, and Rosen in 1935 in order to show that the laws of quantum mechanics lead to nonsensical conclusions. However, the physicistsâ€”against the opinion of Einstein and his two collaboratorsâ€”were not much surprised when Allain Aspect, together with his team, performed Einsteinâ€™s Gedanken experiment in reality, and it has turned out that quantum mechanics was right. Aspect was able to perform this experiment owing to enormous progress in experimental methods, but also owing to a theoretical idea of John Bell that enabled him to express Einsteinâ€™s intuitions in the form of precise formulae (the so-called Bell inequalities), which could be compared with the results of measurements.
What happens to photons in Aspectâ€™s experiments? When our intuition fails, we must look for help from the mathematical structure of the theory. In quantum mechanics, two photons that once interacted with each other are described by the same vector of state. Strictly speaking, positions of elementary particles behave like spin; an elementary particle is nowhere in space until its position is measured. The state vector of a given quantum object contains information only about probabilities of outcomes of various measurements.
We are met here not only with particles that live â€œbackward in timeâ€ but also with particles for which space distances are no obstacles. It looks as if elementary particles did not exist in space and timeâ€”as if space and time were only our macroscopic concepts, the usual meaning of which breaks down as soon as we try to apply them to the quantum world. Moreover, can one speak about the individuality of a particle (before its properties are measured) that exists neither in space nor in time? If we agree to consider as a single object something that is described by a single vector of state, could we treat two photons (which previously interacted with each other) situated at two different edges of the Galaxy as the single object?
Contemporary physics has questioned the very applicability to the quantum world of such fundamental concepts as space, time, and individuality. Is not our common sense put upside down?
Some philosophers claim that what cannot be said clearly is meaningless. The intention of this claim is praiseworthy; its aim is to eliminate verbosity, which does not contain any substance. However, modern physics has taught us that the possibilities of our language are limited. There are domains of realityâ€” such as the quantum worldâ€”at the borders of which our language breaks down. This does not mean that within such domains anything goesâ€”far from it. It turns out that mathematics constitutes a much more powerful language than our everyday means of communication. Moreover, mathematics is not only a language that describes what is seen by our senses. Mathematics is also a tool that discloses those regions of reality that without its help would forever remain inaccessible for us. All interpretational problems of modern physics can be reduced to the following question: How can all these things that are disclosed by the mathematical method be translated into our ordinary language?
I think that the greatest discovery of modern physics is that our common sense is limited to the narrow domain of our everyday experience. Beyond this domain a region extends to which our senses have no access.
The world of classical mechanics seemed simple and obvious, but in fact it never was simple or obvious. The method discovered by Galileo and Newton did not consist in performing many experiments with pendulums and freely falling bodies, the result of which would later be described with the help of mathematical formulae. Newton, led by his genius, posed a few hazardous hypotheses that suggested to him the mathematical shape of the laws of motion and those of universal gravity. His formulae did not describe the results of experiments. Nobody ever saw a particle uniformly moving to infinity because it was not acted upon by any forces. Moreover, there is no such particle in the entire Universe. And it is exactly this statement that is at the very foundations of modern mechanics.
The world of classical mechanics is doubtlessly richer than the world we penetrate with our senses. The most fundamental principle of physics was discovered within the domain of classical mechanicsâ€”a principle that could be reached only by mathematical analysis. It is called the principle of the least action, and its claim is indeed extraordinary. It asserts that every physical theoryâ€” from classical mechanics to the most modern quantum field theoryâ€”can be constructed in the same way. First, one must correctly guess a function called Lagrangian (which is different for different theories). Then, one computes an integral of this function, called action. And finally, one obtains the laws of this theory by postulating that the action assumes the extreme value (usually the least one, but sometimes the greatest one). Physicists often speak about a superunification of physics, that is, about such a theory that would contain everything in itself. We do not yet have such a theory, but its chances that we will are becoming greater and greater. In fact, we already have, in a sense, the unification of the method; all major physical theories are obtainable from the principle of the least action.
With our senses we cannot grasp the fact that all bodies around us move in such a way that a certain simple mathematical expression (the action) assumes the minimal value. But the bodies move in this way. We live surrounded by things that cannot be seen, or heard, or touched. It was SchrÃ¶dinger who once asked himself: Which achievements of science have best helped the religious outlook of the world? In his answer to this question he pointed to the results of Boltzmann and Einstein concerning the nature of time. Time, which can change its direction depending on the fluctuations of entropy, which can flow differently in different systems of reference, is no longer a tyrant Chronos, whose absolute regime destroys all our hopes for nontemporal existence, but a physical quantity with a limited region of applicability. If SchrÃ¶dinger lived today, he could add many new items to his list of achievements that teach us the sense of Mystery. Personally, I think, however, that particular scientific achievements do not do this work best, but rather the scientific method itself. Spectacular results of the most recent physical theories are but examples of what was present in the method of physics for a long time, although it was understood only by a very few.
Two Experiences of Humankind
If we pause for a moment, in our competition for new achievements, to look backward on the progress of science during the last two centuries, we can see an interesting regularity. In the nineteenth century humankind went through the great experience of the efficiency of the scientific method. It was a deep experience. Today, we speak of the century of â€œvapor and electricityâ€ with a touch of irony in our voice. We must know, however, that the road from a candle to the electric bulb, and from a horse-drawn carriage to the railroad train, was longer and more laborious than that from the propeller plane to the intercontinental jet. In the twentieth century technology made a great jump, but in the nineteenth century it had started almost from nothing. But even then it was obvious that it would change the shape of the civilized world. In the nineteenth century technology was treated, like never before or after, as a synonym of progress and of the approaching new era of overwhelming happiness. Positivistic philosophy, regarding science as the only valuable source of knowledge, and scientism, wanting to replace philosophy and religion with science, could be considered as a philosophical articulation of this great experienceâ€” the experience of the efficiency of the scientific method. In the nineteenth century, any suggestion that there could exist any limits beyond that the scientific method does not work, would have been regarded as a senseless heresy. Nobody would have taken it seriously.
The nineteenth century came together with its wars and revolutions. In my opinion, the revolution that took place in the foundations of physics, in the first decades of the twentieth century (and which, I think, is still taking place), had more permanent results for our culture than the political turmoil that shaped the profile of our times. First of all, it turned out that classical mechanicsâ€” once believed to be the theory of everythingâ€”in fact has but a limited field of applicability. It is limited on two sides: from belowâ€”in the domain of atoms and elementary particles the Newtonian laws must be replaced by the laws of quantum mechanics; and from aboveâ€”for objects moving with a speed comparable to that of light, classical physics breaks down and should be replaced by Einsteinâ€™s theory of relativity. Moreover, the new theories are also, in a sense, limited: the finite value of Planckâ€™s constant essentially limits the questions that can be asked in quantum physics, and the finite velocity of light determines horizons of the information transfer in the theory of relativity and cosmology.
The method physics used from the times of Galileo and Newton (and possibly even from the time of Archimedes) consists in applying mathematics to the investigation of the world. The certainty of mathematical deductions is transferred to physics, and it is one of the two sources of the efficiency of the physical method (the other one being controlled experiment). It came as a shock when, in the third decade of the twentieth century, Kurt GÃ¶del proved his famous theorems which assert that limitations are inherent in mathematics itself: no system of axioms could be formulated from which entire mathematics could be deduced (or even a part of mathematics that is at least as rich as arithmetic). Such a system would be either incomplete or self-contradictory.
Today, there is no doubt that the twentieth century has confronted us with the new great experienceâ€”the experience of limitations inherent in the scientific method. Philosophers have understood this relatively late. In the first half of the twentieth century, positivism, in its radical form of the logical empiricism, dominated the scene. Only in the 1960s did it become evident that one cannot philosophically support an outdated vision of science. I do not here have in mind those anti-scientific and anti-intellectual currents that nowadays so often fanatically fight science in the name of supposed interests of humanity. I have in mind a philosophy of science that recognizes the epistemological beauty of science and its rational applications in the service of man, but does this based on the correct evaluation of both scientific method and the limitations inherent in it.
Science and Transcendence
Science could be compared to a great circle. The points in its interior denote all scientific achievements. What is outside the circle represents not-yet discovered regions. Consequently, the circumference of the circle should be interpreted as a place in which what we know today meets with what is still unknown, that is, as a set of scientific questions and unsolved problems. As science progresses, the set of achievements increases and the circle expands; but, together with the area inside the circle, the number of unanswered questions and unsolved problems becomes bigger and bigger. It is historical truth that each resolved problem poses new questions calling for new solutions.
If we agree to understand the term transcendenceâ€”as suggested by its etymologyâ€” as â€œsomething that goes beyond,â€ then what is outside the circle of scientific achievements is transcendent with respect to what is inside it. We can see that transcendence admits a graduation: something may go beyond the limits of this particular theory, or beyond the limits of all scientific theories known till now, or beyond the limits of the scientific method as such. Do such ultimate limits exist?
Usually three domains are quoted as forever inaccessible to all attempts of the mathematico-empirical method: the domain of existence, the domain of ultimate rationality, and the domain of meaning and value.
How does one justify the existence of the world? Why does something exist rather than nothing? Some more optimistic physicists believe that in the foreseeable future one will be able to create the Unique Theory of Everything. Such a theory would not only explain everything, but it would also be the only possible theory of that type. In this way, the entire Universe would be understood; there would be no further questions. Let us suppose that we have such a theoryâ€”the set of equations fully describing (modeling) the Universe. One problem would remain: How can one change from the abstract equations to the real world? What is the origin of those existents that are described by the equations? Who or what ignited the mathematical formulae with existence?
Science investigates the world in a rational way. Knowledge is rational if it is rationally justified. Here new questions arise: Why should we rationally justify our convictions? Why is the strategy of rational justifications so efficient in investigating the world?
One cannot give a rationally justified answer to the first of these questions. Let us try doing this; that is, let us try to rationally justify the statement that everything should be rationally justified. However, our justification (our proof ) cannot presuppose what it is supposed to justify (to prove). Therefore, we cannot assume that our convictions should be rationally justified. Consequently, when constructing our proof we cannot use rational means of proving (because they presuppose that we are to prove something); that is, the proof cannot be carried out.
There is no other way out of this dilemma but to assume that the postulate to rationally justify our convictions is but our choice. We have two options, and we must choose one of them: either, when doing science, we do it in a rational way or we admit an irrational way of doing science. Rationality is a value. This can be easily seen if rationality is confronted with irrationality. We evaluate rationality as something good and irrationality as something bad. When choosing rationality we choose something good. It is, therefore, a moral choice. The conclusion cannot be avoided; at the very basis of science there is a moral option.
This option was made by humankind when it first formulated questions addressed to the world and started to look for rationally justified answers to them. The entire subsequent history of science could be regarded as a confirmation of this option.
Now follows the second question: Why is the strategy of rational justifications so efficient in studying the world? One could risk the following answer: The fact that our rational methods of studying the world lead to such wonderful results suggests that our choice of rationality is somehow consonant with the structure of the world. The world is not a chaos but an ordered rationality. Or: the rational method of science turns out to be so efficient because the world is permeated with meaning. We should not understand this in an anthropomorphic manner. Meaning, in this context, is not something connected with the human consciousness; it is this property of the world because of which the world discloses its ordered structure, provided it is investigated with the help of rational methods.
SchrÃ¶dingerâ€™s Question Once More
After all these considerations, it would be worthwhile to go back to SchrÃ¶dingerâ€™s question: Which achievements of science have best helped the religious outlook of the world? I think that contemporary science teaches us, as never before, the sense of mystery. In science, we are confronted with mystery on every step. Only outsiders and mediocre scientists believe that in science everything is clear and obvious. Every good scientist knows that he is dancing on the edge of a precipice between what is known and what is only feebly felt in just-formulated questions. He also knows that the newly born questions open vistas that go beyond the possibilities of our present imaginationâ€”imagination that has learned its art in contact with these pieces that we had so painfully extracted from the mysteries of the world.
Let us imagine a very good scientist of the nineteenth century, for instance, Maxwell or Boltzmann, who is informed by his younger colleague coming to him from our twenty-first century about recent developments of general relativity or quantum mechanics. Maxwell or Boltzmann would never believe in such â€œnonsense.â€ Now consider this question: How would we behave if a physicist from the twenty-second century told us about his textbook physics? Only a very shortsighted scientist can be unaware of the fact that he is surrounded by mysteries.
Of course, I have in mind relative mysteries, that is, such mysteries as now go beyond the limits of our knowledge but perhaps tomorrow will become well-digested truths. Do not such mysteries point toward the Mystery (with the capital M)? Does not what today transcends the limits of science suggest something that transcends the limits of all scientific methods?
I have expressed these ideas in the form of questions on purpose. Plain assertions are too rigid; they assert something that is expressed by its words and syntactic connection between them, but remain silent about what is outside the linguistic stuff. Therefore, let us stick to questions that open our intuition for regions not constrained by grammatical rules. Are these unimaginable achievements of science, which revolutionize our vision of the world (time flowing backward, cured space-time, particles losing their individuality but communicating with each other with no interaction of space and time), not clear suggestions that the reality is not exhausted in what can be seen, heard, touched, measured, and weighed?
- Does not the fact that there exists something rather than nothing excite our metaphysical anxiety?
- Does the fact that the world is not only an abstract structureâ€”never a written formula, an equation solved by nobody, yet something that can be seen, heard, touched, measured, and weighedâ€”direct our thought to the Ultimate Source of Existence?
- Does not the fact that the world can, after all, be put into abstract formulae and equations suggest to us that the abstract thought is more significant than concrete matter?
- Does the rationality that is presupposed but never explained by every scientific investigation not express a reflection of the rational plan hidden in every scientific question addressed to the Universe?
- Does not the moral choice of the rationality that underlies all science offer a sign of the Good that is in the background of every correct decision?
These questions are not situated far away, â€œbeyond the limits.â€ The concreteness of existence, the rationality of the laws of nature, the meaning touched by us when we make our decisions are present in every atom, in every quantum of energy, in every living cell, in every fiber of our brain.
It is true that the Mystery is not in the theorems of science but in its horizon. Yet this horizon permeates everything.
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