The answer to the question “why has algebraic calculation become the paradigm of knowledge for our times” is not a proposition: it reveals a transformed basic position, or a transformation of the initial existing position towards things, a change of questioning and evaluation, of seeing and deciding, a transformation of what we are as human beings and what we think we are as human beings in the midst of what is. This transformation is a true paradigm shift.
We cannot use science to tell us what science is: we cannot conduct an experiment or use the other methodologies of the sciences to teach us what science itself is. The question concerning our basic relations to nature (including our own ‘human nature’, our own bodies), our knowledge of nature as such, our rule over nature is itself in question in the question of how we stand in relation to all the things that are. This questioning will lead to the ‘abyss’, and our response to our questioning can only come through discussions that will make us mindful of the implicit assumptions which we hold with regard to what we call knowledge.
In connection with the historical development of natural science, things become objects, material, and a point of mass in motion in space and time and the calculation of these various points. When what is is defined as object, as object it becomes the ground and basis of all things, their determinations as to what they are, and the kinds of questioning that determine those determinations. In TOK we call this grounding our “knowledge framework”. This “knowledge framework” is grounded in the principle of reason: nothing is without a cause, or nothing with reason (reasons). That which is animate is also here in this determination of object: nothing distinguishes humans from other animals or species (Darwin’s Origin of Species). Even where one permits the animate its own character (as is done in the human sciences), this character is conceived as an additional structure built upon the inanimate. This reign of the object as material thing, as the genuine substructure of all things, reaches into the area that we call the “spiritual”; into the sphere of the meaning and significance of language, of history, of the work of art, and all of the areas of knowledge of TOK. Works of art, poems, and tragedies are all perceived as “things”, and the manner of our questioning about them is done through “research”, the calculation that determines why the “things”/the works are as they are.
Scientific and everyday “things” are not at all the same. In ordinary language, the sun “rises” and “sets” while science says that it does not. What is the relation between the sun of science and the sun of common sense? An original reference to things is missing between the things rendered by science and the ordinary things around us. To relate these two “approaches” (stances), we need to understand how approaches come to be.
Ordinary things are always particulars, this one or that one; science studies universalities. The common sense things are a “this one” or “that one”; for science, any specific thing or event must be “derivable” from general theories or concepts (“Nothing is without (a) reason”–Leibniz). We say that we lack an “explanation” (a scientific account) of a thing as long as we cannot derive its nature and occurrence from universal, basic theoretical postulates (axioms, principles, premises, postulates). This is the basic “axiomatic” character of modern science. In contrast, any ordinary thing is always a “this one”, a singular, particular thing. Like your TOK oral, science moves inductively from the particular to the universal, from the thing to the theory about the thing. But the theory was always presumed to begin with.
The particularity of things seems to completely depend on their space and time, that each is here or there, now or then. If two things are alike, this one is different from that one only because it is here now, while the other is there, or is here later. It is space and time that makes ordinary things particulars and space and time are created by our encounter with the things as particulars.
Scientific propositions, too, concern events in space and time and not only generalizations. How does science use space and time so that events can be both specifically determined and derivable from universal theory?
Space and time are generated in the encounter between human beings and the things that humans point out, locate and make specific. Is space really involved in the very make-up of specific things? Is not space merely a system of external relations between things? Space seems to be not really “in” the thing but is only the “possibility” of arrangements of its parts (designated by the prepositions “next to”, “in”, “out”, etc.) How does the possibility of spatial structuring come into what something is?
“Possibility” or potentia refers to how our basic approach makes it “possible” for things to be as they are encountered, located, and found by us. The thing is given there, over against us. Just as we cannot see space, we cannot see time in the thing. Yet, only space and time are in the particularity of each thing. The thing’s character of being always a “this one” is derived in the thing’s relation to us and our relation to the thing. We point at things and so call them “this one” or “that one”. Space and time are generated in this interplay. This generation of space and time creates the “open” region where we and the thing come to stand in our relation to each other. This generation of the “open” region is done through what the Greeks called logos. Logos is the interplay of how we relate to the things: it is our ways of knowing the thing in question, the interaction between our personal and shared knowledge.
“This” and “that” is the most original and earliest mode of saying anything and thereby selecting and determining a thing. Only after our interplay with things do they come to have a resulting nature of their own. A noun becomes possible only on the basis of our pointing i.e. “things” arise only in the context of their relation to us and our pointing them out. The interplay, the “between” is not something subjective. What something is depends on us and the thing itself. This “between” is not as though first we and things could have existed separately and then interacted. Rather, what a human being is is always already a having things given and a thing is already something that “gives” and encounters us in this “giving”.
What a thing is depends on whether we take the thing of science or the thing of common sense. What a thing is depends on some interplay with us, upon some truth in which it stands. Our stance towards things and the things’ stance towards us is the ‘unconcealment’ or the ‘disclosure’ of what the things come to be for us.
It is through human action in concrete situations that “things” come to be acted on and taken as of a certain character. The character of things is no mere viewpoint (subjectivity), but is made in our actions and in situations whether we are applying the scientific method to a closed system that we have made or riding the bus to the mall. Only in perceiving and acting upon things do we constitute ourselves as humans, what we call our personal knowledge, just as only thereby do the things become things.
The model of the thing gives it a separate location in space and we impute a separate location to anything we approach as a thing. This leads to a great many separations: we separate subjects and objects, inside and outside, feelings and situations, individuals and inter-personal relationships, individual and community, the time moment “now” and the time moment “later”, symbol and knower, body and mind, etc. These many divisions are not separate issues, since each involves the same conceptual construct of things, such as separately located, a unit “thing” existing here now in a certain unit of space and at a “moment” i.e. a unit bit of time. Time, too, is conceived as made up of bit things, units, moments. Why? It is not because we perceive and study time and find it to be such and such. One does not perceive time as such. We perceive of time as moments because our approach is one of thing units.
Ancient and Modern Physics: The Aristotelian and Newtonian World Views
The understanding of Greek natural science can be said to be encapsulated in Aristotle’s three works: Metaphysics, Physics, and Categories. Modern science begins with Newton’s The Mathematical Principles of Natural Philosophy. Philosophy and science are one and the same thing: they are the theory of the real. In saying this we are saying that both science and philosophy are ontological i.e. a theory or way of looking that considers the being of beings; and they are metaphysical in that they attempt to understand the “what” and the “how” of beings or the things that are. The metaphysical assumptions of modern science are contained within the framework established by the principle of reason (Leibniz) and its realization within the language of mathematics used by natural scientists.
This history of the ‘thing’ model approach begins with the Greeks and it was an attempt to derive universals from the particularity of the things. We will likely take for granted that “space” is everywhere the same until we realize that the notion of such a space was lacking among the Greeks. Instead, they thought that each thing had its own proper place, and that the movement of a thing was always back to its proper place. Unless externally restrained, an earthen thing tended “downward” and a fiery one “upward.” Each thing thus tended to move in a certain way of its own accord, and this was termed each thing’s “internal principle of motion”. Greek things were not mere bodies that had to be moved. If allowed to do so, they moved themselves back to their own places. Thus, there were different kinds of places in the Greek model. We realize that our own everywhere-uniform space, too, is very much a model, perhaps better than the Greek, perhaps not, but at any rate not self-evident as the remarks on quantum and relativity physics below illustrate.
In the Newtonian model, just as in the Greek, the nature of space is related to what a thing and motion are. For us there is no “internal principle of motion” by which a body moves itself. Rather, bodies are moved, put into motion only by something else, and they remain in motion until stopped by something else. All our “principles of motion” are “outside principles”: something else outside the body is always posited to explain why a body comes into motion. Our laws of motion are the same for all places, and, hence, there is “space,” everywhere just the same. Of course the earthen things, when allowed to, can still be observed to move “downward” just as they did in ancient Greece. But how we grasp what the things are differs. We posit gravitational attraction outside the thing to explain why it moves.
When the different motions of different things are explained by different outside causes, all “bodies” (things) are viewed as fundamentally the same in their basic nature. Of course they do not all look or act the same, but then we think of them as made up of little “things” (a few types, each always the same: atoms, electrons, protons), and we explain all differences as different arrangements of these same things. What, where, and when anything is or moves will always be derivable according to the same basic principles.
The world is conceived as made of arrangements of uniform units of matter and space. If two constellations are made of the same parts and in the same patterns, exactly the same events will occur. And if time and space do not make two otherwise identical constellations different (as for Leibniz they do not), such two things would really be only one thing. The idea of parallel universes and string theory in modern physics is encapsulated here.
This aspect of the scientific approach is its basic “mathematical” character. Modern science is mathematical, not because it so widely employs mathematics but because the basic plan of uniform units makes it possible to quantify (calculate) everything one studies. It makes everything amenable to mathematics. From this, modern algebra and calculus arise, and needed to arise as well as modern statistics. What is crucial is whether or not Greek number and modern number are the same, and if they are not, what essential changes in our human being occur as a result of this change in our understanding of the mathematical logos.
Two related reasons for calling the basic scientific approach “mathematical” can be derived i.e., two reasons for mathematics becoming such an important tool in this approach: First, because it is a model of uniform units and hence makes uniform measurement possible everywhere, and, second, because it is “axiomatic”—that is, it is posited (as an axiom in geometry). Furthermore, the model copies our own thought procedures. Its uniform units are uniform thought steps transformed into a ground plan (framework) postulated as the basic structure of things i.e. the principle of reason rules not only our own thoughts but also the being of the universe. Here these two lines of argument will be discussed in turn:
- The approach to things as consisting of uniform units makes mathematics applicable to things: numbers are compositions of uniform units. Seventeen consists of the same units as fourteen, only there are three more of them. Since the units are the same, it would not matter which three of the seventeen units were considered to be three more than fourteen. There is a serial procedure employed in counting. In this procedure we obtain various numbers because we always keep in mind the units already counted. Our counting “synthesizes” (puts together) fourteen and another, another, and another. We keep what we have with us as we add another same unit. Our own continuity (the thinking subject) as we count gets us to the higher number. As Descartes phrased it, without the unity of the “I think,” there would be only the one unit counted now, and no composition of numbers. We get from fourteen to seventeen by taking fourteen with us as we go on to add another, another, and another. Thus, our activity of thinking provides both the series of uniform steps and the uniting of them into quantities (calculation). These units and numbers are our own notches, our own “another,” our own unity, and our own steps. Why do two plus two equal four? The steps are always the same; hence, the second two involves steps of the same sort as the first two, and both are the same uniform steps as counting to four. Thus, the basic mathematical composing gives science its uniform unit-like “things” and derivable com-positions. Therefore, everything so viewed becomes amenable to mathematics or algebraic calculation. If we remember our description of TOK through our Venn diagram involving personal and shared knowledge, the ‘nature’ we encounter is the Same as the uniform units which measure it. In the Open region or the overlapping of the two circles of the Venn diagram, what is opened is revealed or ‘unconcealed’ as mathematical units.
- The modern model of things is “mathematical” for a second reason. “Mathematical” means “axiomatic”: the basic nature of things has been posited as identical to the steps of our own proceeding, our own pure reasoning. The laws of things are the logical necessity of reason’s own steps posited as laws of nature. It is this that makes the model/framework/approach “mathematical” and explains why mathematics acquired such an important role. The everywhere-equal units of the space of uniform motion of basically uniform bodies are really only posited axioms. They are the uniform steps of pure, rational thought put up as axioms of nature. Descartes had said it at its “coldest” and most extreme: Only a method of reducing everything to the clear and distinct steps of rational thinking grasps nature.
Is not such an approach simply unfounded? Everything may follow from the starting assumptions, but what are the founding assumptions based upon? How can that be a valid method?
The axiomatic method lays its own ground. “Axiomatic” means not only to postulate axioms and then deduce from them; it does not refer to just any unfounded assumptions one might posit and deduce from. Rather, the axioms that rational thought posits assert the nature of rational thought itself (the principle of reason and reasons as explanations). Axiomatic thought (reason) posits itself as the world’s outline. It is based on itself. It creates the model (framework, approach) of/to the world, not only by means of but also as its own steps of thought. As we have seen, it is rational thought that has uniform unit steps and their composites, logical necessity and so forth. The axiomatic ground plan of nature is simply the plan of the nature of rational thought asserted about nature. This, then, is the basic “mathematical” character of modern science. It is founded on the “axiomatic” method of “pure reason” which Kant retains but limits in his Critique of Pure Reason.
In Descartes and Leibniz is the extent to which science’s axiomatic thought-plan reigns. Even God is subject to it. Philosophically explicated (Descartes and Leibniz), the lawful character of nature meant that God’s thinking (the thinking that creates nature) was axiomatic, logical thought. The power of axiomatic thought is thus limitless. It creates nature. And so it was held that God himself could not act otherwise than he does and that he is subservient to logical thought. Nature could not possibly be otherwise than along the lines of that which follows logically. These concepts are radically challenged by relativity and quantum physics.
Medieval philosophy had bequeathed three different main topics of philosophy: God (theology), world (cosmology), and man (psychology), which are similar to the three sorts of “things” identified in the beginning of this discussion. All three now became determined by man’s axiomatic thought. There was thus a “rational theology,” a “rational psychology,” and a “rational cosmology”. Reason was limitless. Using pure reason, man could conclude not only about man, world, and God but also about what was possible and impossible in any possible reality. It was this God that is spoken of in Nietzsche’s famous statement: “God is dead”.
Modern Physics: Relativity and Quantum Mechanics
In the natural Sciences, true paradigm shifts involve changes in the concepts on which physics, chemistry and biology are based. They are not merely the spectacular discoveries and advances in understanding that occur in how the object under study is understood such as is suggested by Thomas Kuhn in his book The Structure of Scientific Revolutions. In the beginning of the 20th century, the physicists’ “world view” was radically and irreversibly changed through the thinking put forward in relativity and quantum physics, whose chief “discoverers” were Albert Einstein and Werner Heisenberg respectively.
Einstein’s theory is of space, time and motion and is called The Theory of Relativity. There are the theories of special and general relativity. The quantum theory involves the nature of matter and the forces that act upon it. Max Planck made observations that electromagnetic radiation was emitted in discrete packets or quanta. Heisenberg, with his “uncertainty principle”, developed the mathematical matrices which elaborated the results of quantum physics’ experiments. Heisenberg also clarified the revolutionary implications of the discoveries in the quantum field. Heisenberg was well aware of the profound philosophical implications that flowed from quantum theory, and he explained these by saying that the language and concepts that are familiar to us from common sense and common everyday experience lose their meaning in the world of relativity and quantum physics. Questions about space and time, or the categories that are used based on the qualities of material objects such as movement and position which are entirely “reasonable” in our everyday language, cannot always be answered in any kind of meaningful way. That this is the case raises profound implications and consequences for our understanding of the nature of reality and for our “world view”.
The change in concepts made necessary by Einstein’s theory of relativity are more easily accommodated into what is called Classical Physics or Newtonian Physics than the changes in concepts demanded by quantum physics. Concepts such as time dilation and length contraction, curved space and black holes as odd as they are to common sense can be related to the concepts of Classical Physics to such an extent that even Roman Catholic Pope Francis can assert that they are “real” and aspects of God’s creation. http://www.independent.co.uk/news/world/europe/pope-francis-declares-evolution-and-big-bang-theory-are-right-and-god-isnt-a-magician-with-a-magic-9822514.html. His Holiness, while asserting that God does not or did not wave a magic wand in His creative act, nevertheless comes dangerously close to the blasphemy of making God’s will scrutable in his recognition of the principle of reason in his statements regarding evolution and the origin of the universe.
If we ask at what time an event occurs or whether two events separated in space occur at the same moment, these questions may not be answerable as the language of the questions stand because the theory tells us that there is no absolute universal time and also no concept of simultaneity. Such things are relative and need a specific frame of reference before the questions can have any meaning. While the ideas are strange and unfamiliar, they are not absurd to common sense. They also do not present problems for interpretation. The theory of relativity in both its special and general forms is not controversial.
The deepest philosophical problem presented by the theory of relativity is its possibility or potentia, contrary to the thinking of Aristotle, that the universe had its origin at a finite moment in the past and that this origin represented the abrupt coming into being not only of matter and energy but of space and time as well. The Big Bang Theory illustrates that time and space are not categories of intuition as Kant understood them but are as much a part of the physical universe as matter. The idea, first presented in the thinking of the Greeks, was that time was a moving image of eternity and the universe itself was eternal. The theory of relativity and subsequent theories developed from it gives a scientific counterpart to the notion of creation ex nihilo first proposed by St. Augustine in the 5th century. Our traditional understanding of physical causation (the principle of reason) changes with modern physics and it is only through quantum cosmology that a new picture of the origin of space-time (such as in the work of Stephen Hawking) has been arrived at.
Quantum mechanics on the other hand presents us with much greater conceptual and philosophical problems. The metaphysical questions, the “what” and the “how” of beings, become extremely murky in the quantum field. In your IB Higher Level Physics you learn quantum physics prescriptively and apply it without thinking of the metaphysical problems it poses. No one questions the results and the applications of quantum physics–the questions arise only when we think about what quantum physics means, about what knowledge is.
Heisenberg’s uncertainty principle shows us that all physical quantities that can be observed are subject to unpredictable fluctuations so that their values are not precisely defined. The position x and the momentum p of a quantum particle such as an electron cannot be measured precisely simultaneously. The “uncertainty”of the values, Ax and Ap respectively, are such that the product of the two, AxLp, cannot be less than a certain constant number. More accuracy in position must be traded for less in momentum, and vice versa. Planck’s constant (after Max Planck) is numerically very small so that the quantum effects are seen only in the atomic domain. They are not noticeable to our everyday lives and common sense.
This uncertainty is inherent in nature and not merely the result of technological limitations in measurement i.e. our sense perception as a way of knowing nature. The particle simply does not possess simultaneously precise values of these two categories or attributes.
The misapplication of the uncertainty principle in analyzing risk possibilities in stock markets (i.e. its application to economic “realities”) was one of the causes leading to the collapse of the banking system in the 2008 financial crisis. The uncertainty present in this case is due to missing information rather than to any fundamental limitations in what may be known about the economic system: money does not behave in the same manner as atomic particles; the things of common sense do not behave in the same manner as quantum particles.
The implications of the uncertainty principle are deep in that they are a challenge to the principle of reason itself. The quantum particle does not move along a well-defined path through space. An electron may leave position A and arrive at position B, but it is not possible to ascribe a precise trajectory linking the two. The Rutherford atomic model of the atom, with electrons circling a nucleus in distinct orbits, is badly misleading. Heisenberg says that such a model of the atom can be useful in creating a certain picture or representation in our minds but it is only a representation that has a vague correspondence with reality i.e. it is not the truth of the situation as it is.
The smearing of position and momentum leads to an inherent indeterminism in the behaviour of quantum systems. Even the most complete information about a system, which may be as simple as a single free moving particle, is insufficient to enable a definite prediction to be made about the behaviour of the system: two identical systems may produce different results.
This uncertainty of results in quantum systems is overcome by its enablement of indicating the relative probabilities of the alternatives to be specified and calculated precisely. Quantum mechanics is a statistical theory. It can make definite predictions about ensembles of identical systems, but it can tell us nothing definite about a single individual system. Where it differs from other statistical theories such as weather forecasting or economics’ predictions is that the chance element is inherent in the nature of the quantum system and not due to the lack of information of our limited grasp of all the variables that effect the system i.e. the current debate regarding climate change as an example.
The famous historical debate between Einstein and Heisenberg indicates the importance of the discoveries of quantum physics and its implications. Einstein famously stated: “God does not play dice with the universe”. He maintained that the correctness of quantum physics was incomplete and that there must exist a deeper level of hidden dynamic variables that give to the system an apparent indeterminism and unpredictability. Einstein hoped that beneath the chaos of the quantum world might lie a scaled-down version of the well-behaved, familiar world of cause and effect dynamics i.e. that the principle of reason was still operable and its systems did indeed shed light on a world outside ourselves. Up to this time, the experimental results have confirmed the propositions inherent in the viewing and the mathematical results of quantum physics.
Both Heisenberg and Neils Bohr strongly opposed Einstein’s attempt to hold on to the classical world view presented through the systems established by the principle of reason. The debate began in the early 1930s with Einstein suggesting what is known as the EPR paradox (see below for a description of the experiments based on this paradox conducted by John Bell in the 1980s). Einstein’s classical world view is in agreement with our common sense world view: there is an external world that has objective reality. It recognizes that our observations intrude and distort that world but their disturbance is incidental and can be made arbitrarily small. The micro world of atoms and particles is different only in size but not in ontological status from our macro world of common sense experience. An electron is a micro version of the billiard ball and has the same potentia or possibilities: being somewhere i.e. having a fixed position, moving in a certain predictable way, and so on. In the classical world view, our observations do not create reality but uncover it. The atoms and particles continue to exist, having a presence within well-defined categories even when we do not observe them.
Heisenberg rejects the objective reality of the quantum world. An electron does not have a well-defined position and a well-defined momentum without an actual observation of its position or it momentum; but both cannot be measured simultaneously. An electron cannot be regarded as a thing in the same sense that a billiard ball is a thing. Heisenberg asserts that we cannot meaningfully talk about what an electron is doing in between observations because it is the observations alone that create the being of the electron. An electron’s position when measured creates an electron-with-a-position; a measurement of its momentum creates an electron-with-a-momentum. Neither entity can be considered to be already in existence prior to the measurement being made.
What is an electron according to Heisenberg’s view? It is not a physical thing but an algebraic calculation of a sort of potentia or possible outcomes of measurements. It is a manner of connecting different observations through the logos of quantum mathematics as formulated by Heisenberg. The “reality”is in the observations and the logos, not in the electron. Heisenberg states: “In the experiments about atomic events we have to do with things and facts, with phenomenon that are just as real as any phenomenon in daily life. But the atoms or elementary particles themselves are not as real; they form a world of potentialities or possibilities rather than one of things or facts.”
The “dogmatic realism” of Einstein is the one to which the majority of scientists hold. They believe that their investigations actually refer to something real “out there”in the physical world and that the lawful physical universe is not just the invention of scientists. The enormous successes that the the principle of reason and its systems have produced, through simple mathematical laws, upholds their belief that science is dealing with an already existing external reality. Heisenberg reminds us that quantum mechanics is also founded on simple mathematical laws that successfully explain the physical world but do not require that world to have a separate, independent existence in the sense of the dogmatic realism of Einstein.
Heisenberg asks how we are to speak about the “being”of atoms and sub-atomic particles when their existence is so “shadowy”? What is the meaning of the words we use when related to the qualities (categories) of these “things”? Are atoms, electrons, and protons “things”at all? The “facts”on which we build the world of experience are all based on macroscopic things: measurements on a Geiger counter, spots on a photographic plate, etc. These are “things” we can meaningfully communicate to each other in plain language. Without this existence of classical, common sense, familiar objects, the reality of which seems assured and unquestionable, we can make no sense at all of the atomic and sub-atomic worlds. All our measurements and observations of the quantum world are made with reference to classical equipment using the scientific method, and everyone can agree that no vagueness or ambiguity is present in the concepts and categories used to describe them.
Neils Bohr’s principle of complementarity recognizes the ambiguity in quantum systems: the same system can display contradictory properties. An electron can behave as a wave or as a particle. Bohr asserts that these are complementary rather than contradictory. Bohr asserts that there are complementary faces of a single reality. One experiment may reveal wave features while another may reveal the particle nature of an electron. Both cannot be revealed at once; the scientist chooses which qualities to reveal through her choice of experiment. Position and momentum are complementary qualities: space is position, time is momentum. The experimenter must decide which quality to observe.
The question “Is an electron a wave or a particle?” is like asking “Is the USA above or below Australia?” The answer is “neither and both”. The electron possesses particle-like qualities as well as wave-like properties, either of which can be manifested but neither of which has any meaning without a specific experimental context. It is the viewing which determines the result. The presents a problem for language in that familiar words such as wave, position, particle, etc. are used but they do not have precise meanings. The physicist, according to Heisenberg, has to use the mathematical framework which gives very precise accounts of the experimental facts. Results can only be communicated mathematically.
Heisenberg’s matrix mechanics is a mathematical grid that relates results in statistical fashion. Any talk about “what is really going on” is our attempt to represent and model a world of which we have no knowledge. In examining the thinking of Descartes and Kant in the light of modern physics, Heisenberg shows that words and their associated concepts do not have absolute and sharply defined meanings. They arise through our experiences of the world and we do not know the limits of their applicability. We cannot expect to unconceal any fundamental truths about the world through the manipulation of words and concepts.
Although the problems presented by quantum physics are primarily epistemological (what is knowledge and what is it knowledge of?), some experiments have been conducted to explore the EPR thought experiment of Einstein. John Bell in 1965 contended that any theory based on “objective reality”for which faster-than-light indicators are forbidden must satisfy certain mathematical inequalities. Quantum physics should fail to satisfy them, according to Bell, and that one is obliged to give up either “objective reality” (with Bohr and Heisenberg) or the special theory of relativity. To test Bell’s theory, experiments were performed in the 1980s using pairs of photons from a common atomic source. After many careful tests, the results were clear: Bell’s inequalities were violated in conformity with the predictions of quantum physics. Quantum scientists were not surprised by the results saying they could not have been otherwise.
Quantum physics requires that the mathematical formalism (the principle of reason) that has characterized the history of classical physics needs the addition of epistemological assumptions for it to be applied to the atomic world. The Copenhagen interpretation of quantum physics accepts the prior existence of the classical macroscopic world. The effects arrived at exist in principle. Using inductive reasoning, physicists would like to derive the classical world as some sort of macroscopic limit of the quantum world, not assume it a priori.
What actually happens inside a piece of measuring equipment when the measurement of a quantum particle is made? Copenhagen physics treats the apparatus classically, but if it is treated more “realistically” as a collection of quantum particles grave difficulties arise. The same shadowy vagueness of the quantum world invades the entire system. Instead of the sense perception of the apparatus bringing to presence a “real”actuality from a range of potential possibilities, the combined system of apparatus + particle adopts a state that still represents a range of potentia or possibilities. The Schrodinger’s Cat thought experiment is an example of this. If the apparatus is set up to measure whether an electron is in the right or left half of the box, and to display this a pointer is thrown either to the right or left respectively, the end result is to put the combined system into a state in which neither outcome is selected. Instead, the state is a superimposition of the two states, one consisting of the electron and the pointer on the right, the other consisting of them on the left. If the two alternatives are mutually exclusive, the problem might not be insurmountable, but in experiments there can also be interference between the alternatives so that there is no clear either/or dichotomy and no actual measurement can be said to have taken place. The states remain superimposed.
Quantum cosmologists attempt to apply quantum mechanics to the universe as a whole in an effort to understand the mystery of the questions of the origins of matter, becoming and being. If the entire universe is a quantum system, there is no greater macroscopic environment into which quantum shadowness can fade away. Quantum cosmologists accept the full range of quantum potentia as actually existing realities. The above example of the pointers would be considered two universes, one with an electron and pointer to the left, the other with them on the right. For the cosmologists, a measurement involves postulating an infinity of co-existing parallel worlds or “realities”.
There are many knowledge problems that can be elaborated through thinking about the implications and consequences of quantum and relativity theories. Certainly “knowledge” itself is not now considered what it has been understood as traditionally in our shared knowledge. Applying quantum systems to our “common sense” macro world has given rise to many irrational movements and theories as can be seen in their application to the human sciences of economics and politics specifically. But in our macro world an apple remains an apple, a banana a banana, and a gun a gun.