Quantum Theory
The Magical Flower of Winter is an essay series exploring reality and our relationship to it. It deals with philosophy, science and our views of the world, with an eye on the metacrisis and our future. Sign up to receive new essays here:
The best possible knowledge of a whole does not necessarily include the best possible knowledge of all its parts.
Erwin Schrödinger - Discussion of Probability Relations between Separated Systems
Many believe physics to be the only authority on what reality is. This belief can be coherent to the extent that by reality is meant a particular subset of what we think of as real, physical reality, described by Einstein in the following way: «Physics is an attempt conceptually to grasp reality as it is thought independently of its being observed. In this sense one speaks of "physical reality."»1 We have seen how this term “independently” is problematic when it comes to grasping reality as a whole, that when it comes down to it, a reality independent of us is incoherent2. Quantum theory is the most explicit testament to this need for a view of reality that is co-dependent. What follows will not be a rigorous introduction to quantum theory, but an illumination of those aspects of it that break with intuitive thinking, thinking that is ultimately classical, and to a large extent intertwined with particularism (reductionistic and physicalist realism). This essay builds on the common theme of my project, that of outlining a view of reality as a whole, and as such this essay cannot be read outside the context of this project, though I have made the attempt to make it stand on its own. Any interpretation of physics is metaphysical, for it involves the interpreter, and interpretation is inevitable when faced with models of reality. Any position that does not see the inextricable dependence of physics on the physicist is bound to a model that one is unable to see is just a model. In the words of Heisenberg, one of the founding fathers of quantum theory: «Natural science does not simply describe and explain nature; it is a part of the interplay between nature and ourselves; it describes nature as exposed to our method of questioning… it makes the sharp separation between the world and the I impossible.»3
The Classical World
Our day-to-day experience of the world is one of solid, determinate and extended objects interacting in a fixed space, with durations of time that, though psychologically subjective, are unerringly measured out by the ticking clocks around us. The legacy of Newton is a model of reality as a big unchanging and absolute box, space, acting as a static background in which things deterministically evolve in a time that is equally absolute. Einstein broke this model of space and time with his theory of relativity, a development I will treat separately. For now, let us keep to the things.
The Quantum Break
[T]he change in the concept of reality manifesting itself in quantum theory is not simply a continuation of the past; it seems to be a real break in the structure of modern science.
Werner Heisenberg - Physics and Philosophy
The deeper we question reality, the more pronounced we see the co-dependent and co-creative nature of which we are part. Objects are no longer particulate or solid, these concepts do not translate invariantly into the quantum realm4. The prototypical example is the double-slit experiment. Shooting a particle against a screen with two openings, let us suppose that it always goes through an opening, and hits a detector screen on the other side (See Fig. 1). The particle can ricochet slightly on the opening, so that it won’t hit the same spot on the detector screen each time, thus the detected position obeys a normal distribution. After many runs, the result is the sum of two spatially shifted normal distributions. All this follows intuitively from classical physics, in which space and time are absolute and objects are solid.
If we now go from the macro-realm of everyday intuition to the micro-realm, things will behave differently (See Fig. 2). Shooting electrons towards a scaled-down slit-setup we no longer observe classical particle behavior, but wave behavior. Even if we were to shoot one electron at a time the recorded pattern on the observation screen would be that of a wave. Classical intuition commands us to expect that a particle only goes through one slit, but the interference pattern we observe cannot arise without the particle going through both slits at the same time. What is going on? Our classical intuition breaks down. The quantum realm owes no allegiance to our concept of “particle” or our spatiotemporal particulate expectation of causality where these “particles” can only do one thing at a time. So is the electron then really a wave? Once again it is not that straightforward. If we try to observe what is going on at the slits (indirectly so as to allow passage through) we will record an electron passing through a single slit, and the interference pattern disappears. If we don’t look it’s a wave, if we look it’s a particle. We cannot think of the electron as either a particle or a wave, but some other “thing” altogether that is both. It’s not either/or, but both/and! This is Bohr’s principle of complementarity.
Thus, electrons have both wave-nature and particle-nature, depending on context, how we measure it. Similarly, light has both wave-nature and particle-nature: the same exact experiment can be carried out with light instead of electrons (or any other quantum “particle”), and we will observe both wave-behavior and particle-behavior depending on context. Particulate light, photons, can only appear with quantized energy, and it is this discreteness of energy and other properties, first discovered by Planck, that gives name to the quantum theory, and that historically constituted the most radical break with preceding thought5. As we shall see, quantum behavior is paradoxical because we cling to intuitive expectation, we are bound to a view of reality wherein conformity to classical concepts is hard to free ourselves from, but if we are able to see that these too are contextual, the insights from quantum theory can click into place in another, coherent view of reality. This is not to say that our classical concepts are useless, but that they too have their limited domain of applicability. The breakdown of our concepts of solidity and localization is further captured by Heisenberg’s uncertainty principle: complementary properties of a system, like position and momentum, cannot be simultaneously known. Knowing one of these to a high precision will decrease the precision with which we know the other. This principle also demonstrates the co-dependent relation: to acquire knowledge we must interact, but any interaction changes what we sought knowledge about.
The Measurement Problem
The dependence on context, of which we as observers are part, must be commented on. The quantum state of a system or particle is usually represented by a wave function, which relates to the probability of detecting the particle in coordinates of spacetime, so we can think of the wave function as assigning a probability to each point in spacetime for detecting the particle there6. The wave function obeys a deterministic wave equation: Schrödinger’s equation. The wave equation evolves the wave function dependent on the constraints and initial conditions of the system (i.e. context. In the example above these are the source of particles, the slits and detection surface etc.), thus the probability at each spacetime point evolves in a deterministic manner. Because we are not yet interfering with the system, the wave function will evolve through both slits, and with respect to the wave-nature we have a situation where the particle-that-is-not-”yet”-a-particle has gone through both slits. This is known as superposition, made famous by Schrödinger’s thought experiment of a cat that is interpreted as being both dead and alive simultaneously. When we measure the system represented by the wave function, we observe a single outcome, i.e. we find that the particle is detected at a single spacetime coordinate. Schrödinger’s equation is incapable of accounting for this irreversible reduction of wave function to a single outcome, and some now say that our interaction by detection collapses the wave function. This constitutes the measurement problem: How do we account for this irreversible and instantaneous reduction of a wave spread out in spacetime to a single point? This problem is a legacy of the particularist framework, in which physical reality is conceived as an external world independent of our being part of it. We are of course part of the context, but unaccounted for when the wave function or particle is considered as an isolated system, when in reality there is a whole of which both the system and we are part. This of course means that the “correct” wave function is one that describes both the double-slit system and us (standard accounts now talk of the double-slit system and a measuring apparatus, but the apparatus is merely an intermediary). This forces us into thinking of ourselves as part of a whole in superposition, where there are probabilities assigned for “versions” of us detecting all possible particle locations, yet we still only observe single outcomes. Importantly, this whole does not conform to our classical concepts. It is in the context of our experience that we find particles, waves, single outcomes and cat’s (whether alive or dead). Detached from such a background, there is only the whole, wherein it is meaningless to talk of these conceptual constructs. I will return to making sense of this vast whole later in the essay, but I can hint that the resolution revolves around shifting focus from our model of reality as primary back to reality as primary.
Entanglement and Non-Separability
…Bell’s theorem, together with the results of Aspect’s experiments, demonstrates that the world is non-local…
Tim Maudlin - Quantum Non-Locality and Relativity
Now that we have seen how our intuitive and classical expectations of particularity and causality might not be obeyed by reality at the micro-level, let us further see what happens to locality, the classical expectation that all things are bound to each other in spatiotemporal proximity, and that no effect can have a cause that doesn’t obey the spatiotemporal limits set down by relativity. Hints that the causal spatiotemporal structure of reality might not be as bulletproof as one classically would think started with the famous EPR-paradox by Einstein, Podolsky and Rosen7. Through the analysis and developments of many physicists thereafter, this paradox of entanglement can be illustrated in the following way:
We can entangle two particles by producing them in such a way that the the quantum state of the pair is such that due to conservation laws, if we measure the property S of one of the particles in the pair, we will know what the corresponding property S has to be of the other particle in the pair, based on our measurement of the first. For reasons of illustration (and tradition), if we imagine that S can either be “up” or “down”, the conservation law is simply that the total S has to cancel out (“up” and “down” cancel, their sum is conserved), and if one is measured “up”, the other then has to be “down”, and vice versa, see Fig. 4. The paradox comes into play if we now consider spatially separating the two entangled particles from each other: if we were to measure the property S of one particle, we would immediately know something about the other particle, even when the separation between the two parts can be lightyears! This seemingly breaks with the principles of locality and relativity, for how can this be immediate if reality is local and nothing can travel faster than the speed of light? Furthermore, we cannot posit that the particles had the properties we end up measuring all along, because in a modified version of the experiment one finds that the property we measure is dependent on our way of measuring it, i.e. properties are context-dependent8. This is to say that measurement does not disclose a property that was there all along, but that measurement is co-creative of the property measured. Bell9 famously cast this paradox in terms of a set of inequalities that, if violated by experiment, would indicate that reality is fundamentally non-local and non-separable. This means that there is no way for the quantum state of each particle to be separable from each other, i.e. the entangled quantum state is a whole that is prior to and more than the sum of parts, which provides a non-local causal connection across spacetime10. Conclusive experiments violating Bell’s inequalities were first carried out by Aspect et.al. (for which they received the Nobel prize in 2022), thus confirming the non-local and non-separable nature of reality, and the limits of the causal framework. How can this be made sense of?
Once again, it is our classical expectations that lead to paradox. Though experience and much of our conceptual machinery seems so, reality isn’t always local and separable. We must once again latch our thought to the whole which precedes the conceptual constraints our models clothe reality in, like the separability of systems, and local spacetime. Bell’s theorem and consequent developments furthermore refutes the possibility of some description of reality “as it really is” with hidden, (unobservable) variables that can explain and locally connect our immediate knowledge of entangled properties. It is not our description that is non-local, reality is. Once again, from our everyday and classical intuition we expect all “things” to behave in space and time just as they do at the macro-level. But this is parochial: in the quantum realm, “thing”-ness, and both space and time are not fundamental entities. These concepts are not a static background against which quantum reality operates, these are structures that make themselves known as a whole (Some would say emergent, but this classification is inseparable from the reductive world view. As previously stated11, emergence is the name the reductionist gives those phenomena that show forth the holistic aspects of reality). The entangled system cannot be thought of as consisting of separable parts, it is a whole. And this whole (that is both wave-like and particle-like, therefore something more, something other), not being separable, does not conform to our spatiotemporal characterization and separation of it: for it is not fundamentally spatiotemporal! Furthermore, we play a part for this system and its properties, thus this whole isn’t separate from us either, we are all part of a larger whole, parts of which under the right circumstances, in the right contexts, may conform to a classical framework, but whose nature in-and-of-itself is not this framework, this model we have erected and found both lacking and paradoxical. What the concept and confirmation of entanglement shows forth is the non-local, non-separable nature of reality, as well as the limits of the epistemic: if there is such a thing as a complete description of reality, then this must be a non-local hidden-variable description, though a complete description of reality is impossible due to the limits of reducibility.
Interpretations
As I showed in World Views, though our hunger for explanation is insatiable, when it comes to reality-in-itself, what is unspeakable cannot be spoken of. However, many do the attempt, not cognizant of the limits to explanation and the epistemic, and an abundance of interpretations result. I will briefly deal with the most dominant ones below, but I can in no way do them the full justice they deserve here. The fundamental incompleteness of the epistemic, that the quantum state is indeterministic, was most famously resisted by Einstein: «Some physicists, among them myself, cannot believe that we must abandon, actually and forever, the idea of direct representation of physical reality in space and time; or that we must accept the view that events in nature are analogous to a game of chance.»12 An understandable position given the deterministic paradigm he sprang out of. Like Einstein, we all «...like to think that the moon is there even if [we’re] not looking at it.»13 Everyone behaves as if local realism is true, but the structure of reality in realms beyond our everyday perception does not conform to our local and realist beliefs. The expectation that fundamental theories of reality should be causally deterministic highlights our forgetting the richness of experience and the limits of the epistemic. Though the latter can explain and predict a lot of reality, it is forever fundamentally limited when it stands against our full experience of reality. The indeterminism of the quantum state tells us we need to reappraise our role as experiencers, and that our knowledge will never be complete (i.e. determinate). This is where Einstein could not go, though it can be argued that Einstein was not so much against the quantum theory, but for a particular, and in part particularist, conception of science14: «The belief in an external world independent of the perceiving subject is the basis of all natural science. Since, however, sense perception only gives information of this external world or of "physical reality" indirectly, we can only grasp the latter by speculative means. It follows from this that our notions of physical reality can never be final. We must always be ready to change these notions - that is to say, the axiomatic basis of physics - in order to do justice to perceived facts in the most perfect way logically.»15 What Einstein believed in was a theory that superseded quantum theory, a theory with a radically different conceptual structure, capable of once again providing a deterministic and complete account of reality. But as we have seen, such a “theory” cannot be conceived of independently of us as experiencers, as perceiving subjects, for reality and experience is irreducibly co-dependent and co-creative16.
The Copenhagen Interpretation
It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature.
Niels Bohr, quoted in Petersen (1963)
The Copenhagen interpretation is the standard, developed by Bohr, Heisenberg and Born, among others, though it is an amalgam of views that cannot be said to represent the view of any single physicist, as even its founders disagreed on many points. The account I have given so far is to a large extent in line with the Copenhagen interpretation, but with important differences as regards what I have called the whole and co-dependence. Bohr’s principle of complementarity stands central, as well as Heisenberg’s uncertainty principle. The Copenhagen interpretation does not regard reality as a whole, but rather as something which cannot be inquired about outside the experimental situations the mathematical formalism allows. The interpretation relies on our classical concepts being what experiments and results must be cast in: «however far the phenomena transcend the scope of classical physical explanation, the account of all evidence must be expressed in classical terms»17, i.e. interpretation of the quantum theory must be in classical terms, for it is these that connect physics to our experience, and it is our experience that physics ultimately must answer to. Given the discussion of incommensurability in World Views, this is to neglect the efficacy of meaning variance: interpreting quantum theory in classical terms reshapes them, they change in the process, so that our interpretation of experience must also covariantly change. Followers of the Copenhagen interpretation were in a bind due to this: they saw that the quantum theory introduced subjective elements by context-dependence, but they worked to rid themselves of this in order to reclaim an objective description18. As we have seen in previous essays our observations and theories are always and already epistemised, anything that can be said is inseparable from the epistemic web, which constitutes an irreducible context. The objective is only ever an unreachable and ideal limit of the epistemic. What this means is that there will always be a remainder of context-dependence to any description of reality which cannot be removed: it constitutes the very ground against which the description is given meaning, and this ground is itself context-dependent. Even physics answers to this holistic conception of the epistemic19. This co-dependence must be embraced in a view of reality as a whole, not denied.
Everettian and Many-Worlds interpretation
The question is one of terminology: to my opinion there is but a single (quantum) world, with its universal wave function. There are not “many worlds,” no “branching.” etc. except as an artifact of insisting once more on a classical picture of the world.
Hugh Everett, quoted in Lévy-Leblond (1976)
The trap of mistaking a model of reality for reality and the potential for abuse inherent in language is clearly exemplified by the path to the “many-worlds” interpretation, from its roots in the Everettian interpretation. Everett (1957) formulated a “relative state” interpretation of quantum mechanics that takes reality to be represented by a single, universal wave function. Observation does not collapse this state, thus there is no measurement problem to this formulation, but observers and the observed acquire a relative state which is part of the universal state, which holds the potential for all possible outcomes. We should recognize that the universal wave function is an approach to the ontic, the whole, which cannot be represented. To my mind, Everett’s proposal was largely on the right track as long as one acknowledges this. Unfortunately, his work was misconstrued by DeWitt (1973) and subsequent followers, and renamed the “many-worlds” interpretation. DeWitt’s interpretation assigns reality to every possible piece of the universal wave function (which cannot be known), and each “branch” is now a “real” world in its own right. Not only does this assume reality to be separable, but it neglects to take our experience as primary, which is of one world. We cannot claim reality of that which contradicts our experience, because our experience is what dictates the meaning of the term “reality” in the first place. Reality is a whole, «larger» than what we can observe and describe (once again, our words are inadequate, this whole is not spatially larger, but holds a «potential» that is more than than what we observe as actual), which is irreducible to separable branches we can assign «world» or «reality» to. The “many-worlds” conception of the Everettian interpretation is an example of mistaking the map for the territory: the “branches” were just a useful image for purposes of illustration, but at the end of the day they do not connect to our experience except as parts of a whole prior to them.
de Broglie-Bohm Theory
…relativity and quantum theory agree, in that they both imply the need to look on the world as an undivided whole, in which all parts of the universe, including the observer and his instruments, merge and unite in one totality. In this totality, the atomistic form of insight is a simplification and an abstraction, valid only in some limited context.
David Bohm - Wholeness and the Implicate Order
de Broglie-Bohm theory20 (also known as pilot wave theory or Bohmian mechanics) is an example of a hidden variable theory, a deterministic theory allowed by Bell’s inequalities due to being non-local. This approach posits the independent reality of particles, and the hidden variables are the actual positions of all the particles in the universe, which in the theory are “guided” by a pilot wave that satisfies the Schrödinger equation. The momentum of any one particle depends on the positions of all the particles in the universe, which makes the theory non-local in a way that is incompatible with relativity21. This theory has received ample criticism when it hasn’t been ignored altogether, but it is a novel attempt at saying something about the whole, but I think it unfortunately ends up trying to say too much. As we have seen, “particles” are not fundamental, these are contextual and co-creative manifestations or excitations of the whole. On the other hand, the non-locality of everything depending on everything else does convey an aspect of the wholeness of reality, but an aspect that cannot be reduced. Thus, the limits of the epistemic and the irreducibility of the ontic rears its head also against this interpretation.
There are many other interpretations that deserve mention (e.g. “QBism” and Rovelli’s “relational quantum mechanics”), but these will have to be visited another time. Neither has any mention been made of quantum field theory, an important development that will also have to wait.
Disentanglement
To see a World in a Grain of Sand
And a Heaven in a Wild Flower
Hold Infinity in the palm of your hand
And Eternity in an hour
William Blake - Auguries of Innocence22
The probabilistic and indeterminate aspects of quantum theory can be understood and interpreted in many ways, but I think the following provides the most resolution. We think that if we could perfectly replicate the conditions of a dice throw, we may repeat the throw and get the same outcome every time. We are, however, unable to do this indefinitely, because context (or chaos or disorder) will creep in eventually23. It is not the dice or the throw that decides the outcome when these are controlled for, it is everything else, the environment, the context, the whole. Any framework is limited, this is an irreducible property of the epistemic, and as such the whole cannot be fully accounted for. The idealized situations of classical physics that yield determinate descriptions do not correspond to reality in any complete sense, and if context was part of classical physics this too would be an indeterminate and probabilistic theory. All our theories rely on parts and laws, but the whole that is reality is more than the sum of these. We are driven to dreams of completeness, of there being a “real” and independent state of affairs «hidden behind» the conceptual structure, of which we simply are not aware and into which our formalism can’t penetrate. But anything «hidden» is a shadow of formalism. This seems absurd to us, that there shouldn’t be an underlying determinate state of affairs, but this is because our experience is of determinate things. We think that the “hidden” reveals itself to be there in our experience, so we metaphysically extrapolate to its existence independent of that experience, while it is the very act of experiencing that co-creatively makes the determinate out of the whole.
To resolve the riddle of the measurement problem and wave function collapse I hinted that the focus must be shifted from our model of reality as primary back to reality as primary. There is a need to stop conceiving of an independent physical world that must give rise to and account for observer-effects, and instead conceive of what ultimately is our only evidence, our experience, as primary, and experience as giving rise to a physical world, and models thereof, now without paradox. Experience is the only evidence, the only given, we can work from. We keep falling prey to the ontic projection fallacy24, we keep wanting to conceive of an independent and objective quantum state from which all the phenomena can be predicted, that our model should be complete in a sense. But the observer is not part of this quantum state, and with experience as primary, this independent quantum state will forever be inadequate for making sense of measurement. Our experience is irreducible to the epistemic, and by a change in our experience, which is part of the whole, there is consequently a change in the epistemic, i.e. the wave function or quantum state. Bohr likened this holistic-relational resolution of wave function collapse to a change in frame of reference25: the properties of a system is dependent on which frame of reference one views the system from26. A change in frame of reference constitutes a discontinuous change in properties. But there is no underlying process that explains this “collapse”, this discontinuous change, except a change in context, a difference in the whole. Wave function “collapse” is a change in perspective. We keep looking for a mathematical solution to a non-mathematical problem.
We must take care when thinking of a world behind the world, for this is a spatial metaphor that quickly can lead to particularism, but of course metaphor itself is inescapable, all epistemics is representation. What quantum theory shows is that there is a groundless ground in-between the joinery that is our depiction of it, an infinite potential that springs forth27, a whole that can’t be named world or reality before it has come through, before it is actual. Prior to this it is unspeakable, because prior to this it “is not”. The whole is the infinite depth by which we can “hold infinity in the palm of our hand and eternity in an hour”. Importantly, a world is not a world without a subject to be a world for, thus we cannot separate ourselves from the world without that separated world becoming something other than how our experience of it is. Our language breaks down here, the concepts that we have an intuition about acquire their meaning and intuitivity from everyday contexts, and consequently they do not translate invariantly to conceptual realms far afield from our perceptions, this we have seen repeatedly throughout this project. For the inescapable indeterminism that quantum theory shows us, a parallel can be drawn to how language and meaning requires flexibility in order to work28, that in order for meaning to be variable, the ground needs to be shaky. Does not indeterminism provide the very same flexibility for physical reality? Do we not need the very fabric out of which our always-novel experience is made to have a stretch to it that only indeterminism can contribute?
It should be clear that any and all critique in this essay is leveled at the dogmatic scientism, the position that particularist science is the only path to truth, which lies at the core of particularism as a world view. Science is irreplaceable as a quest to understand our experience, but it is essential to also know the limitations of this quest. The quantum revolution took place a century ago, yet the dominant world view is still enmeshed in particularism, having absorbed incoherent variants of quantum theory where any notion incompatible with physicalism, realism or reductionism where swept under the rug. The reasons for the strong grip of particularism are many, and some of them I have covered previously29. In the next essay I will look at further reasons for a view of reality as a whole from the perspective of the theory of relativity.
Thank you for reading! If you enjoyed this or any of my other essays, consider subscribing, sharing, leaving a like or a comment. This support is an essential and motivating factor for the continuance of the project.
References
Aspect, A., Grangier, P. & Roger, G. (1982). Experimental Realization of Einstein-Podolsky-Rosen-Bohm Gedankenexperiment : A New Violation of Bell's Inequalities. Physical Review Letters. 49 (2): 91–94
Bell, J. S. (1964). On the Einstein Podolsky Rosen Paradox. Physics Physique Физика. 1 (3): 195–200.
Bell, J. S. (2004). Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy. Cambridge University Press. [1987]
Bohm, D. (1952). A Suggested Interpretation of the Quantum Theory in Terms of 'Hidden Variables' I. Physical Review. 85 (2): 166–179.
Bohm, D. (1980). Wholeness and the implicate order. Routledge.
Bohm, D. & Hiley, B. J. (1995). The undivided universe: an ontological interpretation of quantum theory. Routledge.
DeWitt, B. S. & Graham, R. N. (Eds.) (1973). The Many-Worlds Interpretation of Quantum Mechanics (Princeton Series in Physics). Princeton University Press.
Einstein, A., Podolsky, B. & Rosen, N. (1935). Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?. Physical Review. 47 (10): 777–780.
Einstein, A. (1982). Ideas and Opinions. Three Rivers Press. [1954]
Everett, H. (1957). "Relative State" Formulation of Quantum Mechanics. Rev. Mod. Phys. 29, 454.
Feyerabend, P. K. (1981). Niels Bohr’s World View in Philosophical Papers Vol. 1: Realism, Rationalism and Scientific Method. Cambridge University Press.
Fine, A. (1986). The shaky game : Einstein, realism, and the quantum theory. University of Chicago Press.
Heisenberg, W. (1958). Physics and Philosophy: The Revolution in Modern Science. HarperCollins.
Kochen, S & Specker, E. P. (1967). The problem of hidden variables in quantum mechanics. Journal of Mathematics and Mechanics. 17 (1): 59–87
Kuhn, T. S. (2022). The Last Writings of Thomas S. Kuhn: Incommensurability in Science (Ed. Bojana Mladenovic). University of Chicago Press.
Lévy-Leblond, J.-M. (1976). Towards a proper quantum theory (hints for a recasting). Dialectica, 30(2/3), 162–196.
Maudlin, T. (2002). Quantum Non-Locality and Relativity: Metaphysical Intimations of Modern Physics. Wiley.
Pais, A. (1979). Einstein and the Quantum Theory. Rev. Mod. Phys. 51, 863.
Petersen, Aa. (1963). The Philosophy of Niels Bohr. Bulletin of the Atomic Scientists.19:7. 8-14
Schlipp, P. A. (Ed.) (1948). Albert Einstein: Philosopher-Scientist. Evanston.
Schrödinger, E. (1935). Discussion of Probability Relations between Separated Systems. Mathematical Proceedings of the Cambridge Philosophical Society, 31(4), 555–563. doi:10.1017/S0305004100013554
Schlipp (1948) p. 81.
See my previous essays.
Heisenberg (1958) p. 81.
See my discussion of incommensurability and meaning variance in World Views.
Kuhn (2022) conveys an elucidating take on the conceptual path from quanta, or elements, of energy as a calculational tool, to its interpretation in the completed quantum theory.
The probability is equal to the wave function multiplied by its complex conjugate.
Einstein et.al. (1935).
Kochen & Specker (1967).
See Bell (1964, 2004).
There is however no way to utilize this connection for information signaling, see e.g. Maudlin (2002). This means that entanglement is compatible with relativity.
Einstein (1982) p. 334-5. Hence his famously quoted belief that “God does not play with dice”.
Pais (1979).
See Fine (1986) for an enlightening presentation of the development of quantum theory and Einstein’s views.
Einstein (1982) p. 266.
See World Views.
Bohr, quoted in Schilpp (1948) p. 209, emphasis in original.
See e.g. Heisenberg’s own account in Heisenberg (1958).
See my other essays, in particular Language and Meaning, Wittgenstein and the Private Language Argument, Science and Explanation and World Views.
See e.g. Bohm (1952), Bohm & Hiley (1995).
Thus, this explicit non-locality is of a more troubling kind than that showed by entanglement. There are several attempts to resolve the conflict with relativity.
Radioactive decay shows how equal conditions lead to different outcomes, how the time of radioactive decay is fundamentally indeterministic and intimately dependent on every part of the whole.
See World Views.
See Feyerabend (1981).
This will become clear in the upcoming essay on the theory of relativity.
A tendency, as Heisenberg (1958) puts it.
Great piece of writing. Keep it up!