Incompleteness of quantum physics
Encyclopedia
Incompleteness of quantum physics is the assertion that the state of a physical system, as formulated by quantum mechanics
, does not give a complete description for the system, assuming the usual philosophical requirements ("reality", "nonlocality", etc.).
Einstein, Podolsky, and Rosen
had proposed their definition of a "complete" description as one which uniquely determines the values of all its measurable properties. The existence of indeterminacy
for some measurements is a characteristic of quantum mechanics; moreover, bounds for indeterminacy can be expressed in a quantitative form by the Heisenberg uncertainty principle.
Incompleteness can be understood in two fundamentally different ways:
Incompleteness understood as 1) would motivate search for a hidden variables theory featuring nonlocality
, owing to results of Bell test experiments
. There are many variants of 2) which is widely considered to be the more orthodox view of quantum mechanics.
may have been the first person to carefully point out the effect the new quantum physics would have on our notion of physical state. For a historical background of Einstein's thinking in regard to quantum mechanics, see Jankiw and Kleppner (2000), although his best known critique was formulated in the EPR thought experiment
. See Bell (1964).
According to Fuchs [2002], Einstein developed a very good argument for incompleteness:
Einstein's argument shows that quantum state is not a complete description of a physical system, according to Fuchs [2002]:
, he made a remark that is now famous:
Einstein was mistaken according to Stephen Hawking
in Does God Play Dice,
Chris Fuchs [2002] summed up the reality of the necessary incompleteness of information in quantum physics as follows, attributing this idea to Einstein "He [Einstein] was the first person to say in absolutely unambiguous terms why the quantum state should be viewed as information (or, to say the same thing, as a representation of one’s beliefs and gambling commitments, credible or otherwise).
Fuchs adds:
The kind of information about the physical world that is available to us according to Fuchs [2002] is “the potential consequences of our experimental interventions into nature” which is the subject matter of quantum physics.
and the generally accepted Copenhagen Interpretation
of quantum mechanics, the philosophical requirements assumed by Einstein are not true: according to this interpretation, quantum mechanics is neither "real", since a quantum mechanical measurement does not simply state, but instead prepare the physics of a system. Quantum mechanics is also not "local", essentially because the state of a system is described by the Hilbert vector
, which includes the value at every site, 
.
So in this respect Einstein was simply wrong, although he "pinpointed" the formalism of quantum mechanics exceptionally sharply.
[Laudisa and Rovelli 2005], the way distinct physical systems affect each other when they interact (and not of the way physical systems "are") exhausts all that can be said about the physical world. The physical world is thus seen as a net of interacting components, where there is no meaning to the state of an isolated system. A physical system (or, more precisely, its contingent state) is described by the net of relations it entertains with the surrounding systems, and the physical structure of the world is identified as this net of relationships. In other words, “Quantum physics is the theoretical formalization of the experimental discovery that the descriptions that different observers give of the same events are not universal.”
The concept that quantum mechanics forces us to give up the concept of a description of a system independent from the observer providing such a description; that is the concept of the absolute state of a system. I.e., there is no observer independent data at all. According to Zurek [1982], “Properties of quantum systems have no absolute meaning. Rather they must be always characterized with respect to other physical systems.”
Does this mean that there is no relation whatsoever between views of different observers? Certainly not. According to Rovelli [1996] “It is possible to compare different views, but the process of comparison is always a physical interaction (and all physical interactions are quantum mechanical in nature).”
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
, does not give a complete description for the system, assuming the usual philosophical requirements ("reality", "nonlocality", etc.).
Einstein, Podolsky, and Rosen
EPR paradox
The EPR paradox is a topic in quantum physics and the philosophy of science concerning the measurement and description of microscopic systems by the methods of quantum physics...
had proposed their definition of a "complete" description as one which uniquely determines the values of all its measurable properties. The existence of indeterminacy
Quantum indeterminacy
Quantum indeterminacy is the apparent necessary incompleteness in the description of a physical system, that has become one of the characteristics of the standard description of quantum physics...
for some measurements is a characteristic of quantum mechanics; moreover, bounds for indeterminacy can be expressed in a quantitative form by the Heisenberg uncertainty principle.
Incompleteness can be understood in two fundamentally different ways:
- QM is incomplete because it is not the "right" theory; the right theory would provide descriptive categories to account for all observable behavior and not leave "anything to chance".
- QM is incomplete, but is a faithful picture of nature.
Incompleteness understood as 1) would motivate search for a hidden variables theory featuring nonlocality
Nonlocality
In Classical physics, nonlocality is the direct influence of one object on another, distant object. In Quantum mechanics, nonlocality refers to the absence of a local, realist model in agreement with quantum mechanical predictions.Nonlocality may refer to:...
, owing to results of Bell test experiments
Bell test experiments
The Bell test experiments serve to investigate the validity of the entanglement effect in quantum mechanics by using some kind of Bell inequality...
. There are many variants of 2) which is widely considered to be the more orthodox view of quantum mechanics.
Einstein's argument for the incompleteness of quantum physics
Albert EinsteinAlbert Einstein
Albert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...
may have been the first person to carefully point out the effect the new quantum physics would have on our notion of physical state. For a historical background of Einstein's thinking in regard to quantum mechanics, see Jankiw and Kleppner (2000), although his best known critique was formulated in the EPR thought experiment
EPR paradox
The EPR paradox is a topic in quantum physics and the philosophy of science concerning the measurement and description of microscopic systems by the methods of quantum physics...
. See Bell (1964).
According to Fuchs [2002], Einstein developed a very good argument for incompleteness:
- The best [argument of Einstein] was in essence this. Take two spatially separated systems A and B prepared in some entangled quantum state |ψAB>. By performing the measurement of one or another of two observables on system A alone, one can immediately write down a new state for system B. Either the state will be drawn from one set of states {|φiB|} or another {|ηiB|}, depending upon which observable is measured. The key point is that it does not matter how distant the two systems are from each other, what sort of medium they might be immersed in, or any of the other fine details of the world. Einstein concluded that whatever these things called quantum states be, they cannot be “real states of affairs” for system B alone. For, whatever the real, objective state of affairs at B is, it should not depend upon the measurements one can make on a causally unconnected system A.
Einstein's argument shows that quantum state is not a complete description of a physical system, according to Fuchs [2002]:
- Thus one must take it seriously that the new state (either a |φiB> or |ηiB>) represents information about system B. In making a measurement on A, one learns something about B, but that is where the story ends. The state change cannot be construed to be something more physical than that. More particularly, the final state itself for B cannot be viewed as more than a reflection of some tricky combination of one’s initial information and the knowledge gained through the measurement. Expressed in the language of Einstein, the quantum state cannot be a “complete” description of the quantum system.
Reality of incompleteness
Although Einstein was one of the first to formulate the necessary incompleteness of quantum physics, he never fully accepted it. In a 1926 letter to Max BornMax Born
Max Born was a German-born physicist and mathematician who was instrumental in the development of quantum mechanics. He also made contributions to solid-state physics and optics and supervised the work of a number of notable physicists in the 1920s and 30s...
, he made a remark that is now famous:
- Quantum mechanics is certainly imposing. But an inner voice tells me it is not yet the real thing. The theory says a lot, but does not really bring us any closer to the secret of the Old One. I, at any rate, am convinced that He does not throw dice.
Einstein was mistaken according to Stephen Hawking
Stephen Hawking
Stephen William Hawking, CH, CBE, FRS, FRSA is an English theoretical physicist and cosmologist, whose scientific books and public appearances have made him an academic celebrity...
in Does God Play Dice,
- Einstein's view was what would now be called, a hidden variable theoryHidden variable theoryHistorically, in physics, hidden variable theories were espoused by some physicists who argued that quantum mechanics is incomplete. These theories argue against the orthodox interpretation of quantum mechanics, which is the Copenhagen Interpretation...
. Hidden variable theories might seem to be the most obvious way to incorporate the Uncertainty Principle into physics. They form the basis of the mental picture of the universe, held by many scientists, and almost all philosophers of sciencePhilosophy of scienceThe philosophy of science is concerned with the assumptions, foundations, methods and implications of science. It is also concerned with the use and merit of science and sometimes overlaps metaphysics and epistemology by exploring whether scientific results are actually a study of truth...
. But these hidden variable theories are wrong. The British physicist, John BellJohn Stewart BellJohn Stewart Bell FRS was a British physicist from Northern Ireland , and the originator of Bell's theorem, a significant theorem in quantum physics regarding hidden variable theories.- Early life and work :...
, who died in 1990, devised an experimental testBell test experimentsThe Bell test experiments serve to investigate the validity of the entanglement effect in quantum mechanics by using some kind of Bell inequality...
that would distinguish hidden variable theories. When the experiment was carried out carefully, the results were inconsistent with hidden variables. Thus it seems that even God is bound by the Uncertainty Principle, and can not know both the position, and the speed, of a particle. So God does play dice with the universe. All the evidence points to him being an inveterate gambler, who throws the dice on every possible occasion.
Chris Fuchs [2002] summed up the reality of the necessary incompleteness of information in quantum physics as follows, attributing this idea to Einstein "He [Einstein] was the first person to say in absolutely unambiguous terms why the quantum state should be viewed as information (or, to say the same thing, as a representation of one’s beliefs and gambling commitments, credible or otherwise).
Fuchs adds:
- Incompleteness, it seems, is here to stay: The theory prescribes that no matter how much we know about a quantum system—even when we have maximal information about it—there will always be a statistical residue. There will always be questions that we can ask of a system for which we cannot predict the outcomes. In quantum theory, maximal information is simply not complete information [Caves and Fuchs 1996]. But neither can it be completed.
The kind of information about the physical world that is available to us according to Fuchs [2002] is “the potential consequences of our experimental interventions into nature” which is the subject matter of quantum physics.
The Copenhagen Interpretation
According to Niels BohrNiels Bohr
Niels Henrik David Bohr was a Danish physicist who made foundational contributions to understanding atomic structure and quantum mechanics, for which he received the Nobel Prize in Physics in 1922. Bohr mentored and collaborated with many of the top physicists of the century at his institute in...
and the generally accepted Copenhagen Interpretation
Copenhagen interpretation
The Copenhagen interpretation is one of the earliest and most commonly taught interpretations of quantum mechanics. It holds that quantum mechanics does not yield a description of an objective reality but deals only with probabilities of observing, or measuring, various aspects of energy quanta,...
of quantum mechanics, the philosophical requirements assumed by Einstein are not true: according to this interpretation, quantum mechanics is neither "real", since a quantum mechanical measurement does not simply state, but instead prepare the physics of a system. Quantum mechanics is also not "local", essentially because the state of a system is described by the Hilbert vector
, which includes the value at every site, .So in this respect Einstein was simply wrong, although he "pinpointed" the formalism of quantum mechanics exceptionally sharply.
Relational Quantum Mechanics
According to Relational Quantum MechanicsRelational quantum mechanics
Relational quantum mechanics is an interpretation of quantum mechanics which treats the state of a quantum system as being observer-dependent, that is, the state is the relation between the observer and the system. This interpretation was first delineated by Carlo Rovelli in a 1994 preprint, and...
[Laudisa and Rovelli 2005], the way distinct physical systems affect each other when they interact (and not of the way physical systems "are") exhausts all that can be said about the physical world. The physical world is thus seen as a net of interacting components, where there is no meaning to the state of an isolated system. A physical system (or, more precisely, its contingent state) is described by the net of relations it entertains with the surrounding systems, and the physical structure of the world is identified as this net of relationships. In other words, “Quantum physics is the theoretical formalization of the experimental discovery that the descriptions that different observers give of the same events are not universal.”
The concept that quantum mechanics forces us to give up the concept of a description of a system independent from the observer providing such a description; that is the concept of the absolute state of a system. I.e., there is no observer independent data at all. According to Zurek [1982], “Properties of quantum systems have no absolute meaning. Rather they must be always characterized with respect to other physical systems.”
Does this mean that there is no relation whatsoever between views of different observers? Certainly not. According to Rovelli [1996] “It is possible to compare different views, but the process of comparison is always a physical interaction (and all physical interactions are quantum mechanical in nature).”