Is gravity a consequence of quantum entanglement?
THEORY / 036: Does Quantum Entanglement Threaten Einstein's Theory? (Spectrum of science)
Spectrum of Science 9/09 - February 2009
Does Quantum Entanglement Threaten Einstein's Theory?
By David Z. Albert and Rivka Galchen
The creator of the theory of relativity was opposed to the "spooky action at a distance", which forces spatially separated parts of a quantum system to behave together. In fact, the entanglement shakes some of the foundations of physics.
|-||Our world of experience seems to behave "locally": We can only influence objects that are directly accessible to us.|
|-||But there is one in quantum mechanics strange long-range effect, the so-called entanglement: two entangled particles react synchronously, without any material intermediate carrier.|
|-||This non-local effect poses a serious problem for Einstein's special theory of relativity and shakes the foundations of physics.|
Our intuition tells us: in order to move a stone, you have to touch it or pick up a stick, which in turn touches the stone. Or you give an order that vibrates in the air and reaches the ear of someone else, who in turn hits the stone with a stick - or something like that. In general, according to this intuition, anything can only directly influence things in its immediate vicinity. We call this intuition, which is confirmed thousands of times by our everyday experience, "locality".
Of course there are also indirect effects; but in each case they are transmitted through a seamlessly connected chain of events, each of which leads directly to the next. If we seem to come across an exception to this rule, this impression vanishes on closer inspection: We turn on light with the push of a button and seldom consider that this happens through wires; or we listen to the radio and are usually not aware that the device is receiving invisible waves.
Quantum mechanics contradicts some intuition, but none that is deeper than the assumption of locality. From the beginnings of scientific natural research to the emergence of quantum mechanics, scholars believed that a complete description of the physical world was, in principle, equivalent to the individual description of each of its smallest and most elementary building blocks. The complete history of the world can be expressed by the sum of the stories of all parts.
Quantum mechanics violates this belief. Real, measurable, physical properties of particle ensembles can go beyond the sum of the individual particle properties, deviate from them or have nothing to do with them at all. For example, according to quantum mechanics, it is possible to arrange two particles in such a way that their distance is exactly one meter, although neither of the two has a precisely defined location.
In addition, the so-called Copenhagen Interpretation, which the great Danish physicist Niels Bohr proclaimed at the beginning of the last century and which is still the standard interpretation of quantum mechanics today, claims: The reason for this is not that we do not know the exact locations of the individual particles, but that these exact locations just don't exist. So asking about the location of a single particle is as pointless as asking about the marital status of the number five. The problem is not epistemological, that is, a question of our knowledge, but ontological, that is, a question of being.
When particles are connected in this way, physicists say that they are quantum-mechanically entangled. The entangled property does not always have to be the spatial location. Two particles can have opposite spins, although neither of the two spin directions is definitely fixed. Or exactly only one of the particles is excited, but neither of the two is definitely the one that is excited. Particles can be entangled regardless of their location, their nature and the forces exerted on one another - in principle, an electron and a neutron at opposite ends of the Milky Way too. Thus the entanglement creates an intimacy within the matter that was previously completely unthinkable.
This phenomenon underlies new and promising research areas such as quantum information and quantum cryptography; this may soon result in computers and tap-protected data channels with unimagined possibilities (see "Quantum computers with ions" by Christopher R. Monroe and David J. Wineland, SdW 6/2009, p. 34).
But the entanglement also apparently results in the phenomenon of non-locality, which is deeply opposed to everyday understanding: the possibility of influencing something physically without touching it directly or via a chain of connecting links. Non-locality means that a fist in Cologne can break a nose in Berlin without affecting anything else in the whole country - an air molecule, an electron in a wire or a flicker of light.
Albert Einstein had numerous objections to quantum mechanics; He by no means only criticized their randomness with the all too often tried quotation "God does not throw the dice". The only objection, which he formulated stringently in a scientific publication, concerned the strange nature of the quantum mechanical entanglement. This criticism is known today as the EPR Argument, after the three authors Einstein, Boris Podolsky, and Nathan Rosen (see caption 2). In their 1935 article "Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?" They answer the title question with a clear no.
Their argument is based on a special instruction in the quantum mechanical algorithm for predicting experimental results. Suppose we measure the location of a particle that is quantum-mechanically entangled in such a way that neither of the two, as mentioned above, has a precise location on its own. When we get the measurement result, we of course change our description of the first particle, because we now know for a moment where it was. But the algorithm also forces us to change our description of the second particle - instantly, regardless of how far it is or what lies between the two particles.
Before Einstein emphasized this consequence, entanglement was an undisputed part of the quantum physical worldview. But he found it not only strange but dubious. It struck him as "spooky". Above all, it seemed to be non-local.
A changed concept of reality?
Back then, no one was willing to consider the possibility of real physical nonlocalities - Einstein, Bohr, or anyone else. In their article, Einstein, Podolsky and Rosen assumed that the non-locality of quantum mechanics could only be a sham effect; it must be a mathematical anomaly, but in any case an expendable artifact of the algorithm. Certainly one can concoct quantum mechanical predictions without using non-local steps.
So they came to the following conclusion: If - as everyone assumed at the time - there is no real physical non-locality in the world and if the experimental predictions of quantum mechanics are correct, then this theory must ignore certain aspects of the world. There must be parts in the history of the world that quantum mechanics does not mention.
Bohr responded to this publication practically overnight. His hasty refutation took up none of the concrete scientific arguments, but criticized - in an unclear and sometimes downright oracular way - the use of the word "reality" and the definition of "elements of physical reality" in the EPR article. The Dane talked extensively about the distinction between subject and object, about the conditions under which one could ask meaningful questions, and about the nature of language. It is necessary "to finally renounce the classical ideal of causality and to fundamentally revise our attitude towards the problem of physical reality."
Bohr left no doubt that he agreed with Einstein, Podolsky and Rosen on one point: Of course, a real physical non-locality was out of the question. The apparent non-locality is just one more reason why we have to give up the old-fashioned claim, which is so obvious in the EPR article, that we can read a realistic picture of the world from the equations of quantum mechanics - that is, a picture of what is actually in front of our noses of you Moment to the next exists. Bohr practically insisted that we not only perceive the world blurred, but that beyond this shadowy and indefinite image there can be nothing real.
That answer was an oddly philosophical response to a clearly scientific objection. Stranger still, it was immediately promoted to the official standpoint of theoretical physics. Thinking about it further soon became heresy. The physicists thereby sacrificed their old claim to discover the real nature of the world and banished metaphysical questions for a long time to the realm of the imagination.
Even today, there is a great deal of confusion about this important part of Einstein's legacy. Walter Isaacson assures the numerous readers of his Einstein biography, published in 2007, that his doubts about quantum mechanics have since been dispelled. But that's not true.
It took 30 years for anyone to seriously look at the EPR argument. According to a famous 1964 article by Irish physicist John S. Bell: Bohr was wrong when he believed his understanding of quantum mechanics to be incontestable, while Einstein was mistaken about what was wrong with it. In order to understand what the error really was, one has to give up the idea of the locality.
The crucial question is whether the non-localities in the quantum mechanical algorithm are mere appearance or not. Bell was apparently the first to investigate exactly what this question meant. How can real physical non-localities be distinguished from merely apparent ones? Bell argued thus: If there is a local algorithm that makes the same experimental predictions as the quantum mechanical algorithm, then Einstein and Bohr rightly rejected the nonlocalities of quantum mechanics as mere artifacts. If, on the other hand, no algorithm is able to avoid non-localities, it must be real physical phenomena. Bell now analyzed a special entanglement case and concluded that such a local algorithm was mathematically impossible. Thus the physical world is actually non-local.
This conclusion turns everything upside down. For Einstein, Bohr and everyone else it was always agreed that any genuine incompatibility between quantum mechanics and the principle of locality would endanger the whole theory. But as Bell now showed, locality is not only incompatible with the abstract theoretical apparatus of quantum mechanics, but also with certain empirical predictions of theory. Since 1981, Alain Aspect's experiments at the Institut d'Optique in Palaiseau (France) in particular have left no doubt that these predictions are indeed correct. So it was not quantum mechanics that began to falter, but the principle of locality - and with it presumably also the special theory of relativity, because it seems to presuppose locality (see caption 6).
Most physicists to this day suppress the full meaning of Bell's work. Bell had shown that any theory that can reproduce the empirical predictions of quantum mechanics for entangled pairs of particles - including quantum mechanics itself - must by its very nature be physically non-local.
This message has been practically ignored. Instead, almost everyone claims that Bell only showed the following: Any attempt to replace the orthodox quantum mechanical worldview with some hidden parametric, deterministic or philosophically realistic theory that is more in line with our classical metaphysical expectations should be nonlocal, to reproduce the quantum mechanical predictions for EPR systems. Bell's work was noticed, but by blinkers.
Only a small minority of physicists avoided this misunderstanding, realizing that Bell's evidence and Aspect's experiments had revealed the world itself to be nonlocal. But they too believed almost without exception that this non-locality posed no particular threat to the special theory of relativity.
This belief is based on the idea that the special theory of relativity is inextricably linked with the impossibility of sending messages faster than light. From the theory of relativity it can be concluded that no material carrier of a message can be accelerated to speeds beyond that of light. And it can also be concluded that a faster-than-light message would arrive in some frames of reference before it was sent - which would unleash all the paradoxes of time travel.
As early as 1932, the brilliant Hungarian mathematician John von Neumann proved that the non-locality of quantum mechanics can by no means be used for instantaneous information transfer. For many decades, practically all physicists interpreted this proof as a guarantee for a peaceful coexistence of quantum mechanical nonlocality and special relativity.
It wasn't until 30 years after Bell's article that some physicists grasped the full extent of the problem. The first clear, open and logically flawless discussion was provided by Tim Maudlin of Rutgers University (New Jersey) in 1994 with his book "Quantum Non-Locality and Relativity". As he showed, the question is much more subtle than the usual platitudes about instant messages.
Maudlin's work appeared against the backdrop of a changed intellectual climate. Since the early 1980s, Bohr's conviction that there could be no old-fashioned, philosophically realistic description of the subatomic world began to crumble noticeably everywhere. Several promising approaches seem to provide a good description of the species Bohr rejected, at least in a non-relativistic approximation. These included, on the one hand, the Bohmian mechanics that David Bohm had developed in the early 1950s - it inspired Bell's work, but was otherwise largely ignored - and, on the other hand, the GRW model by GianCarlo Ghirardi, Alberto Rimini and Tullio Weber (see "David Bohm's Quantum Theory" by David Z. Albert, SdW 7/1994, p. 70). The old, metaphysical claim of physics to literally and directly tell us what the world really is - a claim that had been suppressed for more than 50 years - was slowly starting to reawaken.
Maudlin's book focused on three important points. First: The special theory of relativity makes statements about the geometric structure of space and time. The impossibility of transmitting mass, energy, information or causal influences faster than light does not guarantee that the geometrical statements of the theory are correct. That is why von Neumann's proof of information transfer alone offers us no guarantee that quantum-mechanical non-locality and special relativity can coexist peacefully.
Second: The special theory of relativity is actually compatible with a huge variety of hypothetical mechanisms for the faster than light transfer of mass, energy, information and causal influences. For example, Gerald Feinberg of Columbia University in New York published an inherently consistent relativistic theory of tachyons in the 1960s; It is physically impossible for these hypothetical particles to propagate more slowly than light. Maudlin invented other examples.
Accordingly, the mere existence of quantum mechanical non-locality does not mean that quantum mechanics is incompatible with the theory of relativity. So there is hope.
But, as Maudlin third emphasized, the special kind of action at a distance that we encounter in quantum mechanics is completely different from the relativistic influences in Feinberg's tachyons or in Maudlin's other examples. The non-local influences between quantum mechanical particles depend neither on their spatial arrangement nor on their physical properties, but exclusively on whether the particles in question are quantum mechanically entangled or not. The quantum mechanical non-locality seems to require above all absolute simultaneity - which would actually threaten the core of the special theory of relativity. That's the problem.
Very recently, two new results have emerged from this debate. One points the way to a possible reconciliation of quantum mechanical non-locality and relativity theory; the other exacerbates the impression that any combination of the two must brutally violate our deepest intuitions about the world.
Can the theory of relativity be saved?
The first result comes from Roderich Tumulka, a young German mathematician who is currently working at Rutgers University. In an article published in 2006 he showed how all empirical predictions of quantum mechanics for entangled particle pairs can be reproduced by a cleverly modified GRW theory. As a reminder, this theory makes a proposal to derive the predictions of quantum mechanics in a philosophically realistic way. Tumulka's modification, although not local, is nevertheless very compatible with the spacetime geometry of the special theory of relativity.
This approach is still quite immature. No one is currently able to write a satisfactory version of Tumulka's theory that can be applied to particles that are attractive or repulsive to one another. In addition, his theory introduces a new non-locality into nature - not only spatial, but also temporal! In order to calculate the probability of a future event, one not only has to enter - as is usual with physical theories - the current state, but also certain facts about the past. After all, Tumulka's approach has removed some of the reasons for Maudlin's concern about the peaceful coexistence of nonlocality and relativity.
The other new result was discovered by one of us (Albert). It says: In order to reconcile quantum mechanics and the theory of relativity, we must sacrifice another, particularly deep-seated belief. We take it for granted that everything that can be said about the world can in principle be told in the form of a story. More precisely, everything that can be physically said can take the form of an infinite series of dated individual statements: »At the point in time t1 is this the physically exact world state «and» at the time t2 is the the state of the world ”and so on. But when quantum entanglement and relativistic spacetime geometry work together, the physical history of the world becomes infinitely richer.
The problem is that the special theory of relativity merges space and time in such a way that the quantum mechanical entanglement between spatially separated physical systems changes into a kind of entanglement between physical situations at different times. This creates something that - to take up our initial formulation about the peculiarity of quantum theory - goes in a very concrete way beyond a sum of situations at separate times, deviates from them or has nothing to do with them.
As with almost all theoretical results in quantum mechanics, the wave function also comes into play here. The Austrian physicist Erwin Schrödinger introduced this mathematical structure 80 years ago to define quantum states. From the wave function follows the phenomenon of entanglement, the indeterminacy of the particle locations - and not least the non-locality of quantum mechanics.
But what is the wave function actually? This is the question that basic theorists are talking about. Is it a concrete physical object or a kind of law of motion, is it an internal particle property or a relationship between spatial points? Or is it just our current information about the particles? Mathematically, quantum mechanical wave functions are represented in an abstract, multi-dimensional configuration space. If we want to understand concrete physical objects by this, we have to accept the idea that world history takes place neither in the three-dimensional space of our everyday experience nor in the four-dimensional space-time of the theory of relativity, but in this gigantic, non-visual configuration space, from which somehow the illusion of the three-dimensional everyday space emerges. Our three-dimensional idea of locality should also be understood as a product of that abstract space. The non-locality of quantum physics would be our window into a deeper level of reality.
Suddenly, more than a century after its inception, the status of special relativity is a radically open question with a surprising number of answers. This situation arose because physicists and philosophers finally picked up the loose ends of Einstein's long-ignored criticism of quantum mechanics - further evidence of Einstein's genius. It could very well be that the underrated thought leader erred where we believed him to be right and was right where we believed he was wrong. Perhaps we perceive the universe with less clouded senses than has been claimed for too long.
David Z. Albert is professor of philosophy at Columbia University in New York and author of the books "Quantum Mechanics and Experience" and "Time and Chance". Rivka Galchen teaches creative writing at the same university. She publishes stories and essays, often on scientific subjects. Her first novel "Atmospheric Disturbances" was published in May 2008 in the USA.
Albert, D. Z .: Quantum Mechanics and Experience. Harvard University Press, 1992.
Bell, J. S .: Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy. Cambridge University Press, 2nd edition 2004.
Fine, A .: The Shaky Game: Einstein, Realism, and the Quantum Theory. University of Chicago Press, 2nd edition 1996.
Maudlin, T .: Quantum Non-Locality and Relativity: Metaphysical Intimations of Modern Physics. Wiley-Blackwell, 2nd edition 2002.
Wheeler, J. A., Zurek, W. H. (Eds.): Quantum Theory and Measurement. Princeton University Press, 1983. (contains the EPR article and Bohr's answer)
Weblinks on this topic can be found at www.spektrum.de/ artikel / 1002937.
Captions of the images of the original publication not published in Schattenblick:
Despite Einstein's objections, quantum theory is nonlocal. Does this leave his own theory of relativity unaffected?
The EPR thought experiment
Like Albert Einstein, Boris Podolsky and Nathan Rosen ("EPR") showed that the quantum entanglement of two particles produces amazing results when two observers, Alice and Bob, who are far apart from each other, each examine one of the particles.
Electrons have spins, the orientation of which is indicated by arrows (above). If Alice wants to measure the spin of an electron (below) and chooses, for example, a vertical measuring axis, she finds either an upward spin or a downward spin, each with a certain probability. If she chooses a horizontal axis, she finds left-spin or right-spin.
Two particles can be entangled that their spins are oriented in opposite directions, although neither of the two spins, taken by itself, has a defined direction. Suppose Alice measures upward spin on her particle (below). Even if Bob and his particle are at any distance from Alice and he measures it along the vertical axis as she does, he will always find that his particle has the opposite downward spin.
EPR concluded: Since Bob can be one hundred percent certain that he is measuring downward spin, the spin of his particle must have already pointed downward before he measured it. But Alice could just as well have chosen a horizontal measuring axis and obtained a right spin, for example. From this it would follow, however, that Bob's particle had left spin from the start.
EPR concluded: Since no quantum state allows Bob's particle to have downward spin with certainty and also left spin with certainty, quantum mechanics must be an incomplete theory.
According to our everyday experience the world is local: we can only move a stone by touching it directly or by touching a stick that touches the stone. We always have to create a coherent chain of such direct, local connections. But since the beginning of modern natural science in the 17th century, »non-localities« kept appearing.
1687: Isaac Newton's universal law of gravitation, the first scientific description of gravity, is a law of action at a distance. Newton tries to remedy this non-locality and develops an unsuccessful theory in which tiny invisible particles fill the apparently empty space.
1785: Charles Coulomb sets up a formula for the electrostatic forces that is analogous to Newton's law of gravitation. Electrical effects seem to be based on action at a distance.
1831: Michael Faraday describes magnetism through lines of force. The physicists reckon with electric and magnetic fields that fill space. The forces acting on a particle are at least formally described as a close-up effect. But these fields are only used as convenient arithmetic aids, not as real.
1849: Hippolyte Fizeau and Jean Bernard Foucault measure the speed of light at 298,000 kilometers per second; but no one yet knows what light really is.
1865: James Clerk Maxwell's equations reveal that electromagnetic fields have a dynamic life of their own and traverse the vacuum at 298,000 kilometers per second. The electromagnetism is local and light is an electromagnetic wave.
1905: Einstein's special theory of relativity combines Maxwell's equations and the principle that the same physical laws must apply to uniformly moving observers. But instead the idea of absolute simultaneity is abolished.
1915: In Einstein's general theory of relativity, the curvature of space-time for gravity plays the same role as the electromagnetic field in Maxwell's theory. Gravitation is local: if a mass vibrates, gravitational waves propagate at the speed of light.
1935: Einstein, Podolsky and Rosen declare quantum mechanics to be incomplete because it requires non-local phenomena. Niels Bohr (right) contradicts: We have to accept quantum mechanics and sacrifice old ideas of "reality" for it.
1964: John S. Bell extends the EPR argument to cases in which spins are measured along different axes and shows that no local theory can correctly predict the experimental results of quantum mechanics. The predictions of any local theory must always satisfy the so-called Bell inequalities.
1981 until today: As Alain Aspect, Anton Zeilinger and others proved through experiments with entangled light states, the world obeys the rules of quantum mechanics and not Bell's inequalities. The world is actually non-local.
Other ways out
Some physicists believe that John S. Bell's mathematical proof of the non-locality of the quantum mechanical world leaves certain loopholes open.
Bell, of course, assumed that quantum experiments would produce unequivocal results. But according to the multi-worlds interpretation, every quantum measurement splits the universe into branches in which all the different results occur in parallel (see “Parallel Worlds”, Spectrum Dossier 1/2009). This is why our universe can be "local" when copies of the experimenter inhabit countless invisible parallel universes. This approach, of course, creates many tricky problems.
Give up the realism?
Since Bell assumed that the world was "locally realistic," many believe that he proved that either locality or realism is violated. So the world could be local if it violates realism. But that's a misunderstanding: the original argument by Einstein, Podolsky, and Rosen excludes the possibility of quantum locality without resorting to the realism used by Bell.
Bell's Theorem and Physical Reality
The non-locality of our physical world follows from a theorem proved by John S. Bell in 1964 and from increasingly sophisticated experiments since the 1980s. The theorem is based on the puzzling behavior of entangled particles, as pointed out by Einstein, Podolsky and Rosen in 1935 (see caption 2). The EPR argument assumes that the world is local. Therefore, a spin measurement that Alice carries out on one partner of a pair of particles cannot instantly change the state of the distant partner particle in Bob. So Bob's particle must have defined spin values for any measuring axis from the start. Consequently, quantum mechanics must be incomplete, because it does not fix these values, but only guarantees that Bob's measurement always matches Alice's measurement result.
Bell now asked: Suppose Alice and Bob's entangled particles have defined values; can such particles supply the quantum mechanically predicted values for all measurement axes chosen by Alice and Bob? Let us remember: Alice and Bob each have to choose a measuring axis along which they determine the spin; these axes can be tilted against each other by 45 or 90 degrees, for example. As Bell proved mathematically, numerous measurements along different axes produce a statistical distribution of the results that deviates from the predictions of quantum mechanics. Quantum mechanics cannot satisfy any preselection of defined values.
For practical experiments Instead of electrons, the researchers prefer entangled photons whose polarization is measured along different axes. The results confirm the quantum mechanical predictions. Thus, according to Bell's theorem, these photons cannot have any defined values. Since this contradicts the EPR argument, the assumption that nature is local must be wrong. We live in a non-local universe.
Why relativity and nonlocality do not get along well
The special theory of relativity creates a geometric relationship between space and time. This relationship makes the concept of an "instantaneous action at a distance" not only strange, but downright meaningless.
Alice and Bob stand around a table in different places. They interpret the spatial directions right, left, forwards and backwards differently. As the special theory of relativity shows, moving observers experience not only space but also time differently.
Alice and Bob cannot agree on which events are simultaneous, nor on a theory that includes actions at a distance. Here Alice "instantly" sets off the distant explosion by pressing a button at midnight.
Alice's space and time axes (red) cross where Alice is exactly at midnight. Bob flies east over Alice at almost the speed of light. Its movement tilts its space and time axes (blue) relative to Alice's reference system. He therefore experiences the explosion earlier than Alice.
© 2009 David Z. Albert and Rivka Galchen, Spectrum of Science Verlagsgesellschaft mbH, Heidelberg
Spectrum of Science 9/09 - February 2009, pages 30 - 37
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published in Schattenblick on October 7, 2009
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