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Archive for the 'philosophy of science' Category
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Now I was being told that another deep aspect of nature was also unified with space and time — the fact that there are fermions and bosons. My friends told me this, and the equations said the same thing. But neither friends nor equations told me what it meant. I was missing the idea, the conception of the thing. Something in my understanding of space and time, of gravity and of what it meant to be a fermion or boson, should deepen as a result of this unification. It should not just be math — my very conception of nature should change…Whereas the math worked, it didn’t lead to any conceptual leaps. Lee Smolin, The Trouble with Physics, The Rise of String Theory, the Fall of a Science, and What Comes Next [Houghton Mifflin Company, 2006 p.94, 96]
In the Pentagon of Power: The Myth of the Machine [2 vol., 1967-70], architect, historian, and critic Lewis Mumford (1895-1990) coined the expression “the sin of Galileo” to refer to the manner in which the world had become merely an abstract mathematical object through Galileo’s application of mathematics to physics. To Mumford this change was dehumanizing and ultimately productive of the alienation of modern life. As a “sin,” of course, this kind of thing had nothing to do with Galileo’s problems with the Church.
Mumford’s idea about the alienation of modern life is really a dangerous nostalgia for mediaeval society. The meaning of life may have been clearer in past centuries than now, but it went along with pervasive poverty and an authoritarian political and religious hierarchy. The “alienation” of modern life follows largely from the wealth, leisure, and autonomy that technology and a consumer economy make possible. People are left to figure out or decide on the meaning of life for themselves. Those with the most leisure — intellectuals and teenagers — suffer from such alienation the most. The disapproval of intellectuals for what most people enjoy — television, sports, drinking, smoking, sex, and violence — is the same immemorial moralism of mandarins, priests, and aristocrats that always disapproved of vulgar, i.e. popular, pleasures, the same yearning for the day that political authority, namely them, can once again govern meaning and morality in life for everyone.
The sense that we are alienated from nature is also a dangerous nostalgia: No people absolutely vulnerable to famine, disease, insects, wild animals, nomadic invasions, etc. are going to complain much about conditions that limit or erase the danger of such things. Only those who have forgotten how hard and merciless life used to be are going to feel “alienated” by the culture that protects them from those things. For them, outlawing DDT and forbidding the draining of “wetlands” are important steps in protecting nature, whether or not people begin to die again around the world because of the malaria that is spread by mosquitoes who breed in the “wetland” swamps and who can no longer be effectively killed once produced. Those who live in comfort in Europe or the United States don’t have to worry about people in Sri Lanka dying of malaria, though there now actually are places in Europe and the United States that feel some of these effects — just not at major universities or newspapers yet.
Nevertheless, there is an important sense in which we can apply the idea of the “sin of Galileo”: Galileo represents an important shift in how mathematics is seen. With him, and with even more peculiar characters like Johannes Kepler and Isaac Newton, the Platonic-Pythagorean notion that mathematics reveals the inner structure of reality returns.
Mediaeval understanding had mostly followed Aristotle, seeing mathematics as no more than an device for calculation, something made up by us that had no essential connection to reality. Thus, where Plato had seen the four elements as consisting, atom-like, of four of the five Platonic solids, tetrahedrons for fire, octahedrons for air, icosahedrons for water, and cubes for earth, Aristotle ignored this completely and saw the four elements in Presocratic terms as distinguished by two sets of opposites — hot and dry for fire, cold and wet for water, hot and wet for air, and cold and dry for earth. Both Plato and Aristotle were, of course, wrong; but Plato was not far off the mark: The Platonic solids do occur with the packing of atoms in crystals. Common table salt, for instance, the mineral Halite (NaCl), occurs in cubic crystals. Aristotle’s opposites, on the other hand, have no modern form, unless we want to reach for the analogy of the presence or absence of sub-atomic properties like strangeness, charm, etc., which nevertheless have nothing to do with hot and cold or wet and dry.
Both Plato and Pythagoras thought that mathematics would reveal the inner nature of things. With Copernicus, Galileo, and Newton, this expectation seemed to be born out, although, curiously, modern philosophers of mathematics tend to prefer the idea, again, that we have made it all up ourselves. “God made the integers, all the rest is the work of man,” is a very famous and often quoted statement by Leopold Kronecker (1823-1891). Great scientists themselves, from Einstein to Hawking, still think of mathematics as revealing the Thoughts of God. From Kronecker’s statement we can conclude that he was not interested in the Thoughts of God; and, perhaps not surprisingly, he does not seem to have substantively advanced physics himself.
The Platonic-Pythagorean-Galilean view of mathematics, however, is clearly limited. The “sin” of Galileo in a new sense must be the belief that because we have a mathematically successful theory, this means that we understand what is going on. This is clearly not true. Newton’s theory of gravity was one of the most successful theories of all time. It was the paradigmatic mathematical theory of nature. But even at the beginning there were unanswered questions about it, especially in that it postulated action at a distance — that two bodies would affect each other gravitationally even without being in contact and without anything whatsoever mediating that contact. Gravity was something that was nothing in itself that nevertheless exerted a force invisibly across a complete Void. The mystery of this was highlighted by Newton’s own belief that it was the Will of God. This paradox and mystery, intense at first, slowly lost its power as the success of the theory silenced opposition.
Newtonian mechanics did not fall because of philosophical objections to action at a distance; but it fell to theories that, serendipitously, actually did not postulate action at a distance. These were, at first, Einstein’s general relativity, in which the curvature of space-time eliminated the need for “forces” altogether, and then quantum mechanics, which postulated an exchange of virtual particles to mediate forces. These alternate explanations, between Einstein and quantum mechanics, now accentuate the circumstance that successful mathematical theories do not enable us to understand reality. Since Einstein’s theory works for gravity, and quantum mechanics works for the other forces of nature, one might perhaps be tempted to say that gravity involves a curvature of space-time and the other forces involve an exchange of virtual particles. But this is not what physicists have expected: It is going to be one or the other. More recently, “super-symmetry” theories have extended Einstein’s approach to the other forces, with the addition of ten extra dimensions of space to account for them. The mathematical, if not the observational, success of these theories have animated physics in the last couple decades; but the strangeness of the whole business has come full circle with the conclusion of some that the extra dimensions are not “really” there but simply represent abstract mathematical dimensions that do not need to exist in the world. This would seem to leave things even more unexplained than before: Einstein’s geometry of reality becomes, once again, a calculating device.
Thus, indeed, a successful mathematical theory does not enable us to understand what is going on in reality. Multiple aspects of quantum mechanics reinforce this impression, since, as people say, no one understands quantum mechanics, but you get used to it. Why this could happen is explained by Popper’s view of scientific method: Theories are simply sufficient, not necessary, to observations. That is because theories are only falsified, never verified. Thus, different theories, in principle, could explain the same phenomena; or, a theory could mathematically predict the phenomena, without otherwise making any sense. This seems to be the case with quantum mechanics.
Refusing commit the “sin of Galileo” thus means the realization that scientific theories have both mathematical and conceptual sides to them. A theory may be mathematically strong but conceptually weak, or vice versa. It is widely acknowledged that Einstein’s Relativity is conceptually lucid and compelling, while quantum mechanics is mathematically exemplary while conceptually incoherent. It is revealing that, despite this, quantum mechanics for a long time was expected to replace Einstein. Great physicists like Richard Feynman positively reveled in the conceptual incomprehensibility of quantum mechanics. Now the shoe seems to be on the other foot, as super-symmetry extensions of Einstein’s theory apparently embrace the other forces of nature as quantum mechanics never could gravity — despite the people who don’t seem to think it is important to posit the real dimensions required by these extensions.
Recognizing the “sin of Galileo” must put scientists, and their sympathizers in philosophy, in the uncomfortable position of admitting that “philosophical objections” are not always absurd vapors to be dismissed but can often be significant warnings about the deficiencies of a scientific theory. The objections themselves, indeed, will not always be cogent and will rarely produce the answer; but, like the canary in the mine, they are a significant warning that something is not quite right. Nor is it always philosophers voicing the objections. Albert Einstein himself was intensely unhappy with the direction quantum mechanics took with Werner Heisenberg and Niels Bohr. Either Einstein himself must be dismissed as an old fool, which he was for many years, or it must be recognized that philosophical objections are often germane. Indeed, a compelling vindication of Einstein’s doubts is still not complete, though thankfully Roger Penrose’s The Emperor’s New Mind goes a very long way to completing it.
It is perhaps too much to expect that mathematicians and philosophers will ever collaborate in the way that composers and librettists do; but this is what, over time, will and must in effect happen. The major difficulty is with the philosophers: They tend either to be so enamored of their own theories, like the Hegelians, that they don’t even notice real science, or they are so awe struck and humbled by science, like the Logical Positivists, that they cannot summon up the audacity to actually criticize it. The middle ground of philosophers like Kant, Nelson, and Popper, who mostly understand science rather well but retain the faculty of criticism, is quite rare. Schopenhauer demonstrates the difficulty of hitting the mean, since he has rather interesting things to say about the laws of nature but then makes extremely foolish statements about the wave theory of light. Preferring Goethe’s theory of light to Newton’s, Schopenhauer misses the point of the new physics of Thomas Young and Michael Faraday. Loving the pure philosophical theory better than the good science, Schopenhauer could not have anticipated that science would ultimately return to his beloved qualitates occultae in the form of the strangeness, charm, top, bottom, leptonic charge, baryon number, etc. now found in particle physics.
Thus, recognizing the sin of Galileo does not provide us with a method for distinguishing the true from the false, but only with a caution, like Popperian philosophy of science in general, for how we regard the results of science or its relation to philosophy. This is a real enough caution, however, which must rule out many commonly expressed attitudes, especially those that disparage the independence or usefulness of philosophical knowledge, or those which are eager to dismiss science as damned with some kind of political bias — but that is another story.
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Is quantum teleportation possible?
by Katie Howard
What is teleportation? Roughly speaking, there is a Lab A and a Lab B, and each lab has a box. The goal of teleportation is to take any object that is placed in Box A and move it to Box B.
Of special interest to science fiction fans (among others) is human teleportation, where a brave telenaut (whom we shall call Jim) enters Box A and uses the teleportation machine to travel to Lab B.
It turns out that human teleportation appears possible in principle, though is probably impossible in practice. Nevertheless, teleportation of much smaller objects like individual spins is not only possible, but has been accomplished in the laboratory. Our goal here is to explain both how teleportation is done and why it is interesting.
Quantum information has a number of uses, such as to create quantum computers or to perform quantum cryptographic protocols. One of the most basic tasks you can imagine performing for quantum information is moving it around. Of course, you could just encode the information in a single photon and send it through an optical fiber, but it might get lost along the way. This is a serious problem, since quantum information cannot be copied without losing its essential quantumness. One possible solution is to use a quantum error-correcting code to protect the qubits being sent. This will work, but is still technically quite difficult. A rather more straightforward way is to use a protocol known as quantum teleportation.
Quantum teleportation, in some sense, can be viewed as splitting up the “quantum” and “information” parts of quantum information. For
In the above circuit, time moves from left to right. The top two lines represent qubits held by
Note that quantum teleportation has very little to do with moving about large objects: it is simply a way of substituting classical information for quantum information when we want to move the latter about. A large object like a chair needs an enormous amount of classical information to describe it completely, but the exact quantum state of a chair is unlikely to be of any interest. Therefore quantum teleportation is not going to be useful if you want to move a chair from
What is the teleportation machine supposed to do?
- Fully measures the state of the input
- Transmits the results via the line
- Reconstructs the original from the received description.
Step 1 is already impossible in a quantum world because of the Heisenberg uncertainty principle. We could measure the position of all the particles forming Jim but then we wouldn’t get a chance to measure the momentum of those particles. Alternatively, we could measure the momentum but then not the position. One can also envision a mixed strategy where we measure some positions and some momenta, however the uncertainty principle basically guarantees that we will never obtain enough information to rebuild even a modestly good copy of Jim.
The surprising result of quantum teleportation is that even though the “measure and reconstruct” procedure does not work, there is an alternative procedure that effectively realizes teleportation in the quantum world.
In fact, it was not until the publication of a 1993 paper by Bennett, Brassard, Crepeau, Jozsa, Peres and Wootters that we realized quantum teleportation was possible. That is some 70 years after the formulation of the theory of quantum mechanics!
Effectively we realized that quantum teleportation, which we thought to be impossible, is only very very hard. What is the difference between the two notions? Traveling faster than the speed of light is impossible, traveling at say 99% of the speed of light is possible but very hard to do.
The upgrade in status from impossible to very very hard may not be very significant to those who would like to actually build such a device. But to a physicist it makes a world of difference, and is a very exciting discovery.
So let me begin by describing the setup for quantum teleportation, which is almost identical to the setup for classical teleportation described above. Again, we will have Labs A and B, each with a box, and we will try to move the contents of box A to box B. The two labs will be separated by a wall and only connected by a phone.
We have to be careful in specifying what kind of phone. If this phone allows sending quantum information back and forth, then the problem of quantum teleportation becomes relatively trivial. It is similar to the classical case when we allowed trucks to move objects between A and B.
The interesting case is when the phone allows only the passage of classical information. You can think of the phone as measuring all signals as they pass through the phone. All standard phones are classical phones.
In effect, what we are asking here is can we use our standard classical communication tools to transmit the state of a quantum system.
Thus far our setup for quantum teleportation is equal to the one for classical teleportation. But there is one important difference. In the quantum case, Labs A and B must begin with something called an entangled quantum state, which will be destroyed by the teleportation procedure.
Roughly speaking an entangled state is a pair of objects that are correlated in a quantum way. Below we will describe a specific example known as the “singlet state” of two spins. However, let us first explore the consequences of this extra requirement for quantum teleportation.
To prepare an entangled state of two particles, one essentially has to start with both particles in the same laboratory, let’s say Lab A. Now we have the problem of sending one of the particles to Lab B. In principle, we could use quantum teleportation to send this particle to B, but this process would destroy one entangled state to create another entangled state, a net gain of zero. In any case, we have to worry about how the first entangled state is created.
The only solution is that sometime in the past the wall that separates Lab A and Lab B must not have been there. At that time the scientists from the two labs met, created a large number of entangled states, and carried them to their respective laboratories.
Think of two friends who lived nearby, but now one is moving away. They can create some entangled states that the friend who is moving can carry with him when he leaves, and then they can use those to teleport things back and forth. However, if they had never met in person and have no friends in common (who could have met with both of them) then quantum teleportation becomes impossible.
So returning to our brave telenaut Jim, he will be able to teleport to the labs of his friends. But also he could use two teleportations to travel to the labs of people whom he has never met personally, but who are friends of his friends. Similarly, he can teleport to the labs of the friends of his friends of his friends, and so on. However, teleporting to say a distant planet or to some other place we have never had contact with is impossible.
The entanglement requirement poses a second problem, since as we mentioned above it is destroyed when used. Entanglement is effectively a resource that is slowly depleted as teleportations occur. It can be renewed by meeting in person and then carrying entanglement back from Lab A to Lab B, but it has to be transported without the use of teleportation. In principle this is difficult, otherwise we wouldn’t have bothered using teleportation from A to B in the first place. However, the idea is that one difficult journey from A to B can allow in the future many quick transfers from A to B.
I should mention one last important detail of quantum teleportation. In the classical case we decided to run Jim through the shredder in Lab A after “faxing” him to lab B. But it seems like this step was optional, and we could have chosen to end up with two copies of Jim. In the quantum case this is not possible, because quantum information cannot be copied. The only way to teleport an object to Lab B is to destroy the object at Lab A.
Philosophically, one can say that if there can only ever be one copy of Jim at any time, and the copy of B survives the teleportation process in a pain free manner, then whatever is destroyed at in Lab A could not have been a copy of Jim.
However, we shall leave moral questions of this sort to the philosophers, and instead turn our attention now to the mathematics of quantum teleportation.
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by Katie Howard
- Outcome independence: the outcome of the experiment at site A does not depend on the outcome of the experiment at site B.
- Parameter independence: the outcome of the experiment at site A does not depend on the choice of detector setting at site B.
The concept of locality prohibits any influences between events in space-like separated regions. Think of it in terms of Maxwell’s equations, where the electric and magnetic fields are plane waves travelling at a constant speed, which is the speed of light. If there is causality between two non-local events, the time delay must be larger than the time light takes to travel from the first to the second event.Leggett has proposed to consider theories that maintain the assumption of outcome independence, but drop the assumption of parameter independence. It is worth remarking at this point that the attribution of fundamental importance to this factorization of the locality assumption can easily be criticized. Whilst it is usual to describe the outcome at each site by ±1 this is an oversimplification. For example, if we are doing Stern-Gerlach measurements on electron spins then the actual outcome is a deflection of the path of the electron either up or down with respect to the orientation of the magnet. Thus, the outcome cannot be so easily separated from the orientation of the detector, as its full description depends on the orientation.Nevertheless, whatever one makes of the factorization, it is the case that one can construct toy models that reproduce the quantum predictions in
They are able to falsify this combined assumption because the (wrong) assumption implies, through
The sane conclusion is, of course, that we must finally do what all fully sane friends of Max Born did in 1926, take quantum mechanics seriously, and abandon “realism” (I don’t mean political realism which is good but quantum realism which is bad!): only probabilities may be predicted and it makes no sense to talk about the “real” values of observables of a quantum system before these values are measured. Only results of experiments have a physical meaning.
Nevertheless, some people still insist that it is plausible that “realism” holds and locality is what is violated. Relativity requires that the fundamental degrees of freedom - such as quantum fields - must evolve according to local and causal laws. This statement must be true with accuracy: it’s not only beautiful but it has been experimentally validated.
On the other hand, Zeilinger now argue that they have falsified a large class of “nonlocal realist” theories, too, because the measured correlations are higher even than what “nonlocal realist” theories allow. I don’t quite know how they can achieve such a goal. It is clearly a theoretical goal.
I think that every sane quantum physicist can predict the result of all these experiments and there can’t be any new surprises here: quantum mechanics works and physics behind all these experiments is controlled by the same simple laws that give clear predictions to every setup. On the other hand, they must be using some “improved” version of
Nevertheless, I endorse their position that the results of all these experiments make any attempt to preserve “realism” - i.e. to deny the probabilistic nature of quantum mechanics - highly contrived. The more you understand how these experiments work, the more you agree with us.Such models of physical realism, suggesting that the results of observations are consequence of the properties carried by physical systems, are called hidden-variable theories. The idea is that all measurement outcomes depend on pre-existing properties of objects that are independent of the measurement. The limitation of quantum theory then would be that we do not know all variables, they are hidden from us.
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by Katie Howard
Quantum mechanics is the theory used to ‘describe’ the processes that take place in the micro-world. From the start quantum mechanics has been a ’strange’ theory, in the sense that it seemed to contradict in various ways the image of a micro-world consisting of ‘objects’ moving around in a three dimensional space, and interacting with each other in this three dimensional space. So from the advent of the theory a lot of disagreement existed as to the ‘physical meaning’ of this quantum theory, and a lot of discussions of a philosophical nature have taken place among the founding fathers. Only however during the last years experiments have been performed that, independently of the strangeness of the quantum theory, confront us directly with the strangeness of the reality of the micro-world. We have in mind the experiments on the EPR problem. In our opinion to be able to ‘understand’ the reality of this micro-world, it will be necessary to introduce new concepts, and become aware of old ‘classical’ prejudices. Certainly in not such a radical way as proposed by what is sometimes called the ‘California interpretation’ of quantum mechanics, but also in not such a vague way as is proposed by what is called the ‘Copenhagen interpretation’ of quantum mechanics. Since we nowadays have very ’specific’ results, on very refined experiments, we should start ‘imagining’ how this ‘micro-reality’ is.
Quantum Information is an interesting example where purely fundamental andeven philosophical research can lead to a new technology of information andcomputational science. Superposition and entanglement are the essence of a new quantum information technology era.
Numerous tests of quantum mechanical nonlocality has been performed over the last 20 years. In such experiments one uses the quantum mechanicalproperty that it is possible to create photon pairs in entangled states that reveal nothing about individual photon properties but still allow strong correlations between the measured quantities. Imagine a pair of subatomic particles (electrons, for example) bound together in a state with zero “spin” (rotational momentum). These particles, as it happens, can’t possess zero spin themselves; they must spin either “up” or “down.” It follows, because of the zero spin of their bound state, that the particles must individually possess different spin states — one must be “up,” the other “down.” We release our bound particles, and they shoot away from one another near the speed of light. They lie 600,000 kilometers apart within a second. If we measure the spin of one, we will instantly, across that vast distance, know the spin of its partner.