SCEST21: Schrodinger's Cat, and Einstein's Space-time, in the 21st Century
A blogspot for discussing the connection between quantum foundations and quantum gravity
Managed by: Tejinder Pal Singh, Physicist, Tata Institute of Fundamental Research, Mumbai
If you are a professional researcher / student researching on these topics, and would like to post an article here with you as author, you are welcome to do so. Please e-mail your write-up to tpsingh@tifr.res.in and it will be uploaded here.
Keywords: Quantum foundations; Quantum gravity; Schrodinger's cat; Spontaneous collapse theory
____________________________________________________
November 21, 2019
Schrodinger's cat in the 21st century
Tejinder Singh
If a physical theory agrees with some of the data, but not with all the data, it should be replaced by a falsifiable new theory which agrees with all of the data. The new theory should reduce to the old theory in those domains where the old theory agrees with the data.
Such a strategy worked successfully in the transition from Newtonian mechanics to special relativity, and it worked successfully in the transition from Newtonian gravitation to Einstein's general relativity. We can say that special relativity is a cover for Newton's mechanics, and general relativity is a cover for Newtonian gravitation. But the transition from Newtonian mechanics to quantum mechanics is a different story altogether!! Quantum mechanics is not a cover for classical mechanics.
Quantum mechanics was invented to explain data such as the black-body radiation spectrum, atomic spectra, and the photoelectric effect, which Newton's mechanics fails to explain. And quantum theory explains these, and much much more, beautifully. But quantum theory fails to explain the data that Newton's mechanics explains! So we need a new theory which will agree with both quantum mechanics, as well as with classical mechanics.
At the heart of the disagreement between classical and quantum mechanics is the very elegant quantum linear superposition principle, which says that if a quantum system can be in State A and if it can be in State B, then it can also be in the superposed state A+B. In particular, the superposition principle is known to hold for positions of a particle. If an electron can be here, and if the same electron can be there, it can also simultaneously be here as well as there. This is how we understand the appearance of interference fringes on the screen in a double-slit experiment with electrons.
The quantum superposition principle has been experimentally verified to hold for photons, neutrons, atoms, small molecules, and is known to hold for objects as heavy as 25,000 a.m.u. That is, an object made of 25,000 nucleons. Experimentalists would love to test the principle for even heavier objects, but its technologically extremely challenging. They are at it.
But the superposition principle fails for large objects that we see in our day to day life, obviously. We never see a chair to be here and there at the same time. Nor do we see a planet to be in the north and in the south at the same time. Yet the motions of chairs and planets is successfully described by Newton's mechanics. This is what we mean when we say that quantum mechanics fails for large objects and disagrees with classical mechanics. In fact, Schrodinger's equation predicts that a chair can be here and there simultaneously. The mass of the object described by the Schrodinger equation is completely arbitrary. This mass can be as large as we please. Hence Schrodinger's equation should hold for a chair, and superposition should have been observed, but its not observed. Another way to appreciate the problem is that the chair is made of elementary particles which themselves obey the superposition principle. Why is it that when we put many such particles together, superposition breaks down?
What is the way out of this contradiction between quantum mechanics and Newtonian mechanics? We need a cover for Newton's mechanics, which will agree with quantum mechanics for small objects. Such a new theory was proposed by physicists Ghirardi, Rimini, Weber and Pearle (GRWP) in the 1980s. Their idea is beautiful and simple. They said, look - quantum mechanics says that a superposition, once created, lasts forever. This is because the Schrodinger equation is linear and deterministic. On the other hand, Newton's mechanics does not allow for position superpositions at all. GRWP said, let's make a very very small modification to quantum theory. Let us propose that superposition of two position states of a particle, say a proton, does not last forever, but lasts for an extremely long time T. That is, the mean superposition life-time of two position states of a proton is not infinite, but a large number T. For definiteness, they proposed T to have the value 10^17 seconds, (which also happens to be the age of the universe) for a nucleon. After a time T, the superposition is assumed to spontaneously collapse to one or the other states which were superposed (here or there). This is the GRWP theory of spontaneous collapse. Remember, T is the mean lifetime, and collapse is a random (Poisson) process in time. There is always a tiny probability for spontaneous collapse to take place in a time much smaller than T.
This small modification to quantum theory suffices to provide us with a new theory which reduces to Newton's mechanics for large objects. Again, this works in a very elegant manner. Consider, for a start, a deutron - the nucleus of the deutirium atom, which is a bound state [also an entangled state] of a neutron and a proton. Now, for a deutron to undergo a spontaneous collapse, starting from a superposed state, it is enough for either the proton to undergo a spontaneous collapse, or for the neutron to undergo spontaneous collapse. One particle will take the other with it, because they are bound (entangled). You can then reason that the superposition lifetime for the deutron is halved, it is T/2, because there are two independent ways in which the collapse can happen.
There, now you have it. A large object such as a chair is made is of an enormous number of nucleons and electrons. If there are N particles in the chair, the chair can be in a superposed state (here and there) only for a time T/N. [Because any one particle collapsing will take the whole chair with it]. But N for a chair is huge, say 10^23. Since T is assumed to be 10^17 seconds, T/N is a mere millionth of a second. The superposed state for a chair lasts for such a short time, that we do not even notice it. Schrodinger's cat is dead as well as alive for a millionth of a second; after that it is dead, or alive. That is why large objects appear to obey Newton's mechanics.
In this way, the theory of spontaneous collapse is the cover for Newton's mechanics. The cover theory reduces to quantum mechanics for small objects. This is because for small objects, the superposition life-time is so enormous as to be practically infinite, as demanded by quantum mechanics.
The GRWP theory would occupy the same place of pride as special relativity and general relativity, if it were to be confirmed by experiment. Experimentalists are working hard to test it. The current experimental bound on T is that T > 10^8 seconds. Recall that GRWP say that T=10^17 seconds. and quantum mechanics says that T is infinite. Still nine more orders of magnitude to go before GRWP is ruled out. Note that a confirmed detection of spontaneous collapse below GRWP value will also prove the theory of spontaneous collapse. The theory will be ruled out if experiments will push the bound on T beyond the GRWP value. If T is higher than the GRWP value, then for large objects T/N will approach time scales larger than a millionth of a second, which means we would see a chair here and there at the same time. Thus, values of T larger than the GRWP value do not provide a cover theory for Newton's mechanics.
A blogspot for discussing the connection between quantum foundations and quantum gravity
Managed by: Tejinder Pal Singh, Physicist, Tata Institute of Fundamental Research, Mumbai
If you are a professional researcher / student researching on these topics, and would like to post an article here with you as author, you are welcome to do so. Please e-mail your write-up to tpsingh@tifr.res.in and it will be uploaded here.
Keywords: Quantum foundations; Quantum gravity; Schrodinger's cat; Spontaneous collapse theory
____________________________________________________
November 21, 2019
Schrodinger's cat in the 21st century
Tejinder Singh
If a physical theory agrees with some of the data, but not with all the data, it should be replaced by a falsifiable new theory which agrees with all of the data. The new theory should reduce to the old theory in those domains where the old theory agrees with the data.
Such a strategy worked successfully in the transition from Newtonian mechanics to special relativity, and it worked successfully in the transition from Newtonian gravitation to Einstein's general relativity. We can say that special relativity is a cover for Newton's mechanics, and general relativity is a cover for Newtonian gravitation. But the transition from Newtonian mechanics to quantum mechanics is a different story altogether!! Quantum mechanics is not a cover for classical mechanics.
Quantum mechanics was invented to explain data such as the black-body radiation spectrum, atomic spectra, and the photoelectric effect, which Newton's mechanics fails to explain. And quantum theory explains these, and much much more, beautifully. But quantum theory fails to explain the data that Newton's mechanics explains! So we need a new theory which will agree with both quantum mechanics, as well as with classical mechanics.
At the heart of the disagreement between classical and quantum mechanics is the very elegant quantum linear superposition principle, which says that if a quantum system can be in State A and if it can be in State B, then it can also be in the superposed state A+B. In particular, the superposition principle is known to hold for positions of a particle. If an electron can be here, and if the same electron can be there, it can also simultaneously be here as well as there. This is how we understand the appearance of interference fringes on the screen in a double-slit experiment with electrons.
The quantum superposition principle has been experimentally verified to hold for photons, neutrons, atoms, small molecules, and is known to hold for objects as heavy as 25,000 a.m.u. That is, an object made of 25,000 nucleons. Experimentalists would love to test the principle for even heavier objects, but its technologically extremely challenging. They are at it.
But the superposition principle fails for large objects that we see in our day to day life, obviously. We never see a chair to be here and there at the same time. Nor do we see a planet to be in the north and in the south at the same time. Yet the motions of chairs and planets is successfully described by Newton's mechanics. This is what we mean when we say that quantum mechanics fails for large objects and disagrees with classical mechanics. In fact, Schrodinger's equation predicts that a chair can be here and there simultaneously. The mass of the object described by the Schrodinger equation is completely arbitrary. This mass can be as large as we please. Hence Schrodinger's equation should hold for a chair, and superposition should have been observed, but its not observed. Another way to appreciate the problem is that the chair is made of elementary particles which themselves obey the superposition principle. Why is it that when we put many such particles together, superposition breaks down?
What is the way out of this contradiction between quantum mechanics and Newtonian mechanics? We need a cover for Newton's mechanics, which will agree with quantum mechanics for small objects. Such a new theory was proposed by physicists Ghirardi, Rimini, Weber and Pearle (GRWP) in the 1980s. Their idea is beautiful and simple. They said, look - quantum mechanics says that a superposition, once created, lasts forever. This is because the Schrodinger equation is linear and deterministic. On the other hand, Newton's mechanics does not allow for position superpositions at all. GRWP said, let's make a very very small modification to quantum theory. Let us propose that superposition of two position states of a particle, say a proton, does not last forever, but lasts for an extremely long time T. That is, the mean superposition life-time of two position states of a proton is not infinite, but a large number T. For definiteness, they proposed T to have the value 10^17 seconds, (which also happens to be the age of the universe) for a nucleon. After a time T, the superposition is assumed to spontaneously collapse to one or the other states which were superposed (here or there). This is the GRWP theory of spontaneous collapse. Remember, T is the mean lifetime, and collapse is a random (Poisson) process in time. There is always a tiny probability for spontaneous collapse to take place in a time much smaller than T.
This small modification to quantum theory suffices to provide us with a new theory which reduces to Newton's mechanics for large objects. Again, this works in a very elegant manner. Consider, for a start, a deutron - the nucleus of the deutirium atom, which is a bound state [also an entangled state] of a neutron and a proton. Now, for a deutron to undergo a spontaneous collapse, starting from a superposed state, it is enough for either the proton to undergo a spontaneous collapse, or for the neutron to undergo spontaneous collapse. One particle will take the other with it, because they are bound (entangled). You can then reason that the superposition lifetime for the deutron is halved, it is T/2, because there are two independent ways in which the collapse can happen.
There, now you have it. A large object such as a chair is made is of an enormous number of nucleons and electrons. If there are N particles in the chair, the chair can be in a superposed state (here and there) only for a time T/N. [Because any one particle collapsing will take the whole chair with it]. But N for a chair is huge, say 10^23. Since T is assumed to be 10^17 seconds, T/N is a mere millionth of a second. The superposed state for a chair lasts for such a short time, that we do not even notice it. Schrodinger's cat is dead as well as alive for a millionth of a second; after that it is dead, or alive. That is why large objects appear to obey Newton's mechanics.
In this way, the theory of spontaneous collapse is the cover for Newton's mechanics. The cover theory reduces to quantum mechanics for small objects. This is because for small objects, the superposition life-time is so enormous as to be practically infinite, as demanded by quantum mechanics.
The GRWP theory would occupy the same place of pride as special relativity and general relativity, if it were to be confirmed by experiment. Experimentalists are working hard to test it. The current experimental bound on T is that T > 10^8 seconds. Recall that GRWP say that T=10^17 seconds. and quantum mechanics says that T is infinite. Still nine more orders of magnitude to go before GRWP is ruled out. Note that a confirmed detection of spontaneous collapse below GRWP value will also prove the theory of spontaneous collapse. The theory will be ruled out if experiments will push the bound on T beyond the GRWP value. If T is higher than the GRWP value, then for large objects T/N will approach time scales larger than a millionth of a second, which means we would see a chair here and there at the same time. Thus, values of T larger than the GRWP value do not provide a cover theory for Newton's mechanics.
You are welcome to leave your comments and suggestions on the above post, and on the concept of this blog.
ReplyDeleteIt's a great article, Sir.
ReplyDeleteThe GRWP theory sets a time-bound on the superposition, but I have a thought - why it even needs to be that way. Suppose we have 10^23 particles bounded to each other by some force (I will restrict myself to call them entangled). All having their own superposition states. Being so much in number and bonded physically to each other, their superposition cancels out and the system as a whole appears to be just where it is the whole time. Of course, it is possible that some particles may free themselves out and still be in some superposition but that won't affect the chair. It will also eliminate the use of 'spontaneous collapse' in this.
According to quantum mechanics, the superpositions *do not* cancel out. QM claims to hold for any object, irrespective of the number of particles in it.
DeleteSir, please tell why the superposition don't cancel out in quantum mechanics. Is it a postulate or any theoretical/experimental work proved it?
ReplyDeleteIt is a consequence of the Schrodinger eqn: if an object has N particles labelled 1, 2, 3, ....N then the object can be a in superposition of two position states a and b, and the state of the object will be given by
Delete|1a> |2a> ....|Na> + |1b> |2b>....|Nb>
Such a state is allowed and demanded by the Schrodinger eqn, for any N
Does the GRW theory have any advantage over Penrose's objective reduction?
ReplyDeleteBoth are in a sense incomplete, but in my view GRW has advantages over Penrose. GRW is a well-dfined mathematical theory, and accounts for dynamical wave function collapse. But it does not explain what causes collapse. Penrose suggests that gravity causes reduction, but he does not have a mathematical theory with equations. Recent work in trace dynamics by Adler, and my own work, strongly suggests connection of GRW with gravity.
ReplyDelete