Week 11: April 9, The Enigma of Measurement: Detecting the Quantum World
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1 Week 11: April 9, 2018 Quantum Measurement The Enigma of Measurement: Detecting the Quantum World Two examples: (2) Measuring the state of electron in H-atom Electron can be in n = 1, 2, 3... state. In general, it is in the superposition of all these states. That is Ψ = Ψ 1 + Ψ 2 + Ψ However, in any measurement, we will find that it is all one of these possible states. A measurement on another H-atom, described by same Ψ may find it in a different state. If we make measurements on large number of H-atoms, we can determine the probability of its being in n = 1, 2, 3... state. However, this information is completely encoded in the quantum state represented by Ψ. (2) Let us understand this using double slit experiment. In the absence of detector, each quantum spreads though both slits in a coherent superposition. When the detector is switched on, there is an instantaneous change of state of the entire extended quantum occurs. This puts the composite system detector plus quantum into the following entangled state: The quantum comes through first slit and detector indicates first slit superposed with quantum comes through second slit and detector indicates second slit. That is, the measurement state is an entanglement of the quantum with the detector. Dramatization of the problem The Curious Tale of Schr odinger Cate Many World Interpretation of Quantum Mechanics Many world interoperation was originally proposed by Hugh Everett in Work received very little attention: the physicist and historian Jammer mentions that it was one of the best kept secrets in this century. In 1967 Bryce de Witt wrote an article drawing attention to Everett s work. He wrote two 1
2 papers that glamorized the idea. To understand many worlds consider the double slit experiment. Every electron is detected at a certain point on the screen. The standard quantum theory says that the electron entangles with zillions of atoms-size regions of the screen and collapses into one of these regions. In many worlds, the electron does not collapse, instead reality splits into zillions of separate realities, in each of which the electron impacts a different atom-size region. Up to this point, this is consistent with the standard quantum theory. However, this interpretation asserts that all these different realizations actually exist and persist for ever. The problem with many world interpretation is, why do we not see zillions of impacts?? The many world theory says that the universe itself splits simultaneously into zillions of separate universes, in each of which one possibility exists. In the universe that we happen to inhabit, the electron ends up in one specific location ( on in an atom) on the screen. One reason some people like many worlds is that it does away with quantum randomness. No single outcome is chosen in preference to the others. They all occur, but in different universes. However, this many world interpretation cannot be tested experimentally. To many, it is absurd that when a quantum process can evolve into more than one possibility, the universe some how coexist with many other universes one accommodating each possibility. The other universes are not observable and are simply out there somewhere, and their number is exponentially large. The many world idea might seem more plausible today because of the cosmic inflation hypothesis developed by Alan Guth and Andrei Linde during It states that beginning a trillionth of a trillionth of a trillionth of a second after the initiation of Big Bang, universe was pushed into short bust of exponentially accelerating expansion at speed faster than speed of light for a very brief time. This has experimental support in the observation of cosmic back ground radiation emitted at the Big Bang. This hypothesis suggests that inflation continues for ever in at least some regions of the universe, producing an infinite number bother universes a possibility that many astronomers take seriously. However, it is hard to see its relation to many-world interpretation of quantum physics. 2
3 An Entangled Nonlocal Universe Spooky Actions at a Distance Instantaneous action across a distance Locality Principle Processes occurring at one location should have no instantaneous effect at another location. Instantaneous action across a distance is predicted by quantum physics and has also been experimentally verified. This means that this common sense notion of locality principle is violated in quantum world. In other worlds, the quantum world is non-local. The quantum non locality is a direct consequence of the unity and spatial extension of the 3
4 quantum particle.. as the particle has a finite probability of existence in a regime which defines its spatial extent. If a change occurs at one place inside that region, change must occur simultaneously across the entire region where the particle can exist. Is this is not in conflict with postulate of relativity which says that information cannot travel faster than speed of light. That is two spatially seated regions cannot influence each other instantaneously??? As Heisenberg argued, this is not the case as the outcome is indeterminate at both locations. EXAMPLE (1) : Suppose some central location in space send a SINGLE superposed photon to Alice on earth and Bob on Mars. That is the photon has 50 percent chance of reaching Alice and 50 percent chance of reaching Bob. It takes 15 minutes to communicate by radio between earth and Mars. Can Alice manipulate her own detector in some manner to send an instant message to Bob?? The answer is NO because the probably of Bob detecting the photon remains unchanged no matter what Alice does. If Alice could cause the photon to either appear or not appear at her site location ( that would mean that the photon will appear with 100 percent certainty at Bob s location ), then she could send Bob some message. That is, let us suppose Alice and Bob agree in advance that if Bob receives a photon, then Yankees won and if he does not, that means they lost. But she cannot do such a thing as she cannot control the quantum indeterminacy. So there is NO conflict between instantaneous collapse of a single quantum and relativity s ban on superluminal ( greater than speed of light ) communication. EXAMPLE (2): Nonlocal communication using two quanta that are entangled Any alternation of one of the quanta would lead to instant changes in the other. Consider two electrons with total spin zero. That is, one electron has spin pointing up and the second electron has spin pointing down. Let us say, one is on the earth and the second is on Mars. If the spin of the electron on each changes from up to down, instantaneously, the spin of the second electron on mars will change from down to up. That is, this is nonlocal effect. It is like coin flips at earth and mars are correlated. If we get a head on earth, it has to be tail on the mars and vice versa. ( This is again not in conflict with relativity because it cannot be used to transmit information or energy). 4
5 The following entanglement and associated nonlocal effects have been demonstrated experimentally. Two photons separated by 144 km. Two atoms separated by one meter. Two tiny diamonds ( each contain atoms separated by 15 cm. Two gas clouds each made of a trillion Cs atoms at millimeter separation. A variety of systems of atoms and photons. 5
6 What we we do with Quantum Entanglement?? It may have useful applications in communications and computing technologies. So just like energy is a useful resource, quantum entanglement can be useful. Quantum entanglement can be useful for increasing the ability of computers to solve some computational problems that is in quantum computers. Teleporting a quantum state from one location to another. Note that we are not simply transferring knowledge of a state from one place to another that could be done using a telephone. The goal of quantum teleportation is to move or transmit a quantum state of an object at one location to an object at another location without actually knowing the state or sending the object itself. If we know the quantum state of a photon, we can transmit this state to your friend simply by placing a phone call or sending an . The friend can then prepare a new photon in that state. NO teleportation needed. The interesting case is, if someonee hands you a quantum object and does not tell you the state but ask you to teleport it to someone say Bob anyway. Now, you cannot make a copy of the state a principle of quantum physics called the No Cloning principle. and you cannot determine the state by making measurements on that single object. Therefore, you do not possess the information needed to instruct Bob how to create or mimic that quantum state... ( Suppose the quantum object is the H-atom. Its quantum state is fully described by its wave function that tells us the probability for it to be in n = 1, 2, 3... states. My measurement, the atom will collapse to one of these n values. ) HOW DOES ENTANGLEMENT Allow TELEPORTATION??? Suppose Prof. X sends Alice a photon for which he knows its state Ψ but Alice does not know anything. Now Alice wants to transport this state to Bob with knowing what that Ψ 6
7 is. (You can imagine Alice and Bob together have a e-post office that people go to quantum teleport.) This e-post office that involves Alice and Bob at two different locations have one of two photons that are entangled. That is the e-post office consists of an entangled photon pair, which we call A-B pair where Alice has A and Bob has B. With this pair, they are ready to transport the state Ψ of the photon X. First Alice entangles X and A photon, without changing the state Ψ of the X-photon. Now that A-photon is entangled with the B-photon, the three photons X, A and B get entangled. Alice generates a code that characterizes this entanglement between A and X and calls Bob and informs him about this code.this allows Ψ to be teleported. Note that Quantum Teleportation is not instantaneous. The needed entangled pair forms the e-post office tool to accomplish it and is available before hand, that is before one starts the teleportation of Ψ. Teleportation can take place in a short time it takes Alice to entangle X and A and inform Bob by telephone or . NOTE: In principle, all objects can be characterized by a wave function Ψ, and hence can be teleported. What is Quantum State Teleportation Good For??? There are some possible practical applications... One possible future use will likely be for passing quantum information, or data, between quantum computers 7
8 Using Quantum Physics to perfectly secure communication Internet, money transfer... Art of sending messages encryption systems - Is there an Encryption method that cannot be cracked??? In classical world, we can make copies...or replicas. But in quantum world, we cannot examine every aspect or property of the system because some of them are complementary to each other that is subjected to Heisenberg uncertainty principle. The so called no-cloning principle implies that quantum state of an object can not be determined by any single measurements. Three Theories: Hidden Variable Theoty Many World Interpretation of quantum world Shut up and calculate World Watching the Ytube video: The Invisible Reality: The Wonderful Weirdness of the Quantum < NOTE that quantum state is analogous to the classical coin that has been flipped but not yet looked at. There are two big differences, however: (1) Quantum uncertainty is intrinsic or fundamental. (2) Quantum state when created by entanglement, retains subtle, nonlocal correlations. 8
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