Physics
Schrödinger's Cat
Schrödinger's Cat is a thought experiment that illustrates the concept of superposition in quantum mechanics. In the experiment, a cat is placed in a sealed box with a device that has a 50% chance of releasing poison. According to quantum theory, until the box is opened and the cat is observed, it exists in a superposition of both alive and dead states. This highlights the peculiar nature of quantum superposition and the role of observation in determining an outcome.
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8 Key excerpts on "Schrödinger's Cat"
- David Prutchi(Author)
- 2012(Publication Date)
- Wiley(Publisher)
Schrödinger meant this example to be a criticism of the Copenhagen Interpretation of the wavefunction, which implies that the cat remains both alive and dead (to the universe outside the box) until the box is opened. That is, when asked whether the cat is dead or alive during the hour of waiting, the Copenhagen Interpretation would answer that the cat is in a superposition of dead and alive until you look in the box. Then, and only then, does the act of measurement (looking in the box) “collapse the wavefunction,” resulting in a cat that’s definitely alive or dead.Einstein and Schrödinger simply could not accept that reality is suspended when it is not being observed. This thought experiment really highlights the main philosophical issues that result from quantum mechanics, including the meaning of the quantum waves, the process of measurement, and the involvement of measuring instruments and observers in processes being studied.Today, physicists no longer find the process mysterious and intractable, mostly because no physical meaning is given to the wavefunction. Instead, Ψ is understood to be just an abstract mathematical function that contains statistical information about possible experimental outcomes. Whenever the quantum system is measured, the mathematical form of Ψ simply changes, which is common behavior for an abstract mathematical representation, and which doesn’t cause any philosophical problems.MANY-WORLDS INTERPRETATION
The leading alternative interpretation was developed in 1957 by American physicist Hugh Everett, who proposed that the universe splits every time there’s an event with more than one possible outcome. Each different universe evolves with one of the possibilities realized. As shown in Figure 120 , the bizarre, but logically consistent Many-Worlds Theory
eBook - PDF- Franck Laloë(Author)
- 2019(Publication Date)
- Cambridge University Press(Publisher)
2.2 Schr¨ odinger’s cat, measurements 29 of their own observations, and to reduce the state vector? Some theories take this point of view, a case in which, when the wave function includes a cat component, the animal could remain simultaneously dead and alive for an arbitrarily long pe- riod of time, a paradoxical situation indeed. The last sentence of Schr¨ odinger’s quotation concerning photographs has of- ten been considered as obscure. Schr¨ odinger probably wishes to emphasize the difference between an incomplete knowledge (an out-of-focus photograph) of a well-defined object, and an object that is inherently not sharply defined in space (a cloud) – between an indeterminacy that is related to lack of information or an inher- ent indeterminacy. In other words, he is already questioning the complete character of quantum mechanics (Chapter 3). 2.2.2 Misconceptions A common misconception is that the paradox is easily solved by just invoking decoherence (§7.3.3), which explains why it is impossible in practice to observe quantum interferences between states where a cat is alive or dead. We come back to this point in §7.3.3.b in more detail, and discuss it only briefly here. Actually, (de)coherence is irrelevant in Schr¨ odinger’s argument: the cat is actually a symbol of the absurdity of a quantum state that encompasses two incompatible possibili- ties in ordinary life, coherent or not. It does not change the absurdity of the final situation whether the state in question is a pure state (sensitive to decoherence) or a statistical mixture (insensitive to decoherence). Actually, the standard evolution of the state vector, including decoherence, does not change the norms of any of the two components (the components where the cat is alive or dead): it only creates more and more ramifications inside both these components, without ever changing any of the two norms, which give the probability of survival of the cat.
eBook - PDFQuantum Mechanics
A Paradigms Approach
- David H. McIntyre(Author)
- 2022(Publication Date)
- Cambridge University Press(Publisher)
The mathematics of quantum Nucleus Cyanide Geiger Counter Cat FIGURE 4.3 Schrödinger cat gedanken experiment. 104 Quantum Spookiness mechanics is clear and allows us to calculate precisely. No one is disagreeing about the probability that the cat will live or die. The disagreement is all about “what it really means!” To steer us toward the clear mathematics, Richard Feynman admonished us to “Shut up and calculate!” Two physicists who disagree on the words they use to describe a quantum mechanical experiment generally agree on the mathematical description of the results. Recent advances in experimental techniques have allowed experiments to probe the boundary between the classical and quantum worlds and address the quantum measurement issues raised by the Schrödinger cat paradox. The coupling between the microscopic nucleus and the macroscopic cat is representative of a quantum measurement whereby a classical meter (the cat) provides a clear and unambiguous measurement of the state of the quantum system (the nucleus). In this case, the two possible states of the nucleus (undecayed or decayed) are measured by the two possible positions on the meter (cat alive or cat dead). The quantum mechanical description of this complete system is the entangled state 0 c system 9 = 1 12 1 0 c undecayed 9 0 c alive 9 + 0 c decayed 9 0 c dead 92 . (4.14) The main issue to be addressed by experiment is whether Eq. (4.14) is the proper quantum mechanical description of the system. That is, is the system in a coherent quantum mechanical superposition, as described by Eq. (4.14), or is the system in a 50 > 50 statistical mixed state of the two possibilities? As discussed above, we can distinguish these two cases by looking for interference between the two states of the system. To build a Schrödinger cat experiment, researchers use a two-state atom as the quantum system and an electromagnetic field in a cavity as the classical meter (or cat).
eBook - PDF- Franck Laloë(Author)
- 2012(Publication Date)
- Cambridge University Press(Publisher)
One is contained in a very powerful continuous equation of evolution that applies to all systems; the other is the cat, which is the symbol of a limit that the same equation should never reach. 24 Present situation intellectual abilities that are necessary to perform a measurement and resolve several Von Neumann branches into one? At what stage of evolution can a living creature perceive its own state, projecting itself onto one of the alive or dead states? Or do humans only have access to a sufficient level of introspection to become conscious of their own observations, and to reduce the state vector? Some theories take this point of view, a case in which, when the wave function includes a cat component, the animal could remain simultaneously dead and alive for an arbitrarily long period of time, a paradoxical situation indeed. The last sentence of Schrödinger’s quotation concerning photographs has often been considered as obscure. Schrödinger probably wishes to emphasize the differ- ence between an incomplete knowledge (out-of-focus photograph) of a well defined object, and an object that is inherently not sharply defined in space (a cloud) – between an indeterminacy that is related to lack of information or an inherent indeterminacy. In other words, he is already questioning the complete character of quantum mechanics (§3). 2.2.2 Misconceptions A common misconception is that the paradox is easily solved by just invoking decoherence (§6.3.3), which explains why it is impossible in practice to observe quantum interferences between states where a cat is alive or dead. We come back to this point in §6.3.3.b in more detail, and discuss it only briefly here. Actually, (de)coherence is irrelevant in Schrödinger’s argument: the cat is actually a symbol of the absurdity of a quantum state that encompasses two incompatible possibilities in ordinary life, coherent of not.
eBook - ePubThe Science of Light
From Galileo’s Telescope to Quantum Physics
- Serge Haroche(Author)
- 2023(Publication Date)
- Odile Jacob(Publisher)
Q factors ten times longer, which would allow us to maintain cats containing ten times more photons for time intervals on the same order. Thus, there is no clear boundary between the classical and quantum worlds. Pushing this limit by making Schrödinger’s cats bigger and bigger is more a problem of technology than one of fundamental physics. It is nevertheless an essential problem if we wish to exploit quantum logic for practical applications in information processing.Returning to the image of Schrödinger’s cat, we now understand why it’s practically impossible to prepare a real animal in a coherent superposition of living and dead states. Such a superposition would imply that it was in a well-determined quantum state at the beginning of the experiment. However, our feline is a complex system coupled to a vast environment of molecules and thermal photons indispensable to its survival. It is therefore permanently entangled in an environment in which information on everything that happens to it is recorded immediately. In a nutshell, decoherence theory tells us that the cat is, from the very beginning of our experiment, a classical object that can only be alive or dead, never alive and dead. If it is enclosed in a box with a radioactive atom, it is the cat, the classical system, that will act as a measuring instrument to determine the state of the atom. By passing from life to death, it will determine the moment of the atom’s quantum jump. The Schrödinger’s cat fable has only served us as a metaphor to describe the non-classical superposition states of a few particles studied in cavity-photon or trapped-ion experiments.What drove us above all in our research was curiosity, as well as the passionate desire to highlight in the most demonstrative possible way the strange laws of quantum physics—without seeking any specific application. In this sense we have followed in the footsteps of the theory’s founding fathers, with the advantage of having a technology they could not even have dreamed of. Our work has always mixed theoretical and experimental aspects. While we were putting together our apparatus, we were thinking in parallel about the experiments we could do. In a series of theoretical papers, we proposed, before we carried them out, the methods permitting the atom and photon manipulations described above.
eBook - ePub- Michael Esfeld(Author)
- 2020(Publication Date)
- Palgrave Macmillan(Publisher)
The formalism of quantum mechanics given in the textbooks is an algorithm to calculate measurement outcome statistics. It is not physics in the sense of a theory that tells us what there is in the physical world and how what there is behaves (or that enables inferences that answer these questions), as pointed out most recently by Maudlin (2019, introduction). Taking it to be physics in this sense runs into the well-known paradoxes such as the measurement problem, which is nicely illustrated by Schrödinger’s cat. 22 The cat is represented as being in a superposition of being both alive and dead given the evolution of the wave-function according to the Schrödinger equation. However, when measured, it is found to be either alive or dead. The issue hence is how the theory accounts for determinate measurement outcomes and how it conceives the evolution of the individual physical objects, such as the individual particles sent through the double slits experiment, or the particles in the Schrödinger cat experiment. Given the state of the art in foundational research in quantum physics, there are two types of options that one can pursue in order to achieve a quantum theory that answers these questions. 23 The one type of option is to take the quantum mechanical wave-function and its evolution as the guide to physical reality and to make intelligible how one can live with the ensuing consequences. The most notable consequence is that everything that is possible in the dynamical evolution of the wave-function according to the—linear and deterministic—Schrödinger equation then is taken to become in fact real. Thus, the very same cat in the Schrödinger cat thought experiment is both alive and dead, albeit in different branches of the universe that do not interfere with one another. Hence, according to this option, many branches of the universe—known as “many worlds”—exist in parallel. This option goes back to Hugh Everett (1957)
eBook - ePub- Arthur Fine(Author)
- 2009(Publication Date)
- University of Chicago Press(Publisher)
If decay occurs the counter tube fires and, by means of a relay, sets a little hammer into motion that shatters a small bottle of prussic acid. When the entire system has been left alone for an hour one would say that the cat is still alive provided no atom has decayed in the meantime. The first atomic decay would have poisoned it. The ψ -function of the total system would yield an expression for all this in which, in equal measure, the living and the dead cat are (sit venia verbo 2) blended or smeared out. The characteristic of these examples is that an indefiniteness originally limited to atomic dimensions gets transformed into gross macroscopic indefiniteness, which can then be reduced by direct observation. This prevents us from continuing naively to give credence to a “fuzzy model” as a picture of reality. Schrödinger finishes by observing, “In itself this [fuzzy model] contains nothing unclear or contradictory.” For, he notes, “There is a difference between a blurred or out-of-focus picture and a photograph of clouds and patches of fog.” The long passage just quoted, of course, is the original version of Schrödinger’s famous cat paradox. This thought experiment is rivaled only by that of EPR in its impact on discussions of the conceptual foundations of quantum mechanics, and, like EPR, it too has recently moved beyond this specialized context to become a subject of popular imagination. 3 Even the structure of the two imagined experiments are similar insofar as they both concern problems over coupled systems, focusing on the situation of one subsystem (respectively, the unmeasured one, or the cat) after its physical interaction with the other subsystem has effectively ceased
- Gerard T. Hooft(Author)
- 2016(Publication Date)
- Springer Open(Publisher)
For the same reason, ontological states can never evolve into a superposition of a dead cat and a live cat. Regarded from this angle, it actually seems hard to see how any other interpretation of quantum mechanics could have survived in the literature: quantum mechanics by itself would have predicted that if states | ψ angbracketright and | χ angbracketright can be used as 68 5 Concise Description of the CA Interpretation initial states, so can the state α | ψ angbracketright + β | χ angbracketright . Yet the superposition of a dead cat and a live cat cannot serve to describe the final state. If | ψ angbracketright evolves into a live cat and | χ angbracketright into a dead one, then what does the state α | ψ angbracketright + β | χ angbracketright evolve into? the usual answers to such questions cannot be correct. 2 The Cellular Automaton Interpretation adds some notions to quantum mechanics that do not have any distinguished meaning in the usual Copenhagen view. We in-troduced the ontological basis as being, in some sense, superior to any other choice of basis. One might naturally argue that this would be a step backwards in physics. Did Copenhagen, in Sect. 5.4 , not emphasise that all choices of basis are equivalent? Why would one choice stand out? Indeed, what was stated in rule #i in Sect. 5.4 was that all basis choices are equivalent, but what we really meant was that all basis choices normally employed are equivalent. Once we adopt the Copenhagen doctrine, it does not matter anymore which basis we choose. Yet there is one issue in the Copenhagen formalism that has been heavily disputed in the literature and now is truly recognized as a weakness: the collapse of the wave function and the treatment of measurements. At these points the superposition axiom fails. As soon as we admit that one superior basis exists, this weakness disappears.
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