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Before reading this answer (and to those who are downvoting), I am addressing if the cat is both alive and dead. I don't think the question is asking for a complete explanation of the Schrodinger's cat experiment, nor is it asking how this links to all of the deeper mysteries of quantum mechanics and how we should think of them. Therefore, while there is ...
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This is is known as the Wigner's friend thought experiment. According to the many World's interpretation, the superpositions are not a problem. The whole universe ends up in a superposition where all experimental outcomes are realized, but such a superposition is entangled with the environment, from a macroscopic point of view it takes the form of a ...
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Manishearth's answer is correct, and this is just a minor extension of it. Manishearth correctly points out that the problem is your statement:
There is a definine velocity and momentum, we just don't know it.
Your statement is the hidden variables idea, and courtesy of Bell's theorem we currently believe that hidden variables are impossible.
Take the ...
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There is a definine velocity and momentum, we just don't know it.
Nope. There is no definite velocity--this was the older interpretation. The particle has all (possible) velocities at once;it is in a wavefunction, a superposition of all of these states. This can actually be verified by stuff like the double-slit experiment with one photon--we cannot explain ...
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Note: There is a short summary at the bottom.
This is actually also described in Nielsen&Chuang: You don't learn about general measurements, because they are completely equivalent to projective measurements + unitary time evolution + ancillary systems, all of which is described in your usual QM formalism.
The Measurement Postulate
Let's start from ...
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In a bubble chamber experiment, film was the detecting medium, but film was taken automatically, by the thousands of frames. These bobbins of film went to the various laboratories involved in the experiment, and were scanned for interesting events which were measured and the cross sections for the interactions recorded.
This is a clear example of an ...
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The objects on the l.h.s. of the position-momentum uncertainty relation
$$ \Delta x \Delta p \geq \frac{\hbar}{2}$$
are standard deviations of quantum mechanical operators, defined for any operator $A$ by
$$ \Delta A:=\sigma_A=\sqrt{\langle A^2 \rangle - \langle A\rangle^2}$$
where $\langle \dot{}\rangle$ denotes taking the expectation value with respect to ...
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This is really a footnote to Chris' answer but it got a bit long for a comment.
It sounds odd to claim that a particle has no position, but it's easier to understand if you appreciate that a particle is just an excitation in a quantum field. When Heisenberg was developing his ideas physicists still thought of particles as little billiard balls. With the ...
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Until we have an accepted solution of the Measurement Problem there is no definitive definition of quantum measurement, since we don't know exactly what happens at measurement.
In the meanwhile, measurement is simply defined as part of the postulates and recipe associated with the notion of a quantum observable. Mostly an observable is thought of as an ...
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There are time-scales related to interactions, or, equivalently, interaction rates. These interaction rates are often calculated in lowest order based on Fermi’s Golden Rule. An experiment that measures electron interference needs to make sure that the time-of-flight of the electrons from the electron source to the observation screen is much shorter than any ...
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Basically the answer is yes, the cat is both dead and alive. People used to discuss this sort of thing in terms of the Copenhagen interpretation (CI) and the Many-Worlds interpretation (MWI), but those discussions tend not to be satisfying, because both CI and MWI are designed so that in almost all real-world measurements, they give the same predictions. A ...
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Seems like the whole universe is receiving information about the electron's position.
Yes, the influence that an electron exerts on the rest of the universe does depend on the location of the electron, but that's not enough to constitute a measurement of the electron's location. We need to consider the degree to which the electron's influence on the rest of ...
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There are many steps:
Step 1, select a state $\Psi$.
Step 2, prepare many systems in same state $\Psi$
Step 3, select two operators A and B
Step 4a, for some of the systems prepared in state $\Psi$, measure A
Step 4b, for some of the systems prepared in state $\Psi$, measure B
Now if you analyze the results, assuming strong (not weak) measurements then ...
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This question strikes close to the heart of The measurement problem, which is the question of what (if anything) the process of measurement represents; and is all but synonymous with the question of how one ought to interpret quantum mechanics.
As such, the answer to this question is (a) subject to debate; and (b) absent any substantial philosophical and/or ...
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Entanglement is a real property that can be shown by the violation of the Bell inequalities. How this is commonly done is that a pair of particles are created with entangled spin states in a configuration called Bell states. If entanglement is real, then measuring the state of one particle will give me definite knowledge of the state of the other particle. ...
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Quantum statistical irreversibility ("the second law") and quantum measurement irreversibility are almost the same thing. Indeed,the latter is the special case of the former where one assumes a more specific situation in which you consider the statistical mechanics of a small system coupled to a large one. Equilibrium and nonequilibrium statistical mechanics,...
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Simply put, it averages out.
Ignoring quantum physics for a moment, consider the random movement of molecules in a gas. The number of particles bouncing against each wall per second is random, too. But the variation in this number is roughly proportional to the square root of collisions. Therefore, the relative variation is inversely proportional to the ...
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This is not a settled question. Just as it is still debated whether or not there is wavefunction collapse, so is it debated what exactly we should understand by a measurement. In the following, we will go through the ideas behind the von Neumann measurement scheme, which is one way to try and talk about measurement in quantum mechanics.
An interaction ...
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Good question. The textbook formalism in Quantum Mechanics & QFT just doesn't deal with this problem (as well as a few others). It deals with cases where there is a well-defined moment of measurement, and a variable with a corresponding hermitian operator $x, p, H$, etc is measured. However there are questions which can be asked, like this one, which ...
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Assuming wave-function collapse is correct (which can be a relatively hefty philosophical claim in some circles), then think of measurement this way:
When you measure an observable on a system, you collapse the wave-function of the system into a Dirac delta function in the eigenbasis for that observable.
If you measure position, you get a delta function in ...
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I think most arguments in the literature can be boiled down to the point that decoherence does in no way touch the linearity of the Schrödinger equation, and thus cannot make an "or" from an "and".
This is complicated in the literature by very technical discussions, which I would like to avoid.
Let me explain the basic point in more details. A widely ...
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What you describe is the process known as decoherence: any interaction of a quantum system with its environment (e.g. with photons or other particles passing by, and, yes, most likely interacting through gravity, although we don't have a theory to fully describe this yet) has the potential to destroy its genuinely quantum nature, turning quantum ...
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As StephenG mentioned in a comment, the paper you're asking about is the subject of a commentary in arXiv:quant-ph/0509130, by Markus Bier; Li and Li attempt a rebuttal of that comment in Appendix C of v2 of their paper.
The comment by Markus Bier is phrased in dry academic language, and there are certain aspects of the phrasing that simply do not fit ...
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An observation is an act by which one finds some information – the value of a physical observable (quantity). Observables are associated with linear Hermitian operators.
The previous sentences tautologically imply that an observation is what "collapses" the wave function. The "collapse" of the wave function isn't a material process in any classical sense ...
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You are misunderstanding the Uncertainty Principle. The Uncertainty Principle says that a particle cannot simultaneously have a definite momentum and a definite position. This is not due to our incomplete knowledge of parameters. This is a fundamental law of the universe and arises from the fact that the momentum and position operators do not commute in ...
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Imagination has nothing to do with it. Or everything to do with it.
The harsh reality is that electrons are neither particles nor waves. Light is neither particles nor waves. Both electrons and light are simply what they are, and we can model those things well using equations from quantum physics. However, nothing is either fully a particle or fully a ...
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There are many interpretations, and while there are good arguments in favor of one or another, they are currently not distinguished experimentally. Therefore it is often considered prudent to leave the question of which interpretation is best to the field of philosophy, and focus in a physics course on the falsifiable aspects of the theory. The field of ...
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I feel like all the answers here are missing the point.
The cat is not both alive and dead at the same time. That would be, as you put it, ludicrous. The truth is that the cat is in a superposition state of the states "alive" and "dead".
The problem is that there is no way to make sense of this statement without studying the underlying mathematics. Humans ...
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Quantum entanglement and measurement are different point of views of the same underlying physical phenomena, say, the most distinct feature of the evolution of coupling between two physical systems.
From an external point of view, when two physical systems interact, they become entangled. This apply even if one of the systems is large and semi-classical (...
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