# Tag Info

18

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 ...

15

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 ...

14

First of all, let me start out by pointing out to you that there have been experimental violations of Bell's inequalities. This provides damning evidence against hidden variable models of quantum mechanics, and thus essentially proves that the random outcomes are an essential feature of quantum mechanics. If the outcomes of measurements in every basis were ...

14

What you describe in your question is the "Copenhagen interpretation" of quantum mechanics. There are more nuanced views of this nowadays that don't treat "measurements" quite so asymmetrically, see e.g. sources that talk about decoherence. I recommend watching the classic lecture "Quantum Mechanics in your face" by Sidney Coleman for a nice take on this ...

14

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 ...

11

The short answer is that we do not know why the world is this way. There might eventually be theories which explain this, rather than the current ones which simply take it as axiomatic. Maybe these future theories will relate to what we currently call the holographic principle, for example. There is also the apparently partially related fact of the ...

11

it is the error created by photons striking on elementary particles It's not. Heisenberg's uncertainty principle actually has nothing to do with any particular experiment, or any particular interaction. It's a purely mathematical statement about waves. Its true meaning is explained in detail on the Wikipedia page, but the gist is that if you have a ...

11

We can satisfy your requirement "the photon was emitted at a correct angle" by "the photon was prepared in a momentum eigenstate". If the photon has definite momentum $\bf{k}$, then its direction of travel is well defined, as you have specified. A photon is a discrete excitation of a "mode", i.e. a solution of Maxwell's equations. For a photon in a ...

11

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 ...

10

So, why can't the uncertainty relations be violated in such a case, if I could, say, measure the position of the object with this wave function That's the catch. You can't. Or rather, you can measure the position, but the result you get will vary from one measurement to the next, because the wavefunction $\exp(x^2/2i - cx)$ is not an eigenstate of ...

9

Assuming that the incoming "first" particle is prepared in a pure state, interaction with another particle does seem necessary. Such an interaction might simply be the spontaneous emission of a photon or other particle by the original incoming particle, however. Most importantly, such an interaction is not itself sufficient. For a measurement event to ...

9

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 ...

8

Interactions merely involve a correlation developing. For example, if an electron is put through a Stern-Gerlach apparatus, a correlation develops between the distance travelled in the x direction and the distance deviated in the y direction. It is reversible. The measurement which occurs when the particle hits the photographic plate is irreversible. It ...

7

Trivially for any set of measurements $\{E_i\}$ where $\rho$ and $\sigma$ have equal expectation value for each $E_i$, $$\sum_i\mbox{Tr}(\rho E_i) \log \left[ \frac{\mbox{Tr}(\rho E_i)}{\mbox{Tr}(\sigma E_i)}\right] = \sum_i\mbox{Tr}(\rho E_i) \times 0 = 0.$$ Note that the log-sum inequality theorem says that $$\sum_i a_i \log\left(\frac{a_i}{b_i}\right) ... 7 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 ... 7 The idea that "nothing is objectively real prior to measurement" is a peculiar philosophical mishmash, kept in currency by the conjunction of two things: (1) the difficulty of producing an objective theory, without a special status for "measurements" or "observers", that reduces to quantum mechanics; (2) a multitude of nonquantitative philosophical ideas, ... 7 Let us be clear about the problem. A photon is a quantum mechanical entity and follows the laws of quantum mechanics. There is always a probability attached to any possible path it can take so the strict answer is "no, the path of the photon is not deterministic". BUT the problem changes when speaking of a large ensemble of photons, which is any light we ... 7 The Uncertainty Principle will never, as far as we know, prevent you from simulating any physical system. The reason for this is that quantum mechanics is - except for that little problem with measurements - completely deterministic. To be more precise, say you want to simulate a given system within quantum mechanics. You begin by describing your ... 6 If you think for a moment about how lengths and speeds in our universe are set (that is, independent of how we choose to measure them, by meters or seconds or whatever), you'll see that these must ultimately come from different ratios of fundamental constants. I don't know and would be very surprised if there's a way to change these ratios so that all ... 6 The spin of a single electron has been measured since the very first moment when the people understood that every electron possesses a spin. A Stern-Gerlach experiment - a magnetic field - is enough to measure the spin: http://en.wikipedia.org/wiki/Stern-Gerlach_experiment 6 Nick, Don't be surprised that this is confusing. There are a lot of concepts intermixed in the discussion of the uncertainty principle that are frequently not clearly understood and are intertwined unintentionally. Although one often sees that these are stated in statistical terms, the standard deviation does not directly require multiple observations of ... 6 For a particle which has a position-space wavefunction \psi(x), the uncertainty in position, denoted \sigma_x or \Delta x (I prefer the former), is given by$$\begin{align} \sigma_x^2 &= \langle x^2\rangle - \langle x\rangle^2 \\ &= \int_{-\infty}^{\infty}\psi^*(x)x^2\psi(x)\,\mathrm{d}x - ...

6

You're asking what would happen if we could view things with an unlimited high resolution. You view the emissions of the synchotron photons as discrete events and you ask is the path linear between these emissions. The problem is - quantum particles do not have trajectories so it's not meaningful to ask about the actual path followed by the particle. All ...

6

In a true measurement procedure of position, the outcome is an interval $(a-\delta,a+\delta)$, $\delta>0$ being the precision of the instrument. In view of Luders-von Neumann's postulate on the reduction of the state, if the state before the measurement was described by the normalized vector $\psi \in L^2(R)$, immediately after the measurement the state ...

6

Aren't the particles this quantum state consists of interacting with each other? Why doesn't that cause the state to collapse? We have a mathematical model for the observations we can make of any system in the micro world. This model is quantum mechanics and its predictions have been verified experimentally over and over again. Observables are ...

6

I've never seen a single prediction based upon MWI. I've also never heard of the Cophenhagen interpretation called an approximation. If that were the case, then the Copenhagen interpretation must fail in at least one limit. Does Max provide such limits? Both of these statements seem to lean towards sensationalism than towards mathematical rigor.

5

There's a prescription by Deutsch for the quantum mechanics of closed timelike curves. It works on the level of density states, instead of Hilbert space states. Given his prescription, he showed that a fixed point solution always exists no matter what the initial conditions are. However, this solution isn't unique in general. Also, pure states can be ...

5

If you're talking about building a quantum computer, then there are some modes of the system which you need to keep isolated so that you can make sure that any coherence of these modes is preserved, but there are other modes of the system that you use to control the system, and these aren't isolated. This idea is also used in quantum error correction. This ...

5

In QM, a "wave" isn't what we normally imagine: something that moves up and down and moves in one direction, like water. It's just a function that evolves with time and has a (in general) different value at every point in space. See this applet for some examples of atomic orbitals which are infact electron wavefunctions (the applet actually shows the ...

5

You should look at the link that Qmechanic gives, as it is closely related to your question. The "randomness" in quantum mechanics is widely misunderstood. There is nothing random in the wavefunction (or quantum field theory description) and as long as all interacting systems stay entangled the behaviour is completely predictable. We only see randomness ...

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