# Tag Info

38

The first paragraph is basically right, but I wouldn't ascribe the uncertainty principle to particles, just to the universe/physics in general. You can no more get arbitrarily good, simultaneous measurements of position and momentum (of anything) than you can construct a function with an arbitrarily narrow peak whose Fourier transform is also arbitrarily ...

25

Are we talking quantum mechanics? Then I'd say that a "measurement" is any operation that entangles orthogonal states of the system under consideration with orthogonal states of the environment. "Measurement" is the important thing in most formulations of QM. Colloquially speaking, an observer is something that performs measurements. The only other place ...

25

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 ...

21

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 ...

21

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 ...

20

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 ...

18

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 ...

18

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 ...

17

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 ...

17

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 ...

15

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 ...

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

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 ...

13

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 ...

13

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 ...

13

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. ...

12

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 ...

12

It's tempting to think of the light as a little ball (the photon), and since little balls have a definite position the little ball has to be in a superposition of a state where it goes through one slit and a state where it goes through the other. However this is not a good description of what actually happens. The light is not a photon, and it's not a wave ...

12

Your example is probably not a good one to understand Heisenberg uncertainty with, because it mixes two uncertainty phenomena together: The observer effect (See Wikipedia page of same name); Heisenberg uncertainty itself. The observer effect is the obvious and everyday observation that we can't extract information from a system without disturbing it in ...

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

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 ...

11

Well, the wave function of the electron in the ground state of a hydrogen atom (and very similarly in other atoms) behaves like $$R(r) \sim \exp(-r / a)$$ where $a$ is the Bohr radius, effectively the radius of the atom. The exponential is in principle nonzero for an arbitrarily large $r$, so the electron may be found arbitrarily far from the nucleus at a ...

11

This is one of the key results of quantum field theory: particles are not single points, they are disturbances in quantum fields that are spread out over space. Typically the disturbance is not spread out very much, otherwise it looks more like what we know as a wave than a particle. The technical term for what you're calling a "smear" is a wavepacket.

11

It doesn't really matter, because the phrase "simultaneously affects the other particle" is misleading. Let's suppose you have a pair of totally anticorrelated photons. You measure one of them, then you'll know the outcome of the other one. The phrase "the measurement simultaneously affects the other particle" is not physical, because until you actually ...

10

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 ...

10

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 ...

10

The claim that during the experiment they let the detector on but did not stored the data so it showed waves, only when they stored the data it showed as particle. is inaccurate and inconsistent with quantum mechanics. In a double-slit experiment, any device that can even in principle provide which-way information will destroy the interference ...

10

But knowing the time it took for the photon to go from the source to the observing screen, you can deduct the distance of the photon path and so which slit it passes through ... and indeed such information will make it impossible for fringes to appear. Interference experiments use wavepackets that have a long duration, which makes it impossible to ...

9

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 ...

9

You should forget everything you've been told about the wave particle duality. It's an outdated concept long since superceded by quantum field theory, and I think it's actively unhelpful because it causes confusion. There isn't any wave particle duality because an electron isn't a particle and it isn't a wave. Instead it's an excitation in a quantum field. ...

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