# Tag Info

34

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 ...

19

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 ...

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 ...

17

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 ...

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 ...

16

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 ...

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

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 ...

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 ...

12

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 ...

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

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 ...

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

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

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 ...

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 ...

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 ...

8

Although the uncertainty principle stems from the mathematical structure of QM, i.e., originates from the noncommutivity of some observable letting them behave as fourier transform pair as explained in another answer, I still think it is a statement on measurements, (i.e., imposes fundamental limits on measurements) since QM itself seems to be a theory of ...

8

The short answer is : it is a fundamental property of nature. The very short answer is "quantum" The long answer: From the beginning of the 20th century, slowly but certainly Nature revealed to us that when we go the very small dimensions its form is quantum. It started in the middle of the nineteenth century , with the table of elements which showed ...

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 ...

7

Understanding the uncertainty principle really only involves accepting the idea that, at small scales, elementary particles behave like waves. The uncertainty principle is a well-known property of waves. One of the consequences of this idea is that position and wavelength cannot be measured to an infinite precision simultaneously with one another. Imagine, ...

7

None of the interpretations are right or wrong, since they are interpretations of the same mathematical formalism which predict the same events. Interpretations are a philosophical adjunct that provides a "what is REALLY happening" view. If an interpretation is tested and shown to be wrong, then it is no longer an interpretation - just wrong physics. ...

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 $$\sum_i a_i \log\left(\frac{a_i}{b_i}\right) ... 7 The idea that "nothing is objectively real prior to measurement" is a peculiar philosophical mishmash, kept in currency by the conjunction of two things: (1) the difficulty of producing an objective theory, without a special status for "measurements" or "observers", that reduces to quantum mechanics; (2) a multitude of nonquantitative philosophical ideas, ... 7 An observation is an act by which one finds some information – the value of a physical observable (quantity). Observables are associated with linear Hermitian operators. The previous sentences tautologically imply that an observation is what "collapses" the wave function. The "collapse" of the wave function isn't a material process in any classical sense ... 6 For a particle which has a position-space wavefunction \psi(x), the uncertainty in position, denoted \sigma_x or \Delta x (I prefer the former), is given by$$\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 ...

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