122 votes
Accepted

Why do travelling waves continue after amplitude sum = 0?

What you cannot see by drawing the picture is the velocity of the individual points of the string. Even if the string is flat at the moment of "cancellation", the string is still moving in that ...
user avatar
  • 108k
79 votes
Accepted

What is the reason that Quantum Mechanics is random?

If it helps, it's not that the nature of the universe is random, it's that we model it as random in Quantum Mechanics. There are many cases in science where we cannot model the actual behavior of a ...
user avatar
  • 43.1k
69 votes

Why do travelling waves continue after amplitude sum = 0?

ACuriousMind's excellent description was missing a picture. Here it is: This clearly shows that for the wave moving to the right, the front is moving up and the rear is moving down. For the opposite ...
user avatar
  • 117k
41 votes

Why do travelling waves continue after amplitude sum = 0?

Just to complement the other excellent answers, here's an animation showing what two wave pulses with opposite amplitude passing through each other actually look like: You can clearly see that, at ...
user avatar
38 votes
Accepted

How can Schrödinger's cat be both dead and alive?

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 ...
user avatar
  • 53.8k
36 votes

Extension of Schrödinger's cat thought experiment

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 ...
user avatar
  • 9,698
36 votes
Accepted

Do all waves of any kind satisfy the principle of superposition?

If a wave $f(x,t)$ is something that satisfies the wave equation $Lf=0$ where $L$ is the differential operator $\partial_t^2-c^2\nabla^2$ then, because $L$ is linear, any linear combination $\lambda f+...
user avatar
  • 4,525
36 votes

What is the reason that Quantum Mechanics is random?

As Feynman said when laying out the first principles of quantum mechanics: How does it work? What is the machinery behind the law?” No one has found any machinery behind the law. No one can “explain” ...
user avatar
  • 1,115
33 votes

Am I in a superposition?

This is a deceptively simple question, and I would like to answer it in the context of Condensed Matter Theory. We will start with the question: why do objects in our everyday life appear to be ...
user avatar
  • 1,187
32 votes

Extension of Schrödinger's cat thought experiment

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 ...
user avatar
  • 223k
30 votes
Accepted

If a thousand people whisper inaudibly, will the resulting sound be audible?

Yes, always. I would like to disagree with stafusa's answer here, expanding on Rod's comment. Interference will not occur, since for whispering the sources of sound will be statistically independent. ...
user avatar
30 votes
Accepted

A light problem: What happens when light completely destructively interferes?

The energy went back into your spherical source. For the first pulse the source had to provide energy. For the second pulse the source had to absorb energy. The mistake is simply assuming that the ...
user avatar
  • 68.9k
28 votes

Do all waves of any kind satisfy the principle of superposition?

As coconut wrote, the superposition principle comes from the linearity of the operator involved. This is the case for electromagnetic radiation in vacuum. Approximations to water waves are also linear ...
user avatar
25 votes
Accepted

Why is it difficult for water waves to cancel each other?

Interference requires exactly same frequency in both the sources and also needs them to be coherent i.e. their phase relation must remain same throughout. It's very hard to create such things for ...
user avatar
  • 2,721
23 votes
Accepted

Are there any nonlinear Schrödinger equations?

Previous answers focus on the fundamental approach to Quantum Mechanics where the Hamiltonian operator is always a linear operator. However, they miss an extremely important situation where a non-...
user avatar
  • 24.9k
22 votes
Accepted

Does "natural" superposition of particles exist?

One of the common misconceptions that people starting out with QM often have is to think that a system is either in a superposition state or it is not. Actually superposition is only defined relative ...
user avatar
  • 7,692
21 votes

How is a quantum superposition different from a mixed state?

Apart from the already mathematically detailed answers given above, perhaps it would be useful to have a physical picture in mind -- the double slit experiment. The classical 50:50 picture ...
user avatar
21 votes

Do all waves of any kind satisfy the principle of superposition?

No. Despite what several answers on this thread will tell you, there are plenty of phenomena which are perfectly deserving of the term "wave" which do not satisfy the superposition principle....
user avatar
21 votes

If a thousand people whisper inaudibly, will the resulting sound be audible?

The amplitude of the sum of $1000$ equally loud uncorrelated noises will be about $\surd1000$, or approximately $32$, times the amplitude of a single noise. That might be enough to make an inaudible ...
user avatar
21 votes

What is the reason that Quantum Mechanics is random?

It's weirder than you thought. The wavefunction itself is fully deterministic. People often say "it's the measurements that are probabilisitic" but that isn't right either. The measurement ...
user avatar
  • 4,708
21 votes

Can particles be in a superposition of times as well as positions?

I don't think this question has an exciting answer. Strictly speaking, superposition refers to a wavefunction occupying multiple states at a particular time, so the question you've asked is "why ...
user avatar
  • 9,164
20 votes
Accepted

Is water really $H_2O$? On a comment concerning the quantum mechanical description of water made by Hilary Putnam

I'm not sure I would have phrased it exactly that way, but I think his statement is by-and-large defensible. The crux of the issue is that, in liquid water, there is no sharp line between ...
user avatar
  • 15.9k
20 votes
Accepted

Can only one particle exist at a defined point in spacetime?

A particle isn't located at a point. Particles are always delocalised over a non-zero volume of space, so while the expectation value of a particle's position is a point, the particle is not located ...
user avatar
20 votes
Accepted

In classical physics (classical electrodynamics), why linearity of Maxwell's equations prevent interaction of electromagnetic waves?

Linearity implies the superposition principle. The superposition principle means that if $\psi_1(x,t)$ is a solution to the (vacuum) wave equation, and $\psi_2(x,t)$ is also another solution to the ...
user avatar
  • 6,930
19 votes
Accepted

Why is a wave pulse a superposition of sine waves?

In this case it's probably best to be pragmatic. A pulse can be described as a superposition of sine waves that extend infinitely into space and time. But it's just that: a mathematical description ...
user avatar
  • 1,473
19 votes

Do we or do we not observe (measure) superpositions all the time?

To answer the question, you have to specify what observable’s eigenstates the “superpositions” you’re talking about are superpositions of. If you measure the energy, you always get one single energy ...
user avatar
  • 50k
17 votes

Schrödinger's cat and the difficulty of macroscopic superposition state

$\renewcommand{\ket}[1]{\left \lvert #1 \right \rangle}$ $\renewcommand{\bra}[1]{\left \langle #1 \right \rvert}$ We can see how decoherence really works, why it messes up superposition states, and ...
user avatar
17 votes

Is particle superposition reflected in the particle's gravitational footprint?

The simple answer is that we don't know because we have no theory of quantum gravity. If I interpret your question correctly you're thinking about semiclassical gravity, where matter is quantised and ...
user avatar
17 votes
Accepted

Why is the general solution of Schrodinger's equation a linear combination of the eigenfunctions?

You are starting from the incorrect point. The argument follows by linearity of the equation. Suppose $\Psi_k(x,t)$ is solution of the time dependent Schr$\ddot{\hbox{o}}$dinger equation: $$ i\hbar \...
user avatar
  • 39.5k

Only top scored, non community-wiki answers of a minimum length are eligible