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1500 questions
57
votes
7 answers
What is the Physical Meaning of Commutation of Two Operators?
I understand the mathematics of commutation relations and anti-commutation relations, but what does it physically mean for an observable (self-adjoint operator) to commute with another observable (self-adjoint operator) in quantum mechanics?
E.g.…
adustduke
- 793
57
votes
7 answers
Why should an action integral be stationary? On what basis did Hamilton state this principle?
Hamilton's principle states that a dynamic system always follows a path such that its action integral is stationary (that is, maximum or minimum).
Why should the action integral be stationary? On what basis did Hamilton state this principle?
tsudot
- 971
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57
votes
4 answers
Hilbert space of harmonic oscillator: Countable vs uncountable?
Hm, this just occurred to me while answering another question:
If I write the Hamiltonian for a harmonic oscillator as
$$H = \frac{p^2}{2m} + \frac{1}{2} m \omega^2 x^2$$
then wouldn't one set of possible basis states be the set of…
Lagerbaer
- 14,836
57
votes
14 answers
Why is it impossible to measure position and momentum at the same time with arbitrary precision?
I'm aware of the uncertainty principle that doesn't allow $\Delta x$ and $\Delta p$ to be both arbitrarily close to zero. I understand this by looking at the wave function and seeing that if one is sharply peeked its fourier transform will be…
catmousedog
- 718
57
votes
8 answers
Principle of physics used in the lift of skateboard
What is the principle of physics used in this popular stunt?
Initially, I thought aerodynamics due to an increase in the angle of attack, but its magnitude is not sufficient to balance the whole body and skateboard. Please, can anyone help me to get…
Rajakr
- 726
57
votes
4 answers
Why are aerodynamic / streamlined shapes always stumpy at the front?
I'm building an autonomous boat, to which I now add a keel below it with a weight at the bottom. I was wondering about the shape that weight should get. Most of the time aerodynamic shapes take some shape like this:
The usual explanation is that…
kramer65
- 613
57
votes
2 answers
Rubber band stretched produces heat and when released absorbs heat.. Why?
I always used to wonder why this happens..
when one stretches a rubberband to nearly it snapping point holding it close to your skin - preferably cheek(helps feel the heat), it emits heat. While releasing the stretched rubberband holding it close…
vijay143
- 573
57
votes
4 answers
Can bosons that are composed of several fermions occupy the same state?
It is generally assumed that there is no limit on how many bosons are allowed to occupy the same quantum mechanical state. However, almost every boson encountered in every-day physics is not a fundamental particle (with the photon being the most…
Friedrich
- 1,172
57
votes
7 answers
Why isn't the Euler-Lagrange equation trivial?
The Euler-Lagrange equation gives the equations of motion of a system with Lagrangian $L$. Let $q^\alpha$ represent the generalized coordinates of a configuration manifold, $t$ represent time. The Lagrangian is a function of the state of a particle,…
Trevor Kafka
- 1,816
57
votes
7 answers
Why do we have an elementary charge but no elementary mass?
Why do we have an elementary charge $e$ in physics but no elementary mass? Is an elementary mass ruled out by experiment or is an elementary mass forbidden by some theoretical reason?
asmaier
- 9,794
57
votes
3 answers
Is there a physical limit to data transfer rate?
Is there a physical limit to data transfer rate (e.g. for USB $3.0$, this rate can be a few Gbit per second)? I am wondering if there is a physical law giving a fundamental limit to data transfer rate, similar to how the second law of thermodynamics…
Shing
- 2,774
57
votes
5 answers
If I can see someone's eyes, can they see mine?
Besides the obvious cases where I'm behind a "one-way" mirror or have goggles/glasses on: is there one where I can see someone's eyes, and they can't see mine?
Tobi
- 1,819
57
votes
6 answers
Why do we feel heat from infrared light but not from shorter wavelengths?
My guess would be that light with a higher energy such as visible or UV would feel hotter, but this is not the case!
Is this something to do with human senses or is there a physics explanation?
Giulio Crisanti
- 2,010
57
votes
3 answers
Why do we use AC for long distance transmission?
Why do we use AC (Alternating Current) for long distance transmission of electrical power?
I know that AC is such a current that changes polarity (magnitude and direction) and has fixed poles.
EiNsTeIn
- 703
57
votes
0 answers
Systematic approach to deriving equations of collective field theory to any order
The collective field theory (see nLab for a list of main historical references) which came up as a generalization of the Bohm-Pines method in treating plasma oscillations often used in the study of large N asymptotics (e.g. of matrix models). I have…
Zoran Škoda