4
votes
2answers
750 views

Understanding the Jacobian Matrix

Taking the example of a two dimensional system, desribred by the following ODE's: \begin{align} \frac{dx_1}{dt}&=f_1(x_1,x_2)\\ \frac{dx_2}{dt}&=f_2(x_1,x_2) \end{align} The Jacobian Matrix ...
5
votes
0answers
263 views

Zamolodchikov's c-theorem paper

I am reading the 1986 paper [1] where Zamolodchikov proves the c-theorem and I would like to understand how equations (7a), (7b) and (8) are derived from the Callan-Symanzik equation. For ...
1
vote
2answers
67 views

The concept of torque among other unknowns

Someone asked me this question and I am going to try to ask it as 'proper' as possible. Imagine there is a door and it needs a mass on the floor at the edge of the door to keep it from swinging shut. ...
2
votes
2answers
161 views

How to accurately mark with arrows an electric circuit

As I understood, we choose to mark the current with arrows going from the plus pole to the minus pole (even though we know that in reality it is the contrary). As I'm looking at electric circuits, I ...
0
votes
1answer
55 views

Defects of smart glass (electrochromic glass)?

Smart glass is a type of glass that uses electrochromic mechanism to change it's light transmission properties in response to voltage, and it's made by sandwiching certain materials between two panes ...
1
vote
0answers
44 views

Can multiple lasers be concentrated in a circular area using some optical arrangements?

Can multiple lasers be concentrated in a circular area using some optical arrangements such as using a paraboloid surface? If yes, why do in high laser power systems do they use only 2D arrays of ...
3
votes
2answers
93 views

Is the coefficient of restitution frame independent and energy conservation?

In this question I am ignoring relativistic effects. The following statements I think are true: change in Kinetic energy is not invariant under change of frame Force is invariant under change in ...
4
votes
2answers
122 views

Weinberg QFT Chapter 5: gamma matrices consistency

Currently reading through Weinberg's QFT book (Vol. 1) [readable in parts here]. In his derivation of the causal Dirac field in Ch. 5, he chooses his gamma matrices as (5.4.17) \begin{align} ...
2
votes
1answer
420 views

Generalization of canonical commutation relation

The canonical commutation relation $$[x,p] = i\hbar$$ can be generalized to $$[p_i,F(\vec{x})] = -i\hbar\frac{\partial F(\vec{x})}{\partial x_i}, \ [x_i, F(\vec{p})] = i\hbar\frac{\partial ...
2
votes
1answer
89 views

A question regarding collisions

Let us consider a system of 2 identical spherical bodies connected by a massless string that is taut. If one body is placed at the origin then the other is placed at some coordinate $(x,y)$. The ...
1
vote
1answer
109 views

Johnson-Nyquist noise for resistive element with temperature gradient

In Nyquist's 1928 paper, Thermal agitation of electric charge in conductors, the voltage noise for a resistor is derived assuming a circuit in thermal equilibrium and one temperature. How does the ...
1
vote
0answers
66 views

Natural units in a parallel universe [closed]

Taking ispiration from this question units and nature . The natural Plank units set the gravitational costant $G$, the planck costant $\hbar$, the speed of light $c$, the Boltzmann costant $k_B$ and ...
0
votes
1answer
89 views

How should I calculate uncertainty of measurement calculated as average of two measurements

I am measuring force with two channel transducer. Both channels (separately) of this transducer has been calibrated and I can calculate uncertainty of measurement for each of it. However I want to ...
2
votes
1answer
86 views

Fermion propagator decomposition

I've seen the following decomposition for the fermion propagator for a fermion with momenta $p-k$, and where both $p-k$ and $p$ have a mass of $m$: $$\frac{(\not p-\not k)+m}{(p-k)^2-m^2}\gamma_\mu= ...
0
votes
1answer
56 views

Energy without temperature

If you know the entropy $S$ of your system. Is there a general way to calculate the internal energy $U$ of your system? So the entropy $S$ is the only thing I know of my system. I have no information ...
0
votes
1answer
147 views

2 vacuum pumps in parallel [closed]

I have a problem with a vacuum pump that cannot generate enough vacuum to grip an uneven item. There is a spare vacuum pump in parallel which I will turn on and run at the same time to try and get ...
3
votes
1answer
158 views

What is the four-dimensional representation of the $SU(2)$ generators?

Recently, I have been learning about non-Abelian gauge field theory by myself. Thanks @ACuriousMind very much, as with his help, I have made some progress. I am trying to extend the Dirac field ...
0
votes
2answers
142 views

Bouyant force in air on hollow object

I understand that the buoyant force is equal to the weight of the air displaced by the volume of the object. I also know that if we had a perfectly solid cube or a hollow cube closed on all sides so ...
1
vote
0answers
59 views

My idea on parallel universes [closed]

I have a question I've long wanted to ask somebody and I see no place better than here to do it! I am not a physicist in any way, Im just a big fan :) So, I have an idea of parallel universes in my ...
5
votes
1answer
369 views

Switching from sum to integral

I'm specifically asking about an equation in An Introduction to Quantum Field Theory, by Peskin and Schroeder. Example from page 374: $$\mathrm{Tr} \log (\partial^2+m^2) = \sum_k \log(-k^2+m^2)$$ ...
2
votes
1answer
59 views

The influence of the antenna height

I am working on a model of a transmitter. The transmitter is attached to the wheel of the vehicle and thus constantly changes it's height. In other words capacitance between antenna and ground is ...
5
votes
2answers
320 views

Poisson brackets of the Kepler Problem

For the hamiltonian of a particle of unit mass in a kepler potential: $$H = \frac{1}{2}\mathbf{p} \cdot \mathbf{p} - \frac{\mu}{r}$$ The angular momentum vector is given by: $\mathbf{L} = \mathbf{r} ...
2
votes
0answers
34 views

Should the answer to Einstein & Quantum gravity be found in conditions of our local observable universe? [duplicate]

It seems like the discourse over a unified Einstein and Quantum Gravity disregards the phenomena encountered in our local observable universe, such as we find throughout the Intergalactic Medium. One ...
0
votes
1answer
177 views

Right hand solenoid example

I am just studying for my physics final exam. I came across this example and am not satisfied with the answer. My answer is that Z is South and the current would flow from Y to X because of the ...
1
vote
2answers
77 views

Does a ball spin more from left to right than it does from right to left?

I swear that in a manual on tennis published by the German Tennis Association (Deutscher Tennis Bund) it stated as fact that all things being equal a ball will move more from left to right than from ...
2
votes
2answers
78 views

Determining Acceleration Based On Graph

I understand how to solve this problem, but I am unsure how to generate an equation for the graph (below). My current attempt involves using the mass provided along with the derivative of the line ...
0
votes
1answer
308 views

Dependence of scattering on particle size and refractive index

How does the intensity of light scattered by a medium depend on the refractive index and the size of the particles dispersed in the medium? I found plenty of literature about the dependence of ...
2
votes
0answers
62 views

Can I use ultrasound to detect metal underground? [closed]

I am doing research which aim to detect metal underground. I know that most metal detectors are based on the concept of change of inductance of an inductor caused by mutual inductance with a ...
6
votes
2answers
266 views

Why don't forces on two surfaces of a fluid need to balance?

In my textbook (Resnick Halliday Krane), the derivation for pressure in a fluid at a given depth is done assuming that the fluid is homogeneous. Thus, the book concludes that the pressure in a fluid ...
1
vote
1answer
154 views

What is the magnetic field on surface of a current carrying conductor?

Biot Savart's law says there should be none as the current element is along the displacement vector, hence as $\sin \theta = 0$, so, the magnetic field must be zero. But, as per Ampere's loop rule ...
3
votes
3answers
202 views

How is a photon measured?

If photons transmit the electromagnetic force, which is observable: the photon or the electron? Do we ever directly measure a photon, or do we only measure it's effect on electrons. For example ...
1
vote
1answer
57 views

Qualitative idea of viscosity [duplicate]

Suppose we are considering some fluid. As I currently understand, viscosity exists because of the following: supposing we draw one infinitesimal surface on the fluid, then the fluid parcels on either ...
2
votes
1answer
121 views

Does an externally driven Foucault pendulum really demonstrate the rotation of the Earth?

There's a Foucault pendulum at my school. It's a 105 kg ball suspended from the ceiling with a 20.73 m wire (source in French). There seems to be a driving mechanism on top, where the wire is ...
0
votes
1answer
46 views

Is the moment of zero velocity identical for objects of differing mass?

Assume we have two perfect spheres of identical size but different mass (e.g., one made of steel and one made of enamel) and an environment where the only forces in play are gravity and velocity ...
0
votes
0answers
72 views

A mass, bar, point and a spring

I am making a simple little program that needs to simulate a physics concept. However, I am not exactly sure how the physics concept actually works. I really like diagrams to illustrate my physics ...
1
vote
2answers
127 views

Perceived acceleration in an artificially modulated gravitational field

It's intuitive that while accelerating in a locally constant gravitational field, there is no perception of acceleration, since the body accelerates uniformly. What if a body were in a rapidly ...
4
votes
1answer
119 views

Nuclear fusion and the Sun [closed]

I am working on a science project on the Sun. I have found that in order for nuclear fusion to work, it needs both helium 3 and 4. Why can't nuclear fusion be done with just helium 4? How can we ...
18
votes
2answers
3k views

Why would the lack of air in a mine in an asteroid prevent you from flooding it?

In Isaac Asimov's I, Robot novel, two scientists stationed in an asteroid where mining activities are performed say "We could flood the mines, if this weren't an airless asteroid" when considering ...
0
votes
1answer
65 views

Do quantum physics apply universally at all scales? [duplicate]

Do quantum physics apply universally at all scales? Where do quantum physics apply? Does the nucleus of an atom abide by the laws of quantum physics? Like do we know the definitive/velocity ...
0
votes
2answers
3k views

Definition of Equivalent Resistance [duplicate]

Is the equivalent resistance of two parallel resistors the resistance of the individual resistors or the sum of their resistances? Is the $R_e$ of two series resistors their sum?
2
votes
0answers
47 views

Why is the effective action $\Gamma[\phi_c] \propto -(VT)$ (spacetime volume)?

I'm asking about equation $(11.50)$ in Peskin and Schroeder where they state that the effective action evaluated at the classical field is given by $$\tag{11.50}\Gamma[\phi_c] = -(VT)\cdot ...
1
vote
4answers
969 views

What's so special about the speed of light? [duplicate]

What's so special about the speed of light? Why do many equations in physics include the speed of light in vacuum $c$? Why do so many thing depend upon it? Why can't it be the speed of sound? ...
1
vote
1answer
125 views

Do Quantum Fluctuations happen evenly through universe?

I was wondering if Quantum Fluctuations are completely unpredictable, but do our observations tell us if these fluctuations happen evenly through space or are there regions where more quantum ...
1
vote
1answer
77 views

How to show that $(\xi\eta-\eta\xi)|A\rangle = 0$?

On page 49 of of Dirac's book, The Principles of Quantum Mechanics, he states A state may be simultaneously an eigenstate of two observables. If the state corresponds to the ket vector ...
0
votes
1answer
83 views

What is the overall rate of heat conduction through two pipes of different dimensions if the thermal conductivity is not constant?

I am trying to work out how I would find the rate of heat transfer through two pipes made of the same material that are joined at their ends but which have different cross-sectional areas and lengths. ...
1
vote
1answer
94 views

Folding of wave-vector in Band Theory of Metals

In the Kronig-Penney model in the Band Theory of Metals, we derive the energy levels as function of wave vector as shown in the figure. But my professor showed that we represent the levels folded ...
0
votes
1answer
69 views

How do I determine the electric charge on two (initially discharged) spheres after an impact with a charged sphere?

This is the first part of a problem on my book: Two identical conducting spheres, initially discharged, of mass $ m = 0.5 \ kg $ come in contact, in consecutive moments, with another sphere, ...
3
votes
1answer
159 views

Is the Universe still believed to be flat?

I have read a handful of old articles from mid 2013 expressing that the Universe may, in fact, be curved. http://www.nature.com/news/universe-may-be-curved-not-flat-1.13776 ...
0
votes
0answers
36 views

What does negative absolute temperature mean? [duplicate]

I always understood that the concept of absolute temperature stems from the third law of thermodynamics and that the lowest theoretical possible temperature is zero degrees Kelvin. However, ...
2
votes
2answers
287 views

Electric and Magnetic field's phase difference shift in linearly polarized electromagnetic waves

I am a high school student and we currently studying the electromagnetic theory. In my textbook i read that the oscillating electric the magnetic fields have phase difference equal to π/2 rad near the ...

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