# All Questions

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### Definition of Casimir operator and its properties

I'm not sure which is the exact definition of a Casimir operator. In some texts it is defined as the product of generators of the form: $$X^2=\sum X_iX^i$$ But in other parts it is defined as an ...
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### How can I solve for time without knowing the vertical velocity?

A guy posted this problem on a forum: There is a bird sitting on a pole of height h. you throw a rock at it and the moment the rock leaves your hand the bird starts flying horizontally away from ...
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### Explanation for Negative $\rho$ (radial distance) in Cylindrical Coordinates

My question : What does it mean when we arrive at negative values for distance variables like $\rho$ in cylindrical coordinates? (after some discussion here,I revised the question, at the end of the ...
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### Lifting house with balloons [closed]

I have an assignment about the movie Up. Here is the question: Critique the brief floating scene. Did the animators use enough balloons during this scene? What important variables, (which affect ...
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### What stabilizes neutrons against beta decay in a neutron star?

Free neutrons are known to undergo beta decay with a half-life of slightly above 10 minutes. Binding with other nucleons stabilizes the neutrons in an atomic nucleus, but only if the fraction of ...
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### Pendulum in an elevator

Suppose we have a pendulum tied to the ceiling of an elevator which is at rest. The pendulum is oscillating with a time period $T$, and it has an angular amplitude, say $\beta$. Now at some time ...
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### Temperature of a small system

What is wrong if I define temperature of a small system (I mean, a system which has not a large number of particles) by $$1/T = dS/dE$$ ?
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### Why do lumps of sugar break more easily when blowing in it?

My question is simple, when you have a small lump of sugar, it's hard to break it with your bare hands, but when you blow in it, it appears to be more easy. (it's a piece of advice i learned for my ...
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### Why does Lagrangian of free particle depend on the square of the velocity ?

Why does Lagrangian of free particle depend on the square of the velocity ? For example, $L(v^4)$ also doesn't depend on direction of $v$.
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### What types of materials can be electrically charged by rubbing?

What types of materials can be electrically charged by rubbing? Is there a certain type of materials in which static electricity can be produced by rubbing together two different materials?
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### Stress energy tensor of a perfect fluid and four-velocity

In the following demonstration, there is an error, but I cannot find where. (I explicitely put the $c^2$ to keep track of units). We consider a metric $g_{\mu\nu}$ with a signature $(-, +, +, +)$ : ...
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### Pendulum Wave Period

Recently I've seen various videos showing the pendulum wave effect. All of the videos which I have found have a pattern which repeats every $60\mathrm{s}$. I am trying to work out the relationship ...
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### Calculate how hot PLA will become

I am trying to attach the shaft of a brass heating tip to a PLA component. My problem is that the tip will have to reach a temperature of about 200°C and the PLA can only handle a temperature of about ...
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### Apparent and real depth object in water [closed]

Did I get my formula right? Seems like the correct answer is $d_o = 1.33 \times d_i$ but I thought the formula I should use is $d_i = - \frac{n_2}{n_1} d_o$
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### Evolution principle of the physical laws

I wanted to know if there is a physical theory that considers that the laws of physics undergo an evolutionary process. That see the law of physics or the absence of them, as something dynamic, and ...
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### Phasor representation of voltage in frequency domain

In a text on application of electromagnetism in transmission line, there introduces a phasor for the voltage (in frequency domain) $$\tilde{V}(x) = V^+e^{-i\beta x} + V^-e^{i\beta x.}$$ Here $V^+$ ...
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### How is the distance to a $\gamma \mathrm{-ray}$ burst (GRB) measured in just a few days?

Recently the Fermi Gamma-ray Space Telescope recorded the most energetic Gamma Ray burst (GRB 130427A) yet observed with a peak $\gamma \mathrm{-ray}$ energy of $94\, \mathrm{GeV}$. Various sources ...
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### What is Convective acceleration of flow velocity?

I know that $\frac {dv}{dt}=a$ is acceleration, but: what is convective acceleration of a flow velocity? what is difference between $(v\cdot \nabla) v$ and $v\cdot (\nabla v)$, ?
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### What is a sudden singularity?

I've seen references to some sort of black hole (or something) referred to as a sudden singularity, but I haven't seen a short clear definition of what this is for the layman.
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### Phase space in quantum mechanics and Heisenberg uncertainty principle

In my book about quantum mechanics they give a derivation that for one particle an area of $h$ in $2D$ phase space contains exactly one quantum mechanical state. In my book about statistical physics ...
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### Does it make a sense to speak about age of electron or atom?

It's possible that this question is too soft or even quite senseless for this forum, but I will ask nevertheless. Everyday (macroscopic) things, like a grandfather's pendulum clock or the grandfather ...
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### Physical explanation for why total internal reflection occurs

I have been trying to understand total internal reflection (and have read several posts on this site already). Mathematically, I feel that I understand how the evanescent wave decays exponentially as ...
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### Time evolution operator to find expectation value

I have a state $\Psi (x,0) = \sum_{n=0}^{\infty} c_{n}u_n(x)$ and want to find the expectation value of any observable A at time t, $\langle \Psi(t)|\hat{A}|\Psi(t)\rangle$. I know that I should ...
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### Clarification regarding Newton's Third Law of Motion and why movement is possible [duplicate]

Newton's third law states that to every action, there is an equal and opposite reaction. If that's the case, then how do things move at all? Shouldn't all applied forces be canceled by the equal and ...
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### Energy conservation in nuclear reactions and radiactive decay

Reading "Fundamentals of Nuclear Physics" by Atam P. Arya, I understand that in a nuclear reaction, let say $x+X \to y+Y$ meaning that "when a particle $x$ strikes a target nucleus $X$, the outcome of ...
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### Where does one find pair-correlation functions for various materials?

What is the canonical source for finding pair-correlation functions for atoms in various materials? I am interested in both numeric computations and experimental measurements (like might be obtained ...
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### Optimal tunnel shape for travelling inside the earth [duplicate]

Say you were to travel from Paris to Tokyo by digging a tunnel between both cities. If the tunnel is straight, one can easily compute that the time for travelling from one city to the other ...
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### Capacitor Charging and Discharging when connected to the ground

When we charge a capacitor using a battery and then remove the battery, the plates of capacitor becomes charged. One holds positive charge and the other one gets equal negative charge. o. k. ? Now ...
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### Air pressure relative to a force on a bag?

Assume an airtight bag occupied by air such that the pressure inside the bag is equal to the atmospheric pressure. Assume the surface tension of the bag is negligible. What is the change in air ...
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### Status of experimental searches for tachyons?

Now that the dust has settled on the 2011 superluminal neutrino debacle at OPERA, I'm interested in understanding the current status of experimental searches for neutrinos. Although the OPERA claim ...
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### Liquid benzene magnetic susceptibility

In a solid state physics problem, I'm asked to make a rough estimate of the contribution to the diamagnetic susceptibility of the outer electron of each carbon atom. The wavefunction of these ...
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### Could entropy explain dark energy? [closed]

This was 3rd beer idea, so please bear with me. What if the universe was not actually expanding but the speed of light was slowing? Wouldn't that be indistinguishable to our observations? Either way ...
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### Definition of electric charge and proper explanation

Is there a definition of electric charge and proper explanation of it? It is said "Electric charge is the physical property of matter that causes it to experience a force when close to other ...
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### What counts as “observation” in Schrödinger's Cat, and why are superpositions possible?

So if I understood correctly, Schrödinger's Cat is a thought experiment that puts a cat inside a box, and there's a mechanism that kills the cat with 50% probability based on a quantum process. The ...
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### Why Quantum Mechanics as a non-fundamental effective theory?

My question: What (physical or mathematical) reasons (not philosophical) do some physicists ('t Hooft, Penrose, Smolin,...) argue/have in order to think that Quantum Mechanics could be substituted by ...
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### Casimir force using Pauli-Villars regularization

In Zee's Quantum field theory in a nutshell, 2nd edition, p. 74 he claims that:  \sum_a c_a \Lambda_a \sum_n \frac{\omega_n}{\omega_n + \Lambda_a} = - \sum_a c_a \Lambda_a \sum_n ...
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### Independent systems and Lagrangians

Definition 1: The notion of independent systems has a precise meaning in probabilities. It states that the (joint) probability or finding the system ($S_1S_2$) in the configuration ($C_1C_2$) is ...
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### The most general form of the metric for a homogeneous, isotropic and static space-time

What is the most general form of the metric for a homogeneous, isotropic and static space-time? For the first 2 criteria, the Robertson-Walker metric springs to mind. (I shall adopt the (-+++) ...
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### Bound State of Only Massless Particles? Follows a Time-Like Trajectory?

Is there any way in which a bound state could consist only of massless particles? If yes, would this "atom" of massless particles travel on a light-like trajectory, or would the interaction energy ...
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### Proof for commutator relation $[\hat{H},\hat{a}] = - \hbar \omega \hat{a}$

I know how to derive below equations found on wikipedia and have done it myselt too: \begin{align} \hat{H} &= \hbar \omega \left(\hat{a}^\dagger\hat{a} + \frac{1}{2}\right)\\ \hat{H} &= ...
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### What is the importance of the Fermi energy $E_F$ or the chem. potential $\mu$ for topological superconductors

A lot of effort is put into shifting the Fermi energy of a topological insulator to exactly zero which then provides some advantages when this TI is coupled with a superconductor. I don't understand ...
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### How can we detect a black hole? [duplicate]

If black holes are phenomena of very high density (gravitational singularities) which don't emit radiation how can we detect them so far away from us where so much other radiation can hide the black ...
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### Reaching the speed of light via quantum mechanical uncertainty?

Suppose you accelerate a body to very near the speed of light $c$ where $v = c - \epsilon$. Although this would take an enormous energy, is it possible the last arbitrarily small velocity needed -- ...