Walter
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Why is the $dx$ right next to the integral sign in QFT literature?
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18 votes

IMHO, the notation $\int_a^b\mathrm{d}x\,f(x)$ is much cleaner than $\int_a^b f(x)\,\mathrm{d}x$, because the integration variable ($x$) and its associated integral range $(\int_a^b$) are kept ...

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Why the galaxies form 2D planes (or spiral-like) instead of 3D balls (or spherical-like)?
9 votes

Just to add to the otherwise excellent answer by Triveth. He still leaves the origin of elliptical galaxies unexplained, i.e. how do the stars attain the spheroidal shape? After all, most stars form ...

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How will the Milky Way / Andromeda combined galaxy appear in 4 billion years?
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4 votes

In $4\times10^9$yr, M31 and MW (Milky Way) will have merged to form an elliptical galaxy. The internal spiral structures of either progenitor and their bars will be destroyed in the process, leaving a ...

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Does buoyancy change on smaller scales?
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4 votes

You're confusing buoyancy with surface tension. The former applies to (macroscopic) objects which are (at least partly) immersed, while the latter applies to inter-fluid surfaces. Thus, a ...

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Using tensors on Lagrangian and Hamiltonian
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4 votes

If $$\mathcal{L} = \boldsymbol{a}\dot{\boldsymbol{q}} + \tfrac{1}{2}\dot{\boldsymbol{q}}^t\mathsf{\boldsymbol{T}}\dot{\boldsymbol{q}} - U(\boldsymbol{q})$$ with some constant vector $\boldsymbol{a}$ ...

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How can contact binaries persist?
3 votes

Short answer: They don't. Contact binaries are a possible evolutionary phase of close binary systems, where both stars fill and/or overflow their Roche limit, i.e. 'kiss' each other at the L$_1$ ...

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Origin of pressure gradient in Navier-Stokes integral
3 votes

This is the pressure-gradient term integrated over all volume, converted to a surface integral and using Gauss' theorem. Note that physicists prefer the differential form of such equations (see also ...

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If someone from another part of the observable universe had their own Hubble Telescope, would they see different things than we did?
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2 votes

Well, this depends obviously how far they are away. If their observable universe and ours overlap, then objects in that overlap will be observable by us and them. However, we will see them from ...

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Schrödinger equation solutions confusion
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2 votes

A plane wave is obviously a solution to the Schrödinger equation, but it cannot be normalised and hence cannot represent a particle. The condition for $\psi(\boldsymbol{x},t)$ to be normalisable, i....

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Difference between naive and Coriolis-force calculation
2 votes

The relation $\Delta v_x = \Omega h$ correctly expresses the difference in the inertial velocity between the top and bottom of the building/tower; this is not the cause of the problem. The naive ...

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Newtonian motion of a particle confined to a smooth surface
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2 votes

If $m$ < $n$, then your $F$ is a function from $m$-dimensional flat space to $n$ dimensional flat space, which maps $\mathbb{R}^m$ onto a $m$ dimensional surface in $\mathbb{R}^n$. If the motion ...

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How are smoke cells an example of Brownian motion?
2 votes

The smoke is a mixture of air and tiny 'dust' particles, which are much larger than the air molecules and undergo Brownian motion. Watching the dust particles under a microscope in a smoke cell (where ...

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What is meant by invariant under change of coordinates **to first order**?
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2 votes

The appropriate definition of symmetry uses infinitesimal quantities, not just small quantities. Thus, in terms of your question, the Lagrangian is symmetric if $dL/d\epsilon=0$ at $\epsilon=0$. In ...

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Elastic collisions and conservation of momentum
2 votes

In an elastic collision the masses of both objects, the total kinetic energy, and the total linear momentum are conserved. The kinetic energy has contributions from the motions of the objects as well ...

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A question over Liouville’s Theorem
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1 votes

Liouville's theorem holds for all Hamiltonian systems. If your definition of an asymptotically stable point $\boldsymbol{x}^*$ means that trajectories from points $\boldsymbol{x}$ in some ...

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Canonical Perturbation theory of Keplerian orbits
1 votes

The problem is that the $x^3$ term also contributes to the first order (in $J_r$) correction to $H$ and we must go to second-order perturbation theory. Using the Deprit perturbation series (...

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What is the difference between damping and elasticity forces?
1 votes

This is simply because for (most) structures the damping is weak, in the sense that $c^2\ll4km$, when the damping time $2m/c$ (the time over which the damping term takes energy out of the system) is ...

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Stable disk for $N$-body simulation
1 votes

Your logic is correct, including the choice of tangential velocity as x = r*cos(phi); y = r*sin(phi); vx=-v*sin(phi); vy= v*cos(phi); Where you (tried to) set v in centrifugal balance. However, ...

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Physics of heating a swimming pool
1 votes

Let's make a simplified ideal model of the situation: ignore heat losses to environment (evaporation, surface conduction) and gains from other sources (pumps running hot). Also, assume that the flow ...

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Pointwise and uniform convergence. Examples from physics
1 votes

Sciences use mathematics only as a tool. In almost all such applications, mathematical problems (such as pointwise vs uniform convergence) are not inherent to the scientific problem at hand, but arise ...

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For a projectile to cover maximum vertical distance in the least time, what will be the angle of projection?
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1 votes

When neglecting air drag, the vertical and horizontal motions decouple and we have the equations \begin{align} \ddot{x} &= 0,\\ \ddot{y} &=-g. \end{align} The initial conditions (at $t=0$) are ...

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Does it make sense to model the Universe from an outside perspective?
1 votes

I think your considerations are led by the daily experience that what you see actually happens as you see it. However, this is an illusion. All you perceive are photons, but they can (1) take their ...

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Interpreting Schrödinger Equation's solution for a free particle
0 votes

As to your first question: the meaning is that the particle is not a free particle after all. This is the problem of a particle in a one-dimensional infinitely deep square potential well: $\Phi=0$ for ...

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Why are stars spherical whereas (some) galaxies are disks?
0 votes

The post you're referred to explains reasonably well why spiral galaxies are discs. So why are stars not disc like. The simple answer is: a disc-like object cannot be a star. But what is a star? A ...

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Can the Coulomb gauge and the Lorenz gauge be satisfied simultaneously?
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Only in certain simple situation can both gauges be satisfied. $V=0$ is obviously one of them. For a general electric and magnetic field configuration, however, only one gauge can be satisfied.

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Could one calculate the relative speed of the Sun viewed from the Earth?
0 votes

No, this makes no sense. The 'speed' that you would obtain (and which other answers provide) is not actually a speed. It is merely an angular speed (that of the Earth's spin) multiplied with a ...

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Bead on a rotating wire - Conservation of angular momentum, fix points
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0 votes

In a coordinate system rotating at constant angular rate $\omega$, neither energy nor angular momentum are conserved and one has coriolis and centrifugal forces. The bead is forced outwards by the ...

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Does a material exist that reduces a magnetic field without being affected by the magnetic field itself?
0 votes

NO. actio = re-action: if A affects B, then B affects A. So, any material that reduces the magnetic field, and if only by deflecting it, is affected by it in some way.

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