# Tag Info

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The no-go results from Algebraic and Constructive QFT you mention deal with related but slightly different matters. (Edit: the previous version of the following paragraph was slightly misleading - Haag's theorem is actually stronger than I stated before; see below for details) Haag's theorem (which actually slightly predates the inception of Algebraic ...

5

In signal processing, the Nyquist–Shannon sampling theorem says you need at least 2 samples of a frequency to be able to perfectly reconstruct it. So in your question, a sampling rate of $200\: \mathrm{MHz}$ means you can perfectly reconstruct frequencies in the range of $0 - 100\: \mathrm{MHz}$. So what happens when frequencies above $100\: \mathrm{MHz}$ ...

3

Before looking for the critical parameters, let's review how mushroom clouds work. A large amount of energy is released at the source of the explosion, effectively a point source for our discussions. That large energy release causes a blast wave that propagates outward and leaves behind a core of very hot, high density gas. If the blast wave was strong, the ...

3

You have pinpointed an important nuance of quantum information theory. A perfectly entangled state is, in some sense, like a single bit in a one time pad: just two copies of a shared random bit. In fact, the teleportation protocol is perfectly analogous — not the same, but certainly analogous — to transmitting a message securely using a one-time ...

3

It started with conservation of quantum numbers, from baryon number when we did not know about quarks, to lepton number, when we discovered the positron.For the neutrino momentum and energy conservation played a role too, since it is only seen as a missing mass. In time the symmetries in the assignments of the quantum numbers became more and more evident ...

2

Batteries produce a charge difference across the terminals as a result of a chemical reaction. A chemical gets changed into another one. Even in a rechargeable battery a chemical change takes place that is reversed. An electrolytic capacitor uses chemistry to create a thin layer with an electric field across it. The thinner layer than a "regular" capacitor ...

2

This is a really good question, with a mind-bending answer. Check this out: (A) Pick a random electron at a random time. How long (on average) do I need to wait until the next time it collides? (B) Pick a random electron at a random time. How long (on average) has it been since the last time it collided? (C) Pick a random electron that just collided. How ...

1

Warning : I absolutely don't know nothing about the subject. If you are a french locutor, applyed notion of kinematical inversion (and dynamical inversion) to the Tottori earthquake are explained in this thesis (Sara Di Carli), see page $4$ for a abstract, and pages $11-29$ for details. The Haskell Model(1964) seems to be the first model. In the ...

1

Actually I think I disagree with the answer by BMS (the group of asymptotic symmetries of asymptotically flat spacetimes?). However I am not sure to have understood BMS'answer completely. In my opinion, there is no difference between the definition of work in pure mechanics and work in thermodynamics (I stress that I am speaking of thermodynamics and not ...

1

Here is one issue where thermodynamics and mechanics could differ in the definitions of work. In mechanics, a non-careful, ambiguous, but common definition for the work done by a force $\vec{F}$ is $\int\vec{F}\cdot d\vec{s}$. The problem with this is that we're not told which infinitesimal displacement $d\vec{s}$ to use; one could use (1) the infinitesimal ...

1

The name seems appropriate if consider that it probably comes from the case when the manifold is the cotangent bundle of a manifold. Then a point on $T^*M$ is a pair $(x,\alpha)$, where $x$ is a point on $M$ and $\alpha$ a one form. The definition of the tautological one form is: the value of the form at a point $(x,\alpha)$ on a tangent vector is obtained ...

1

I) On a general symplectic manifold $({\cal M},\omega)$ (typically called phase space by physicists), one can locally choose a symplectic potential $\theta\in \Gamma(T^{*}{\cal M}|_{\cal U})$, which is a one-form such that $$\tag{1} \mathrm{d}\theta~=~\omega,$$ cf. Poincare Lemma. Here ${\cal U}\subseteq {\cal M}$ denotes a local neighborhood. Note ...

1

For instance, a Lagrangian $L = \partial_i \phi \partial^i \phi + m^2\phi^2$ has the same equation of movement that the Lagrangian $L' = \partial_i \phi \partial^i \phi + m^2(F\phi - \frac{F^2}{2})$. The Euler-Lagrange equation for $L'$ simply give $\Box \phi +m^2F=0$ and $F = \phi$, so we have $\Box \phi +m^2\phi=0$, which are the Euler-Lagrange ...

1

This term is used all the time in introductory classical physics. In that context, stationary usually means not moving in the laboratory frame. Thus, a block sitting on a table not doing much would be referred to as being stationary. If one studies relative motion, then stationary could mean not moving in whatever frame you're discussing.

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Let's say you have a catapult that can be turned into a trebuchet by attaching a sling to the end of the projecting rod. And let's say that it always launches the object with its projecting rod moving at some particular angular velocity instantaneously before it is stopped. Adding the sling has some benefits in terms of launching something at an enemy. The ...

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Both operate on the same principle: the velocity of a point on a rigid body undergoing rotation is proportional to its distance from the pivot. The sling is simply an ingenious way to extend the distance of the the projectile from the pivot without extending the rigid arm. As the trebuchet arm moves in an arc, the sling exerts a centripetal force on the ...

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