13 votes

What makes energy "the" conserved quantity associated with temporal translation symmetry?

The OP's question is basically stating that in a system with time-translation invariant dynamics, we can define a conserved quantity by arbitrarily assigning a real number to each orbit; when the ...
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  • 4,585
12 votes

What makes energy "the" conserved quantity associated with temporal translation symmetry?

What is special about the conserved quantity $Q(x, p) := \frac{1}{2} (x^2 + p^2)$, when also the quantity $Q_2(x, p) = \sin(x^2 + p^2)$ is conserved too, by the same temporal translational symmetry? ...
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11 votes

Where does all the energy in black holes go?

Energy inside black holes doesn't "go" anywhere. Energy and mass are the same thing ($E=mc^2$). There's a "no hair" theorem that says that black holes can be completely described ...
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10 votes
Accepted

Where is the energy going in this simple harmonic motion

In case 1, the collision between the two masses is inelastic (because they stick together), and so some of the energy is "lost", or rather, some of the energy is converted to thermal energy ...
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  • 3,767
7 votes

What makes energy "the" conserved quantity associated with temporal translation symmetry?

For what it's worth, OP seems to be mischaracterizing Noether's theorem by seemingly ignoring one of its main assumptions: That the physical system is equipped with an action formulation $$S~=~\int\! ...
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  • 167k
4 votes
Accepted

What law of thermodynamics is broken here?

This is not a good question. Yes, as stated, the engine appears to violate the first law. It can also be claimed that the second law is violated, but this is not that straightforward because some of ...
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  • 7,257
2 votes
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Are there non time-symmetric systems that increase total energy over time?

Noether's theorem implies that if $L$ does not depend on time, then $H$ (Hamiltonian) is conserved. But $H$ is not always energy in the physics sense. See When is the Hamiltonian of a system not equal ...
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2 votes

What makes energy "the" conserved quantity associated with temporal translation symmetry?

If I understand the question correctly, then a flow $\Phi^t$ uniquely determines a Hamiltonian vector field $\mathbf X := \mathrm d\Phi^t\big|_{t=0}$. Such a vector field can be written as $$\mathbf ...
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2 votes
Accepted

Why don't perpetual motion machines with superconducting magnets work?

A perpetual motion machine that merely 100% conserves energy and thus operates forever like a perfect flywheel is of little interest and is not the same as as a perpetual motion where you can ...
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  • 6,892
2 votes

What exactly is the limiting factor of the efficiency of a heat engine?

What exactly is the limiting factor of the efficiency of a heat engine? The short answer to the title of your post, the limiting factors are the maximum and minimum temperatures between which the ...
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  • 55.5k
2 votes

A Tough Mechanics Problem

I’ll just outline a method of obtaining the equations of motion. I don’t know if you’re familiar with Lagrangian mechanics. If you are, use polar coordinates for position of $B$ which specifies the ...
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  • 1,145
2 votes

What makes energy "the" conserved quantity associated with temporal translation symmetry?

There are nice answers already. I just want to add one small observation. If $H$ is the energy, ordinary time is defined by the Hamiltonian flow with $H$, so observables evolve according to $$\frac{dO}...
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2 votes
Accepted

Conservation of energy and work done by a torque

The solid is assumed to be a rigid body. Friction causes rotation and does do rotational work with respect to the center of mass. But, for no slipping of a rigid body, the net work from friction is ...
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  • 5,825
2 votes

Where does all the energy in black holes go?

The short answer is: To the future! EDIT: reading OP's question again, they seem to point out, that the temperature of inbound particles is measured by a distant observer as being near zero. But since ...
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1 vote

Why is some mass converted into energy when neutrons and protons combine to form nucleus?

In classical mechanics, it is easy to understand that a ball lying on the floor is bound to the earth, and can only be freed by giving it kinetic energy. Neutrons and protons and nuclear physics are ...
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1 vote

Why is some mass converted into energy when neutrons and protons combine to form nucleus?

A nucleus is a complicated object, so let's start with the simplest possible bound system of a positronium atom i.e. a bound state of an electron and a positron. This shows the same phenomenon as the ...
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1 vote

Where does an electromagnetic wave's energy come from?

I haven't thought much about this. But here's my intuition: Imagine we have a mechanical grabber. And this grabber can grab something and then apply a sinusoidal force to it at frequency $\omega$. $$ ...
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  • 9,154
1 vote

Where does an electromagnetic wave's energy come from?

since EM waves carry energy; where exactly does it come from according to the laws of thermodynamics? From other available energy around the radiating body. Energy conservation is local, if some ...
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1 vote

Where does an electromagnetic wave's energy come from?

One way to think about it is to realize that any work done on charges, (imagine touching it with something) means some type of electromagnetic interaction. And when charges interact and move, the ...
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1 vote

Where does an electromagnetic wave's energy come from?

This is a famously messy problem. The most developed classical model is that of Abraham and Lorentz. Whether this is satisfactory depends a lot on your taste. In practice, it's not used much. For ...
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  • 3,159
1 vote

Angular Momentum Conservation and Conservation of Energy

The sphere is initially slipping. Only when its speed drops to $5u/7$ does it start rolling. The sphere's speed drops because it is moving on a rough surface. The friction between the slipping sphere ...
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1 vote

What exactly is the limiting factor of the efficiency of a heat engine?

Let us consider gas, cylinder, and a piston. The only energy that the gas has is thermal energy. The only work the gas does is pushing the piston From 1 and 2 it follows that: lost thermal energy =...
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  • 1,495
1 vote

How does general relativity resolve the fact that energy is not positive definite in Newtonian gravity?

Suppose you have two masses interacting gravitationally in the Newtonian limit. The mechanical energy is given by $$ E = \frac12\mu\dot r^2 + \frac12 \frac{\ell^2}{\mu r^2} - \frac kr $$ where $\...
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  • 70.1k
1 vote

A Tough Mechanics Problem

To get started with problems like this, recognize the DOFs of the system. I see 2 DOFs, one being $x$ how much block A has slid, and the second one $\theta$ the swing angle of block B. The describe ...
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  • 32.9k
1 vote

Why don't perpetual motion machines with superconducting magnets work?

When current changes in time, the medium is no longer exactly superconducting. There are energy losses, if not due to internal dissipation mechanisms, then due to EM radiation of the changing current.
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1 vote

Are there any mathematically conceivable arrangements of an indeterministic universe that are not physically possible?

The answer to your first question depends on what you mean by "mathematically conceivable". If your definition of "mathematically conceivable" is wide enough then, yes, there will ...
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  • 33.1k
1 vote

Moment of Inertia for a car

A rough cut estimate for a passenger vehicle's moment of inertia about the axis normal to the pavement is $m \cdot a \cdot b$, where $m$ is mass, $a$ is the distance from center of mass to front axle, ...
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1 vote

How does stimulated emission work, exactly?

I just don't understand one thing, if photons carry energy, shouldn't the electron be forced to higher excited states? This typically does not happen because the photon usually considered when ...
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