13 votes

How can a pulsar slow down?

Radiation can indeed take away angular momentum. Thinking about this just from a classical point of view the flux of energy carried by electromagnetic waves (in vacuum) is $$ \vec{S} = \frac{1}{\mu_0} ...
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  • 110k
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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  • 4,605
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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  • 7,006
8 votes
Accepted

Null conserved angular momentum

Yes, if the angular momentum of a particle is conserved and it is zero, the particle must move along a straight line. Indeed, by using the triple product identity, we have $$ {\bf r} \times ( {\bf r} \...
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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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6 votes

Energy to momentum

Yes, light has momentum, so you could use your collected electrical energy to create a beam of light to propel the satellite. However, you need to bear two points in mind- firstly, the recoil from the ...
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  • 18.2k
5 votes

Is it possible to move without throwing or pushing another object or energy?

Is there any way that a closed system can move without throwing or pushing anything outside of it? Yes, it can move at a constant velocity without throwing or pushing anything outside of it. Edit: in ...
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  • 64.3k
4 votes
Accepted

(Why) Is orbital angular momentum conserved for point masses?

Imagine you had a particle traveling at constant $\mathbf{v_0} = \dot{z_0}\mathbf{\hat{k}}$ upwards. At time $t = 0$, your particle is at $\mathbf{r} = z_0 \mathbf{\hat{k}}$ and you apply an ...
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  • 179
4 votes

Can conservation of angular momentum be proven?

I am answering the title Can conservation of angular momentum be proven? Conservation laws are called laws because they are axiomatic, experiments and observations of the last centuries have given ...
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  • 221k
4 votes

Is it possible to move without throwing or pushing another object or energy?

Please restrict the answer to classical physics. The center of mass of your object cannot change its momentum without transferring momentum to or from some other object. You could make the object ...
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  • 22.8k
3 votes

Is it possible to move without throwing or pushing another object or energy?

It sounds like what you describe is a reactionless drive. That is a hypothetical method of propulsion which does not rely on conservation of momentum. Such a thing is not believed to be possible.
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  • 337
3 votes
Accepted

Do photosynthesis and respiration violate the law of conservation of energy?

I have been taught that for making one molecule of glucose in photosynthesis 18 ATP molecules are used up but in respiration, oxidation of the same glucose molecule releases 38 ATP In the Calvin ...
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3 votes

How can a pulsar slow down?

If the pulsar slows down, its angular momentum decreases. This implies that there's some angular momentum radiated away. Rotational energy decreases too, of course. There could be several ...
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  • 6,676
3 votes
Accepted

Why does angular velocity changes as i strech my hands?

Your angular velocity changes depending on your arms' extension due to conservation of angular momentum. Conservation of angular momentum implies that the quantity $$\bf \vec L=I{\bf\vec\omega}={\text{...
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  • 24.8k
3 votes

Energy to momentum

There is such a thing as a Photon Rocket or Photon Drive. This takes advantage of the fact that photons have momentum. However, you are not going to get a lot of thrust out of one.
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  • 1,993
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

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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  • 50.8k
2 votes

Is it possible to move without throwing or pushing another object or energy?

Classically, the short answer is no as you've expressly asked to ignore the most obvious solution, an object moving at uniform velocity. This means the object must at some point accelerate (otherwise ...
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2 votes
Accepted

Noether current associated with transformation $\delta \psi=i\alpha \psi$

Mindful of @Robbie's comment, let's first rewrite your calculations as $$\begin{align}0&=\partial_\nu\frac{\partial\mathcal{L}}{\partial\partial_\nu\psi}-\frac{\partial\mathcal{L}}{\partial\psi}\\&...
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  • 21.7k
2 votes

Is it possible to move without throwing or pushing another object or energy?

Let's say you are in space, in your space gym, which is simply a big lightweight inflatable ball. Inside the ball is you, some nice air, and your gym equipment. You can move the space gym by grabbing ...
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  • 371
1 vote

Null conserved angular momentum

The angular momentum is defined relative to a chosen point. For it to be zero, the velocity vector of the center of mass of a non-rotating rigid object must be directed toward that point.
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1 vote
Accepted

If we know information existed when life first began on earth, then can’t we surmise that information existed prior to earth life?

It's difficult to tell what you mean by information here. In physics, information is often used to refer to the number of possible states of a system, similar to Shannon entropy. Under most ...
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  • 66
1 vote

Do photosynthesis and respiration violate the law of conservation of energy?

Photosynthesis is driven by absorbing the energy of the light, whereas in non-photosynthesizing organisms the energy comes with food - i.e., the glucose is not resynthesized, but imported from ...
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  • 37.2k
1 vote
Accepted

Integrate continuity equation in QM

The integral $$\int \psi^*\psi\ r^2\ dr\ d\Omega$$ is just the same as integral $$\int P(\mathbf{r},t) d^3\mathbf{r}$$ representing the total probability of finding the particle anywhere. Remember ...
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1 vote

(Why) Is orbital angular momentum conserved for point masses?

Angular momentum(and torque) does not necessarily mean that there are rotations in place. you can define angular momentum for straight lines, however, that isn't very useful to solve any problem. If ...
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  • 354
1 vote

Can conservation of angular momentum be proven?

You write our linear velocity $v$ was constant according to our first claim where the “first claim” was The linear velocity is related to it by the equation $𝑣=𝑟𝜔$ But $v=r\omega$ is a scalar ...
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  • 70.1k
1 vote

Energy to momentum

You're right, the only way to change linear motion in space is by throwing stuff out, and why is that a problem? Instead consider, most obviously, a nuclear submarine which any number of people think ...
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1 vote

Energy to momentum

The most direct method is to use the Earth's magnetic field. It is generally used only for attitude control (i.e. generating angular momentum), but nothing (except the low efficiency, of course) stops ...
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