7 votes

What gives particles mass? Also why are particles like photons considered massless when they have energy and momentum?

The idea that a photon is massless is a pedagogic convention, that has not always held sway. When I was taught special relativity in the '70s, there were two kinds of mass that were distinguished. ...
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6 votes

Does this prove that the force and momentum formulas are wrong?

Assuming that OP means Newton's second law by force formula, Note that it says $$\mathbf{F}_\text{net}=m\mathbf{a}_\text{net}$$ In you situation, you are putting two forces from opposite sizes so that ...
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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

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

Does this prove that the force and momentum formulas are wrong?

Force does not require speed (or momentum). That is a common misconception. In your scenario, you have a stationary object, so Newton's 1st law applies: $$\sum F=0\quad \Leftrightarrow \quad F_\text{...
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  • 46.3k
3 votes

Do you have to leave something behind to go forward? (ie a contained system)

If the initial total momentum of the system is zero, then the position of the center of mass will stay constant no matter what, regardless of the elasticity of collisions. This means that if the box ...
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  • 7,257
3 votes

What gives particles mass? Also why are particles like photons considered massless when they have energy and momentum?

Mass is energy that a particle has when it is at rest. Photons are never at rest, and so don't have mass. A related fact is that in the limit that the photon's momentum goes to zero, its energy also ...
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  • 33.3k
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
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
2 votes

Why is derivative of Lagrangian with respect to generalized position and velocity equal to this?

The relation below is simply the definition of the generalized momentum. It requires no proof, as is true by definition: $$ p_i = \dfrac{\partial \mathcal{L}}{\partial \dot{q_i}} $$ Now according to ...
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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

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
2 votes
Accepted

Stationary Schrödinger Equation in Momentum space

Here, $\hat{V}(p)$ is an operator that should be acting on $\hat{\psi}(t,p)$ and therefore that should be acting on $P(p)$. If $\hat{V}(p)$ simply multiplies the wavefunction by some function of $p$ ...
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1 vote

Does this prove that the force and momentum formulas are wrong?

When you say that force and momentum formulas are based on motion, that is not completely true. For example, Hooke's law says that the degree to which a spring is stretched or compressed is ...
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  • 18.2k
1 vote
Accepted

Linear Momentum in General Relativity

Is there a metric that describes this case? Yes. It is the Schwarzschild metric (valid outside of the gravitating body if we are talking about something like a star). When written in the form where ...
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  • 12.5k
1 vote

Is linear momentum times distance any meaningful quantity? $\vec{r} \cdot \vec{p}$ or $pr = mvr$ comparing to $\vec{r} \times \vec{p}$

You could use it to derive the centripetal acceleration equation. Suppose we have a particle moving around in a circle and a position vector to it from the center of the circle. Consider the quantity: ...
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1 vote

Is light's momentum $0$?

If you start with the energy momentum relation $$ E^2 = \left(m_{0} c^2\right)^2 + \left(pc\right)^2 $$ where $m_{0}$ is the rest/invariant mass, and apply it in the rest frame (where $p = 0$), you ...
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  • 2,718
1 vote

Can we convert momentum to coulombs in any simple sense?

Charge and momentum are separately conserved. So you cannot convert one into the other. However, in geometrized units, charge and momentum both have dimensions of length. So in that unit system they ...
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  • 64.3k
1 vote
Accepted

Superposition of momentum plane waves for a WF: discrete of continuous?

It seems your text didn't say clear enough, what the $x$ domains are for these two different situations. The discrete sum $$\Psi(x)=\sum_n\alpha_n e^{ixp_n/\hbar}$$ is the decomposition when the $x$ ...
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1 vote
Accepted

Do Einstein field equations only relate local spacetime curvature to local energy-momentum of matter?

Yes, they cannot be extended to relate global curvature to global energy-momentum, not in general at least. You can see this by noting that the Einstein Field Equations can be derived by demanding ...
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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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  • 5,693
1 vote

Energy to momentum

You should read up on solar sails, electric sails, and magnetic sails if you are interested in propulsion near stars. A solar sail uses the momentum of solar photons to drive a ship, while electric ...
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1 vote

On what ground do you multiply $m$ with $v$ in the momentum equation $p=mv$?

Strictly speaking, a definition doesn’t need justification. However, some definitions are useful and important, and it is relatively easy to show why they are useful. In the case of momentum, ...
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  • 64.3k
1 vote

Moving cart, falling rain, and constant velocity

$F_{net} = \frac {d}{dt} (mv) = v\frac {dm}{dt} + m\frac {dv}{dt} = v\frac{dm}{dt}$ for constant velocity $v$, mass $m$, rate of change of mass $dm/dt$ (the value you listed as $x$ in the question). ...
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  • 8,398
1 vote

Intuitively Understanding Work and Energy

"Most of the fundamental ideas of science are essentially simple, and may, as a rule, be expressed in a language comprehensible to everyone." (Einstein and Infeld, The Evolution of Physics) ...
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