In introductory mechanics, the momentum of a particle is its mass times its velocity. In electrodynamics, the momentum of a field is proportional to the cross-product of the electric field with the magnetic field. In special relativity, momentum is generalized to four-momentum.

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How to get the accurate relativistic momentum form for photons? [duplicate]

I have studied from Griffiths, the relativistic form of momentum is $$p = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} m_0v$$ Now when I evaluate the momentum for photon, I just insert $v=c$ and $m_0=0$ and I ...
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Pair production - mathematically?

Allover the web i am only seeing a statement similar to this: Pair production is not possible in vaccum, 3rd particle is needed so that conservation of momentum holds. Well noone out of many ...
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80 views

4-Momentum conservation for particle annihilation

Disclaimer: this is a homework question, so I am happy with just a hint or the expressions needed to proceed with my understanding. I am working on the momentum conservation of a ...
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4answers
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How does the 'water jet pack' work?

So I was cruising around at YouTube and saw this sweet video, and as I was watching started to wonder: "How is this possible?". For a little bit of background, in case you decide to not watch the ...
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Lorentz force in Dirac theory and its classical limit

It is well known that in Dirac theory the time derivative of $P_i=p_i+A_i$ operator (where $p_i=∂/∂_i$, $A_i$ - EM field vector potential) is an analogue of the Lorentz force: $\frac{dP_i}{dt} = ...
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Does a force really act on a body during a collision?

Consider two bodies A(black) and B(red) having equal mass. A is moving at a constant speed towards B, which is stationary. At certain point of time, they collide elastically, $\therefore u_{A}=v_{B}$ ...
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Why is momentum conserved in an inelastic collision and kinetic energy is not conserved? [duplicate]

We know that in an inelastic collision that total momentum of the system before collision equals the total momentum after collision. But total kinetic energy before collision is not equal to total ...
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5answers
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The elusive difference between force and impulse

Impulse is defined as the product of a force $F$ acting for a (short) time $t$, $J = F*t$, and that is very clear. What I find difficult to understand is how a force can exist that doesn't act for a ...
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3answers
471 views

Expectation of momentum in the bound state

Is it logically correct to assert that the expectation of the momentum $$\langle \hat p \rangle=0$$ for any bound state because it is bound to some finite region? What is the physical interpretation ...
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2answers
747 views

Origin of motion and relative speed of bodies in the universe

Charged particles can hit the earth at relativistic speeds. But it seems that all large bodies have fairly low relative speed. Of course, speed can increase considerably when a body orbits close to a ...
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Newton's 3rd Law: How can I break things?

If I punch a wooden board hard enough and it breaks in two, has the board still exerted a force of equal magnitude on my fist? When the board breaks in two due to my force, the halves have a ...
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4answers
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Is it possible to lift yourself off from the ground?

Say for instance a person who was strong enough to lift double his body weight. If he placed his hands under his bottom and tried to lift$^1$ himself$^2$ off the ground, could he? -- $^1$In a ...
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The relationship between angular and linear momentum

Why is orbital angular momentum not 0 when spin and linear momentum are not collinear? Why can it be 0 when spin and linear momentum are parallel? Like in the example of a scalar field at rest ...
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2answers
1k views

Conservation of linear momentum magnitude along a trajectory

I was once criticized for "taking angular momentum as momentum going in a circle". I was loosely trying to state, in classical mechanics, that in using conservation of momentum, one can switch between ...
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1answer
516 views

How to get the new direction of 2 disks colliding?

I'm developing a 2D game including collisions between many disks. I would like to know how I can get the angle corresponding to the new direction of each disk. For every disk I have this information ...
2
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1answer
434 views

Rocket drive and conservation of momentum

I am currently reading through some lecture notes of Physics 1 and in a chapter about the dynamics of the mass point, there is an example covering the rocket drive. Let $v$ be the velocity of the ...
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3answers
761 views

Train crash: are these situations alike? [duplicate]

I was just wondering... I believe that if a car travelling 50 miles per hour crashes into a wall, the result should be the same as crashing to another car also travelling 50 miles per hour (but in the ...
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2answers
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Elastic Collision And Momentum

The question I am working on is, "Two blocks are free to slide along the friction-less wooden track shown below. The block of mass $m_1 = 4.98~kg$ is released from the position shown, at height $h = ...
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4answers
241 views

Which is the right explanation for rocket motion? [duplicate]

What actually causes a rocket to move? Is it the pressure in the rocket engine or the amount and velocity of mass that is being ejected out. The reason I am asking is, I found these two explanations ...
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2answers
308 views

Ball flying towards me - Newton's third law is violated?

I was trying to answer the question of the flying ball here on the basis of Newton's third law and momentum conservation. Here is what I have tried. Lets take a ball mass of $m_1$ (index 1 is the ...
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4answers
678 views

Where does the energy required to stop a moving body come from and go?

For a long time, I have been thinking about this: In order to stop a moving body, I have to apply impulse to change the existing momentum to $0$. For the impulse I have to impart force on the moving ...
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2answers
151 views

Determine $p_x$ from $[x,p_x]=i\hbar $ [closed]

With $[x,p_x]=i\hbar $, how to determine the form of the operator $p_x$?
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Can a Skydiver Land On a Large Slide and Survive?

Please forgive my lack of artistic ability, but here's my question: Consider that a skydiver, without using his parachute, were to fall exactly parallel to a giant curved slide that starts at ...
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755 views

Best current bounds on nonconservation of momentum?

It's not straightforward to test conservation of momentum experimentally, and many experiments that seem like tests really aren't. For example, in a Newtonian system of identical particles that ...
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355 views

How multiple objects in contact are resolved in an inelastic collision, when edge normals don't “line up”

In a case I understand, let's say I have an object A moving at velocity V toward 3 objects in contact B, C, and D: The momentum of A is the mass of A times its velocity. To figure out how the ...
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Directional derivatives in the multivariable Taylor expansion of the translation operator

Let $T_\epsilon=e^{i \mathbf{\epsilon} P/ \hbar}$ an operator. Show that $T_\epsilon\Psi(\mathbf r)=\Psi(\mathbf r + \mathbf \epsilon)$. Where $P=-i\hbar \nabla$. Here's what I've gotten: ...
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What happens when two bodies collide in a dynamics point of view?

I'm a high school student learning about energy and momentum. What confuses me is the things with elastic and inelastic collisions. I completely (in my opinion) understand those concepts in energy ...
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7answers
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Ball flying towards me or me flying towards ball

Suppose a ball is flying towards me at a speed of 10m/s and that, on impact, I feel "x" amount of pain. If, instead, it was me flying towards the ball at the same speed, with all other conditions ...
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540 views

Translation Invariance without Momentum Conservation?

Instead of the actual gravitational force, in which the two masses enter symmetrically, consider something like $$\vec F_{ab} = G\frac{m_a m_b^2}{|\vec r_a - \vec r_b|^2}\hat r_{ab}$$ where $\vec ...
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2answers
280 views

Is it possible to determine the outcome of any impact knowing only the ratio of masses? [duplicate]

In elastic collisions in 2-D if two balls $A$, $B$ ($m_A = m_B$, $R = 1$) have equal mass we can determine in advance the outcome of the collision. If cue-ball $A$ impacts object-ball $B$ (at rest) ...
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3answers
3k views

The elusive difference between impulse and momentum

1) In classical mechanics, impulse is the product of a force, F, and the time, t, for which it acts. The impulse of a force acting for a given time interval is equal to the change in linear ...
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4answers
1k views

Uncertainty Principle for a Totally Localized Particle

If a particle is totally localized at $x=0$, its wave function $\Psi(x,t)$ should be a Dirac delta function $\delta(x)$. Accordingly, its Fourier transform $\Phi(p,t)$ would be a constant for all $p$, ...
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Fourier Transforms of position and momentum space in Quantum Mechanics

Fourier transformations: $$\phi(\vec{k}) = \left( \frac{1}{\sqrt{2 \pi}} \right)^3 \int_{r\text{ space}} \psi(\vec{r}) e^{-i \mathbf{k} \cdot \mathbf{r}} d^3r$$ for momentum space and ...
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2answers
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What is the Momentum Operator?

I know the equation for the momentum operator, but what exactly is the momentum operator? It's bizarre to me that taking the derivative of the wave function, which is an operator, should return ...
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2answers
336 views

What is the reason behind why a quantum particle cannot be at rest?

So I've seen different reasonings for this; which is correct, or are they both corollaries of each other? 1) For a particle to be at rest, we would know its momentum and therefore by Heisenberg's ...
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Energy is actually the momentum in the direction of time?

By comparatively examining the operators a student concludes that `Energy is actually the momentum in the direction of time.' Is this student right? Could he be wrong?
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4answers
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Can a particle have momentum without energy?

Can a particle have linear momentum if the total energy of the particle is zero? Even if a particle has a certain velocity, can its potential energy cancel out the kinetic energy as to add to zero ?
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269 views

Where does de Broglie wavelength $\lambda=h/p$ for massive particles come from?

I'm curious where the de Broglie relation $p=\frac{h}{\lambda}$ comes from? I know that for light (which has no rest mass), the following is true: $E=pc$ and $E=hf$ so, $$pc=hf \Rightarrow ...
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3answers
314 views

Why Can a Skydiver Hit the Ground and Be Killed? [duplicate]

This is a follow on question from Physics SE Question "Can a Skydiver Land On a Large Slide and Survive?". User Steeven gives this answer here. User Dargscisyhp asks: What is it exactly that ...
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0answers
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Is there a general formula to translate from *canonical* to *physical* momentum?

In Peskin and Schroeder, after having derived a conserved tensor $T^{\mu \nu}$ associated with translations in space-time (the stress-energy tensor), it is said that the charges $\int d^3 x T^{0i}$: ...
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2answers
532 views

Why the photon can't produce electron and positron in space or in vacuum?

$$\frac{hc}{\lambda} = K_e + K_p + 2m_e c^2$$ could be the energy conservation equation for a photon of wavelength $\lambda$ decaying into a electron and positron with kinetic energies $K_e$ and $K_p$ ...
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4answers
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What is the relationship between kinetic energy and momentum?

I can't seem to figure out the relationship between $E_k$ and $p$ or $F$. I understand that the units are pretty different. But for example: A bullet with a mass of 10.0g is moving at the speed of ...
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votes
1answer
221 views

How does one account for the momentum of an absorbed photon?

Suppose I have an atom in its ground state $|g⟩$, and it has an excited state $|e⟩$ sitting at an energy $E_a=\hbar\omega_0$ above it. To want to excite the atom, one generally uses a photon of ...
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3answers
135 views

How is the conservation of momentum satisfied in long-range attraction such as electromagnetism and gravity?

I'm not a physicist, but my understanding is that electromagnetism (including attraction between opposite charges) is mediated by the photon, and gravity is probably (hypothetized to be?) mediated by ...
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1answer
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Is it possible for photon to run in circle by its own gravity?

I have heard that gravity came from energy and momentum so photon has gravity too. Then there are theory state that photon has energy tied to frequency. So if a photon has very very high frequency ...
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1answer
293 views

In QED, why is the $e^- + e^+\leftrightarrow\gamma$ process forbidden on-shell?

QED has a vertex that couples a single photon to two fermions. This vertex describes the annihilation of an electron-positron pair into a photon. Why is this process forbidden for all three particles ...
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663 views

How can particles travel in a straight line?

A particle can be set off in a certain direction by giving them momentum. Momentum is a vector, so the particle heads off in a specific direction. But the wave function of the particle allows it to ...
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3answers
8k views

What is the difference between impulse and momentum?

What is the difference between impulse and momentum? The question says it all...I know the second of of them is mass * velocity, but what is the first one for, and when is it used? Also, what are its ...
5
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2answers
512 views

Would a sneeze by a cosmonaut in a spacesuit affect his movement?

Naive question; feel free to shoot me down It is a truism that any motion in space would continue indefinitely unless it is opposed by an external force. If a cosmonaut were to sneeze within his/her ...
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4answers
10k views

Hammer vs large mass on nail

Why is a hammer more effective in driving a nail than a large mass resting over the nail ? I know this has to do with momentum, but cant figure it out.