All Questions
Tagged with conservation-laws inertial-frames
80
questions
4
votes
1
answer
289
views
Energy of moving Sine-Gordon breather
A few days ago I stumbled across the formula for the energy of a moving breather for the sine-Gordon equation
$$ \Box^2 \phi = -\sin\phi.$$ The energy in general is given by ($c=1$)
$$ E = \int_{-\...
- 41
1
vote
0
answers
30
views
Energy conservation and Lorentz invariants [closed]
In relativistic collision theory,How can we deduce energy is conserved by using Lorentz transformation?
0
votes
1
answer
72
views
Is momentum conserved relative to all reference frames?
Assuming that there is an observer S in a train that is equipped with a cannon moving to the right relative to another observer S' in a train moving to the left relative to S, which is also equipped ...
9
votes
5
answers
3k
views
If energy is relative, then how it can remain conserved?
If energy depends on frame of reference of observer, then how it can remain conserved?
Same question also for linear and angular momentum.
I think energy is conserved when seen from a specific frame ...
- 91
0
votes
1
answer
105
views
Invariance of continuity equation for Galilei transformations
I want to prove that the continuity equation for fluids, $$\dfrac {\partial \rho}{\partial t} + \nabla \cdot (\rho \textbf{u}) = 0$$ is invariant by Galilei transformations. My attempt:
Using index ...
- 115
0
votes
1
answer
1k
views
General Lorentz boost of four-momentum in CM frame, particle physics
In particle physics, we observe a scattering of the type: $$a+b \rightarrow c+d$$
Known quantities in the LAB frame are a, b and c. I want to transform c into the CM frame of the initial state and ...
- 43
3
votes
1
answer
754
views
Proof that conservation of momentum is Lorentz invariant
In classical mechanics, if
$$\frac{\mathrm d}{\mathrm d t}\sum_i m_i\vec{v_i}=0$$is true for one frame of reference, then it is easy to prove that this is true for all frames (since different frames ...
- 1,801
0
votes
2
answers
120
views
Can kinetic energy be transferred between two objects even if they are not in contact?
This question is better explained with a thought experiment. It is inspired by this answer, stating that the amount of work done depends on the inertial frame.
Consider a one-dimensional space with ...
- 101
0
votes
2
answers
789
views
If two objects collide and one is initially at rest, is it possible for both to be at rest after the collision?
I know that the straight answer to my question is no. Since the initial momentum is not zero, the final momentum is not zero.
What about when object A impacts object B that is rigidly fixed to earth ...
- 137
9
votes
6
answers
3k
views
Apparent kinetic energy paradox
Imagine two cars (A and B) of mass $m$ that want to destroy themselves by colliding. They need a velocity of magnitude $2v$ with respect to each other to achieve the destruction that they want and ...
- 300
0
votes
2
answers
222
views
How to understand continuity equation intuitively as Lorenz covariant?
As we know, it is natural that we derive the differential form of continuity equation
$${\frac {\partial \rho }{\partial t}}+\nabla \cdot \mathbf {j} =0$$
from the integral form, in the view of ...
- 15
0
votes
4
answers
485
views
Centre of mass frame
I was just looking at the equation:
$$v2-v1=-e(u2-u1).$$
This equation is to describe the collision between two masses, where $v$ is the final velocity and $u$ is the initial velocity, $e$ is the ...
- 13
4
votes
1
answer
430
views
Charge conservation vs. Lorentz invariance of charge - including non-conserved charges
Conservation of a charge
$$ Q = \int dV \, j^0 $$
follows from current conservation
$$ \partial_\mu j^\mu = 0 $$
and
$$ \dot{Q} = - \oint dS \, j = 0 $$
where the Gauß divergence theorem has been ...
- 917
2
votes
2
answers
193
views
Global conservation + Lorentz invariance = local conservation?
On the page 83 of "Quantum Field Theory Lectures of Sidney Coleman", Coleman showed an interesting example:
It seems that global conservation law and local conservation law can be related. ...
- 192
14
votes
4
answers
3k
views
Why should momentum be conserved in special relativity?
This is more of a philosophical question than an actual physics question, but I don't see a clear reason why relativistic momentum, or energy for that matter, should be conserved.
The equivalence ...
- 860