All Questions
12
questions
0
votes
0
answers
30
views
How is potential energy incorporated into mass in special relativity? [duplicate]
I've seen it said before that we often ignore potential energy in relativity because it can be included in the mass term. It is commonly said that a hydrogen atom has less mass than the sum of its ...
- 160
0
votes
2
answers
91
views
How can we say potential or chemical energy is part of an object?
I'm posing this question primarily in the context of special relativity. Also, I'd like to leave gravitational potential energy out of the picture since that would take us into a different direction ...
- 8,640
0
votes
1
answer
207
views
How to Derive Potential Momentum?
The only derivation/definition of potential momentum I've seen is using the fact that:
$$E^2-p^2c^2=m^2c^4$$
And if you add a potential, you must subtract something else from the momentum called the ...
- 11
0
votes
0
answers
77
views
If kinetic and potential energy are relative, how do they exert a gravitational force? [duplicate]
I am imagining two bodies flying through empty space near the speed of light relative to their (distant) surroundings. Let’s say they are a bowling ball and a tennis ball. They are not moving with ...
- 1
0
votes
1
answer
57
views
What qualifies as “Energy” in the Einsteinian sense of the word?
As an absolute beginner to special relativity (and all the 1900s Einstein stuff), I find it hard to grasp the real meaning of the term energy used in the popular equations. I’ve heard it is possible ...
- 33
1
vote
3
answers
395
views
Relativistic energy of harmonic oscillator
What is the relativistic energy of an harmonic oscillator:
$$\frac{m_0 c^2}{\sqrt{(1-\frac{v^2}{c^2})}}+\frac{1}{2}kx^2$$
Or
$$\frac{{m_0 c^2}+\frac{1}{2}kx^2 }{\sqrt{(1-\frac{v^2}{c^2})}}$$
I think ...
- 199
0
votes
1
answer
50
views
Does Special Relativity Set a Canonical Zero of Energy?
In special relativity, one has the equation
$$
E^2 = m^2 + p^2
$$
It seems like this is saying that there is an absolute zero of energy: the energy of a massless, momentumless particle.
On the other ...
- 1,590
1
vote
2
answers
102
views
What is the relativistic energy of a bounded static particle?
Premise: The speed of light is set $c = 1$.
Let's consider an electron in an external electromagnetic field. Its four-momentum will be
$$p^{\mu} = (E, \bar p) = (\gamma m_e, \gamma m_e \bar v),$$
...
1
vote
1
answer
81
views
Mass-Energy equivalence in case of minimal coupling
The energy-momentum relation of a free particle is (in SI Units):
$$
m^2c^4 =- c^2 \vec{p}^2 + E^2
$$
Minimal coupling is a way to fix a gauge freedom for the choice of canonical momentum (which I ...
- 6,763
0
votes
0
answers
60
views
Potential energy and particle collisions/decays
Why is it that the (possible) potential energy of particles is not taken into account when studying the available energy in particle collisions, or decays? By this, I mean that one simply uses the ...
- 3,207
14
votes
5
answers
8k
views
Does potential energy of an object increases its relativistic mass?
I know that in relativistic condition the increase in kinetic energy of an object increases its relativistic mass as $$m=\frac{m_0}{(1-v^2/c^2)^{1/2}},$$ and mass is another form of energy.
So my ...
- 141
6
votes
2
answers
2k
views
Is the Einstein Energy-Momentum equation $E^2 = p^2c^2 + m_0^2c^4$ valid only for Free Particles?
Is the energy -momentum relation
$$E^2 = p^2c^2 + m_0^2c^4$$
satisfied only by free particles or even bound particles?
Does the Energy refer to total Energy(including potential) or only (kinetic +...
- 103