1
vote
2answers
82 views

Can matter be created from energy? [duplicate]

The small, hot, dense early universe the size of an atom was made up entirely of energy, it wasn't until after the expansion began and the universe cooled down some of that energy began converting ...
3
votes
2answers
95 views

Energy definition in special relativity

I'm going through the early homework assignments for my special relativity course and I've got myself a little confused about energy. I've got a basic understanding of what the 4-momentum is, having ...
0
votes
1answer
24 views

How would one compute the angle of deflection, in a relativistic collision - underspecified system?

Consider the simplistic case of two identical mass particles colliding elastically with the second particle initially stationary and the first particle travelling with energy $E$. By conservation of ...
6
votes
3answers
192 views

$E=mc^2$ resembles kinetic energy formula?

The simplest equation expressing mass–energy equivalence is the famous $E=mc^2$ where $c$ represents the speed of light. Compare this with $E_K = \frac{1}{2}mv^2$. Since $E=mc^2$ can be applied to ...
3
votes
1answer
77 views

Does divergence of Taylor series for relativistic $E(p)$ for $p\ge m$ have any physical significance?

When one wants to include weak relativistic effects in classical equations, usually kinetic energy term is expanded into Taylor series about $p=0$. But the complete dispersion relation is ...
0
votes
2answers
49 views

Query into the cumulative velocity of mounted platforms

Consider throwing a stone at an object from rest, it travels at Vms-1. Now throw that stone whilst running at Ums-1. It seems in the latter scenario the total speed of stone is V + U. Now imagine ...
2
votes
1answer
66 views

Relativistic fomulae for energy and momentum?

I know that the relativistic formulae for energy and momentum are: $E = \gamma mc^2$ and $\textbf{p} = \gamma m\textbf{v}$; Can we derive these formulae? If yes, where from?
0
votes
0answers
34 views

How to find the speed of free tachyon after emission the light?

Let's have the model in which free tachyon emits the light. We have $$ E = E_{1} + E_{\omega}, \quad \mathbf p = \mathbf p_{1} + \frac{E_{\omega}}{c}\mathbf n , \quad cos(\mathbf p_{1} , \mathbf n ) = ...
1
vote
2answers
147 views

Derivation of rest energy in Landau & Lifshitz

In Landau & Lifshitz The Classical Theory Of Fields there's a statement: $$\mathscr E=\frac{mc^2}{\sqrt{1-\frac{v^2}{c^2}}}\tag{9.4}$$ This very important formula shows, in particular, that ...
32
votes
6answers
1k views

What keeps mass from turning into energy?

I understand the energy and mass can change back and forth according to Einstein. It is fluid; it can go from one to the other. So, what keeps mass from just turning into energy? Is there some force ...
5
votes
4answers
253 views

A question abou $E=pc$ for massless particles

Since photon has no (rest)mass and $$E^2=(pc)^2+(mc^2)^2$$ we derive that $E=pc$ for particle with no (rest)mass. However, if we transform the non-relativistic formula for kinetic energy ...
0
votes
1answer
42 views

Propulsion Energy in Special Relativity

I have a question regarding how to calculate the energy required to move objects within the frame of special relativity. To that extent, I understand the mass of an object as it approaches the speed ...
0
votes
0answers
53 views

Kaon spontaneously splits into two pions (just need an confirmation)

I just need a confirmation on a problem that I am dealing. In my problem I have a statioary kaon which spontaenously splits into two pions which are headed in different directions. Is it possible to ...
3
votes
2answers
373 views

Potential energy in Special Relativity

In Special Relativity, the energy of a free particle is $E^2=p^2c^2+m^2c^4$. But what would be the energy when there is potential energy? If it's something like $E=\sqrt{p^2c^2+m^2c^4}+U$, what ...
0
votes
1answer
319 views

Formulas for kinetic energy

I was reading ABC of relativity from Bertrand Russell and some formulas about kinetic energy caused me some problems. Here is the extract : The kinetic energy is, in the usual form ...
1
vote
3answers
806 views

Integration by parts to derive relativistic kinetic energy

I have come across a weird integration during derivation of relativistic kinetic energy. Our professor states that i can get RHS out of LHS using integration by parts: $$ \int\limits_0^x \! ...
5
votes
2answers
569 views

Impulse from absorbing a photon? Is there an increase in rest mass?

I'm going through A P French's special relativity. In one chapter (6) the following is set up: Suppose that a stationary particle of mass $M_0$ is struck by a photon of energy $Q$, which is ...
8
votes
3answers
429 views

Where's the energy in a boosted capacitor?

Suppose I look at a parallel plate capacitor in its rest frame and calculate the electrostatic energy, $E$. Next, I look at the same capacitor in a primed frame boosted in the direction perpendicular ...
8
votes
4answers
695 views

Potential energy in $E_f^2=(mc^2)^2+(pc)^2$?

Let's consider $$E_f^2=(mc^2)^2+(pc)^2$$ where the $mc^2$ is the rest energy due to the rest mass -- in Finnish "lepomassa". $$ \sqrt{(mc^2)^2+(pc)^2} - mc^2~=~(\gamma-1)mc^2$$ is the kinetic ...
3
votes
2answers
135 views

Mass-Energy Equivalency

We call $E=mc^2$ the Mass-Energy Equivalency because it equates mass and energy together. But, by that same logic, shouldn't we call $E=\frac{1}{2}(mv^2)$, the equation of kinetic energy in Newtonian ...
0
votes
4answers
375 views

Mass-Energy relation

Einstein mass- energy relation states $E=mc^2$. It means if energy of a paricle increases then mass also increases or vice-versa. My question is that what is the actual meaning of the statement ...
0
votes
4answers
656 views

Find total energy and momentum of an moving electron in a rest frame

I have an electron moving with speed $u'$ in a frame $S'$ moving with speed $v'$ relative to a rest frame $S$. How do I find the total energy and momentum of the electron in the rest frame $S$? I ...
0
votes
2answers
387 views

Does the potential energy related to a particle determines its rest mass?

Would it be possible to determine the rest mass of a particle by computing the potential energy related to the presence (existence) of the particle, if this potential energy could be determined ...
2
votes
2answers
469 views

Is the potential energy in a compressed spring a Lorentz invariant?

The total energy of an object comes from the time part of the four-momentum, and so isn't a Lorentz invariant. On the other hand, is the potential energy of a compressed spring a Lorentz invariant?
1
vote
2answers
264 views

Are the higher-order terms in the series for energy really negligible?

To show that energy in special relativity reduces to $E=m+mv^2/2$ for low velocities, if we make a Taylor expansion of $m\gamma$ around $v=0$ we get $$E=m+mv^2/2+3mv^4/8+\cdots$$ But why can we cutoff ...
3
votes
1answer
214 views

Hamiltonians and Lagrangians, Euclidean and Hyperbolic: Are they related?

The Lagrangian of a system is the difference between its kinetic energy $T$ and potential energy $V$, and is relativistically invariant: $L = T - V$ The Hamiltonian of the same system is the sum ...
0
votes
1answer
193 views

Decay of particle (for example $\pi^+$); Find energy [closed]

I don't understand how to solve this: A $\pi^+$ decays into a muon and neutrino. Find the pion's energy if max $E_\nu$ / min $E_\nu$ = 100/1; $m_\nu = 0$ $m_\pi*c^2 = 140\text{ peta-eV}$
0
votes
0answers
58 views

Taylor approximation of e(v) [closed]

Relativistic mass $\displaystyle m(v)=\frac{m_o}{\sqrt{(1-(v/c)^2}}$ $m_o$ = mass of object measured at rest $c$ = speed of light ($3\times 10^8\;m/s$) $v$ = speed If the total relativistic energy ...
2
votes
1answer
515 views

Conservation of Energy in Special Relativity

In classical Newtonian mechanics, from what I understand, conservation of energy stems from the fact that all known forces are conservative forces, and vector calculus tells us that they can be ...
2
votes
2answers
195 views

Which new insight did $E=mc^2$ give us?

I had a special relativity course at university. Now I'm trying to extract what new insight $E=mc^2$ did give us. I mean that moving mass has/is energy (kinetic) not new. The energy merely changed ...
1
vote
2answers
335 views

Connection between momentum and energy

What is the connection between momentum and energy? Which of the answers is the correct? A particle can have zero momentum but energy. A particle can have zero energy but momentum. ...
1
vote
0answers
373 views

How equivalent are heat energy and work energy in connection with a spinning flywheel?

Let's say we have two identical spinning flywheels, that have arbitrary geometry, and are made of copper. Now we apply some heat energy at the center point of flywheel A, causing it to slow down a ...
0
votes
2answers
334 views

Momentum Energy and Higgs

So, as an object accelerates it gains energy. And energy is mass. So an object becomes more massive as it approaches the speed of light. But, if mass is ONLY due to an object's interaction with the ...
19
votes
3answers
538 views

a priori validity of $W=\int Fdx$ in relativity?

There are lots of different ways of arriving at the relativistic relations involving mass, energy, and momentum such as $E=mc^2$ and $m^2=E^2-p^2$ (the latter with $c=1$). One that I've seen in some ...
2
votes
1answer
402 views

whats the rate of energy increase required for constant acceleration between 0.0c and 0.99c?

I was wondering how much energy would be required to accelerate 1000kg to 0.99c at 1G. What I don't understand is what the rate of increase of energy is required as velocity increases. I was looking ...
0
votes
1answer
585 views

Derivation of relativistic energy

The concept of relativistic energy comes from it's conservation in relativistic mechanics for an elastic collision. It seems to me that another possible derivation could equate the energy of a single ...
22
votes
5answers
3k views

Do photons gain mass when they travel through glass?

Please correct me if I'm wrong, but I believe that photons slow down when travelling through glass. Does this mean they gain mass? Otherwise, what happens to extra kinetic energy? I understand now ...