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19

As far as the theory goes, you are absolutely correct, the (negative) binding energy between atoms in a molecule contributes to the total mass of that molecule, so a stable molecule is less massive than the sum of the masses of its constituent atoms. However (as you yourself calculated), the mass difference is absolutely tiny, and as far as I know, it has ...


18

As far as we can tell, the speed of light in vacuum is indeed constant. Photons don't slow down or speed up as they fall into or rise out of a gravity well. However, just as a massive object's kinetic energy changes as the object falls into or rises out of a gravity well, photons also gain or lose energy. In the case of photons, this energy change manifests ...


5

With respect to your question, the immediate thing you need to clarify is: constant with respect to what? How SR answers that question The speed of light is usually held to be constant with respect to reference frames. In other words, if we're both at the same place in outer space, but you're passing by me in your spaceship, then every photon in either of ...


3

No, in perfect vacuum, photons do not slow down. Although, gravity of massive objects like stars or planets can bend the trajectory of photon (the Theory of General Relativity) like a lense. If you are referring to the fact that Black Hole is black because no photons can escape its massive gravitational force and you thought it is because the gravity of the ...


2

Is the speed of light constant or does the math just happen to work out? None of the above. It's a tautology. What happens is that instead of having just one car, you count 9192631770 cars passing you by. See the defiition of the second which involves microwaves passing you by. Then you declare that a second has elapsed. If those cars are going slower, ...


2

Lorentz invariance refers to the action $S=\int\mathcal{L}(x)\,\mathrm{d}x$, not to the Lagrangian. To determine the condition on the Lagrangian which we must have, we make the coordinate change $x\to \Lambda x=:x'$ (a Lorentz transformation) and use the general fact that the Jacobian of a Lorentz transformation is unity, so ...


2

Yes, bonds have mass, like every other kind of energy. This can be significant; if you had a glueball (a hypothetical particle made of massless gluons), it would have mass, and all of the mass would be from the bond energy! Same would go if you somehow managed to bind photons together.


2

Hint: $T = E - E_0 = m\gamma c^2 - mc^2 = mc^2(\gamma -1)$ and $p = |\vec p| = m\gamma |\vec v| = m\gamma v$


2

We can write total energy $E$ two ways: \begin{equation} E^2=p^2c^2+m^2c^4 \\ E=T+mc^2, \end{equation} where $T$ is kinetic energy. Eliminating $E$ from those two equations will give you the desired result.


2

I would like to hear a deeper explanation of what we believe anti-matter to be, why it annihilates with matter and how this relates to relativity. This is the table of elementary particles deduced from innumerable measurements: Each particle has a characteristic mass and several characteristic quantum numbers. To each particle there corresponds an ...


1

If I measure the speed of a particle in the lab and then write down in my notebook the value I measured, the number an observer in a different inertial frame reads from my notebook will be the same (although the numerals may be Doppler shifted, length contracted, etc.). In the same way, the name of my cat is "Mittenz" independent of any choice of ...


1

How is relativity related to anti-particles? As far as I know relativity doesn't say anything about antiparticles. But particle physics does. Have a look at the Einstein-de Haas effect which "demonstrates that spin angular momentum is indeed of the same nature as the angular momentum of rotating bodies as conceived in classical mechanics". An electron ...


1

The statement that a positron is like an electron moving backwards in time is in itself perfectly explainable with classical physics. As the charge of the particles is opposite, the force caused by the electrical and the magnetic field i.e. q(E + v x B) will be opposite. So, fields accelerating electrons, will decelerate positrons at the same rate and vice ...


1

The general theory of relativity predicts that kinetic energy will contribute to gravitational mass. Here is a paper that explores the gravitational effect of kinetically energetic particles within a system: http://arxiv.org/PS_cache/gr-qc/pdf/9909/9909014v1.pdf. Here is an interesting article by Frank Helle on the production of gravity by relativistic ...


1

You should check out the barn paradox! It's about the same thing. The problem is that there's an extra effect in relativity you haven't accounted for: observers don't agree on the order of events. For example, in the earth frame, we may have the ordering Back of ball at sun Something passes between sun and Earth Front of ball at Earth In the ball's ...


1

W-Boson events decaying into two leptons (e.g. electron and electron-neutrino) The convention is of course to say that a leptonic decay of a $W^-$ boson produces a negatively charged lepton (such as an electron, $e^-$) together with an anti-neutrino (of the matching weak state, such as an anti-electron-neutrino, $\overline\nu_e$). the angle $\theta$ ...


1

The equation $E = m^2c^2 + p^2 c^2$ is restricted to Special Relativity. However, in classical physics we have $$ \vec{F} = m \vec{a}, $$ and $$\vec{F} = m \vec{g},$$ whence $$ m \vec{a} = m \vec{g}. $$ This can be written as $$ m \big( \vec{a} - \vec{g}\big) = \vec{0}. $$ From a mathematical point of view we have $$ \big( m = 0 \big) \vee \big( \vec{a} - ...


1

Sorry I didn't get around to learning the latex. I read this paper (the only one accessible to dummies like me): http://www2.warwick.ac.uk/fac/sci/physics/current/teach/module_home/px435/dirac.pdf It was a fairly stupid question. The answer is that there are solutions where OpB outputs non-zero and then OpA takes it to zero, and those are just solutions of ...


1

Mass is a Lorentz invariant quantity! The relativistic mass is not the real mass, it is is just called relativistic "mass" for obvious reasons. This term is abandoned by most textbooks, as it often causes this confusion.



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