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20

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 ...


4

The short answer is yes. An object moving at non-relativistic velocity $\vec{v}$ in a weak gravitational field will have a proper time $\Delta \tau$ elapse that is related to the time $\Delta t$ on distant clocks (far from the Earth) by the equation $$ \frac{\Delta \tau}{\Delta t} \approx 1 - \left( \frac{1}{2} \frac{v^2}{c^2} + \frac{G M_E}{r c^2} \right) ...


3

Per Bort's comment, this is easier to think about from the spaceship's frame rather than the debris's frame. A rock is traveling toward your spaceship at .99 times the speed of light. You send out a pulse of light that intercepts the rock when it's one light-minute away from the ship. The pulse bounces back and arrives at the ship 1 minute later. The ...


3

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 ...


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

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 ...


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

From a perspective on the spaceship, the radar beam travels away from me at the speed of light, so I might imagine that I would have ample warning of an object positioned at rest one light-hour away. One light-hour away in which frame? If that one light-hour away is from the perspective of the rest frame of that object, you don't have much time at all. ...


1

If the pulse of light is going directly down, it will miss the base of the mast. There ought to be nothing confusing at all about the speed of light being independent of the speed of the source. Light has an E=hf wave nature. Sound has a wave nature too, as do ocean waves and seismic waves. The speed of the waves depend on the properties of the medium. In ...


1

In the MM experiment, it does not actually matter whether the light beams are exactly perpendicular: what matters is that the light traveling along one "leg" would experience the ether drag head-on, while the other would experience it from the side. As the table rotates, the effect of the ether (if it exists) would shift from one arm to the other, and would ...


1

The answer to your question depends on fine definitions. Locally the speed of light is always the same; more precisely, the universal, Lorentz invariant speed $c$ (which is also the maximum speed of a cause-effect relationship and experimentally observed to be the same as the speed of light) is constant. This means that any measurement of light speed in any ...


1

If you with your rods and clocks are in free fall (ie: your metric is the Minkowski diag(-1,1,1,1) ) in a vacuum and the light ray passes near you, you will always measure the standard speed c= 2.99792458 E+8 m/sec. However, the speed of light is observed to be different if the observer and his rods and clocks are in a different gravitational environment ...


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

It's not so much that it is ticking that is crucial here but the fact that the watch is in a higher energy state that in its, say unwound state. This fact increases the rest mass of the watch by an amount $\Delta E/c^2$, where $\Delta E$ is the potential energy input to elastically stress the spring and thus wind the watch. A wound, broken, unticking watch ...


1

Both give the correct time. The frequency of a pendulum is: $$ \nu = \frac{1}{2\pi}\sqrt{\frac{g}{l}} $$ Whatever your height above the Earth, if you measure $g$ and measure $l$ then use the calculated frequency as a measure of time, the pendulum will correctly measure time and its measurements will agree with the atomic clock. If you fail to take account ...


1

Not quite. Galilean relativity, which has absolute time, is definitely causal; you can't have future events influence past ones because all observers agree on all times. However, it is interesting how much relativity you can get with incomplete axioms. There's a derivation on page 38 here that shows you can get the Lorentz transformations, but with a ...


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

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 ...



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