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6

The term rest mass is a poor one because it implies it's the mass measured in the rest frame. But photons have no rest frame, and indeed any particle subject to some form of confinement has a $\Delta p\gt 0$ so its rest frame is somewhat poorly defined. The modern term is invariant mass, which is simply the mass in the equation for the total energy: $$ E^2 ...


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In general, yes you need to know the orbital inclination angle $i$ in order to fully solve the orbit. The radial velocity amplitude $K$ is just modified to $K \sin i$ (where $i=0$ is a face-on orbit). Combining this with the orbital period and Keplerian orbits gives you the "mass function" $$ \frac{M_1^3 \sin^3 i}{\left(M_1 + M_2\right)^2} = \frac{K_{2}^3 \...


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The apparent line-of-sight velocity (red shift / blue shift) is $v\cos\theta$ where $\theta$ is the angle between the plane of the stars' orbits and the line-of-sight line from the Earth. If the stars eclipse one another at a certain point in their orbit (eclipsing binaries) then we know that the Earth is in their orbital plane, so $\theta=0$ and the ...


3

Suppose you start with your (stationary) 1kg block of gold. If you raise its temperature you have to add energy to it, and that means it's different after you've raised its temperature. For example you could shine an infrared lamp on it, in which case you've added the energy from the IR lamp. The mass changes because if you add an energy $E$ the mass goes up ...


3

In a vacuum all frequencies and amplitudes of light travel at the same speed of c = 299 792 458 m/s. Frequency is equivalent to colour. Amplitude relates to intensity. When light travels in material mediums (air, water, glass, etc) it travels at a slower speed v < c which depends on frequency. The ratio of c/v is what we measure as the refractive ...


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No. To make a long story short, if the Higgs field changed its coupling to particles with time then particles in the distant past would have different masses. This would mean atomic spectra of distant galaxies would has differences from spectra now here on Earth. No such change is observed.


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Charged particles can't have Majorana masses of any type because they would violate the charge conservation law. The Majorana mass is really a term that is converting a particle into its antiparticle. It implies that the particle must be considered "physically indistinguishable" from its antiparticle. The Majorana mass term violates the lepton number or its ...


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Because "spontaneous symmetry breaking" does not actually break any symmetries. This is a pretty important principle that is not always adequately taught. In spontaneous symmetry breaking the symmetry in question is always a full symmetry of the theory. The difference between a spontaneously broken symmetry and an unbroken symmetry is just in how the ...


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OK, let's accept your conceit. You ran after $\nu_1$, the lightest neutrino, for the sake of argument, and jumped on it. You ran real fast, as your Lorentz factor γ is several millions, (In natural units $\hbar=c=1$, in the lab frame, $E=p+m_1^2/(2p)+...$, not yours). You watch what is happening around you. You do not oscillate to anybody: You are a non-...


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Not surprisingly, physicists have looked for variations in the speed of light as a function of frequency in vacuum. The state of the art in 1972 can be found in Z. Bay and J. A. White, 'Frequency Dependence of the Speed of Light in Space', Phys. Rev. D 5(4) 796-799 (1972). Using data from pulsar emissions (radio, visible, x-ray) and other sources (see paper),...


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There is the statement in the video, "particles vibrate", and vibrations lead to the concept of frequency. The confusion comes because in fist quantization, the solutions of the Schroedinger and Dirac equations, the wavefunctions have a sinusoidal dependence, which lead to a probability density distribution for the particles, and the de Broglie wavelength ...


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Materials that seem homogeneous often have internal strains, or voids, or even inclusions. Under stress, rather than uniform deformation (bending), those flaws may undergo brittle fracture, or stretch excessively, or become chemically active. A cosmic ray can create internal damage, a particle decay track. So, after some kinds of handling (bending, ...


1

Actually, the explanation as to why rotation of a mass affects the metric in principle is simple. Rotation means there is angular momentum, and angular momentum contributes to the energy-momentum-stress tensor in general relativity. If this was a nonrelativistic rotation we would say that the rotation carries kinetic energy. The rotation contributes as a ...


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The gauge symmetry group associated to the SM is $SU\left(3\right)_{c}\times SU\left(2\right)_{L}\times U_{Y}\left(1\right)$. Then we can not build the lagrangian of the SM with terms of the form $m\bar{\psi}\psi$ because they are not gauge invariant. A term of this kind mix the right and left handed parts, which transforms differently. In order to give mass ...


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A time dependent coupling would mean that this coupling is in fact a field in its own right. This field would correspond to some new particle that would need to be very heavy, otherwise it would have been detected in experiments directly or indirectly by modifying the way the known standard model particles interact with each other . But if the particle ...


1

You do not need a unit for force when measuring inertial mass in Newtonian Mechanics. The only things you really need are the Newton's second law and the concepts of inertial frame and acceleration. The way you shall proceed is the following. Take a collection $\{m_i\}$ of (unknown) masses and a spring. Use the spring horizontally to accelerate the masses ...


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The time dilation factor with respect to an observer at infinity is $$\sqrt{1-\frac{\text{2 G M}}{\text{c}^2\text{ r}}}$$ so if we plug in G=1, c=1, r=10 and M=+1 we get the clocks running slower by a factor of 0.8944 if they are in a distance of 10GM/c² from the center of the positive mass. If we change the sign of M to M=-1 we get a time dilation factor ...



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