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18

Phonons are indeed massless, as you can see from their dispersion relation or from the fact that they are Goldstone bosons. The phonon dispersion relation that you wrote down tells us that we can excite a phonon mode, with some finite momentum, using an arbitrarily small amount of energy, hence they have no rest mass (in condensed matter language, they are ...


17

The most precise measurement of the mass of an electron was reported by Sturm et al in Nature 506, 467–470 (27 February 2014), quoting a relative precision of $3\times 10^{-11}$, meaning they determined the mass to better than $3\times 10^{-41}~\rm{kg}$. If that is not the best, at least it gives you an upper bound... Note that if you could weigh such a ...


7

If you pay careful attention your notice that cosmic ray passing the earth just now. You are moving at 99.999%$c$ relative that particle. In fact the whole planet is doing so. From which we conclude that you don't even need a lot of money to make people go close to $c$, you just need the appropriate frame of reference. Now, I know perfectly well that that ...


6

Phonons follow a wave equation, which is at least in first approximation simply a standard wave equation, the only difference to relativistic particles is that the speed of the waves is not c but the speed of sound $c_s$. But this does not change the mathematics of the equation, so that in general there may be phonons which follow a massless wave equations ...


4

I want to offer a different perspective from the already existing answers, which all seem to somehow refer to the Standard Model or other specific physical theories to say that mass is not an integral multiple of some fundamental mass unit, hence not discretized. The reason why mass is not like that - and can indeed conceivably have continuous values in a ...


3

You have drawn a Feynman diagram. Feynman diagrams are iconic shorthand for integrals over the variables of the problem. The calculation gives the probability for the reaction to happen, in this case the decay of a neutron . The observables are the four vectors of the initial (neutron) and final particles. The integral is over the variables . Here is a ...


3

UPDATED ANSWER : The centre of gravity will always be the same as the centre of mass in a uniform gravitational field (constant in magnitude and direction). This applies for bodies with non-uniform density as well as those with uniform density. The Earth's gravitational field can be considered uniform if the dimensions of the object are much smaller than ...


3

This is a quite subtle problem. You have to be careful about three different situations. A ball can be thrown with velocity (relative to the ground): a) $v_0-v_e$. b) $v(t)-v_e$, where $v(t)$ is the velocity of the car just after the ball is thrown. c) $v(t)-v_e$, where $v(t)$ is the velocity of the car just before the ball is thrown. You actually stated ...


3

See moment of inertia is analogous to mass. Moment of inertia can be thought of as a physical "property" of the object similar to that of mass. And as we know that mass does not depend on any force or gravitational field or any other external effect, so does moment of inertia. Hope this answers your question.


2

Any time you have an equal and opposite force acting on two bodies, the effect is proportional to $\frac{1}{m}$ for each one. The combined effect is proportional to $$\text{(effect)} = \left( \frac{1}{m_1} + \frac{1}{m_2} \right) \text{(action)}$$ When inverted to find which action has a desired effect we get the reduced mass $$ \text{(action)} = \left( ...


2

As far as we know the classical (i.e. non-quantum) laws of gravity apply at all length scales. There are theoretical reasons to suppose that the classical description fails at scales approaching a Planck length, but this is far, far smaller than the size of a neutron. So inside a neutron we would expect the classical laws of gravity to apply, and in ...


2

Yes the human body has a gravitational field, and yes it's large enough to be measured experimentally (see the Cavendish experiment).


2

Negative energy or mass is not forbidden in Relativity, but gravity is not a force but geometry, so if you have a negative mass it would repell positive mass as well as negative mass, just like positive mass would attract negative and positive mass all together. If you place a positive and a negative mass near each other the positive mass would attract the ...


2

The left-handed neutrino is a 2-spinor field $\eta_A$, $A=0,1$, and the Majorana mass term is a bilinear, $\Delta L = \pm 2$ term without the complex conjugation in each term, $$ m\cdot \eta_A \eta_B \cdot \epsilon^{AB} + \text{Hermitian conjugate}$$ Note that this Majorana term is the only bilinear term without derivatives that one may construct from a ...


1

All three are "correct", and all three refer to mass-energy equivalence discovered by Einstein. Equations (2) and (3) are algebraically identical, and are generalizations of (1). Equation (1) only takes into account an object's rest mass, whereas equation (2) also takes into account the momentum $p$ of the object, and (3) takes into account velocity $v$. ...


1

The method with measuring the instantaneous weight while swinging the arm with a fixed angular velocity sounds rather impractical. You might try to combine data from multiple sources. I assumed that you are talking about the bit of limb from elbow up to and including the hand, with the hand stretched, but it turns out that you wish to exclude the hand. The ...


1

It can be stated this way: In this particular diagram, the W boson is in a state named off-shell i.e. we say that this boson is virtual. Virtual particles are allowed to have any mass value. They can't although violate charge conservation at the vertex. This 80 GeV mass of the W boson, is for a real W boson, which is on the on-shell state. The real ...


1

Depends in the context you are considering. There are two aspects to think about: the theoretical definition, which depends on a model, an image of reality the operational definition: the way you measure it. Rest mass is a concept from Relativity, which is a part of classical physics. Here, we can think of particles as points of mass, with no wave ...


1

There is only one real fundamental speed limit, $c$. Historically, we first discovered it in the context of light, so we call it the speed of light. In reality, it has a little bit deeper significance--it turns out all massless particles travel at $c$ and only at $c$, at least in vacuum. A massive particle can theoretically travel at any speed less than ...


1

If you measure a force (weight) for a given acceleration (gravity) in order to determine the mass of an object and you haven't started measuring then the mass is undefined. As soon as you apply an acceleration $a>0$ and you measure corresponding force $F>0$ you can determine the mass. Equations are useful only when they can be used to measure things, ...


1

Well when there is no answer available, I do not think it hurts to try to come up with one. As far as existence is concerned, Geometry and Topology can exist without physical matter, but not vice versa. In fact, there is so much empty space without matter, but no matter without being in space. Empty space has some Geometry and Topology. However, to ...


1

Many of them are calculated. All the ones that have $u$ or $Da$ as the unit are in atomic mass units, referenced above in the table. They just count up the atoms and add. For bacteria, yeast, and the like it will vary from one specimen to another. Not much precision is quoted and it is likely they use the volume (easy to measure with a photograph) and ...


1

When you state that the two masses are 'kept at rest' I assume you mean that the pulley is prevented from turning. The load on the pulley is then $(M+m)g$. [If the pulley is not prevented from turning, then to keep the masses at rest we would have to lift the heavier mass $M$ until it became, effectively, the same weight as the smaller mass. The total ...


1

In addition to the already given answears this also might be of interest: When hammer and feather are dropped simultaneously they arrive at the same time, when dropped independently the hammer attracts the planet more than the feather, so you are right, the total time until impact is then smaller for the hammer. If you pick up the hammer and let it fall to ...



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