# Tag Info

9

Analyzing the acceleration of the center of mass of the system might be the easiest way to go since we could avoid worrying about internal interactions. Let's use Newton's second law: $\sum F=N-Mg=Ma_\text{cm}$, where $M$ is the total mass of the hourglass enclosure and sand, $N$ is what you read on the scale (normal force), and $a_\text{cm}$ is the center ...

6

We know that we can describe a spin $1/2$ massless particle using only a single Weyl field (lets say left-handed $\psi_{L}$). To introduce a mass term we have to use two spinor fields (one left-handed and one right-handed) and this gives the Dirac mass term. The question is now that if we can describe a massive particle with a single Weyl field. Well yes, ...

6

I believe you've already spotted the answer to your question with this sentence: And a black hole will shift the trajectory entirely. This is all dependent on the proximity to the source of gravity. You can "shift light" (bend its trajectory) as much as you want with as little mass as you want using a black hole. Just let the light get arbitrarily ...

6

It is incorrect to say that the energy of a string directly gives us the mass of the particle. While it is true that more the oscillations on the string, higher the mass, the relation between the oscillations and the mass it not that of a simple proportionality. What's really happening is that the string has some energy $E$ (due to oscillations on it) and a ...

5

Imagine an hourglass with just one stone inside. When the stone start to falling a scale would stop to measure it's weight, but it will measure a spike corresponding to the moment when it hits the bottom. The bigger the airtime, the bigger the spike. It is like concentrating the weight of the stone in a very specific time interval: when it hits. However the ...

5

Another way to say this: Speed of photon, graviton, gluon all equal to c? or Whether all massless particles necessarily have the same speed? You must not have been introduced to the concept of a virtual particle: In physics, a virtual particle is a transient fluctuation that exhibits many of the characteristics of an ordinary particle, but that ...

5

With the first question you are correct. Any "thing" with nonzero mass cannot achieve light speed. From this equation you can see why $$m=\frac{m_{0}}{\sqrt{1-\frac{v^2}{c^2}}}$$ where $m_{0}$ is the rest mass of the body (i.e. the mass it has when its speed is zero). As you can see from the equation, when $v=c$, the right hand side will blow up to ...

3

If basic symmetry and homogeneity assumptions about the Universe hold, then yes, all massless real particles (see Anna V's answer for virtual particles must travel at a universal constant $c$, the speed of a massless particle, in all frames of reference. Given these basic symmetry and homogeneity assumptions, one can derive the possible co-ordinate ...

3

OK, I watched the video. It consists of two parts. The first part talks about General relativity and the introduction of a cosmological constant, which from the argument should not exist in completely empty space. He then goes to the Quantum Field Theory vacuum which has the continuous creation and annihilation of all possible fields of virtual particles ...

3

I agree with the answer of Quantum physicist , that zero mass for neutrinos was an input to the standard model , not a prediction, because measurements showed a mass compatible with zero. But I will add that the discovery that neutrinos must have mass does not destroy the Standard Model, just different Lagrangian for the neutrinos has to be included. ...

3

Standard model doesn't predict that neutrinos are massless. It's a "Model", where initially neutrinos are considered massless, because no mass was observed. The way we know, now, that neutrinos have masses, is through the mixing between the different neutrino types, through a matrix called the PMNS matrix (similar to the CKM matrix for quarks). This mixing ...

3

You say: A distant quasar would be less massive in its frame of reference than our observations would suggest and this refers to the notorious expression for the relativistic mass: $$m = \gamma m_0$$ The trouble is that relativistic mass is a troublesome concept that causes more problems than it solves. For example, the gravitational field of a ...

3

Your teacher is correct that the mass of an object if it is moving with very high energies appears to increase according to the formula , it is called the "relativistic mass" . Where E is the energy of the particle and c the velocity of light. But each elementary particle ( these are concepts that apply to elementary particles to start with) is ...

3

This is really a footnote to Carl's answer: As Carl explains, in Mathematics we approach the zero volume/infinite density as a limit and this is a perfectly well defined process. However in Physics we generally don't believe that infinite quantities exist and the occurrence of an infinity is usually a sign that our theory needs modification. In the case of ...

1

I thought the same thing for a long time. I wondered why gluons don't fly out of the nucleus at the speed of $c$. The difference is that photons don't interact with other photons and gravitons don't interact with other gravitons. They can move around and pass through each other. On the other hand, gluons do interact with each other. In fact, gluons form ...

1

What I think you're trying to get at is the vaccum energy. Weight is always associated with a force, so on earth we feel the force of gravity on our body and we call that our weight. Now Einstein showed us that there is an equivalence between mass and energy. What we know from Quantum Field Theory is that there is some underlying amount of energy just ...

1

You need to read up a bit about calculus. This is a case not only of using an idealized situation (cf. the ancient jokes about assuming a spherical cow with a uniform distribution of milk), but, as with delta functions, understanding how a function behaves in the limit, rather than its actual value at that limit. I still recall my first introduction: take ...

1

On your first question: absolutely, energy gravitates (or induces curvature in spacetime) the same way that mass gravitates. If you read general relativity, you will learn that it is in fact the Stress-Energy Tensor that is the source of gravitational interaction (or equivalently spacetime curvature). Energy can be localized very easily; a parallel-plate ...

1

Apart from the fact that the concept of relativistic mass is best avoided, as John Rennie mentioned, it is also a concept of special relativity: it can only be defined in an inertial frame (a Minkowski spacetime) where special relativity is valid. However, the expansion of space is a consequence of general relativity. There is no global inertial frame ...

1

Well, the particles won't always follow circular paths (for instance, the particles in this video). But, if you apply a constant magnetic field across the chamber, charged particles moving in the field will be deflected according to the Lorentz Force Law. The centripetal acceleration for a particle moving in a circle is $a=\frac{v^2}{r}$, where $v$ is the ...

1

If the two objects are equal in mass (or close to it), both orbit their barycenter, which would be a point outside either body. If one object suddenly loses half its mass, the COM of the binary system moves with respect to the current locations of both objects, resulting in changes to acceleration for both ($a=\frac{GM}{ r^2}$, where r is distance to ). i.e, ...

1

The apparent weight is indeed larger when the hourglass is running than at rest. See here for a detailed write-up. This effect has even been verified experimentally. In a nutshell: the net effect of the flow is to move sand from the top surface (where it has a downwards velocity $v$) to the bottom pile, at rest. Thus, the sand is decelerating and the force ...

1

There are quite a few things to consider here. First, The "hourglass" if this vessel is filled with air the results will be much more complex to determine. Second, the diameter of the grains and their uniformity will influence the measurements. Third, The size of the opening will also impact grainflow. Fourth, The sensitivity of the scale in relation to ...

1

First of all, it is the NATURAL behavior of ALL particles (with our without mass), to move along time-like geodesics (if they're massive) or null geodesics (if they are mass-less). So they could accelerate relative to each other (without any external or external forces). Moving along geodesics could pull the particles together or even scatter them to the ...

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