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5

The statement from the Wikipedia articles is, as written, wrong. The EM field tensor - as a tensor - does change under change of reference frames. It is covariant, but not invariant under the Lorentz group, while the electric and magnetic field are neither, but they are covariant under the rotation group. The electric and magnetic fields are ordinary, ...


3

If rest mass does not change with v then why is infinite energy required to accelerate an object to the speed of light? The momentum of a material particle, a conserved quantity, is theoretically and experimentally a non-linear function of velocity given by $$\vec p = m \frac{\vec v}{\sqrt{1 - \frac{v^2}{c^2}}}$$ which goes to infinity as $v ...


3

In principle there is an effect, but firstly it's tiny and secondly it averages to zero. The mass of the ISS is about 420 tonnes, or about 5000 times the mass of an astronaut. That means if an astronaut pushes themselves off a wall at 1 m/sec the ISS moves in the other direction at about 0.0002 m/sec. But the ISS isn't very large so after only a couple of ...


2

Torque is defined as $\vec \tau = \vec r \times \vec F$, where $\vec r$ is the displacement vector from the origin to the point at which the force is applied. This means that torque depends very much on the choice of origin. Then again, the choice of origin also affects the inertia tensor. So long as you get all of the physics correct, you can choose any ...


2

If I understand correctly you are asking how observer dependent is electromagnetic radiation. The first thing is that non uniformly accelerated charges are described in a inertial frame by Larmor's formula and Abrahm-Lorentz force which take into account the radiated field and the recoil on the particle. Now in Newtonian mechanics and special relativity ...


2

Technically the electron and proton are both orbiting the barycenter of the system, both in classical and quantum mechanics, just as in gravitational systems. You find the same dynamics for the system if you assume the proton and electron are moving independently about the barycenter, or if you convert to a one-body problem of a single "particle" with the ...


2

In the context of general relativity it is often stated that one of the main purposes of tensors is that of making equations frame-independent. Question: why is this true? Actually this isn't quite true. General relativity doesn't have frames of reference (except locally, which is trivially true because GR is the same as SR locally). A better way of ...


2

Option 4, none of the above. Your option 1 is wrong because points don't rotate. Your option 2 is closer to correct, but ultimately still wrong. You're overly hung up on points (the origin). It might help to get a handle on what "rotation" is. Points don't rotate. Better said, a rotated point is indistinguishable from the original. What about one ...


2

I think you are considering two different situations: 1) Team Pole passes through the barn at constant velocity, simultaneously (in Barn's frame) grab the pole, and continue on with the same constant velocity. In this case, your second calculation is correct. The pole's length does not change from Team Barn's perspective. The pole remains length $L_0$ ...


2

It's just a drawing convention. Rather than "vertical", time is orthogonal to the x-axis. The reason it is not shown vertical is because the paper surface is 2D, and the author uses the vertical axis for drawing the altitude with respect to the ground. Just recall the way you draw the 3D axis. Here, the author uses X (horizontal),Y (vertical) and time ...


1

In relativity the rest mass is the mass of an object measured from a reference frame in which it is at rest. But this is not the mass involved in acceleration or inertial mass. Inertial mass, or the opposition of the body to the change of movement (directional or in magnitude), will grow with the speed of the body: $$m = \frac{m_o}{\sqrt{1-v^2/c^2}}$$ ...


1

As long as you don't forget that Andromeda galaxy is cca. 2.5million light years away, then there should be no paradox at all. The observers are only seeing different slices of history that took place 2.5million years ago (plus/minus 1day), the decisions has already been made long time ago. It's like when you take a newspaper from a pile, more recent papers ...


1

The interpretation is that two events being simultaneous as measured in frame $S$ doesn't imply that the events are simultaneous in frame $S'$. Which events count as being "simultaneous" depends on the frame of reference. This is known as the relativity of simultaneity. Added clarification due to comment: The coinciding of the origins is an event, call ...


1

One expects the energy stored in the capacitor to transform like the zeroth component of the four-vector $(U,\vec p)$. In its rest frame the field configuration around the capacitor has $$(U,\vec p)_\text{rest}=(U_0,\vec 0),$$ and by the Lorentz transformation the moving observer will see $$(U,\vec p)_\text{moving}=(\gamma U_0, \gamma\vec\beta U_0),$$ where ...


1

The short answer is: protons are much more (1800 times) massive than electrons. That makes them (approximately) the center of mass of the system, that's why electrons are the ones orbiting protons and not vice versa. The term 'orbiting', however, means something essentially quantum. It is the reason of the stability of the atom (electrons don't radiate ...


1

The fact that different observers in relative motion can measure the same light ray to move at a speed of c has to do with the fact that each observer defines the "speed" in terms of distance/time on rulers and clocks at rest relative to themselves. It's crucial to understand that different observers use different rulers and clocks to measure speed, because ...


1

No. My answer is negative, even if I confirm the statements of other answers: "The first thing is almost completely arbitrary, especially in full general relativity. The second thing is an unambiguous result of an experiment."(Jerry Schirmer) "In Einsteinian relativity all observers can still agree on a number of facts, they are just ...


1

A particle moving at the speed of of light does not experience time, as it has no rest frame. Furthermore, a particle cannot continuously accelerate and eventually reach the speed of light, since massless particles can only move as fast as light. They either move at the speed of light or do not exist at all.



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