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23

"A state of rest" is a relative term. Relative means - measured in comparison to the things around it. When you sit in a train and sip from a cup of coffee, you can do so because the cup is still relative to you even though both of you might be hurtling through the countryside at 200 km/h. For most experiments, objects can be considered "at rest" if they ...


7

Your misconception has nothing to do with gravity - you're just getting a little mixed up about acceleration vs. relative acceleration. Let's dispense with gravity, since it's a red herring here. Say there are two cars. Car A accelerates at $+3 ~\rm m/s/s$ (to the right). Car B accelerates at $-5 ~\rm m/s/s$ (that is, to the left). So far, so good, right? ...


6

Revolving around the sun is equivalent to free fall around the sun, so the revolution allows you not to 'feel' the sun's gravity. The rotation of the earth is something that can be measured: (i) a centrifugal force which is a small offset on gravity, and (ii) causes the coriolis force. Both these are small effects, so can often be ignored for laboratory ...


4

You might be confusing some issues. In special relativity, space and time do not stretch or compress. It really comes down to measurements with clocks and rulers made by people that are moving uniformly with respect to each other. One option that is consistent with observations for SR is that there is one family whose clocks and rulers are right and ...


2

It doesn't have to be modified, it's fine as it is. There's no paradox at all. The force that attracts both to each other is indeed $F=G\frac{M_A M_B}{r^2}$. But the acceleration they experience is not the same (at least provided $M_A \neq M_B$) because their inertias (masses) are not the same. For one $F=M_A a_A$, for the other $F=M_B a_B$. There's no ...


2

Absolute four-momentum is not an observable. Relative four-momentum is. We cannot find the four-momentum of the lab itself, but we can (and do, regularly) measure the four-momentum of particles relative to a given lab, which then allows us to calculate the four-momentum of said particles relative to any frame you care to name. Whoever said that wasn't ...


2

"Rest, in physics, refers to an object being stationary relative to a particular frame of reference or another object." - Wikipedia (emphasis mine) While on Earth, the planet is often treated as the default frame of reference. It is not a perfect frame of reference, but for many purposes it is good enough. Since there is no absolute frame of reference, ...


1

Considering light travels at relativistic speeds much faster than you can in your car, the exposure is the same. The same logic does not apply as for rain as rain doesn't fall at relativistic speeds.


1

\begin{equation} t_{\beta}^{\prime} = \gamma t_{\alpha} + \frac{v\gamma t_{\alpha}}{c} \tag{01} \end{equation} Your equation (01) is right, but your equation (02) is wrong : \begin{equation} t_{\beta} \ne \frac{1}{\gamma}t_{\beta}^{\prime} \tag{02} \end{equation} The right (02) equation is : \begin{equation} t_{\beta} =\gamma t_{\beta}^{\prime} ...


1

The clocks are all in sync in the ground frame, but they are not in sync in the train's frame. An observer on the train would think that the clocks in the front of the train are ahead, while those to the rear are behind. Measuring the forward traveling beam against the nearby clocks will show a long time difference, while measuring the rearward traveling ...


1

If the rigid body is rotating then in general the primed axes will be changing with time. An easier way to see this is to look at the Euler angles themselves as in this diagram. If, for instance, $\alpha$ is changing, then both the line of nodes (the $N$-axis in the diagram) and the $z'$-axis (the $Z$-axis in the diagram) are changing.


1

Yes, though the effect is greater on earth-bound or terrestrial tracking stations than on spaceborne or orbiting satellites. See Table 2.9 ("Perturbing accelerations acting on a GNSS satellite") and sec. 10.1.2 ("Site Displacement Modeling: Solid Earth Tides, Pole Tides, and Permanent Tides") in the BERNESE Software Manual


1

There is no reason why we could not be viewing the BB in our frame. We can only view anything from our position in space-time, and in our frame. We don't see the whole BB 3-sphere, just that 2-sphere section of it which is located at just the right distance that light can reach us in the time that has since elapsed. That's why what we see is spread over a ...


1

When you're in a moving vehicle and see trees or buildings, who is moving? Are you moving forward, or are the trees and buildings moving backward? Its counter-intuitive for beginners but both these views are absolutely correct. We can only describe the motion of an object from a reference frame. A reference frame is a specific configuration from where you ...



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