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Velocity is relative. There is no special reference frame that would be "at rest". But acceleration is not and was never claimed to be. Reference frames in free fall are special and reference frames that are accelerating relative to the ones in free fall contain inertial forces (circular motion involves acceleration towards the centre; the corresponding ...

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The laws of physics have the same form for all, but there are different measurements which are equally "real"? Correct. Having said that, it is often sensible to differentiate between 'apparent' and 'proper' (or 'intrinsic') values, the latter normally measured in the rest frame of the object in question and giving an upper or lower bound for an ...

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Special relativity deals with "inertial" or "non-accelerating" frames. Physics in inertial frames are equivalent independent of their velocity and the velocity of inertial frames are relative. You are free to assume any inertial frame is stationary and all other frames are moving relative to it. Rotating frames are not inertial, they are accelerating ...

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General covariance applies only to freely falling observers -- once you invoke non-gravitational forces, like the inward pressure of the wall, the observer is no longer freely falling.

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Special relativity only addresses motion in inertial frames, so it doesn't really apply to angular motion. In general relativity, angular motion actually does have some "relativity" to it as well. When you're in close proximity to a spinning object, you'll actually be dragged along with it. This is known as the Lense-Thirring effect, or just ...

3

if the occupants of the space station were not aware of it's design and could not look out a window then there is no way to tell if it is rotating or they are near a earth size planet that causes the gravity. orbiting around another space station will causes a sensation of gravity, seems you are contradicting yourself, if there is any rotational motion ...

3

Are Lorentz transformations more adequate representations of motion, than the more intuitive velocities? Yes. The non-associativity that bothers you simply arises because there is no group of three dimensional boosts. Confined to one dimension, boosts form a rather lovely one parameter subgroup of the Lorentz group $SO^+(1,3)$. So everything "works", ...

3

The term virtual is used in other places in physics. For example in virtual images in a a mirror : we see an object in great verisimilitude, even ourselves. Why is the image called virtual and not real? Because it has the optical properties of the imaged object but not a large number of other attributes, mass being the simplest. In addition, its existence ...

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Yes, you are right. The four momentum of a virtual photon needn't to lie on the mass shell. Thus the zeroth component of the four momentum of a virtual photon is independent of its spatial components. The reason for this is that the zeroth component of the four momentum of a virtual photon arises from the Fourier transform of the step function. See S. ...

2

In special relativity, it is crucial to distinguish between frame independent (proper) quantities and frame dependent (coordinate) quantities. The proper length of a rod is frame independent, while the coordinate length of a rod is frame dependent. In a frame in which the rod is at rest, the proper length and coordinate length are equal. In a relatively ...

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What you want is that your function does not transform under Lorentz transformations that take $$p^\mu \to {\Lambda^\mu}_\nu p^\nu.$$ To build invariants from one vector there is only the possibility to construct the invariant product with itself $$p^2 \equiv p^\mu p_\mu \to p^\mu p_\mu.$$ There is one more thing though. The Lorentz group has two branches: ...

2

A photon cannot be said to have its own inertial reference frame, because inertial reference are defined to be a family of coordinate systems that satisfy the two fundamental postulates of SR, one of which is that light moves at c in all frames. You could construct a coordinate system where the photon was at rest, but since this coordinate system wouldn't be ...

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Easy way to distinguish between gravity and rotating space station: Throw a ball straight up in the air. If it comes straight down, gravity. If it moves away from you (behind your tangential velocity), it's a rotating space station.

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I don't believe we need to invoke GR for this. So, to state your problem with variables, two objects $A$ and $B$ with identical rest masses $m_{0}$ start at the origin at $t=0$ and then head in opposite directions along the $X$ axis with equal speeds $v$, $A$ moving in the positive direction and $B$ in the negative direction. To an observer $O$ stationary at ...

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This frame is exist. You got wrong result because you ignored that this two photon move in the opposite direction. Set that the first photon move along the z axis and the second photon move against z-axis.$\omega_1$ and $\omega_2$ are the frequency of the first and the second photon correspondingly in the reference frame. In new frame shout be $k'_1=-k'_2$ ...

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How did the experiment of Michelson and Morley disprove the existence of the conjectured ether? What if the ether moves along with the direction of the rotation of the earth? They tried the experiment at different times of year (when the Earth would have been moving in different directions in an inertial frame centered on the Sun) to try to rule this out. ...

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How to understand non-associative composition of velocities in STR? Special relativity introduces a weirdness about how your axes can be related to other observers' axes: if your axes are aligned with observer A's axes and theirs are aligned with observer B then special relativity (i.e. the Lorentz transformations) say that B's axes will be rotated with ...

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An observer cannot change the whole universe just by accelerating his spaceship. This is why "apparent" means "real for the observer". Spacetime is relative, and the relative spacetime diagram of an observer is changing. In short: The only absolute, undilated time value is the proper time of an object. Proper time is dilated by time dilation for observers ...

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