If the light velocity is a vector quantity, why vector addition cannot be applied to it? Or the light velocity is not a vector quantity?

deformere692qr
2022-05-10
Answered

If the light velocity is a vector quantity, why vector addition cannot be applied to it? Or the light velocity is not a vector quantity?

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nelppeazy9v3ie

Answered 2022-05-11
Author has **22** answers

The speed of light is a vector quantity and vector summation works perfectly well for it (at least in Special Relativity). You just cannot change the frame of reference.

For example if you have one object moving at c in one direction and another object moving at 1/2c in the opposite direction, then the middle between the two will move at c/2 in the same direction as the first. This is from point of view of a stationary observer.

The distance between the two objects grows as 3/2c. This is in the stationary reference frame of course, the objects themselves will see each other moving at speed of light.

For example if you have one object moving at c in one direction and another object moving at 1/2c in the opposite direction, then the middle between the two will move at c/2 in the same direction as the first. This is from point of view of a stationary observer.

The distance between the two objects grows as 3/2c. This is in the stationary reference frame of course, the objects themselves will see each other moving at speed of light.

asked 2022-05-10

Observer A and B are at the same "depth" in a gravity well. Observer B then descends into the well. A will observe B's time as going slower than their own. B will observe A's time as going faster than their own.

What happens if B were to ascend the well back to A's depth, would B's local time speed back up to the same rate as A's, but B would be younger (relative to A)?

What about the paradox caused by relative motion (ignoring gravity)? If A is moving relative to B, A and B will both observe the other's time as going slower. If A and B were together initially, then B moves away and returns, do their clocks agree?

What happens if B were to ascend the well back to A's depth, would B's local time speed back up to the same rate as A's, but B would be younger (relative to A)?

What about the paradox caused by relative motion (ignoring gravity)? If A is moving relative to B, A and B will both observe the other's time as going slower. If A and B were together initially, then B moves away and returns, do their clocks agree?

asked 2022-05-10

Take the following gedankenexperiment in which two astronauts meet each other again and again in a perfectly symmetrical setting - a hyperspherical (3-manifold) universe in which the 3 dimensions are curved into the 4. dimension so that they can travel without acceleration in straight opposite directions and yet meet each other time after time.

On the one hand this situation is perfectly symmetrical - even in terms of homotopy and winding number. On the other hand the Lorentz invariance should break down according to GRT, so that one frame is preferred - but which one?

So the question is: Who will be older? And why?

And even if there is one prefered inertial frame - the frame of the other astronaut should be identical with respect to all relevant parameters so that both get older at the same rate. Which again seems to be a violation of SRT in which the other twin seems to be getting older faster/slower...

How should one find out what the preferred frame is when everything is symmetrical - even in terms of GRT

On the one hand this situation is perfectly symmetrical - even in terms of homotopy and winding number. On the other hand the Lorentz invariance should break down according to GRT, so that one frame is preferred - but which one?

So the question is: Who will be older? And why?

And even if there is one prefered inertial frame - the frame of the other astronaut should be identical with respect to all relevant parameters so that both get older at the same rate. Which again seems to be a violation of SRT in which the other twin seems to be getting older faster/slower...

How should one find out what the preferred frame is when everything is symmetrical - even in terms of GRT

asked 2022-05-19

Looking for specific Relativity example

The example had to do with two people walking along a sidewalk in opposite directions, and an alien race on a planet millions of light-years away planning an invasion of the Solar System. The example showed that in one walker's reference frame the invasion fleet had departed, but in the other reference frame the fleet had not.

At the time, the explanation made perfect sense, but I have forgotten the details and have never run across this example again.

Does anybody know where this was, or have the text of the explanation?

The example had to do with two people walking along a sidewalk in opposite directions, and an alien race on a planet millions of light-years away planning an invasion of the Solar System. The example showed that in one walker's reference frame the invasion fleet had departed, but in the other reference frame the fleet had not.

At the time, the explanation made perfect sense, but I have forgotten the details and have never run across this example again.

Does anybody know where this was, or have the text of the explanation?

asked 2022-05-01

Under the Lorentz transformations, quantities are classed as four-vectors, Lorentz scalars etc depending upon how their measurement in one coordinate system transforms as a measurement in another coordinate system.

The proper length and proper time measured in one coordinate system will be a calculated, but not measured, invariant for all other coordinate systems.

So what kind of invariants are proper time and proper length?

The proper length and proper time measured in one coordinate system will be a calculated, but not measured, invariant for all other coordinate systems.

So what kind of invariants are proper time and proper length?

asked 2022-05-19

An electron is shot towards a target that is negatively charged. While the electron is traveling, the target makes an abrupt move towards the electron. While the information that the target moved is traveling from the target to the electron, the electron behaves like an electron that is moving towards a target that is in the original position.

How can energy be conserved when an electron that is moving towards a nearby charge behaves like it was moving towards a far away charge? Seems we end up with electron being at 2 meters distance from the target, while the electron had enough energy to travel to at most 4 meters distance from the target.

It also seems to me that "moving the target requires energy" is not a solution to this problem.

How can energy be conserved when an electron that is moving towards a nearby charge behaves like it was moving towards a far away charge? Seems we end up with electron being at 2 meters distance from the target, while the electron had enough energy to travel to at most 4 meters distance from the target.

It also seems to me that "moving the target requires energy" is not a solution to this problem.

asked 2022-05-09

If there were a light cone centered at some point P, and you were to look at that light cone from different reference frames, would it change its shape? I know that points inside and outside the light cone would remain inside/outside of the light cone in every frame, but does the light cone itself shift? If it does, how would it shift?

asked 2022-04-12

Why is travelling around the speed of light a problem? And why is it that the speed of light is the maximum?