Effects of Velocity Aberration?

[Bahmanyar]

Flying two aircraft (parallel and synchronous).
From the first emitted light beam. As this beam reaches the second plane?
Perpendicular (FIG. 1), or with a bend (FIG. 2)?

 

[PAllen]

It will arrive perpendicular from the point of view of the plane and not perpendicular from the point of view of the ground.However, the ground observer can also compute that the plane would measure the angle as perpendicular.

 

[Nugatory]

Flying two aircraft (parallel and synchronous).
From the first emitted light beam. As this beam reaches the second plane?
Perpendicular (FIG. 1), or with a bend (FIG. 2)?

Figure 2 isn't quite right. The path observed from the ground is not perpendicular, but it's also not a curve - it's a slanting but straight line.

 

[Bahmanyar]

Please do not answer on the basis of the theory of relativity. but in practice how things are?
Please note the "velocity aberration", "Sagnac effect", "GPS" and so on

 

[Nugatory]

Please do not answer on the basis of the theory of relativity. but in practice how things are?

We already have answered on the basis of the way things are. The path of the light is straight according to both observers; and it is perpendicular to the flight path as viewed from the aircraft and not quite perpendicular to the flight path as viewed from the ground (although for aircraft traveling at speeds not more than a few thousands of kilometers per hour relative to the ground the deviation from exactly perpendicular will be very small).

Of course this answer is also consistent with the theory of relativity. If relativity said something different, then we'd need to discard relativity in favor of some other theory - but fortunately it doesn't.

 

[PAllen]

Please do not answer on the basis of the theory of relativity. but in practice how things are?
Please note the "velocity aberration", "Sagnac effect", "GPS" and so on

You ask a question about a phenomenon correctly described by relativity, in the relativity forum, and request that the answer not involve relativity?!

Velocity aberration and Sagnac effect are consequences of relativity (e.g. classical aberration follows from Galilean relativity, while relativistic aberration follows from special relativity). GPS works due to adjustments as predicted by special and general relativity. Your example is a case of aberration of light, but equally of the Lorentz transform from which aberration of light may be derived. Thus your further request is both silly and self contradictory.

 

[Stephanus]

Flying two aircraft (parallel and synchronous).
From the first emitted light beam. As this beam reaches the second plane?
Perpendicular (FIG. 1), or with a bend (FIG. 2)?

I am, myself, still struggling with SR. But I'll try to answer what I know is true.
Yes, as Nugatory says, Fig 2 is wrong.
I think this is what the ground observer would see:

And it depends on how fast the planes move. The faster, the more slanting the light will be. I don't think this is the Relativty theory, but...
And since the speed of light is always the same, then you can calculate how long it will travel from the below plane to the upper plane.
It is the hypotenuse of $t^2 = A^2 + B^2$
Supposed the distance the plane travels is B in time unit for light to travel from below to above, slanted.
And the distance of the plane is A, in the time it takes for light to travel PERPENDICULAR from below to above.

Suppsed the planes travel at 0.6c(V). And it takes light to travel from below to above at 5 seconds(t).
So, V=0.6c
t=5

Then, $B = Vt = 3$
The hypotenuse will tell you that A distance is $A = \sqrt{t^2-B^2} = 4$
It takes 4 seconds for light to travel perpendiculare from below to above. I think this is still not relativity, but...
The time it takes according to the planes clock to travel B distance is 4 seconds. I think this is the relativity thing.
As in Lorentz contraction.
I'm terribly sorry if my calculation is wrong and it misleads Bahmanyar, but I'm sure the good advisors/mentors will immediately step into correct it if it is wrong..

 

[Stephanus]

And if the planes travels, say 0.9999999 (seven 9's) the speed of light, then the light beam will look almost horizontal, and it takes about 8944 seconds for light to reach the plane above. But it will always take 4 second according to the planes clock for light to travel from below to above.

Note, the picture of the planes can't be drawn here. They are far away. And I'm sorry, I'm not familiar with Sagnag effect and velocity abberation

 

[pervect]

Please do not answer on the basis of the theory of relativity. but in practice how things are?

An odd question, since relativity, as far as we know, does answer the question the "way things are". It's been well tested.

 

[Bahmanyar]

"Sagnag effect" here:
https://en.wikipedia.org/wiki/Error_analysis_for_the_Global_Positioning_System#Relativity"velocity abberation" here:
http://relativity.livingreviews.org/Articles/lrr-2003-1/
p: 17, formulas (40)

 

[Bahmanyar]

It's been well tested.

Where exactly? I need just examples, not a theory. We are all tired of the theory

 

[Stephanus]

Where exactly? I need just examples, not a theory. We are all tired of the theory

GPS for example. The clocks in GPS must be adjusted because of GR. And in some solar eclipse phenomenon in late 1910s if I'm not mistaken during WWI. Of course at that time world war ONE was not named World War ONE, people just didn't realize that there would be the second.
And the discovery or to be more precise the disposing of planet Vulcan that hypothetically disturbed the orbit of Mercury.

 

[Nugatory]

N

"Sagnag effect" here:
https://en.wikipedia.org/wiki/Error_analysis_for_the_Global_Positioning_System#Relativity"velocity abberation" here:
http://relativity.livingreviews.org/Articles/lrr-2003-1/
p: 17, formulas (40)

Neither the Sagnac effect nor velocity aberration have much to do with the exchange of light signals that you started this thread with, so I'm not sure why you're asking about them.

However, if you're looking for experimental proof that the light signals behave as PAllen and I have explained... It's tested by military phased-array radars and laser targeting systems hundreds of times every day.

 

[Bahmanyar]

It's tested by military phased-array radars and laser targeting systems hundreds of times every day.

Their source is not moving.
I am interested in an option when the light source moves, and is moving parallel to the Earth

 

[Nugatory]

Their source is not moving.
I am interested in an option when the light source moves, and is moving parallel to the Earth

Ahhh... Both of the devices I mentioned are routinely mounted on both moving ships and fast-moving aircraft, and used to track other moving targets.

 

[DrGreg]

I previously posted this diagram to illustrate something bouncing between the roof and floor of a train, but the same principle applies to this thread, if we imagine the floor and ceiling to be the two aircraft.

Here's something (it could be a pulse of light, it could be a ball) bouncing up and down in a train.

An observer in the train (top) infers the thing is moving vertically up and down.

An observer on the ground (bottom) infers the thing is "sliding sideways" in a zig-zag path.

This is valid in both relativistic and Newtonian mechanics.

 

[Orodruin]

The original question has been answered. That you do not like the answer does not change the answer, it is simply how the world behaves.

Thread closed.