Riddle me this...

[Butch]

If I look to the north and I spy a quasar receding at near c, and I look to the south and I see a quasar receding at near c... What is their velocity relative to each other?

[Strange]

Good question. It depends which frame of reference you use. In your frame of reference, they are separating at nearly 2c.

 

But from the point of view of each quasar, the other one is moving away at just under c. This is because velocities do not actually add linearly (they seem to in our slow world, but the difference becomes noticeable at higher speeds).

 

http://hyperphysics.phy-astr.gsu.edu/hbase/Relativ/einvel.html

Just realised, that answer is completely wrong!

 

It would be correct if you were asking about, for example, two spaceships heading away from you in opposite directions.

 

But the quasars in your example are receding because of expansion. This implies a couple of things. Firstly, they will be near the edge of our observable universe, and will therefore be outside each other's observable universes. But, if they could, somehow, observe the speed of separation, it would be nearly 2c.

Edited November 17, 2016 by Strange

[swansont]

If they were close enough such that we could ignore expansion effects, their speed relative to each other would be (u + v)/(1+uv/c^2)

 

If u = v = 0.900c, the result is .995c

[Sriman Dutta]

If they were close enough such that we could ignore expansion effects, their speed relative to each other would be (u + v)/(1+uv/c^2)

 

If u = v = 0.900c, the result is .995c

That proves that addition of velocities in SR is not linear, as in Galilean Relativity.

[AbstractDreamer]

Depends on where you're standing when you decide to look.

If you are on Earth at the North Pole, you can't look North.

 

 

Also depends on your angle of gaze . Relative to you, North and South might not lie on a straight line through you. So the direction of velocities of the quasars might not be parallel to each other.

Edited November 18, 2016 by AbstractDreamer

[swansont]

That proves that addition of velocities in SR is not linear, as in Galilean Relativity.

It doesn't prove it, per se, since this is a prediction of SR, and it's a thought problem. Evidence comes from experiment.

Depends on where you're standing when you decide to look.

If you are on Earth at the North Pole, you can't look North.

 

 

Also depends on your angle of gaze . Relative to you, North and South might not lie on a straight line through you. So the direction of velocities of the quasars might not be parallel to each other.

 

The OP posed a question, and gave conditions for it. One answers the question that was asked, not what the answer would be if a different question was asked.

[AbstractDreamer]

Around my head is sphere of space, but the surface of Earth is locally flat.

 

Magnetic "North" lies on plane in this sphere around my head perpendicular to my latitudinal line.

Magnetic "North" lies on a longitudinal line on the surface of the Earth.

 

A direction on a plane should have two values, you cant just assume zero for a value if one is not provided. OP did not specify he was looking horizontally North, or any angle along the vertical axis.

 

As North does not exist if you look straight up or straight down, therefore the velocities of the quasars are only relatively parallel IF the vertical angle is 0 (zero)

 

Your calculations are based on the assumption he is looking horizontally North and horizontally South, which were not stated in your solution.

 

Without specific values or assumptions, calculations and answers are meaningless though not necessarily wrong.

Edited November 18, 2016 by AbstractDreamer

[swansont]

No, it was not stated, but it was implied. You're reading way too much into this.

[AbstractDreamer]

There's also the refractive index of the atmosphere that will alter the direction of the velocities as experienced by the observer from their "true" direction. So if the observer is looking horizontally north and horizontal south, relative to him/her self, then for sure the velocities of the quasars relative to each other are not parallel.

 

Overall its a poorly phrased riddle.

[Strange]

It is not a riddle. Refractive index of air is pretty close to 1, so any effects of refraction can be ignore. I think it is pretty clear that the question was simply about two things moving in opposite directions.

[imatfaal]

!

Moderator Note

 

Can we lose the nitpicking please? This is not the design of an experiment nor a piece of legal draftsmanship - the import is obvious and has been answered.

 

Take a spherical cow... https://en.wikipedia.org/wiki/Spherical_cow

 

And obligatory XKCD

 

 

Do not respond within the thread to this moderation