Trisecting an angle

[xilman]

Originally Posted by garo

In a manner of speaking yes I think they are as no light from one ever reaches the other. I'm no expert so anyone can explain why I am wrong I'd appreciate it.

As far as observers in each galaxy are concerned, the other galaxy is travelling at less than the speed of light so they do indeed see light from the other galaxy.

Try a thought experiment: forget about the galaxies for a moment and think only of a couple of observers on a trajectory such that they only just miss each other, together with a third observer right next to the point of closest approach. The third observer first sees the other two approaching at 0.6c and then, after they pass, receding at 0.6c in opposite directions.

What do the other two see? They first see their opposite number approaching at less than the speed of light. For a brief instant, light from one travels to the other at right angles to the direction of flight. Then they recede from each other at less than the speed of light.


Paul

[alpertron]

Originally Posted by cheesehead

Well, they are moving away from each other at 1.2c, in our frame of reference.

But they're not moving away from each other at 1.2c in either of their own frames of reference.

You are right because the time in those galaxies runs slower compared with our frame of reference. Thus their relative speed is less than c.

Without going that far, the people who went to the Moon "gained" about 1/10000th of a second (considering that you need five days to reach the Moon, it is not too much).

[fatphil]

Originally Posted by garo

In a manner of speaking yes I think they are as no light from one ever reaches the other. I'm no expert so anyone can explain why I am wrong I'd appreciate it.

Two people receding from an inertial observer who measures their velocities to be +/-0.6c along a fixed axis would observe each other's velocities to be +/-0.88c along the same axis. Light from one would reach the other one, would be reflected, and then would reach the originator.

This is all derivable just using high-school maths (in fact, maths that a bright 10 year old could grasp) as long as you're prepared to accept a few assumptions. Basically, assume the speed of light is constant, and that distance is measured by bouncing light off the object, measuring how long the reflection takes to return, and scaling that by the known constant speed of light.

In this particular example, draw the space/time cone for the inertial observer, the two lines with gradients +/-0.6 (OK, I've got the axes oriented unconventially) corresponding to the two 'moving' objects. At an arbitrary point in time, send a light beam (line with gradient +/-1) from one object to the other, and when it arrives, bounce it back (line with gradient -/+1). Notice that the originator does indeed get his response. Conclusion - they are not receding from each other at a superluminal speed.

Get some graph paper, and draw it - it's very enlightening.

[garo]

I think I misunderstood what the OP was saying. I understand how relativistic mechanics will show that the galaxies recede at 0.88c in each others frames of reference.

I thought it had to with the stretching of space-time. There are galaxies that are receding from us at faster than the speed of light. No light from them will ever reach us. Right?

[xilman]

Originally Posted by garo

I think I misunderstood what the OP was saying. I understand how relativistic mechanics will show that the galaxies recede at 0.88c in each others frames of reference.

I thought it had to with the stretching of space-time. There are galaxies that are receding from us at faster than the speed of light. No light from them will ever reach us. Right?

Correct, on the assumption that such galaxies exist.


Paul

[Fusion_power]

Stipulating that FTL galaxies do exist, this would predict that we should be able to detect galaxies receding from us at a broad range of fractions of C. This could only occur as a result of distortion from space time expansion. Why do we not detect such a range especially approaching C? The local group of galaxies is essentially moving in tandem. More distant galaxies should progressively be moving away from us at faster and faster speeds up to and including the point at which they become invisible because they are receding from us at the speed of light.

This should provoke a few comments! We're pretty far off topic though.

Fusion

[wblipp]

Originally Posted by garo & xilman

g: There are galaxies that are receding from us at faster than the speed of light. No light from them will ever reach us. Right?
x: Correct, on the assumption that such galaxies exist.

Could you say some more about this? I thought that the hypothesized galaxies would be at some distance "d" from us right "now," and that light leaving such a galaxy would travel towards us at constant speed c, reaching us in due course. Where did I go wrong?

[xilman]

Originally Posted by wblipp

Could you say some more about this? I thought that the hypothesized galaxies would be at some distance "d" from us right "now," and that light leaving such a galaxy would travel towards us at constant speed c, reaching us in due course. Where did I go wrong?

The problem is that the spacetime between us stretches while the photon is in transit. If the expansion of spacetime is greater than c, the photon never reaches us. The distance between us is not a constant and so t=d/c is not the time a photon takes to reach us.

BTW, what do you mean by "now"? Simultaneity of spatially separated events is not well defined in relativity.


Paul

[xilman]

Originally Posted by xilman

BTW, what do you mean by "now"? Simultaneity of spatially separated events is not well defined in relativity.
Paul

Let me rephrase that. Simultaneity is well defined, but the observed temporal ordering of two acausally connected events depends on the observer.


Paul

[wblipp]

Originally Posted by xilman

The problem is that the spacetime between us stretches while the photon is in transit.
...
BTW, what do you mean by "now"?

I guess the part I missed must be the logic that says the only way for a galaxy to be receeding from us that fast is to be this far away. I thought we were dropping some of the reality constraints, and I didn't see any reason why we wouldn't see light from a nearby galaxy merely because it was receeding at faster than light speed.

I knew "now" was problematical - that's why I quoted it.

[cheesehead]

Originally Posted by Fusion_power

we should be able to detect galaxies receding from us at a broad range of fractions of C. This could only occur as a result of distortion from space time expansion. Why do we not detect such a range especially approaching C?

But we do observe galaxies receding from us at almost all fractions of c. Recently I've seen announcements of galaxies with measured redshifts greater than 6. A redshift (AKA z-parameter) of 6 corresponds (assuming the redshift is all due to the Doppler effect) to a recession velocity of 0.96c.

See http://hyperphysics.phy-astr.gsu.edu...o/redshf2.html for the calculation formulas.

See http://www.journals.uchicago.edu/ApJ...883408314Guest for a May 2002 article about a z=6.28 quasar.