This is a point I never was clear about. The
lack of "smearing" of double stars moving at
speed in their orbits showed how Einstein's
theory was only too true.

Just how prominent would such "light trails"
have been. Would a small telescope have shown
the effect? Or would a large scope be needed?
I read somewhere that Lorentz checked this.

Read this:

http://spiff.rit.edu/classes/phys314...tein_long.html

and then ask your question again.

(A small telescope and a good clock are all you need).

Thanks. I was wondering if it was an optical
procedure of examining the "Airy disc" of a
star moving transversely across the field of
view compared with others moving towards or
away from us.

I do not infer any "smearing" or "light trails" from this presentation. All I see is a displacement of the apparent position of the transversely moving object at position B, as a result of its greater distance and thus the greater time required for its light to reach us.

I think the author has it backward. With constant light speed, independent of the object's motion, the light takes longer to get here from B than from A or C. Thus we should have the illusion that it is late in reaching B, and making up time in getting to C.

Yes, I think you're right -- I did have a mistake in that panel.
I have modified it -- please look again.

The idea is this: if the speed of light changes due to the
motion of its source, then when a star is moving away from
us in its orbit, the light leaving the star in our direction
would be moving slowly; therefore, it would take a slightly
longer time to reach the Earth. And if the star were moving
towards us in its orbit, the light leaving its surface in our
direction would be moving faster than usual; therefore,
those light rays would take less time than usual to
reach us here on Earth.

This difference in light's speed (which does not actually
happen, remember!) would introduce a large variation in the time
at which we would observe the components of the binary
star to be side-by-side (from position "A" in the diagram to
position "C", and then from position "C" to position "A").
If the speed of light is constant, and the orbit is circular,
then the interval from A-C will be the same as from C-A.

Yes, there is a small difference in some of the observed
times due to the time it takes light to cross the orbit,
as Hornblower writes, but that

a) is much smaller than the size of the variations
introduced by the changing speed of light,
for some reasonable orbital parameters

b) does not cause the interval from A-C to differ
from that of C-A

This astrophysical test of the constancy of the speed of
light becomes interesting if one can find a binary star
in which the orbital motion is very fast. One paper discussing
such a system is

"Is the speed of light independent of the velocity of the source"

http://adsabs.harvard.edu/abs/1977PhRvL..39.1051B

The time difference only makes sense to me if we are observing the change in time from D to B and B to D. [You may want to add point D to the illustration.]

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Thanks for the note -- I've added a "D" now.

My intuition said the same thing as yours. Then I took some time and set up a simple example, with a binary of radius R units located a distance D away from the Earth, with orbital speed v, etc. I worked out the time at which light would be emitted at points A, B, C, D, and also the time at which each beam of light would reach the Earth.

There's a small difference between B-D and D-B if the speed of light is constant, due to the extra distance light must travel from the far side of the orbit. However, the intervals A-C and C-A are identical if the speed of light is constant.

On the other hand, if one postulates that the speed of light varies in a Galilean manner due to the motion of its source, then the intervals from A-C become shorter than those from C-A. The size of this difference can be much larger than the size of the D-B, B-D difference.

It's hard for me to explain this in a simple manner -- I have to perform the calculations and compare the times when light from A,B,C,D arrives at the Earth to see it.


(You can now find links to two technical papers, one by DeSitter from 1913 and one by Brecher from 1977, at the end of my web page on this subject).

I thought I remembered a report of Einstein
being interviewed and him describing
Lorentz looking for "ghosting" in double
stars. It seemed like a direct optical effect
was being looked for.

Hmmmm. I assume the observer is closest to D, so I see no extra distance in the B-D & D-B path, but I do see a difference in the C-A & A-C path since B is furthest from the observer.

I'm rusty, but I think my Galilean math may still be tolerable.

Points B & D are the transverse velocities and would exhibit no light velocity difference. Comparing velocities at points C and A, however, will exhibit the greatest difference. Thus, the D-B and B-D should have the greatest time variation. [This is also true with redshift/blueshift for constant c.]

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You are correct as far as instantaneous velocity goes. At points B and D, the velocity of the star is transverse to the line of sight, and so there would be no change in the speed of light emitted by the star under Galilean principles.

However, if you compute the time difference between the arrival time of light emitted when the star is at point A, and when the star is point C, and when the star is at point A again, you'll see that this pair of points is the pair which shows the largest difference in light arrival times.

Agreed. Comparing our Galilean model to a constant speed of light model, we would see the star arrive at point C earlier than at any other point compared to our other model, and later at A than at any other point. [t = d/V; V = Vc - Vo cos(phase angle). Vc is speed of light, Vo is orbital vel., phase angle 0 deg at A].

I don't see, however, any time difference between the intervals of C to A and A to C. Ignoring the orbital distance, what time dilation is observed from A to B is regained in B to C. This matches the time intervals of D to A and C to D, respectively.

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Have you tried computing the arrival times of light waves emitted at the various points in the orbit yet?

I have now.

I think the confusion might be in the need to include the orbital radius for actual time dilation (via the Galilean model). [Maybe not, however.]

t = [d + r * sin()]/[Vc - Vo * cos()], r being the orbital radius

Vo = 200 kps
Vc = 300,000 kps
d = 5.00E+11 km
ro = 1.00E+08 km

Attached Images

Binary time delay.jpg (141.7 KB, 4 views)

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Original professor’s drawing:
http://spiff.rit.edu/classes/phys314...stein/sr8.jpeg


Here’s a good animation of the situation, showing the stars’ motions, at the same time that we also see the Doppler shift as observed through a spectroscope on earth:

Animated illustration:
http://www.phy.duke.edu/~kolena/binary/binary.html

I have a question about this.

The illustration I’ve linked from the professor’s website shows the light speed being “c” relative to the moving binary. However, it shows the light waves moving (downward) toward a distant observer at two different speeds, relative to that observer. One fast speed starting at position C and one slower speed starting at position A. In other words, the “c” speed is relative to the star that emits the light, but I don’t see where it’s shown as also being “c” relative to the observer.

I’ve had some difficulty finding a diagram or an animation that shows where in space the red and blue shifts take place. And I can’t find a drawing or animation that shows how the light speed of the waves is “c” relative to the stars and also “c” relative to an observer at the earth at the same time, in the same drawing or animation.

Does anyone have any ideas about this?

All evidence indicates that light in a vacuum travels at the same speed, "c", no matter who is looking, and no matter what source emitted it.

This whole discussion, and the figure to which you refer, is based on the hypothetical premise: "What if the speed of light WAS affected by the motion of the source?" That is, IF the speed of light waves was faster if they were emitted from an object moving towards you, and slower if they were emitted by an object moving away from you, THEN what consequences would arise?

It turns out that the consequences would be certain measureable differences in the times at which we would see a binary star to be at certain points in its orbit, BUT we don't see those particular differences. This is a weak piece of evidence that the speed of light does not depend on the properties of its source.

There are much stronger pieces of evidence in laboratory experiments.

Nice one!

The speeds shown are the speeds of the bodies, not light. This is also the case for the other link. [The positive radial velocity values represent motion away from us, the observer.]

What is wrong with the animation you just gave?

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The animation doesn’t take into account the travel time for the light. And it doesn’t show where the red and blue shifts actually take place when we have moving emitters and a stationary observer. The animation is set up for a stationary observer. The top view shows what the binaries are doing at one epoch in time, where they are located, and the bottom view shows how light from that motion will be seen through a spectroscope on a (stationary) earth many years later, when the light finally arrives.

What I’m trying to find is an illustration that shows both a moving light emitter and a stationary light observer, and also showing the waves leaving the moving emitter at “c”, relative to the emitter, while they are received at the non-moving observer at “c”, relative to the observer, and where in space the red and blue shifts take place, all in the same illustration.