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This is a Blog on relativity and cosmology for engineers and the like. My website "Relativity-4-Engineers" has more in-depth stuff.

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38 comments

One-way Speed of Light

Posted December 18, 2012 10:00 AM by Jorrie

It is well-known fact that the one-way speed of light is not a measurable parameter, because it is actually defined to be the same as the two-way speed of light in all inertial frames. Put differently, we define the synchronization of two clocks (that are not co-located, but stationary relative to each other) in such a way that the one-way speed of light comes out the same as its two-way speed. Hence to measure the one-way speed of light using such clocks does not make much sense. The outcome is a given before the test.

However, people have not stopped trying to see if it could be done without synchronized clocks. All 'official' efforts have so far been refuted, proving that they are in fact two-way measurements. Physicist Don Lincoln of Fermi-lab has told me about a method they use that is (almost?) an irrefutable one-way test.

Here is a quote from his post on another Blog. The sketch is my own doing, upper is cable calibration and lower is laser pulse speed test:

[quote=Don Lincoln]

Take two photon detectors. These can be arbitrarily thin - less than a millimeter if necessary. Take the two detectors and place them side by side. From each detector take a cable of a convenient length. Put both of those cables into fast electronics (a modern digital oscilloscope will work just fine).

Fire a light pulse through both detectors. Since these two detectors are adjacent to one another, the transit time from one to the other is of order (1 mm)/(speed of light) = (1 x 10-3 m)/(3 x 108 m/s) = 3 x 10-12 seconds. If sub- 3 picosecond speed is needed, there are ways.

Using your oscilloscope, you can calibrate your cables to establish what "simultaneous" means. In the abstract, the cables can be of identical length. This means that the signals from the two detectors will arrive simultaneously at your oscilloscope.

Now move one detector far away...maybe 1000 feet. Do not disconnect the cables, so you have identical conditions. Fire the light pulse (use a laser) through one detector to hit the other. The signals from the two detectors will transit the cables and hit your oscilloscope at a single spatial point. Since you have already established that the transit time in the cables of both detectors are identical, the only difference between the signal arrival time at your detector is the transit time of light from one to the other. If you have measured the distance exactly, you can then determine the speed of light by distance over time.

If you do not want to measure the distance between the two detectors, you can verify the isotropy of space (and consequently, the identical nature of the 1-way speed of light). First do as I said, and fire a laser that first hits detector 1 and then hits detector 2. Record the transit time seen in your oscilloscope. Now have a laser pointing in the opposite direction, hitting detector 2 and then detector 1. Again, record the transit time.

Since the distances are the same, and the only difference is the direction in which the light is travelling, you can establish that light going one way takes the same speed as the other way. I believe that within the uncertainties of your equipment, this detector configuration will establish that the speed of light is the same in either direction.
"

[/quote]

What do you think? Did Don measure the one-way speed of light, or has he got a 'hidden two-way' assumption in there somewhere?

-J

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#1

Re: One-way Speed of Light

12/18/2012 3:44 PM

I'd wonder about the fact that, in the first case, the signal traverses both cables in an out-and-back path, whereas in the second case the signal only traverses the stretched cable in one direction, reverse to the laser beam's path and thus perhaps undoing the purpose of a one-way test.

My own thought was, with the advent of ultra high speed cameras, why not set up a camera perpendicular to the path of the beam and 'time' the beam as it traverses a known distance. In my sketch below a light source L emits a series of bright pulses. These pulses first strike reflector R1 and then reflector R2. R1 and R2 are separated by known distance S. The camera is set up at some large distance D from the meaured path and is at right angles to the path, halfway between R1 and R2. The ultra high speed camera is connected to some timer electronics to record the times t1 and t2. The one-way velocity is then just v = S / (t2-t1).

Or have I fallen into a special relativity trap? It's been decades since I studied this stuff.

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#2
In reply to #1

Re: One-way Speed of Light

12/18/2012 11:45 PM

"Or have I fallen into a special relativity trap? "

Not a relativistic trap, but a Galilean one. Since the whole frame stays inertial, relativistic effects do not show up. However, there is still a 2-way element in your test. If light happened to move at c' to the right and c'' to the left, you will get some function of the average speed between the two directions, without knowing c' or c''.

Or can you see a trick to counter this?

-J

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#35
In reply to #1

Re: One-way Speed of Light

01/29/2013 10:26 AM

You were thinking perhaps of something like this? (filmed at an effective rate of one trillion frames per second).

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#37
In reply to #35

Re: One-way Speed of Light

01/29/2013 3:24 PM

Yea, I guess this camera experiment is similar to USBs proposal. Amazing technique.

The secret to Don Lincoln's method is that he first establishes a simultaneity definition for the two ends of the cable and then uses this definition to determine the one-way speed of light. This is precisely equivalent to synchronizing two clocks by means of light signals and then using the clocks to determine the one-way speed of light.

The arguments for and against the "measurement" of the one way speed of light are usually colored by semantics, but Don's method has such a nice ring to it. It fooled me for a while...

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#3

Re: One-way Speed of Light

12/19/2012 6:38 AM

The signal in the cable is also electromagnetic. It is a round trip measurement.

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#4
In reply to #3

Re: One-way Speed of Light

12/19/2012 7:55 AM

It is a little easier to analyze with cables, because everything does not cancel out, like when only light is used. Assume a cable length of 1 unit, in whatever units are convenient. Let the cables have a 'refraction index' of n = c/v, where c is the two-way speed of light in vacuum and v is the propagation speed in the cable. Now assume that the light speed in vacuum is c' to the right and c'' to the left, so that

[1] 1/c = 1/2c' + 1/2c'', as has been determined experimentally [for ease of writing, I use 1/2c' to mean 1/(2c')].

The equivalent equation for the cables are then

[2] n/c = n/2c' + n/2c''

The time differential ΔT measured on the oscilloscope is

[3] ΔT = 1/c' + n/c'' - n/2c' - n/2c'' = 1/c' - n/2c' + n/2c''

Although ΔT is clearly a function of c' and c'', there are two interesting observations to be made:

(a) If we choose a cable with n=2, then

[4] ΔT'' = 1/c' - 2/2c' + 2/2c'' = 1/c''

This is clearly a one-way speed.

(b) If we reverse the experiment, so that the laser signal goes from right to left, then eq. [4] becomes

[5] ΔT' = 1/c'' - 2/2c'' + 2/2c' = 1/c'

If we have found that ΔT' = ΔT'', does this not leave us with the inescapable conclusion that c' = c'' within experimental error?

-J

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#5
In reply to #4

Re: One-way Speed of Light

12/19/2012 8:25 AM

Thank you you the equations. Can you really assume delta. T prime equals delta T double prime? Additionally can you assume the velocity of the sigal is identical both directions?

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#6
In reply to #5

Re: One-way Speed of Light

12/19/2012 8:34 AM

"Can you really assume delta. T prime equals delta T double prime?"

What if I observed/measured them to be the same? (Note that primed here did not mean differentiation w.r.t. time. Could have used T1 and T2).

"Additionally can you assume the velocity of the signal is identical both directions?"

But I did not; I assumed they are c' and c''.

-J

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#8
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Re: One-way Speed of Light

12/19/2012 9:17 AM

I probably should have asked about assuming N is the same each direction

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#7
In reply to #4

Re: One-way Speed of Light

12/19/2012 8:47 AM

Yes, I see the problem with my sketch.

Referring to your discussion above, does this require that v in the cable be the same, regardless of propogation to the left or to the right? If the speed of propogation is v' when the speed of light is c', and v" when the speed of light is c", do you get the same results?

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#9
In reply to #7

Re: One-way Speed of Light

12/19/2012 10:13 AM

"Yes, I see the problem with my sketch."

In fact, your setup is equivalent to having the oscilloscope with cables at the halfway point. I suppose you can choose S and D so that the effective x-axis propagation speeds of the two camera signals correlate with my n/c' and n/c''.

"Referring to your discussion above, does this require that v in the cable be the same, regardless of propagation to the left or to the right?"

Yes, I think relative to the cable it will be v' = n/c', whatever that that c' happens to be, with n obviously the same for identical cables.

It is obviously only when you want to transform those speeds to another inertial frame that the cable translational speed comes in. But we are always working in only one inertial frame with static cables, so no such effects to worry about.

-J

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#10
In reply to #4

Re: One-way Speed of Light

12/19/2012 11:25 AM

The math appears correct to me, but how do you know n=n'=n"? In other words, how does one know in advance that the cable media is spatially isotropic?

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#13
In reply to #10

Re: One-way Speed of Light

12/19/2012 12:59 PM

"The math appears correct to me, but how do you know n=n'=n"?"

AFAIK, the refractive index of a given material is a constant if conditions are constant. Even if the two cables differ slightly, the 'tuning' of the lengths takes care of that. In the calculations, it is only the speed of light that is not spatially isotropic; hence the actual propagation speed in the cables (v=c/n) are not isotropic.

-J

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#17
In reply to #13

Re: One-way Speed of Light

12/19/2012 3:22 PM

Back to the original statement of the problem for a sec. The idea is to avoid using synchronized clocks.

So maybe this idea is forbidden at the start, but suppose each detector has a timer that records the instant of detection. Both detectors report the time the pulse was detected. Thus, in the second step, the detector sends a signal back down the straight cable not of the detection of the pulse but of the time it saw the pulse. Then it wouldn't matter what the speed of propogation of the signal is, in the cable. The only assumption you are making then is that the cable is the same length in both steps, looped-back or pulled straight.

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#19
In reply to #17

Re: One-way Speed of Light

12/19/2012 4:12 PM

"So maybe this idea is forbidden at the start, but suppose each detector has a timer that records the instant of detection."

The question then arises: are the two calibrated cables equivalent to two spatially separated, synchronized clocks?

-J

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#23
In reply to #13

Re: One-way Speed of Light

12/20/2012 9:55 AM

Maybe I am being naive, but it would appear to me that even minute changes in temperature from one spot to another (or from one cable to the other) would result in n <> n' <> n" (in other words the material is not isotropic with respect to state). This seems more likely than the speed of light being different for two directions in space.

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#27
In reply to #23

Re: One-way Speed of Light

12/20/2012 11:06 AM

"it would appear to me that even minute changes in temperature from one spot to another (or from one cable to the other) would result in n <> n' <> n" (in other words the material is not isotropic with respect to state). This seems more likely than the speed of light being different for two directions in space."

This would normally be covered under "within experimental errors", with experimental errors determined independently of the test - not too difficult and it is commonly done in the accelerator labs.

Remember that the whole purpose of the calculations that I have used is to show that the speed of light is not different for two directions in space. I have used c' and c'' to show what observed times would look like if they were different. The purpose of the thread is to talk about the possibilities for determining the one-way speed of light (within experimental errors), without using synchronized clocks.

Anyway, comments like yours are welcome - the assumptions must be questioned.

On your later comment: AFAIK ('as far as I know') is quite common internet slang on forums: http://www.internetslang.com/AFAIK-meaning-definition.asp. It's a nice cop-out for not knowing...

--

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#28
In reply to #27

Re: One-way Speed of Light

12/20/2012 11:23 AM

Cheers! Best wishes for the Christmas Holiday, or any other you may be currently celebrating. Please read my subsequent blog entry, with an alternative proposed experiment. I wish I could answer this with a thought experiment, but I only have one tiny bright spot in my brain, according to the doctors.

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#24
In reply to #13

Re: One-way Speed of Light

12/20/2012 10:04 AM

How do you know this assumption is true. I think I should dog you on this one. Also, what is AFAIK? Never heard of that acronym before. HTFSIK what AFAIK is?

Again, how does one go about "tuning" these magical cables? Does it matter to the experiment if using polarized light? Circular or elliptically polarized?

Besides, "if" is always a mightly big word in experimental chemical physics, physics, or physical chemistry.

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#22
In reply to #4

Re: One-way Speed of Light

12/20/2012 12:36 AM

I wrote in #4: "The time differential ΔT measured on the oscilloscope is

[3] ΔT = 1/c' + n/c'' - n/2c' - n/2c'' = 1/c' - n/2c' + n/2c' "

If I again swap the actual setup so that the scope and laser x-mitter are on the right, but I generalize the result for n, which means c' and c'' are swapped in the equation. If I then get the same measured time difference value both ways, i.e. ΔTright = ΔTleft, I can equate and simplify to get:

[6] (n-1)/c' = (n-1)/c''

which from #4 eq. [1] means c' = c'' = c, not so?

This may not be a determination of the one-way speed of light, but I think it shows that the one-way speed of light is the same as the two-way speed in this setup.

-J

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#11

Re: One-way Speed of Light

12/19/2012 11:29 AM

Is this another attempt at the Michelson-Morley experiment? If a difference is found, are we going to re-introduce lumeniferous aether into our physics?

I'm an old man and I remember light. When I was a kid, our light had to travel barefoot and uphill both ways.

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#12
In reply to #11

Re: One-way Speed of Light

12/19/2012 12:15 PM

Through the snow!

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#15
In reply to #12

Re: One-way Speed of Light

12/19/2012 2:08 PM

I see your location is Lubbock. Them's my old stomping grounds. I worked for TI until they closed that plant and laid off everybody. Next time the dust blows, get some grit in your teeth for me.

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#25
In reply to #15

Re: One-way Speed of Light

12/20/2012 10:09 AM

As a matter of fact, it re-opened as X-fab. By the way, yesterday there was an 80 mph blow, and the speed of wind was definitely anything but isotropic, and the medium of was not homogeneous. Visibility during this Haboob was less than 400 meters, and there was a tragic multi-car pileup on the north bound I-27. And yes, I got even more gritty yesterday.

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#14
In reply to #11

Re: One-way Speed of Light

12/19/2012 1:10 PM

"Is this another attempt at the Michelson-Morley experiment?"

No, the MMx is purely a two-way experiment. This one tries to answer the question: "can we measure the one-way speed of light?". Maybe the meaning of "measure" also comes into play...

-J

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#16
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Re: One-way Speed of Light

12/19/2012 2:35 PM

I think "measure" is one of the slippery points here. If I am not mistaken, the point of placing emitter and detector side-by-side is to give them a common frame of reference in order to say they can be synchronized to a timer. Moving the emitter to the right of the field may mean the synchronization is questionable.

As far as I can see with this set-up is that the light pulse takes a path from left to right via the laser, then moves right to left via the cable back to the detector. That it traverses two media still makes it look like a closed loop to me.

The outward laser time delta is properly accounted for, but you could use the same math to show a similar delta created by adding more cable to the outward leg of the cable loop.

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#18
In reply to #16

Re: One-way Speed of Light

12/19/2012 4:05 PM

"The outward laser time delta is properly accounted for, but you could use the same math to show a similar delta created by adding more cable to the outward leg of the cable loop."

This is interesting. Say I add more length to the looped cable, until I find the two pulses to arrive simultaneously again. I then take a piece of cable with length identical to the length that I added, loop it back to the scope and measure the signal propagation time through this piece. Do I now have another measurement of the one-way light propagation time?

-J

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#20

Re: One-way Speed of Light

12/19/2012 4:41 PM

"Here is a quote from his post on another Blog."

But that is your quote from another blog!

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#21
In reply to #20

Re: One-way Speed of Light

12/19/2012 9:37 PM

Sorry, I linked to the thread; Don Lincoln's reply is the 4th one from top.

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#29
In reply to #21

Re: One-way Speed of Light

12/20/2012 12:10 PM

From your reply: "What about the oscilloscope measurement of the photon flight times? As far as I can tell, the oscilloscope will still give about 1000 ns each way, without any need for recalibration. What is puzzling to me (if I have it right): why is there this 'fundamental' difference between the two-clock measurement and the two-cable measurement? Is there a deep truth hidden in this experiment?"

You haven't actually performed this experiment, and are making assumptions of its outcome. If the distance between the probes is different for each test because of the rotation, then the oscilloscope will measure different times of transition too, but can be explained the same as the clock synchronization can. We have enough real mysteries without making up hypothetical mysteries.

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#30
In reply to #29

Re: One-way Speed of Light

12/20/2012 3:15 PM

"We have enough real mysteries without making up hypothetical mysteries."

S, I suppose we should not complicate this thread by bringing in the accelerated frame here, which that other reply was about.

Apparently, the after-acceleration-frame is so complex that I had two experts (on two different forums) refusing to be dragged into it... ;)

-J

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#26

Re: One-way Speed of Light

12/20/2012 10:49 AM

"The two postulates on which Einsteins Special Relativity (SR) rests, can be briefly stated that in every non-accelerating, non-rotating (inertial) frame of reference:
1. The results of experiments are independent of the translational motion of the frame in which they are performed.
2. The speed of light in free space is c for all observers, regardless of the motion of the observer or the source." --from other blog ...

Suppose now that the source and detector do have relative motion with respect to one another: If the measurements are made on Earth, the frame of reference is rotating and is accelerating (by the fact that the sun's gravity well accelerates the earth around the orbit). However, all two way measurements of the speed of light involved relatively stationary points within this frame of reference, and a lot of experimental scientific papers have been published based on a constant c. IF there is an anisotropy in the propagation of light in space-time why? No fair stating that this is because space-time is expanding. We are not looking for Doppler shifts here.

If laser is pointed from point A through point B, the distance being known from point A to point B to within 0.01% (measured using something other than light beams, or I suppose using the two-way measurement with light beams), and the detector is either yes or no (i.e. is a light pulse detected or not), then the detector is nothing more than a single mirror aligned such that when it passes by point B, its surface returns a light beam to the detector. For simplicity, a hard vacuum exists between point A and point B. All spurious electric and magnetic fields have been shielded away from the light path. The light path is from west to east (for now west-east = right). Detector is set up to rotate on the edge of a disk. Rotation period of the detector disk is set to match the two-way speed of light (or suitable harmonic thereof), for the distance A-B. Phase of the detector mirror is adjustable, and rotation speed is constant within 0.01%. If everything is set up correctly, a signal is detected if the "right" c is the same as the two way c. Suppose a signal is detected (a pulse that corresponds to each and every pulse the laser makes, and laser pulse width can be modulated to a few nanoseconds). Thus, the experiment answers "yes" 106 times in the "right" experiment. The entire apparatus is on a large turntable. Rotate the apparatus 180 degrees (π radians if you prefer), accurate to within 1 arc minute (for simplicity), and repeat the experiment now from east to west (left). IF the dectector answers "yes" 106 times in the left direction, and nothing changed other than orientation, then c=c'=c", otherwise, there is further issue to explore the possibility of anisotropic propagation of light in vacuo.

Furthermore, one could also try this experiment where the whole experiment rotates at various speeds. If there is even one "no" answer by the detector, then maybe there is something to be concerned with. If there are any further doubts, one could also rotate the entire experiment, and/or the detector in 3-dimensional orbits, although the apparatus becomes more and more complicated. At first, it should suffice to test the hypothesis in the primary case, then advance to various independent axes of rotation, then spherical angular motion as a final attempt to fool with mother nature.

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#31
In reply to #26

Re: One-way Speed of Light

12/20/2012 3:46 PM

James, it seemed to me that you may have misread my final comment in #27: "It's a nice cop-out for not knowing..." I meant that for guys like me, writing AFAIK when we don't really know...

Your test proposal with the mirror on the rotating mirror is sensible. It is much like the measurement idea with the two holes on two rigid disks with a rigid axle connecting them. They are lined up when not rotating so that a light pulse travels through both holes to a detector on the other side. When the two disks are rotating in unison, there will only be multiples of a certain rpm that will allow pulses to pass through to the detector, similar to your test. Hence a single clock and a distance measurement can measure the speed of light.

The usual argument against this type of test is that the rotation has certain mechanical and relativistic effects on the circumference and alignment of the two disks, complicating any conclusion to be drawn. The two static cables seem to have less of these issues.

-J

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#32
In reply to #31

Re: One-way Speed of Light

12/21/2012 11:07 AM

"The usual argument against this type of test is that the rotation has certain mechanical and relativistic effects on the circumference and alignment of the two disks"...

It is really easy to get "out of sync" with other posters in these blogs. Sorry for the mishap about AFAIK. Is it really possible, to have relativity come into play with objects that are mechanical with rotation speeds far below sonic speed at the periphery? Maybe Doppler effect is involved somehow? Even if the rotation direction of the detector (mirror) remains the same as the whole experiment is slowly rotated through π or 2π could there be some change in Doppler...not having to do with directional speed of light.

The whole topic confuses me, but it is a bit of a stretch for me to consider expanding space-time, especially when space remains static (other than gravitational stretching), whilst time is the dimension that apparently is expanding. This brings up another question: If time is expanding, how do we know time is linear? How do we know that at the moment of "creation", the universe had a much more compressed time than we allow for, and that time itself has decayed to a much less compressed state, leading to apparent age?

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#33
In reply to #32

Re: One-way Speed of Light

12/22/2012 12:03 AM

James, you asked about Doppler effects on the disks. There are no linear Doppler effects involved, because the distance between the disks do not change. There is a relativistic "transverse Doppler" effect that should be small for low speeds. Anyway, this sort of test is more controversial than the straight cable test, where nothing but the signals move.

On expanding space - it has no effect at the small scales we are working with here, so it has no bearing on the problem. Time, as far as we can tell, is not "changing over time", but rather when there is spacetime curvature. The cosmos as a whole has a sort comic time that is constant on average. Time does progress a little slower inside the clusters, galaxies and on stars/planet surfaces, but this is taken into account when astro-observations from any location are interpreted.

I does mean that Don Lincoln's test must be done perfectly horizontal (or level); if not, the difference in altitudes between the ends of the cable must be brought into the calculations. Time progresses slower at the lower end.

-J

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#34
In reply to #33

Re: One-way Speed of Light

12/22/2012 12:19 PM

Thank you for the kind explanation. Cheers!

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#36

Re: One-way Speed of Light

01/29/2013 10:42 AM

Bravo! (one again). Jorrie, for that you deserve to treat yourself to one of those fab S.A. steaks you once told me about. If I were there I'd do it myself. Two thumbs up!

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#38
In reply to #36

Re: One-way Speed of Light

01/29/2013 3:32 PM

It's called the "Blue Bull steak", after the famed provincial rugby team called the "Blue Bulls", what else? Me, I can't devour that 1+ kg thing anymore...

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