Binary Stars and the Velocity of Light
Published in physic.philica.com
I. One of the purported proofs that c, the velocity of propagation of light in empty space, is independent of the velocity of its source was offered by Willem deSitter in 1913.1,2 He contended that if the velocity of the source adds to, or subtracts from c, the orbital periods of binary stars must seriously differ from the observed values. deSitter's contention is considered proof of Einstein's Second postulate (EP), fundamental to the theory of Special Relativity, "that light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body."3 The EP purports that when light is emitted into empty space, its velocity in empty space instantly becomes, and always remains, exactly c, losing any velocity its source may have had.
If the EP is true, any light (electromagnetic radiation) emitted by any source moving at any velocity relative to anything will always move through empty space at one fixed velocity, c. The velocity of that source relative to any spatial reference has no effect on c, and cannot cause that light to be Doppler-shifted. However, the EP says nothing about the velocity of an observer relative to light already moving through empty space at velocity c.
II. The Doppler Effect. In classical physics a Doppler-shift (an observable change in the frequency of light) results from the relative velocity of the source and observer of the same light. The observed change in frequency is Df=fe(v/c), where fe is the frequency of the light at its source, v is the relative velocity of that source and an observer toward each other. When v is negative (source and observer are moving away from each other) Df is negative, causing a red-shift. When v is positive (source and observer are moving toward each other) Df is positive, causing a blue-shift. According to the EP, the velocity of an observer relative to light affects the velocity of that light relative to the observer, but not the velocity of propagation of that light through the intervening space. If the EP is true, v, the actual relative velocity of source and observer does not determine the sign or magnitude of a Doppler-shift. Instead, those parameters are determined solely by the velocity of the observer relative to the light emitted by that source. If so, we cannot determine the velocity of any source relative to an observer. Since all light from all sources everywhere and everywhen purportedly moves through space at exactly c, any observer must find that light from every source in the universe has a Doppler-shift that depends only on that observer's velocity relative to c. If the EP is true we cannot determine the velocity of any astronomical source of light relative to the earth by measuring the Doppler-shift of its light.
An observer on earth, moving at velocity s toward many different sources must find light from all of those sources to have virtually the same Doppler-shift. This is not what is observed, indicating that the EP is not true.
III. Observation of light from binary stars. Assume that one star of a binary system is essentially at one focus of the orbit of the second star (the orbiter), and that the plane of that orbit is at some angle less than 90 degrees relative to the line of sight of an observer on earth. Assume that at the instant when the light that observer receives from the orbiter has maximum red-shift (MRS), the orbiter has maximum velocity v away from the earth. Then the orbiter is at its maximum distance from one side of the central star, as seen by that observer. This point is one "end" or limb of the semi-orbit. Also assume that at the instant when the light the observer receives from the orbiter has maximum blue-shift (MBS) the orbiter has maximum velocity v toward the earth. Then the orbiter is at its maximum distance from the other side of the central star, as seen by that observer. This point is the other "end" or limb of the semi-orbit. The time interval between successive observations of MRS and MBS is the semi-orbital period (=half of the orbital period) of the orbiter. That interval, which we will designate P/2, is typically in the range of days to decades. The distance, D, from the earth to the central star is estimated by standard astronomical methods, and is the same as the distance from the earth to the orbiter at the instants when MRS and MBS are observed. Assuming its radial velocity relative to the earth is small compared with c, the time required for light from the central star to reach the earth is Ts=D/c, which typically is hundreds to thousands of years.
Now let's assume, contrary to the EP, that the velocity of propagation of light from the orbiter in the direction of the earth is (c-v) at the instant of MRS and (c+v) at the instant of MBS. Then the time Tr=D/(c-v), required for the MRS light to reach the earth, and the time Tb=D/(c+v), will be very different, even if v is small compared with c. Both Tr and Tb will differ from Ts. For example: suppose D=1000 light-years, and v=0.001c, then Ts=1000.00 years, Tr=1001.00 years, and Tb=999.00 years.
In such a case, deSitter believed that if the Doppler-shifted light actually propagates empty space at velocities (c-v) and (c+v), the observed value of the semi-orbital period P/2 would have to be Tr-Tb=2.00 years longer than the value actually observed. So deSitter concluded that while light is Doppler-shifted at the ends of the semi-orbit, it moves through empty space at c, not (c-v) or (c+v).
Unless there is some known cause for a Doppler-shift other than relative motion of source and observer, deSitter's conclusion is not possible unless the earth is moving toward, and then away, from the orbiter of every binary star at its specific velocity v, in synchronism with every orbiter's orbital position. The radial velocity of the earth relative to the central star, and therefore relative to the orbiter at MRS or MBS, is not likely to equal to v, the velocity which corresponds to the Doppler-shift in the light from the orbiter.
IV. An Alternative View. While deSitter's interpretation may seem logical, it requires some unknown cause for the observed Doppler-shifts if the EP is true. How can we explain this seeming anomaly? deSitter did not consider the possibility that light can propagate the same distance D at (c+v) and (c-v), and still reach the earth at times separated by the correct semi-orbital period, P/2. if P/2 is small compared with D/(c-v) and D/(c+v). Let's consider that possibility, which is consistent with the usual situation. If we assume:
v=the velocity of the orbiter relative to the earth at the instants of MRS and MBS, and
Tr=D/(c-v), so D=Tr(c-v), and
Tb=D/(c+v), so D=Tb(c+v).
Then: N = (Tr-Tb)/(P/2) = [D/(P/2)][1/(c-v)-1/(c+v)]
= [D/(P/2)][2v(c2v2)] (A)
If v is much smaller than c:
N = 2Dv/(P/2)c2 (B)
N is the number of semi-orbital periods corresponding to the difference in the time the MRS light requires to reach the earth and the time the MBS light requires to reach the earth. When N is an integer, the MBS light will reach the earth at a time P/2 before the MRS light. Because of the magnitude of Tr-Tb, it is not possible for the observer to measure the time between successive observations of MBS and MRS to differ significantly from P/2.
Essentially-correct measurement of P/2 in binary stars does not require the velocity of propagation of light between source and observer to be independent of the velocity of the source.
N must be an integer because it is the quantity of semi-orbital periods corresponding to Tr-Tb. If N is not an integer, the value of D, which can not always be accurately measured, is not correct. Equation (A) or (B) may be used to improve the accuracy of measurements of D. This may seem to require binary stars to have only certain values of P/2. This is not true provided that D is precisely known.
Does (B) work when applied to a real binary star? Let's use values for a real binary system, provided by English astronomer John Watson, where D=6x1018 meters, v=2x104 meters/sec, c=3x108 meters/sec., P/2=8.640x104 sec. Then:
N = 2Dv/(P/2)c2 = 2(6x1018)(2x104)/(8.64x104)(9x1016)=30.86.
In order for N to be an integer, D must be increased by the factor 30.86/30 to 6.172x1018 meters, a correction of 2.87%. This is probably less than the accuracy with which D can be estimated.
V. Observation of binary stars provides evidence that the velocity of propagation of light is not independent of the velocity of its source. The Doppler-shift of the orbiter's light is due solely to the velocity of that body along its orbit around the central star, because the earth is not moving relative to the orbiter at velocity v at the instants when MBS and MRS are observed.
CONCLUSION: The velocity at which light is propagated in empty space is not "independent of the state of motion of the emitting body." Einstein's Second postulate is invalid.
1. W deSitter: Amsterdam Acad. 15, 1297 (1913).
2. W deSitter: Amsterdam Acad. 16, 395 (1913).
3. A Einstein: "On the Electrodynamics of Moving Bodies", English translation in THE PRINCIPLE OF RELATIVITY , Dover Publications inc, New York, 1952.
Information about this Article
Published on Friday 1st September, 2006 at 14:39:15.
Peer review added 3rd September, 2006 at 08:27:34
There is a mistake in the article. The SR says that the speed of the light in the frame moving with the speed of the light is also c. Thist feature comes from the well-known equation for a speed addition:
added 3rd September, 2006 at 16:38:02
Reply to Reviewer 1: The equation you cite assumes a priori that the value of c is “a universal constant” and “independent of the velocity of its source”. My article maintains that deSitter did not “prove” that either of these assumptions is valid. I offer an explanation of observation that does not require either assumption to be valid.
Peer review added 7th September, 2006 at 05:07:58
I would refer the author to Brecher’s 1977 paper, “Is the Speed of Light Independent of the Velocity of the Source?”, in Physics Review Letters #39. There is no need to rely on DeSitter’s century-old observations to make the empirical case that c is independent of source velocity. (E Mitchell)
Peer review added 3rd October, 2006 at 04:15:27
So I got a paragraph past the abstract, and found this: “If the EP is true, v, the actual relative velocity of source and observer does not determine the sign or magnitude of a Doppler-shift.”
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