This article (appeared in shows why speed of light has been constant for at least last 170 000 years. This shows also that Universe is (much) older that 170 000 years. Some creationists (Setterfield, Humphreys) have presented some c-decay or other physical models that allow light rays from distant galaxies at 15 billion light years to travel to earth just in 6000 years. Here You can see how astronomical periods and spectra puts hard stop to any such kind of Young Universe models. This article is still scetchy, rough. I'll fulfill it with more eclipsing binary examples (tables) later etc. ---------------------------------------------------------------- FILE : AUTHOR : Kari Tikkanen, Oulu, Finland DATE : Sep 16, 1998 VER : 1.0 ----------------------------------------------------------------


This article tries to explain shortly for laymen why the speed of light, c, 'must' be quite constant in relation to A) atomic (or quartz) clock and B) dynamic (earth's/star's rotation or orbiting) clock. Assumptions: There exist distant astronomical objects so that distancy is at least 170,000 ly (light years).(*) The possible change of speed of light doesn't change distances or lengths. Markings : YECs = Young Earth Creationists (Earth 6000 yrs old). ly = light year = 9.454 E12 km = 9 454 billion kilometers c(t) = speed of light in year t. c_now = speed of light nowadays = 299 792 km/s. Light day = 821.3 km = 510.5 miles. dP/P = proportional change of period per year light years and light days mean distance mesurements at c_now. A) If c had changed during time in relation to atomic clock and periods then we'd see differences in atomic spectra of distant objects. But stars don't show any remarkable trend in our galaxy and not our neighbourhood galaxies LMC, M31. Theirs distances are 170 000 ly and 2,700 000 ly respectively. But there could be possibility that atomic spectra and periods would be dependent on c in such way that no change of c from distant astronomical spectra could be seen on earth (Setterfield suggest this). But we can fullfill this loophole in following section B. B) So there's left possibility to measure c by 'rotating clocks', dynamical clocks dependent on gravitation and mass, dependent not just of earth's years, months days, hours and seconds but also distant stars and pulsars rotations or dynamical movements. Setterfield's (& other's?) models suggest usually that c has more or less exponentially decayed during time since 6000 years ago so that c has travelled billions lys in 6000 years. Those models suggest that change nearly stopped in our century so that our local direct measurements up to 9 decimals won't see change any more. BINARY STAR EXAMPLE, U SGE (U Sagittae) Let's now look at star example. First some measured facts. Double star, eclipsing binary U Sge apparently pulsed at 3.38061933 days interval according to General Catalogue of stars in 1905. Hipparcos-satellite measured distance to be 1000 ly. It also measured period of U Sge to be 3.3805 +- 0.00013 days in the year 1991. So change of the period in 86 years was dP= 3.3805- 3.38061933 +-0.00013 days = -1.2E-4 +-1.3E-4 days. Proportional change per year is now easy to calculate: -1.2E-4 +-1.3E-4 dP/P= ----------------- = -4.1E-7 +-4.5E-7 per year 86 * 3.3805 ========================= Eclipsing star U Sge is so 'bright' that man can see it with binoculars if man knows where to look. C-DECAY EXAMPLE: Now let's go back in time and space in c-decay-YECs model. Light ray pulses (pp) starts from U Sge in the year Jan 1,1500 AD. Interval of those pulses are in fact 0.33806 days in 'this reality'. According to c-decay-YECs c was (for ex) 10x faster than now. c(1500)=10*c_now. So distance of pulses(p-p)= 10*0.33806= 3.3806 light days. 1500 AD: U SGE c(1500)=2 997 920 km/s + p---p---> Pulses gets to 10 ly from U Sge in the next year Jan 1,1501. U Sge send pulses all the time at 0.33806 days interval (also now, too!) but c has decayed to be only 9x faster than now, c(1501)= 9 x c_now. 1501 AD: U SGE c(1501)=2 698 128 km/s + q--q-------------p---p------> <----10 ly --------> So distance of pulses (q-q) is now little shorter ! it is only 9 * 0.338 =3.04254 light days. Then years go by..c-decays..Newton borns.. Einstein comes.. but in our century speed of light keeps quite constant. We observe U Sge in the year 1988 and those pulses p--p hit the earth and us: EARTH c=c_now=299 792 km/s 1988 AD: O -----------q--q--------------p---p-> The change of speed of light doesn't change the distances of p--p and q--q.(Look Assumptions). But as c has decayed, the timings have changed too. Though p--p was 0.338 days at start, it is 3.3806 days in 1988 because light is decayed to 1/10th from original. (..Then ten years more goes by..) But now,in the year 1998, q-q pulses finally hit us: EARTH c=c_now=299 792 km/s 1998 AD: O ---------------q--q-> The interval q-q is shorter than p-p (as in fig). q-q = 3.04254 light days and p-p = 3.3806 light days. ********************************************************** SO APPARENT PERIOD OF U Sge SHOULD HAVE BEEN SHORTENED FROM 3.3806 days TO 3.04 days IN TEN YEARS in this rough example. It means -10%/10 yrs = -1% proportional change of period (dP/P) per year should have been seen. ********************************************************** Any change of c causes different changed *distances* between ticks of pulsars or eclipsing rays of binaries at start moment. Later the travelling *distance* is totally independent of c. ----------------------------------------------------- | +... . . . . . . . . . -> | ----------------------------------------------------- Fig. If c-decays then 'ticks' have diff. distances BINARIES SHOW REASONABLE CONSTANT PERIODS U Sge and many other eclipsing binaries are known to have quite constant periods. Changes of periods are in range of aprox +-1E-6 per year. Some of them are at thousands light years from us. Some binaries has been observed in LMC (170,000 ly). Though not change of period of LMC-binaries may not been measured, no remarkable miraculously different period has been observed. This also indirectly refer to constancy of c. Some binaries (Algol, Beta Lyr) have been observed for nearly 200 years. Binaries lie in different distances. Many of those measured trigonometrically by Hipparcos-satellite. In practice periods of binaries overlap and cover the space-time to the thousands of (light) years. MANY PULSARS SHOW VERY STABLE PERIODS I have collected 477 pulsars from NASAs archives (Appendix). Theirs constancy of periods and that some of them are found up to LMC all together shows constancy of speed of light. Here are some statistics of those: dP/P /yr Max for Crab Nebula 397.6 E-6 85% of pulsars (407/477) < +1.00 E-6 50% = Median (239/477) < +0.114E-6 4% of pulsars ( 22/477) < +1.00 E-9 MIN for PSR 2322+2057 (J2000) 4.6 E-11 +-2.0E-11 And for 18 pulsars we have |dP/P| < 1E-9 . For 3 pulsars we have 1.0E-10 < dP/P < 1.2E-10. NO ROOM FOR PROPER CHANGE OF C Some binaries (Algol, Beta Lyr) have been observed for about 200 years. Binaries lie in different distances. And for some 30 years of pulsars has been listened to. This means that our knowledge of light or radio rays from binaries and pulsars overlap or cover the space-time to the tens of thousands of lys and in practise to 170,000 lys. This all means no proper room for either continous or discrete change of c. Mathematically: | dP/P| |-----| < epsilon for many stars in many distances | dt | This means | dc(t)/c| |--------| < delta for various point on c(t) curve. | dt | It can be shown that epsilon =approx= delta when they are small (nearly 0). It also can be shown that if |dc(t)/t| =approx= 0 for all t then it implies that c(t) =approx constant for all t. ========================= If we allow dP/P=1E-9 /yr as maximum trend of periods then we can estimate dc/c=1E-9/yr (for small changes). In 170,000 year this gives for change of speed of light dc = 170,000*1E-9= 1.7E-4= 0.017%. So with this estimate we can allow only maximum ranges of 299 792 +- 2 km/s for c 6,000 years ago ============================================= and 299 792 +- 5096 km/s for c 170,000 years ago. ============================================= OTHER POSSIBILITIES: No other proper possibilities are left. Well, at least not interesting. If rotating & orbiting of earth and atomic spectra and quartz clocks ticks would linearly change at the same time with decaying c, then -perhaps we'd see no difference to 'scientists standard model of millions years old universe and earth'. (We'd have no clock to measure it ?) -YECs wouldn't be interested in. Earth could cycle millions times around sun: 'Millions "years" old earth! No way!' FINAL CONCLUSION: ******************************************************* * Astronomical measurements suggest strongly the * * constancy of speed of light in last 170,000 years. * ******************************************************* --- (*) SN1987 in LMC has been shown to be at about 170,000 ly's distance by trigonometrical measurements of halo-echo. SOME WEB-LINKS: - W.T.Bridgman's Web-site "A Changing Speed of Light?" -'s C-decay critique" "The Decay of c-decay" by R.P.J.Day ------------------------------------------------------------ APPENDIX: {-------------------------------------------------------------- PULSAR STATISTICS FOR PULS558A (Taylor 1993-Catalog from NASA) --------------------------------------------------------------- dP missing from 81 -> #477 were selected to PULS.TMP ---- P RANGE = 0.00156..4.308 sec MEDIAN = appr. 0.58 sec MEAN = 352.37/477 s = 0.73873 sec . P/P RANGE = (-0.22 .. 397.70) E-6 /yr MEDIAN = = app. 0.114 E-6 /yr MEAN =1616.568E-6/477= 3.389 E-6 /yr <1.000E-6 /year 407/477 = 85.3% <0.114E-6 /year 239/477 = 50.1% < 1E-9 /year 22/477 = 4.6% MAX for Crab Neb puls (M1) PSR0531+21 => dp/p=397.7E-6/yr MIN for (J2000)2322+2057 => dp/p=(4.6+-2.0)E-11/yr Histogram: step 0.1 E-6: -0.3..-0.2 #1 -0.2..-0.1 #0 -0.1.. 0 #4 0.. 0.1 #221 ********************* 0.1.. 0.2 #74 ******* 0.2.. 0.3 #39 **** 0.3.. 0.4 #20 ** 0.4.. 0.5 #17 ** 0.5.. 0.6 #8 * step 0.001E-6 -0.001..0 #1 * 0 .. 0.001 #17 ***************** .. 0.002 #7 ******* .. 0.003 #6 ****** .. 0.004 #5 ***** .. 0.005 #4 **** .. 0.006 #7 ******* Only after having step 0.0001 man gets maximum other than 0..step: 0..0.0001 #2 ..0.0002 #6 ..0.0003 #1 best range is (0.00010..0.00012)E-6 --> #3 Dist RANGE = 0.12 .. 49 kpc = 390 .. 160 000 ly MEDIAN = app. 3.75 kpc = 12 200 ly MEAN = 4.9226 kpc = 16 000 ly DIVIDED DISTANCE SECTIONS STAT: ------------------------------------------------------ no of Sum Mean Dist range pulsars dP/P[E-6/yr] (dP/P)[E-6/yr] ------------------------------------------------------ 0 .. 20 000 ly 352 1110.239 3.154 20 .. 40 000 ly 102 187.180 1.835 40 .. 60 000 ly 13 12.807 0.985 60 .. 80 000 ly 3 0.637 0.212 80 ..100 000 ly 5 2.357 0.471 100 000 ly- 2 303.346 151.67 ------------------------------------------------------ (the last 2 are in LMC: 3.25 E-6 and 300.1 E-6) PULS.TMP columns explanations: 23=RA 2000 39= Dec 2000 71=Distance adopted (kpc) 83=Period (sec) 106=+-P 115=dP (s) 132=+-dP (s) 142=JD of obs. 163=dispersion 177=distance from DM -----------------------------------------------------------------}