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Supernova SN1987A and the Speed of Light

How Good Are Those Young-Earth Arguments?
A Close Look at Dr. Hovind's List of Young-Earth Arguments and Other Claims
by Dave E. Matson
Copyright © 1994-2002


A6. The Distance to Supernova SN1987A and the Speed of Light


When supernova SN1987A exploded, a fair amount of ultraviolet light was given off in addition to the usual, visible light. About a year after the explosion, the light struck a ring of gas some distance from the star, illuminating different parts of it at different times. "Its absolute diameter was determined based on the timing of ultraviolet spectral lines, where observed light curves are fitted to models. The angular size on the sky is known from Hubble telescope measurements." (Ron Ebert, Internet, 5/20/98). (The angular size is roughly how big something appears to you. I. e., your small fingernail, held at arm's length, has about the same angular size as the moon viewed without instruments.) It turned out that this ring of gas is titled about 43 degrees to our view. Knowing the actual diameter and the angular diameter, the distance is easily calculated using a simple, trigonometric formula, and was done with an error of less than 5%.


Distance equals the actual diameter of the object divided by twice the tangent of half the angular size


Figure #4


No matter how a perfect circle is viewed in space, the longest line across it from our viewpoint will give the true, angular diameter. Knowing the real size of an object (say, in miles) and how large it appears (in degrees), one can calculate the distance. The distance formula falls right out of the definition for the tangent function. Take the moon, whose diameter is 2160 miles, whose angular size is 0.5 degrees. That yields a distance of 248,000 miles, which is quite decent. (If you are not familiar with trigonometry just skip this.)


Many creationists would have you believe that the speed of light was once very high and has been slowing down ever since. The motivation for this reasoning is to keep the age of the universe at about 6000 years while accounting for the fact that we can see the distant stars. As I will later show you in detail, if there is any truth to that claim, then the light we now see from SN1987A must have been traveling considerably faster when it left the vicinity of that supernova. That means our telescopes today would see things happening there in slow motion! As it so happened, by studying changes in the light levels, astronomers were able to calculate the half-lives of the cobalt-56 and cobalt-57 created in the aftermath of that supernova explosion. Far from exhibiting a slower decay rate, their decay rates matched the cobalt-56 and cobalt-57 decay rates measured in our laboratories. Therefore, the light leaving the vicinity of SN1987A was traveling at its normal speed, and that means we are seeing things almost 200,000 years ago!


Still, the creationist has one ace up his sleeve. What if the cobalt-56 and cobalt-57 created by SN1987A was actually decaying much faster, a rate that only appeared normal in our telescopes because of the slow-down factor? We might be seeing a slow motion replay of fast decay rates, or we might be seeing a normal replay of normal rates. It would appear to us, either way, that no change had occurred. Does this sound confusing?


To this one might say, "Get an education!" Relativity is central to modern science and the speed of light is a fundamental constant. Light can't go faster than about 186,000 miles a second and that's that. One could then recite volumes of laboratory studies, experiments, and observations to impress the reader with the power and reliability of special relativity. However, that approach might seem rather dogmatic to someone lacking an education in the sciences. Thus, I will pretend that light once traveled much faster in the past (as might be imagined in Newtonian physics) and work out some of the consequences.


My first point is based on a straightforward observation of pulsars. Pulsars put out flashes at such precise intervals and clarity that only the rotation of a small body can account for it (Chaisson and McMillan, 1993, p.498). Indeed, the more precise pulsars keep much better time than even the atomic clocks on Earth! In the mid-1980s a new class of pulsars, called millisecond pulsars, were discovered which were rotating hundreds of times each second! When a pulsar, which is a neutron star smaller than Manhattan Island with a weight problem (about as heavy as our sun), spins that fast it is pretty close to flying apart. Thus, in observing these millisecond pulsars, we are not seeing a slow motion replay as that would imply an actual spin rate which would have destroyed those pulsars. We couldn't observe them spinning that fast if light was slowing down. Consequently, under the reasonable assumption that if light slowed down in a fundamental way, it would have slowed down everywhere, we can dispense with the claim that the light coming from SN1987A might have slowed down. Therefore, the decay rates observed for cobalt-56 and cobalt-57 were the actual decay rates and we are seeing things as they were 170,000 years ago.


A more quantitative argument can also be advanced for those who need the details. Suppose that light is slowing down according to some exponential decay curve. An exponential decay curve is one of Mother Nature's favorites. It describes radioactive decay and a host of other observations. If the speed of light were really slowing down, then an exponential decay curve would be a very reasonable curve to start our investigation with. Later, we will be able to draw some general conclusions which apply to almost any curve, including those favored by creationist Barry Setterfield.


We want the light in our model to start fast enough so that the most distant objects in the universe, say 10 billion light-years away, will be visible today. That is, the light must travel 10 billion light-years in the 6000 years which creationists allow for the Earth's age. (A light-year is the distance a beam of light, traveling at 186,000 miles per second, covers in one year.) Furthermore, the speed of light must decay at a rate which will reduce it to its present value after 6000 years. Upon applying these constraints to all possible exponential decay curves, and after doing a little calculus, we wind up with two non-linear equations in two variables. After solving those equations by computer, we get the following functions for velocity and distance. The first function gives the velocity of light (light-years per year) t years after creation (t=0). The second function gives the distance (light-years) that the first beams of light have traveled since creation (since t=0).


V(t) = V0 e-Kt


S(t) = 1010(1 - e-Kt)


V0 = 28,615,783 (The initial velocity for light)
K = 0.00286158 (the decay rate parameter)


With these equations in hand, it can be shown that if light is slowing down then equal intervals of time in distant space will be seen on Earth as unequal intervals of time. That's our test for determining if light has slowed down. But, where can we find a natural, reliable clock in distant space with which to do the test?


As it turns out, Mother Nature has supplied some of the best clocks around. They are the pulsars. Pulsars keep time like the Earth does, by rotating smoothly, only they do it much better because they are much smaller and vastly heavier. The heavier a spinning top is the less any outside forces can affect it. Many pulsars rotate hundreds of times per second! And they keep incredibly precise time. Thus, we can observe how long it takes a pulsar to make 100 rotations and compare that figure to another observation five years later. Therefore, we can put the above creationist model to the test. Of course, in order to interpret the results properly, we need to have some idea of how much change to expect according to the above creationist model. That calculation is our next step.


Let's start by considering a pulsar which is 170,000 light-years away, which would be as far away as SN1987A. Certainly, we can see pulsars at that distance easily enough. In our creationist model, due to the initial high velocity of light, the light now arriving from our pulsar (light beam A) took about 2149.7 years to reach Earth. At the time light beam A left the pulsar it was going 487.4686 times the speed of light. The next day (24 hours after light beam A left the pulsar) light beam B leaves; it leaves at 487.4648 times the speed of light. As you can see, the velocity of light has already decayed a small amount. (I shall reserve the expression "speed of light" for the true speed of light which is about 186,000 miles per second.) Allowing for the continuing decay in velocity, we can calculate that light beam A is 1.336957 light-years ahead of light beam B. That lead distance is not going to change since both light beams will slow down together as the velocity of light decays.


When light beam A reaches the Earth, and light is now going its normal speed, that lead distance translates into 1.336957 years. Thus, the one-day interval on our pulsar, the actual time between the departures of light beams A and B, wrongly appears to us as more than a year! Upon looking at our pulsar, which is 170,000 light-years away, we are not only seeing 2149.7 years into the past but are seeing things occur 488.3 times more slowly than they really are!


Exactly 5 years after light beam A left the pulsar, light beam Y departs. It is traveling at 480.5436 times the speed of light. Twenty-four hours after its departure light beam Z leaves the pulsar. It is traveling at 480.5398 times the speed of light. Making due allowances for the continual slowing down of the light, we can calculate that light beam Y has a lead in distance over light beam Z of 1.318767 light-years. Once again, when light beam Y reached Earth, when the velocity of light had become frozen at its present value, that distance translates into years. Thus, a day on the pulsar, the one defined by light beams Y and Z, appears in slow motion to us. We see things happening 481.7 times slower than the rate at which they actually occurred.


Therefore, if the above creationist model is correct, we should see a difference in time for the above two identical intervals, a difference which amounts to about 1.3%. Of course, the above calculations could be redone with much shorter intervals without affecting the 1.3% figure, being that the perceived slowdown is essentially the same for the smaller intervals within one day. As a result, an astronomer need only measure the spin of a number of pulsars over a few years to get definitive results. Pulsars keep such accurate time that a 1.3% difference--even after hundreds of years--would stand out like a giant redwood in a Kansas wheat field!


So, what are the results of this definitive test? Many pulsars have been observed which show nothing remotely close to a 1% change in their rotation rates over a five year period. Although we have technically disproved only the above model, we have, nevertheless, thrown a monkey wrench into the machinery for decaying light-speed. Every such scenario must have the slow motion effect described above. Furthermore, the slow motion effect is directly related to how fast the light is moving. If a model requires light in the past to move one hundred times faster than observed today, then, at least for some interval of time measured in that part of space, we would observe things moving one hundred times as slow.


That's the fatal point which no choice of light-velocity decay curve can wholly remedy. The creationist model, in order to be useful, must start with a high velocity for light so that objects ten billion light-years away can be seen in a universe a mere 6000 years old. Consequently, such a universe must appear, in general, to be slowing down more and more the farther we look into the depths of space. And the farther we look, in general, the more dramatic the perceived slowdown should be.


Such a slowdown shouldn't be confused with the legitimate slowdown calculated on the basis of special relativity. Einstein showed that if an object is moving away from us at a significant fraction of the speed of light, we would see events on that object slowing down noticeably. It would not be an illusion as is the case for the creationist scenario with its absolute, Newtonian time frame. Thus, we would see a dramatic slowing down at cosmological distances, where galaxies are moving away from us at a significant fraction of the speed of light. However, this legitimate cosmological effect is important only for really great distances, and it plays no significant role in our calculations. At 170,000 light-years, for instance, the effect would be virtually nil.


It might seem that if we started out with a fantastically high velocity for light, which then decayed precipitously, we could reduce the problems. In the extreme case, light might start out at "infinity" and suddenly drop to normal values. Certainly, that would allow us to see the most distant parts of our universe while keeping it only 6000 years old. It would also preserve normal light speeds over the last 6000 years. Unfortunately, astronomers would not be able to see anything further than 6000 light-years away! We would not see supernova 1987A at all! The last photon leaving SN1987A under the "infinite" speed would already have reached us instantly. The next photon to leave would be traveling at a normal speed, and it would still be out there in space on its way to us. Consequently, we could not see anything further than 6000 light-years away. Since we don't have that kind of problem, we may "can" that extreme case!


In a less extreme case, we might start with a very high velocity for light, which rapidly decays to normal. Thus, the decay curve would have near-normal speeds for most of the years between t=0 and t=6000 (Figure #5). Historical measurements of the velocity of light would not detect any change, which is the actual case. However, the effect relative to our calculated model (which is represented by Figure #6) would be to move the latest departure time of light beam A (from the supernova) closer to the time of creation and to jack up its speed. (Compare the light speeds at t=x and t=y, Figures #5 and #6). That is, because the velocity of light decays so rapidly (Figure #5), any light leaving the more distant objects in the universe would have to get an earlier start so as to cash in on that speed before it's gone. After all, we do see those objects, meaning that the light had to travel the full distance in less than 6000 years. The drawback (Figure #5) is that when the light leaves the supernova its speed is changing rapidly (a steeper slope on the decay curve). That means the pulsars would appear to keep very poor time as observed today over a period of a few years.


Figure #5
"Suppose the speed of light was initially very high, and that it decayed to today's value rather rapidly. An object 177 thousand light years away could be seen today if the area under the decay curve plotting speed of light versus time is equal to 177 thousand. Where the slope is steep there will be uneven pulsar spin rates."


Two curves for exponential decay of the velocity of light in a vacuum.


Figure #6"Suppose the light curve decays less rapidly. An area of 177 thousand fits with a time (t) that is further to the right (more recent). That allows a less steep slope when the supernova explodes at t equals y."


Two curves for exponential decay of the velocity of light in a vacuum.


Suppose, then, that we took a much less extreme case of the above. Pretend that Figure #6 is the graph of a much more moderate light decay curve. While this curve is more in accord with the fact that pulsars keep good time, the problem is by no means solved. Pulsars keep such good time that even a little deviation, as predicted by this latter model, would show up dramatically. Astronomers don't find that kind of deviation for every pulsar, if any. Furthermore, in choosing a model that allows the speed of light to decay more slowly to its present value, we are left with another problem. Historical measurements would clearly reveal that light was faster in the past (Figure #6). The slower light decayed to its present speed, the more obvious that latter problem becomes.


We might even try a flat curve that doesn't decay at all, except for a rapid drop in historical times. Such a curve is a bit contrived, but it would be in accord with the historical measurements as well as with the fact that pulsars keep good time (flat slope). However, in order to see objects 10 billion light-years away in a 6000 year-old universe, the light speed for that curve would have to be set at 1.6 million times the present speed of light! The spinning pulsars we see would have flown apart! That is, their actual rotational speeds would have to be so much greater than observed as to present a physical contradiction.


Having surveyed the extreme cases, as well as the middle ground (the case with the calculations), we may confidently reject the claim that the velocity of light started out fast and then decayed to its present value. Every possible decay curve, save the kind of impractical curiosities a mathematician might construct, is ruled out by simple observations. Consequently, when we look at a supernova that is 177,000 light-years away, we are looking 177,000 years into the past. When astronomers observe a galaxy billions of light-years away, they are looking billions of years into the past.


There are other good reasons for rejecting the claim that light once had a much higher velocity. It is a fundamental constant tied to energy by the equation E = mc2. If we could somehow monkey around with the speed of light, the whole universe would be radically altered! It's not just another pretty number!


I will not pursue this matter beyond the above disproof. However, let me leave you with a few references for further reading:


  • Ebert, Ronald. 1997. REPORTS of the National Center for Science Education, "Does the Speed of Light Slow Down Over Time?" Vol.17 No.5 (Sept./Oct.), p.9-11 P.O. Box 9477, Berkeley, CA 94709-0477

A few creationists have argued that the universe really isn't that big. In particular, Slusher, working for the Institute for Creation Research, argued in 1980 that the universe is based on a Riemannian space which allowed no point to be more than 15.71 light-years away. The great distances observed would be an illusion based on mistaking the Riemannian space for Euclidean space.


This model, however, requires that the distance to supernova SN1987A be measured at less than 15.71 light-years in contradiction to the 170,000 light-years actually measured. Unexploded versions of SN1987A would be seen at the same time, one of them being at a perceived distance of 170,000 light-years! A few decades later, the light from the explosion would circle around again, thus causing us to see SN1987A explode all over again! This is madness, not science! See Strahler (1987, pp.114-116) for a thorough debunking of this Riemannian space nonsense. (George Friedrich Bernhard Riemann, 1826-1866, was a German mathematician whose work on curved space proved helpful to Einstein, but not with the absurd radius of curvature assigned by Slusher!)


Yet another idea, advanced by Henry Morris and others, is that star light was created in situ during the Genesis creation week. However, we have now left the realm of science for theology. There is no scientific way to separate star light from its origin in a star. Not only is it theology, but it's bad theology. God creates a universe which forces him to be a deceiver! It goes beyond the need for any reasonable appearance of age as a result of functionality. There is no need, for example, to see supernovae explode before their time. An observer would ultimately see the supernova leap back together and explode all over again when the light from the real explosion finally arrived! It makes God out to be an idiot.


When the creationist smoke screen finally dissipates, the debate hall falling silent at last, the young-earth advocate finds himself back on square one. He is looking at stars many millions of light-years away, stars putting out light which takes many millions of years to reach us! Attempts to speed up the velocity of light or to shrink down the universe have come to naught. What does remain is prime evidence for the old age of our universe.


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