It all started with a discussion around the tea-table a few days ago, about the fact that a lightyear is a measurement of distance and not of time, because a light year is the distance travelled by a photon over the period of a year. (
So the question is does light travel slower on leap years?
Here I set out to prove that it does.
So let’s take a look at this more closely..
Firstly a light-year is a measure of distance, so this is a fixed length (since it’s based on SI units), and can be represented by
Now this is where we need to look more closely at the problem, since a year is not a standard length. Every four years we have an extra day added to cope with some differences in measurement of astronomical (sidereal and solar, I believe) time. So in effect we are doing this calculation over four years, but with two differing values of
A quick search of wikipedia shows that
We also have two values of
We’ll convert the time into seconds (so it’s an SI unit), using the
So what are the speeds of light?
So quickly plugging the values into my calculator, gives
Similarly
This looks right, since a leap year is longer than other years, and light would therefore have to travel slower to cover the same distance.
How can we check this?
A physicist might do this with a torch, a tape measure and a stop watch, but since we are good mathematicians, we check the results, by seeing if we can use these answers to get back to the original figures, but by using a different question.
Since we know the ratio of the lengths of time, we should be able to use the ratio of the speeds to reproduce this.
i.e.
So here are the numbers…
So how much slower is light in a leap year?
Well, that’s easy, we simply boil down the ratio of
So doesn’t this make life complicated?
The short answer is yes, it does, so science has conveniently forgotten the fact that the speed of light is variable (it tends to conflict with some of Einstein’s theories), and has instead chosen a different method of approximating the speed of light. This basically amounts to creating an average speed over four years, or 1461 days. Doing this calculation, we have
I’ve heard that the speed of light is slower in denser environments, could this be a reason?
It’s a well known fact that if you increase the density of objects, light slows down as it passes through them. This is especially true for black holes, which have infinite density, and light never makes it out! However even I have to admit that the notion that the universe becomes more dense to slow light for a period of time every four years is preposterous!
So just remember, that even though the scientists would have you believe that
d=s*t for those who like the maths, or the area under a speed-time graph). Then someone else remembered that 2008 is a leap year, and contains an extra day..So the question is does light travel slower on leap years?
Here I set out to prove that it does.
So let’s take a look at this more closely..
Firstly a light-year is a measure of distance, so this is a fixed length (since it’s based on SI units), and can be represented by
d. Secondly we have a value t that represents the time this takes (1 year). Finally we have a c that is a representation of the speed of light. So we take our old d=s*t equation, and juggle it to get s=d/t. Then we plug in our variables instead, so we have c=d/t.Now this is where we need to look more closely at the problem, since a year is not a standard length. Every four years we have an extra day added to cope with some differences in measurement of astronomical (sidereal and solar, I believe) time. So in effect we are doing this calculation over four years, but with two differing values of
t, tn for three years and tl for the leap year. This will give us two values of c, cn for non leap years, and cl for leap years.A quick search of wikipedia shows that
d is 9,460,730,472,580,800 mWe also have two values of
t, tn which is 365 days, and tl of 366 days.We’ll convert the time into seconds (so it’s an SI unit), using the
60*60*24 (seconds, minutes, hours) or 86400 seconds a day. tn is 31,536,000 seconds, and tl is 31,622,400.So what are the speeds of light?
So quickly plugging the values into my calculator, gives
cn a result of 9,460,730,472,580,800 / 31,536,000, or 299,997,795.3 m/s.Similarly
cl produces a result of 9,460,730,472,580,800 / 31,622,400, or 299,178,129.192 m/s.This looks right, since a leap year is longer than other years, and light would therefore have to travel slower to cover the same distance.
How can we check this?
A physicist might do this with a torch, a tape measure and a stop watch, but since we are good mathematicians, we check the results, by seeing if we can use these answers to get back to the original figures, but by using a different question.
Since we know the ratio of the lengths of time, we should be able to use the ratio of the speeds to reproduce this.
i.e.
cl/cn=tl/tn. If we juggle this to get a value on one side, we should get (cl/cn) * tn=tl/tSo here are the numbers…
(299997795.3/299178129.192) * 31,536,000 which produces an answer of 31,622,400. So this is self-consistent at least.So how much slower is light in a leap year?
Well, that’s easy, we simply boil down the ratio of
tn/tl, or 31,536,000 / 31,622,400. Lo and behold, it becomes 365 / 366, or 99.726776% of the speed in other years.So doesn’t this make life complicated?
The short answer is yes, it does, so science has conveniently forgotten the fact that the speed of light is variable (it tends to conflict with some of Einstein’s theories), and has instead chosen a different method of approximating the speed of light. This basically amounts to creating an average speed over four years, or 1461 days. Doing this calculation, we have
c = (4 * d) / ((3 * tn)+tl). Which gives the following math to calculate. ( 4 * 9,460,730,472,580,800) / ((3 * 31,536,000) + 31,622,400) This equates to 299,792,458 m/s, which is the average speed of light often quoted by scientists. Astronomers also fudge the time, by creating the Julian year, which comprised 365.25 days to make the calculation consistent.I’ve heard that the speed of light is slower in denser environments, could this be a reason?
It’s a well known fact that if you increase the density of objects, light slows down as it passes through them. This is especially true for black holes, which have infinite density, and light never makes it out! However even I have to admit that the notion that the universe becomes more dense to slow light for a period of time every four years is preposterous!
So just remember, that even though the scientists would have you believe that
c is a constant, it isn’t!
