[Fruityloop (OP)]

I am going to show what I believe is evidence that the speed of light isn't constant relative to all observers.  I obviously have no proof, just evidence from an argument.  But first I need to lay out a scenario... 
     Imagine that you are standing still and you are holding a stopwatch in your hand.  There are people in a line walking swiftly past you.  They are moving at a constant speed and are equally spaced apart from one another.  You start the stopwatch when one person reaches you and you stop it when the next person reaches you.  You note how long this took and you record this time as X.  You then start walking in the same direction as the people are walking past you, but you're not walking as fast as they are.  You do the same thing again...you start your stopwatch when a person passes you and you stop it when the next person passes you.
You note two things...
1) The people are passing you more slowly.  Relative to you their speed is decreased.
2) The time between people is greater than X.
Now you start walking towards the people and again you record the amount of time between people passing you.
Again two things are noted...
1) The people are passing you more quickly.  Relative to you their speed is increased.
2) The time between people is less than X.

All of this is simple and quite obvious.  Now we are going to replace you with the Earth and the people walking past you are going to be replaced by the instant of minimum brightness from an eclipsing binary star system.  If we find that the time between the instants of minimum brightness is greater when we are moving away from the star system and less when we are moving towards the star system, the logical conclusion we should come to is that the light is passing us more slowly when we are moving away from the stars and passing us more quickly when we are moving towards the stars.
http://calgary.rasc.ca/algol_minima.htm

In May and November, the Earth is moving at "right angles" to the line to Algol. During this time we see minima happening regularly at their 2.867321 day intervals. However, during August, the Earth is rapidly moving towards Algol at about 107,229 km/hr as explained on my How Fast Are We Moving? page. (The Earth moves approximately 202 times its own size in one day.) So in 2.867321 days the Earth moves about 7,379,039 km closer to Algol. But the varying light from Algol doesn't know this(emphasis added) - its light waves left Algol 93 years ago and are travelling at a constant speed. The result - we "catch a bunch of minima early" during August as shown on Chart 2. Exactly the opposite happens during February - the Earth is moving away from Algol that fast and it takes longer for the group of minima to reach us so we see them taking longer between events. How long? 7,379,039 km divided by the speed of light 299,792.458 km/sec is 24.61382 seconds - this rough calculation explains the deviations we see in Graph 2. So in May and November when we are not moving towards or away from Algol - the period seems constant. It is our rapid movement towards or away from the events in August and February that causes the timing differences.

When we are 'running away'... the time between minimums is 2.8675875347 days.
When we are 'running towards'... the time between minimums is 2.8670608912 days.
When we are 'standing still'... the time between minimums is  2.867321 days.

I realize the analogy isn't exact because the analogy is in a line and the actual Earth and star system is in 3D space.  However, if the binary star system were in the same plane as the Earth's orbit around the Sun I think we should expect similar results.

[Colin2B]

the logical conclusion we should come to is that the light is passing us more slowly when we are moving away from the stars and passing us more quickly when we are moving towards the stars.

No, the solution is as described in the link you provided, the light travels different distances.
If you assume the light speed changes, what would you propose happens to Maxwell's Equations and the knock back onto Gauss' laws, Faraday's and Ampere's Laws?

[Fruityloop (OP)]

Here's a technical paper in which the author is calling into question Einstein's SR.
It's an interesting read...

http://web.stcloudstate.edu/ruwang/eefinal.pdf

[alysdexia]

GPS deals with GR so you can dispose the paper out of hand.

SR is simply the result of the Doppler effect under finite celerity and GR is the result of Rindler events under finite celerity.

[Fruityloop (OP)]

It takes a longer time between eclipses because the light, relative to us, is no longer moving at c. The speed of the Earth around the Sun is 66,629 mi/hr. We are not moving directly towards and away from Algol, so our speed in that direction is actually 66,629 mi/hr * cos(17.516339) = 63,539.49055 mi/hr. So the speed of light relative to us when we are moving away is 186,264.3501 mi/sec. So the time taken increases by (186,282/186,264.3503) = 1.000094757. So 2.867321 days * 1.000094757 = 2.867592699 days. That's very close to 2.8675875347 days when the Earth is moving away from Algol at maximum speed.

[evan_au]

the light, relative to us, is no longer moving at c

On the contrary, the light is still moving at c.
But light has to travel around 4.6 million miles farther every orbit, and this takes more time.
6 months later, the Earth is 4.5 million miles closer every orbit, so the eclipses seem to occur sooner.

[Janus]

It takes a longer time between eclipses because the light, relative to us, is no longer moving at c. The speed of the Earth around the Sun is 66,629 mi/hr. We are not moving directly towards and away from Algol, so our speed in that direction is actually 66,629 mi/hr * cos(17.516339) = 63,539.49055 mi/hr. So the speed of light relative to us when we are moving away is 186,264.3501 mi/sec. So the time taken increases by (186,282/186,264.3503) = 1.000094757. So 2.867321 days * 1.000094757 = 2.867592699 days. That's very close to 2.8675875347 days when the Earth is moving away from Algol at maximum speed.

The problem is the you are assuming that what you are trying to prove is true before you even start your proof.
I can do the same assuming that the light does travel at c with respect to the Earth.
At the moment the light from one eclipse of Algol occurs, Algol is a certain distance from Earth.  If Earth and Algol are moving apart at 66629 mph, then  2.867321 days later, when the light for the next eclipse occurs, Algol will be 4585121.54 miles or 24.6162 light seconds further away from the Earth when that light leaves,  This means that the light from this eclipse, traveling at c relative to the Earth, take 24.6162 seconds longer to travel to the Earth than the light from the earlier eclipse did.  If the eclipses occurred 2.867321 days apart at Algol, the Earth would see them 24.6162 seconds or 0.00028491 days further apart 2.867321 + 0.00028491 =2.86760591 days apart which is also close to the given time. (quibbling about the small difference here does no good because the Earth's orbital speed itself varies by some 2240.3 mph (.6223 miles per sec) over over the course of an orbit, which would result in a larger difference in answers than what we got.)

The point is that I can get the same type of spacing between observed eclipses by assuming that light does travel at c relative to the Earth.

There are two possible models to explain Doppler shift ( which in this case is seen by the timing between observed eclipses.).
One is the Classical Doppler shift, where light moves at a constant speed relative to some medium (the Aether for example).
With this model, the observed Doppler shift is dependent on both the source's and receiver's motion relative to the medium. If the source is in motion and the receiver is at rest, the receiver sees a different value for the Doppler shift than if the source is at rest and the receiver is in motion even if the relative velocity difference between the two is the same in both cases.
The other model is Relativistic Doppler shift, which assumes no medium and that both receiver and source measure light as traveling at c relative to themselves.   With this model, the only factor that determines the Doppler shift measured by the receiver is the relative velocity between the two.

Experiments can and have been performed to test which of these models makes the best prediction in real life, and the winner is Relativistic Doppler shift.

So it doesn't matter that you think you've proven by your thought experiment, experiments in real life have proven otherwise.
You can never prove anything through a thought experiment.  Thought experiments are good for figuring out the consequences of a set of assumptions, but no good in determining whether or not those assumptions are sound. For that, you have to perform a practical experiment to test to see if the results predicted by the thought experiment actual occur in real life.  If the results don't match, and the experiment was designed properly, then this means that something was wrong in your thought experiment.  And if it isn't in the structure of the thought experiment, it has to be in one or more of the assumptions. 

[Fruityloop (OP)]

I'm standing next to railroad tracks and there is a train with boxcars passing me at 30 m.p.h and the cars are 30 ft long and separated by 100 ft.  It will take 65/22 seconds for the front of each car to reach me.  I start running at 15 m.p.h. in the same direction as the boxcars are moving.  Now the boxcars are passing me at 15 m.p.h. and it takes 65/11 seconds for the front of each boxcar to reach me.  The boxcars are taking more time to reach me and they are passing me more slowly.  Replace the boxcars with the eclipses from Algol and replace me with the Earth and we have the situation described above.  I fail to see what the frequency of light has to do with this.  The frequency of the light may change towards the red end of the spectrum because Algol is receding from us. So what?

[Janus]

I'm standing next to railroad tracks and there is a train with boxcars passing me at 30 m.p.h and the cars are 30 ft long and separated by 100 ft.  It will take 65/22 seconds for the front of each car to reach me.  I start running at 15 m.p.h. in the same direction as the boxcars are moving.  Now the boxcars are passing me at 15 m.p.h. and it takes 65/11 seconds for the front of each boxcar to reach me.  The boxcars are taking more time to reach me and they are passing me more slowly.  Replace the boxcars with the eclipses from Algol and replace me with the Earth and we have the situation described above.  I fail to see what the frequency of light has to do with this.  The frequency of the light may change towards the red end of the spectrum because Algol is receding from us. So what?

If I measure the time between the passing of two wave crests of light, this is the equivalent to the time between the passing of the boxcars. The frequency for light is just the inverse of this measurement expressed in waves per sec instead of seconds per wave.
But the difference between boxcars and light is the the wavelength (distance between crests also changes).  So as the time between passing crests increases so does the distance between crests and the speed of the light relative to the observer stays the same.

I don't care how many examples of boxcars or people passing you post, light is neither boxcars nor people and does not behave the same.  Again, this has been demonstrated again and again by real life experiments.    No matter how much you might want it to, light in the real universe does not behave in the way you are describing.

This might not make sense to you, but the universe is under no obligation to limit itself to rules of operation that you personally approve of.

[Fruityloop (OP)]

I can do the same assuming that the light does travel at c with respect to the Earth.
At the moment the light from one eclipse of Algol occurs, Algol is a certain distance from Earth.  If Earth and Algol are moving apart at 66629 mph, then  2.867321 days later, when the light for the next eclipse occurs, Algol will be 4585121.54 miles or 24.6162 light seconds further away from the Earth when that light leaves,  This means that the light from this eclipse, traveling at c relative to the Earth, take 24.6162 seconds longer to travel to the Earth than the light from the earlier eclipse did.  If the eclipses occurred 2.867321 days apart at Algol, the Earth would see them 24.6162 seconds or 0.00028491 days further apart 2.867321 + 0.00028491 =2.86760591 days apart which is also close to the given time. (quibbling about the small difference here does no good because the Earth's orbital speed itself varies by some 2240.3 mph (.6223 miles per sec) over over the course of an orbit, which would result in a larger difference in answers than what we got.)

The point is that I can get the same type of spacing between observed eclipses by assuming that light does travel at c relative to the Earth.

This is true, but there is a subtle difference.  If light were traveling at c relative to the observer then the time taken from emission to reception would depend upon the distance from sender to receiver at the time of emission.  This would lead to some strange effects.  Let's say that Algol is 93.5 light-years from Earth.  The Earth is at the maximum distance away from Algol and is approaching Algol.  Every time an eclipse occurs the Earth is closer to Algol.  This means that the period of time between eclipses will be shorter.  93.5 years later, when the Earth is closest to Algol, the Earth will start receiving those eclipses.  So we would have the strange effect of having a shorter period of time between eclipses as the Earth is moving away from Algol.
 

[Janus]

I can do the same assuming that the light does travel at c with respect to the Earth.
At the moment the light from one eclipse of Algol occurs, Algol is a certain distance from Earth.  If Earth and Algol are moving apart at 66629 mph, then  2.867321 days later, when the light for the next eclipse occurs, Algol will be 4585121.54 miles or 24.6162 light seconds further away from the Earth when that light leaves,  This means that the light from this eclipse, traveling at c relative to the Earth, take 24.6162 seconds longer to travel to the Earth than the light from the earlier eclipse did.  If the eclipses occurred 2.867321 days apart at Algol, the Earth would see them 24.6162 seconds or 0.00028491 days further apart 2.867321 + 0.00028491 =2.86760591 days apart which is also close to the given time. (quibbling about the small difference here does no good because the Earth's orbital speed itself varies by some 2240.3 mph (.6223 miles per sec) over over the course of an orbit, which would result in a larger difference in answers than what we got.)

The point is that I can get the same type of spacing between observed eclipses by assuming that light does travel at c relative to the Earth.

This is true, but there is a subtle difference.  If light were traveling at c relative to the observer then the time taken from emission to reception would depend upon the distance from sender to receiver at the time of emission.  This would lead to some strange effects.  Let's say that Algol is 93.5 light-years from Earth.  The Earth is at the maximum distance away from Algol and is approaching Algol.  Every time an eclipse occurs the Earth is closer to Algol.  This means that the period of time between eclipses will be shorter.  93.5 years later, when the Earth is closest to Algol, the Earth will start receiving those eclipses.  So we would have the strange effect of having a shorter period of time between eclipses as the Earth is moving away from Algol.
 

Which is why the Relativistic model of Doppler shift is the only valid one.   If you assume that light travels at a fixed speed relative to the source and not so to the receiver, you get one answer for Doppler shift, if you assume that The light travels at a fixed speed relative to the receiver and to the source you get another answer.  If you assume that light travels at a fixed speed relative to both as measure by both (due to the fact that receiver and source measure time and space differently due to their relative motion), then you get a third answer.
And as I've already indicated, we have done experiments to find out which model gives the correct answer, and the Relativistic model came out the winner.
This was demonstrated some yeas ago with in a practical situation.  NASA had sent a pair of probes to one of the moons of one of the gas giants.    One of pair was a lander and the other an orbiter. The lander would send info to the orbiter to be relayed back to Earth.  The problem was that there was a glitch in the communication between the two.  A communication protocol had been set up that required a very narrow frequency tolerance between the two and they were offset from each each other and they couldn't talk back and forth.   The solution they came up with was to adjust the orbit of the probe so that when it was receiving from the lander, their relative velocity was just the right magnitude for Doppler shift to correct for the offset. 

So here's the thing.  Relativistic Doppler shift only depends on the relative velocity difference between source and receiver, while a model that assumes that the speed of light relative to the one doing the measuring depends on it motion, then the Doppler shift depends on both the  source's and receiver's motion with respect to some fixed frame.  Now we are dealing with an receiver which is orbiting a moon, which is in turn orbiting a planet, which in turn is orbiting the Sun.   This means that after every orbit of the probe, the Moon will have moved some in its orbit and will be moving at a slightly different velocity relative top the Sun than is was before, this means that both the Orbiter's and lander's velocities will have changed, which in turn changes the Doppler shift.  Thus in order to keep the shift to the precise value needed for the correction, NASA would have had keep adjusting the orbiter's orbit.   They didn't. (If they had, it would have meant that there was something amiss with the prediction of Relativistic Doppler shift and there would have been quite a stir in scientific circles.)

The problem you are having is that you are trying to apply Newtonian physics to a universe that operates by Einsteinian rules.
 The Earth measures light coming from Algol as moving at c relative to the Earth both when it is moving towards and away from Algol.  The Earth now has a different velocity relative to the Earth 6 months from now or 6 months ago, and thus measures time and space differently. (This is the whole gist of Relativity, it involves a whole new model for space and time than Newtonian Physics uses.)

[Fruityloop (OP)]

How was NASA able to use the relativistic doppler shift equation when the speeds involved are so small compared to the speed of light?

[Janus]

How was NASA able to use the relativistic doppler shift equation when the speeds involved are so small compared to the speed of light?

It's not like Relativistic Doppler shift just "kicks in" at some given velocity.  Relativistic Doppler shift is found by

 where beta = v/c, and v is the relative velocity between source and receiver.
There is no lower limit for v when using this equation.
"Classic" Doppler shift is expressed in this form:


In this case v_r and v_s are the respective velocities of the receiver and source to the frame which light travels at c relative to.

The point is that v in the first equation ( the orbital velocity of the orbiter to lander) is much smaller than the changes in v_r and v_s caused by the orbits of the the planet and moon in the second equation.  Thus these would have had a larger effect on the Doppler shift than was allowed for by NASA.  If NASA had used the wrong equation to work out the needed adjustment, it wouldn't have worked, and it did work.

NASA had a problem. They applied a solution. That solution involved using the presently accepted model for Doppler shift which uses the first equation I gave above, and that solution solved the problem.  Or are you claiming that NASA has been lying about this.



The point is that Relativistic Doppler shift only

[jeffreyH]

@Fruityloop Janus has given valid answers to your questions. It would be to your advantage to take them on board.