# The velocity of light

1. May 13, 2004

### David

Einstein said in his 1916 book:

”If an observer sitting in the position M1 in the train did not possess this velocity, then he would remain permanently at M, and the light rays emitted by the flashes of lightning A and B would reach him simultaneously, i.e. they would meet just where he is situated. Now in reality (considered with reference to the railway embankment) he is hastening towards the beam of light coming from B, whilst he is riding on ahead of the beam of light coming from A. Hence the observer will see the beam of light emitted from B earlier than he will see that emitted from A.”

What Einstein means by “he is hastening towards the beam of light coming from B” is that the light beam from the flash at B is converging on the observer that is moving toward B at the relative velocity of c + v, with v being the velocity of the observer toward B. What he means by “he is riding on ahead of the beam of light coming from A” means the light from the A flash is converging on the observer at the velocity of c – v.

This is very simple. The observer-relative speed of the light, relative to the moving observer is NOT “c”, it is NOT constant. It is c + v in one direction and c – v in the other direction.

This is why the earth sees a blueshift in the light of the star the earth is moving toward in its revolution around the sun and this is why the earth sees a redshift in the light of a star the earth is moving away from during its revolution around the sun. This is caused by the Second Cause of the Doppler effects that I told you about earlier. This is a Doppler Law of Physics. It can not be revoked.

2. May 14, 2004

### yogi

David - I do not think your conclusions about what Einstein was saying are consistent with SR - it is true that signals sent from sources you are approaching and those sent from sources from which you are receding will arrive at different times if they are sent when you are midway between them, you would nonetheless in SR measure both signals to have the same relative velocity c with respect to you according to SR.

That you may doubt whether SR is correct in making that postulate is another question - these were Einstein's conventions - but this particular "one way isotrophy" convention does not get tested in most experiments - what we test is over and back effects - the transformation that leads to one way isotrophy (the vx/c^2 term) doesn't appear in the interval - and it is the constancy of the interval that we commonly use to calculate time dilation, length contraction, mass increase etc. The interval can be arrived at without the one-way isotrophy postulate (for example the light clock which we have just rambled through on another thread gives you the (1-v^2/c^2)^1/2 directly, so therefore it is not inconsistent to believe in all the the successes of SR and still have doubts about the necessity and correctness of the second postulate.

Regards. Yogi (One of the cranks)

3. May 14, 2004

### David

No need to play around with word games or tricky thought experiments with me. That type of stuff doesn’t work on me. I’m talking about “physics”, not “science fiction stories”. And this is a “physics” board, not a “Si-Fi” board.

The reason the guy on the moving train will see the B flash first is because he is moving toward B and thus he and the light beam from B are converging on each other at the additive light-speed velocity of c + v. That’s a basic law of physics and of nature, and it’s a basic Doppler Law. That’s why the guy on the train will see the light as blueshifted, even though the waves of light are not “compressed” in the space between B and the moving observer.

4. May 14, 2004

Staff Emeritus
I’m talking about “physics”, not “science fiction stories”.

Good for you.

The reason the guy on the moving train will see the B flash first is because he is moving toward B and thus he and the light beam from B are converging on each other at the additive light-speed velocity of c + v. That’s a basic law of physics and of nature, and it’s a basic Doppler Law.

Oops, you just slid into sci-fi. Your "basic law of physics" is only an approximation, valid at low speeds.

5. May 14, 2004

### David

Max Born, Nobel Prize winner, writing in “Einstein’s Theory of Relativity”, 1962 edition:

“The fact that the observed frequency of a wave depends on the
motion both of the source of light and of the observer, each with
respect to the intervening medium, was discovered by Christian
Doppler (1842), The phenomenon may easily be observed in the
case of sound waves. The whistle of a locomotive seems higher when
it is approaching the observer and becomes deeper at the moment of
passing. The rapidly approaching source of sound carries the
individual phases of the waves forward so that the crests and hollows
succeed each other more rapidly. The motion of an observer to-
wards the source has a similar effect; he then receives the waves in
more rapid succession
.

Now the same phenomenon must hold in the case of light
.”

(snip)

Born continues:

"This relation between the frequencies f and f’ shows how the frequency is diminished when the observer has a velocity v in the direction of the light. From (40) and (41) one obtains the obvious result

c’ = c – v"

Born knew this and I know this. All the scientists of the 19th Century and during the first 60 years of the 20th Century knew this.

This is why the earth observes a redshift in the light coming from a star that is fixed relative to the sun, when the earth is moving away from the star as the earth revolves around the sun.

This is a completely different reason than the reason why the earth observes a redshift when the star itself is moving away from the earth. The first reason I gave is due to the c – v effect, as explained by Max Born, the Nobel Prize winner. The second reason is due to the starlight wavelength being physically stretched out in space. Unfortunately, only one reason or cause for the Doppler effects is taught in school today, while the other reason is ignored.

6. May 14, 2004

### ahrkron

Staff Emeritus
Some things have happened since then, one would expect.

7. May 14, 2004

### Staff: Mentor

Read the relativity section! - LOL

How convenient that you stopped quoting at this point! :rofl:

Just two sentences later, Born goes on to say (emphasis mine):
"But we have chosen a method using the invariance of the number of waves becaused they can be used later in the theory of relativity. There we will see that the relations c' = c - v and λ' = λ are not at all self-evident but are actually replaced by others."​

Stop playing games. The section you are quoting is Born's treatment of the classical pre-relativity Doppler effect. Why not read the section where he treats it relativistically?

8. May 14, 2004

### David

If you choose a method of “using the invariance of the number of waves”, then you are being misleading, because the number of waves per second (ie the “frequency” shifts) are caused by two different reasons, as I’ve explained. Of course, you can ignore the reasons if you wish.

9. May 14, 2004

### David

Doc,

So, if you ignore the two different reasons, and if the standard model of a redshift caused by a star that is moving away from the earth is due to a "physical lengthening" of the wavelengths of the light coming from the star, then how would you use SR theory to explain the redshift observed at the earth and caused by the earth moving away from a star that is fixed relative to the sun?

10. May 15, 2004

### Staff: Mentor

David, you are the one quoting Nobel-prize winner Max Born. If you disagree with what he's saying, why quote him?

It is quite sad that you repeatedly attempt an argument from authority by quoting Einstein and Born--as if those guys didn't understand relativity and would agree with your misconceptions.

11. May 15, 2004

### David

Doc, et al,

How would you use SR theory to explain the redshift of starlight observed at the earth as the earth revolves around the sun, and caused by the earth moving away from a star that is fixed relative to the sun?

12. May 15, 2004

### Staff: Mentor

relativistic Doppler formula

Here's the relativistic Doppler formula:
$$\nu_{observed} = \nu_{source}\sqrt{\frac{1 + \frac{v}{c}}{1 - \frac{v}{c}}}$$
Where v is the relative speed of the source and observer: v is positive when the source is approaching the observer. In the case you mention, v is negative, thus a "red shift" is observed.

For a derivation, check Born's book.

13. May 15, 2004

### David

My question was, “How would you use SR theory to explain the redshift of starlight observed at the earth as the earth revolves around the sun, and caused by the earth moving away from a star that is fixed relative to the sun?”

I didn’t ask you for the amount of redshift.

Your equation gives the amount of shift, but where in the equation does it reveal if the shift is caused by a wavelength change or an observer-relative light velocity change?

You will recall that there are two separate causes of Doppler shifts: 1) wavelength change (moving emitter), 2) observer-relative wave speed change (moving observer).

Since the star is fixed relative to the sun, that leaves out a wavelength change. Where in your equation does it say that Doppler Cause #2 is the one that causes the shift when the earth is moving relative to the star?

Doppler Law provides a definite answer to this question.

14. May 16, 2004

### David

You make this stuff up faster than anyone can refute it.

From the light’s point of view, there is always distance. That’s why it takes light time to get from one place to another. Light doesn’t have a personal opinion, it just moves, and it moves over a great distance to get from star to star. Light and radio waves wouldn’t have “wavelengths” if there was “no distance” from the light’s point of view.

15. May 16, 2004

### David

Oh, come on! Many distant galaxies exhibit redshifts that indicate they are moving away from the earth at 2, 3, 4, and 5 c.

The Davis-Lineweaver paper tells how their light reaches us from the superluminal galaxies.

You are living in the past. This is not 1905, this is the 21st Century. You are just posting 100 year old rumors, superstitions, and urban legends.

16. May 17, 2004

### Staff: Mentor

Yes, interesting stuff! Note that the authors claim no contradiction with SR, since those galaxies are outside our inertial frame. I am not qualified to provide a detailed analysis of that paper, since I am no expert on general relativity. (Perhaps an expert can comment?) But I believe it is commonly understood that the cosmological redshift can only be understood via general relativity: special relativity cannot be applied on a cosmological scale. You cannot interpret the cosmological redshift as a relativistic doppler shift --- or any kind of doppler shift.
Well, I don't know about that. It seems that you're the one who hasn't yet caught up to special relativity. You still cling to the quaint pre-relativistic "Doppler Law".

17. May 17, 2004

### jcsd

This is due to general relativity which hasn't been mentioned so far, you have to realize that special relatvity is the special case of general relatvity. The reason why it hasn't been mentioned so far is the fact that in all the examples given there's been no reason to assume any significant deviation from the Minowski metric, so only the special case needs to be considered.

It is wrong to call these galaxies superluminal as it implies something that's not happening as their local coordinate velocity is still less than c in all (local, obviously) inertial rference frames. The red shift isn't due to relative motion between the two objects but the expansion of space.

Last edited: May 17, 2004
18. May 17, 2004

### David

Look, when you run away from me at 5 mph, you are “moving” away from me.

If you get in a car and move away from me at 60 mph, you are still “moving” away from me, even though you can say you are being “carried along” by the car.

The fact is, Lorentz invented the “speed limit” in 1895, and it was his limit for the speed of “ponderable bodies” through the “universal ether”. Einstein adapted it in 1905 to be the “speed limit” for “space”.

All the astronomy books, going back to the early 1930s, said the galaxies were “moving through space”, right up until the 1980s or ‘90s, when the first astronomer found the first superluminal galaxy, then all of a sudden the “expanding space” idea was invented. Now none of the galaxies are “moving” but are being “carried along” by “expanding space.”

Look, I’m an older guy. I’ve learned in life why some people in some fields tell one story for 50-60 years, then all of a sudden they change the story. This galaxy-motion story was changed in the 1990s in an attempt to try to salvage the 1905 “constancy” postulate, after superluminal galaxies were finally discovered.

And let me tell you something else. When I studied astronomy in 1956, when I was in junior high school, and when I built a 6 inch telescope, and when I saw Mars during its close approach that year, all the astronomy books and school science textbooks I could find said there were “green plants” growing all over the surface of Mars. This story had been told for more than a hundred years, until we finally sent a rocket to Mars and saw no “green plants” growing on it. Turns out the “green” was just an optical illusion, with green being the negative of red (reddish orange) and so the dark areas of the reddish Martian desert looked a little greenish through earth-based telescopes. So I feel I have the right to challenge any unreasonable theory, such as the “expansion of space” theory that is supposed to "carry along" the "unmoving galaxies", which is new and is just used as a device to salvage the “constancy” postulate, since superluminal galaxies were finally discovered.

Now, if you apply this information to the basic Lorentz theory, what do you have? How can you relate what we observe to the original Lorentz concept of a “speed limit”. Think of what he originally said, think of the limit to how fast we can push particles here on earth, and how fast the distant galaxies are moving, and what do you have? The implication is very important, but no one has written any science papers about it yet.

19. May 17, 2004

### David

LOL, yes, D&L were very diplomatic! They basically disproved the SR “constancy” postulate, but they said they didn’t contradict SR. Very clever. Maybe I should take that approach.

Did you like the part of their paper where they said that newly-emitted photons in superluminal galaxies are traveling backwards, away from the earth, for thousands of years, then the photons finally slow down their backward movement and gradually start traveling toward the earth? I just loved that part.

Nope, it's a Doppler shift.

SR originally was supposed to apply to a cosmological scale, but Einstein later realized it didn’t.

I think it would help you if you read some of his other papers, other than the few that were published in “The Principle of Relativity”. His earliest papers are the most interesting, but some of them contained stuff that he later changed and amended. Like any scientist, he learned more the older he became, and the older he became the more he learned.

There are certain things about the Doppler Law that can not be changed. The TWO fundamental reasons for the shifts, for example.

What Lorentz did was ADD some quantum electrodynamics stuff to the Doppler Laws, regarding oscillating atoms moving through fields. Lorentz was the one who invented the “relativistic” Doppler shift, which includes the two Doppler Laws, plus the electrodynamic effects on oscillating atoms moving through fields. At first, in 1905, Einstein mistook the electrodynamical effect for a “kinematical” effect, but he later realized his error and made changes accordingly, such as in his 1911 and 1916 papers. Those papers do consider the Lorentzian electrodynamical effects on moving atoms. In fact, the “Electrodynamic” part of the 1905 paper considers those effects, but the “Kinematical” part does not. I can explain the difference in the two parts if you would like for me to.

20. May 17, 2004

### DrChinese

What you are saying is reasonable on the surface, but...

If science is doing its job, then we will converge on a progressively better set of theories to describe nature. This appears to be happening - we are moving forward, not backward. Lineweaver and Davis, as strange as it is (and it certainly is strange to me), is not actually violating anything we had set in stone for decades anyway. After all, the expansion of space (Guth's inflation) was postulated a long time ago, so evidence confirming it shouldn't be a total surprise. (Even if it is weird. Not any weirder than QM, think?)

So it is not really a strong argument to point out past errors in scientific history and try to extrapolate from those. The CMBR was discovered around 1965, QM in 1927 and GR in 1915. There is a lot explained by these big 3.

Clearly the special relativistic formulas have been tested many times, including frequency shift due to relative motion. Not sure how you can argue that point. If two objects were each approaching a common midpoint at a substantial percentage of the speed of light, they will in fact approach each other faster than the speed of light measured by some observers. But light they emit cannot be measured to have a speed of any other value than c by any observer. Do you dispute that?

21. May 17, 2004

### David

Actually it was Newton who first suggested the expansion of the universe and the big bang theory. He called it a “projectile impulse”. He proposed 4 possible conditions of the universe: 1) contraction, 2) expansion, 3) infinite, 4) rotation.

He was right about two of those; rotation on a local scale and expansion on the large scale.

The Davis Lineweaver paper is essentially a “local ether” theory, with their term local “comoving space” acting as the “ether”, although they don’t define what gives local comoving space ether-like qualities.
What I find most amusing about their paper is when the light from a distant superluminal galaxy moves backwards away from the earth before it moves forwards toward the earth.

22. May 17, 2004

### David

Apparent frequency shift due to relative motion is a Doppler effect, explained by Doppler in 1841.

The oscillation rate slow-down in atoms moving through fields is an electrodynamics effect, explained by Lorentz in 1895.

There is no “wristwatch” or “balance clock” slow-down due to “relative motion” as “predicted” in SR theory, because “relative motion” does not cause balance wheel wristwatches or balance wheel clocks to slow down.

23. May 18, 2004

### jcsd

I'm sorry but you really couldn't be more wrong:

Friedmann Lemaitre cosmology has been around since the 1920's and was taken up after Hubble found the redshift in the 1940's, so basically it's always been the case that redshift has been attributed to the expansion of space.

What you also don't underdstand is that red shift can't be attributed to any superluminal velocity in special relativity as the equation is:

$$\frac{\lambda}{\lambda_0} = z + 1 = \sqrt{\frac{c+v}{c-v}}$$

In the case where $v > c$ you find that $\lambda$ is an imaginary quantity! Let me tell you that the wavelengths that we measure from these galaxies with superluminal recession velocity are NOT imaginary.

It's only when you take into account the fact that space is expanding and use general relativity that you find that galaxies may have superluminal recession velocities.

24. May 18, 2004

### DrChinese

I specified I was discussing Guth's inflationary scenario, not the general expansion of space.

Yes, I agree with you about D&L: at first it seems counterintuitive that the light gets farther away before it finally begins to get closer. However, after I thought about it a while, I realized that something like what they describe must occur if we can see older galaxies at all.

Assume NO ongoing superluminal expansion/inflation: Suppose you had a galaxy emitting light at T=1 billion (years after BB). If we are now at T=13.7, we would have to be exactly 12.7 billion years away from it to see it now if there were no ongoing inflation. But at T=1 billion we couldn't have been far enough away from that galaxy for it to take more than a couple of billion years for that light to arrive. Something had to have slowed it down for us to see it today. Either that, or our calibration of the age of universe/our position and velocity through space/etc. are WAY off.

25. May 18, 2004

### DrChinese

Well said. As you point out, it is easy to confuse SR scenarios with GR scenarios.

Davis & Lineweaver does not introduce any new physics that I am aware of. I think it is really putting everything together in a package that ties it all together nicely. So I don't agree with David's dismissal of their content. The fact is that superluminal (high redshift) galaxies have been observed, and that renders most objections moot. D&L explain why this is consistent with both SR and GR.