You need to recognize that c+v and c-v are just expressions in the math. They do not need relativistic velocity addition.

You let yourself fool by the magomathician of mathpages.com, but you won't fool me. Just like c and v are physical quantities, c + v and c - v are physical quantities, too. We're talking about physical theories as a description of reality and not about some nonsensical and meaningless formulae.

c is a velocity. v is a velocity. Velocities are physical quantities. Adding two physical quantities of the same type yields a physical quantity of that type.

Classically, the terms c + v and c - v represent the speed of light with respect to the aether.

In Special Relativity, the terms c + v and c - v are illegal. You have to use relativistic addition instead, which is derived from the Lorentz transform.

The (mathpages.com)-author says that they are "the sum and difference of the speed of light and the speed of some other object, both with respect to a single inertial coordinate system". He deceives by embezzling that the sum of the two speeds in Special Relativity is calculated using (c + v) / (1 + (cv)/c^2).

Point a lightbeam in one direction, and you have light moving at c. Throw a stone in the other direction, and you have a stone moving at v. Given Special Relativity, the light does not move at c + v with respect to the stone, but at (c + v) / (1 + (cv)/c^2) = c.

Point a lightbeam in one direction, and you have light moving at c. Throw a stone in the same direction, and you have a stone moving at v. Given Special Relativity, the light does not move at c - v with respect to the stone, but at (c - v) / (1 - (cv)/c^2) = c.

The same happens in the "stationary circular loop" (optic gyroscope) of the mathpages author. The observer at the fixed start point has one of the beams moving away in one direction while the endpoint moves in the opposite direction. c + v then is the classical speed of the light beam with respect to the end point, while in Special Relativity the speed of the light beam with respect to the end point is (c + v) / (1 + (cv)/c^2) = c.




Conclusion: The mathpages author tries to sell his readers the classical maths as relativistic maths. Unfortunatly for him, one can easily see through his deception. Everyone knows that nothing moves faster than light in Special Relativity.

Correction of post #60

Classically, the terms c + v and c - v represent the speed of light with respect to the aether.
Classically, the terms c + v and c - v represent the speed of light with respect to the observer.

In MM, light is sent along arms perpendicular and parallel to presumed motion with respect to the ether. Assuming the arms are equal length, with Lorentz contraction, the time parallel to motion turns out to be the same as the time perpendicular to motion. You can find this derivation on the web and in most undergrad physics textbooks that deal with relativity.

In a Sagnac device, light is sent along a rectangle in opposing directions. As I recall, the set it up so two sides of the rectangle were parallel to lines of latitude, and a fair distance apart. At different latitudes, they move due to earth's rotation and different speeds. Thus the light paths clockwise and counterclockwise are not equivalent. I didn't find this on the internet, but it works out. (It is a bit of algebra.) With Lorentz contraction you just get an extra factor close to 1 multiplying the time difference. Like I've been saying, this doesn't change the Sagnac results in any meaningful way.

Yes, the interferometers are not of the same type. They're all different. Sagnac, Michelson-Gale, Michelson-Morley, mathpages-fiber optic gyroscope. But that's not the point. The point is rather:

The Michelson-Gale experiment detects and measures the relative speed of the Michelson-Gale interferometer moving around the center of the earth. The Michelson-Morley experiment detects and measures the relative speed of the Michelson-Morley interferometer moving around the center of the sun --- ah, no, no, no, the Michelson-Morley interferometer does not detect any movement. The question is: Given Special Relativity, why is it possible (in principle, whichever type of interferometer used) to detect the relative movement of the apparatus around the center of the earth, but not the relative movement of the apparatus around the center of the sun? What is the difference between the two types of movement, that gives the reason why we do have an experiment to detect one while we do not have an experiment to detect the other. Aren't both movements in principle equal: An apparatus is moving around a distant center of some object. Shouldn't Special Relativity allow to detect either both movements or none? What's the problem of Dr Michelson? Why did he succeed in detecting one movement but not the other?

Neither the word 'earth' nor the word 'sun' appear in the postulates or the formulae of special relativity. Yet we have a strange asymmetry.

And again regarding c+v and c-v. Light goes at speed c in my reference frame.

Ok, light goes at c in your reference frame (and in any other reference frame).

If I have a target L1=100m away, it takes time t1=L1/c to get there. If I have another target at L2=101m, it takes t2=L2/c to get there. Believe it or not, that's true in relativity, too!

Yes, it is.

It doesn't matter if in the target was moving at speed v and happened to be at L2=101m when the light got there. Both the light (always moving at c) and the target (at v) are moving in my reference frame.

That's true.

But given the experiment on mathpages, the observer is the screen which shows the fringes (called 'end point' there). The target is that screen. The target is moving with respect to the reference frame which you called yours above (the one where the light source is fixed, called 'start point' there). Now, in Special Relativity, light moves at speed c with respect to the reference system where the light source is fixed, and at the same time also moves at speed c with respect to the reference system, where the screen is fixed. Sounds strange? Yes, sure. But that's the way it is in Special Relativity. Light moves at speed c with respect to both (to any) reference systems.

So I have a target at L and it's moving away at v, and light takes time t to reach it. While the light travelled a distance ct in my reference frame, the target travelled a distance vt and is now L+vt away in my reference frame. From ct = L+vt you get t = L/(c-v), even though light was always going at speed c.

Yes, the light is going at speed c with respect to the reference system where the start point rests. And with respect to the reference system where the end point rests, it is going at c + v (or c - v for the other beam). That's  classically correct. But in Special Relativity, it has to be c (or c for the other beam). Because in Special Relativity light never goes faster than c but rather always equal to c, neither in the reference system of the start point nor in the reference system of the end point.

That's the reason why the mathpages-guy in the case of Special Relativity should replace c + v and c - v by c and c yielding zero displacement in fringes.


Special Relativity was designed to yield zero displacement in fringes for the Michelson-Morley experiment. No wonder that it yields zero displacement in fringes for the Michelson-Gale experiment, too. In principle, there is no difference between both experiments. A device moves around a distant point. Special Relativity knows nothing about planets, masses, or the solar system. How could Special Relativity be able to distinguish between a movement of an interferometer around the center of the earth and one around the center of the sun?

Short answer is the some devices measure translation, while other measure rotation. Translation is relative in SR, but rotation is not considered relative in SR for various reasons. A Sagnac device (and MGP is a Sagnac device) measures rotation.No, he shouldn't. Dont mix the lab frame and the loop frame. (Sometimes you'll see people say the axis of rotation of the sagnac device - that's the lab frame.)

Now you start a new approach. But that does not work: The Michelson & Gale interferometer basically is in orbit around the center of the earth and the Michelson and Morley interferometer basically is in orbit around the center of the sun. No reason to distinguish rotation and translation here.

Also: Are you now attacking the mathpages-guy who does not care about rotation. He does not even treat a Sagnac disc with piecewise linear light paths, rather he uses a fiber optic gyroscope where even the light runs in circles.

You just show that you're getting desperate.

Because the light pulses get to the end point at different times, you have to be careful how you treat time when changing frames in relativity. Synchronized clocks in one frame will not generally be synchronized in the other frame.

You and the mathpages-guy, you're not careful and treat the whole thing classically. I showed you how to do it: You need the relativistic addition of velocities to get the correct speed of light with respect to both reference frames.

Also: Are you now attacking the mathpages-guy, who does not mention clock synchronization?

Finally: Clock synchronization? What are you referring to? To synchronize clocks, you would need at least two of them. I  have never heard of one. Not even one clock is used in the experiments. The mathpages-guy seems to not know about clocks either.


C'mon, Stanley N, give it up. You're really getting desperate.

"Clocks" are device in SR for handling time-relative events. Sagnac devices concern events happening at different "times", so you do need to take some care with that.

Let me explain how interferometers work in the experiments we are talking about.

A light beam is split using a beam splitter, that is a partially reflecting mirror. Each of both beams then travels a different path until they are recombined. The recombined beam is the sum of two possibly shifted parts of the original beam. Its amplitude is greater or lower due to interference. In this way, the measurement is done continuously. There are no events happening, and there are no clocks to determine points in time when events happen. Given that there are no clocks, no two or more clocks can be or need to be synchronized.

At this point in our discussion, any reader can see that you are trying to fool us. You demand synchronization of clocks where there are no such devices.

You demand synchronization of clocks where there are no such devices.

Clocks, again, are conceptual devices in understanding time differences in SR. And the way we've been discussing sagnac devices is by way of a time difference in the lab frame. You seemed to want to go to the loop frame. If you really don't know anything about "clocks" or the equivalent, I suppose it would be difficult for you to see why they might be relevant. The "mathpages" author pretty much stays in the lab frame.

In the future, please refrain from slurs and personal attacks.

This film is basically an abridged version of Journey to the Center of the Universe, although some things appear new. I don't think JCU mentioned Shankland vs. Miller, for example.

If you really don't know anything about "clocks" or the equivalent, I suppose it would be difficult for you to see why they might be relevant.

As was shown, you're the one who doesn't know anything about clocks in Special Relativity.

In the future, please refrain from slurs and personal attacks.

Please allow me to continue to pay back in your currency.