Measuring Speed of Light: Transit Time & Interference

[dom_quixote]

The methods of measuring the speed of light are based on the transit time of light to and from a certain path.
In this way, apparently there is no way to measure the forward speed and the return speed separately and if these speeds are the same.

Light is an electromagnetic wave located in the sensitive range of the human eye.

Electromagnetic microwaves, also known as quasi-optical waves, propagate in vacuum, air, waveguides and bifilar metallic transmission lines.

There is an experiment that allows you to determine the length of a microwave in a bifilar transmission line.

The principle involves reflection and interference of electromagnetic waves. Interference results in the addition of waves (antinodes) and subtraction (nodes) in very well defined space intervals along the transmission line.

If the microwave round trip speeds on the line had different speeds, it would be expected that the nodes and antinodes would constantly change position along the transmission line.

 

[berkeman]

Do you have a technical reference and a question? Thanks.

 

[russ_watters]

This is a Relativity question so I'll move the thread to that forum. Not a physicist but my understanding is that it is inherently impossible to test the one-way speed of light. One will explain....

 

[Dale]

If the microwave round trip speeds on the line had different speeds, it would be expected that the nodes and antinodes would constantly change position along the transmission line.

That would only be expected if one didn’t do the math. If one does the math one would find that the predictions match.

This is easy to state because phase is a relativistic invariant so it cannot be changed under a coordinate transformation, and changing the one way speed of light is merely a coordinate transformation

 

[Nugatory]

This thread is about whether creating a standing wave in a fixed-length wave guise is sufficient to measure the one-way speed of light. Discussion of that question is welcome here.

Several interesting posts about people being to see into the near-IR have been removed from this thread. They will show up in their own thread soon.

 

[Ibix]

@Dale's answer is the shortcut to the result.

To flesh it out a bit, realise that picking an anisotropic speed of light is just mucking around with your simultaneity convention. With a changed definition of "at the same time" all points on the wave are no longer at the same phase at the same time. But the nodes and antinodes do not reposition themselves or start to move. So you'll find that the timings of the peaks of the antinodes do flow in the direction you chose as the slower speed of light, but the flow is faster than the slow speed (in fact, I think it is at the speed you chose as the faster speed of light edit: nope, see #11), yet the waves do not move: the nodes are always in the same place and the antinodes are always in the same place.

 

[dom_quixote]

Do you have a technical reference and a question? Thanks.

The technical reference can be found in any standing wave class.
My question is the following:
Can the proposed experiment verify redshift in the laboratory?

 

[Ibix]

Can the proposed experiment verify redshift in the laboratory?

There's no redshift here in any coordinate system.

 

[vanhees71]

This thread is about whether creating a standing wave in a fixed-length wave guise is sufficient to measure the one-way speed of light. Discussion of that question is welcome here.

Several interesting posts about people being to see into the near-IR have been removed from this thread. They will show up in their own thread soon.

How can a standing wave measure the one-way-speed of light? After all it's a superposition of two waves moving in opposite directions ;-)).

 

[Dale]

The technical reference can be found in any standing wave class.

I call complete BS on this. Please post this supposed “standing wave class” where a varying one way speed of light is shown to produce “nodes and antinodes would constantly change position along the transmission line”.

I doubt any such claim is ever made in an actual class, and if it is made it certainly cannot be backed up with correct math.

Can the proposed experiment verify redshift in the laboratory?

No. As I said earlier, a coordinate transform cannot change the outcome of any experiment.

 

[Ibix]

Here's a Minkowski diagram of the experiment. As usual, time is up the page and x position across; the blue lines represent the worldlines of the reflectors and orange lines the worldlines of successive wavecrests of the left- and right-moving waves.

You can see that wavecrests meet simultaneously (meaning that antinodes reach their maximum amplitude simultaneously) since their crossings form horizontal lines. You can see that the maxima happen in the same places because they also form vertical lines.

Now let's switch to an anisotropic light speed convention. All this does is shear the diagram:

I'm afraid my Minkowski diagram software isn't set up to do this so it's simply the original diagram sheared in an art package. In particular, please note that simultaneity in this revised diagram is still represented by horizontal lines - the sloped (and therefore non-simultaneous) x-axis is how this coordinate system draws the original frame's x axis.

You can see that the wavecrests no longer meet simultaneously since the crossing points do not form horizontal lines. They still form vertical lines, though, so the crossing points do not move. (Note that I was wrong to say that the timings of the amplitude maxima flow at the speed of the faster speed of light - they flow much faster than that, at the implied speed of the x-axis of the original frame. You can figure out what that is in terms of your faster and slower light speeds if you want.)

 

[dom_quixote]

Here's a Minkowski diagram of the experiment. As usual, time is up the page and x position across; the blue lines represent the worldlines of the reflectors and orange lines the worldlines of successive wavecrests of the left- and right-moving waves.
View attachment 328475
You can see that wavecrests meet simultaneously (meaning that antinodes reach their maximum amplitude simultaneously) since their crossings form horizontal lines. You can see that the maxima happen in the same places because they also form vertical lines.

Now let's switch to an anisotropic light speed convention. All this does is shear the diagram:
View attachment 328478
I'm afraid my Minkowski diagram software isn't set up to do this so it's simply the original diagram sheared in an art package. In particular, please note that simultaneity in this revised diagram is still represented by horizontal lines - the sloped (and therefore non-simultaneous) x-axis is how this coordinate system draws the original frame's x axis.

You can see that the wavecrests no longer meet simultaneously since the crossing points do not form horizontal lines. They still form vertical lines, though, so the crossing points do not move. (Note that I was wrong to say that the timings of the amplitude maxima flow at the speed of the faster speed of light - they flow much faster than that, at the implied speed of the x-axis of the original frame. You can figure out what that is in terms of your faster and slower light speeds if you want.)

Ibix,
Thanks for the illustrations.
Unfortunately, I was unable to interpret the Minkowsky diagram, performed with reflecting mirrors.

Below, I send a didactic video with the experiment of stationary radio waves in the VHF band, starting point for the hypothesis of the displacement of the nodes and antinodes of the standing wave.



To demonstrate standing electromagnetic waves and how transmission lines work using a solid state transmitter.

 

[Dale]

a didactic video

I missed the part where they did the math to derive how that experiment would differ with different one way speeds of light. Could you post the timestamp?

That would only be expected if one didn’t do the math. If one does the math one would find that the predictions match.

This is easy to state because phase is a relativistic invariant so it cannot be changed under a coordinate transformation, and changing the one way speed of light is merely a coordinate transformation

The video simply is not relevant to the issue at hand. You are making a claim that a change in the OWSOL would somehow alter the standing wave pattern. You have yet to substantiate that claim. I have provided a first-principles reason why the claim is wrong, @Ibix provided both a more detailed reason and an image showing why the claim is wrong. This video does not show the contrary.

 

[vanhees71]

Here's a Minkowski diagram of the experiment. As usual, time is up the page and x position across; the blue lines represent the worldlines of the reflectors and orange lines the worldlines of successive wavecrests of the left- and right-moving waves.
View attachment 328475
You can see that wavecrests meet simultaneously (meaning that antinodes reach their maximum amplitude simultaneously) since their crossings form horizontal lines. You can see that the maxima happen in the same places because they also form vertical lines.

Now let's switch to an anisotropic light speed convention. All this does is shear the diagram:
View attachment 328478
I'm afraid my Minkowski diagram software isn't set up to do this so it's simply the original diagram sheared in an art package. In particular, please note that simultaneity in this revised diagram is still represented by horizontal lines - the sloped (and therefore non-simultaneous) x-axis is how this coordinate system draws the original frame's x axis.

You can see that the wavecrests no longer meet simultaneously since the crossing points do not form horizontal lines. They still form vertical lines, though, so the crossing points do not move. (Note that I was wrong to say that the timings of the amplitude maxima flow at the speed of the faster speed of light - they flow much faster than that, at the implied speed of the x-axis of the original frame. You can figure out what that is in terms of your faster and slower light speeds if you want.)

One should, however be aware that Minkowski diagrams are constructed by definition according to the standard Einstein synchronization convention, i.e., using the "two-way-speed of light" in the usual way. Maybe that's why I don't understand, why the 2nd diagram should depict an "anisotropic lightspeed convention". Do you mean an "anisotropic synchronization convention"? If so, then the 2nd diagram is, however, not a Minkowski diagram anymore.

 

[Dale]

As a quick summary of the actual math for this experiment, use Minkowski coordinates $(t,x,y,z)$ and Anderson coordinates $(T,X,Y,Z)$ with parameter $\kappa$. This leads to the following coordinate transforms (in units where $c=1$) $$T = t-\kappa x$$ $$X=x$$ $$Y=y$$ $$Z=z$$ with the corresponding one way speeds of light (in the $x$ direction) $$c_+=\frac{1}{1-\kappa}$$ $$c_-=\frac{1}{1+\kappa}$$

The position four-vectors are $r^\mu=(t,x,y,z)$ and $R^\mu=(T,X,Y,Z)$. Now for a travelling plane wave in the $x=X$ direction the wave four-vector is $$k^\mu(r) = (\omega, k, 0, 0) $$ $$K^\mu(R)=(\omega-\kappa k, k, 0,0)$$ The travelling waves in the $-x=-X$ directions are obtained by setting $k=-k$, and the standing wave is the sum of the two.

The phase of the forward travelling wave is denoted $\phi_+$ and the phase of the backward travelling wave is denoted $\phi_-$ which are obtained as $$\phi_\pm = k^\mu r_\mu = \pm k x - t \omega$$ The nodes are obtained by solving the equation $$\phi_+ - \phi_- = n 2\pi$$ $$x=\frac{n \pi}{k}$$ Similarly in the Anderson coordinates $$\phi_\pm = K^\mu R_\mu = \pm k X - (T + X \kappa) \omega$$ And again the nodes are obtained by solving the equation $$\phi_+ - \phi_- = n 2\pi$$ $$X=\frac{n \pi}{k}$$

Since $x=X$ the position of the nodes is not a function of $\kappa$ and their values are unchanged when changing the one way speed of light.

 

[Ibix]

Do you mean an "anisotropic synchronization convention"? If so, then the 2nd diagram is, however, not a Minkowski diagram anymore.

Indeed. It's related to a Minkowski diagram by a shear, or the coordinate transform $t=t_i-\alpha x_i$ where $t_i,x_i$ are the usual inertial frame coordinates and $\alpha$ is a constant with dimensions of inverse velocity and $|\alpha|<c^{-1}$.

Unfortunately, I was unable to interpret the Minkowsky diagram, performed with reflecting mirrors.

Get a piece of paper and hold it on your screen with its edge parallel to the x axis of the graph. What you see at the edge of the paper is the cavity at one time. Slide the paper upwards to see time advance - you will see one set of lines moving left (representing the left-moving wave crests) and one set of lines moving right (the right-moving wave crests). Occasionally you will see the crests moving in opposite directions crossing - this is a maximum of the resultant standing wave. Note that several crossings will disappear beneath your sheet of paper at the same time - these maxima happen at the same time. You will see two sets of crossings, because every other half wave is out of phase with the previous one. But the location of a set is always the same - they don't move because this is a standing wave.

Now repeat the process on the second diagram, keeping the paper edge horizontally across the screen. Note that the left-going and right-going lines move across your paper edge at different speeds as you move it - light speed is anisotropic in this coordinate system. You'll find that the crossings no longer happen at the same time, but they still always happen in the same places. So you still have a standing wave.

 

[dom_quixote]

The technical reference can be found in any standing wave class. My question is the following: Can the proposed experiment verify redshift in the laboratory?

There's no redshift here in any coordinate system.

According to the Special Theory of Relativity, time is relative. However, there is a chronological order in the works related to the isotropy of the speed of light, which I present below.

1 - Experiments by Michelson & Morley (1887, 1902 to 1905);

Of this experiment Einstein wrote, "If the Michelson-Morley experiment had not made us sorely uncomfortable, no one would have regarded the theory of relativity as [almost] redemption.

2 - Presentation of the Lorentz Transforms (1904);

In 1889, Fitzgerald, an Irishman, suggested that perhaps it was a contraction of the experimental equipment itself, which occurred when it passed through the aether, and which caused the change in the speed of light to be undetectable, that is, he suggested that the bodies contracted when they moved at speeds close to the speed of light. Independently, in 1895, Lorentz suggested a hypothesis of the same type, but more detailed, in which, to ensure the complete impossibility of detecting the ether, he added the hypothesis of a change in the «local time» marked by the clocks used in the experiment. The Lorentz transformations, introduced by him in 1904, describe this effect of decreasing length and dilating time for objects moving at speeds close to the speed of light.3 - Presentation of Einstein's TRR (1905);

Special Relativity is a theory published in 1905 by Albert Einstein, concluding previous studies by Dutch physicist Hendrik Lorentz, among others. It replaces the independent concepts of space and time of Newton's Theory with the idea of spacetime as a unified geometric entity. Space-time in special relativity consists of a differentiable manifold of 4 dimensions, three spatial and one temporal (the fourth dimension), equipped with a pseudo-Riemannian metric, which allows notions of geometry to be used. It is in this theory, too, that the idea of invariant speed of light arises.

4 - Mindowski Diagram (1908)

The Minkowski diagram, in general, is a graphical description of a part of Minkowski space, usually where the space has been reduced to a single dimension. That is, a space-time diagram that places a moving frame on a stationary frame to represent the Lorentz transformation in a geometric model. The diagram was developed in 1908 by Hermann Minkowski and provides an illustration of the properties of space and time in the special theory of relativity.

5 - Einstein's Cosmological Constant [1917]

Einstein originally introduced the constant in 1917[2] to counterbalance the effect of gravity and achieve a static universe, a notion that was the accepted view at the time. Einstein's cosmological constant was abandoned after Edwin Hubble confirmed that the universe was expanding

6 - Redshift (1912 to 1922)

Beginning with observations in 1912, Vesto M. Slipher found that most spiral galaxies, then mostly considered spiral nebulae, had considerable redshifts. Slipher first reports his measurement in the inaugural volume of the Lowell Observatory Bulletin. Three years later, he wrote a review in Popular Astronomy magazine. In it, he states that "the initial discovery that the great spiral of Andromeda had the quite exceptional speed of –300 km(/s) showed the means then available, capable of investigating not only the spectra of the spirals, but also their velocities" . Slipher reported the velocities of 15 spiral nebulae scattered across the celestial sphere, all but three having observable "positive" (ie recessive) velocities. Subsequently, Edwin Powell Hubble discovered an approximate relationship between the redshifts of such "nebulae" and the distances to them with the formulation of his eponymous Hubble law. These observations corroborated Alexander Friedmann's 1922 work, in which he derived the Friedmann–Lemaître equations. They are now considered strong evidence for an expanding universe and the Big Bang theory.

Note:

All citations and historical dates taken from Wikipedia.Please note that the answers given to the interferometer problem are FAIRLY based on work done before the observations made by the redshift studies.

But what if redshift was known before Lorentz's work?

 

[Ibix]

The historical order in which things were discovered doesn't change anything. And standing waves between two mirrors in a lab have nothing to do with cosmological redshift, since the mirrors are not comoving.

 

[Dale]

This sub-forum is primarily for technical questions. For historical questions please post in the “ Art, Music, History, and Linguistics” sub-forum.

Further posts here about historical topics will be deleted.