Maxwell's Equations Compatible With Variable Speed of Light

Feb 9, 2023
"How do Maxwell's equations predict that the speed of light is constant" View:

The derivation says nothing about whether or not the speed of light relative to an observer varies with the speed of that observer. Maxwell believed that it did vary:

John Norton: "[Maxwell's] theory allows light to slow and be frozen in the frame of reference of a sufficiently rapidly moving observer."

The speed of light relative to an observer OBVIOUSLY varies with the speed of the observer. Assume that a light source emits equidistant pulses and an observer starts moving towards the source:


The speed of the light pulses relative to the stationary observer is

c = df

where d is the distance between subsequent pulses and f is the frequency at the stationary observer. The speed of the pulses relative to the moving observer is

c'= df' > c

where f' > f is the frequency at the moving observer.
Feb 9, 2023
The fundamental double lie of post-truth (Einsteinian) physics. Maxwell's theory predicted constancy of the speed of light, the Michelson-Morley experiment proved it:

Brian Cox, Jeff Forshaw, Why Does E=mc2?: (And Why Should We Care?), p. 91: "...Maxwell's brilliant synthesis of the experimental results of Faraday and others strongly suggested that the speed of light should be the same for all observers. This conclusion was supported by the experimental result of Michelson and Morley, and taken at face value by Einstein."

The truth: Maxwell's theory did not predict constancy of the speed of light; the Michelson-Morley experiment actually DISPROVED it.
Jun 7, 2023
If the speed of Light is a constant, then how do you account for the Red Shift and the Blue Shift noted in approaching and receding galaxies?

We as a species have only measured the Speed of Light at the bottom of a very deep Gravity Well. We cannot confirm the Speed of Light (as measured on Earth) is or is not the value we assign, until we get far enough out of this gravity well into interstellar space.

With the Universe filled with Dark Matter and Quantum 'particles', there may not be an absolute speed of light.

The old Nuclear Conversion Formula E=MC^ results in 241 MEV per deficit AMU (post fission) using the 'accepted' value of C. Experiments have shown that Cx300 is possible in specialized mediums, which could lead to E=MC^ being as much as 72,300 MEV per deficit AMU (post fission event).
The Red shift and Blue shift of galaxies denote the frequencies of light, not their speed.

Redshift and blueshift describe the change in the frequency of a light wave depending on whether an object is moving toward or away from us.

When an object is moving away from us, the light from the object is known as redshift, and when an object is moving towards us, the light from the object is known as blueshift.

Astronomers use redshift and blueshift to deduce how far an object is away from Earth, the concept is key to charting the universe's expansion.

First, you need to remember that visible light is a spectrum of color each with a different wavelength. According to NASA, violet has the shortest wavelength at around 380 nanometers, and red has the longest at around 700 nanometers. But they all move at the same speed.

When an object (e.g. a galaxy) moves away from us it is 'red-shifted' as the wavelength of light is 'stretched' due to the expansion of space, not space-time, so the light is seen as 'shifted' towards to red end of the spectrum, according to ESA.

The concept of redshift and blueshift is closely related to the Doppler effect — which is an apparent shift in soundwave frequency for observers depending on whether the source is approaching or moving away from them, according to the educational website The Physics Classroom. The Doppler Effect was first described by Austrian physicist Christian Doppler in 1842 and many of us experience the Doppler effect firsthand almost every day without even realizing it.

We've all heard how a siren changes as a police car rushes past, with a high pitch siren upon approach, shifting to a lower pitch as the vehicle speeds away. This apparent change in pitch to the observer is due to sound waves effectively bunching together or spreading out. It is all relative as the siren's frequency doesn't change. As the police car travels towards you the number of waves is compressed into a decreasing distance, this increase in the frequency of sound waves that you hear causes the pitch to seem higher. Whereas then the ambulance goes past you and moves away, the sound waves are spread across an increasing distance thus reducing the frequency you hear so the pitch seems lower.

This principle of the Doppler effect applies to light as well as sound. The wave length of light determines its colour; the wavelength is the distance from crest to crest

The terms redshift and blueshift can apply to any part of the electromagnetic spectrum, including radio waves, infrared, ultraviolet, X-rays and gamma rays. So, if radio waves are shifted into the ultraviolet part of the spectrum, they are said to be blueshifted or shifted toward the higher frequencies. Gamma rays shifted to radio waves would mean a shift to a lower frequency or a redshift.

The redshift of an object is measured by examining the absorption or emission lines in its spectrum. These lines are unique for each element and always have the same spacing. When an object in space moves toward or away from us, the lines can be found at different wavelengths than where they would be if the object were not moving (relative to us).

Doppler shifting happens because motion tends to shrink and stretch waves whether it is sound or light. The constant speed of light doesn't effect the Doppler shift or the frequency of the light.

Think of radio waves, for instance. As tune up and down your AM and FM dials, you are listening at certain frequencies of the electromagnetic spectrum. But the speed of light, at which all electromagnetic emissions travel at, remains the same.

The medium through which electromagnetic waves move may change their speed, like the copper in a wire or the water in a pool. But their speed remains constant through the same medium.

May 20, 2023
Frankly, I see so much theorising around the "speed of light" built around presumptions of a flat, linear & ubiquitous rate of passage of time, when we already know that, from the pov of the light beam, time throughout the rest of the universe simply doesn't exist. Light crosses the entire (infinite) universe in zero time. What we are "measuring" in c (which we can never actually measure but only deduce) is actually our own rate of passage through time – our local time, as every point in the universe has its own timeline. (Or time stalk, as I prefer to visualise it. And any two static points will have a parallel time stalk; if one moves relative to the other, their relative positions on their respective time stalks begins to slant.)
Even redshift is wrong: We have never measured it as we cannot see a single object shift into the red, we can only compare it to other objects that are closer. This is the big difference with the Doppler comparison. Redshift is simply the observation of Time (on the observer's timeline) passing slower here (at the place of observation) than at the distant point where it was (or in reality, is) emitted. So frequency appears lower at reception than at emission.
Now if we can extrapolate from redshift how the rate of passage of Time has changed, we might develop some very different extrapolations on other theories, including expansion, inflation, "dark energy" & the "Big Bang" itself. :cool:
PodCastAllLangs wrote:" Even redshift is wrong: We have never measured it as we cannot see a single object shift into the red, we can only compare it to other objects that are closer."

The JWST was constructed to observe those very objects which have been shifted into the infrared and are thus invisible to our eyes and the narrow band of visible light our eyes can discern. The JWST observes the increasing redshift of objects which is directly proportional to their distance from us and hence, the farther back in time where they resided when the redshifted light was emitted.

We call the narrow part of the spectrum which our eyes can see "visible light". But everything from radio waves to microwaves to gamma rays are all part of the same electro-magnetic spectrum. The only difference between a radio wave and a gamma ray is the wavelength. Wavelength is the distance between the peaks of the waves.


Light behaves like a wave, so light from a luminous object undergoes a Doppler-like shift if the source is moving relative to us. Since 1929, when Edwin Hubble discovered that the Universe is expanding, we have known that most other galaxies are moving away from us. Light from these galaxies is shifted to longer (and this means redder) wavelengths - in other words, it is 'red-shifted'.

Since light travels at such a great speed relative to everyday phenomena (a million times faster than sound) we do not experience this red shift in our daily lives.

The redshift of an element or molecule emitted by a distant galaxy or quasar is easily measured by comparing its spectrum with a reference laboratory spectrum. Atomic emission and absorption lines occur at well-known wavelengths. By measuring the location of these lines in astronomical spectra, astronomers can determine the red shift of the receding sources.

However, the redshifts observed in distant objects are not due to the Doppler phenomenon, but are rather a result of the expansion of the Universe.

Doppler shifts arise from the relative motion of source and observer through space, whereas astronomical redshifts are 'expansion redshifts' due to the expansion of space itself. a process drivn by dark energy.

Two objects can actually be stationary in space and still experience a red shift if the intervening space itself is expanding.

A convenient analogy for the expansion of the Universe is a loaf of unbaked raisin bread. The raisins are at rest relative to one another in the dough before it is placed in the oven. As the bread rises, it also expands, making the space between the raisins increase.

If the raisins could see, they would observe that all the other raisins were moving away from them although they themselves were stationary within the loaf. Only the dough - their 'Universe' - is expanding, not the size of the individual raisins.

The James Webb Space Telescope was specifically constructed to receive red-shifted light, which is shifted to lower frequencies our eyes are unable to discern. Observing in the infrared is important for a few reasons. One reason is because the ultraviolet and visible light emitted by the very first luminous objects that formed in the universe when it was young has been stretched by the expansion of the universe so that it reaches us today, over the intervening 13 billion years later, as infrared light.

Webb's mirrors collect light from the sky and direct it to the science instruments. The instruments filter the light, or spectroscopically disperse it, before finally focusing it onto the detectors. Each specific instrument has its own detectors. The detectors are where photons are absorbed and ultimately converted into the electronic voltages that we measure. Webb needs extraordinarily sensitive detectors to record the feeble light from galaxies, hovering stars, and planets. It needs large-area arrays of detectors to efficiently survey the sky. Webb has extended the state of the art for infrared detectors by producing arrays that possess a lower noise, a larger format, and are longer lasting than their predecessors.

Another reason is because stars and planets form in clouds of gas and dust, and this dust obscures our view. Infrared light penetrates these far more local clouds and allows us to see inside.

The light that was emitted as visible light long ago reaches us today as longer wavelengths in the infrared frequencies of the electro-magnetic spectrum because the universe has been expanding since its beginning with the Big Bang and this expansion has stretched out the light waves as they have propagated through the expanding space. Longer wavelengths of light are redder, and this associated effect is called "redshift." However, this change in frequency does not effect the speed of light, c, in a vacuum.

Webb's Near Infrared Camera (NIRCam) will take a series of pictures using filters that pick up different wavelengths in the infrared, and use the changes in brightness it detects between these images to estimate the redshifts of the distant galaxies. Redshifting is the stretching of light toward longer wavelengths that occurs as light travels through the expanding universe, which can be used to gauge distance based on the amount of the red shift observed from the actual frequency of the emitted .



See: Part 4_Redshift.pdf


The exact value of the Hubble constant is still somewhat uncertain, but is generally believed to be around 65 kilometers per second for every megaparsec* in distance. This means that a galaxy 1 megaparsec away will be moving away from us at a speed of 65 km/sec, while another galaxy 100 megaparsecs away will be receding at 100 times this speed. So essentially, the Hubble constant reflects the rate at which the universe is expanding.

To determine an object's distance, we only need to know its velocity. Velocity is measurable thanks to the red shift. By taking the spectrum of a distant object, such as a galaxy, astronomers can see a shift in the lines of its spectrum and from this shift determine its velocity. Putting this velocity into the Hubble equation, they determine the distance. Note that this method of determining distances is based on observation (the shift in the spectrum) and on a theory (Hubble's Law). If the theory is not correct, the distances determined in this way are all nonsense. Most astronomers and astro-physicists believe that Hubble's Law does, however, hold true for a large range of distances in the universe. (It should be noted that, on very large scales, Einstein's theory predicts departures from a strictly linear Hubble law. The amount of departure, and the type, depends on the value of the total mass of the universe. In this way a plot of recession velocity (or redshift) vs. distance, which is a straight line at small distances, can tell us about the total amount of matter in the universe and may provide crucial information about the mysterious dark matter.)

* Megaparsec - one parsec is equal to about 3.3 light years. So if one megaparsec is equal to one million parsecs, then that’s about 3.3 million light years away. The mega- parsec was said to have been first used by the international scientific and astronomical community in the year 1920. In reality, astronomers cannot use the normal units of measurements such as meters and square meters as the measurements would be too big a number. For convenience, astrologists looked for a way to emphasize a great distinction in measurements, especially if you’re talking about measuring galaxies or clusters in space.


Accurate modelling of redshift-space distortions (RSD) is challenging in the non-linear regime for two-point statistics e.g. the two-point correlation function (2PCF). We take a different perspective to split the galaxy density field according to the local density, and cross-correlate those densities with the entire galaxy field. Using mock galaxies, we demonstrate that combining a series of cross-correlation functions (CCFs) offers improvements over the 2PCF as follows: 1. The distribution of peculiar velocities in each split density is nearly Gaussian. This allows the Gaussian streaming model for RSD to perform accurately within the statistical errors of a (1.5h−1Gpc)3 volume for almost all scales and all split densities. 2. The PDF of the density field at small scales is non-Gaussian, but the CCFs of split densities capture the non-Gaussianity, leading to improved cosmological constraints over the 2PCF. We can obtain unbiased constraints on the growth parameter fσ12 at the per-cent level, and Alcock-Paczynski (AP) parameters at the sub-per-cent level with the minimal scale of 15h−1Mpc. This is a ∼30 per cent and ∼6 times improvement over the 2PCF, respectively. The diverse and steep slopes of the CCFs at small scales are likely to be responsible for the improved constraints of AP parameters. 3. Baryon acoustic oscillations (BAO) are contained in all CCFs of split densities. Including BAO scales helps to break the degeneracy between the line-of-sight and transverse AP parameters, allowing independent constraints on them. We discuss and compare models for RSD around spherical densities.

May 20, 2023
"redshifts... are rather a result of the expansion of the Universe."
So we assume, and expansion of the universe was the conclusion derived conveniently from the observed redshift. Which seems to me to be circular logic. Redshift could also result from a different speed of light (or rather, a different rate of passage of time) at these distances & periods in our past, compared to our perception of it here & now (including against our reference lab spectrum).
If, instead of the universe expanding, it is Time that is contracting non-linearly, how do you think that would affect our perception of a distant light source? (And a whole lot else!)
If e.g. one light-second at a point in the distant universe was (/is) double the distance of what a light-second is here/now, surely the wavelength would appear to us as double what it was (/is) on emission?
(There seem to be petabytes of explanations everywhere of redshift = expanding universe but virtually nothing on the possibility & effects of a non-linear – e.g. hyperbolic – rate of passage of time.)
PodCastAllLangs said," Redshift could also result from a different speed of light (or rather, a different rate of passage of time) at these distances & periods in our past, compared to our perception of it here & now (including against our reference lab spectrum). "

The redshift of light, the movement of light from the narrow visibility achieved in our eyesight to the invisible infrared, can now be seen clearly thanks to the James Webb Space Telescope (JWST), for which it was designed.

Astronomers use redshifts to measure how the universe is expanding, and thus to determine the distance to our universe’s most distant (and therefore oldest) objects. What is a redshift? It’s often compared to the high-pitched whine of an ambulance siren coming at you, which drops in pitch as the ambulance moves past you and then away from you. That change in the sound of an ambulance is due to what’s called the Doppler effect. It’s a good comparison because both sound and light travel in waves, which are affected by their movement through air and space.

Sound can only move so fast through the air; sound travels at about 750 miles (1,200 kilometers) per hour. As an ambulance races forward and blares its siren, the sound waves in front of the ambulance get squished together. Meanwhile, the sound waves behind the ambulance get spread out. This means the frequency of the sound waves is higher ahead of the ambulance (more sound waves will strike a listener’s ear, over a set amount of time) and lower behind it (fewer sound waves will strike a listener’s ear, over a set amount of time). Our brains interpret changes in the frequency of sound waves as changes in pitch.

Like sound, light is also a wave traveling at a fixed speed: 186,000 miles (300,000 km) per second, or some one billion kilometers per hour. Light, therefore, plays by similar rules as sound.

But, in the case of light, we perceive changes in wave frequency as changes in color, not changes in pitch.

In our expanding universe, a measurement of speed translates to a measurement of distance and time.

Here’s a recent example. Astronomers said in early January 2020 that the most distant quasar known at this time – quasar J0313-1806 – has a record-setting redshift of z = 7.64. In accordance with astronomers’ interpretations of redshift, we’re seeing quasar J0313-1806 – a highly luminous galaxy nucleus in the early universe, thought to be powered by a supermassive black hole – just 670 million years after the Big Bang, or more than 13 billion light-years away.

Or consider an even more distant object, not a very bright quasar, but instead just a regular galaxy in the early universe. GN-z11 is a high-redshift galaxy found in the direction of the constellation Ursa Major, the Great Bear. GN-z11 is currently the oldest and most distant known galaxy in the observable universe, with a redshift of z = 11.09. That redshift corresponds to a distance of 13.4 billion light-years. So we see this object as it existed 13.4 billion years ago, just 400 million years after the Big Bang.

Astronomers make use of markers in the spectrum of starlight. This is the study of spectroscopy. If you shine a flashlight beam through a prism, a rainbow comes out the other side. But if you place a clear container filled with hydrogen gas between the flashlight and the prism, gaps appear in the smooth rainbow of colors, places where the light literally goes missing.

The hydrogen atoms are tuned to absorb very specific frequencies of light. When a beam of light consisting of many colors passes through the gas, those frequencies get removed – absorbed – from the beam. The rainbow becomes littered with what astronomers call absorption lines. Replace the hydrogen with helium, and you get a completely different pattern of absorption lines. Every atom and molecule has a distinct absorption fingerprint that allows astronomers to tease out the chemical makeup of distant stars and galaxies.

When we pass starlight through a prism (or similar device suitable for telescopes, such as diffraction gratings), we see a forest of absorption lines from hydrogen, helium, sodium, and so on. However, if that star is hurtling away from us, all those absorption lines undergo a recessional Doppler shift and move toward the red part of the rainbow. This is what we call a redshift.

For stars heading toward us, the opposite happens, and the lines are shifted toward the blue end of the spectrum; they are blueshifted (generally, astronomers only use the term redshift to simplify things, and just put a negative sign in front of it if it’s a blueshift).

By measuring how far away the lines are located from where they’re supposed to be in the spectrum, astronomers can calculate the speed of a star or a galaxy relative to Earth, and even how a galaxy rotates: by measuring a different redshift for one side of the galaxy compared to the other, you can see which side is moving away from you and which side is moving toward you.

With this tool, the motion of the universe is revealed and a host of new questions can be investigated.

And galaxies aren’t the only things that can be investigated with redshifts. Astronomers have learned to tease out the subtle tug of a distant planet on its parent star, thus revealing the planet to astronomers. If a star in our Milky Way galaxy has a hidden planet – and if astronomers see that the star sometimes exhibits a slight redshift and other times a slight blueshift – the astronomers infer that star is alternating between moving toward and away from us. They refer to this movement as a “wobble” of the star in space. Something must be pulling on the star, causing it to wobble. By measuring how far the absorption lines shift, an astronomer can determine the mass of the invisible companion and its distance from the star, and come to the conclusion that a planet is in orbit around the star!

Two positions of distant star showing its rays shorter and longer depending on movement.

As a planet orbits a star, it tugs the star back and forth with tiny movements. Astronomers see the star wobbling as an alternating red and blueshift of its spectrum. Image via ESO.

In addition to finding other worlds, redshifts also led to one of the most important discoveries of the 20th century. In the 1910s, astronomers at Lowell Observatory and elsewhere noticed that the light from nearly every galaxy was redshifted: most galaxies in the universe were racing away from us! A Belgian scientist, Georges Lemaître, who was also a priest, recognized that the recession velocities of the galaxies could be explained by a startling truth: the universe is expanding! In 1929, American astronomer Edwin Hubble matched up redshifts with distance estimates to the galaxies and uncovered something remarkable: the farther away a galaxy, the faster it’s receding. This relation, the Hubble law, was renamed in 2018 by the International Astronomical Union to the Hubble–Lemaître law.

What came to be known as the cosmological redshift was the first piece of the Big Bang theory, and ultimately a description of the origin of our universe.

The list of the most distant astronomical objects is always changing as astronomers find higher and higher redshifted objects on the brink of the observable universe. Galaxies, quasars and even gamma-ray bursts travel for eons across the cosmos, delivering their faint red light, and revealing a little more of the secrets of the universe.

Graph with line of plus signs from lower left to upper right.
Edwin Hubble and colleagues found a correlation between distance to a galaxy (horizontal axis) and how quickly it’s moving away from Earth (vertical axis). The movement of galaxies in a nearby cluster adds some “noise” to this plot. Image via William C. Keel/ Wikipedia.

Bottom line: A redshift reveals how an object in space (star/planet/galaxy) is moving compared to us. It lets astronomers measure a distance for the most distant (and therefore oldest) objects in our universe.



According to Einstein's theory space and time are both distorted for objects moving relative to each other. There is another way to look at it that I like better. The Lorentz Aether Theory contended that all things were distorted when they moved. It did not warp space and time. All the distortion was in the material things that moved. Space and time remained constant. Things that moved experienced dimensional and time distortion. This allowed H. Ziegler to assign a cause for relativity phenomena.

The Lorentz transformations are still used to calculate the distortions even in Einstein's theory. But the Lorentz theory is largely forgotten as is H. Ziegler. Doppler shifting happens because motion tends to shrink and stretch waves whether it is sound or light. The constant speed of light doesn't effect, noris it effected by the Doppler shift.

The statement "the speed of light is constant" refers to the local speed with which light passes through any given point in spacetime, according to an observer that is also passing through that point. The significance of this caveat for cosmology is explained here:

What does general relativity say about the relative velocities of objects that are far away from one another?

For the present question, the "local" caveat is important because successive wavecrests are spatially separated from each other: successive wavecrests cannot both pass through the same spacetime point. So there is no contradiction between "the speed of light is constant" and cosmological redshift.

Whenever a given wavecrest passes through a given point in spacetime, its speed is the usual constant 𝑐 according to an observer who is also passing through that point. In contrast, the relative "speed" between two spatially-separated entities (such as successive wavecrests) is not fundamentally limited; it's not even obvious how such a speed should be defined. This is related to the possibility of a cosmological horizon.

The speed of light is a constant for any and all frames of reference (FoRs).

We have three kinds of "shifts "
[1] Doppler red or blue shift:
Is the change in frequency of a wave [mainly sound] when the emitter or the receiver is moving, resulting in a change in frequency

[2] Cosmological red or blue shift:
This occurs when there is an expansion of space between the emitter and receiver rather then either the emitter or receiver moving.
Again as happens with Doppler, it results in a change of frequency, and occurs when we view very distant objects in the Universe

[3] Gravitational red shift:
This occurs when light is emitted from a dense gravitational source resulting in a reduction in frequency and subsequently "time dilation. "