# What was James Bradley's calculation to calculate the speed of light?

Looking into the history of how the speed of light came to be determined, to what we know it to be today, James Bradley is often mentioned. He was credited with the discovery of the aberration of light and having used the aberration of light to calculate the speed of light. There are many online sources that confirm this, though the year of discovery and calculated speed of light differs here and there.

I've read through Bradley's "A Letter from the Reverend Mr. James Bradley Savilian Professor of Astronomy at Oxford, and F.R.S. to Dr.Edmond Halley Astronom. Reg. &c. Giving an Account of a New Discovered Motion of the Fix'd Stars" published in "Philisophical Transaction vol 35" which explains his findings of the aberration of light but makes no mention of calculating the speed of light.

How did James Bradley calculate the speed of light and what publication of his shows these calculation?

Despite many online sources crediting James Bradley with having calculated the speed of light to a 295.000 km/sec (britannica) or 301.000 km/sec (wikipedia), a small nuance ought to be added. Like Ole Romer before him in 1676, James Bradley calculated the speed of light relative to something else but both never provided a value in Earth-based units.

He wrote,

This therefore being 20",2, AC will be to AB that is the Velocity of Light to the Velocity of the Eye (which in this Case may be supposed the same as the Velocity of the Earth's annual Motion in its Orbit) as 10210 to One from whence it would follow that Light moves or is propagated as far as from the Sun to the Earth in 8' 12".

(source)

The calculation to get to the ratio of 10210 is,

size of a radian (206265") / angle of aberration (20",2)

This ratio also holds for the speed of light to the speed of the earth. Not sure though exactly how britannica and wikipedia arrive at their respective values.

## How the Speed of Light was First Measured

The speed of light in a vacuum stands at “exactly 299,792,458 metres per second“. The reason today we can put an exact figure on it is because the speed of light in a vacuum is a universal constant that has been measured with lasers and when an experiment involves lasers, it’s hard to argue with the results. As to why it comes out somewhat conspicuously as a whole number, this is no coincidence- the length of metre is defined using this constant: “the length of the path travelled by light in vacuum during a time interval of 1/299,792,458 of a second.”

Prior to a few hundred years ago, it was generally agreed or at least assumed that the speed of light was infinite, when in actuality it’s just really, really, really fast- for reference, the speed of light is just slightly slower than the fastest thing in the known universe- a teenage girl’s response time if Justin Bieber were to say on Twitter, “The first to reply to this tweet will be my new girlfriend.”

The first known person to question the whole “speed of light is infinite” thing was the 5th century BC philosopher Empedocles. Less than a century later, Aristotle would disagree with Empedocles and the argument continued for more than 2,000 years after.

One of the first prominent individuals to actually come up with a tangible experiment to test whether light had a speed was Dutch Scientist, Isaac Beeckman in 1629. Despite living in a time before lasers- which gives me the chills just thinking about- Beeckman understood that, lacking lasers, the basis of any good scientific experiment should always involve explosions of some kind thus, his experiment involved detonating gunpowder.

Beeckman placed mirrors at various distances from the explosion and asked observers whether they could see any difference in when the flash of light reflected from each mirror reached their eyes. As you can probably guess, the experiment was “inconclusive”.

A similar more famous experiment that didn’t involve explosions was possibly conducted or at the very least proposed by Galileo Galilei just under a decade later in 1638. Galileo, like Beeckman also suspected that the speed of light wasn’t infinite and made passing references to an experiment involving lanterns in some of his work. His experiment (if he ever conducted it at all), involved placing two lanterns a mile apart and trying to see if there was any noticeable lag between the two the results were inconclusive. The only thing Galileo could surmise was that if light wasn’t infinite, it was fast and that experiments on such a small scale were destined to fail.

It wasn’t until Danish Astronomer, Ole Römer entered the fray that measurements of the speed of light got serious. In an experiment that made Galileo flashing lanterns on a hill look like a primary school science fair project, Römer determined that, lacking lasers and explosions, an experiment should always involve outer space. Thus, he based his observations on the movement of planets themselves, announcing his groundbreaking results on August 22, 1676.

Specifically, while studying one of Jupiter’s moons, Römer noticed that the time between eclipses would vary throughout the year (based on whether the Earth was moving towards Jupiter or away from it). Curious about this, Römer began taking careful notes about the time I0 (the moon he was observing) would come into view and how it correlated to the time it was usually expected. After a while, Römer noticed that as the Earth orbited the sun and in turn got further away from Jupiter, the time Io would come into view would lag behind the expected time written down in his notes. Römer (correctly) theorised that this was because the light reflected from Io wasn’t travelling instantaneously.

Unfortunately, the exact calculations he used were lost in the Copenhagen Fire of 1728, but we have a pretty good account of things from news stories covering his discovery and from other scientists around that time who used Römer’s numbers in their own work. The gist of it was that using a bunch of clever calculations involving the diameter of the Earth’s and Jupiter’s orbits, Römer was able to conclude that it took around 22 minutes for light to cross the diameter of Earth’s orbit around the Sun. Christiaan Huygens later converted this to more commonplace numbers, showing that by Römer’s estimation, light traveled at about 220,000 kilometres per second. This figure is a little off (about 27% off) from the figure noted in the first paragraph, but we’ll get to that in a moment.

When Römer’s colleagues almost universally expressed doubt in his theory about Io, Römer responded by calmly telling them that Io’s 9th of November eclipse in 1676 was going to be 10 minutes late. When the time came, the doubters stood flabbergasted as the movement of an entire celestial body lent credence to his conclusion.

Römer’s colleagues were right to be astounded in his estimation, as even today, his estimation of the speed of light is considered to be amazingly accurate, considering it was made 300 years before the existence of both lasers, the internet, and Conan O’Brien’s hair. Okay so it was 80,000 kilometres per second too slow, but given the state of science and technology at the time, that is remarkably impressive, particularly given he was primarily just working off a hunch to begin with.

What’s even more amazing is that the reason for Römer’s estimation being a little too slow is thought to have less to do with any mistake on his part and more to do with the fact that the commonly accepted diameter of the Earth’s and Jupiter’s orbits were off when Römer did his calculations. Meaning yes, Römer was only wrong because other people weren’t as awesome at science as he was. In fact, if you slot the correct orbit numbers into what is thought to be his original calculations from reports before his papers were destroyed in the aforementioned fire, his estimation is nearly spot on.

So even though he was technically wrong and even though James Bradley came up with a more accurate number in 1729, Römer will go down in history as the guy who first proved that the speed of light was not infinite and worked out a reasonably accurate ballpark figure on what the exact speed was by observing the movements of a speck orbiting a giant ball of gas positioned about 780 million kilometres away. That right there ladies and gentlemen is how a badass, lacking lasers, does science.

with that said, you can’t muck with the isotropy of the speed of light arbitrarily without modifying Maxwells equation. The type or functional form of any isotropy is limited. Within these limits, it’s a matter of conversion.

I suggest a forum search if you want more discussion. The topic has beaten to death numerous time here on PF.

Does this video even make sense? And if so, is it right or wrong?

It is correct. The one way speed of light is indeed a convention.

I would disagree a bit with him about some of his statements to the effect that we cannot know the one way speed of light. Because it is a convention, not only can we know but we do know with certainty simply by choosing our convention.

It is easy to set up experiments where the light path is one way. The issue is that all such experiments depend on some method of clock synchronization. Your assumption about clock synchronization determines the speed you get. In the case of Romer’s measurement he was using slow clock transport and assumed the isotropy of slow clock transport. This is equivalent to assuming the Einstein synchronization convention.

I’m skeptical. One could use a pulsed light source and two partially silvered mirrors separated by some distance. A single distant observer with a single clock could reside equally distant from each mirror. The distant observer would see two pulses separated by the time of flight of the pulse between the mirrors. The source is moved and the pulse sent along the reverse direction.

Now this experiment doesn’t solve the problem as usually discussed because the equal length paths to the distant observer each contain a lateral component in opposite directions. However, the magnitude of these contributions depends on the functional form of the speed anisotropy.

Are you basically suggesting sending light pulses along one edge and the other two edges of a closed triangular path? That's a two-way measurement.

More generally, choosing an anisotropic speed of light just leads to a non-orthogonal coordinate system on spacetime. That doesn't have any measurable consequences beyond making the maths nastier.

The point is that you need a local observer with one clock at a defined rate (e.g., using the definition of the second in the SI via the Cs standard). So what you can measure concerning the speed of light are local observables at the place of this one clock. The standard example is "radar", i.e., a signal that is sent to a distant object, being reflected and then detected again, measuring the time it takes to detect the signal again. That's measuring the two-way speed of light of course.

To measure a one-way speed of light you need two clocks, one at the place of the emission and one at the place of detection of the light signal. To make sense of the clock readings as a "one-way speed of light" the clocks must be somehow synchronized, and it depends on the synchronization procedure you use, which "one-way speed of light" you measure.

This is assumes already that the one way speed of light is isotropic.

That is actually the identifying feature of a two way measurement. Actual one way measurements require two clocks so they require an assumption about simultaneity.

Two way measurements don’t assume simultaneity since they use a single clock, but to infer a one way speed they have to assume isotropy. What you are describing assumes isotropy, so it is a two way measurement, as also evidenced by the use of a single clock.

This doesn’t work. In the limit the directions become arbitrarily close but the distance becomes arbitrarily long. The time difference from any anisotropy in the speed of light decreases as the directions become close, but it increases as the distance increases. The two effects together mean that even in the limit of a distant observer the anisotropy assumption is still non-negligible.

It has nothing to do with that. The mirror isn’t a clock. The experiment is a two way experiment because the direction of the light is changed, a single clock is used, and the calculation of the speed of light depends on an assumption about the isotropy of the speed of light. All of those are characteristics of two way measurements.

I recommend that you actually work through the math of your proposed experiment. Either you will see where the isotropy assumption comes in or I can point it out.

Okay, let me write this out with some care. We have a very large optical bench fresh from the manufacture with an x and a y coordinate system. We're going to measure the time of flight for light pulses using a detector and a standard issue time of flight box. First off our assumption is that the speed of light is dependent on direction which for our table I can write as, ##c( heta)##, where ## heta## is the angle between a light ray and the x axis. We make the following further assumptions that ##c( heta)## is a real single valued analytic function of ## heta##.

We place two beam splitters (1,2) of negligible dimension, 1 at ##x=-W, y=0## and 2 at ##x=W, y=0##. The detector, D, is placed at ##x=0,y=L##. The beam splitters are adjusted so pulses from each will be directed to the detector and to the other beam splitter. Now, the time of flight depends on distance and direction. Now, we fire a pulse through 1 to 2. The pulse is split at 1 and then at 2. The time of flight between 1 to 2 is

The split pulses travel along different legs of the triangle to the detector. Their time of flights are,

The time between received pulses is,

##Delta_A = Delta_ <12>+ Delta_ <2D>- Delta_<1D>##

Reversing the direction of the pulse (sending through 2 then 1)

##Delta_B = Delta_ <21>+ Delta_ <1D>- Delta_<2D>##

So, my question / observation is will ##Delta_A = Delta_B## for all ##c( heta)##? Clearly not since there are choices which make ##pm(Delta_ <2D>- Delta_<1D>)## negligible while ##Delta_ <12>- Delta_<21>## is not.

## Hippolyte Fizeau and the Speed of Light

On September 23 , 1819 , French physicist Armand Hippolyte Louis Fizeau was born. He is well known for his calculation of the speed of light and his suggestion to use length of a light wave be used as a length standard.[4]

#### Hippolyte Fizeau – Early Years

Hippolyte Fizeau was born in Paris as the eldest son of Béatrice and Louis Fizeau, who was professor of Pathology at the Paris Medical School . He attended the prestigious Collège Stanislas in Paris where he became a friend with one of his fellow students , Léon Foucault .[6] In September 1839 . Famous Louis Daguerre [5] put on a free course on his new photographic techniques in Paris and the two friends Fizeau and Foucault attended. They watched Daguerre expose a plate in a camera pointing out the window, then after talking about his process for about 30 minutes, he developed the plate using a variety of chemicals to reveal the picture. Although Fizeau and Foucault were impressed they also realized the limitations of the process – it would be wonderful to be able to take portraits , they thought, but the subject could not be expected to remain motionless for 30 minutes. After the course ended they began to experiment to try to speed up the process. [1]

#### Astronomical Photography

Fizeau entered the Paris Medical School in 1840 , but he soon gave up on medicine because of severe migraines and spent some time travelling during which time he regained his health . His new focus of attention should be physics . He attended Arago ‘s lectures at the Observatory , and enrolled in a course on optics at the Collège de France . Furthermore, he began to deeply study notebooks containing the lecture notes taken by his brother who attended courses at the École Polytechnique . It was Arago ,[7] who encouraged Fizeau and Foucault in 1845 and suggested that they might attempt to make photographs of an image of the sun produced by a telescope. Thus, Fizeau and Foucault produced what is considered the first astronomical photography .

#### Measuring the Speed of Light

It was in the field of optics that Fizeau earned a lasting reputation . The original inspiration came from François Arago , who looked for a decisive test between the corpuscular and wave theories of light. If the wave theory was true, the velocity of light had to be greater in moving media, such as water flowing in a tube . The project implied the working out of a terrestrial method of measuring the speed of light , and Arago suggested that this could be done by using a rotating mirror .[2] In 1849 , Fizeau calculated a value for the speed of light more precise than the previous value determined by Ole Rømer in 1676 .[8] He used a beam of light reflected from a mirror eight kilometers away. The beam passed through the gaps between teeth of a rapidly rotating wheel . The speed of the wheel was increased until the returning light passed through the next gap and could be seen.

Fizeau calculated the speed of light to be 313,300 kilometres per second , which was within about five percent of the correct value (299,792.458 kilometers per second ). Fizeau published the first results obtained by his method for determining the speed of light in 1849 . In 1851 he carried out a series of experiments in an attempt to detect the luminiferous ether —a hypothetical material that was thought to occupy all of space and to be necessary for carrying the vibrations of light waves . The experimental results failed to demonstrate the existence of the ether, but his work helped lead to the discarding of the ether theory in the early years of the 20th century.[3] Fizeau was elected a member of the Academy of Sciences in 1860 , an a member of the Bureau des Longitudes in 1878 . He received the decoration of the Legion of Honour in 1849 and became officer in 1875 . In 1866 the Royal Society of London awarded him the Rumford Medal .

#### Further Achievements

Fizeau also worked in the field of thermodynamics, where he constructed an interference dilatometer to measure the thermal expansion of solid bodies. In 1850 he measured the speed of propagation of electricity in conductors with Eugène Gounelle (1821-1864). In 1853 he described the installation of a capacitor to increase the efficiency of induction. He then studied the thermal expansion of solids and applied the phenomenon of light interference to measure the expansion of crystals.

Hippolyte Fizeau died at Venteuil on 18 September 1896, at age 76.

At yovisto academic video search you can learn more about the physics behind the speed of light in the NASA documentary ‘Einsteins Cosmic Speed Limit‘.

## Comparing the Speed of Light in Air to the Speed in Water

The next person to measure the speed of light was French philosopher Armand Hippolyte Fizeau, and he didn't rely on astronomical observations. Instead, he constructed an apparatus consisting of a beam splitter, a rotating toothed wheel and a mirror placed 8 km from the light source. He could adjust the speed of rotation of the wheel to allow a beam of light to pass toward the mirror but block the return beam. His calculation of ​c​, which he published in 1849, was 315,000 km/s, which wasn't as accurate as Bradley's.

A year later, Léon Foucault, a French physicist, improved on Fizeau's experiment by substituting a rotating mirror for the toothed wheel. Foucault's value for c was 298,000 km/s, which was more accurate, and in the process, Foucault made an important discovery. By inserting a tube of water between the rotating mirror and the stationary one, he determined that the speed of light in air is higher than the speed in water. This was contrary to what the corpuscular theory of light predicted and helped establish that light is a wave.

In 1881, A. A. Michelson improved upon Foucault's measurements by constructing an interferometer, which was able to compare the phases of the original beam and the returning one and display an interference pattern on a screen. His result was 299,853 km/s.

Michelson had developed the interferometer to detect the presence of the ​ether​, a ghostly substance through which light waves were thought to propagate. His experiment, conducted with physicist Edward Morley, was a failure, and it led Einstein to conclude that the speed of light is a universal constant that is the same in all reference frames. That was the foundation for Special Relativity Theory.

## What was James Bradley's calculation to calculate the speed of light? - Astronomy

The OISC is proud to be a Project of Community Partners a 501 (c) (3) non-profit corporation in the State of California.

The Speed of Light Exhibits

One of the most famous experiments in all human endeavor is the measurement and understanding of the Speed of Light. Albert Einstein's Theory of General Relativity establishes that nothing can go faster than the Speed of Light. In science fiction stories, people routinely travel faster than light to reach distant stars and planets that are so far away, humans could never reach them. If humans are to reach for the stars, we must develop new understandings of natures laws.

The OISC is dedicated to inspiring young people to study science as we move into the 21st century of possibilities.

To that end, we installed our first Speed of Light Exhibit at the Irvine Civic Center in Oct. 2004.

We are now preparing for our second exhibit to be at the UC Irvine Beall Center for Art + Technology in July 2008

SOL Exhibit @ The Beall Center - Outline Find out how you can be part of this project and help us into the future by downloading the Speed of Light Project Overview and then contact the OISC.

We are also sponsoring an Art Competition to help promote this exhibit.

### The Michelson Speed of Light Experiment at the Irvine Ranch

(scroll down to the bottom for links to posters used in the Oct. 2004 Irvine Civic Center Exhibit)

C = 186,282.3960 miles per second, plus or minus 3.6 feet per second

C = 299,792.4562 kilometers per second, plus or minus 1.1 meters per second

Albert Michelson was known as finest experimental physicist alive

At the heart of the experiment (pictured in the shack and graphic above), an arc light was bounced off a rapidly rotating set of mirrors, back and forth down a mile-long tube and home, to the mirrors, which by then would have moved slightly. If the speed of the mirror, the angle of the bounce and the length of the tube are known, it is possible to calculate the speed of light.

Above, Albert Einstein and Albert Michelson met at Mount Wilson in 1931, just before Michelson's death. From left to right are Milton Humason, Edwin Hubble, Charles St. John, Michelson, Einstein, W.W. Campbell and Walter S. Adams.

Above map, if rebuilt on its old site today, the Irvine Ranch speed of light experiment would run through an industrial park, in what is now the city of Irvine, near Newport Corporation, a world leader in the optics and laser indusrty.

In 1887, Michelson and Edward Morely used the interferometer to find out how light waves moved through the theoretical "ether" in the universe. According to the principals of classical physics, the movement of the earth through this mysterious substance affected the speeds of light rays moving through it. Michelson and Morely used the interferometer to bounce light waves out and back at right angles, expecting to see one of the beams lag behind.

Instead, the beams returned at exactly the same time. In years to come, these findings would be cited as one of the first proofs this mysterious ether did not exist, that the speed of light was a constant, and that classical physics was not enough to explain the physical universe.

While Michelson and Morely were testing the "ether drift," Einstein had begun to speak of clocks that moved backward, mass that was not constant and light made up of things called "photons." For scientists, these heresies were as profound as those of Copernicus, the first to suggest that the earth was an orbiting planet, and not the center of the universe.

The drama surrounding Michelson's experiments was heightened by this atmosphere of turmoil. Although his work helped trigger a revolution in the study of physics, Michelson never decided which side he was on, according to his biographers.

His daughter, Dorothy Michelson Livingston, wrote that Michelson never gave up his belief in "ether," even though he accepted Einstein's work.

In 1930, that belief may have helped bring Michelson to Santa Ana, for his last and most ambitious test.

Athelie Clark, the oldest living member of the family that once owned the gigantic Irvine Ranch, remembers a day in the late 1920s when Michelson came to lunch.

At the table in the opulent dining room of James Irvine's Victorian home sat Michelson, James Irvine Sr., James Irvine Jr. and the scientist Robert Millikan. Clark sat and listened, understanding little of what was being said.

"I remember being told that he was a very famous man who was looking for a site for an important experiment," said Clark, now 85.

"His hair was gray and unruly. He seemed extremely gracious to me."

"Gracious" was one of the nicer words used to describe Michelson's manner. Throughout his career, as honors piled up, he had earned a reputation as both brilliant and unstable. He was an accomplished tennis player. an excellent painter and violinist, and so good at billiards that opponents complained that his knowledge of physics gave him an unfair advantage.. His few close friends described him as extremely loyal, fond of practical jokes, and quite cool under pressure.

Yet Morely, Michelson's early partner, said he feared that Michelson had suffered a "softening of the brain" early in his career, after Michelson was hospitalized for exhaustion in the 1880s. Michelson's first wife tried to have the scientist committed. One of his maids sued unsuccessfully for assault.

Dorothy Michelson Livingston wrote that her father often worked for days without sleeping or eating, that he sat alone at meals so his thinking would not be disturbed, that in turns he could be arrogant, distant, imperious and rude. A messy divorce made front-page headlines for weeks. The physicist also suffered from recurring nightmares, including one in which he rode a motorcycle up an endless hill.

"Americans have this obsession with mad scientists, and Michelson
fit the image," said UCLA physicist Wuerker. "He was the most famous American scientist of his day. Anything he did was news."

Mad or not, he was definitely prodigious.

In 1907 when Michelson won the Nobel Prize for physics, his career was only getting started. He beat off several challenges to his findings and honed his earlier work. In 1920, he was the first to measure the diameter of a star, called Betelgeuse, an achievement hailed in The New York Times as "astounding."

In 1926, the most spectacular of Michelson's experiments split the night sky between Mount Wilson and Mount Baldy** (See the bottom of this page).

With mirrors, turbines, his interferometer and an arc light, he measured the speed of light to within two miles per second of its currently accepted speed.

Horace Babcock, the emeritus director of the Mount Wilson observatory, remembers visiting the experiment as a child, seeing the light shooting out of the cracks in the shack where Michelson was at work.

Michelson wasn't satisfied with the results of the Mt. Wilson experiment. For one thing, he worried that "shimmers" of air between the mountains might have fouled his results. He also didn't trust the work of the United States Geodetic Survey team, which had measured the distance between peaks.

He wanted to repeat the test in a vacuum to measure a more precise speed and, perhaps, show the presence of the "ether."

Clark says Michelson settled on the Orange County site for the experiment after lunch in the Irvine family home, when James Irvine Jr. took the physicist for a drive in the family Packard. Michelson liked the low, flat bean field on the north end of the ranch, near what is now the Marine helicopter base. The Irvine's agreed to donate the use of the land.

The project took shape quickly. Michelson's assistants built a metal shack to hold the turbines, the arc light and other equipment from Mount Wilson and a network of tubing, metal pipes, wires, plugs and switches. From the shack, they built a mile-long tube of 3-foot-diameter, corrugated steel pipes sealed airtight by layers of steel, cloth, inner tubes and rubber paint. Inside the tubes were a series of mirrors, each on a motorized balancing machine.

In the center of the shack was the interferometer, which Michelson sometimes called his "she devil." At the heart of the machine, a wheel covered with finely-honed mirrors spun at exactly 512 revolutions per second. When light struck this wheel, it bounced back and forth through the tunnel, eventually returning to the spot it had started from. By then the mirror would have changed its angle slightly, reflecting the light at an angle. By knowing the distance the light had traveled, the speed of the mirror and the angle of the bounce, Michelson could calculate the speed of light.

Clark remembers that the shack was "absolutely spotless" inside. While the experiment was running, her father often would drive house guests over to look at the shack- when he wasn't driving them to the other side of the ranch, where battle scenes were being shot for the film "All Quiet on the Western Front." Once, towards the end of the experiment, she says Michelson asked her to come inside, to look through a window that showed the length of the tube.

"It was very dark," she said. "I looked in the window and saw a long, dark hole that disappeared into nothing. There were little tiny sparks shooting back and forth. I'd never seen anything like it."

Michelson's last experiment did not go smoothly. On the day of his arrival, the pump being used to suck air out of the pipe broke down, halting the project. Leaks in the pipe were a regular problem, and fears of an earthquake were persistent. Michelson and his assistants fought over details.

His daughter described one of those fights, in which an assistant drove to Pasadena and called the physicist to the lobby of the Hotel Maryland. The two men stood in the lobby arguing with each other, wearing pajamas, scribbling diagrams on the back of a Chinese laundry ticket, until Michelson noticed that a crowd had gathered.

Michelson himself was not well. His health had begun to deteriorate years before, in what his doctor referred to as the "vile climate of Chicago," where Michelson had taught. His bladder was removed in 1929. The train trip to California exhausted him. His heart was weak and his circulation was slow. As the Orange County experiment progressed, he began to spend more and more time in bed, alert but physically weak.

Michelson got out of bed in April, 1931, when Einstein came to visit. Michelson's daughter remembers sitting between them at dinner, seeing that neither could keep his hair combed, and struggling to keep from laughing. The two men attended banquets together, and talked to each other privately.

At the end of April, Michelson's doctor confined him to his house, after suffering what the papers said was a nervous breakdown. In
early May, his assistants brought him early data from the tests. On May 9, Michelson suffered a stroke, followed by a cerebral hemorrhage. After lingering in a coma for several hours, he died.

The Register of Orange County, California ran the obituary on page 1.

Why would a dying man attempt an experiment as ambitious as Michelson's in Orange County?

R.S. Shankland, a leading historian of physics, believes Michelson came to Santa Ana to look one last time for the ether that had been so central to the science of his youth.

The final report on the Irvine Ranch experiments was published in 1933. The findings were extremely close to those accepted today, but many physicists consider the results of the tests on Mount Wilson more accurate. Some of the metal tubing now is used as drainage pipes at the Mount Wilson observatory.

There are markings at the site of the test, and though a nearby street was named in Michelson. s honor, it is commonly mispronounced. The Irvine Company has been sold and resold. James Irvine's mansion burned to the ground and was abandoned. If the vacuum tube were rebuilt on its old site today, it would run through the parking lot of a Home Club and the lobbies of two manufacturing firms on Armstrong Avenue in Irvine.

Wuerker, a UCLA physicist, thinks Michelson's work in Orange County is worth more than that. For one thing, he says, Michelson can be thought of as the man who gave this country a scientific tradition, on the day he won the Nobel Prize.

Even though Michelson's work here is not widely recognized, Orange County has become a hotbed for experimental physics. At the University of California, Irvine, this work is helping push physics beyond the edge of Einstein's world.

And in several of those experiments, UCI scientists are investigating incredibly small particles that move near the speed of light. These particles have no affect on the speed of light, but they do appear everywhere, invisible and mysterious, like an ether.

**An error about Michelson's measurement of the velocity of light in 1926 (as described above) was reported by Don Nicholson of the OSSC .

The measurement was made between Mount Wilson and Lookout Mountain, not Mount Baldy.

The piers on which the retro reflector were mounted are still in place on Lookout Mountain.

## 4.6 References

&uarr Galilei, G., Dialogues Concerning Two New Sciences, translated by Crew, H., Salvio, A. de, Macmillan, 1914 (1638).

&uarr Seeger, R. J., Men of Physics: Galileo Galilei, His Life and His Works, Elsevier, 2016.

&uarr Rømer, O., Phil. Trans. R. Soc. London 1676, 12, 893–894.

&uarr Helden, A. van, JHA 1983, 14, 137–140.

&uarr Heath, T., Aristarchus of Samos, the ancient Copernicus, Cambridge University Press, 2013.

&uarr Schilling, G., Atlas of Astronomical Discoveries, Springer Science & Business Media, 2011.

&uarr Bradley, J., Phil. Trans. R. Soc. London 1728, 35, 637–661.

&uarr Lang, K. R., Essential Astrophysics, Springer Science & Business Media, 2013.

&uarr Fizeau, H., Breguet, L., Sessions of the Academy of Sciences 1850, 30, 562–563.

&uarr Foucault, L., Sessions of the Academy of Sciences 1850, 30, 551–560.

&uarr Michelson, A. A., Experimental determination of the velocity of light, Honeywell, 1964.

&uarr Essen, L., Gordon-Smith, A. C., Journal of the Institution of Electrical Engineers-Part I: General 1946, 93, 147.

&uarr Maddaloni, P., Bellini, M., De Natale, P., Laser-Based Measurements for Time and Frequency Domain Applications: A Handbook, Taylor & Francis, 2016.

&uarr Einstein, A. in The principle of relativity original papers, The University of Calcutta, 1920 (1905).

## Abstract

This paper features an indirect method to measure the speed of light. First, the electrical permittivity of air ε0, is obtained, by using a capacitance meter to measure the capacitance of a parallel-plate capacitor, by varying the separation between its plates. By means of a least squares adjustment, the slope of the straight line is calculated which is related to ε0.

Next, the magnetic permittivity of air μ0 is obtained by using a solenoid through which different currents are circulated and the magnetic field is measured in its centre using the Hall sensor of a Smartphone. By means of a least squares adjustment, the slope of the straight line is calculated which is related to μ0.

Once ε0 and μ0 have been obtained, the speed of light is calculated by the expression c = 1 ε 0 μ 0 with its corresponding absolute and relative errors, to verify if the obtained value is compatible with the exact value of c.

## The electromagnetic spectrum

As scientists and engineers began to explore the implications of Maxwell's theory, they performed experiments that verified the existence of the different regions, or groups of wavelengths, of the electromagnetic spectrum. As practical uses for these regions of the spectrum developed, they acquired now-familiar names, like "radio waves," and "X-rays." The longest wavelength waves predicted by Maxwell's theory are longer than 1 meter, and this band of the electromagnetic spectrum is known as radio waves. The shortest wavelength electromagnetic waves are called gamma rays, and have wavelengths shorter than 10 picometers (1 trillion times shorter than radio waves).

Interactive Animation: Interactive Electromagnetic Spectrum

Maxwell's elegant equations not only unified the concepts of electricity and magnetism, they also put the familiar and much-studied phenomenon of light into a context that allowed scientists to understand its origin and behaviors. Maxwell appeared to have established conclusively that light behaves like a wave, but interestingly enough he also planted the seed of an idea that would lead to an entirely different view of light. It would be another thirty years before a young Austrian physicist named Albert Einstein would cultivate that seed, and in doing so spark the growth of a revolution in our understanding of how the universe is put together.

### Summary

The study of electricity and magnetism were artfully united in John Clerk Maxwell’s theory of electromagnetism. This module explores the experimental connection between electricity and magnetism, beginning with the work of Oersted, Ampere, and Faraday. The module gives an overview of the electromagnetic nature of light and its properties, as predicted by Maxwell’s mathematical model.

### Key Concepts

In the mid-1800s, scientists including Andre Ampere and Michael Faraday noted a connection between electricity and magnetism and carried out a series of experiments that showed how they interact.

James Clerk Maxwell built on the work of Faraday and developed a single set of equations defining both electricity and magnetism, unifying the concepts into one theory of electromagnetism.

We now know that the electromagnetic spectrum is made up of a series of waves of varying wavelength and visible light is just one small portion of this spectrum.