# Einstein on his discovery of the speed of light

1. Oct 18, 2012

### Niaboc67

This is quoted from "The Elegant Universe"

"the velovity of light is a kind of cosmic speed limit, a speed that nothing in the universe can exceed." - The Elegant Universe, On Einsteins Discovery

My Question is, How did einstein test/know this? How could he have possibly known what the speed of light was.This being before computers way back in the early 1900s, what tools could he have had at his disopal to propmt him to say that light is the fastest thing in the universe? Also was there some type of equation he figured out to prove this? if so could someone please provide an example of it?

Thank you

2. Oct 18, 2012

### Integral

Staff Emeritus
The constancy of the speed of light was derived by Maxwell in 1867. It was a very popular topic for the rest of the 19th century, while Physicists struggled to deal with it. I believe it was called the Great Schism. It should be well covered in a reasonable history book.

3. Oct 18, 2012

### QuantumPion

The speed of light was originally determined accurately in 1849 by Armand Fizeau using an apparatus consisting of shining a beam of light through a rotating mirror with slots. However, a good approximation of its value was determined from astronomy observations even earlier.

4. Oct 18, 2012

### haruspex

True, but nobody that early would have appreciated that its speed in vacuo was a universal constant, and that is substance of the OP question.
Likewise, when Maxwell derived the speed of light from his equations he believed light travelled through an 'aether', and therefore would not have constant speed as measured by an observer moving through the aether.
Michelson and Morley set out to measure the Earth's movement through this aether and in 1887 found they could not detect any difference between light following the Earth around the sun and light coming from the opposite direction. This is the experimental basis for Einstein's breakthrough.

5. Oct 19, 2012

### harrylin

https://en.wikisource.org/wiki/The_Principles_of_Mathematical_Physics?match=fr

Explanation included in the text.

Last edited: Oct 19, 2012
6. Oct 19, 2012

### sophiecentaur

I think it was another way round, actually. It was in order to explain all the other observations (Lorenz contraction, for instance) that Einstein concluded that the speed of light would have to be invariant. It was the only satisfactory explanation for what other people had found. so he didn't need to measure it or even just use evidence of other people's measurements - there was all the other stuff too.

7. Oct 19, 2012

### Staff: Mentor

How could Einstein knew that Lorentz contraction happens?

If you assume that physics is the same for all observers - especially the velocity of light in vacuum - that speed naturally occurs as a speed limit.

8. Oct 19, 2012

### sophiecentaur

Michelson Morely, perhaps?
I'm not sure there is any reason to assume that either, except if you know about QM and look at the spectra of distant stars, perhaps OR it just appeals aesthetically. Is there some chicken and egg here?

9. Oct 19, 2012

### Staff: Mentor

Michelson-Morley does not show length contraction - especially not in the frame where the measurement happens (no moving parts). If you interprete the experiment in terms of special relativity for some moving observer (e.g. the sun), you get length contraction, sure. But that is an interpretation, not a measurement.

Newtonian mechanics is the same for all observers, and the Maxwell equations do not have an explicit "use this system" in them - they were derived based on experiments on earth, which changes its motion relative to any non-accelerated observer all the time. More general, no experiment was known to depend on the reference frame.
Aesthetics was relevant, too, I think.

10. Oct 19, 2012

### Niaboc67

Very interesting everything that has been stated so far. I think my curiosity asks now what and HOW were the exact experiment that preformed to determine the speed of light. Technically Fizeau wasn't the first to calculate it "accurately" because his calculation was an inaccurate one, as well we have the Ole Romer team determining it as well. I would say that goes to the team that most precisely determined it in 1975, at least so far. If i have things in order chronically the idea/theory to the transformation goes as so:

I. Ole Romer - In 1676 Made the first quantitative measurements of the speed of light. He did this by being influenced by the works of Phillip III of Spain with his method of determining the longitude of ships out to see (no detail on how this was performed). As well as being influenced by Galileo on his method of establishing the time of day and thus longitude based on the eclipses of the moon, also no real idea of the process used. Romer had a team of people working with him to calculate this with observatories. Over several months Romer and Jean Picard observed 140 eclipses of Jupiter' moon, lo. while in Paris Giovanni Domenico Cassini observed the same eclipses. By comparing the times of the eclipses, the difference in longitude of Paris to Uranienborg was calculated. Cassini had observed the moons of Jupiter between 1666 and 1668, and discovered discrepancies in his measurements that, at first, he attributed to light having a "finite speed". In 1672 Rømer went to Paris and continued observing the satellites of Jupiter as Cassini's assistant. Rømer added his own observations to Cassini's and observed that times between eclipses (particularly those of Io) got shorter as Earth approached Jupiter, and longer as Earth moved farther away. Cassini made an announcement to the Academy of Sciences on 22 August 1676:

This second inequality appears to be due to light taking some time to reach us from the satellite; light seems to take about ten to eleven minutes [to cross] a distance equal to the half-diameter of the terrestrial orbit.

Romer actual experiment goes as follows. Assume the Earth is in L, at the second quadrature with Jupiter (i.e. ALB is 90°), and Io emerges from D. After several orbits of Io, at 42.5 hours per orbit, the Earth is in K. Rømer reasoned that if light is not propagated instantaneously, the additional time it takes to reach K, that he reckoned about 3½ minutes, would explain the observed delay. Rømer observed immersions in C from the symmetric positions F and G, to avoid confusing eclipses (Io shadowed by Jupiter from C to D) and occultations (Io hidden behind Jupiter at various angles). In the table below, his observations in 1676, including the one on August 7, believed to be in opposition H,[5] and the one observed at Paris Observatory to be 10 minutes late, on November 9. By trial and error, during eight years of observations Rømer worked out how to account for the retardation of light when reckoning the ephemeris of Io. He calculated the delay as a proportion of the angle corresponding to a given Earth's position with respect to Jupiter, Δt = 22·(α⁄180°)[minutes]. When the angle α is 180° the delay becomes 22 minutes, which may be interpreted as the time necessary for the light to cross a distance equal to the diameter of the Earth's orbit, H to E.[6] (Actually, Jupiter is not visible from the conjunction point E.) That interpretation makes it possible to calculate the strict result of Rømer's observations: The ratio of the speed of light to the speed with which Earth orbits the sun, which is the ratio of the duration of a year divided by pi as compared to the 22 minutes 365·24·60⁄π·22 ≈ 7,600.

II. James Bradley - in 1795 he discovers the Aberration of light which is attributed with the finite speed of light. At the instant of any observation of an object, the apparent position of the object is displaced from its true position by an amount which depends solely upon the transverse component of the velocity of the observer, with respect to the vector of the incoming beam of light (i.e., the line actually taken by the light[where?] on its path to the observer). The result is a tilting of the direction of the incoming light which is independent of the distance between object and observer. Which was based on Romers points that light is finite, it was only until Bradley proved it seems that it was fully accepted as fact.

III. Jean Baptiste Joseph Delambre - In 1809, again making use of observations of Io, but this time with the benefit of more than a century of increasingly precise observations, the astronomer reported the time for light to travel from the Sun to the Earth as 8 minutes and 12 seconds. Depending on the value assumed for the astronomical unit, this yields the speed of light as just a little more than 300,000 kilometres per second. The modern value is 8 minutes and 19 seconds, and a speed of 299,792.46 km/s.

IV. Armand Hippolyte Louis Fizeau - In 1849 he was the first person to measure the speed of light on Earth. He used a beam of light reflected from a mirror 8 km 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. He calculated the speed of light to be 315,000 km/s.

V. In 1865, James Clerk Maxwell proposed that light was an electromagnetic wave, and therefore travelled at the speed c appearing in his theory of electromagnetism.

VI. Albert Einstein postulated that the speed of light with respect to any inertial frame is independent of the motion of the light source,[4] and explored the consequences of that postulate by deriving the special theory of relativity and showing that the parameter c had relevance outside of the context of light and electromagnetism.

VII. After centuries of increasingly precise measurements, in 1975 the speed of light was known to be 299,792,458 m/s with a measurement uncertainty of 4 parts per billion. On wikipedia it does not tell who this was proven by nor how.

Just so there is no confusion most of what i posted above is wikipedia. So during the time Einstein was creating his theory of relativity he only knew that light was finite and that nothing could exceed it, not the precise measurements of which were discovered in 1975. My curiosity strikes me more as i read through, does anyone know the process of Romer and his team, were they using synchronized watches to figure out the time delays of lo? if anyone can illuminate on anything stated that would be fantastic.

Last edited: Oct 19, 2012
11. Oct 19, 2012

### haruspex

That's an interesting summary of the history, but I would challenge a couple of details.

V. As I understand it, Maxwell realised from his studies of electricity and magnetism that a simple harmonic exchange of energies between the two forms should naturally arise. When he calculated the velocity such a wave would have, he found it close to the speed of light as then measured. It was on this basis that he postulated light to consist of an electromagnetic wave. I'm not aware of any other clues to the relationship that would have been known at the time.
Note also that Maxwell did not appreciate that 'c' would be the same regardless of relative uniform motion.

Va. You can't leave out Michelson-Morley. It was their experiment that showed there was no electromagnetic ether through which the wave propagated, and indeed that the speed of light was a constant to observers moving in inertial frames. This is what led Einstein to substitute this as a postulate for the Newtonian "velocities add" postulate.

12. Oct 19, 2012

### harrylin

Why?? As Poincare explained in the text that I linked, determining the exact speed of light was of little importance. It was foremost, in relation to Maxwell's electromagnetic theory of light, experiments to detect the motion of the Earth and experiments on electrons that led to this assumption (summarised in the sections 2.2 The Principle of Relativity, and 2.4 Lavoisier's Principle). Didn't you read it?

13. Oct 19, 2012

### mrspeedybob

Einstein himself lays out his logic very clearly. I think a good step toward understanding relativity is to read Einsteins original paper. It's a surprisingly easy read. You'll get a good conceptual understanding of it before the math gets thick and heavy.

14. Oct 19, 2012

### Niaboc67

I did not, i quickly sifted through it. But see i am quite a busy person i normally have 20 tabs open at once so i can only focus on a few things. I tend to come back to other pages that people link me to after some time because SO MUCH information. It takes a bit of time for me to set aside for things as well as to digest and comprehend them. I will read through that page though, but the speed of light may not be of importance to them, but i have an affinity for the knowledge and history, plus at some point i feel it will be useful knowledge towards my endeavors. That is the reason i ask as well as for others to shed share and spread knowledge about this to help anyone who may be interested in the topic.

15. Oct 20, 2012

### harrylin

No worries.
As you saw from my citation, it was not Einstein who discovered that nothing can go faster than the speed of light.

More on the history and similar discussions:
http://en.wikipedia.org/wiki/Relativity_priority_dispute

16. Oct 20, 2012

### DiracPool

Getting back to the original question, Einstein’s great coup was recognizing that the speed of light was the governing standard of measure in physically modeling universal interactions. This was obviously an unintuitive notion, as most people assumed time was the invariant measure.

That writing had been on the wall for some time, though. The pre-Maxwell guys came up with a rough estimation experimentally for c that Maxwell recognized was spookily consistent with his wave equation. M&M found the same speed of c regardless of which way they pointed their interferometer, and Lorentz reformulated his mechanics equations to compensate for these anomalies.

So, again, the writing on the wall was there, but it took Einstein to take the bold risk of treating the primacy of c as rule, not an anomaly to be reconciled later. He presented this as a stipulation in his relativity paper in 1905. A stipulation? Of his own free will? What does that mean? I personally think that he adopted the non-intuitive idea that c was constant a few years before his annulus miribalis. Then he secretly spent the next few years writing the BIG 5 papers using his secret knowledge-weapon.

I mean, this is not unprecedented, right? There are solid arguments that Newton invented the calculus well prior to the publication of the Principia, while making it look like he derived all his physical principles and laws irrespective of it.

What do you think?

17. Oct 20, 2012

### Niaboc67

It seems plausible that he was working on it for awhile prior to releasing his papers.

18. Oct 21, 2012

### harrylin

I think that you misunderstand the word "constant" in the second postulate; that is a widespread misunderstanding - even a myth, as explained in the AJP:
"ajp.aapt.org/resource/1/ajpias/v74/i3/p193_s1" [Broken]

While the "one-way speed of light" depends very much on "definition", the constancy of the "two-way speed of light" was based on Maxwell's theory and experience. Einstein (re-)derived the invariance of the speed of light and its working as limit speed from the two postulates, see: