This question can be understood in different ways. Therefore, there are different answers.
Is there a different speed of light in air or water?
Yes. Light is slowed down in transparent substances such as air, water, or glass. How many times the light slows down is determined by the refractive index (refractive index) of the medium. It is always greater than one. This discovery was made by Leon Foucault in 1850.
When they talk about the "speed of light", they usually mean the speed of light in a vacuum. It is she who is designated by the letter c.
Is the speed of light constant in a vacuum?
In 1983, the General Conference on Weights and Measures (Conference Generale des Poids et Mesures) adopted the following definition of the SI meter:
A meter is the path length of light in a vacuum during 1/299 792 458 seconds
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This also determined that the speed of light in a vacuum is exactly equal to 299792458 m / s. Short answer to the question "Is c a constant": Yes, c is a constant by definition!
But that's not the whole answer. The SI system is very practical. Its definitions are based on the best known measurement methods and are constantly revised. Today, for the most accurate measurement of macroscopic distances, a pulse of laser light is sent and the time it takes for the light to travel the required distance is measured. Time is measured by an atomic clock. The accuracy of the best atomic clock is 1/10 13. It is this definition of the meter that provides the minimum error in measuring the distance.
The definitions of the SI system are based on some understanding of the laws of physics. For example, it is assumed that particles of light, photons, have no mass. If the photon had a small rest mass, then the definition of the meter in the SI system would not be correct, because the speed of light would depend on the wavelength. It would not follow from the definition that the speed of light is constant. It would be necessary to refine the definition of meter by adding the color of the light to be used.
It is known from experiments that the mass of a photon is very small or equal to zero. The possible non-zero mass of a photon is so small that it is irrelevant for determining the meter in the foreseeable future. It cannot be shown that this is an exact zero, but in modern generally accepted theories it is zero. If, nevertheless, it is not zero, and the speed of light is not constant, then theoretically there should be a quantity c - the upper limit of the speed of light in a vacuum, and we can ask the question "is this quantity c a constant?"
In the past, meter and second were determined in different ways based on better measurement techniques. Definitions may change in the future. In 1939, the second was defined as 1/84600 of the average length of a day, and the meter as the distance between the risks on a rod of an alloy of platinum and iridium stored in France.
Now, with the help of an atomic clock, it has been established that the average length of a day changes. The standard time is specified, sometimes adding or subtracting a fraction of a second from it. The Earth's rotation speed slows down by about 1 / 100,000 of a second per year due to the tidal forces between the Earth and the Moon. There can be even greater changes in the length of the standard meter due to the compression of the metal.
As a result, at that time the speed of light, measured in units of m / s, changed slightly over time. It is clear that the changes in the value of c were more caused by the units used than by the inconstancy of the speed of light itself, but it is wrong to assume that the speed of light has now become constant, just because it is a constant in the SI system.
The definitions in the SI system revealed that in order to answer our question, we need to clarify what we mean when we talk about the constancy of the speed of light. We have to define definitions of units of length and time to measure the quantity c. In principle, different answers can be obtained when measuring in a laboratory and when using astronomical observations. (One of the first measurements of the speed of light was made in 1676 by Olaf Roemer based on the observed changes in the eclipse period of Jupiter's moons.)
For example, we could take the definitions established between 1967 and 1983. Then the meter was defined as 1650763.73 wavelengths of red-orange light source on krypton-86, and the second was defined (as it is today) as 9192631770 periods of radiation corresponding to the transition between two hyperfine levels of cesium-133. Unlike previous definitions, these are based on absolute physical quantities, and are applicable always and everywhere. Can we say that the speed of light is constant in these units?
From the quantum theory of the atom, we know that frequencies and wavelengths are mainly determined by Planck's constant, the charge of the electron, the masses of the electron and nucleus, and the speed of light. Dimensionless quantities can be obtained from the listed parameters, such as the fine structure constant and the ratio of the masses of the electron and proton. The values of these dimensionless quantities do not depend on the choice of measurement units. Therefore, the question is very important, are these values constant?
If they changed, it would not only affect the speed of light. All chemistry is based on these values, the chemical and mechanical properties of all substances depend on them. The speed of light would change in different ways when choosing different definitions for the units of measurement. In this case, it would make more sense to attribute its change to a change in the charge or mass of an electron than to a change in the speed of light itself.
Reliable enough observations show that the values of these dimensionless quantities did not change during most of the life of the universe. … See the FAQ article Have physical constants changed with time?
[Actually the fine structure constant depends on the scale of energy, but here we mean its low energy limit.]
Special theory of relativity
The definition of the meter in the SI system is also based on the assumption that the theory of relativity is correct. The speed of light is a constant in accordance with the basic postulate of the theory of relativity. This postulate contains two ideas:
- The speed of light does not depend on the movement of the observer.
- The speed of light does not depend on coordinates in time and space.
The idea that the speed of light is independent of the speed of the observer is counterintuitive. Some people can't even agree that this idea makes sense. In 1905, Einstein showed that this idea is logically correct if we abandon the assumption about the absolute nature of space and time.
In 1879, it was believed that light should propagate through some medium in space, like sound propagates through air and other substances. Michelson and Morley set up an experiment to detect ether by observing the change in the speed of light when the direction of the Earth's motion relative to the Sun changes during the year. To their surprise, no change in the speed of light was detected.
Fitzgerald suggested that this is the result of shortening the length of the experimental setup as it moves through the ether by such an amount that it is impossible to detect a change in the speed of light. Lorenz extended this idea to the pace of the clock, and proved that the ether could not be detected.
Einstein believed that changes in the length and pace of clocks are best understood as changes in space and time, rather than changes in physical objects. Absolute space and time, introduced by Newton, must be abandoned. Soon after, the mathematician Minkowski showed that Einstein's theory of relativity can be interpreted in terms of four-dimensional non-Euclidean geometry, considering space and time as a single entity - space-time.
The theory of relativity is not only mathematically based, it is also supported by numerous direct experiments. Later the Michelson-Morley experiments were repeated with greater accuracy.
In 1925, Dayton Miller announced that he had discovered changes in the speed of light. He even received an award for this discovery. In the 1950s, additional consideration of his work showed that the results were apparently related to daytime and seasonal temperature changes in his experimental setup.
Modern physical instruments could easily detect the movement of the ether if it existed. The Earth moves around the Sun at a speed of about 30 km / s. If the speeds were added, in accordance with Newtonian mechanics, then the last 5 digits in the value of the speed of light, postulated in the SI system, would be meaningless. Today, physicists at CERN (Geneva) and Fermilab (Chicago) accelerate particles every day to a speed of light. Any dependence of the speed of light on the frame of reference would have been noticed long ago, unless it is imperceptibly small.
What if, instead of a theory about the change in space and time, we followed the Lorentz-Fitzgerald theory, which suggested that the aether exists but cannot be detected due to physical changes in the length of material objects and in the pace of clocks?
For their theory to be consistent with observations, the ether must be undetectable with a clock and a ruler. Everything, including the observer, would contract and decelerate by exactly the required amount. Such a theory could make the same predictions for all experiments as the theory of relativity. Then the ether would be a metaphysical entity, unless they find some other way of detecting it - no one has yet found such a way. From Einstein's point of view, such an entity would be an unnecessary complication; it is better to remove it from the theory.
General theory of relativity
Einstein developed a more general theory of relativity, which explained gravity in terms of the curvature of spacetime, and he talked about the change in the speed of light in this new theory. In 1920, in the book Relativity. The special and general theory”he writes:
… In the general theory of relativity, the law of constancy of the speed of light in vacuum, which is one of two fundamental assumptions in the special theory of relativity, […] cannot be unconditionally valid. The curvature of a ray of light can be realized only when the speed of propagation of light depends on its position.
Since Einstein was talking about a vector of speed (speed and direction), and not just about speed, it is not clear if he meant that the magnitude of speed changes, but the reference to special relativity says that yes, he did. This understanding is absolutely correct, and has a physical meaning, but in accordance with the modern interpretation, the speed of light is constant in the general theory of relativity.
The difficulty here is that the speed depends on the coordinates, and different interpretations are possible. To determine the speed (distance traveled / elapsed time) we must first choose some distance and time standards. Different standards can give different results. This is applicable to the special theory of relativity: if you measure the speed of light in an accelerating frame of reference, then in the general case it differs from c.
In special relativity, the speed of light is a constant in any inertial frame of reference. In general relativity, an appropriate generalization is that the speed of light is a constant in any freely falling frame of reference in a sufficiently small region to neglect tidal forces. In the above quote, Einstein is not talking about a freely falling frame of reference. He talks about a frame of reference at rest relative to the source of gravity. In such a frame of reference, the speed of light may differ from c due to the influence of gravity (curvature of space-time) on the clock and ruler.
If the general theory of relativity is correct, then the constancy of the speed of light in an inertial frame of reference is a tautological consequence of the geometry of space-time. Travel at speed c in an inertial reference frame is travel along a straight world line on the surface of a light cone.
The use of the constant c in the SI system as a coefficient for the connection between the meter and the second is fully justified, both theoretically and practically, because c is not only the speed of light - it is a fundamental property of space-time geometry.
As with special relativity, the predictions of general relativity have been confirmed by many observations.
As a result, we come to the conclusion that the speed of light is constant, not only in accordance with observations. In the light of well-tested physical theories, it doesn't even make sense to talk about its inconstancy.