# Is Planck time the speed of light?

## Planck’s Constant

Planck’s constant relates the **energy** (E) of a **photon** with the **frequency** of **light**. Moreover, Planck’s constant allows the precise calculation of the energy of light emitted or absorbed and thereby permits the determination of the actual energy of the photon. Along with constant for the speed of light, Planck’s constant (*h* = 6.626 10 -34 joule-second in the meter-kilogram-second system of measurements) is a fundamental constant of nature.

At the beginning of the twentieth century, German physicist, Maxwell Planck, proposed that **atoms** absorb or emit electromagnetic **radiation** only in certain units or bundles of energy termed quanta. The concept that energy existed only in discrete and defined units seemed counter-intuitive, that is, outside the human experience with nature. Accepting his experimental results regarding the radiation emitted by an object as its **temperature** increases, Planck developed a quantum theory that accounts for a wide range of physical phenomena.

Prior to Planck’s work, electromagnetic radiation (light) was thought travel in waves with an infinite number of available frequencies and wavelengths. Planck determined that energy of light was proportional to its frequency. As the frequency of light increases, so does the energy of the light.

Planck began his university studies at the age of sixteen. By the age of twenty-one he had earned a doctorate in **physics**. While a graduate student, Planck studied **entropy** and the applications of the second law of **thermo-dynamics**. When Planck started his studies in physics, Newtonian or classical physics seemed fully explained. In fact, Planck’s advisor claimed that there was essentially nothing new to discover in physics. Despite such warnings, Planck choose to study physics. Planck’s talents and dedication were recognized and upon the death of his mentor Gustav Robert Kirchoff, Planck became a professor of theoretical physics at the University of Berlin were he did the major portion of his work regarding the relationship of light energy to light wavelength. Planck was able to measure radiation from heated bodies because—although atoms are constantly vibrating and generating electromagnetic waves—when heated, an atom vibrates at higher frequencies and gives off radiation at higher levels of energy.

Planck admitted that he did not fully understand quantum theory. In fact he regarded it as only a mathematical aberration or temporary answer until a more intuitive or common sense answer was found. Despite Planck’s reservations, Albert Einstein’s subsequent Nobel Prize winning work on the **photoelectric effect** was heavily based on Planck’s theory and described light as being composed of photons, each with an energy equal to Planck’s constant times the frequency of the light.

Light is now understood as having both photon (particle) and wave-like properties.

In 1916, American physicist Robert Millikan’s experiments gave the first precise calculation of Planck’s constant. Modern laboratories, including the National Institute of Standards and Technology strive for more precise values for Planck’s constant because it is so fundamental to applications of modern physics and **chemistry**.

Planck’s constant, combined with the speed of light, and the universal gravitational constant (G), can yield a quantity with the dimensions of **time** (5.38 x 10 -44 seconds). This quantity is called Planck time a very important concept in **cosmology** (the study of the origin of the cosmos). Because it is a fundamental constant, more precise values for Planck’s constant also improves the precision of related atomic constants, such as **proton mass**, **electron** mass, elementary charge, and **Avogadro’s number**.

## Resources

### Books

Gribbin, John. *Q is for Quantum: An Encyclopedia of Particle* *Physics.* New York: The Free Press, 1998.

Griffiths, D.J. *Introduction to Quantum Mechanics.* Prentice-Hall, Inc. 1995.

Jackson, J.D. *Classical Electrodynamics.* John Wiley and Sons, 1998.

Lide, D.R., ed. *CRC Handbook of Chemistry and Physics.* Boca Raton: CRC Press, 2001.

Trefil, James. *Encyclopedia of Science and Technology.* The Reference Works, Inc., 2001.

## Additional topics

- Other Free Encyclopedias

## Is The Speed of Light Constant?

There are a number of senses to the meaning of this question and so there are a number of different answers. Firstly . . .

## Does the speed of light change in air or water?

Yes. Light is slowed down in transparent media such as air, water and glass. The ratio by which it is slowed is called the refractive index of the medium and is always greater than one. * This was discovered by Jean Foucault in 1850.

When people talk about «the speed of light» in a general context, they usually mean the speed of light in a vacuum. This quantity is also referred to as *c*.

## Is *c*, the speed of light in vacuum, constant?

At the 1983 *Conference Generale des Poids et Mesures*, the following SI (Systeme International) definition of the metre was adopted:

The metre is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second.

This defines the speed of light in vacuum to be *exactly* 299,792,458 m/s. This provides a very short answer to the question «Is *c* constant»: Yes, *c* is constant by definition!

However, this is not the end of the matter. The SI is based on very practical considerations. Definitions are adopted according to the most accurately known measurement techniques of the day, and are constantly revised. At the moment you can measure macroscopic distances most accurately by sending out laser light pulses and timing how long they take to travel using a very accurate atomic clock. (The best atomic clocks are accurate to about one part in 10 13 .) It therefore makes sense to define the metre unit in such a way as to minimise errors in such a measurement.

The SI definition makes certain assumptions about the laws of physics. For example, they assume that the particle of light, the photon, is massless. If the photon had a small rest mass, the SI definition of the metre would become meaningless because the speed of light would change as a function of its wavelength. They could not just define it to be constant. They would have to fix the definition of the metre by stating which colour of light was being used. Experiments have shown that the mass of the photon must be very small if it is not zero (see the FAQ: What is the mass of the photon?). Any such possible photon rest mass is certainly too small to have any practical significance for the definition of the metre in the foreseeable future, but it cannot be shown to be exactly zero—even though currently accepted theories indicate that it is. If it wasn’t zero, the speed of light would not be constant; but from a theoretical point of view we would then take *c* to be the upper limit of the speed of light in vacuum so that we can continue to ask whether *c* is constant.

Previously the metre and second have been defined in various different ways according to the measurement techniques of the time. They could change again in the future. If we look back to 1939, the second was defined as 1/84,600 of a mean solar day, and the metre as the distance between two scratches on a bar of platinum-iridium alloy held in France. We now know that there are variations in the length of a mean solar day as measured by atomic clocks. Standard time is adjusted by adding or subtracting a leap second from time to time. There is also an overall slowing down of the Earth’s rotation by about 1/100,000 of a second per year due to tidal forces between the Earth, Sun and Moon. There may have been even larger variations in the length or the metre standard caused by metal shrinkage. The net result is that the value of the speed of light as measured in m/s was slowly changing at that time. Obviously it would be more natural to attribute those changes to variations in the units of measurement than to changes in the speed of light itself, but by the same token it is nonsense to say that the speed of light is now constant just because the SI definitions of units define its numerical value to be constant.

But the SI definition highlights the point that we need first to be very clear about what we mean by constancy of the speed of light, before we answer our question. We have to state what we are going to use as our standard ruler and our standard clock when we measure *c*. In principle, we could get a very different answer using measurements based on laboratory experiments, from the one we get using astronomical observations. (One of the first measurements of the speed of light was derived from observed changes in the timing of the eclipses of Jupiter’s moons by Olaus Roemer in 1676.) We could, for example, take the definitions of the units as they stood between 1967 and 1983. Then, the metre was defined as 1,650,763.73 wavelengths of the reddish-orange light from a krypton-86 source, and the second was defined (then as now) as 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of caesium-133. Unlike the previous definitions, these depend on absolute physical quantities which apply everywhere and at any time. Can we tell if the speed of light is constant in those units?

The quantum theory of atoms tells us that these frequencies and wavelengths depend chiefly on the values of Planck’s constant, the electronic charge, and the masses of the electron and nucleons, as well as on the speed of light. By eliminating the dimensions of units from the parameters we can derive a few dimensionless quantities, such as the fine structure constant and the electron to proton mass ratio. These values are independent of the definition of the units, so it makes much more sense to ask whether these values change. If they did change, it would not just be the speed of light which was affected. The whole of chemistry is dependent on their values, and significant changes would alter the chemical and mechanical properties of all substances. Furthermore, the speed of light itself would change by different amounts according to which definition of units you used. In that case, it would make more sense to attribute the changes to variations in the charge on the electron or the particle masses than to changes in the speed of light.

[Note that the fine structure constant does change with energy scale but I am referring to the constancy of its low energy limit.]

## Special Relativity

Another assumption on the laws of physics made by the SI definition of the metre is that the theory of relativity is correct. It is a basic postulate of the theory of relativity that the speed of light is constant. This can be broken down into two parts:

- The speed of light is independent of the motion of the observer.
- The speed of light does not vary with time or place.

To state that the speed of light is independent of the velocity of the observer is very counterintuitive. Some people even refuse to accept this as a logically consistent possibility, but in 1905 Einstein was able to show that it is perfectly consistent if you are prepared to give up assumptions about the absolute nature of space and time.

In 1879 it was thought that light must propagate through a medium in space just as sound propagates through the air and other substances. The two scientists Michelson and Morley set up an experiment to attempt to detect the ether, by observing relative changes in the speed of light as the Earth changed its direction of travel relative to the sun during the year. To their surprise, they failed to detect any change in the speed of light.

Fitzgerald then suggested that this might be because the experimental apparatus contracted as it passed through the ether, in such a way as to countermand the attempt to detect the change in velocity. Lorentz extended this idea to changes in the rates of clocks to ensure complete undetectability of the ether. Einstein then argued that those transformations should be understood as changes of space and time rather than of physical objects, and that the absoluteness of space and time introduced by Newton should be discarded. Just after that, the mathematician Minkowski showed that Einstein’s theory of relativity could be understood in terms of a four dimensional non-euclidean geometry that considered space and time as one entity, ever after called spacetime.

The theory is not only mathematically consistent, it is in agreement with countless direct experiments. The Michelson-Morley experiment was repeated with greater accuracy in the years that followed. In 1925 Dayton Miller announced that he *had* detected a change in velocity of the speed of light and was even awarded prizes for the discovery, but a 1950s appraisal of his work indicated that the most likely origin of his results lay with diurnal and seasonal variations in the temperature of his equipment.

Modern instruments could easily detect any ether drift if it existed. The Earth moves around the sun at a speed of about 30 km/s, so if velocities added vectorially as newtonian mechanics requires, the last 5 digits in the value of the speed of light now used in the SI definition of the metre would be meaningless. Today, high energy physicists at CERN in Geneva and Fermilab in Chicago routinely accelerate particles to within a whisper of the speed of light. Any dependence of the speed of light on reference frames would have shown up long ago, unless it is very slight indeed.

But what if we pursued the original theory of Fitzgerald and Lorentz, who proposed that the ether is there, but is undetectable because of physical changes in the lengths of material objects and the rates of clocks, rather than changes in space and time? For such a theory to be consistent with observation, the ether would need to be completely undetectable using clocks and rulers. Everything, including the observer, would have to contract and slow down by just the right amounts. Such a theory could make exactly the same prediction in all experiments as the theory of relativity; but in that case the ether would be no more than a metaphysical construct unless there was some other way of detecting it—which nobody has found. In the view of Einstein, such a construct would be an unnecessary complication, to be best eliminated from the theory.

## General Relativity

Einstein went on to discover a more general theory of relativity which explained gravity in terms of curved spacetime, and he talked about the speed of light changing in this new theory. In the 1920 book «Relativity: the special and general theory» he wrote: *. . . according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity [. . .] cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity of propagation of light varies with position.* Since Einstein talks of velocity (a vector quantity: speed with direction) rather than speed alone, it is not clear that he meant the speed will change, but the reference to special relativity suggests that he did mean so. This interpretation is perfectly valid and makes good physical sense, but a more modern interpretation is that the speed of light is constant in general relativity.

The problem here comes from the fact that speed is a coordinate-dependent quantity, and is therefore somewhat ambiguous. To determine speed (distance moved/time taken) you must first choose some standards of distance and time, and different choices can give different answers. This is already true in special relativity: if you measure the speed of light in an accelerating reference frame, the answer will, in general, differ from *c*.

In special relativity, the speed of light is constant when measured in any *inertial* frame. In general relativity, the appropriate generalisation is that the speed of light is constant in any freely falling reference frame (in a region small enough that tidal effects can be neglected). In this passage, Einstein is not talking about a freely falling frame, but rather about a frame at rest relative to a source of gravity. In such a frame, the speed of light can differ from *c*, basically because of the effect of gravity (spacetime curvature) on clocks and rulers.

If general relativity is correct, then the constancy of the speed of light in inertial frames is a tautology from the geometry of spacetime. The causal structure of the universe is determined by the geometry of «null vectors». Travelling at the speed *c* means following world-lines tangent to these null vectors. The use of *c* as a conversion between units of metres and seconds, as in the SI definition of the metre, is fully justified on theoretical grounds as well as practical terms, because *c* is not merely the speed of light, it is a fundamental feature of the geometry of spacetime.

Like special relativity, some of the predictions of general relativity have been confirmed in many different observations. The book listed below by Clifford Will is an excellent reference for further details.

Finally, we come to the conclusion that the speed of light is not only observed to be constant; in the light of well tested theories of physics, it does not even make any sense to say that it varies.

C.M. Will, «Was Einstein Right?» (Basic Books, 1986)

## Canon Science Lab

The letter «c» represents the speed of light in formula:

c = 2.99792458 x 10 8 m/sec.

The speed of light will always be the same, no matter who measures it or how fast the measurer is moving. It is the fastest thing in the universe. Einstein is credited for this discovery.

### The Perpetually Constant Speed of Light

The speed of light is always constant. This is the foundation of the Special Theory of Relativity for uniform motion. (The General Theory of Relativity is a relative theory about accelerated motion). Based on this principle of the constancy of light velocity, the speed of light came to be used as the ultimate standard for length and time. The Special Theory of Relativity also led to the discovery that energy (E) and mass (m) are equivalent, which formulated E = mc 2 .

The speed of light (c = 2.99792458×10 8 m/sec.) is equivalent to 299,792.458 km/sec. Light thus travels at nearly 300,000km/sec. Since the earth and moon are 380,000 km apart, light from the Moon takes about 1.3 seconds to reach us. And since the sun is 150 million km from the earth, the light we see right now left the sun about 8 minutes ago. A light year (the distance light travels in a year) is 9.5 trillion km.

### Are Units of Length Related to Light?

The basic unit of length is 1 m. The standard for units of length was once determined by the length of a person’s stride or arm. Along with advances in science and technology came the need for a more accurate standard. In 1799, the French adopted a standard based on the size of the earth. They defined 1/10 millionth of the distance from the North Pole to the Equator as «1 meter.»

This is called the «standard meter.» These days the standard meter is being redefined using the fact that light travels in a straight line at a constant speed. Accordingly, 1 meter is now defined as the distance light travels in 1/299.792458 million seconds. This definition allows us to use light to accurately measure the distance of remote objects. We can use a laser beam to measure the distance to the moon with extremely high accuracy (error of 30 cm or less). One second, the basic unit of time, is defined by the wavelength of a laser produced by cesium 133 atoms, but laser beams and light from space can also be employed for accurate time measurements.

### How Much Do Light Particles Weigh?

Once you know that light is the standard for measuring length and time, you might wonder whether light itself has weight. Light is both a wave and a particle. How much do you suppose such particles (photons) weigh? The answer is: photons have no mass. Photons are particles with zero mass, no electrical charge and a spin (rotation) value of 1. They can travel far because they weigh nothing. In quantum mechanics, photons are thought to mediate electromagnetic force.

Although photons have no mass, there are extraordinary cases in which light, specifically evanescent light, clings to extremely small objects, behaving as if it had mass.

### Does Light Have Energy?

In 1900, Planck (a German physicist who lived from 1858 to 1947) announced oscillating electrons radiate electromagnetic waves with intermittent energy. Before that, it was thought that electromagnetic energy fluctuated continuously and could be endlessly split into smaller and smaller parts. According to Planck, energy is emitted in proportion to oscillation frequency.

This proportionality constant is called «Planck’s constant» (h = 6.6260755 x 10 -34 ), and oscillation frequency times Planck’s constant is known as an «energy quantum.» If we try viewing this as light particles, we can consider electromagnetic waves of a certain oscillation frequency to be a group of photons with energy equal to oscillation frequency times Planck’s constant. Photons are zero-mass particles, but because they have energy, they also possess momentum.