Speed Of Light

Today in the modern era we know that the speed of light(denoted by c in physics) in a vacuum is about 186282.4 miles per second(670616640 miles per hour!), but for many centuries this was not known at all. Until the 1500s it was not really known for certain whether the speed of light occurred instantaneously or had a finite speed. There had been no experimentation to gain insight into this question, but there was a lot of speculation and argument about it.

The ancient Greeks were the first to examine this subject sometime around 460 to 430 BC when Empedocles proposed his theory of light, believing it was something that had movement and so there was a definite finite speed. Aristotle didn’t believe this, he thought that the speed of light was due to the presence of something and that there was no movement. Heron of Alexandria thought that the speed of light must be infinite since even very distant objects such as stars appeared instantaneously when one opened their eyes to look at them.

In the 1200s Roger Bacon, using earlier philosophical arguments by Aristotle, believed that the speed of light was finite with some definite value which had yet to be determined. Witelo, very important in the history of philosophy, was a theologian and scientist who in the 1270s believed that the speed of light might very well be infinite in a vacuum, absent of all matter, but would slow down when the denser matter was encountered.

In the early 1600s Johannes Kepler, a German astronomer and mathematician who was famous for his laws of planetary motion, believed that the speed of light in a vacuum was infinite; his reasoning was that since empty space did not present any impediment to the propagation of light, then it’s speed must be infinite. Rene Descartes was a French philosopher, mathematician, and scientist living in the 1600s who also believed the speed of light to be infinite. He differed with Kepler in that he thought the speed of light would be faster the denser the medium it propagated through becoming instantaneous in the densest mediums.

Pierre de Fermat was a French lawyer and mathematician who also lived in the 1600s, some of his most notable work being in the development of infinitesimal calculus. He believed in a definite finite speed of light and that the speed of light would slow the denser the medium it propagated through. As it turns out, this line of reasoning is pretty accurate to the reality of what we know today.

Galileo Galilei was an Italian astronomer, physicist, and engineer who lived from 1564 to 1642 who was known for his achievements in observational astronomy and physics, as well as a developmental role in the scientific method. In 1638 he claimed to have performed one of the very first experiments measuring the speed of light by covering and uncovering a lantern and measuring the perception of its light some miles in the distance. He stated that he couldn’t tell whether the speed of light was instantaneous or not, but he concluded that if it wasn’t it must be very fast. In 1667 students of Galileo, Giovanni Alfonso Borelli and Vincenzo Viviani, repeated this experiment with lanterns which were separated by one mile and were unable to observe any delay. With the known speed of light being 186282.4 miles per second, it would have taken .000005368193667 seconds for the light from the lanterns to transverse this distance of one mile, so to these experimenters back in 1667, the speed would have appeared to be instantaneous.

The Danish astronomer Ole Romer estimated the speed of light in 1676 by observing that the time it took Jupiter’s innermost moon Io to transverse Jupiter was less when Earth was moving towards Jupiter than when it was moving away – his estimate was that it took about 22 minutes for light to cross the diameter of Earth’s orbit. Christiaan Huygens was a Dutch astronomer, physicist, mathematician, and inventor who lived from 1629 to 1695 and to this day is still regarded as one of the greatest scientists of all time. He took Romer’s estimate of 22 minutes and combined it with his own estimate of the diameter of the Earth’s orbit to come up with a figure of 136701.7 miles per second – this was about 26.6 percent slower than the actual speed of light we know today.

Isaac Newton wrote about Romer’s calculations for the speed of light in his 1704 book Opticks, giving a time of seven to eight minutes for light from the Sun to travel to the Earth. Note that the actual known time for light to travel the mean distance from the Sun to the Earth(93 million miles) is about 8 minutes and 19 seconds.

James Bradley was an English astronomer who discovered stellar aberrations in 1729 from which he determined that the speed of light was 10210 times faster than the orbital velocity of the Earth and that it would take 8 minutes and 12 seconds to travel to the Earth from the Sun(8 minutes 19 seconds actual figure). Note that this compares with todays modern figure of 10066 times faster, which would be in error by only 1.43 percent.

Modern measurements of the speed of light have given us a very accurate result of 186282.4 miles per second in a vacuum. And we also know that the speed of light will slow down according to the density of the medium that it propagates through. Of course there is more than one way to measure the speed of light and we will take a look at some of these next.

One great way to measure the speed of light is in outer space because of the almost perfect vacuum that exists there and the fact that there is a very large scale of distance. It is typical to measure how long it takes light to transverse some reference distance such as the diameter of the Earth’s orbit. We have already mentioned how Ole Romer used this method by observing how long it took for Jupiter’s moon Io to go across the surface of Jupiter. Then by using an estimate of the diameter of the Earth’s orbit around the Sun, he came of with a figure of 22 minutes.

Also mentioned previously was the method of observing the aberration of light which was first used by James Bradley. This method involves adding the vector of light from a distant object, such as a star, and comparing it to the velocity of a moving observer, in this case an observer on Earth since the Earth is orbiting the Sun at a mean velocity of about 68350.8 miles per hour. By measuring the angular change of a star’s position(usually in arcseconds) in the sky, it is possible to calculate the speed of light in terms of the Earths velocity around the Sun and converting this to miles per second or miles per hour.

Another excellent method of measuring the speed of light is simply by measuring the time it takes for light to travel a certain distance to a mirror and back. An example of this method is by using a rotating mirror – the mirror rotates at a constant rate and since light does in-fact have a finite speed there will be a slight difference in the angle of reflection of the light on it’s way out compared to it’s way back. Since the difference in angle, the constant speed of rotation of the mirror, and the distance to the mirror are known quantities, the speed of light can be calculated. One way of using this method with a much shorter distance to the mirror is by using a laser for the light source in combination with an oscilloscope with time resolutions less than one nanosecond. The timing delay of the laser light due to the rotation of the mirror can then be measured and the speed of light calculated. This is a common method used in college Physics labs to measure the speed of light. It is important to note that measuring the speed of light through air as opposed to through a vacuum will give a slightly different value for the speed of light.

Electromagnetic constant measurements is another method of measuring the speed of light which doesn’t depend on the propagation of light waves through a vacuum. An example is solving the value of c in Maxwell’s electromagnetic equations in terms of the vacuum permittivity and the vacuum permeability – for the vacuum permittivity the capacitance and the dimensions of a capacitor can be measured and the vacuum permeability is a fixed known constant value. With these values the speed of light can easily be determined. This method was first used in 1907 to find a value for the speed of light of 186231 miles per second – this is an error of about .02738 percent.

There is a simple equation showing the relation of the speed of light(c) in terms of frequency and wavelength – c equals frequency times wavelength. One way of measuring the speed of light using this equation is to use a cavity resonator; a device which will naturally oscillate at its resonant frequencies with greater amplitudes than at other frequencies.

An example of an experiment using this method that you might be able to do on your own is with a common microwave oven. Use something that easily melts, such as margarine, and make sure that it remains stationary and doesn’t move. Turn the microwave on and observe where the first spots of melting in the margarine occur and then measure the distance between two of these points. The melting will occur first where the amplitude of the microwaves is the greatest which is where the microwaves will be somewhat more intense. Now multiply this distance by the frequency of the microwave oven being used; this will usually be on the back of the microwave or the user’s manual. This will give the value of the speed of light, usually within about 5 percent.

Interferometry is one more method to measure the speed of light. A laser beam with a known frequency is split into two beams and then they are recombined. The wavelength of light can be determined by changing the path length while observing the interference pattern and then measuring the change of the path length. Then the equation speed of light(c) equals frequency times wavelength can be used to calculate the speed of light.

Light is considered to be a wave – in classical physics, it is an electromagnetic wave in a narrow range of the electromagnetic spectrum as far as visible light is concerned. Maxwell’s electromagnetic wave equations describe the behavior of light in the classical sense predicting that the speed of light(c) at which light waves propagate through a vacuum is dependent on the distributed capacitance and inductance of the vacuum, known as respectively the electric constant and the magnetic constant in the equations.

In quantum mechanics, the electromagnetic wave propagation of light is described in terms of the theory of Quantum Electrodynamics(QED) which is the relativistic field theory of electromagnetism, also called the strange theory of light and matter by its developer, Richard Feynman, who was truly one of the most brilliant physicists in the history of science – on the same level of brilliance as Einstein and Newton. QED basically describes the behavior of the electrons surrounding the nucleus of an atom, as well as the photons of light, which is roughly 90 percent of everything we experience in our reality. Quantum Electrodynamics, over a long period of time and many experiments, has proven to be the most accurate theory in the history of science – called the jewel of Physics by its creator Richard Feynman.

In QED light is described as quanta of the electromagnetic field, which are also called photons – this includes the entire electromagnetic spectrum, not just the section that is visible light. In QED photons(quantum wave packets) are massless and so always travel at the speed of light in a vacuum, as predicted by the Special Theory Of Relativity. Although it was hypothesized that relativistic effects may not apply to arbitrarily small scales such as variations in the frequency of light, implying a change in the speed of light with different frequencies, no such change with differing frequencies of light has ever been observed, even after a number of rigorous experiments – the speed of light always remains constant through different frequencies – 186282.4 miles per second in a vacuum.

In a medium, light waves usually do not propagate at the speed of c, and different types of light waves will also travel at different speeds. The phase velocity is how fast the phase of a light wave of only one frequency will propagate through either a vacuum or a medium. How fast a light wave travels through a certain material or medium, is described in terms of the phase velocity and is also known as the refractive index of the medium – this is defined as the ratio of the speed of light(c) to the phase velocity.

Using the above explanations it makes it easier to understand that a higher refractive index will indicate a slower speed of light – the refractive index of a material depends on the frequency and intensity of the light waves, and also their polarization and direction of propagation. Often, for practical purposes, the refractive index can be treated as a constant of a certain material, or medium.

Some examples of the refractive index for visible light are 1.0003 for air, 1.3 for water, 1.5 for glass, and 2.4 for diamond. There are some extreme examples of some exotic materials with temperatures near absolute zero(-459.67 degrees Fahrenheit) where the speed of light is only a few feet or so per second. There was an extreme case of the slowing of the speed of light when two different teams of physicists claimed to have brought light waves to a complete stop by using an exotic condensate of the element rubidium cooled to near absolute zero and passing the waves through it. However, in these experiments, the light photons were really being stored in the excited states of the rubidium atoms where they would be re-emitted later. When photons of light are stopped in this way, they are no longer really light.

Einsteins Special Theory Of Relativity has established the fact that nothing in the Universe can travel faster than the speed of light in a vacuum – 186282.4 miles per second. We need to qualify this just a little bit; this is true for a positive mass. There is a hypothetical particle called a tachyon which has a negative mass and always travels faster than the speed of light; tachyons can never slow down to the speed of light but could get very close to it. This is like a mirror situation with positive mass particles – they can never reach the speed of light but can get very close to it; particle accelerators like CERN are an example of this. One thing that should be made clear here is that tachyons have never been proven to exist, they are hypothetical only.

Einsteins famous equation E equals m c squared, where E is energy, m is mass, and c is the speed of light, shows this relationship between mass, energy, and the speed of light. This is a basic version of the equation where the Lorentz factor is one and the velocity of the mass is zero; if the velocity of the mass approaches the speed of light(c), then the Lorentz factor(defined as the factor of the length, relativistic mass, and time change of an object while it is moving) approaches infinity meaning that it would take an infinite amount of energy to equal the speed of light – of course, this is not possible with a positive mass. The speed of light has been established as the ultimate top limit in the Universe for any object with a positive mass – numerous experiments have confirmed that this is absolutely the case. It should be noted here that photons are quantum wave packets which have a zero rest mass – even they can not travel faster than c, although they will always travel exactly at the speed of light in a vacuum.

One other thing should be added – we have been talking about mass here for the upper limit of the speed of light, but there is some evidence that some forms of information might be able to travel faster than the speed of light. I am specifically talking here about the phenomenon known as quantum entanglement, where particles can seemingly transmit the state of their spin a great distance apart – for example, two particles can communicate the state of their spin over any distance, even if one particle were on the other side of the Universe. A particle may have a spin one way and the other particle, when separated, will always have a complementary spin, even over this unbelievably great distance. This is a subject best reserved for a more in-depth discussion of quantum theory, and more specifically quantum entanglement.

This section on faster than light speeds, also known as superluminal motion, may seem contradictory – maybe even controversial – since we have tried to make it clear that nothing can exceed the speed of light. But when we say nothing, we should qualify that as meaning no positive mass. We have mentioned the phenomena of quantum entanglement where limited forms of information can indeed go faster than light; in fact, when this situation occurs it is as if the information were transmitted instantaneously! Another example is that the phase velocity(the rate at which the phase of the wave propagates in space) of x-rays often exceed the speed of light; however, this is massless and conveys no information. So, in this case, no energy, matter, or information travels faster than the speed of light.

As mentioned before, certain quantum effects can result in not only faster than light travel, but can seemingly occur instantaneously. The two particles that are entangled as mentioned previously are one example – they are in a superposition of two quantum states until they are observed. When they are separated and one particle is observed the quantum state of the other particle will be determined instantaneously in a complementary way to the first particle, even if it is on the other side of the Universe. Einstein had a name for this; he called it spooky action at a distance. He thought some unknown factor was involved in causing this phenomenon, so he and some other physicists formulated a thought experiment called the EPR Paradox – Einstein Podolsky Rosen Paradox. John Bell, a Scottish physicist, published in 1964 what has become known as Bell’s Theorem which is a remarkable proof supporting this strange behavior of quantum entanglement. In the many years since then, numerous experiments have completely confirmed Bell’s Theorem. In fact, there has never been any so-called unknown factor or component discovered supporting the EPR Paradox so this remains one of the mysteries of quantum theory. Since the quantum state of the first particle can’t be controlled when observed no meaningful information can be sent this way, only the very limited complementary quantum state.

Beyond a barrier in the Universe known as the Hubble Sphere, a spherical region of the observable Universe which is one thousand quadrillion quadrillion(10 to the 31st power) cubic light years in volume(the observer is at the center of this gigantic sphere), objects(such as galaxies) are receding away from the observer faster than the speed of light due to the expansion of space(the fabric of space-time) itself. Of course, the space-time continuum(not the objects in it) is massless.

At least according to modern physics, the speed of light seems to be an impenetrable barrier. No positive mass can break this barrier, the speed of light in a vacuum – 186282.4 miles per second. And yet, maybe there could be some loopholes in modern theory, at least modern in the context of the present time. After all, the physics theories of a couple of hundred years ago were modern then, and the classical physics of that time are still largely relevant today on a macro scale, but in the last century and continuing into the 21st century there has been a great revolution in physics, especially on the subatomic level and in relativistic terms with the two great theories of our time – The Special Theory Of Relativity and Quantum Theory. So do these theories represent the final great achievement of physics?

The answer to that is probably not; it is hard to believe that this would be the case in a world that has only had automobiles and electricity a little over a hundred years. What might happen in another 100 years, 200 years, 300 years, even thousands of years into a future we could not possibly imagine. The physics of that far off time could very well seem like magic today. Perhaps a way will be found to break the light barrier and it will seem ridiculously easy – the people of that future time may look back at the people of today much as we look back at the people in medieval times. And then again, maybe not; maybe the speed of light will stand forever as an insurmountable barrier, making practical travel to the stars impossible. No one really knows – the only thing I know for sure is that there is good reason to be optimistic that this is not the case.