1. The Significance of the Speed of Light
relating to Einstein’s Special theory of
Relativity
Kenneth A. Hansen
December 14th, 2013
Abstract
This paper explores the values and properties of the natural phenomenon known
as “light” or electromagnetic radiation and its relationship to several other
physical laws since the discoveries made by Albert Einstein. Topics such as light
waves, particle theory, space, time dilation, the force of gravity, subatomic
particles, and Energy are discussed. The goal is to lead the reader to the
conclusion that light waves/particles and its universal constant speed has a
specific value which is directly linked to mass, gravity, time, velocity, wave
amplitude, space, momentum, intensity, frequency, wavelength, subatomic
particles, and Energy. The implication being that the nature of the universe is
deeply intertwined with this universal constant.

2. Table of Contents
Introduction
Einstein’s Special Theory of Relativity
What is Light
Wave or Particle? Properties of Light
Classical vs. Quantum
Particle Model
Wave Model
Interactions with Matter
Planck’s Constant, de Broglie Wavelength, and Tachyons
Speed of Gravity
Neutrinos
Lorentz Contraction
Time Dilation
Conclusion
Bibliography

3. Einstein’s Special Theory of Relativity
and the Speed of Light
Mankind's understanding of the universe has made great strides in the near past.
Today we have primarily Newtonian Mechanics, Relativity Theory, and
Quantum Theory. Newtons laws describe the physics of forces acting upon
bodies. Newton’s laws, however, lose accuracy at close to light speeds. Since an
object gains mass as its velocity approaches the speed of light, the formula F=ma
is strictly non-relativistic and becomes inaccurate. Special Relativity Theory
corrects classical mechanics to handle situations involving motions nearing the
speed of light making it the most accurate model of motion at any speed.
Quantum theory deals with the atomic and subatomic spacetime and permits
only probable or statistical calculation of the observed features of subatomic
particles. My interest is primarily with Einstein’s Special Relativity and
particularly, Light.
The discoveries of Light and its properties have greatly contributed to the
progress of scientific knowledge and should be studied more as light
waves/particles are phenomena created by nature and widely affect the nature of
the universe. The purpose of this paper is to show the importance of the
universal constant of light. The fundamental laws of the universe are deeply
intertwined with the its properties. It was Albert Einstein was the first to shed
light on this fact with the Special Theory of Relativity in 1905. It is the accepted
physical theory regarding the relationship between space and time. It is based on
two postulates: that the laws of physics are identical in all inertial systems; and
that the speed of light in a vacuum is the same for all observers, regardless of the
motion of the light source. The inconsistency of classical mechanics with
Maxwell’s equations of electromagnetism led to the development of special
relativity, which corrects classical mechanics to handle situations involving
motions nearing the speed of light. Special relativity implies a wide range of
consequences, which have been experimentally verified, including length
contraction, time dilation, relativistic mass, mass–energy equivalence, a universal
speed limit, and relativity of simultaneity. It has replaced the conventional notion
of an absolute universal time with the notion of a time that is dependent on
reference frame and spatial position. Rather than an invariant time interval
between two events, there is an invariant spacetime interval. Combined with
other laws of physics, the two postulates of special relativity predict the
equivalence of mass and energy, as expressed in the mass–energy equivalence
formula E = mc2
, where c is the speed of light in vacuum.
Relativistic Mass - In special relativity, an object that has nonzero rest
mass cannot travel at the speed of light. As the object approaches the speed of

4. light, the object's energy and momentum increase without bound. As the objects
velocity approaches the speed of light its mass drastically increases requiring
more energy to further accelerate the object. It would require infinite energy to
bring an object with even the smallest mass to the full speed of light.
A defining feature of special relativity is the replacement of the Galilean
transformations of classical mechanics with the Lorentz transformations. Time
and space cannot be defined separately from one another. Rather space and time
are interwoven into a single continuum known as spacetime. Events that occur at
the same time for one observer could occur at different times for another. In
special relativity space and time are so closely related that mathematically, it can
be useful not to have to specify whether a variable represents a distance or a
time.The theory is called "special" because it applied the principle of relativity
only to the special case of inertial reference frames.
What is light?
Light refers to electromagnetic radiation of any wavelength, whether
visible or not and may be viewed in one of two complementary ways: as a wave
in an abstract electromagnetic field, or as a stream of massless particles called
photons. Depending on the wavelength, light can be in the form of radio waves,
microwaves, infrared radiation, visible light, ultraviolet radiation, x-rays, and
gamma radiation. The speed of light is a universal constant measured to be
299,792,458 meters per second. The first successful measurement of c was made
by Olaus Roemer in 1676. He noticed that, depending on the Earth–Sun–Jupiter
geometry, there could be a difference of up to 1,000 seconds between the
predicted times of the eclipses of Jupiter's moons, and the actual times that these
eclipses were observed. He correctly surmised that this is due to the varying
length of time it takes for light to travel from Jupiter to Earth as the distance
between these two planets varies. He obtained a value of c equivalent to 214,000
km/s, which was very approximate because planetary distances were not
accurately known at that time.
One of the most recent experiments done to measure the speed of light was
when Physicists measured the energy required to change the speed of electrons as
they hopped from one orbital to another inside atoms of dysprosium, all while
Earth rotated over a 12-hour period. This allowed the scientists to measure that
the maximum speed of an electron, which, according to special relativity should
be the speed of light, is the same in all directions to within 17 nanometers per
second. This measurement was 10 times more precise than previous tests of
electrons' maximum speed.

5. Properties of Light
Scientists have observed that light energy can behave like a wave as it
moves through space, or it can behave like a discrete particle with energy that
can be absorbed and emitted. Atoms emit radiation when their electrons return
from an excited state back to their original level. They will absorb energy from
light if the frequency of the light oscillation and the frequency of the electron or
molecular "transition motion" match. This "transition motion" frequency is
related to the frequencies of motion in the higher and lower energy states.
Particle Model (Quantum)
The particle-like or “quantum view” of light is as a particle-like wave
packet. Each wave packet is called a photon. A photon has no mass and no
charge. It is a carrier of electromagnetic energy and interacts with other discrete
particles (e.g., electrons, atoms, and molecules). A beam of light is modeled as a
stream of photons, each carrying a well-defined energy that is dependent upon
the wavelength of the light. Quantum Theory dictates the probabilities of
subatomic particles and can be calculated with wave functions and Schrödinger's
equations. A wave function is the most complete description that can be given to
a physical system. Solutions to equation describe not only molecular, atomic, and
subatomic systems, but also macroscopic systems, possibly even the whole
universe.
Wave Model (Classical)
The propagation of light or electromagnetic energy through space can also
be described in terms of a traveling wave motion. The wave moves energy,
without moving mass, from one place to another at a speed independent of its
intensity or wavelength. This wave nature of light is the basis of physical optics
and describes the interaction of light with media. Many of these processes require
calculus to describe them rigorously. Light exhibits certain behaviors that are
characteristic of any wave and would be difficult to explain with a purely
particle-view. For example: The light from a point light source spreads out
uniformly in all directions. Waves carry energy, and the amplitude of a wave is
generally a measure of how much energy the wave carries. The amplitude of light
is the number of photons hitting a spot per time interval rather than the amplitude
of a single photon.
The energy is relative to amplitude squared. E α A² The frequency and
wavelength are directly proportional to the speed of light by the equation c = λ f.
Shorter wavelengths carry more energy than longer wavelengths.The limit for
long wavelengths is the size of the universe itself, while it is thought that the
short wavelength limit is in the vicinity of the Planck length, although in
principle the spectrum is infinite and continuous. Intensity is similar to
brightness, and is measured as the rate at which light energy is delivered to a unit

6. of surface, or energy per unit time per unit area. Light scattering can be thought
of as the deflection of a ray from a straight path. Electromagnetic waves share six
properties with all forms of wave motion:
Superposition - For many kinds of waves, including electromagnetic, two or
more waves can traverse the same space at the same time independently of one
another. This means that the electric field at any point in space is simply the
vector sum of the electric fields that the individual waves alone produce at the
point. Both the electric and magnetic fields of an electromagnetic wave satisfy
the superposition principle. Thus, given multiple waves, the field at any given
point can be calculated by summing each of the individual wave vectors.
Interference - The first definitive demonstration of the wavelike nature of light
was the classical two-slit experiment performed by Thomas Young in 1801. The
two slits are very small compared to their separation distance. Thus, each slit
produces diffracted spherical waves that overlap as they expand into the space to
the right of the barrier. When they overlap, they interfere with each other,
producing regions of mutually reinforcing waves.
Polarization - Polarization arises from the direction of the E-field vector with
respect to the direction of the light’s propagation. Since a light wave’s electric
field vibrates in a direction perpendicular to its propagation motion, it is called a
transverse wave and is polarizable.
Diffraction - Conclusive evidence of the correctness of a wave model came with
the explanation of observed diffraction and interference. This property of light
that causes it to spread out as it travels by sharp edges or through tiny holes can
be explained by light having wavelike properties. Diffraction is predicted from
Huygens’ principle which states: Every point of a wave front may be considered
the source of secondary wavelets that spread out in all directions with a speed
equal to the speed of propagation of the waves.
Refraction - When a ray of light passes from one medium to another, it changes
direction at the
interface because of the difference in speed of the wave in the media. The ratio of
this speed
difference is called the index of refraction (n) according to Snell’s Law. Snell's
law is a formula used to describe the relationship between the angles of incidence
and refraction, when referring to light or other waves passing through a boundary
between two different isotropic media.

7. Reflection -When a ray of light reflects off a surface (such as a mirror), its new
direction depends on only the angle of incidence. The law of reflection states that
the angle of incidence on a reflecting basic surface is equal to the angle of
reflection.
Interactions of Light with Matter
As light travels through different materials, it scatters off of the molecules
in the material and is slowed down. The important interactions are absorption and
scattering. Absorption is a transfer of energy from the electromagnetic wave to
the atoms or molecules of the medium. Energy transferred to an atom can excite
electrons to higher energy states. Energy transferred to a molecule can excite
vibrations or rotations. The wavelengths of light that can excite these energy
states depend on the energy-level structures and therefore on the types of atoms
and molecules contained in the medium. The spectrum of the light after passing
through a medium appears to have certain wavelengths removed because they
have been absorbed. This is called an absorption spectrum. Selective absorption
is also the basis for objects having color. A red apple is red because it absorbs the
other colors of the visible spectrum and reflects only red light. Light scattering is
the deflection of a ray from a straight path.
Ordinary transparent media like water, glass and crystal slow light slightly.
In 1999 Dr. Lene Vestergaard Hau slowed light to about 38 miles an hour (17
m/s) in a system involving beams of light shone through a chilled sodium gas.
More recently, two independent teams of physicists have brought a light beam to
a full stop, one led by Dr. Lene Vestergaard Hau of Harvard University and the
Rowland Institute for Science in Cambridge, Mass., and the other by Dr. Ronald
L. Walsworth and Dr. Mikhail D. Lukin of the Harvard-Smithsonian Center for
Astrophysics. Using a distantly related but much more powerful effect, the
Walsworth-Lukin team first slowed and then stopped the light in a medium that
consisted of specially prepared containers of gas. In this medium, the light
became fainter and fainter as it slowed and then stopped. By flashing a second
light through the gas, the team could essentially revive the original beam. The
beam then left the chamber carrying nearly the same shape, intensity and other
properties it had when it entered. We have used laser light with fiber optic cables
(silica glass) and until recently the light traveled 31% slower than in a vacuum.
Soon we will be able to transfer data at 99.7% of the speed of light thanks to
researchers at the University of Southampton in England.

8. Planck’s Constant, The de Broglie Wavelength, and Tachyons
The Planck constant was first described as the proportionality constant
between the energy (E) of a charged atomic oscillator in the wall of a black body,
and the frequency (ν) of its associated electromagnetic wave. This relation
between the energy and frequency is called the Planck relation:
The Planck relation describes the energy of each photon in terms of the
photon's frequency. Since the frequency , wavelength λ, and speed of light c are
related by λν = c, the Planck relation for a photon can also be expressed as
The planck constant , which governs the strength of quantum effects, and
the intrinsic weakness of the gravitational force team up to yield the planck
length, which is small almost beyond imagination: a millionth of a billionth of a
billionth of a billionth of a centimeter (10^-33 cm.). If we were to magnify an
atom to the size of the known universe, the Planck length would barely expand to
the size of a tree. The above equation leads to another relationship involving the
Planck constant. Given p for the linear momentum of a particle (not only a
photon, but other particles as well), the de Broglie wavelength λ of the particle is
given by
The de Broglie wavelength relations show that the wavelength is inversely
proportional to the momentum of a particle. Also the frequency of matter waves,
as deduced by de Broglie, is directly proportional to the total energy of a particle.
Some theoretical physicists have speculated on the possible existence of particles
which always travel faster than light, avoiding the complications of acceleration
past the cosmic speed limit. Physicist Gerald Feinberg even gave them a name,
tachyons. If they existed tachyons would be really, really bizarre things, for
example they would always be moving faster than light, dropping to less than
300,000 km/s would be as impossible for them as exceeding this speed is to us.
In 1973 two Australian researchers, Roger Clay and Philip Crouch, claimed
successful detection of a tachyon but no one has ever been able to duplicate this
result, and Clay has subsequently concluded “No positive evidence has been
found using conventional scintillation detectors for producing a tachyon signal”.
Experiments to create tachyons in collisions with particle accelerators at
Amhearst College and Brookhaven National Laboratory (both in the USA) had
negative results.

9. Speed of force of Gravity
The speed of gravitational waves in the general theory of relativity is equal
to the speed of light in vacuum, c. Within the theory of special relativity, the
constant c is not exclusively about light; instead it is the highest possible speed
for any physical interaction in nature. Formally, c is a conversion factor for
changing the unit of time to the unit of space. This makes it the only speed which
does not depend either on the motion of an observer or a source of light and/or
gravity. Thus, the speed of "light" is also the speed of gravitational waves and
any other massless particle. Such particles include the gluon (carrier of the strong
force), the photons that light waves consist of, neutrinos, and the theoretical
gravitons (quantum particles) which make up the associated field particles of
gravity. The strength of gravity and the intensity of light both abide by the
inverse-square law, which states that a specified physical quantity or intensity is
inversely proportional to the square of the distance from the source of that
physical quantity. Newton's law of universal gravitation follows an inverse-
square law, as do the effects of electric, magnetic, light, sound, and radiation
phenomena. In equation form:
Speed of Neutrinos
The speed of Neutrinos has also been found to travel at the speed of light.
CERN’s conclusion for the experiment published January 24, 2013 are as
follows; “ The OPERA experiment after improving its timing system, has
confirmed the result, showing no significant deviation of the muon neutrino
velocity from the speed of light.
Lorentz Contraction
Length Contraction is the phenomenon of a decrease in length measured by an
observer of objects which are traveling at any non-zero velocity relative to the
observer. At extremely high speeds, space is warped to the point that the object's
dimensions are altered. This contraction is usually only noticeable at a substantial
fraction of the speed of light. As the magnitude of the velocity approaches the
speed of light, the effect becomes dominant, as can be seen from the formula:

10. Time Dilation
“It is one of the deepest insights into the nature of reality ever discovered”
-Brian Greene
Just as the frequency and wavelength are in a balance and always equal the
speed of light, so it also goes with velocity and time. The velocity of an
object/observer and the rate of time it experiences are proportional to the
universal constant. This means that if a person is at rest, he/she is “travelling”
through time at 100%. If the person has a velocity 50% the speed of light, he/she
is travelling through time at half the rate. The faster you are moving, less time
elapses. The big detail here is that light that is travelling through a vacuum is not
travelling through the time dimension at all, it is timeless.
Implications
The implications that the speed of light has a direct correlation with
Energy, Mass, Space, Time, Velocity, Momentum, Wavelength, Frequency, and
the force of Gravity. The latest experiment to measure the speed of light
confirmed that the formula E = mc2
is correct to an incredible accuracy of better
than one part in a million, or six decimal places. One of the largest implications
of Einstein’s work is that there are no absolute values, they have become relative.
This makes constants like the speed of light an anchor in an ocean of math.
Another implication is that mass can be converted to energy with E=mc^2. Time
has also become relative. If you were to travel on a spaceship away from earth at
half the speed of light for 10 “earth” years, you would only age five years. Space
is also relative to velocity. If a meter stick was travelling half the speed of light,
its length would appear to be only 86.6025404 centimeters long. The speed of the
attractive force of Gravity and subatomic particles are also limited by the
universal constant.
The behavior of light waves alone has its own implications. It has been
calculated that the sun emits approximately 1 x 10^45 photons/second. The
radiation interacts with our planet in many ways, the ultraviolet rays reflect off of
the ozone layer at the angle of incidence and continue through space. Other
wavelengths make it through and refract through mediums such as gas, liquid,
glass, and crystals. Other light waves diffract off of edges or through small
openings changing their direction. When more than one light wave is travelling
through the same space, they interfere with the crescents and peaks. More than
one light wave can traverse the same space as others and the energy at any one
location at any time can be calculated by the sum of several electric field’s
produced by the electromagnetic waves with superpositioning. Simply put, light

11. is constantly going through space, transporting energy, bouncing off of mediums,
passing through mediums, interfering with other light, being absorbed and
emitted by atoms, and continuously spanning over an increasingly large area.
Light behaves similarly on a larger scale through space. Space between
planets is mostly a vacuum, but not a complete vacuum. It is estimated that there
is less than 1 hydrogen atoms per meter cubed. So most of the light travels
uninterrupted over large distances. As the space around a large planet, star, or
black hole is warped, the linear path of light follows a curved line, so the light
can bend around and continue in a new path or even possibly return towards the
light source. With all of these properties combined it would be safe to assume
that there is energy in the vast majority of space at every moment in time. Light
waves flowing through each-other, sometimes in every direction at any particular
point in space. Even within matter, x-rays and (depending on the energy level)
neutrinos can fit between the atoms with their extremely small wavelengths.
Another characteristic of light is that it does not travel through time at all.
This leads me to believe that its half-life is potentially infinite. It cannot decay
because it is timeless. So as long as all of its energy is not absorbed, a particular
beam of light can exist with energy for eternity. The intensity of light does
decrease over distance. All of these properties, values, relationships, and effects
of light lead me to the conclusion that it is strongly intertwined with the physical
laws governing our universe. To conclude, the knowledge and understanding we
now have regarding Electromagnetic radiation, when seen in this context, should
be seen as a key piece of the puzzle of the Universe that we are tediously trying
to put together.

12. Bibliography
International Bureau of Weights and Measures (2006), The International System
of Units (SI) (8th ed.), p. 112, ISBN 92-822-2213-6
Hartle, JB (2003). Gravity: An Introduction to Einstein's General Relativity.
Addison-Wesley. p. 332. ISBN 981-02-2749-3
Laplace, P.S.: (1805) "A Treatise in Celestial Mechanics", Volume IV, Book X,
Chapter VII, translated by N. Bowditch (Chelsea, New York, 1966)
OPERA collaboration, T. Adam et al., Measurement of the neutrino velocity with
the OPERA detector in the CNGS beam, JHEP 10 (2012) 093.
Resnick, R.; Eisberg, R. (1985). Quantum Physics of Atoms, Molecules, Solids,
Nuclei and Particles (2nd ed.). New York: John Wiley & Sons. ISBN 0-471-
87373-X.
Albert Einstein (1905) "Zur Elektrodynamik bewegter Körper", Annalen der
Physik 17: 891; English translation On the Electrodynamics of Moving Bodies
by George Barker Jeffery and Wilfrid Perrett (1923); Another English translation
On the Electrodynamics of Moving Bodies by Megh Nad Saha (1920).
Tom Roberts and Siegmar Schleif (October 2007). "What is the experimental
basis of Special Relativity?". Usenet Physics FAQ. Retrieved 2008-09-17
Albert Einstein (2001). Relativity: The Special and the General Theory (Reprint
of 1920 translation by Robert W. Lawson ed.). Routledge. p. 48. ISBN 0-415-
25384-5
Richard Phillips Feynman (1998). Six Not-so-easy Pieces: Einstein's relativity,
symmetry, and space–time (Reprint of 1995 ed.). Basic Books. p. 68. ISBN 0-
201-32842-9.

13. Taylor, Edwin F. and Wheeler, John Archibald, Spacetime Physics, 2nd edition,
1991, p. 12.
Brian Greene ,The Elegant Universe, 1999, page 36.
Schrödinger, E. (1926). "An Undulatory Theory of the Mechanics of Atoms and
Molecules". Physical Review 28 (6): 1049–1070
Curtis Wilson (1989), "The Newtonian achievement in astronomy", ch.13 (pages
233–274) in "Planetary astronomy from the Renaissance to the rise of
astrophysics: 2A: Tycho Brahe to Newton", CUP 1989.
David C. Cassidy, Gerald James Holton, Floyd James Rutherford
(2002).Understanding physics. Birkhäuser. pp. 339 ff. ISBN 0-387-98756-8
U. A. Bakshi, A. P. Godse (2009). Basic Electronics Engineering. Technical
Publications. pp. 8–10. ISBN 978-81-8431-580-6. Retrieved 2011-10-16