- The document discusses time dilation, which is the phenomenon where time passes at different rates for observers in different frames of reference due to the constancy of the speed of light. It provides an example using a light clock to show how time passes more slowly for observers moving relative to the clock. - The author outlines the derivation of the time dilation formula using principles of special relativity and geometry. The formula shows that observed time increases relative to proper time by the gamma factor, which depends on velocity. - Real-world examples of time dilation are given, such as muons surviving longer in the upper atmosphere than expected due to time passing more slowly for them. The author concludes that time and space are relative based on the const

1. Alexis Diaz
Alexis Diaz
SPCS 2015 ­ Frontiers of Physics
Time Dilation Paper
19 July 2015
______________________________________________________________________________
The Encroachment of Time Dilation on Prior Knowledge
Abstract
The unprovable nature of postulates has long proven to be problematic in the world of physics .
The problem with postulates is that they are regarded as absolute without question or extensive
research. Hastily written formulas are written to match ideas that the conglomerate of the literate
would perceive to be true and correct. This often perpetuates bias and lack of opposing views
and information. This is the case for the concept of light and its medium. ​This paper suggests
with examples that light has no medium and its speed is a constant. In response to this, it is time
and space that are affected and warped thereafter to ensure that light remains a constant no
matter the speed of its light source. This is known as time dilation and using the knowledge of
today, I will hone in on the inaccuracies that guide the reader to the common misconception that
time is constant for all observers. The primary target of this paper is researchers and physicists;
however, people with all levels of experience may find relevance to daily life as the paper will
discuss the uses of time dilation to an appropriate degree.
Introduction
When we reached the point where we could demonstrate that light was a wave, then it was
presumed that the wave must have a medium in which to travel. Sound waves travel through air,
it is safe to assume light waves must travel through some sort of medium as well. Since no
medium was apparent between the earth and the sun, they assumed it was transparent and thus
not readily observable. They call this theoretical medium the ether. The popular presumption was
that this ether was stationary and filled all of space. This involved the presumption that there was

2. Alexis Diaz
an absolute reference frame in the universe, and that all the movement of planets and stars was
through this ether. It was hypothesized that the ether was required to have light move through the
vacuum of space. Just the way sound requires air to move from one place to another. How else
can waves move through the vacuum of light, unless there was some medium there, known as the
ether. Ether, they theorized was an invisible nothingness that permeates the universe. Its only
physical property is that it allows light to propagate through it.
These presumptions guided my experiment to find evidence of the ether.
Calculating precise measurements of the speed of light, made testing the predicted effects of
ether on the speed of light possible as well.
The Earth orbits the Sun at approximately 66,500 miles/hr. Compared to the speed of light, the
Earth is moving relatively slow and if light travels through ether, then as the Earth moves
through the ether, the speed of light should be different going with the ether than perpendicular
to it and in an attempt to show the effects of the ether on the speed of light, I conducted an
experiment to confirm or disprove the conjecture above. It is designed to measure the speed of
the ether and to find an absolute reference frame, one that could be at rest.
The interferometer was devised to detect minute differences in speed between two beams of light
and was paramount in the experiment’s accuracy.
Light from one source is split in two direction through a half­silvered mirror these beams are
bounced between other mirrors and then recombined back into a single beam.
When two light beams combine, if their waves are completely synchronized​, ​the peaks combine
to make an even more intense peak, known as in phase; if they are one half wavelength off, their
peaks combine and cancel out the intensity, known as out of phase. Slight differences in speed

3. Alexis Diaz
between two light waves will therefore produce a pattern based on the amount of interference
between the two beams, this is known as an interference pattern.
Examining the interference pattern from the two light beams sent out in different directions
would clearly show if the speed of each light beam were different in different directions. No such
difference was detected.
The experiment confirmed that the speed of light is constant, regardless of the speed of light
source. The results are inconsistent with knowledge adhering to the properties of light and the
ether, yet consistent with. One way to resolve the contradiction is my proposition that light is
constant.
Methods
Consider a simple clock consisting of one mirror A and a light source mirror B, between which
a light pulse is bouncing. The separation of A and B is ​d​ and the clock ticks once each time the
light returns to the light source after being reflected.
In the frame where the clock is at rest (diagram
below), the light pulse traces out a path of length 2​d
and the period of the clock is 2​d​ divided by the
speed of light.
Scenario 1: You are in the same inertial frame as the
light clock. You are therefore measuring the proper
time, denoted . The Mirrors are separated bytΔ 0
distance “d”. The light moves with a speed “c
The proper time for one tick is given by: t Δ 0
= c
2d
Scenario 2: You are in a different inertial frame to
the light clock. The light clock is moving with
velocity v, in the x direction. The path the light takes

4. Alexis Diaz
is now different as it has only a finite speed. The time taken for one tick is denoted ∆t, the
observed time.
In the diagram, “d” represents the vertical distance between the mirrors.
In scenario 1, the stationary observer here observes a particular time, but what about a moving
observer? The diagram below shows the change:
Here we have moving mirrors with the photon moving at the same speed and hitting the same
place on the mirrors (so that it would be identical to the first diagram if the mirrors were not
moving). All the parameters here are the same, expect for the movement, and relativity states that
then the time will change. We can start deriving how time differs for stationary and moving
observers. I have outlined each step in the appropriate length below:
The value for the observed time in a moving reference frame (scenario 2) is:
t Δ = c
2L
The value for the observed time in a non­moving reference frame (scenario 1) is:
tΔ 0 = c
2d
Applying Pythagoras’ theorem the length L is given by:
L = √d ( )2
+ 2
vΔt 2

5. Alexis Diaz
Combine the two equations above:
t Δ = c
2
√d )2
+ ( 2
vΔt 2
Rearrange the equation for proper time to make “d” the subject of the equation:
d = 2
cΔt0
Combine the two equations above:
t Δ = c
2
√( ) )2
cΔt0 2
+ ( 2
vΔt 2
Square both sides and simplify:
t [ ]Δ 2
= 4
c2 4
c Δt2 2
o
+ 4
v Δt2 2
t tΔ 2
= Δ 2
0 + c2
v Δt2 2
Collect like terms on the same side of the equation:
t tΔ 2
− c2
v Δt2 2
= Δ 2
0
Factor:
t (1 ) tΔ 2
− c2
v2
= Δ 2
0
Set equal to ∆t as the subject of the formula:
tΔ 2
=
Δt2
0
(1− )c2
v2
Take the square root of both sides:
tΔ =
Δt0
√(1− )c2
v2
Alternatively:
t t Δ = Δ 0 *
1
√(1− )c2
v2
*Note​: you will the square root term expressed as gamma, or , giving the final equation:γ
t t γ Δ = Δ 0

6. Alexis Diaz
If we accept that each pass of light between the mirrors is the a second, then the same unit of
time now takes longer to pass when the clock is in motion. What does this mean? Time cannot be
an absolute value, it changes depending on how we look at it. Specifically, how a second is not
the same for every observer from every perspective. In other words, time slows down for objects
approaching the speed of light. This slowing of time at high speeds is referred to as time dilation.
Conclusion
Time and space are relative. Time dilation can be inferred from the observed fact of the
constancy of the speed of light in all reference frames.This constancy of the speed of light
means, counter to intuition, that speeds of material objects and light are not additive. It is not
possible to make the speed of light appear greater by approaching at speed towards the material
source that is emitting light. It is not possible to make the speed of light appear less by receding
from the source at speed. From one point of view, it is the implications of this unexpected
constancy that take away from constancies expected elsewhere.
Although human speeds are not significant enough to record a substantial effect of time dilation,
we can observe examples of time dilation in nature. Elementary particles, such as muons in the
upper atmosphere, are one of such portrayal. The muons are created in the upper atmosphere and
travel at a high velocity towards the earth’s surface; however it is expected that few would
survive the flight despite the high velocity. Nonetheless when scientists compared results of
muons having traveled distances from the top of a mountain and at sea level, more survived than
initially thought. This is in part of its perspective in the Earth frame, where the muon’s velocity
gives them a longer half life. From the frame of reference of the muon, its lifetime is unaffected,
considering they were travelling at a large fraction of the speed of light relative to us and so time
slowed down for them.
I speculate that one day in the near future our space ships imitate the muon, in terms of speed.
Being able to extend lifetimes by shortening distance relative to the inertial frame. Its benefit will
enable interplanetary travel possible on human time scales. In addition, to the reduction of
psychological and physiological stresses of long space journeys placed on the astronauts.