Relativity is a magnificent equality principle of nature at creating the universe. However, it has many counter-intuitive, mind-blogging concepts, and many of us may have a hard time at understanding it. How could light propagate in vacuum without a media? How could the speed of light remain constant for all observers? Why there are time dilation, length contraction, and loss of simultaneity? Why the laws of nature remain the same for all moving frames? How could space and time be bent by mass and energy? Are our brains wired in such a way so that it is always difficult to understand relativity in a natural way? Or there may exist a new knowledge framework, and a new representation so that relativity become easier to be understood. This video offers a mechanical approach for the first time to explain relativity. It attempts to make relativity easier for the general public to understand.

1. Xiaofei Huang, Ph.D., Foster City, CA 94404, HuangZeng@yahoo.com

2. There are lots of books, videos, and slide shows on
relativity with stories of spaceships, trains, lasers, and
moving light clocks and light rulers. However, people are
still confused by the theory generation after generation.
After reading a whole stack of those books, many of
them don’t understand why light can propagate in pure
vacuum without any medium, why the speed of light is
magically constant, why a moving clock is slower and a
moving ruler is shorter, and most importantly, how
could the laws of physics remain the same for all
uniformly moving frames.

3.  Relativity says that light can travel in vacuum without any
medium. However, this statement is just the emperor’s new
clothes in the theory. It mystifies the propagation of light. It is
also bluntly against our intuition. There is no way for any wave to
propagate in space without any medium.
 Permittivity and permeability are not the properties of space. It
makes no sense to assign those physical properties to space.
Rather, they are the properties of the medium for propagating
electromagnetic waves. All waves need a medium to propagate in
reality, including light.

4. In relativity, it has often been argued that light travels at a
constant speed because it propagates in vacuum as waves
without the need of any medium. It has been treated as a
genius idea at solving the puzzle of the constancy of the
speed of light. However, such a reasoning is also the
emperor’s new clothes in relativity.
This statement mystifies the constancy of the speed of light,
making it unfathomable. It sounds more like a magic than a
logic statement. Also, it is logically incorrect to postulate a
statement, such as the constancy of the speed of light, to
prove the statement itself in a circular way.
What we need here is a true mechanical explanation for the
constancy of the speed of light (if it is true in reality) without
mystifying it. You don’t understand it
because you are dummies.

5. There is a critical logic error in relativity theory. To be more
specific, the constant speed of light should not be treated as
the second key postulate of relativity. The fact is that
relativity holds true regardless of whether or not the speed
is constant. This postulate is simply redundant for the
theory. It is the biggest misconception in the theory,
confusing almost everyone including Einstein.

6. The laws of physics remain the same for all uniformly
moving frames.
There are Two Key Postulates in Relativity
Postulate 1: The Principle of Relativity
As measured in any inertial frame of reference, light is
always propagated in empty space with a definite
velocity c that is independent of the state of motion of
the emitting body.
Postulate 2: A constant speed of light

7. If a particle travels at the common maximal speed limit
in one inertial frame, it must travels at the same speed in
all inertial frames. That is, its speed is constant in this
case.
Two Important Logical Consequences
From the First Postulate
Consequence #2: The Constant Speed
All free objects must share exactly the same maximal
speed limit. Otherwise, the principle of relativity is
violated.
Consequence #1: A Common Maximum Speed Limit

8. The Second Postulate is Redundant
 We can see that the constancy of the speed of an object is a
logical consequence of the first postulate. There is no need
to postulate the constancy of the speed of light. Using it as
the second postulate to explain relativistic effects such as
time dilation, length contraction, and loss of simultaneity
could be confusing to the general public. Often times,
people mistakenly thought it is the cause of those
relativistic effects. However, the truth is that we have those
relativistic effects as long as the common maximal speed
limit is of a finite value. In other words, we suffer from time
dilation and length contraction as long as the common
maximal speed limit is of a finite value, regardless of
whether or not the speed of light is constant.

9. The laws of physics remain the same for all uniformly
moving frames.
We Only Need the First Postulate
Postulate 1: The Principle of Relativity
As measured in any inertial frame of reference, light is
always propagated in empty space with a definite
velocity c that is independent of the state of motion of
the emitting body.
Postulate 2: A constant speed of light

10. Constant Speed of Light as Biggest Misconception
 The constancy of the speed of light is not only a redundant
postulate, but also an inaccurate statement about reality.
 In the real world, the photon never moves like a point object
with a definite position at any given time instance. Instead, it
moves like a wave without a definite position at any given time
governed by quantum laws. The light clocks and rulers used in
the classical relativity thought experiments never exist in reality.
They only exist in our imaginations. Simply put, those thought
experiments are wrong in terms of physical reality.
 With the same argument, the classical motion equation for light,
𝑐2 𝑡2 − 𝑥2 = 0, where the photon is treated as a classical point
object, is also incorrect. It should not be used to derive the
Lorentz transformation, a key transformation in relativity.

11. Constant Speed of Light Should be Hypothesis
 The constant speed of light should be a hypothesis subject to
experimental verification. Up to now, nobody is sure about the
constancy of the speed of light. Neither the Maxwell’s equations,
nor the Michelson-Morley experiment can tell us the constancy
of the speed of light because they are not exactly accurate.
Recently, it has been found that spatially structured photons in
free space travel slower than the speed of light.
 Vacuum isn’t really empty, but is filled with virtual particles. A
virtual particle pair can pop out of the vacuum for a very short
time interval then disappear. Light will interact with those
virtual particles. At present, nobody knows if the interaction
with virtual particles in vacuum will slow down light from its
maximum speed limit.

12. Spacetime Metric should not be Treated as
Fundamental Concept in Relativity
 It has been used as the fundamental concept both
in special relativity and general relativity. However,
the concept is valid only at the classical limit. It
works only for computing the trajectory of a
classical point-like object. It doesn’t work for
quantum particles which behave more like waves
than point-like objects.

13. Reconciling Relativity with Quantum Mechanics
Special relativity has been established around 1905 and
general relativity is around 1915. Both of them are more
than a decade ahead of the establishment of quantum
theory. All the concepts used in relativity are classical
ones. For example, objects have definite position and
velocity at any time instance. Each object has a definite
trajectory in spacetime. However, those pictures are
inaccurate, often times misleading in the quantum
world. You can not simply treat an atomic system as a
solar system because each electron of the atom doesn’t
have a definite orbit. Rather, it has a cloud of probability.
It is desirable to reconcile relativity with quantum
theory.

14. The fundamental reason for relativity remaining as a
mystery is because the mechanical explanation for it is
missing so far. Without it, relativity remains as a mystery
and a magic of nature, hard to be understood by human
brains. It is time to offer a mechanical explanation for
relativity based on quantum theory.

16. Common Speed Limit
 Based on the standard model, the most successful theory of
particle physics, if the Higgs field did not exist, all
elementary particles would travel at the speed of light.
 Some of elementary particles interact with the Higgs field
to have rest mass and slow down to any speed below the
speed of light. The ones which do not interact with the
Higgs field will always travel at the speed of light.
 In quantum field theory, elementary particles are excited
states of the underlying physical field, so called field
quanta. For example, electron field generates electrons and
electromagnetic field generates photons.

17. A Fundamental Field For All
 As mentioned before, to have the principle of
relativity, all particles must share exactly the same
maximal speed limit at any position of space and at
any time. If there is any slightest difference in the
maximal speed limit for different particles, the
principle of relativity is violated.
 To resolve the mystery, the author postulate that all
elementary particle fields are different manifestations
of a more fundamental field, traditionally called the
ether. Different particles correspond to different
excited states of this fundamental field, so that they
have different spins, charges, colors, and masses.

18. A Fundamental Postulate
for Relativity and Gravity
at the most fundamental level of
nature, everything is made of particle
waves and field waves. All of those
waves are different excited states of a
fundamental medium, traditionally
called the ether. Those waves, either
free ones or coupled ones, are
propagating in space with the same
pattern defined by a quadratic partial
differential operator 𝑔 𝜇𝜈 𝜕𝜇 𝜕𝜈.
It is postulated by the author that

19. The Definition of 𝒈 𝝁𝝂
𝝏 𝝁 𝝏 𝝂
 In relativity, 𝑔 𝜇𝜈 𝜕𝜇 𝜕 𝜈 is a shorthand notation for
෍
𝜇=0
3
෍
𝜈=0
3
𝑔 𝜇𝜈
𝜕𝜇 𝜕 𝜈
where 𝜕𝜇 is a shorthand notation for 𝜕/𝜕𝑥 𝜇. As a
convention, 𝑥0 = 𝑡, 𝑥1 = 𝑥, 𝑥2 = 𝑦, and 𝑥3 = 𝑧. 𝑡 is the
time coordinate, 𝑥, 𝑦, 𝑧 are spatial coordinates.

20. Wave Propagation in Gravity-Free Vacuum
When there is no gravity, it has been found in quantum mechanics that
the propagation of particle waves and field waves are governed by the
following operator:
−
1
𝑐2
𝜕𝑡
2
+ 𝜕 𝑥
2
+ 𝜕 𝑦
2
+ 𝜕𝑧
2
This operator is often times denoted as □, called the d’Alembert operator.
In particular, for any free particle, either a boson or a fermion, it satisfies
the Klein-Gordon equation as
□𝜓 𝑥, 𝑦, 𝑧, 𝑡 =
𝑚2 𝑐2
ℏ2
𝜓 𝑥, 𝑦, 𝑧, 𝑡
Here, 𝜓 𝑥, 𝑦, 𝑧, 𝑡 is the wave function of the particle describing the state
of the particle, 𝑚 is the mass of the particle, 𝑐 is a constant defining the
maximum speed limit for all particles, and ℏ is the reduced Planck
constant, one of the most important constant in physics.
3/17/2017 20

21. The electric field E and
the magnetic field B are
uniquely defined by the
electromagnetic four
potential field A.
A Case Study: Electromagnetic Waves
Electromagnetic waves can be imagined as a
self-propagating oscillating wave of electric
and magnetic fields. In general, an
electromagnetic field can be represented by a
4 component vector field, called an
electromagnetic four-potential field, denoted
as A(x, y, z, t). When there is no gravity in a
vacuum space, it satisfies the following wave
function:
−
1
𝑐2
𝜕𝑡
2
+ 𝜕 𝑥
2 + 𝜕 𝑦
2 + 𝜕𝑧
2 𝐴 𝑥, 𝑦, 𝑧, 𝑡 = 0
That is, the propagation of the
electromagnetic four-potential field is
governed by the d’Alembert operator
−
1
𝑐2
𝜕𝑡
2
+ 𝜕 𝑥
2
+ 𝜕 𝑦
2
+ 𝜕𝑧
2
3/17/2017 21

22. Einstein’s Geodesic Equation
as the Classical Limit
Using the universal wave propagation operator 𝑔 𝜇𝜈 𝜕𝜇 𝜕𝜈, the
Klein-Gordon equation can be simply generalized to
𝑔 𝜇𝜈 𝜕𝜇 𝜕𝜈 𝜓 𝑥, 𝑦, 𝑧, 𝑡 =
𝑚2 𝑐2
ℏ2
𝜓 𝑥, 𝑦, 𝑧, 𝑡
It has been proven by the author that the above generalized
wave equation falls back to Einstein’s geodesic equation in
general relativity at the classical limit. Einstein’s geodesic
equation is used to compute the trajectory of a point-like
object in a curved spacetime with its metric as 𝑔 𝜇𝜈.
The wave equation at the top is more general than Einstein’s
geodesic equation because the latter is only the classical
limit of the former.
3/17/2017 22

23. Essentials of Quantum Waves
 the universal wave propagation operator 𝒈 𝝁𝝂
𝝏 𝝁 𝝏 𝝂
manifests itself as the spacetime metric
𝒈 𝝁𝝂 𝒅𝒙 𝝁
𝒅𝒙 𝝂
at the classical limit, where the
covariant metric tensor 𝒈 𝝁𝝂 is the inverse of the
contravariant metric tensor 𝒈 𝝁𝝂
. Simply put, the
geometry of spacetime is a result of the propagation of
quantum particle waves in space and time.
Based on the previous investigation, we can conclude that

24. As a summary, we have
the universal wave propagation
parameters 𝒈 𝝁𝝂
(𝝁, 𝝂 = 𝟎, 𝟏, 𝟐, 𝟑)
define the geometry of spacetime
with the spacetime metric as 𝒈 𝜇𝜈.

25. Quantum Wave Propagation vs Spacetime Metric
 The spacetime metric 𝒈 𝝁𝝂 𝒅𝒙 𝝁
𝒅𝒙 𝝂
is a fundamental
concept in both special and general relativity. From the
previous investigation we can see that it is only the
classical limit of the universal wave propagation
operator 𝒈 𝝁𝝂 𝝏 𝝁 𝝏 𝝂.
 At the most fundamental level of nature, everything
are just waves. Therefore, the wave propagation
operator is more fundamental than the spacetime
metric. The latter belongs to classical physics, valid
only when every object can be treated as a point object
with a definite position and velocity at any given time.

26. The universal wave propagation
operator 𝒈 𝝁𝝂 𝝏 𝝁 𝝏 𝝂 is more fundamental
than the spacetime metric 𝒈 𝝁𝝂 𝒅𝒙 𝝁
𝒅𝒙 𝝂
at understanding relativity .

27. Einstein suggested that gravitational potential is
defined by the spacetime metric 𝑔 𝜇𝜈. Whenever
there are variations of 𝑔 𝜇𝜈, it causes gravitational
acceleration.
The variations of 𝑔 𝜇𝜈 are caused by the presence
of matter and energy and others defined by
Einstein’s field equation in general relativity.

28. Gravitational potential is defined by the
universal wave propagation parameters
𝒈 𝝁𝝂, instead of the spacetime metric𝒈 𝝁𝝂 as
suggested by Einstein.
Since 𝑔 𝜇𝜈
is more fundamental than 𝑔 𝜇𝜈,
the author hypothesizes that

29. Demystifying Relativity-The Essence
At any point of spacetime, the propagation operator 𝑔 𝜇𝜈 𝜕𝜇 𝜕𝜈
can be normalized to the standard form as
− Τ1 𝑐2 𝜕𝑡
2
+ 𝜕 𝑥
2 + 𝜕 𝑦
2 + 𝜕𝑧
2
and remains the same after the Lorentz transformation. That
is exactly the reason why the laws of physics remain the
same regardless of gravity, and the relative motion of an
observer.
Mechanical Explanation for Relativity
In particular, to any observer at his local space, every
hydrogen atom, water molecule, protein, or any other atoms
or molecules remain the same in their structures and
properties regardless of the gravity, and motion of the
observer. Otherwise, life is impossible.

30. we have relativity simply because the
universal wave propagation operator
𝒈 𝝁𝝂 𝝏 𝝁 𝝏 𝝂 is normalizable to
− Τ𝟏 𝒄 𝟐
𝝏 𝒕
𝟐
+ 𝝏 𝒙
𝟐 + 𝝏 𝒚
𝟐 + 𝝏 𝒛
𝟐 and remains
invariant under the Lorentz
transformation.
The author concludes that

31. there is no way for laws of physics to remain
the same regardless of gravity and motion if
 The universal wave propagation operator
is not of the quadratic form 𝒈 𝝁𝝂
𝝏 𝝁 𝝏 𝝂, or
 the propagation operator 𝒈 𝝁𝝂 𝝏 𝝁 𝝏 𝝂 is not
shared by all particles.
It is an elegant design of nature because
The second condition is the reason for
the author to postulate that different
elementary particles are propagating
in the same medium as different
excited states.

32. 𝒈 𝝁𝝂
𝝏 𝝁 𝝏 𝝂=Relativity, Gravity
Simply put, we have

34. Important Property of
Universal Wave Propagation Operator
There is a very important property for the universal wave
propagation operator in its standard form. It is invariant in
form under the Lorentz transformation shown as follows
−
1
𝑐2
𝜕𝑡
2
+ 𝜕 𝑥
2
+ 𝜕 𝑦
2
+ 𝜕𝑧
2
𝑥′
= 𝛾 𝑥 − 𝑣𝑡
𝑦′ = 𝑦
𝑧′
= 𝑧
𝑡′ = 𝛾(𝑡 −
𝑣
𝑐2 𝑥)
Lorentz
Transformation
𝛾 = 1/ 1 −
𝑣2
𝑐2
−
1
𝑐2
𝜕𝑡′
2
+ 𝜕 𝑥′
2
+ 𝜕 𝑦′
2
+ 𝜕 𝑧′
2

35. Note that the Lorentz transformation is defined as
𝑥′
= 𝛾 𝑥 − 𝑣𝑡
𝑦′ = 𝑦
𝑧′ = 𝑧
𝑡′ = 𝛾(𝑡 −
𝑣
𝑐2
𝑥)
where 𝛾 = 1/ 1 − 𝑣2/𝑐2, called the Lorentz factor.
The Lorentz transformation defines a linear transformation
from the spacetime coordinates 𝑥, 𝑦, 𝑧, 𝑡 of the original frame
to the spacetime coordinates 𝑥′, 𝑦′, 𝑧′, 𝑡′ of a new frame. Note
that the spatial origin of the new frame is 𝑣𝑡, 0,0 in the
original frame. That is, the new frame is moving with a
constant velocity 𝑣 with respect to the original one. The two
frames are in relative motion with the velocity 𝑣.

36. the invariance of the universal wave propagation
operator in its standard form
−
𝟏
𝒄 𝟐
𝝏 𝒕
𝟐
+ 𝝏 𝒙
𝟐 + 𝝏 𝒚
𝟐 + 𝝏 𝒛
𝟐
under the Lorentz transformation is the actual cause
for the principle of relativity to hold true in nature. It is
a mechanical explanation for why laws of physics
remain the same for all uniformly moving frames.
A Mystery Solved!
The author concludes that
The essence of special relativity

37. The spacetime metric of classical special relativity is
−𝑐2 𝑑𝑡2 + 𝑑𝑥2 + 𝑑𝑦2 + 𝑑𝑧2
It is a manifestation at the classical limit of the
universal wave propagation operator in its standard
form
−
1
c2
∂t
2
+ ∂x
2
+ ∂y
2
+ ∂z
2
Therefore, the essence of special relativity is the
invariance of the universal wave propagation operator
in its standard form, not the symmetry of spacetime.
The wave propagation is more general and
fundamental than the spacetime metric.
The Essence of Special Relativity

38. The true reason to have the Lorentz
transformation is the invariance of the
universal wave propagation operator under
this transformation such that the relativity
principle holds true.

39. If we use a computer program to simulate
any physical process using the universal
wave propagation operator at the lowest
level, and to simulate the observations of
the process in different frames, we always
find that the spacetime coordinates of
different frames satisfy the Lorentz
transformation.

40. There are many ways to derive the Lorentz
transformation from other conditions, such as the
constant speed of light (+ homogeneity of space and
time + isotropy of space + relativity principle), or the
invariance of the space time interval
Δs2
= c2
Δt2
− Δx2
− Δy2
−Δz2
However, those are purely mathematical ways that build
up logical connections and equivalence among different
mathematical statements and equations, not causality
in physics. In mathematics, it is also perfectly fine to say
that we have the constancy of the speed of light because
spacetime satisfies the Lorentz transformation.
Mathematical Equivalence ≠ Physical Causality

41. The Lorentz transformation is not
caused by the constancy of the speed of
light. This is an example of the right
answer but for the wrong reason in
physics. It simply doesn’t matter whether
or not the speed of light is constant to
have the Lorentz transformation.

42.  The inverse Lorentz transformation can be obtained
simply by exchanging the spacetime coordinates as
𝑥 ↔ 𝑥′
, 𝑦 ↔ 𝑦′
, 𝑧 ↔ 𝑧′
, 𝑡 ↔ 𝑡′
, and replacing the
velocity 𝑣 by −𝑣 because the two frames are moving in
an opposite direction relative to each other.
Specifically, we have
𝑥 = 𝛾 𝑥′ + 𝑣𝑡′
𝑦 = 𝑦′
𝑧 = 𝑧′
𝑡 = 𝛾(𝑡′ +
𝑣
𝑐2
𝑥′)

43.  As postulated here, all particles are excited wave packets of the
same medium. In reality, no matter how stiff the medium is, the
maximal speed limit must be finite. That is the exact reason why
light has a speed limit. So are other particles.
 This can also be explained using the Klein-Gordon equation
mentioned before. Because all particles satisfy the equation as
□𝜓 𝑥, 𝑦, 𝑧, 𝑡 =
𝑚2 𝑐2
ℏ2
𝜓 𝑥, 𝑦, 𝑧, 𝑡
Here, 𝑚 is the mass of the particle, 𝑐 is a constant. When m=0,
then the speed of the particle wave is c. When m > 0, from the
equation at the classical limit, the speed must be any value less
than c, including the value 0. That is the particle can be at rest
when it has a mass.

45. As revealed before, in order to have the laws of
physics remain the same, the spacetime
coordinates of the moving frame and those of
the original one must satisfy the Lorentz
transformation as a constraint. This has
manifestations on the measurements related to
space and time. The examples are relativistic speed
addition law, the constant speed phenomenon,
time dilation, length contraction, and loss of
simultaneity. They are called the relativistic effects.

46.  When time and space are defined by the Lorentz
transformation, the classical speed addition law: 𝑢 = 𝑢′ + 𝑣, is
no longer valid. Instead, it should be replaced by relativistic
speed addition law.
 Assume that there is an object with its measured velocity in a
moving frame as (𝑢′ 𝑥, 𝑢′ 𝑦, 𝑢′ 𝑧). Then its velocity in the
stationary frame can be discovered using the Lorentz
transformation as
(𝑢′ 𝑥, 𝑢′ 𝑦, 𝑢′ 𝑧)
𝑢 𝑥 = (𝑢 𝑥
′ + 𝑣)/(1 +
𝑣
𝑐2
𝑢 𝑥
′ )
𝑢 𝑦 = 𝛾𝑢 𝑦
′ /(1 +
𝑣
𝑐2
𝑢 𝑥
′ )
𝑢 𝑧 = 𝛾𝑢 𝑧
′ /(1 +
𝑣
𝑐2
𝑢 𝑧
′ )
𝛾 = 1 − 𝑣2/𝑐2

47.  From the relativistic speed addition formula, it is
straightforward to prove that if an object is moving at
the speed limit c in one frame, then its measured speed
in any other frames is always c. That solves the mystery
of the constant speed of light. Specifically, if light is
traveling at the speed limit, then its speed remains the
same in all frames. Otherwise, if light is traveling at a
speed less than the speed limit c, then the speed of light
can not be constant.
 From the formula, we can also see that c is the maximal
speed limit for all particles in nature. No matter how
long you add up speed for an object by acceleration, c is
its maximal speed limit. Its speed can be arbitrarily
close to the limit, but never reach the limit.

48.  Whenever we change the state of a clock from
stationary to a steady motion, it appears to slow down
in ticking rate. If we jump to the frame moving together
with the clock, it restores the original ticking rate. This
called time dilation.
 Time dilation can be derived mathematically from the
Lorentz transformation. For a clock stationary in the
second frame (x′, y′, z′, t′), let the elapsed time be Δ𝑡′.
Since it is stationary in it, we have Δ𝑥′ = 0. From the
inverse Lorentz transformation, we have
Δ𝑡 = 𝛾 Δ𝑡′
+
𝑣
𝑐2
Δ𝑥′
= 𝛾Δ𝑡′
Since 𝛾 > 1 when 𝑣 ≠ 0, we have Δ𝑡 > Δ𝑡′.

49.  Assume there are two identical clocks in relative
motion. Then to each clock, the other clock appears to
run slower than itself.
Your clock
is slower
Your clock
is slower

50. To measure the length of a ruler, either stationary or moving,
the key point is to take down the coordinates of the two end
points of the ruler at the same time and subtract them to get
the measured length.
Your should take down the
coordinates of the two end points
of the ruler at the same time!
𝑥1(𝑡) 𝑥2(𝑡)
𝐿 𝐴 = 𝑥2 𝑡 − 𝑥1(𝑡)
𝑥3(𝑡′) 𝑥4(𝑡′)
𝐿 𝐵 = 𝑥4 𝑡′ − 𝑥3(𝑡′)A
B

51. Whenever we change the state of a ruler from stationary to a
steady motion, it appears to be shortened along the moving
direction. If we jump to the frame moving together with the
ruler, it restores the original length. This is called length
contraction.
Length contraction can also be derived mathematically from
the Lorentz transformation. For a ruler stationary in the second
frame (x′, y′, z′, t′), let its length along the 𝑥′-axis is Δ𝑥′. Since
we measure its length at the same time in the first frame
x, y, z, t , we have Δ𝑡 = 0. From the Lorentz transformation, we
have Δ𝑥′ = 𝛾 Δ𝑥 − 𝑣Δ𝑡 = 𝛾Δ𝑥. That leads to Δ𝑥 = Δ𝑥′/𝛾.
Since 𝛾 > 1 when 𝑣 ≠ 0, we have Δ𝑥 < Δ𝑥′.

52.  Assume there are two identical rulers in relative
motion. Then to each ruler, the other ruler appears to
be shorter than itself along the motion direction.
Your ruler
is shorter
Your ruler
is shorter

53. If we use a computer program to simulate
any clock or ruler using the universal wave
propagation operator at the lowest level, we
always get time dilation, length contraction,
and any other relativistic effects.

54. Time dilation and length contraction
are not caused by the constancy of the
speed of light. This is another example
of the right answer but for the wrong
reason in physics. It simply doesn’t
matter whether or not the speed of light
is constant to have time dilation and
length contraction.

55. The most important work on relativity theory has been
done in history by Galileo, Newton, Michelson, Lorentz,
Poincaré, Einstein, and Minkowski. There were also
contributions by Voigt, Fizgetald, and many others. This
presentation is just an attempt to make it easier for the
general public to understand the fascinating theory.