**2020-12-04**| The Clock Paradox (Twin Paradox) and Spherical Wave Proof mathematics are used to show how Special Relativity falls apart. The idea is to use Einstein's own words and check his mathematics in order to disprove Special Relativity.

0:00 Why Worry About Relativity?

1:44 How Can Relativity Be Wrong?

4:09 Wave Medium Doppler Effect

5:20 Wave-Particle Duality

5:58 Reference Frames

8:31 Clock Paradox Explanation

16:42 Spherical Wave Proof Explanation

18:20 Spherical Wave Proof Demo

21:55 Simultaneity Animation Demos

#science #Einstein #timedilation #TheoryofRelativity

Links:

Special Relativity Animations (used at the end of the video):

https://physics.nyu.edu/~ts2/Animation/special_relativity.html#

Einstein's "Special Relativity Paper" (1905):

https://einsteinpapers.press.princeton.edu/vol2-trans/154

Einstein's "Dialogue about Objections to the Theory of Relativity" (1918):

https://einsteinpapers.press.princeton.edu/vol7-trans/82

Einstein's "Photoelectric Effect" Paper (1905):

https://einsteinpapers.press.princeton.edu/vol2-trans/100

If you want hands-on experience with the Spherical Wave Proof, then you can go to the link below and utilize this Python code to help transform the spherical wave coordinates:

https://www.online-python.com/yl146iFWAw

You can modify the moving frame speed (0.0 speed will give you the stationary spherical wave), copy the resulting coordinates, and past them into the Desmos graphing calculator to see the resulting shape (https://www.desmos.com/calculator).

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Stationary Sphere Python Code:

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import numpy as np

import matplotlib.pyplot as plt

x = np.linspace(-5.0, 5.0)

y = np.linspace(-5.0, 5.0)

X, Y = np.meshgrid(x,y)

# Graphing in terms of LightSeconds

speedOfLight = 1

seconds = 1

# Stationary Spherical Wave

stationaryFunction = X**2 + Y**2 - ((speedOfLight**2)*(seconds**2))

# Plot the function

fig, ax = plt.subplots()

ax.contour(X,Y,stationaryFunction,[0])

ax.set_aspect(1)

plt.title('Stationary Observer Light Sphere', fontsize=8)

plt.xlim(-3,3)

plt.ylim(-3,3)

plt.grid(linestyle='-')

plt.show()

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Moving Sphere Python Code:

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import numpy as np

import math

import matplotlib.pyplot as plt

x = np.linspace(-3.0, 3.0)

y = np.linspace(-3.0, 3.0)

X, Y = np.meshgrid(x,y)

# This is the moving reference frame speed, based on percentage of the speed of light

movingVelocity = 0.75

# Graphing in terms of Light Seconds

speedOfLight = 1.0

seconds = 1.0

# Lorentz Factor or Beta from the Relativity Paper

gammaFactor = 1/math.sqrt( 1-(movingVelocity**2 / speedOfLight**2) )

# Moving Frame Time Transform or Tau

tauRadius = (gammaFactor * (seconds - ((movingVelocity*X) / speedOfLight**2)))

# Moving Frame X Transform or Xi

movingX = gammaFactor * (X - (movingVelocity*seconds) )

# Moving Frame Transform Equation

movingFunction = movingX**2 + Y**2 - (speedOfLight**2 * tauRadius**2)

# Plot the Moving Function (X coordinate is shifted over by number of LightSeconds)

fig, ax = plt.subplots()

ax.contour(movingX,Y,movingFunction,[0])

ax.set_aspect(1)

plt.title('Moving Observer Light Sphere', fontsize=8)

plt.xlim(-3,3)

plt.ylim(-3,3)

plt.grid(linestyle='-')

plt.show()

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Moving Sphere Point Plotting Python Code for DESMOS:

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import math

import numpy as np

# Moving Frame Velocity in terms of percentage of the speed of light

movingVelocity = 0.98

# LightSeconds (Speed of light = 1 for each second)

speedOfLight = 1.0

seconds = 1

# Lorentz Factor Equation or Beta from the Einstein Paper

gammaFactor = 1/math.sqrt( 1-(movingVelocity**2 / speedOfLight**2) )

# Build a list of 100 values for the Y-Axis to plug into the Einstein transform equations

yList = np.linspace(-seconds, seconds, num=100)

# Get all 100 answers to the transform equations for Xi and Tau.

for yAxis in yList:

xAxis = math.sqrt((speedOfLight**2 * seconds**2)-(yAxis**2))

xi = gammaFactor*(xAxis - (movingVelocity*seconds))

tauRadius = gammaFactor*(seconds - ((movingVelocity*xAxis) / speedOfLight**2))

# Print all the Moving Coordinates

print(xi, "," , yAxis)

#print(tauRadius)