#### Introduction

In Part 1 of the series, *Proving Einstein Wrong*, we defined three requirements that individually show that relativity is wrong. As a reminder, relativity theory is proved wrong if we:

- Show that relativity contains a significant and incurable mathematical mistake
- Show that relativity is an approximation of the new theory
**Show an experimental result that contradicts relativity**

Part 2 of the series satisfies the first requirement by showing that the spherical wave proof fails. Because Einstein says that the proof is a required part of his theory, its failure means relativity is invalid. In Part 3 of the series we showed that relativity is an approximation of Modern Mechanics. This shattered the myths that relativity is the only or best predictor of many experiments; and that relativity is the only theory that leads to the equation: *E=mc ^{2}*. However, scientists are conservative when it comes to changing their belief in relativity. This means that satisfying two of three requirements will not be enough to change their minds. They will need more. A successful challenge will need to satisfy all of the requirements.

Because Modern Mechanics and relativity often provide similar results, we must find a unique experiment where both make clearly different predictions. Fortunately, such an experiment already exists: it’s called The Michelson–Morley Interferometer Experiment (MMX). [1] Similar to the analysis of the failed spherical wave proof, the Michelson–Morley experiment contains an extremely subtle mistake, which when corrected produces results that supports Modern Mechanics while excluding relativity.

#### Evaluation Criteria

To satisfy the third requirement, we must:

- Show that Modern Mechanics and relativity make different mathematical predictions for the same experiment
- Show that the Michelson–Morley experiment supports Modern Mechanics and invalidates relativity

Similar to the analyses presented in parts 2 and 3 of the series, the evaluation criteria is quantitative rather than subjective. This approach allows others to independently examine and confirm the analysis.

#### The Importance of Types (or Units)

Satisfying the evaluation criteria may seem like an insurmountable task due of the degree in which MMX has been reviewed. Although difficult, satisfying this criteria is not impossible. To show that MMX supports Modern Mechanics and invalidates relativity, we must begin by explaining why both theories make different predictions. This explanation requires that we examine the idea of **types**.

Imagine you live in San Francisco, California. Geographically the city is approximately 7 miles long by 7 miles wide. If asked to determine its area, you would quickly arrive at 49 square miles. Notice the use of the phrase “square miles.” The answer is not 49, nor is it 49 miles. Terms like “miles” or “square miles” are called **units** in mathematic and **types** in computer science. Types are extremely powerful and we use them to create useful equations. For example, when we multiply *velocity* by *time* we produce a result that is measured in terms of *distance (or length)*. *Velocity*, *time*, and *distance* are all types. Mathematically, the relationship between these types is written as the equation, *distance = velocity * time, *or simply:

*d = vt*

*Equation 1*

Equation 1, which is called the **length–based equation**, is an extremely important equation that involves *velocity*. *Velocity* is generalized and can take on any value. For example, when we consider the speed of light, *c*, the equation is rewritten as:

*d = ct*

*Equation 2*

Readers familiar with electronics or radio may recognize another important equation that involves the specific *velocity* *c*. The equation that defines the relationship between *frequency*, *velocity*, and *wavelength* is:

*λ = c / f*

*Equation 3*

Equation 3 is called the **wavelength–based equation**. Equations 2 and 3 operate on different types. Equation 2 defines a mathematical relationship between *length* (eg, meters), *velocity* (eg, meters per second), and *time* (eg, seconds); Equation 3 defines a mathematical relationship between *wavelength* (eg, meters per cycle), *velocity* (eg, meters per second), and *frequency* (eg, cycles per second). .

The proper treatment of types is critically important in mathematics and computer science where the stakes are high and mistakes can lead to catastrophic mistakes. For example, NASA lost a $125 million spacecraft because they did not properly convert values from one type to another. As a simple example where the mistreatment of types will produce a nonsensical answer, wrap a strand of wire around a pencil 100 times to make a coil. This coil consists of *100 cycles* or loops of wire. Now imagine holding this pencil and walking at *4 miles per hour*. Can we replace *distance* with *cycles* and rewrite Equation 1 as:

*time = cycles / velocity
Equation 4*

The answer is: **No**. The use of Equation 4 to conclude that *time* = 25 *hours* (eg, *time = 100 cycles / 4 miles per hour)* is just as disastrous in an equation as is the mistake that led to NASA’s spacecraft loss. It is important to recognize that Equation 4, which we refer to as the **cycle–based equation**, is simply wrong.

#### The Mistake In The Michelson–Morley Equation

As just discussed, the proper treatment of types is critically important in science and engineering where mistakes can lead to disastrous results. However when the mistakes are not clearly disastrous, identifying the problem can be subtle and difficult to find. One place where the mistreatment of types produces incorrect answers is the Michelson–Morley experiment. Michelson and Morley begin by defining the variable *D* as a distance and the variables *c* and *v* as velocities. They use Equation 1 to develop two equations that properly define relationships between *length*, *time*, and *velocity*:

*T = D / ( c – v ) and T _{1} = D / ( c + v )*

*Equation 5*

When *D* is a *length* and *c* and *v* are *velocities*, Equation 5 will correctly calculate *T* and* T _{1}* as measurements of

*time*. There is nothing wrong with these equation. Unfortunately they cannot be used in their analysis, because the variable

*D*is not used as a length. Specifically, Michelson and Morley use

*D*as:

“*D* = 2*10^{7} waves of yellow light.”

In use, the variable *D* is a number of *cycles,* not a *length*. This means their use of *D* represents the implicit use of a cycle–based equation similar to Equation 4 above, which we have shown is wrong. And we have already stated that Equation 1 cannot be used with *cycles* in place of *distance*, which means that their time–based equation is wrong. Simply said, **Michelson and Morley make a mathematical mistake when they use the number of cycles in their equation instead of distance.** This mistakes leads to an incorrect expected displacement (eg, expected result). Fortunately, we understand where their mistake occurs and provide an appropriate correction to salvage the analysis of their raw data.

#### The Modern Mechanics Correction

Modern Mechanics recognizes that *D* is a *frequency* that must be expressed in terms of the ratio *cycles:second.* For example, the *frequency* *F* of yellow light is approximately 5.4*10^{14} *cycles per second*. Using a scalar adjustment we can express this *frequency* as the number of cycles that occur in increments of time other than 1 second. For example, the original frequency *F* of yellow light is expressed equivalently as:

D = 2*10^{7} waves of yellow light per 11 / 299 792 458 seconds

Since *F* is a *frequency* *D* is also a *frequency*, because scalar multiplication maintains the original units. Writing an equivalent frequency in this form is no different than recognizing that 30 miles per half–hour, 60 miles per hour, and 120 miles per 2 hours are equivalent velocities. The distinction between length–based and wavelength–based equations explains how the displacement equation is different in Modern Mechanics than in relativity. In length–based equations times are added, while in wavelength–based equations wavelengths (or more specifically, inverse–wavelengths) are averaged.

Modern Mechanics analyzes the Michelson–Morley experiment using wavelength–based equations where the variable *D* is correctly recognized as a *frequency*. Identification of the original mistake followed by explaining why Modern Mechanics and relativity make clearly different predictions for the experiment satisfies the first item in the evaluation criteria above.

#### Analysis of the Michelson–Morley Experiment

Contrary to how the experiment is often portrayed: *The Michelson–Morley experiment did not directly measure velocity and the result of their experiment is not null (or zero)*. This is easily confirmed by reviewing their original paper. [1]

When the experiment is analyzed using an implicit cycle–based equation, Michelson and Morley compute an Earth orbital velocity (EOV) of about 8km/s. Mathematically, we use statistics to determine a confidence range that contains the EOV. As illustrated in Figure 1, this range is approximately 6km/s to 10km/s.

As shown above, we are 99.9% confident the EOV is between 6km/s and 10km/s. This means that 30km/s is statistically not possible, a finding that excludes many aether–based models as theoretical explanations. A failure to provide an answer that supports an aether–based theory does not automatically mean that relativity – a non–aether based theory – is right. In fact, 0km/s is not statistically supported, which means that means that MMX does not support relativity either! Remember, statistics says that we are 99.9% sure that the EOV is between 6km/s and 10km/s. This means we are less than 0.1% confident that the EOV is 0km/s. This is quantitative evidence that MMX does not support relativity.

As explained in chapters 1 and 7 of * DISRUPTIVE* and in

*Revisiting the Michelson and Morley experiment to reveal an Earth orbital velocity of 30 kilometers per second*, the Modern Mechanics wavelength–based equation will calculate a corrected displacement using Michelson and Morley’s experimental data. [2, 3] In fact, when the experiment is analyzed using the revised displacement, the wavelength–based equation produces an EOV of 32km/s.

As shown above, we are 99.9% sure the EOV is between 23km/s and 41km/s. This means that 30km/s is possible, rendering support for aether–based theories. Like Michelson and Morley’s original analysis, the corrected analysis continues to exclude theories that require 0km/s as the answer.

A second way of analyzing the results is based on the size of the experimental error, which is defined as the difference between the actual and expected results. When MMX is analyzed using Michelson and Morley’s cycle–based equation, the experimental error is 8km/s for theories that predict 0km/s and 22km/s for theories that predict 30km/s. Conversely, the experimental error associated with the wavelength–based equation is less than 3km/s.

One possible criticism of this analysis is the idea that the wavelength–based equations are in some way faked to produce the desired answer: 30km/s. This criticism is overcome by showing that Miller’s repeat 1933 experiment also produces 30km/s when his data is analyzed using the same wavelength–based equation. [2, 3, 4] Originally, his data was analyzed using the cycle–based equation producing 11km/s, an answer that falls outside of the 99.9% confidence interval of the original MMX result. The fact that Miller’s experiment did not confirm MMX partially explains why his work was subsequently discounted. However, when his data is analyzed using the wavelength–based equation, the experimental error is less than 0.3km/s! Not only did he satisfy his goal of building a more accurate interferometer, his measurement is essentially a bull’s-eye!

This analysis demonstrates **that Modern Mechanics is statistically supported by MMX, while simultaneously invalidating relativity.** This satisfies the second item in the evaluation criteria above as well as the third requirement for proving relativity wrong.

#### Conclusion

The Michelson–Morley experiment is widely believed to support relativity theory. However, this conclusion is built upon 1) an incorrect belief that the original Michelson and Morley analysis is correct, and 2) an interpretation of their result as 0km/s that ignores the statistical explanation of experimental error. Because an answer of 0km/s is not statistically supported, **we have satisfied the third requirement that invalidates relativity by showing a specific experiment that contradicts the theory.** Equally important, we have shown that when the MMX raw data is properly analyzed using the wavelength–based equation, the Michelson–Morley experiment was a success.

#### References

[1] Michelson and Morley, *“On the Relative Motion of the Earth and the Luminiferous Ether” *

[2] Bryant, * DISRUPTIVE*, chapters 1 and 7

[3] Bryant, “*Revisiting the Michelson and Morley experiment to reveal an Earth orbital velocity of 30 kilometers per second*”

[4] Miller, “*The Ether-Drift Experiment and the Determination of the Absolute Motion of the Earth*”

––––

**Steven B. Bryant** is a futurist, researcher, and author who investigates the innovative application and strategic implications of science and technology on society and business. He is the author of * DISRUPTIVE: Rewriting the rules of physics*, which is a thought–provoking book that shows where relativity fails and introduces Modern Mechanics, a unified model of motion that fundamentally changes how we view modern physics.

**is available at Amazon.com, BarnesAndNoble.com, and other booksellers!**

*DISRUPTIVE*

*Images ©2015 Steven B. Bryant
Photo of Steven B. Bryant ©2015 Steven B. Bryant, Photo by Amy Slutak
Interferometer image By Case Western Reserve University (http://www.cellularuniverse.org/AA2MM_Aether.htm) [Public domain], via Wikimedia Commons*