Mathematical Slight of Hand: Special Relativity and the Light-like Separated Events Equation Part 2


There’s a mathematical riddle that’s been floating around for a while now. It tells the story of three men staying at a hotel room, each paying 10 dollars to stay there. The manager then realizes that he overcharged the men by 5 dollars, and tells his busboy to give the men the surplus money back to them. Instead, the Busboy pockets 2 dollars and gives 1 dollar back to each one.

Now that the three men have received a dollar back, that means that they’ve each paid 9 dollars. But if you do a multiplication of that number and add in the 2 dollars that the Busboy kept, you end up losing a dollar.


So where’s the extra dollar?

The answer is that the above formulation is flawed in its construction. It changes the action from what the room cost to what the men paid and adds in the two dollars of cost to the different argument, which is faulty logic. Instead of adding that number to the total, it should be subtracted instead. Then the original left over total five dollars should be added back into the total and you get the expected 30 dollars.

Recall, then, that in the last article I wrote, I concluded that the ‘light-like separated events’ equation is formulated on faulty logic, stating that c has both a translation element and a time element which puts the equation in trouble from the start. We’ll start with a form of the equation that is more consistent with the Pythagorean Theorem:


And then I argued that c has both a translation and a time element in it, so you can rightly express the above equation like this.


This is because the left-hand term is simply the result of a simple 3-D Pythagorean Formulation of the Velocity components of a light-ray in a vacuum. The left-hand side is known as speed. It is a scalar value, meaning that there is no direction associated with it. As mentioned before, the changes in x, y, and z values are vector components in Cartesian-coordinates.

The mathematicians try to get around the left-hand side by an abstraction. They state that c, the speed of light in a vacuum, is constant no matter where it is in space and no matter what object a photon of light is emitted from. Therefore, you can replace the translation and time components with a simple number, and thus, once again:


It is from this abstraction that the mathematician gains the rationale to treat time as the fourth dimension and they come up with the concept known as ‘space-time’.

Here’s the problem.

I told you that the right side of this equation is composed of x, y, and z vector components in a Cartesian-coordinate system. But the right side of the equation is not a vector. It is a dot-product of the vector, which produces a scalar. You can’t add vectors and end up with a scalar on the right-hand side. That’s why the components on the right-hand side are squared. There are no dimensions on the right-hand.

The mathematician uses a slight of hand by only producing the radial component of a 3-D radial coordinate system. The variable, or c, in our case, is just a raw value that denotes the speed of the photon. It doesn’t say anything about the direction that photon is going. So the mathematician only partially does the conversion from Cartesian-Coordinates to Spherical-Coordinates, or 3-D Polar Coordinates. To complete this calculation, you must calculate the following angles:


Whereis already calculated from Pythagorean’s Theorem. The new Spherical Vector is then expressed as the scalar value plus the two additional angles needed specify the direction of the photon:


This is a vector in 3-D space in spherical components, unlike the light-like separated events, which is a scalar equation.

Additionally, you can bring about the mathematicians abstraction of c to it’s logical completion by simply acknowledging that the right-hand side of the light-like separated events can be expressed as Cartesian-coordinate conversions of the polar radius.




Mathematics are very notorious for having an “anything goes” attitude for defining its own reality. It’s how it justifies the existence of time as a fourth dimension in our universe. The way that the light-like separated events equation was derived should be treated carefully and with much skepticism, especially when it claims to be describing real events in the Universe.

Cosmic Blunder? Einstein’s Special Relativity and the Light-like Separated Events Equation


The Assumptions that were listed in my last blog form the basis for what is known as ‘Einstein’s Special Relativity’. It is named with the term ‘Special’ because it applies to the case where the observers and the events in the frame are at a constant velocity (I.E. there is no acceleration being applied to anything anywhere in the system).

To summarize the postulates again we post the following.

The laws of physics are invariant, or identical in all inertial systems in non-accelerating frames of reference.

The speed of light in a vacuum is the same for all observers, regardless of the motion of the light source.

These rules were then formulated into a set of equations to describe them in mathematical terms in what is known as the Lorentz Transformations. The start of which is the following assumption for light-like separated events.


Where did they get this equation?

When you stop being intimidated by the number of variables in this equation and realize that there’s a basic form to it, you can see where they derived it from. ‘Light-like separated events’ is a fancy term for the event where a light-ray travels from one point to another. Reverse engineer this equation and you’ll find yourself with a 3-dimensional version of a basic geometry problem. Let’s recall, in basic geometry:




The variable r is a radius formed by the Pythagorean Theorem, and the above equation is just one of two parts used to convert Cartesian Coordinates to a Radial Coordinate System. The ‘Light-like separated events’ equation is just a rearrangement of a 3-dimensional version of the Pythagorean Theorem, which is as follows:


Where eq4  is the 3-Dimensional radius of our 3-Dimensional Cartesian-Coordinates. To get the ‘Light-like separated events’ equation back into its original form, we have to observe a couple things about it.

  1. c is a speed. It is a translation in space covered over a period of time.
  2. eq5are all merely translations. They are not velocity vector components, but merely the distance covered in a certain direction with no time component.

These two observations are important because we can now detect the time-component that is hidden from us by the term. Let us rearrange the ‘Light-like separated events’ equation so that the translation components are separated from the speed components.



That looks a little more familiar, now, doesn’t it? Let’s make one more observation. That is: a distance covered between two points of time is a speed, or velocity. Also, a speed component that is multiplied by a span of time becomes a distance covered, or a translation. There are two ways that we can now reach the original form of the equation that they derived our ‘Light-like separated events’. If is a speed, then it is a distance covered divided by a difference in time.


Did you see what we did there? By separating the speed of light into its distance and time components, we now have a piece of the denominator and numerator that cancel each other out. So we get our Pythagorean Theorem in the form of distance covered:


Alternatively, we can divide the original equation by the time components to turn the Cartesian translation into speed components.


You can now express the right-hand side in the speed components of a Velocity vector to make it more readable.


That’s all this is. The beginning of Lorenz’s transformation can be easily concluded to be deeply flawed in its logic from the very beginning. Based on what we know from above we can observe the following.

In the concept of space-time, time is treated as a fourth dimension amongst its Cartesian coordinates. The “light-like separated events” equation does this by displaying time multiplied by the speed of light as a way of demonstrating it as a fourth coordinate. But the “light-like separated events equation suffers from the fact that the speed of light is merely a distance covered divided by the same time components that it is multiplied by in the original equation. A speed multiplied by a time-span merely becomes a distance covered with no speed components whatsoever, so you cannot treat time as a fourth dimension, because that dimension immediately cancels itself out in this equation.

Fielding Alternatives to Einstein’s Universe: Prologue

We live in extraordinary times.

In the advent of the information age, the availability of information and data to the public is abundant, if not almost overwhelming.  The propagation of news events and reveals to the public have not only become nearly instantaneous, but also more accurate and truthful, with the public gaining more tools to decipher public fact from fiction.  The middlemen of information from its source to the public have become an obsolete vehicle and has almost been replaced by simple connections to an ISP and browser.

The results of such proliferation of information are obvious.  Wars of ideas and concepts have erupted and intensified over social platforms such as twitter and youtube.  We are seeing the status quo, previously held up by our institutions in the last century, under a constant barrage of challenges against it on all levels.  And with everyone able to voice their opinions (at least for now) on every topic and also gain an audience in the process, now nothing in this universe is too sacred to be challenged or debated to the point of being debunked and dismissed.

And when I say that nothing is too sacred to be debunked, that includes Einstein’s universe and his field equations.



I will write to you admitting that the idea of challenging Einstein’s view of the universe is not a new one.  His theory of General Relativity and field equations had their detractors from the beginning–most notably from Nikola Tesla, the inventor of Alternating Current electrical power, who wrote scathingly against them in many derogatory comparisons to beggars looking for kings, etc.  There have always been a steady number of scientists who’ve rejected Einstein’s view of the Universe since then, but now there is a community that has formed and is actively looking to replace Einstein’s model of the universe with something else.

A lot of what I’m writing to you about is based on a particular community within the science /engineering sphere called the Thunderbolts project, for which I’m pouring through their written works and videos, grasping their theories and hypothesis that fly in the face of Einstein.

As such, this series of blogs is meant to be a record of my own explorations of the ideas, as well as the reason and possible necessity of dethroning Einstein as our view of the Universe.  I will do this blog as objectively as I can, because it may well be that Einstein is right, even though the evidence that I’ve seen in their presentations seem compelling that he is not.  But when evaluating the alternative views, we must be sure that we are right in the eyes of science, and that the image of truth not be obscured about what we wish to be true.

With this in mind, when debating Einstein’s relativity, it’s important to discard all opinions on the man.  This means refraining from personal attacks against his character or even our opinions of him against our opinions of other scientists at the time, such as fore-mentioned Tesla.  Instead, we must re-evaluate the ideas that he put forth; we must delve into his mathematics and figure out how he derived them.  We must look at the universe and decide for ourselves whether or not it fits what he describes them to be in his equations.

This is important.  Any platitudes about the man’s perceived character, whether good or bad, or his standing among his peers of scientists and mathematicians at the time are irrelevant and do not help the advancement of science even one iota.  It is infinitely better to tackle the idea because it is the idea that affects our understanding of the universe and, as a result, how we proceed further as a species.

I will leave this blog where my thoughts have been for a while on the topic of astronomy and maybe some hints at my bias towards the subject so my reader may point them out in this series.  At this moment, the mainstream view of the universe, which is based on a merging of Einstein and a big bang theory, have become overburdened with patches to explain its inconsistencies we find against what we think is true.  These patches, which started off with dark matter and dark energy, then led to scientists pushing a universe that have multiple different dimensions beyond the 3 that we can obviously know of through our senses, have broken our current model of the universe to the point where we need to consider throwing the entire concept into the trash bin and start over at Sir Isaac Newton.

There it is.  Now that it’s out, we can start this journey.