For the last couple of weeks or so I've been reading the papers of Miles Mathis on milesmathis.com. From what I can tell his work is sound, and I'm tempted to already include Mathis with my other favorite authors, which is a list I hold in very high regard.

In this post, I will summarize my impressions from the essays I have read so far. There are over 300 in total, making up over 1500 pages. Mathis is seeking to redefine our understanding of motion in more than one dimension. While I am not currently in a position to analyze the experimental validity of all of his claims, my impression is that his work is highly consistent.

I think the reason Mathis's work still has not received broader recognition is that his writing style does not follow the expected academic conventions, and the complexity of the material places it just out of the reach of the average amateur scientist or mathematician. So I'm going to try to present some of his essential ideas to give first-time readers some direction.

Mathis claims, (and I believe him) that he is virtually the only one who is really taking seriously the full implications of Einstein's relativity regarding motion along a curve. His argument begins with an analysis of the concept of velocity:

Time is not a measurement of "time." Time is a measurement of the movement in or on a given clock: the vibration of a cesium atom, the swing of pendulum, the movement of a second hand. And this given clock is uniform only by definition. It is uniform relative to a standard clock. It is only believed to be more uniform, based on previous definitions and previous clocks. - http://milesmathis.com/time.html

Mathis's central claim, from which all his other arguments follow, is that the measurement two-dimensional motion requires the consideration of the time variable, which many present-day mathematical tools, including fundamental parts of calculus, ignore. Measurement is time-independent, motion which we record as a velocity, is time-dependent. As Mathis explained both time and displacement are measurements of movement. Time and displacement just measure movement in two separate ways.

Velocity tells us the ratio of these two measurements. Mathis is claiming that to calculate relativistic effects properly, movement along a curve invalidates the comparison. It does not work to compare movement along a curve to time directly, because movement along a curve changes the observer's frame of reference, so that relativistic shift occurs in their perception of time. Curved motion therefore must be broken up into its one-dimensional components before the velocity can be accurately measured.

These claims lead to the obvious question: where is Mathis's proof?

Mathis discusses experimental data regarding his analysis in depth on his website. Specifically, he talks about data concerning Mercury's orbit, anaylsis of fictitious forces due to the earth's rotation such as the coriolis effect and tides, the dark matter hypothesis, and many other more theoretical problems in higher-level mathematics and physics.

I have not reviewed Mathis's results concerning experimental data, and so cannot comment on these papers other than to say they exist. I was actually drawn to Mathis's work by the depth of understanding I hear in his writing, on math and physics, but also on art.

Mathis's whole argument hinges on his claim that curved motion and straight line motion are fundamentally different. This is because movement in two-dimensions is not a simple translation. Curved motion is two-dimensional--the analysis of curved motion requires multiple frames of reference to analyze it, and therefore it cannot be treated as if it were a motion on a straight line.

One recurring question is “what is time?” Time may be the fourth dimension,
but the only way we have to measure it is in reference to physical
space. There is no way to measure time without tracing the measurement
back to some observable spatial displacement. As Mathis explains, “Every
clock measures movement: the vibration of a cesium atom, the swing of
pendulum, the movement of a second hand. Any given clock is uniform only
by definition."

No type of measurement takes place outside of the three spatial dimensions. All measurement and all forms of quantification take place in terms of displacement. Every other unit we have is a translation from a measured displacement. We can hear a noise is really loud, but noise is the physical vibration of the air, translated into our ears. The word “observation” itself implies visual data.

Note
that Mathis does not claim that Newton’s and Einstein’s equation don’t
work at all. They work fine for many of the situations they are used.
But Mathis is concerned with the future, not the present. In his view,
the present level of theory in science has reached a new low, creating a
situation in which so-called experts are clueless on foundational
questions. So I want to again emphasize, Mathis’s critique is on the
level of theory, not of practical application. He explains:

You may ask how physics has existed with such errors for so long. Shouldn’t all engineering be impossible with errors of this magnitude? Shouldn’t all of our machines immediately break and crash? Not necessarily. Because we make the same mistakes in all our equations, the equations are correct relative to each other. Most of engineering is concerned with relative numbers, not absolute numbers. For example, it is more important in physics—at least as a matter of engineering—that we know the how the gravity of Venus compares to the gravity of Mars, than that we know the real gravity of either one. If we are wrong about all of them in the same amount, most of our machines will still work. Only rarely will a mistake in absolute numbers affect engineering of any kind. - http://milesmathis.com/pi2.html

If
this is the case, why should we even care? What matters are the
practical results right? Who cares about theory, as long as it still
works? But that’s the whole problem--the theory is no longer working.
Mathis is quite critical of the attitude that theory should be
subservient to experimentation:

Due to specialization, the normal procedure is to publish experimental findings augmented by very limited theoretical suggestions. By and large, theory is left to a select and limited number of specialists. Those in the center of the field would claim that this is a sign of their maturity, humility, or other positive quality, suggesting that those on the margin who are rash enough to have their own ideas must be immature, immodest, or otherwise deluded. In doing this they neglect to notice that the entire history of science has proceeded along other lines, and that the contemporary hierarchy would be seen as abnormal, inefficient, and ridiculously regimented by anyone from the past, even by those from the recent past like Einstein and Planck and Maxwell. - http://milesmathis.com/central.html

So what are some of the possible ramifications assuming Mathis is correct?

How theory will play out in culture is impossible to predict specifically, but I will offer some intuitions. Just as Newtonian physics became a metaphor for the clockwork-universe run by invisible pre-set laws, I believe there is the potential within Mathis’s theory to redefine how our culture perceives time. Mathis takes the results of relativity seriously and insists on their even application within all our analytical tools. This means calculus itself is redefined to consider the role that time plays in our mathematical models of the world. Mathis outlines the problems with present-day mathematical culture, saying:

How theory will play out in culture is impossible to predict specifically, but I will offer some intuitions. Just as Newtonian physics became a metaphor for the clockwork-universe run by invisible pre-set laws, I believe there is the potential within Mathis’s theory to redefine how our culture perceives time. Mathis takes the results of relativity seriously and insists on their even application within all our analytical tools. This means calculus itself is redefined to consider the role that time plays in our mathematical models of the world. Mathis outlines the problems with present-day mathematical culture, saying:

The more abstract the mathematical system became, the more successful it could be in avoiding foundational questions. ...

Einstein himself was very wary of abstract math, purposely avoiding it until 1912. Put simply, he 'did not trust it.' ...

A math of proper abstraction and complexity could be used to hide all error, to divert all effort, to deflect all criticism. It could be used like a very heavy, very highly decorated quilt, covering the bedbugs beneath. This new abstract math would come not with a foundation, but with a manifesto. It did not have axioms, it had public relations. It was not sold with an explanation, but with an 'interpretation', and this interpretation was to be accepted on authority. - http://milesmathis.com/death.html

Also, I made this youtube video which analyzes Mathis's alleged disproof of Isaac Newton's 6th Lemma in Principia: http://youtu.be/rAp1t7iDDTA