First, this is NOT an alternative theory.

We'll see. The mods seem to disagree, but I won't let that bias me.

It is well KNOWN AND APPLIED science that physical standard lengths are defined by NIST as a number of wavelengths of a hyperfine transition of a cesium atom, and that one of the reasons it is so defined is due to relativity's determination that the speed of light is a strong invariant.

Actually this is incorrect. The hyperfine transitions (between of the ground state of cesium are used to define time; one second is a defined multiple of how long one such hyperfine transition takes to occur (the multiplier is exactly 9,192,631,770). A meter is defined in terms of a second and the speed of light; it is exactly 1/299,792,458th of the distance light travels in a second. The hyperfine transition of cesium is used because it is extremely stable; this is why cesium is used in atomic clocks.

While it would be impossible to actually disprove any of the analysis of Minkowski relating to Lorentz covariance (spatial relationship to time), a recent discussion with Q-reeus about maximal photon energy has suggested a means to motivate a more careful consideration about exactly what was lost when Minkowski decided to create another invariant called the interval, along with inconsistent expressions for 4D rotations and the relativity of simultanaeity which does not include descriptions of things like quantum entanglement or FTL phenomena which are also NOT ALTERNATIVE SCIENCE, even though it lacks a solid base of mathematics to help us understand how it works.

Minkowski didn't create intervals. He

*discovered *them in the math of SRT. Specifically, he discovered them in the Lorentz transforms. The hyperbolic trigonometric version of the Lorentz transform yields a quantity called "rapidity," which you can find out about by reading Baez'

page on symmetries. <-Linkie As confirmation you can check out the Physics FAQ's

page on velocity <-Linkie where you will also find discussion of rapidity.

You will find that the hyperbolic trig version of the Lorentz transforms explicitly treats velocity as a rotation on a hyper-hyperboloid of revolution. The hyperbolic rotation angle is the rapidity. This is a very intuitive way to think about foreshortening (apparent decrease of length with velocity). It also in the same breath gives an intuitive way to think about time dilation; some distance in x (or y or z or some combination) turns into distance in t; thus, the object with velocity relative to the observer's frame of reference appears shorter, and simultaneously appears to experience time more slowly, to the observer. The equations turn out to be exactly the same transforms that are applied during ordinary rotation in 3D, but with the addition of a hyperbolic dimension, time.

Because distance turns into time and vice versa, 1) it is apparent that although the shape of time is different from the shapes of the space dimensions, they are all "the same sort of thing" since they can be substituted for one another simply by changing velocity; and 2) since the change from distance to time and vice versa is at a fixed rate, if we properly add space and time together we can define an invariant. This invariant is called "interval." To give it its full name, it is "Minkowski spacetime interval."

The interval is

$$d^2 = x^2 + y^2 + z^2 - c^2t^2$$

where

*d* is the Minkowski spacetime interval,

*x, y, *and

*z* are distances in the three spatial dimensions,

*c* is the speed of light, and

*t* is the time.

Note that

*t* must be multiplied by

*c* to yield a distance; we can see therefore that a second of time is equal to a light-second (299,792,458 m) when transformed due to velocity, and vice versa. Note also that the negative sign before the time term makes it hyperbolic. This is apparent in GRT by the standard tensor sign convention of -+++.

None of this has anything to do either with FTL or with entanglement. It's just bog standard SRT.

Also, Minkowski provided a version of length contaction that involved physical rotations in 4 dimensions for matter, and then completely ignored the possibility of providing a similar 4D rotational template for explaining relativistic Doppler shifts of propagating light. Why the omission? Why would the bound energy that is matter undergo Minkowski rotation when propagating unbound energy did not? At last, I have found a partial definitive answer.

You cannot apply these formulae to light or Doppler shifts because at the speed of light the length in the direction of travel becomes zero, and the rate of the passage of time also becomes zero. The Lorentz transform claiming the length of a material object is zero is a clear indication that it has passed beyond its region of applicability. Press further, with a velocity beyond

*c*, and the length becomes an imaginary number; ridiculous results like these are the usual result of trying to use a theory in a domain where it no longer applies. Nobody knows what a length of zero or even worse an imaginary length means; it shows no apparent physical meaning.

There is no omission. Photons simply do not follow the same rules as matter particles do.

I have often pointed out that space may be expressed as light travel time. This is not alternative science either. Light years and light nanoseconds alike have well defined physical meaning.

Consider the expression of a velocity as a ratio of how fast something moves (space or light travel time) vs how fast something else moves. The something else could be the hands of a stopwatch or a beam of light traveling at c.

So for linear velocities, the speed of light can be used to define any 3D (or even 4D) length. Add the element of rotation in an infinitude of possible directions and it is just possible that space and time are more simply related than Minkowski ever believed.

No, it's not. The conversion factor between time and space has been confirmed by a multitude of experiments. So has Minkowski's equation. So have the Lorentz transforms.

With light propagation used as a ruler, the measure of the speed of light becomes unity, a concept often used by Einstein himself.

That's possible, but you have to be really careful how you do it and what conclusions you draw. And most especially, you have to be incredibly careful how you define velocity when you do it; it's possible to define velocity as rapidity, which does not vary in the same manner as defining velocity as a fraction of the speed of light. Rapidity is

*not* a fraction of the speed of light; it's the hyperbolic tangent of that fraction. It is very easy to become confused and draw all sorts of erroneous conclusions.

Let's take that idea a little deeper. The expression for tangential velocity for uniform circular motion is given by v = omega x r, where omega is the angular velocity and r is the radius. What an extraordinary concept this is when light travel times are substituted for physical lengths. Rotational propagation of energy must occur at c x c = c^2.

Like everyone else who has commented on this, I don't see where you got $$c^2$$. But I'll also add that I don't see where you got r. What is the size of a photon? There is no answer to this question that means anything in terms of the photon's spin.

Note also that the rotational axis (not the spin axis! Spin (technically spin angular momentum) is a purely quantum mechanical degree of freedom, and can be measured at any angle, not just the axis of the photon's motion!) must be along the photon's line of motion; otherwise, one side of the photon would be moving faster than the speed of light and the other slower. Another way to say this is to say that light is a transverse wave, not a longitudinal wave. And this fact is confirmed by light's ability to be polarized; longitudinal waves cannot be polarized.

So basically we can't define a photon's size, so we can't define r, and nobody understands where you got $$c^2$$.

[contd]