Relativity Denial: Messin' with c

Relativity, now passing its first century, continues to be one of the bugaboos of pseudo-scientists.  In spite of repeated attempts to prove it logically inconsistent, etc. occasionally by professional scientists about 50 years ago, it continues to be one of the best tested physical theories we have. 

Still, modern-day relativity deniers keep picking up on reports of laboratory experiments which reportedly 'alter' the speed of light.  Perhaps they think that such reports indicate relativity is showing a few cracks of impending failure?  This thinking is sometimes encouraged by sensationalistic science reporting.

Few, okay, probably NONE, of the anti-relativity cranks I've encountered recognize that the results of these experiments are actually predicted due to some rather counter-intuitive effects of the wave nature of light.  Such effects are perfectly consistent with relativity and do not signal a 'problem' with the theory.

I was recently directed by a commenter (comment to be released when I complete responses to it) arguing against relativity to a paper published under Science Express:

"Spatially structured photons that travel in free space slower than the speed of light." Science, 347(6224):857–860, 2015. doi: 10.1126/science.aaa3035.

I guess they were promoting the paper as evidence that the theory of relativity is about to fall.

So I read the paper and was not surprised to find that the authors had found another technique for reducing the speed of photons (yes, it has been done before), consistent with propagating them at the group velocity.  This method works perfectly within the known relationships of wave phase and group velocities for the same old value of the speed of light, c.  Some of this is even described in the introduction to the paper.

Waves can be described by three different speeds, the wave velocity, c, the phase velocity v_p, and the group velocity, v_g.  These three parameters are related by

v_g * v_p = c^2

which is one of the equations in the second paragraph of the paper.  These distinctions are commonly important at microwave frequencies for waveguides.  Note that if v_g goes less than c, v_p will always be greater than c and vice versa.

As the authors of the paper note, they have significantly reduced the GROUP velocity in empty space of a wave packet by a technique that has not been used before, which works for propagating the photons across free space.  The wave velocity, c, as well as other aspects of relativity, is not impacted.  There is no violation of established physics here, in spite of some rather odd wording.

There were a number of statements in the paper alluding to the fundamental nature of the speed of light:

"That the speed of light in free space is constant is a cornerstone of modern physics. ''

"The speed of light in free space propagation is a fundamental quantity. It holds a pivotal role in the foundations of relativity and field theory, as well as in technological applications such as time-of-flight measurements."

But I saw nothing in the paper indicating the results had any actual implications for relativity, a point which the authors clarify:

``Our measurement of group velocity is strictly a measurement of the difference in propagation speed between a reference photon and a spatially structured photon. No direct measurement of the speed of light is made. Within this manuscript, the velocity we measure is strictly the group velocity of the photons"

``Beyond light, the effect observed will have applications to any wave theory, including sound waves.''

Notice that the authors do clarify that this result is important for the wave nature of light, but make no mention for any possible impact on relativity.

Thanks to Dr. Padgett for helpful feedback clarifying the results of this work.

Why do Anti-Relativity Cranks Gravitate to these Stories?

Like most science fiction fans, myself growing up on the original Star Trek (wikipedia), I've always been fond of the idea of Faster-than-Light travel.  Numerous researchers have explored possibilities for object moving faster than light.  I was a big fan of tachyons (wikipedia) when I first read about them in high school and subsequently wrote a review of the physics literature (as it existed up to the late 1970s) as an undergraduate writing project.  I do hope that we will one day find a way to get around the limitation for interstellar travel, but I do recognize that the theory that makes it possible will be an EXTENSION of the existing theory of relativity, much like General Relativity is an extension of Newtonian gravity.

While this may be the motivation of a number of anti-relativity cranks, there are also a number who are opposed to relativity for social, political, or religious reasons.

Perhaps it feeds on the word games which are common in pseudo-science circles.  The popular statement used in the scientific community is that nothing can exceed the speed of light.  Therefore any report of light traveling slower than the maximum speed means that the statement is not strictly true, and therefore must allow all manner of other possibilities.  It's a cute word game, used commonly in politics, religion, and comedy. 

Creationists love to pull these kinds of rabbits out of their hats in debates with evolutionists, as evidence that some important physical law may not be so certain.  Catching an opponent by surprise can win points in debate class, but in science, the details and the math matter. 

Reality does not play word games.

And why they are Wrong...

In many popularizations, we like to say that the speed-of-light is the limiting speed in our universe.  We call it the 'speed of light' because it was the earliest measurement we had of something traveling at this ultimate speed. 

But it may more correctly be defined by some principle more fundamental, and light just happens to max-out at that speed.  Light travels at this speed because the photon is mass-less and the translational symmetry of position and time (no preferred location or time) creates a relationship between rest mass, energy and momentum of particles (a consequence of Noether's Theorem (wikipedia).  A zero rest-mass particle will always travel at the speed of light.

It has been known since the early days of relativity that the Lorentz transformations can be derived WITHOUT the assumption of constancy of the speed of light in all reference frames.  The basic assumptions of uniformity in how we measure time and spatial positions in reference frames (basically saying that any clocks and measuring sticks I can use on Earth will behave exactly the same on a spacecraft traveling at high speed relative to Earth) permit TWO different solutions for transformations between moving reference frames.

One solution is the Galilean transformations. 

The other transformation solution defines an invariant velocity.  These transformations become the Lorentz transformations if the invariant velocity is equal to what we call the 'speed of light'.

Light, under optimum conditions, travels at this cosmic speed limit.  There's nothing wrong with it traveling slower.

Additional Resources: 

• Structured Photons Take it Slow.  J.R. Sambles
• One Universe at a Time: Need for Speed
• Wikipedia: Group Velocity, Phase Velocity
• Java Applet Illustrating Group velocity & Phase velocity
• AstronomyCast: Searching for the Aether Wind: the Michelson–Morley Experiment