"The Alternate View" columns of John G. Cramer

Albert Einstein taught us that **c**, the speed of light in vacuum,
is nature's ultimate speed limit, the highest speed at which matter, energy,
and information can travel through space-time. In several AV columns I've
discussed ways for getting around this annoying natural law, the law that
SF writers and fans most wish to violate. Two AV columns discussed the
possibility of getting around the lightspeed limit by popping through a
trans-spatial wormhole shortcut. See [
*Analog*-6-89, "Wormholes and Time Machines"] and [*Analog*-5-90,
"Wormholes II: Getting There in No Time"]. Two others discussed the
possible use the faster-than-light nonlocal handshaking implicit in quantum
mechanics for FTL messages and travel. See [*Analog*-11-86,
"The Quantum Handshake"] and [*Analog*-9-88,
"Paradoxes and FTL Communication"]. Both of those methods, however,
are beyond our present technology, and the latter is probably impossible.

But now we may have new possibility. No serious physicist, to my knowledge,
has ever suggested that it might be possible to make *photons* travel
faster than **c** through empty space. Faster-than-light light seems
a contradiction in terms. But this changed last February when K. Scharnhorst
of the Alexander von Humboldt University in East Berlin published some
new calculations indicating that, under the right conditions, photons of
light can be induced to break the light-speed barrier.

Before I bring down on myself a flood of objections from readers knowledgeable
about wave velocities, let me say that I am *not* talking about the
difference between the group velocity and phase velocity of light waves.
I'll pause, however, to explain that distinction first. It's well known
in physical optics that a "wave packet" may travel at a different speed
from the individual waves from which it is formed. The crests and troughs
of a light wave with frequency n and wavelength
l travel through space with a speed called the
*phase velocity* and given by the product (nl).
If, however, you want to use light to transmit a packet of information
or a burst of energy, you have to put together a band of such waves of
differing frequencies. The wave packet containing the energy and information
travels with a speed that depends on how frequency varies with wavelength
over the transmission band. This quantity is called the *group velocity*
and is given by the derivative dn/d(1/l),
the rate at which the wave frequency n changes
when the reciprocal of wavelength 1/l is varied.
In free space the group and phase velocities are identical and are both
equal to **c**, but in a dispersive medium where the transmission speed
depends on wavelength, the group and phase velocities can differ both from
each other and from **c**.

For example, microwaves are high frequency radio waves (or low-frequency
light) with wavelengths of a centimeter or so. They are used in applications
ranging from aircraft radar to police speed measuring devices. The phase
velocity of microwaves travelling inside a waveguide (a square pipe used
in microwave plumbing) is considerably __larger__ than **c**. This
is because there is a cavity resonance in the waveguide at a slightly lower
frequency which elevates phase velocities on its upper frequency-slope.
But a wave crest is not a signal. Nature, while permitting FTL wave crests,
consistently refuses to allow signals or energy to travel FTL. It's always
the case, even in wave guides, that the group velocity is less than or
equal to **c**.

The effect that Scharnhorst's paper discusses is independent of frequency
and wavelength, and so is not the result of dispersive (wavelength-dependent)
effects. Phase and group velocity are equal and increase together. Scharnhorst's
effect is a consequence of quantum electrodynamics (QED), the quantum theory
of light and electromagnetism. The theory of quantum electrodynamics tells
us that empty space, when examined on a very small distance scale, is not
empty at all; it seethes with the fireworks of *vacuum fluctuations*.
Pairs of "virtual" (energy non-conserving) particles of many kinds continually
wink into existence, live briefly on the energy credit extended by Heisenberg's
uncertainty principle, and then annihilate and vanish when the bill for
their energy debts falls due a few picoseconds or femtoseconds later. The
seemingly smooth passage of a photon or electron through space at the QED
distance scale, is revealed to be a punctuated chain of interactions and
transformations involving virtual particles.

For example, a travelling photon may briefly be transformed into a virtual electron-positron pair, which moves forward less than one photon wavelength before annihilating to create a new photon indistinguishable from the old one. During the photon's brief existence as a pair, one of the virtual particles may initiate a "game of catch" using a virtual photon as the ball, tossing it one or more times to itself or its partner. These QED complications of the smooth passage of photons through space have the effect of making the photon travel more slowly. In part, this is because the photon spends a fraction of its existence as an electron-positron pair which can only travel at sub-light velocity.

There is, however, a way of suppressing part of the vacuum fluctuations,
of making "empty" space more empty, using a technique based on *the Casimir
effect*. If two conducting parallel plates with no electrical charge
are placed very close together, the presence of this pair of conducting
walls suppresses all virtual photons with wavelengths larger than twice
the plate separation distance, because the wave structure of such a photon
would intercept the walls in less than half a wavelength and the electric
field of the wave would have a forbidden non-zero value within the conductor.
Thus, the more closely the plates are spaced, the broader becomes the spectrum
of virtual photons that are suppressed, and the vacuum between the plates
becomes "emptier" of vacuum fluctuations and lower in energy density.

Since the energy density of normal vacuum is defined to be zero, the
vacuum between the metal plates actually becomes a region of *negative
energy density*. The amount of negative energy increases as the plates
are brought closer together, so there is a physical force pulling them
together which can do work (like lifting a weight) on an external system.
This force, though very weak, has been measured in the laboratory. The
experimental observation of an attractive force between two electrically
neutral metal plates is an experimental confirmation of one of the more
bizarre predictions of QED and is called the Casimir effect.

Scharnhorst has given a new twist to the Casimir effect by considering
the velocity **v** of a photon travelling across the gap between the
plates. If the plates are separated by a gap **d**, the Casimir effect
suppresses all virtual photons with a wavelength of **2d** or greater.
Because these virtual photons are absent, they cannot participate in games
of catch between virtual particles. Therefore a real photon travelling
between the plates spends less time as an electron-positron pair because
the QED vacuum fluctuations are suppressed. For this reason, the photon
travels faster across the gap. Its speed of travel through normal vacuum
is **c**, so its speed **v** in the negative energy vacuum between
the plates is *greater than c! *Einstein's lightspeed barrier
has been broached by a photon!

OK, that's the good news. The bad news is that in reasonable experimental
situations, the Scharnhorst effect is not very big. In fact, it's abysmally
small. With a plate gap of **d**, **v/c** = 1 - (1.6 × 10^{-60}
× **d**^{-4}). If we make **d** as small as experimentally
possible, say 1 nanometer (= 1 × 10^{-9} m) or about ten
atomic diameters, we find that **(v-c) **= 1.6 × 10^{-24}**
c**.

This is an unmeasurably small change in the velocity of the photon,
and only for a very small travel distance at that. But even such as small
boost in speed comes as a surprise to those of us who had considered **c**
as the ultimate speed limit. Moreover, special relativity says that if
in one inertial reference frame an object travels only one part in 10^{24}
times faster than **c**, one can find another reference frame in which
the departure and arrival times of the object are simultaneous and therefore
the velocity is *infinite*.

And, with heroic measures, one might boost the effect. Scharnhorst's
calculation raises some interesting questions about limiting situations.
Light in normal space is "slowed" by quantum fluctuations which cause it
to spend part of the time as an electron-positron pair. It travels slightly
faster in the space of lower (and negative) energy density between the
Casimir plates, where part of the quantum fluctuations are suppressed.
In circumstances achievable in the laboratory, this increase in speed will
be very small. But what about outrageously extreme circumstances? The problem
of doing better than the laboratory situation is that normal metals are
made of atoms which become very lumpy and non-planar at the nanometer scale.
So let's use something else, something smoother, something non-atomic.
Suppose, for example, that we make a pair of Casimir plates from superconducting
neutronium. Or perhaps the two-dimensional equivalent of cosmic string,
a "cosmic wall". Cosmic walls, if they exist at all, are supposed to be
smooth down to Planck-scale dimensions (10^{-35} m) and also are
perfect superconductors. Suppose that between two such plates we makes
a gap on the order of nuclear dimensions, about a femtometer (10^{-15}
m). If one takes Scharnhorst's equation for index of refraction at face
value, **c/v** goes to zero and a photon travels at *infinite*
speed when the gap between the plates is decreased to about 1.13 ×
10^{-15} m, or about the diameter of a proton. Of course, the approximations
used in the calculation may not be valid because of higher-order effects
at such small distances.

Nevertheless, such calculations serve to illustrate the point that once the lightspeed barrier is breached, physics becomes very strange. And perhaps there are there other, simpler ways of suppressing vacuum fluctuations and creating a region of space with a negative energy density. Suppose that we could create a large bubble of space inside which there exists the same negative energy density and suppression of vacuum fluctuations that is present in the above example, where the pair of Casimir plates is separated by a femtometer. Put such a bubble around a space ship and the ship can presumably travel within the bubble at any desired speed. And now suppose that we can move the bubble along so that it paces the ship ... It would seem that we have a FTL drive that is consistent with special relativity and quantum electrodynamics.

One should not get too excited about these prospects until Scharnhorst's calculations are verified and expanded. But at least it appears that a small chink has appeared in Einstein's previously impervious lightspeed barrier.

**References:**

*Casimir Effect:*

H. B. G. Casimir, Proc. Kon. Ned. Akad. Wetensch. **B51**, 793 (1948);

*FTL Photons:*

K. Scharnhorst, Physics Letters **B236**, 354 (1990);

Marcus Chown, New Scientist, 32 (7 April, 1990).