One of the most fundamental physics facts is
that the speed of light in a vacuum is constant for all observers. But can we really be sure that
the speed of light wasn’t different in the past, or perhaps in other parts of the universe? In
fact, variable speed of light theories have long been used to try to explain everything
from dark energy to gravity itself. So let’s explore how constant this
fundamental constant really is. Speed is relative. Drop your smoothie on a
train and it appears to fall straight down, but to me standing on the platform
the smoothie falls diagonally, apparently boosted by the speed of the train. But
shine a laser beam from the train and everyone observes the same speed—299,792,458 m/s in
a vacuum, no matter their relative speeds. The invariance of the speed of light is
more precisely described by something called Lorentz invariance, and it’s the
founding axiom of special relativity. Einstein realized that our measurements
of distance and time have to be relative to the observer—they have to shift to keep
the speed of light the same for everyone. This same axio m is also fundamental to
general relativity, in which gravity is interpreted as a warping of the fabric of
spacetime. Both special and general relativity have been tested with extreme care and
precision over and over and have never failed. More to the point, the speed of light has
been measured in different reference frames and its invariance holds down to the
exquisite precision of current methods. That said, we scientists are supposed to remain
simultaneously skeptical and open minded—somehow applying both mindsets to both old and new
theories. So in that spirit let’s ask whether the speed of light is really invariant. For example,
could it change over time, or be different in different parts of the universe? There are some
who believe that the very effects that relativity predicts are due to the speed of light changing,
not due to changes in space and time themselves. Now before I start talking about what it
means for the speed of light to change, I want to make it clear why many, and perhaps most
physicists think that it’s not only impossible, but it’s not even meaningful to think
about a variable speed of light. The speed of light isn’t really about light.
It’s the speed of any massless particle, and also the maximum speed that information
can travel. It’s the speed of causality. It’s the rate at which one point in space
can communicate with its neighbors, assuming no impediments. So to change the speed
of light, we’d need to change something pretty fundamental about the universe—the
connection between space and time. We measure speed in terms of the amount
of distance traveled per unit of time, whether that’s miles per hour or
meters per second. Changing the speed of light means changing the number
of meters it can travel every second. The problem with this is that our very definition
of meters and of seconds are tied to the speed of light. We can think of the meter as the distance
light travels in 1-over-300 million seconds. Or we can think of the second as how long it
takes light to travel 300 million meters. Einstein said that “time is what clocks measure”, which we can interpret as meaning that it’s a
measure of the rate of change of the universe. One of Einstein’s thought experiments was
the photon clock, in which he imagined a photon bouncing between two mirrors, and each
2-way trip indicates the tick of the clock. What happens if we slow the speed of light? The
clock ticks more slowly, which means time slows. Now real clocks are made of gears or
electronics which are made of atoms which are made of various quantum oscillations bound
up in ways analogous to the photon clock—whether electrons communicating virtual photons with
the nucleus, or quarks exchanging gluons in that nucleus. This argument applies for any
object with mass—the speed of light dictates the rate of internal change, which determines
the rate of the flow of time for all matter. So if slowing light also slows time, would we
even notice? Not according to special relativity, in which space and time are fundamentally
coupled—two sides of the same coin. Changing the speed of light slows time, and
moving the mirrors further apart also slows time. In this picture, distance, time,
and the speed of light scale together, so on our scale there’s no observable
effect. The speed of light is just the unit conversion factor between our arbitrary
choices of spatial and temporal units. The only way for a change in the speed of
light to do anything is if time and space both have their own fundamental units that are
independent of each other. If there’s a basic smallest unit of space and a smallest unit of
time, and these don’t depend on the other, then maybe changing the speed of light would change the
relationship between space and time, at least on the quantum scale. So let’s imagine that this
is possible and explore the consequences. The first real “variable speed of light” or "VSL"
theory was proposed by Robert Dicke back in 1957. Dicke was a brilliant physicist and astronomer
with wide-ranging contributions, so we should at least pay attention to his musings. Dicke
wondered if gravitational fields might not be due to the bending of spacetime, but instead due
to the speed of light slowing down near massive objects. Remember that light changes its direction
as it moves into a medium where its speed is lower—that’s exactly how lenses work. So why
not gravity too? And we know that time does tick slower in a gravitational field. And we now know
that slowing the speed of light should slow time. It seems like a variable speed of light could
be an elegant alternative hypothesis, no? No. Back in 1957 there were only a few
successful tests of general relativity, and some of those were consistent with either
spacetime curvature or a changing speed of light. But nowadays we know that spacetime itself must
be dynamic—we’ve measured how rotating masses drag space around, and how colliding black holes
generate gravitational waves, none of which work with the variable speed of light interpretation.
Dicke’s idea was intriguing, but it doesn’t stand up to the latest evidence. And given that
evidence, Dicke himself would surely agree. OK, so maybe a variable speed of light doesn’t
explain all of gravity. But could it still play a part? There’s one weird fact about our universe
that could possibly be explained by this idea. If we look at the edge of the observable universe in
that direction we see the warm, smooth gas that existed before any stars or galaxies formed.
We see exactly the same in that direction, or that, or that. The universe at early times
was extremely homogeneous—almost the same density and temperature everywhere. That tells
us that at some point in the distant past all of that material had to have been in contact
in order to distribute energy and settle into the same state. But the problem is, based on the
observed rate of expansion of the universe, there just wasn’t time since the Big Bang for those
regions to have communicated with each other. We’ve talked about this so called "horizon
problem" previously, along with the mainstream solution of cosmic inflation.
Inflation hypothesizes that at some very early time those distant regions were
in causal contact with each other, enabling them to share energy at regular light
speed and reach the same temperature. But then the universe underwent a period of extremely
rapid expansion much faster than the speed of light before slowing dramatically. This
threw apart regions that were close enough to be in thermal equilibrium so far apart that
it appears now as if they could never have been. But there is another way to
bring those distant points into causal contact—and that’s by having light just
move faster in the past. This could have kept the early universe connected as it expanded and
reached uniformity. Then, if light slowed down to the current much slower speed, distant
regions would seem causally disconnected. And if this story is right, it could even
be that the speed of light has been gently decreasing ever since. It has been suggested that
this could explain why many galaxies appear to be accelerating away from us. Since light is
supposedly becoming slower it's taking longer and longer for their light to reach us, giving
the appearance that they are accelerating away from us. That may sound good, but variable speed
of light theories don’t have a good explanation for why lightspeed would change in the very
particular way needed to mimic both inflation and dark energy. Cosmic inflation seems a little
cleaner, and is certainly better accepted. The first effort to explain the horizon problem
with a variable speed of light was by John Moffat in 1992. He proposed that the speed of light
may have been 10^30 m/s in the early universe. Moffat lays out some substantial theoretical
work, involving symmetry breaking - analogous to the one that separated the electromagnetic
and weak forces. But in this case the broken symmetry was Lorentz invariance. Moffat’s theory
preserved Lorentz invariance on relatively small scales—like across the galaxy—but allowed
it to vary over cosmological distances and times. Another similar idea came from
Andreas Albrecht and Joao Magueijo. And yet another VSL model depends
on the energy of light—higher energy photons would move faster. Perhaps then
the ultra-high energy photons near the big bang did travel fast enough to connect
distant points of the universe. Then, as the universe cooled, those high energy
photons became rare and so light slowed down. Now we have absolutely never observed speed
differences for lights of different energies at any energy we’ve detected, and
that includes comparing the arrival times of high energy gamma ray light from
gamma ray bursts with the arrival times of lower energy light from the same
explosions. But maybe the effect only kicks in at the really ridiculously
high energies near the big bang. These are fun ideas, but are they testable
given that VSL theories predict the same thing as more standard ideas in
general relativity? Well, there's another way to look for changes in the speed
of light. And that by its effects on physics. “c” appears everywhere in our laws of physics—for
example in the fine structure constant, which defines the strength of electromagnetism.
The formula for alpha includes the charge of the electron, the electric permittivity of the
vacuum, Planck's constant, and the speed of light. We’ve talked about this important
constant of nature in the past, and even about whether it may have changed over
time. Well, if the speed of light has changed then you’d expect the fine structure constant
to change with it. And guess what—there’s no evidence of such a change. You can see our
previous episode for that lack of evidence. None of this proves that the speed
of light has never varied—it just says it can’t have varied much
over the past billions of years. But the real challenge for VSL theories
is how they seem to break physics. All VSL theories break Lorentz Invariance,
and Lorentz Invariance seems pretty important for the universe to make sense. Remember the
example about the smoothie from the beginning of the video? In that example you and I had
a different interpretation of the same event, and yet, we both would agree
on every aspect that mattered, like the fact that the smoothie hits
the floor at a particular location, or that it hits the floor after it's
dropped rather than before it's dropped. The basic self consistency of the universe and
the causal ordering of events is ensured under Lorentz invariance. Break it and it’s pretty
easy to come up with nonsensical scenarios in which different observers have irreconcilable
disagreements about the outcomes of events. A variable speed of light also breaks
the fundamental charge-parity-time or CPT symmetry of the universe,
in that the laws of physics look fundamentally different depending on
which direction of time you're moving. We’ve discussed CPT symmetry before. This
is also problematic because CPT symmetry is believed to be truly fundamental, and
we have no other evidence of it breaking. There are ways around some of these objections.
For example, we can imagine that the change in the speed of light is not exactly fundamental,
but more akin to how that speed changes in a dense medium like water. So what if the
refractive index of the universe changed over time? Well, that increase in the thickness
of the vacuum would have to be pretty enormous in order to slow light by the factor of
10^22 needed to solve the horizon problem. And that change appears to affect all light-speed
waves equally—all frequencies of light, as well as gravitational waves. Regular materials
don’t behave like this. Still, it is a sort of way out. And there are some other narrow paths
through the dense network of refutations of VSL theories. However you need to be pretty
committed to these ideas to find these ways out. Currently there’s no evidence that the
speed of light varies in a fundamental way, and it may be that it’s not even a meaningful
concept. Although that latter point depends on an understanding of the quantum nature of space and
time and their relationship to each other that we don’t yet have. It’s absolutely worth going back
and questioning the founding axioms of even our most successful theories, as long as we keep in
mind that any new theory is going to have to do just as well or better than the old one in all
of its predictions. And that’s a tall order when you’re trying to break relativity, which has such
deep internal consistency and is so powerfully predictive. But relativity is not the final
theory due to its clash with quantum mechanics, so do let’s keep questioning it. Including
whether the cosmic speed limit is fixed, or we can somehow change how fast
information travels though spacetime. So we missed one or two comment
responses recently. Actually, we missed six. It’s my fault - there’s been
a lot going on, including too much travel, and these responses actually take a lot of
thought. So today we’re going back and doing responses for a selection of the missed episodes.
We’ll do one comment from each of these, but we’ll do each very fully. We’ll also do them out of
order. We have the superfluid episode, the one about turning the Sun in to a spaceship, the one
about detecting planet-sized spaceships with LIGO, and then the one about when and how terrible or
awesome the next nearby supernova is likely to be. Before we jump into that, I also need to
note a correction for our episode on the model of the proton interior. We talked about
the important contributions of Stan Brodsky from the Stanford Linear Accelerator, but
managed to use a picture of the wrong Stan Brodsky. Apologies to both Stans. THis is
the Stan Brodsky we meant to shout out.. OK, finally to the comments, and starting
with superfluids. Here’s an insightful comment on our episode on superfluids.
Martinstent5339 suggests that it would be impossible to stir up a superfluid into a
vortex because the fluid would just slip around the spoon rather than being pushed into
a flow. There’s some good intuition here, but the conclusion is not quite right. The
spoon does impart energy to the fluid—after all, the helium atoms have to move if they can’t pass
through the spoon. And those moving atoms push on other atoms, so you do get a new flow which can
translate to a rotation if the spoon is stirring. The point of the superfluid love moving
in unison—in streamline flows, and the vortex is such a flow. What superfluids hate is
atom-to-atom-level exchanges of random chunks of energy—they hate dissipative interactions
which translate to friction, heat buildup, and viscous motion. However, as I mentioned in
that video, it is possible to induce a sort of emergent viscosity by creating tiny vortices
in the superfluid which then interact with each other in a way that disrupts viscous
flow. That happens due to interaction with a non-perfectly smooth container wall, but
stirring with a spoon should do some of that. Let’s move on to the episode where we described
ways to move the entire Sun to different galactic orbits. SABRMatt2010 has a major problem with
the claim that the planets in a star's orbit would just come along for the ride when
thrusting a star because it would create a momentary imbalance in the field that could
destabilize carefully tuned orbital resonances. So you’re absolutely right that moving
the Sun wouldn’t drag the planets along with literally zero effect. Moving the Sun a
very tiny amount changes the center of mass of the solar system and the orbits would have to
shift. If that change was tiny they’d quickly find a new stable orbit not much different
to their last and still close to resonance. If the Sun keeps moving, but moves slowly compared
to the amount of time it takes to recover orbital resonance, then the Sun could be moved without
disrupting the planets. But if you try to move the Sun too quickly then yeah, you could break the
solar system. Fortunatley, the proposed methods do move the Sun very slowly—and I believe that’s case
even for the relatively rapid Caplan thruster. While we’re on gigantic spacecraft, let’s move on
to our episode on detecting gigantic spacecraft from the gravitational radiation they emit
when accelerating. brothermine2292 points out that RAMAcraft aren't the only linear accelerators
that would emit detectable gravitational waves. So would the very rare head-on collision between two
black holes. That’s right, and we did very briefly mention natural causes in the video. A head-on
collision between any compact body - black hole, neutron star, perhaps even white dwarfs,
would causes both objects to massively decelerate in a straight line resulting in linear
gravitational waves that could be detectable. For the black hole there should be a
very weird but modellable gravitational wave ring-down as the two fell together
again. For non-black holes there should be a really clear electromagnetic signature.
So hopefully we can distinguish these cases. And then there’s the episode where we talked
about the prospects of Betelguese going supernova, and when the next nearby supernova
might be, and what it might do to us. ETLee-db6cn points out that a portion of the
Earth will generally be completely shadowed from a supernova, depending on its location in the
sky. So while it’s true that being on the other side of the planet would shield you from the worst
of the actual radiation from the supernova blast, for most death-by-supernova scenarios
it’s not direct irradiation that gets you. The most likely killer is due to the ozone layer
being depleted. Even if that happens only on one side of the planet, the effect quickly
becomes global with atmospheric mixing. There’s also the fringe case when a supernova goes
off while you’re in a region of the galaxy with relatively high gas abundance, which will then
irradiate the entire planet from all direction with X-rays for a long time. But yeah, maybe if
you have a well-stocked bunker and happen to be antipodal to a very nearby supernova, you get to
emerge years later to enjoy the post-apocalypse. And by that time I might have caught up on all the
missed comment responses, so double win really.
