♪ (PBS Digital Studios theme) ♪ Does the speed of light actually
have anything to do with light? ♪ (Space Time theme) ♪ So what is it about the speed
of light that's so special? Why does the universe
seem to conspire to, 1) keep photons from traveling at any speed but 300,000 kilometers per second in a vacuum, according to
any observer, and, 2) keep anything from traveling faster than that speed? The answer: this statement is
false, or at least backwards. The universe doesn't arrange itself
to keep the speed of light constant. In fact, spacetime couldn't
care less about light. The cosmic speed limit is
about something much deeper. This universal constant is, perhaps more accurately,
the 'speed of causality'. In a previous episode, we talked about causality
by way of the 'spacetime interval'. Causal connections give us the only ordering of events that all observers will agree on. But why must causality
have a maximum speed? And why is that speed the
same as the speed of light? To understand this, let's first get our heads around two of the most important insights in physics ever. Ready? First, 1632—frilly collars,
pilgrims in Plymouth, and in Italy, Galileo was
about to be dragged off by the Inquisition for his
book supporting Copernicus and the whole, "Earth is not the
center of the universe," thing. But in his book, there's another, less
well known idea—his 'Principle of Relativity'. This is not Einstein's Relativity, but instead, the brilliant precursor. Not only is Earth or, indeed,
any other location not special, but Galileo posits that no
velocity is special, either. To put it another way, all experiments should give the same results regardless of the velocity of your non-accelerating, or
inertial, frame of reference. This Galilean Relativity
is an incredible insight that Isaac Newton would later
codify into his Laws of Motion. Fast forward to the 1800s—
top hats, steam trains, and mad experiments to uncover
the laws of electricity and magnetism. Enter James Clerk Maxwell,
scientific maestro, who weaves these laws into
his eponymous equations, describing the entire electromagnetic
phenomenon with such elegance. By the late 1800s, we
have Maxwell's equations, Newton's mechanics, various
other awesome theories. And there's this sense
that physics might be done, except there are hints of something horribly wrong lurking in the math—actually, two hints. The first clues to the bizarre
quantum nature of reality had emerged. And more importantly
for this episode, Maxwell's equations had cast confusion
on the sacred Galilean Relativity. In fact, we now know that
even Newton's mechanics were using assumptions that implied an
infinite speed of light, which is really bad. It would imply that space and
time and matter don't exist. But I'm getting ahead of myself. First, let me explain the
issue with Maxwell's equations. Imagine a pony on roller blades
with a monkey skateboarding along its back. And make it an electric monkey. Why? Well, magnetism comes from
moving electric charges. So an electric skater monkey
on a rollerblading pony generates a magnetic
field, obviously. And I can figure out the
field strength from Maxwell's equations based on what I see is the monkey's total velocity. But what is that velocity? Galileo and Newton tell
us that total monkey speed equals pony blade speed
plus monkey skate speed. But what if this very clever pony
also solves Maxwell's equations? She sees the monkey moving at only monkey skate speed, and so gets a totally different magnetic field. So who's right, me or the pony? The key lies in what
we actually measure. We don't measure magnetic field.
We measure its effect. We measure force. And the pony measures
the same force that I do. See, there's a velocity-dependent trade-off between the electric and magnetic fields. The two work together to give you the same electromagnetic—the Lorentz—force, regardless of reference frame. This tells us that the electromagnetic force holds clues to the fundamental interplay between
space, time, and velocity. How do we unravel that connection? It's going to be encoded in the transformation that will allow Maxwell's equations to jump seamlessly between reference frames—the transformation that represents space and time in our reality. This transformation thing,
it's like a mathy magic wand that you wave at your description
of spacetime or your physical laws. And it'll bump you between
reference frames, Harry Potter-style. Wingardium leviosa. An example is the Galilean transformation,
which basically says that velocities add together and space and time
don't depend on velocity. Newton's mechanics use it, and we just applied it to Maxwell's equations to get total monkey speed. But it turns out that there's no way
to write out Maxwell's equations so that they give consistent results
under the Galilean transformation. They aren't invariant
to that transformation. They sort of give the right force at low speeds,
but the fields are a mess. And at high speeds—
forget about it. So does this mean
Maxwell was wrong? No, it means that Galilean
transformation is wrong. The transformation underpinning
Newton's mechanics is wrong. The only transformation that works
is called the Lorentz transformation. And it was discovered even
before Einstein's Relativity. But it was Einstein who realized
that the Lorentz transformation tells us how space
and time are connected and that it also predicts
the speed of causality. Now, you can get to this transformation the way Lorentz and Einstein did by requiring a constant speed of light. As an example, there's
a link to the derivation via the spacetime interval
in the description. But forget about
the speed of light. This transformation is so profound
that it is inevitable based on a few simple statements
about the nature of space and time. Let me show you how. First, we're not going to pretend
that we know how velocities add. We don't know that, "total monkey speed equals pony blade speed plus monkey skate speed." Why would you assume
such as a thing? Next, no preferred
inertial reference frame. Under our new transformation,
the laws of physics will work the same regardless of position, orientation, or velocity. It doesn't matter where the
pony is, how fast it's going, or in what direction
it's skating. This must be true. The Earth is whizzing around the sun,
the sun around the Milky Way. Position, orientation, and velocity
are changing massively. Yet our experiments don't
seem to care about that. Finally, assume that
the universe make sense. Require that we can consistently
transform between reference frames. I should be able to use
the same transformation to get to the monkey's frame
as I use to get to the pony's frame just by using the different velocities. I should also be able
to jump consistently through multiple frames of
reference and back again. E.g., I can go to the monkey's frame
by first going to the pony's frame, and then going from pony to monkey. And I can also get
back to my frame by putting a minus
sign on the velocities. Essentially, we're just
requiring basic consistency in how the dimensions work. Finally, finally—use these axioms
to do a teensy bit of algebra. See the link in the description. The result is the
Lorentz transformation. It's the only one that satisfies all of these pretty fundamental statements about the relativity, symmetry,
and consistency of our universe. It must describe our reality. And therefore, there must
be a cosmic speed limit. Why? This absolute speed limit—let's call it 'c'—is the one parameter defining the Lorentz transformation. Through this parameter,
the Lorentz transformation predicts the cosmic speed limit. Now, the Galilean transformation
turns out just to be a special case of the Lorentz transformation
where c equals infinity. And honestly, just from the symmetry and relativity arguments that we made, c could be infinity. But for other reasons—still unrelated to light—
we know that it cannot be. The Lorentz transformation finally allows us to write down a version of Maxwell's equation that is invariant
to transformation. With it, we can write down
one law for electromagnetism that works in all
frames of reference. This is further evidence
that our new transformation accurately describes
our reality. But it only works for a
very specific value of c. That value has to
be a combination of the fundamental constants
of Maxwell's equations. For the laws of electricity
and magnetism to work, we need a finite maximum cosmic speed,
even without considering light. But check this out: the exact same combination that gives us the cosmic speed limit also happens to define the speed of propagation of electromagnetic waves—the speed of light. c is the speed of light. But it's the speed
of causality first. It's the maximum speed at which any two parts of the universe can talk to each other. In fact, it's the
maximum speed at which any observers can see two
parts of the universe talk to each other. Because of this,
it's the only speed that any massless
particle can travel. So lights or photons, also gravitational waves
and gluons, all have no mass. And so they travel at the
maximum possible speed. Mass is an impediment to motion. No mass, no impediment. So massless things go as
fast as it's possible to go. In fact, the very existence
of mass and space and time tells us that the universal
speed limit is finite. Einstein's interpretation of the meaning
of the Lorentz transformation gives us the Special Theory of Relativity—
time dilation, length contraction, and, of course, mass
to energy equivalence, as described by the famous
equation, E=mc². Awesome episode
on that one here. These are unavoidable
conclusions once we have the basic relationship between
space and time as described by the
Lorentz transformation, and we accept Einstein's
interpretation of it. So what happens without a
universal speed limit and we pretend c equals infinity? There is no matter, because it would take
infinite energy to make any mass. There is only massless particles
traveling at infinite speed. Time dilation and length
contraction are infinite. There is no time and space,
no cause or effect, because all locations and times
communicate with each other instantly. The universe is an
infinitesimal here-and-now. This is all pretty paradoxical, and so there are,
by definition, inconsistencies in this picture. However, the paradox itself tells us that
an infinite speed limit is impossible. The finite speed of causality is fundamental to us having a universe in the first place. And we want a universe, so I can see you back here
on the next episode of "Space Time." Last time on "Space Time," we talked about the edge of the universe and Counter-Strike. Let's get into the comments. Denny Hiu asks how a universe
that is already infinite [can] expand, and what is it expanding into? Great question. The weird thing here is that some infinities can be bigger than other infinities. Imagine an infinitely long ruler
with markings spaced at every inch. If we stretched the ruler
so that the markings are spaced at every two inches,
the ruler is still infinitely long. But every section of the
ruler has twice as much space. Now replace the
markers with galaxies, and that's basically what's
happening with our universe. It doesn't need to
expand into anything. Every chunk of internal
volume is just getting bigger. RedomaxRedomax asks what you would see if you traveled 18 times the distance to the particle horizon to come back to where you started. So that number, 18 times
the particle horizon, only applies if the universe
has positive curvature— making it a hyposphere—and the curvature is the maximum that it could be,
given the current flatness measurements. But if you travelled that distance— again, assuming the universe froze in its expansion, which it won't— then you'd get back to your starting point
a long, long, long time later. If you travelled at
the speed of light, it would take around
750 billion years, or 55 times the current
age of the universe. The Milky Way would have
merged with Andromeda, and all stars besides red
dwarves would be long dead. Epsilon Lazerface says that, "… if you go outside the universe, you become a Super Saiyan." Well, there really would be no way to know that unless you traveled outside *The Universe*. LassieDog999 makes fun of
the way I say "geodesic". "geo-dez-ic" "geo-dee-zic"
"to-may-to" "to-mah-to" If it's good enough for the Queen of England,
it's good enough for me. Tenebrae says, "This was
the most intelligent way they have ever heard of saying,
'We have absolutely no idea.'" Thank you. I knew my PhD would end up
being good for something. ♪ (Space Time theme) ♪
This is how I like to think of it, too. It even helps that the constant is named c.
I feel that the analogies in this video made things vastly more confusing. Also, slow the fuck down.
What is the target audience of this video which needs pony and monkeys to explain speed addition, together with an exagerated cool guy who think he is playing Hamlet while reading the prompter ?
Kindergarten ?
Simultaneity is an illusion. It bothers me when scientists say things like "we see light from stars that have already died" because that doesn't make much sense given how light cones actually work.
I don't know why people keep using 300 000 km/s as an approximation to the speed of light. If 299 792 458 m/s is an upper limit, it's absurd to round up. It should be taught as 299 000 km/s. Not much harder to remember, and it keeps the logical value of the number intact.