In 1905 Einstein proposed the theory of special relativity.
It was based on two simple postulates:
1) The laws of physics are the same for every observer in a non-accelerating reference frame
And 2) the speed of light in a vacuum is the same for everyone regardless of their motion
The first part means is that the laws of physics are equally valid on earth, as they are on
the moon, as they are in space, or any other place in the universe.
The second postulate does not mean that that speed of light is the same everywhere.
The key word there is “in a vacuum”.
In a vacuum, like the vacuum of space, the speed of light is constant.
But in other media, for example in water, or through glass, the speed of light changes.
This is the reason we can see a bending effect when putting a straw in a glass of water,
and the pattern of colors when light goes through a prism.
So the speed of light can change depending on the medium it’s in.
But what if I were to tell you that while the speed of light we perceive changes, the
speed of the individual photons making up the light does NOT change.
It remains the same, C – the maximum speed allowed whether the photon is in space or
whether it’s in water or whether it’s in glass.
What?
How can this be?
Stay tuned because that's coming up right now…
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Now, back to the speed of light.
First, let’s briefly look at why the speed of light is constant, and is the same for
every observer.
One way to explain this is simply to look at Maxwell’s equations.
He first showed that light was an electromagnetic wave, and that its speed was contained in
his equations.
He calculated that it was just the inverse square root of permeability and permittivity
of space.
Permeability is the ability of a medium to resist magnetic fields; permittivity is the
ability of a medium to resist electric fields.
It makes sense that the speed of light would be inversely proportional to these values
because the less resistance the electromagnetic wave encounters, the faster it will go.
Both fields can exist in a vacuum, so vacuum as a medium has a non-zero permeability and
permittivity.
In this way, we can calculate the speed of light in a vacuum.
And it turns out to be exactly what we know it to be 299,792,458 meters per second.
Now the question is why should it be this speed for everybody regardless of their reference
frame. Think of it this way.
If two observers, moving relative to each other, measured different values for the speed
of light, that would mean that the properties of the vacuum would be different for these
two observers.
i.e., the properties of the vacuum would be observer-dependent.
But we know that to the best of our knowledge, the laws of physics don’t change with the
observer.
They are the same for you as for someone travelling fast in the space station.
So this means the speed of light must be the same for all observers.
In fact, this is the logic Einstein used to make this a postulate of his theory of special
relativity.
Now, I mentioned the keyword “in a vacuum,” that is, the speed of light in a vacuum is
the same.
But it’s very different in various of materials.
Different materials slow down light to different degrees.For example, in water its speed is
only around 225,000,000 m/s and in glass it is only 200,000,000 m/s.
This is why things appear distorted when light travels from one medium to another.
Any light traveling at an angle changes direction due to a change in its speed.
So for example, when light travels from air into water, it slows down, causing it to continue
to travel at a different angle, and this leads to refraction of the light which is the distortion
that you see.
Now, as I said in the intro, although the light that you perceive slows down, the photons
making up the light are not slowing down at all.
So let me explain what’s happening.
First, when we say light is an electromagnetic wave, what we are really talking about is
a stream of photons.
Photons are the smallest possible packets of measurable electromagnetic energy.
And streams of photons are what we perceive as light.
That’s what’s entering your eyes right now as you are watching this video.
Electromagnetic waves are composed of changing electric and magnetic fields.
Changing electric fields induce magnetic fields and changing magnetic fields induce electric
fields, and together they make electromagnetic waves.
One quanta of such a wave is a photon.
In empty space, these photons travel unimpeded at their maximum speed, which is c or about
300 million meters per second.
And that’s what we measure.
Unlike empty space, substances such as water and glass are made up of charged particles.
Why charged?
Well, they are made up of atoms, and atoms contain positively charged protons and negatively
charged electrons.
Charged particles are affected by changing electromagnetic fields.
This is something incorporated in Maxwell’s equations.
So when light travels through any transparent medium like glass, water or air, the atoms
of the medium, since they are affected by the electromagnetic fields, start moving and
vibrating.
Now, we also know from Maxwell, that the movement of electric charges creates an electromagnetic
field of its own.
In other words, the atoms, and specifically the movement of their electrons, creates photons.
Photons are light, so you can say the movement of the electrons emits a light of its own.
These are induced electromagnetic waves, and they are at various wavelengths, typically
not the same as the original light that entered the substrate.
Most of these induced light waves cancel each other out, except the ones traveling in the
same direction as the original light wave.
This is why the whole glass does not glow like a light bulb.
Anyway, each of these induced light waves, which again are streams of photons, travel
at the same speed, c.
This is called their phase velocity.
However, what we actually see with our eyes is not these individual waves of light, but
a mixture or summed up wave of light.
In other words, the induced light waves interact with the original undisturbed light wave that
entered the substrate.
Since the light waves are at different wavelengths, there is constructive and destructive interference
in parts of this summed up mixture of light.
And this summed up light wave in glass and water, it so happens travels slower, that
is, LESS than c, the maximum speed of light.
You can see how this happens in the illustration shown here.
This is called the group velocity of the light.
So the apparent speed of light, that is, what we see with our eyes, is the group velocity,
or a summed up wave slower than c, even though all individual waves are traveling at the
maximum speed.
This is the reason that no acceleration or speeding up of individual photons occurs after
the light leaves the substrate.
In fact, the photons had been traveling at the same maximum speed the whole time.
So once it has passed through the glass, what we see is the original light traveling at
c, since there is no longer a summation that causes an apparent slower group velocity of
light.
The slower group velocity only applies to inside the medium,` like glass in this case.
Now, I want to make an important distinction here for you physics purists because what
I have described so far is the classical picture of what’s going on.
But as we know, the most accurate description of the universe is quantum mechanical not
classical.
So let me try to describe the quantum mechanical picture, which is definitely more confusing,
but probably more accurate.
In a nutshell, the summed up group velocity of light, in quantum mechanical terms, is
due to the superposition of all the various paths that the undisturbed light can take
and its interactions with all the atoms of the medium.
What do I mean by this?
Well, this gets into the weirdness of quantum mechanics.
First we have to consider that our light as made up of photons.
In quantum mechanics, every photon is a wave that has some non-zero probability of taking
every path through the glass or whatever transparent substrate its going through.
This may sound absurd, but that’s the way the universe seems to work.
The photon takes every possible path and interacts with every atom, and all the induced photons
created in the substrate.
And what we see as a result is the superposition of these paths and interactions.
These photons by following every possible path ends up interfering with itself and other
photons in such a way that it creates the net effect of a wave that travels slower than
the speed of light.
The result is identical to the classical picture I described earlier, but the details are different.
And if you were to do the math and solve all the quantum mechanical equations that describe
this, which is not trivial by the way, and solve for where and when the beam of light
ends up, you would find that the answer perfectly matches the actual results.
So if you are with me so far, the next time you pour a glass of water and look through
it, I hope you’ll be a little blown away that you actually understand what all those
photons entering your eyes have been doing at the quantum level.
I’ll see you in the next video my friend.