In the history of physics, light was always somewhat of a mystery.
It seemed special. First, we couldn’t figure out if it was particle or a wave.
Sometimes it behaved like a wave, as was the case in early slit experiments.
But sometimes it behaved like a particle, as was the case in the photo electric effect.
The final determination came around 1900 when Max Planck worked out his theory of black body
radiation. For black body radiation to make sense, light had to be quantized.
We now know that Light is fundamentally a quantum object.
It behaves mostly like a wave but can take on particle-like properties upon measurement.
And to describe it correctly we have to consider it
like we do all quantum objects, as being described by the wavefunction of the Schrodinger equation.
But this brought up another question, if light is a wave, how does it propagate?
Sound propagates through the air, so what is the medium for light?
Classical physics came up with the idea of ether to explain this. This was an unseen
background medium that filled all of space, through which things like light
and gravity could propagate.
But in 1905 a certain brilliant scientist by the name of Albert Einstein
killed the idea of ether, with his theory of special relativity.
He explained that light doesn’t travel in any medium, but rather light always travels
at the same constant speed in a vacuum, the maximum speed possible - the speed of light!
We have since measured precisely what this speed is.
Why does the universe have an upper speed limit in the first place?
Why isn’t the top limit infinite?
Or what if the
speed of light was not constant but changed in different reference frames?
It turns out that this would lead to a bizarre universe. How bizarre?…that’s coming up right now!
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The speed of light is dependent on two fundamental properties of empty space. These
properties are called the vacuum permittivity and permeability. These are measured constants
and there is no theory to explain where they come from. You can think of these constants
as representing the resistance of space to the propagation of electromagnetic waves.
And as you may know, light is an electromagnetic wave. Since space exhibits a resistance to its
propagation, this sets a finite limit to the speed of light. If this resistance was much
lower or nonexistent, then the speed of light would be much faster, or perhaps even infinite.
So what if that was the case?
What would happen if there was no resistance, and the speed of light was infinite.
Well, let’s remember the physical significance
of the speed of light in our universe. It is the upper limit of how fast information can flow.
It is inextricably linked to causality and locality. This means that if you are separated
by some distance from an object. You cannot know anything about that object instantly.
Any information about it will only get to you over the finite period of time
that it takes to travel from that object to you.
Imagine if this was not the case. Imagine if information could flow instantaneously
from one part of the universe to another. This would mean that
an event happening at any point in the universe could affect every other point.
So for example, there might be a million hypernovae
at any instant in space quadrillions of kilometers away,
which could kill us instantly because we would experience them simultaneously here on earth.
There would be no such thing as locality. Locality is the idea that objects in
the universe are directly influenced only by their immediate surroundings,
not by everything everywhere. A limited speed of light guarantees this.
Causality is also tied to the speed of light. Einstein’s Special relativity in our universe
guarantees that there is no such thing as simultaneity. This is because if A and B
are two events which occur simultaneously at two different points in space in some reference frame,
then they can't be causally connected, because signals from the spatial position of A cannot
propagate fast enough to reach B. This would not be the case if the speed of light was infinite.
You might ask, how would this break causality? Consider two events that are related to each
other. For example A caused B. If one observer determines that A caused B, a finite speed
of light guarantees that all observers in all reference frames will also agree that A caused B,
because in order for this not to be the case, information would have to travel back in time.
The ordering of events in the universe is measured by the forward flow of time.
In a universe with an infinite speed of light, observers would not be able
to agree on the ordering of events, so there would be no agreement on causality.
We would have no sense of the history of the universe. There would be no redshift.
We would not see the microwave background radiation for example. We would see the universe
as it is in the current moment. But we would also see the full
size of the universe, and know whether it was infinite or not.
The night sky would be completely lit up, because we would see all the light from all the stars
everywhere in the universe simultaneously. So a universe where things were not
causally connected, and effects were non-local, would be completely different.
But an infinite speed of light would have an even more fundamental problem.
Presuming special relativity still applies, and E=MC2 is still correct,
it would mean a universe with no mass, all energy.
How you ask? Well, let’s just rearrange Einstein’s famous equation to M = E/C2. The higher the value
of C, the more energy it takes to create mass. If the universe has a finite amount of energy,
as we presume, it means that an infinite value of C,
would result in not being able to create any mass, regardless of how much energy
we had. So the universe, as we know it, and life as we know it would not exist.
Now I want to clarify that E=MC2 is based on Einstein’s theory of special relativity, which
is anchored on the idea that the speed of light is constant and finite in all reference frames.
So if we make a universe with an infinite speed of light, special relativity would not be correct,
so E=MC2 would also not be correct. So the idea of no mass based on this equation may not be true.
The real issue is that you would need completely different laws of physics in a universe like this.
It would not be universe we live in.
Note also that in the real world, speed is observer independent. In other words,
you would measure the speed of light to be the same regardless of how fast you were traveling.
Even if you were on a train traveling half the speed of light, your measurement of its speed
would be 299,792 km/s. If you were standing still, your measurement would still be 299,792 km/s.
The interesting thing is that even if the person standing still could measure the
speed of light on the same moving train, he would also measure its speed to be 299,792 km/s
This seems unintuitive. How is that possible? Because time for
the person on the train would run slower from the perspective of the person standing still.
It would just seem to him like the light is proceeding more slowly from the flashlight,
but relative to the ground the speed of light would be the same as from his flashlight.
This observer independence is necessary, otherwise there would not be a maximum
speed limit because it would be different for different observers.
When we say the speed of light is constant in the real world,
what we mean that it is constant in a vacuum.
It is different for example in a different medium such as water.
But what if we played God again and allowed the speed of light to vary, even in a vacuum?
Well, now your playing god would have made quite a mess.
In fact, we would have to throw out pretty much everything we’ve learned in modern physics.
You could go to your library, pick out most physics books based on our learnings
over the past 100 years, build the big bonfire, and burn them.
Varying speed of light would mean relativity is wrong, because again there would be no
speed limit anymore. The reason is that you could have any speed depending on your reference frame.
Quantum field theory would wrong because it incorporates special relativity.
Quantum mechanics may be salvageable,
but otherwise we would be back to the classical world of Newton prior to 1900.
We would not have spacetime, but just a 3D world with absolute time. If you remove the
speed limit of the universe, then effectively, light can move at infinite velocity again.
There would be no limit to how fast information could travel,
and the idea of causality, again would go out the window.
The Big Bang, and most of the cosmological models we are used to would also have to be thrown out.
And in fact, you may have to bring back the idea of the luminiferous aether to
explain how light moves according a fixed reference frame of the universe,
because that was the idea behind the aether.
You might ask why does the universe care so much about electromagnetic waves?
Why is this speed of light so important in physics?
The universe doesn’t really care about the speed of electromagnetic waves.
What it cares about is causality. Causality is what’s important.
People don’t have to agree on space or time or the simultaneity of events,
but to have a coherent universe, everyone must agree on causality.
The speed of causality is the maximum speed allowed in the universe.
It is the fastest speed at which two points in the universe can communicate with each other.
And light happens to have this maximum speed because its fundamental particle,
the photon has no rest mass. With no mass, it has no restriction on how fast it can go.
And it was the first thing that we humans happen to have discovered
that traveled at this maximum speed.
Any particle with no rest mass will travel at this maximum speed. For example, the gluon,
the force carrier of the strong force also has no rest mass.
These two fundamental particles, the photon and gluon do not interact with the Higgs field,
so they have no rest mass, and no restriction on speed.
Other particles like electrons and quarks do have rest mass,
and so must travel at below the speed of light.
Another way to look at this maximum speed is to think about how special relativity treats
spacetime. Space and time are treated as being equivalent.
You might ask, well how can space and time be equivalent? One has units of length - meters,
kilometers etc., while the other has units of time - seconds, hours etc.
Well, remember how Einstein showed that Energy was equivalent to mass
through a conversion factor, which is c^2. Something similar applies to spacetime.
The conversion factor that unites space and time in our universe is the maximum speed of causality,
the speed of light. It has units of meters per second,
in other words units of space divided by time.
So one second can also be expressed in terms of meters.
And one meter meters can be expressed in terms of seconds,
related via a factor. This conversion factor linking space with time is the speed of light.
This is why you see it in relativity and just about everywhere else in physics.
It is not like the speed of sound which is just an interesting number,
but saying nothing about the fundamental nature of reality.
Speed of light however does say something fundamental because it links space and time.
Precisely what this number is, is not so important. The universe really doesn’t care what
the actual number is. As long as it is not zero or infinity, and is constant in all reference frames,
we can have a coherent universe like ours. If you enjoyed this video then click the like button,
and if you have a question, post it in the comments. I will do my best to answer it.
I will see you in the next video my friend!