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Imagine if you will that you have a very powerful laser pointer on a clear night and you point
it to the moon. In a little over a second, you’ll see the dot made by your laser on
the surface of the moon presuming the light is powerful enough and tight enough to make
a dot. Let’s then say that you attach your laser
to a spinning device that can spin the laser at about 100 revolutions per second. This
is about the same number of revolutions that your car engine spins when you’re accelerating,
so it’s not all that fast. What you would find is that your laser dot is moving around
the circumference of the moon at about 3 times faster than the speed of light.
How is this possible? We have always been taught that nothing can move faster than light.
So what’s going on? Well, if we look closer at what’s happening,
you’ll find that no photon is really moving faster than the speed of light. The dot is
propagating faster than light, but it’s a different set of photons that are raining
down as the dot moves. The photons are coming from your laser pointer on earth to the moon
at the speed of light, but this is perpendicular to the direction of movement of the dot.
The dot can move at any speed. There is no object that's actually moving with the dot.
And the important feature of this faster than light laser dot is that astronauts on the
moon would not be able to alter it in any way. There is no way that they would be able
to use it to communicate with each other faster than light, because in order to do so, they
would have to send a message to you on earth, and then you would have to alter the laser.
This process would take place at the speed of light.
So the lesson from this thought experiment is that the maximum speed limit is really
not a limit with which things can move, because the dot is arguably a “thing” that can
move faster than light. But the speed limit is a limit on the speed of communication.
It is a limit on causality. A cause cannot have an effect anywhere in the universe faster
than the maximum speed limit that the universe has set.
But what are the implications of having a speed limit on causality. Why is there a limit
in the first place? And how would causality be broken if information could travel faster
than light? What would that mean for the universe?
The fascinating story is coming up right now…
So as we saw from the laser dot thought experiment, there are quote, unquote “things” that
can potentially move faster than light, but these things can carry no energy, momentum
or information of any kind, and thus cannot cause anything.
But why is there an speed limit on causality? Well, one way to look at it is that only a
force can cause anything. Quantum field theory shows that all particles are disturbances
in a field. Forces are manifested by the exchange of virtual particles. So it is the disturbances
of fields that are at the root of forces and thus causation.
Photons, the particles of light, are due to disturbances in the electromagnetic field.
This is why it exerts a force. Light pressure is one way that electromagnetic fields exert
a force on an object. The speed of light is the speed at which the disturbance of the
electromagnetic field can propagate. So in summary, the speed of information is
the speed of a force field. You can’t send information faster than the force field can
change. There has to be a disturbance in a force field for any communication or causation
to occur. Light in a vacuum travels at c, the maximum
speed because photons are massless. Without mass there is no restriction on their velocity
which means they can only travel as fast as it is possible to go.
Massless particles are the only kinds of particles that can travel at that speed, and they must
travel at that speed, otherwise they would have no energy or momentum. In essence, if
they did not travel at the maximum speed, they would not exist, at least not within
the laws of physics as we understand them today.
This can be seen with the extended form of Einstein’s equation for a system in motion,
accounting for relativistic effects. For light, rest mass or, m naught, is zero,
so the only energy is due to its momentum. And momentum is equal to Planck’s constant
divided by the wavelength lambda. It only has energy if it travels at the speed of light,
c squared. It can’t travel at any other speed if it is massless.
Einstein’s theory of special relativity, published in 1905 is based on two postulates.
You’ll notice that neither of the postulates state that nothing can travel faster than
light. The first postulate is that all reference frames are equal regarding the laws of physics.
In other words, there is no difference if you do physics on the moon or the earth. Gravity
is weaker on the moon, but the laws of physics there are the same as here on earth.
The second postulate states that the speed of light in a vacuum is constant, and is independent
of the relative motion of the source of that light.
This was the postulate that changed our paradigm and the world of physics because it implied
rejection of the Newtonian concepts of absolute time and absolute space. Time itself was shown
to be relative to the observer. This was a shocking shift of perspective at the time.
To illustrate this concept, let’s look at the perspective of a stationary observer who
turns on a flash light at the same instant that someone traveling on a train at a large
fraction of the speed of light. He would witness the speed of light from his flashlight as
being the same speed, as the light from the flashlight on the fast moving train. The only
way this can happen is if time within the reference frame of the train is slower relative
to the rest frame of our stationary observer. But the laws of physics remain the same for
everyone in every rest frame, so from the perspective of the person on the train, the
speed of light is also c. And from HIS perspective, he is stationary, and the rest of the world
is moving around the train. This second postulate presumes a finite speed
of light. But let’s imagine for a moment that the speed of light is not finite. It
is infinite. This would mean that have to throw out special relativity altogether.
What would this mean for us and the universe? The speed
of light, that is the speed of propagation of electromagnetic waves in not important.
What is important is the maximum speed that the universe allows for causality. This maximum
speed just happens to also be the speed of light.
But if this maximum speed was infinite, implying that the speed of light is infinite,
well, this would have some absurd implications. For one thing, if the speed of light is infinite,
then using the same equation E=MC^2, it would require an infinite amount of energy to accumulate
any mass in the universe. So no massive particles could form.
The other problem that is sometimes missed is that If the speed of light were infinite,
we would not have light at all. Why? Let’s take a look at how the speed
of light is derived from Maxwell’s equations. c equals one over the square root of the permittivity
and permeability of free space. Permittivity is the resistance of free space to the formation
of electric fields, and permeability is the formation of a magnetic field by an electric
current. Moving electric fields leading to moving magnetic fields which again lead to
moving electric fields is how a light wave is formed.
But if you set c equal to infinity, it would mean that one or both of these terms, mu naught
or epsilon naught would have to be zero. This will effectively kill the existence of dynamic
electromagnetic fields. In other words, it would mean that moving electric field could
no longer cause magnetic fields, and vice versa. This means that no electromagnetic
fields could propagate. In other words, no light.
So when we talk about signals propagating infinitely fast, it is not clear what signals
we would be talking about, since Electromagnetic signals could not form. This means we could
not send radio wave signals, microwave signals, or any other light signals.
What if we kept special relativity, meaning the speed of light is finite, but we allowed
faster than light communication, for example like instant subspace communication like in
Star Trek? The problem with infinitely fast, is the idea
of a cause having an instantaneous effect. The problem is that in special relativity,
it is not clear what instantaneous means. One of the results of relativity is what’s
happening “right now” depends on how fast, and in which direction you’re moving. There
is no absolute now. The now depends on the reference frame.
For example, imagine Alice on earth, and Bob in a rocket traveling about 87% the speed
of light towards Proxima Centauri, our nearest neighboring star.
Let’s look at their world lines on a simple graph, where the horizontal axis represents
movement in one of the three spatial dimensions, and the vertical axis represents time. The
world line for Alice will be straight up, because she will not be moving in her frame
of reference, but she will be moving forward in time. Her clock on her world line will
tick normally for her. 1 second, 2 seconds and so forth.
The world line for Bob, from Alice’s perspective will be diagonal because it will be moving
spatially, and moving forward in time or upwards. Let’s say that Alice and Bob both synchronized
their clocks before Bob left. Now from Alice’s perspective, she will see that Bob’s clock
is moving more slowly than her’s. Bob’s speed at .87C happens to be such that the
time dilation is exactly 2, so his clock runs twice as slow as Alice’s. 2 seconds for
Alice is only 1 second for Bob. So no problem so far.
However, you have to remember that this is special relativity, which means that from
Bob’s perspective, he is not moving, and the earth is moving away from him at 0.87c.
So from Bob’s perspective, his clock is running normally, ticking one second, two
seconds, etc. And it is Alice’s clock that is running at ½ the speed of Bob’s clock.
This is special relativity, and it is the way things work in our universe. Now why is
it that we cannot send messages faster than c, the speed of light. Well, as I said in
a prior video, this is because it would break causality, and create all kinds of other paradoxes
and havoc. How? Let’s look at it in this example with Alice
and Bob. Suppose Alice sends a message to Bob using a hypothetical subspace signal,
like was done many times in Star Trek, which allows instant communication. If Alice sends
the signal when her clock reads 4 seconds, it would arrive to Bob when his clock reads
2 seconds. Instant communication. Alice’s now is 4 seconds, and Bob’s time at that
moment is 2 seconds from the time they synchronized their clocks.
Now if we look at this from Bob’s perspective, Bob receives the signal at 2 seconds, when
Alice’s clock was at 4 seconds. But her clock is running slower than Bob’s from
Bob’s perspective. This means that the signal from Alice would have to travel back in time
from Bob’s perspective. Now you might say, ok what’s the problem?
Well, the problem is that now we have causality issues, because now after Bob receives the
signal at 2 seconds, he could read the signal and reply at 4 seconds using the same hypothetical
subspace frequency. This means that
she received the reply before she sent the message at 4 seconds.
If this was permissible within the laws of physics, Alice could use Bob to send messages
to herself in the past. For example, she could send a message to herself at 2 seconds, to
not the send the message at 4 seconds. In that case, how did she receive a reply to
a message that she never sent. Anything that allows information to travel
to the past causes paradoxes like this and the grandfather paradox, among others. So
such a thing is not permissible, and does not happen according to physics as we understand
it. Cause always has to precede the effect. Otherwise we would have a chaotic universe
that we probably would not recognize, and one that would be unlikely to contain life.
The bottom line is that objects and observers in relative motion, measure time differently.
Movement in space affects how time is measured. There is no absolute time. And there is no
absolute now. Although everyone experiences the same spacetime, they all divide up space
and time differently. They have different coordinates depending on their motion.
Information can’t travel faster than light. And this is the part you are not going to
like, because as a Star Trek and Star Wars fan, I abhor what I am about to say right
now. Since objects contain information, they cannot travel faster than light. Based on
the laws of physics as we understand them today, this mean that warp speed, hyper drive,
quantum drives – that is a drive that allows objects to move faster than light is impossible.
My heart hopes that a future Einstein, perhaps someone who may even be watching this video
right now, proves these equations to be incomplete and finds a loophole that allows us to keep
the hope alive. Zefram Cochrane, I hope you’re out there.
And if you’d like to learn relativity theory more in depth, there are several superb courses
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our channel. And if you have a question, please post it in the comments. I try to answer all
questions posted by subscribers. Be sure to check out my videos on special relativity
and general relativity, if you want a little bit more in depth about what I talked about today.
I will see you in the next video my friend.