Without a doubt, Albert Einstein’s theory of special relativity makes some very mind-blowing
predictions.
Clocks run at different rates, objects shrink, and things can’t go faster than light.
And all of these things are absolutely true.
Relativity has been thoroughly tested and there is no credible criticism of the theory.
(Although you wouldn’t know it from the piles of unsolicited correspondence I get
on the subject.)
So, let’s talk about that last one- the idea that you can’t go faster than the speed
of light.
This is a well-demonstrated fact.
So why is it true?
If you ask a well-educated scientific layperson, they will tell you that it’s because the
mass of an object increases as the velocity increases.
In fact, you’ll hear this said by people with physics degrees.
There’s only one thing.
It’s just not true.
Now I realize that me saying that is going to confuse a lot of you.
Like this guy here, for example.
So, what’s going on?
Why is it that even some physicists will say that the mass of an object increases as the
speed increases?
Heck, why is it that even I have said that upon occasion?
(Shh- don’t tell anyone.)
The reason is a combination of how scientists teach relativity and our intuition at low
velocity.
I’m going to explain it to you first conceptually and then show just a little math for the physics-minded
viewer.
So, it starts with the concept of inertia.
Inertia is the property of matter which resists changes in motion.
Basically, it’s equivalent to the idea that I can push this toy car easily, but this much
bigger car is harder to push.
And, at low speeds, inertia is equivalent to mass.
At very high speeds, this is no longer true.
Mass and inertia are no longer the same.
An effect that didn’t matter before begins to matter a great deal.
So, this is where it is easier to show what is going on with physics equations.
I know some of you have equation anxiety, but don’t worry.
I promise I’ll be gentle.
If you’ve ever had a physics class, you’ve encountered a concept called momentum.
Momentum has a meaning very similar to the colloquial meaning.
Colloquially, once something has momentum, it’s hard to stop.
Well, in physics, we write momentum using this simple equation here.
P stands for momentum, m stands for mass, and v stands for velocity.
So, you see momentum can get big if mass is big or if velocity is big.
Or, I suppose, if both get big.
Momentum is related to inertia.
Something with a lot of momentum is hard to stop, but that could be a slow moving, but
very massive train, or a very light, but superfast, bullet.
That equation and those intuitions are pretty familiar.
The problem arises when we start going at speeds that are very fast.
At very high speeds, this equation no longer applies.
The correct equation is this one here.
We see that it looks like the normal momentum equation, but there is this added term, the
gamma term.
In fact, this equation with the gamma term is really the right momentum equation and
it works just fine even in day to day life.
So I told you that the equation for momentum was p equals m times v and also p = gamma
times m times v. How can they both be true?
That’s because at pretty low speeds, gamma has a numerical value of 1.
Think about some really fast things.
The fastest fastball ever thrown?
Gamma is about 1, or more specifically, this number here.
How about a bullet from a sniper rifle?
That’s pretty fast, but gamma is still pretty close to 1.
This time it’s this number here.
In fact, in order to make gamma to be 1% different from 1, which is to say 1.01, you need a velocity
so fast that it can circle the Earth at the equator in a single second.
So, in any situation you’ve ever encountered, gamma is basically one and you can just drop
it from the equation.
But when you start going very fast, you can’t do that anymore.
At ten percent the speed of light, gamma is 1.005.
At 50 percent the speed of light, gamma is 1.155 and at 90 percent the speed of light,
gamma is 2.294.
When you get to 99 percent the speed of light, gamma is 7.089.
And as you get even closer to the speed of light, gamma gets bigger and bigger.
As you approach the speed of light, gamma becomes infinite.
The equation here on the screen is how you calculate gamma.
The symbol v is velocity and c is the speed of light.
I just put it here if you want to play with the numbers yourself.
If you don’t care to do that, you don’t need worry about it, but I know some of my
viewers really do love their equations.
So let’s get back to the idea that mass increases as you go faster and faster.
How did that arise?
Well basically, it boils down to how we physicists introduce relativity to new students.
Almost all people who are learning about relativity have taken an introductory physics class and
they are very familiar with the classical momentum equation.
So what physicists did was to invent an idea that they called relativistic mass.
Relativistic mass was just gamma times the actual mass.
If you do that, you can then write the momentum equation as just: momentum = relativistic
mass times velocity.
That equation looks just like the introductory momentum equation.
Taking this approach is helpful when you teach relativity.
That way, you can focus your lesson not on new and unfamiliar equations, but rather on
big ideas, especially the idea that momentum at high speeds acts differently than it does
at low speeds.
But this idea of relativistic mass comes at a price.
The price is a misconception.
For instance, people might take relativistic mass and Newton’s equations for gravity
and come up with some silly hodgepodge equations that don’t accurately reflect what is going
on.
For instance, if a particle moving very, very close to the speed of light has a near-infinite
gamma, I’ve had people tell me that this means that it has infinite mass and such a
particle passing near the earth will have an infinite force.
This isn’t true, but it confuses the heck out of some people.
Now I should be honest and admit that there is some debate in the physics community about
this relativistic mass idea.
For those of you who want to dig into this whole thing a bit more, I have put a URL in
the description for this video that gives you something to read.
But I would have to say that the majority of physicists who deal with relativistic situations
on a daily basis really dislike the concept of relativistic mass.
We say that an object has only one mass, which is the mass you measure for an object when
it isn’t moving with respect to you.
Some people call that the rest mass, but it’s really the ONLY mass.
So I suppose that, on behalf of physics educators out there, I should apologize for this confusing
concept.
Relativistic mass is a great way to develop intuition on why you can’t go faster than
the speed of light- after all, if mass gets infinite, it gets harder and harder to push
it.
So it has some pedagogical value.
But if I may be permitted a biblical reference, there comes a time when we must put aside
childish things.
And relativistic mass is one of those things one must move beyond if you want to really
understand relativity.
Of course, this leaves us wondering why we can’t go faster than light.
Without relativistic mass, we’re left with the momentum equation, which tells the story,
but really doesn’t develop your intuition.
So, I’ll tell you what.
I’ll make another video that explains the real reason that you can’t go faster than
light and that might very well be one of the coolest things ever.
By the way, this video is a little more technical than others I have made.
I’m not sure if you viewers will like it or will find it to be harder than feels comfortable.
Feel free to let me know in the comments down there and I’ll take your opinion into consideration
when I make other videos.