E = mc^2 Explained


This Lecture is acompanied by the slides available here: English Project (ikoursh.github.io)

Slide 1

By the end of this lecture, you will all get a glimpse at the real meaning of the most famous equation of all time. You will start to understand what the universe is made of.

To do this I will need 2 things.
First, your undivided attention.
And second, your willingness to learn and an open mind.

You will not need any prior knowledge in this field.
This lecture was created as to be understandable to everyone, not only physics students.

But enough talk, let's get started.

Slide 2

E = m*c^2. We all recognize this equation. But what does it mean? let's take a look at its parts.

Slide 3

E denotes energy. M denotes mass. and C denotes the speed of light. Those of you with a sharp eye might see that unlike energy or mass, "speed of light" does not start with "c".

Slide 4

This has a meaning, for now, I want you to think of c as a very large number, bearing no real significance, think "constant".

Slide 5


Before we talk about what this equation means, let's talk about what it doesn't.

I personally believed for a long time, that this means that mass could be "converted" into energy. So, I want to be very clear on this, you will never find mass to energy "alchemy".
We'll get into examples after we discuss the real meaning, but please trust me about this. Any process that you can think of will never convert mass into energy.

But, let's go back to the question at hand. To better think about the real meaning of the equation, let's re-write it and move it back to its original form as described in einstein's paper.

Slide 6

We divide both sides by c^2 and we get a ratio. Mass = E/c^2.

Slide 7

This ratio implies that the mass of an object is not equal to the sum of its parts. Instead, the composite object is also influenced, by the arrangement of its parts and their movement.

Slide 8

Let me give an example. Imagen 2 wind up clocks that are the same, atom for atom, except, that one of them is fully wound up and running, but the other one has stopped. The clock that is running, wounds up having more mass the one that has stopped.

Slide 9

This is because the moving watch has more energy. The energy that is found as potential energy in the spring, kinetic energy of the arm, and heat energy from the cogs.

Slide 10

All of the energy found in the moving watch contributes to its mass, via m = E/ c^2.

Slide 11

This means that the total mass of the clock is equal to the sum of its parts + this m extra.

Slide 12

Now because energy is divided by c^2, the extra energy makes a fraction of a percent of the watches total energy, this is why we tend to think of mass as amount of matter, but it's not 0, and with accurate enough equipment, you could measure it.

Now you may think that this whole lecture, is simply a technicality and that extra mass really doesn't matter because its so small.

Slide 13

So let me give you another example.
Take the sun for instance, the sun emits an enormous amount of energy as light. Now, while light itself doesn't have any mass, the sun loses about 4 billion kilograms every second to light radiation.
Now that is peanuts compared to the sun's total mass, but it can still affect its gravitational pull over time.

Does this mean the sun "converts" its mass into energy? No! that energy came from kinetic and potential energy already inside the sun. Now that is not there it simply does not contribute to the sun's total mass.

Slide 14

Now that we have gained a feeling for what the equation means, I want to talk about why it's true.
To do this, let's discuss what mass really is.

Slide 15

As it turns out mass has 2 properties:
1) It resists acceleration
2) It creates and is affected by gravitational fields

Now, I will ignore the second property in this lecture because we do not have time to delve into general relativity, but for argument's sake, please accept that the second property is an eventuality of the first one.

Put simply, the second property emerges from the first.

Slide 16

You might remember from physics class that F=ma.
If not, its fine, everyone here already has an intuition for this.
The more mass an object has, the more difficult it is to move it. This "type" of mass, is called inertial mass, and it's defined by the degree to which an object resists acceleration.

Slide 17

Now that we have an inclination for what mass is, I want to propose a thought experiment:
Image, a massless box with mirrored walls, impossible, I know, but it is an analogy for something real.
Now, let's fill the box with photons (little packets of energy that transmit light) that are also massless. These photons will bounce around the box in all directions. Whenever they hit a wall, they will transfer their momentum to the box, but because the chance of any photon hitting any wall is equal, there is no overall force on the box.

Slide 18

Now, let's give the box a nudge. The back wall of the box moves into the incoming photons.
It feels a little more pressure from their impact than before.

In the meantime, the front of the box is moving away from the incoming photons, and thus, feels less pressure.
There's a net backward force on the box that feels like a resistance to the change in speed. If the box stops accelerating then everything goes back to normal.

This resistance to a change in speed, aka acceleration, feels exactly like mass. In fact, it's indistinguishable from mass, because it is mass.
The photon box has mass even though non of its components have mass. Somehow, mass has emerged in the ensemble where it doesn't exist in the parts.

Slide 19

How much mass does the box have? Its the energy of the photons divided by the squared speed of the photons, m = E/c^2.

This is amazing! you can find einstein's equation by looking at how momentum is transferred in this system under constant acceleration.
But this is true for all forms of energy, not just confined photons.

Slide 20

Take the energy of a compressed spring.
We can describe the additional mass in form of potential energy. Now, would you agree that it is harder to further compress an already compressed spring than a relaxed one? Yes!

Slide 21

But that is exactly what you do when you try to move it. The spring does not move all at once, instead, there is a pressure wave communicating that acceleration. If you solve the necessary equations, you will get E=mc^2

Slide 22

Finally, let's take a look at protons and neutrons. For those of you who don't remember these are the 2 particles that make up the nuclease of an atom. The vast majority of the mass of objects comes from these particles. But even they are made out of something smaller.

Slide 23

A proton or neutron is made out of 3 quarks held together by the strong nuclear force. The exact nature of these quarks is irrelevant, think of them as just random particles.
There is only one problem. These quarks are nearly massless. They contain about 1% of the mass of a proton, yet somehow, protons and neutrons make up the vast majority of the mass of objects.
This is because of m = E/c^2.

Slide 24


A proton is like a combination of the photon box and the compressed spring. Quarks bouncing off the walls in the binding gluon field,

Slide 25


which itself acts as a compressed spring.

Even the mass of these quarks along with electrons comes from energy.

In fact, the punchline of this lecture is that mass is not really a thing at all. it is just a property. A property that all energy exhibits.


This is a link to a playlist that includes both source videos, along with the necassery background videos





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