January 27, 2023

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Albert Einstein and the Equation Above All Equations – Long read by NRK Trøndelag

Think of an equation, any equation.

If you’re a mathematician or physicist, or just generally interested in science, you have many equations to choose from. Perhaps you are now thinking of one of Maxwell’s equations, perhaps the second major theory of thermodynamics? It is likely that you returned to Pythagoras?

If you’re not a mathematician, physicist, or generally interested in science, there’s a good chance you’ve thought about E = mc2. Then the big question is: Do you know what the equation tells us?

If you already know this, you should keep reading to make sure I explain it satisfactorily. If you don’t know, you should also read – imagine how embarrassing it would be if everyone in Norway, except you, read the whole article?

The Netflix series “In Search of Eternity” is about infinity, and not surprisingly, “E=mc2” is one of the equations on the board behind mathematician Stephen Strogatz. By the way, did you know that it is impossible to take a screenshot from Netflix? I had to use my phone to take a picture of my computer screen, as if I belonged to my reborn grandparents.

Image: Netflix

Hollywood’s favorite formula

Where the father of the equation, Albert Einstein, became a symbol of intelligence, the equation itself has become a cultural symbol of complex science. write E = mc2 On the board, or in a notepad, is the simplest and most obvious way to tell that a character is doing something advanced, something most people don’t have access to.

But is E = mc2 Really inaccessible?

e = mk2, or the law of mass energy as it is also called, is a consequence of the special theory of relativity. And it must be said that the theory of relativity, at least the general theory, is relatively inaccessible to the general public.

Mariah Carey's album cover e=mc2

Are you one of those people who first thought of this Mariah Carey record when they heard about E=mc2?

Photo: Island Records

To the science professionals on Twitter who get mad every time journalists portray math and physics as something hard and weird – I’m so sorry, but relativity theory is just a bit of a problem for most people to get a good grip on, let’s be honest.

However, the Law of Collective Power is not necessarily as far-fetched as Hollywood makes it out to be. And if you don’t necessarily understand all the implications and mechanics (spoiler: you probably won’t Everyone effects and mechanisms), it is not difficult to understand the main features of the law, and thus to understand more about how nature works.

What do you know about E = mc2?

What can energy be transformed into?

First, we have to look at what each single letter in the equation means.

E simply stands for energy. In physics, unlike, say, crystal-making, one operates with a very concrete form of energy – The ability to perform work. We measure this, for example, in joules, which is the energy required for production One watt in one second.

M stands for mass, which we measure in kilograms. Unfortunately, this does not mean that it is the same as what we call weight or heaviness, that would be too simple. If you’re standing on a bathroom scale on Earth, which is probably the only planet I’ve ever stood on a bathroom scale, it shows a number. For example 80 kilos.

If you stand on a bathroom scale on the surface of the moon, it will show, on the other hand, just over 13 kilos. Your mass hasn’t changed, but the force of gravity has. Thus mass is the amount of matter, while weight is the force that the material exerts on a substrate. Having said that – as long as you’re weighing something close to the surface of the Earth, which you’re willing to do, we can say that the scale shows mass.

Illustration of an astronaut wearing a space suit

C is a little more straight forward, it’s simply the speed of light in empty space. About 300,000 kilometers per second. The two at the end mean that the speed of light must be multiplied by itself – The speed of light increased in others. Which means you end up getting too many.

Well, then we know that E = mc2 can be translated into Energy is equal to mass multiplied by the speed of light per second. And what does that mean? This means that Every mass has energy, and all energy has mass.

In other words: Matter can become energyand perhaps less intuitively – Energy can become matter.

hard fusion

This mass can be converted into energy which is something we are constantly making use of, it is exactly the mechanism that turns the sun into a heater.

Hydrogen nuclei combine to form helium. The mass of a helium nucleus is less than the combined mass of a hydrogen nucleus. Where did the excess mass go? It has become energy that radiates from the sun.

That’s what it’s called fusion.

We have tried, for a number of years, to learn how to make use of fusion in the context of energy production, but we still haven’t been able to crack the code.

Recently, researchers have been able to National Ignition Facility in California to get more energy from laser-induced fusion than you put into it. An important step on the road to power plant merger, but we’re still a few decades away.

In nuclear power plants we use the opposite mechanism, nuclear fission. The atomic nucleus splits into two smaller parts, each of which has less mass than the nucleus of which they were part. The remaining mass becomes heat energy, which we can in turn convert into electricity.

Illustration of an atom splitting into two halves

Do you want to use your knowledge that matter can be converted into energy for something more devastating than power generation? Then you can, for example, make a bomb.

The hydrogen bomb works more or less the same way the sun does – namely, by fusion. An atomic bomb is like a small nuclear power plant, where fission causes the explosion.

Albert Einstein sticking his tongue out at the photographer

This photo was taken on Einstein’s 72nd birthday, in 1951. Photographers shouted that he should smile for the camera, Einstein chose to laugh. The result was a picture of the famous battle.

Photo: TopFoto / Topfoto

Less mass = more energy

Once we get on the topic of bombs, it’s time to talk about it quantity ratio.

The atomic bomb that exploded just over 500 meters above Hiroshima in August 1945 contained 64 kilograms of uranium. A tiny gram of this has been converted into energy.

However, that tiny gram turned into enough energy to instantly destroy a city and kill tens of thousands of people.

Explosion illustration - we see an orange mushroom cloud

The mass-energy law doesn’t say that energy equals mass, but rather that energy equals mass multiplied by the speed of light raised to a second. It can also be written in the following way:

E = m times 89,875,517,873,681,176

It’s hard to work with such large numbers, but the fact that the number is so high nonetheless tells us something in plain text:

A small mass can transform into huge amounts of energy, and it takes huge amounts of energy to make a small mass.

It is this bias that makes atomic bombs so effective. This bias also means that we don’t see much energy being converted into mass.

But it will be completely full.

If you kick a ball, you add energy to the ball. When the ball is in motion, it will have slightly more mass than when it was at rest.

This isn’t particularly intuitive, and even less quantifiable, but you simply have to accept that it is the way it is.

Two sides of the same story

Let’s be honest – the Law of Collective Energy has far more and more complex implications than what we’ve been through so far. Equations that are a consequence of the theory of relativity tend to have just that.

But if you are, the next time you see E = mc2 On the blackboard in a TV series I’m now thinking “that says something about mass and energy are two sides of the same thing, this mass can turn into energy, this energy can turn into mass”, so it’s more satisfying than just thinking “this means that the character The one who wrote that on the blackboard is very clever,” which is always a thing.


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