What If You Removed Every Electron From 1kg of Metal? (And Placed it on Earth)（原声文稿）

Imagine someone placed one kilogram ball of metal on Earth, but just for fun, he takes all the electrons away.

Now you have a kilogram of matter completely dry of electrons sitting on the surface. What happens next?

Not ask whether this is actually possible to do this.

This is just a thought experiment, meant to demonstrate how strong this electromagnetic interaction actually is.

And, spoiler alert, it wouldn't end pretty for us at all.

So let us analyze this scenario step by step. T is equal to zero. The ball was just placed there.

First, let's calculate the total positive charge of the ball.

To do this, we first need to calculate the number of protons inside the ball.

If the ball is made of iron -56, this has 26 protons and 30 neutrons per nucleus.

Proton has the rest energy of roughly 938 megaelectron volts and neutron has 939 megaelectron volts.

Then the total mass of one nucleus is 26 times the mass of the proton plus 30 times the mass of the neutron.

But this is not all, we now have to subtract the binding energy of iron which is total of 492 megaelectron volts.

This is the energy needed to tear apart the nucleus into individual pieces, which makes the nucleus lighter.

Now to convert electron volts to kilograms, we have to multiply by the elementary charge and divide by the speed of white squared.

This means that 1 mega electron volt of energy is roughly 1 .78 times 10 to the minus 30 kilograms. We denote this as constant km.

So now we can write an equation that looks like this.

Normally we should also subtract the mass of electrons we have taken out, but what electron is just 0 .5 megaelectron volts, which we can safely neglect.

From this we can calculate the number of nucleons to be 1 .07 times 10 to the 25.

Now multiply this by the number of protons in each nucleon, and you get roughly 2 .8 times 10 to the 26 protons in 1 kilogram of iron.

Each proton having charge of 1 .6 times 10 to the minus 19 coulomb will get a total charge of 4 .45 times 10 to the 7 coulomb.

Now, what does this mean?

A coulomb is absurdly large unit.

For example, if you have two balls one meter apart each having one coulomb of charge, they would act on each other by a force equal to 900 million kilograms. Even this is very hard to imagine.

For example, a famous Burj Khalifa is approximately 500 million kilograms.

Now our metal ball is roughly 45 million coulomb.

Imagine two of these one meter apart.

That would be 1 .78 x 1024 kg, while the whole Earth is roughly 6 x 1024 kg.

The pure fact that these two numbers are actually comparable already tells us that the effects of this metal ball would be catastrophic.

Now we are still at time equals 0, 45 million coulomb ball.

Now, there are plenty of electrons around in the air or the earth itself.

One kilogram ball of metal would have radius of roughly 3 cm.

An electron just outside of this ball would immediately start filling the force according to Coulomb's law.

And the force you would calculate is roughly 70 N.

Each electron, though, is just this small piece of mass.

And if you calculated it that would equal to an acceleration of 7 .8 x 10 to the 31 meters per second squared.

At this acceleration the electron would have Rindler horizon just 1 .15 femtometers behind and experience under new temperature of 3 x 10 to the 11 Kelvin.

in. Such an electron would radiate roughly 10W of Bremstraum radiation due to its acceleration.

So all the electrons around would immediately turn into ultra -artivistic bullets, rushing towards the bow, now generating a strong gamma burst of Bremstraum radiation.

The critical electric field, where electron -positive pair production becomes important, is approximately So this is the situation right after the ball was placed there, but you can imagine that But this ball will not retain its shape for a very long time.

The same way the electron near the ball is attracted to it by a force of roughly 70 N, the same force pushes every proton in the outer shell in the opposite direction.

The whole ball wants to expand outwards and for the nuclei at the surface the acceleration is not that much slower than for the electrons.

Just roughly 3 orders of magnitude lower.

Now, if you wanted to bring another nucleus from infinity onto the surface of this ball, you would take 55 joules of energy.

So this is also the kinetic energy each nucleus from the surface will reach at infinity.

This is almost the same as oh my god particle, the most energetic cosmic ray particle ever recorded. But now you have a huge number of them.

The total electrostatic energy of the ball is around 3 .5 x 10 to the 26 joules.

And if you look at the power output of the Sun, you find out that it produces this amount of energy every second.

So this ball would contain as much energy as the entire power output of our Sun for one second. Let that sink in.

This ball would have 4 billion times more energy than if it just turned its entire mass into energy by E equals mc squared.

The outer shell of the ball would become highly relativistic in just 10 to the minus 20 seconds.

So what it would actually experience is an instant release of energy.

Half of it would go straight into the ground and the surrounding air and half of it would be repelled into space.

So eventually Earth would have to deal with at least with half of the electrostatic energy of this ball.

That is roughly 400 times more energy than the impact that wiped out dinosaurs.

So eventually everything would play out as one large mass extinction explosion. But there will be one change.

Currently, the surface of the Earth carries a negative charge of about minus 5 times 10 to the 5 Coulomb, while the upper atmosphere is positively charged, making the net charge of the planet neutral.

This creates an electric field of around 120 volts per meter between the surface and the ionosphere.

After the explosion, the Earth would become heavily positively charged to roughly 2 .25 That gives a field of about 5000 volts per meter, now pointing outwards.

That is 40 times larger electric field, this would lead to a highly altered electrical activity of the whole planet.

I know that this is a very hypothetical situation, but the point of this video is to actually realize how big the difference in strength there is between gravity and electromagnetism.

There are four fundamental forces in the universe that we know of so far.

The strong nuclear force, big nuclear force, electromagnetism and gravity.

Now if we say the strong nuclear force has a relative strength of one, then the electromagnetism is about 100 times weaker. And the big nuclear force is 10 to the 13 times weaker.

But when it comes to gravity, it is 10 to the 38 times weaker.

So electromagnetism is 36 orders of magnitude stronger than gravity. And think about the difference.

If you placed 1 kilogram of neutral particles in the same space as our ball, they would basically not feel anything.

It takes an entire planet to fill a decent amount of force.

Now do this with the charged particles and you get completely violent environment at the energy scale of the sun's entire output.

And more than half of the particles were actually neutrons, which are neutrals.

But think about it, these numbers are all over the place, 40 orders of magnitude.

What if gravity had a ratio not of 10 to the minus 38, but of 10 to the minus 37 or 39?

That would lead to a completely different physics, where life could never exist.

And this goes with any other constants of nature.

The numbers could be in principle anything, anything between zero and infinity.

And this goes to anthropic principle.

The constants are the way they are, because otherwise there will be no observers talking about it.

But this also suggests that there must be an infinite pool of universes where these constants are different, universes that never get observed.

And certainly, there is a combination of these constants that could produce physics, life and complexity much more interesting than this one.

Maybe something like magic is possible there.

So that will be it for this video. Thank you for watching and I see you in the next one.