# Q: Would it be possible in the distant future to directly convert matter into energy?

Physicist: You hear about nuclear devices taking advantage of “E=mc2” to turn matter into energy, so nuclear power seems like it might be a good way to go.  But it so happens that everything that releases energy loses mass in the process.  The statement that nuclear devices turn mass into energy, while true, is giving them more credit than they deserve.  Even a wind-up clock loses mass as it winds down (just not much).  Any kind of energy that you can tie up in matter; chemical, nuclear, electrical, whatever, genuinely increases the weight of the object in question.  A charged 9-volt battery, for example, literally weighs about a tenth of a nano-gram more than an absolutely identical uncharged battery.  But it’s hard to notice an increase of one part in 500 billion.

What this question is about is a process like: step 1) take a brick, step 2) turn it into energy and no brick.

In order to convert matter into energy requires us to get past a few conservation laws.  These are the conservation laws that keep us from turning into energy just whenever.  For example, there’s a conservation law that says that the total number of protons + neutrons has to stay the same forever, and there doesn’t seem to be an easy way around that.

But there may be a cheat!  A difficult way, if it’s possible at all, to circumvent the conservation laws may be to create a tiny black hole, feed it matter, and collect its “Hawking radiation“.  Black holes aren’t very particular about what kind of energy or matter they absorb, and the Hawking radiation they produce is mostly just light.  So, problem solved!  Make a black hole, feed it any kind of matter, and collect the energy it generates.  But, there’s a whole lot involved in that that’s impossible, or nearly impossible.  Despite all of the hoopla surrounding CERN, creating artificial black holes is pretty difficult.  Even if they had managed to create a black hole, the kind that we’d need would have to be just a whole lot bigger.

Hawking’s whole thing is that a black hole, through some pretty fancy quantumy tricks, radiates energy as though it were hot and that the temperature that it acts like it has is greater the smaller the black hole is.  The black holes that exist today are huge and extremely cold (much colder than even the back ground radiation of the universe).  But, as a black hole radiates energy it loses mass and shrinks, which makes it “warmer”, which makes it radiate hotter, and so on.  So, oddly enough, if you want to get a black hole to radiate more energy you need it to be smaller.

Powering humanity takes about 17 trillion watts, which would require a black hole no more massive than 4.6 million metric tons and no larger than 0.0000000000000000014 meters (14 attometers) across.  Black holes are hella dense.  The bad news there is that a black hole that small can’t “eat”, because it’s already smaller than any particle (electrons, the smallest particle, are 400 times larger), so nothing will fit into its “mouth”.  Technically, for quantum-ish reasons, it’s more accurate to say that it’s unlikely that the black hole would be able to eat an available particle.

A “feedable” black hole, assuming you could get the particle guns perfectly lined up to fire matter into it (even as it’s basically exploding) would need to be at least, say, proton-sized.  That puts a cap on it’s power output at a measly 200 mega-watts, give or take.  You can’t even power a flux capacitor with that.

Quick aside: This stuff here about “feedability” and whether or not particles can fit into a black hole are non-issues.  Black holes “burn” long enough that they do not continuously need new matter.  This was a mistake born out of misunderguestimation.  There’s a correction at the bottom of this page under “my bad!”.

So, maybe, in the far off future we could (somehow) create thousands of tiny black holes and harness them for power.  Harvesting energy from micro-black holes is a tricky business and they’d have to be kept off-world, somewhere in space.  Unlike other power sources, they can’t be turned off, and on a strictly practical note, when something weighs a few millions of tons and is smaller than the point of the world’s sharpest pin, it’s difficult to hold on to.  It would fall through the floor of your power station faster than you could say “hey, who left this black hole over here?” so orbit or higher is really the way to go.

Long story short, there are easier, safer ways to get power than matter annihilation and black holes.  Although it’s still a much better option than coal.

By the by, while the physics behind them is horrifying the equations governing Hawking radiation are pretty clean.  The power output, P, for a black hole of mass M (in watts and kilograms) is $P=\frac{3.56\times 10^{32}}{M^2}$.  Or, using the black hole’s radius (in meters), $P = \frac{7.82\times 10^{-22}}{R^2}$.

My bad!: A concerned reader pointed out that you don’t need to keep feeding a micro black hole to get power out of it.  They stay hot for so long that you can set it and forget it.  All the same, you still need to get a tremendous amount of material into an impossibly small region to get the ball rolling.

In the case of a 4.6 million ton black hole capable of powering Earth, you can expect it to keep going strong for over 250 thousand years.  In fact, it’s power output would increase substantially with time.  The danger is that civilization may forget to move their black hole power sources far away before they burn out.  In the last minute of a black hole’s life it destroys about 1 megaton of matter, which translates to about 1.5 billion “Little Boy” bombs, with about a fourth of that being radiated in the last second.  Not the sort of thing that should be parked in orbit.

Power output of a black hole in gigawatts vs. time in years, starting at an output of 17 trillion Watts.

The black hole’s last few decades aren’t particularly pleasant either.

By the way, if you feel the need to run through this sort of thing yourself, the mass of a black hole at a given time, t, is $M(t) = \left( M_0^3 - 1.19\times 10^{16}t\right)^{1/3}$, where Mo is the initial mass.  It’s easy enough to figure out how much energy that translates too: $E=Mc^2$.

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### 18 Responses to Q: Would it be possible in the distant future to directly convert matter into energy?

1. Myrddin Emrys says:

I thought the general idea for black hole generators was to create a moderately big black hole (via future technology, aka magic), and then let it run down. Kind of like winding a lock, except it provides more and more power as it winds down. When it vanishes in an orgasm of Hawking radiation, you move on to the next one.

You don’t keep feeding it… you create it and let it expire.

2. The Physicist says:

Crap!
You are utterly right!

3. Tim Anderson says:

How come black holes can get past those pesky conservation laws?

4. The Physicist says:

Gravity doesn’t care what’s causing it (be it matter, anti-matter, dark matter, even light), and all of our models of black holes today are essentially just models of gravity, including our description of Hawking radiation.
So, the Hawking radiation (which is just a lot of light) is the same regardless of what went into creating the black hole.
At least, that’s according to our models. We’ve never seen it in practice.

5. Will says:

Gravity does some very strange things sometimes.

6. Alexander Cooke says:

In the last SECOND, the energy release is equal to 5 terra tons.
Also the issue is making them, In placing a massive amount of energy in a tiny space some of it is going to not go in the black hole
With the 4,600,000 ton black hole, if even 0.1% doesn’t go in. Then there will be an explosion with a yield o 180 terra tons.

7. anti_neutrino says:

I don’t know if i’ve asked this question in the wrong post, but i want someone to clear my confusion as i’m becoming more bothered by the minute.
If a photon has zero rest mass, then
de-Broglie’s equatino states that,
energy of photon E = hc/λ,
and its total energy E = mc^2
So,
mc^2 = hc/λ
λ = h/mc
And as I remember ,my lecturer said that by this relation one can calculate the rest mass of a photon. But how can that be when its rest mass is zero?

8. The Physicist says:

Like you say, the equation “E = mc^2″ doesn’t apply to light, exactly because it has no mass and never comes to rest. Perhaps the lecturer meant the equivalent mass of the light’s energy?

9. anti_neutrino says:

no, he didn’t. but is it correct to relate the energy of a photon with the total energy of a body? Can you tell me an intuitive way to understand de broglie’s wave equation?

10. The Physicist says:

“Correctness” depends on what you’re doing.
The frequency, f, of an individual photon is determined by its energy: E = hf.
The wavelength, λ, of a photon can be expressed in terms of its momentum, P. E = Pc and λf = c, so hf = Pλf and P = h/λ.
De Broglie just applied those equations for light to the kinetic energy and momentum of matter. His first test case was the electron, which had a known mass and wavelength (in atoms), and everything fit, so he published.

11. anti_neutrino says:

E = mc^2 doesn’t apply to a photon. But i read on a website that to show the consequence of its zero rest mass, one can consider the equation,
E^2 = m^2c^4 + p^2c^2.
And by putting m = 0,
E = pc
So my question is, how can one consider this equation when it doesn’t apply to light?
And, if p = mv,
then how can E still be equal to pc, when ‘m’ in it becomes zero?

12. The Physicist says:

The really wild thing about light is that that equation does apply!
There’s an old post that basically says what you just said here, but the gist of it is: momentum is more than just moving mass (p=mv), light can carry momentum too.

13. Kovar Nosra says:

This is all quite interesting, however, extremely intelligent men have been writing equations on the blackboard for quite some time now. Yet, it would seem that we (humans) have been unable to get past the theoretical. Are we by any chance looking at it the wrong way?

14. Phyllis McLemore says:

Since people are vibrating all that electrons and quarks vibrate then why the question of converting mass into energy and vise versa? Mass is a series of waves and coils that are always vibrating frequencies.

15. Phyllis McLemore says:

Matter is already energy, just vibrating at tighter, more condensed wavelengths. If mass can be measured then that is a sure sign it is already frequencies vibrating subatomic wavicles.
How come I am not told I am right about anything? I have got the simple answer, not complicated enough? Thinking that I am already vibrating frequencies, then I know I can heal myself really fast with my thoughts, which are frequencies. That is why it matters that the words solid and mass and physical and matter are not true. They should not be used because they are super misleading to the general public.
The general public, which is about a trillion people, don’t know that they are not solid, but a series of waves and coils that can be measured. People just go about their usual days thinking that they have to go to a doctor to get well when they can raise their frequencies with their thoughts and heal themselves.
I didn’t make this up. Books upon books in the market tell people how to heal themselves with imagery, which is not solid. Imagery is a vibrating picture of frequency waves that can be changed like a chameleon changes its skin. Cancer and AIDs etc are all frequencies that can be changed and are in fact literally created by the patients own mind constantly. People are vibrating their thoughts internally which changes a perfect body into something that hurts. Bernie Segal M.D. wrote a book about this same thing and so did Weiss. Withheld emotions cause the frequencies of dis-ease.

16. Micah Dameron says:

Great article Physicist.

It seems like if we could come up with a way to break those atomic bonds every energy problem ever known or imagined would be over. Nothing would be impossible for us. Even seemingly impossible things are possible with that much energy.

Why aren’t more scientists looking in to this? There’s a handful working on Cold Fusion right now, but as far as I can tell mainstream science seems pretty lachrymose about energy problems, when there’s enough kJ of energy stored in just our house to power the entire world.

17. The Physicist says:

There are scientists looking into the energy problem from every angle. While cold fusion might produce a lot of energy, it’s clearly not easy.
The modern energy crisis isn’t a question of supply, so much as it’s a question of economics. For example, you can easily power a (well-designed and efficient) house on the energy from 1 or 2 square meters of solar panels, but once that’s set up you’ll no longer be paying for power. That’s good for you, but it’s bad for all the folk who would prefer that your money was their money.

18. Micah Dameron says:

What you say is sort of true, but there is such a giant market (demand) for “green energy” right now, I have to assume that there isn’t an economically viable way of capitalizing on it, because if it were, those people who so desperately want your money would be getting your money that way instead.