# Converting energy into mass

Hi,

I've been having a discussion with a professor (who I respect). We do not agree on wether you can convert energy into mass (or vice versa). I say: you can't, he says: you can.

We agree on the following hypothetical experiment:
Take some Uranium, put it into a nuclear fisionreactor and measure: afterwards the fisionproducts weigh y kilogram less then the original Uranium.
All(!) the energy that is released goes into a (huge) glass of water. We measure:
a. the glass of water becomes y kilograms heavier
b. the glass of water is heated up. If I calculate how much heat-energy the glass+water gains, it will be y times c squared.

My questions:
1. is this experiment correct?
2. is mass converted into energy in this experiment?

(if the experiment is correct, I would say: there is no conversion there of mass into energy: afterwards *both* the energy is still there, as is the mass.)

Paul

## Answers and Replies

Bandersnatch
I would say: there is no conversion there of mass into energy: afterwards *both* the energy is still there, as is the mass.
I thought the experiment was to show the conversion process, not the supposed breaking of energy conservation.

It'd be good for you to start by defining what you mean by mass.

Drakkith
Staff Emeritus
The essence of Einstein's equation is that energy has mass, not that mass and energy can be 'converted' to one another. A hot glass of water has more mass than after it has cooled down, but if you measure the total mass of the glass and the external system that the heat is radiated into, you will find that it is the same before and after. Of course, there's a lot of confusion since there have been different meanings of 'mass' over the years...

nihil
Dale
Mentor
2021 Award
I've been having a discussion with a professor (who I respect). We do not agree on wether you can convert energy into mass (or vice versa). I say: you can't, he says: you can.
In all likelihood your professor is actually answering a related question: "can energy be converted into matter".

Mass, energy, and momentum are three related properties of a system. They are all three conserved. An isolated system with a given mass, energy, and momentum at the beginning will have that same mass, energy, and momentum at the end.

The famous equation ##E=mc^2## doesn't say that mass is converted into energy, it says that a system with energy (but not momentum) has a fixed amount of mass which is directly proportional to the energy.

Drakkith
Staff Emeritus
It may help to look at Einstein's paper, Does the Inertia of a Body Depend Upon its Energy Content?

You can look at the paper yourself, so I'll just summarize what Einstein is getting at.

Let there be two bodies, with body A at rest and body B in motion with respect to a coordinate system (x,y,z). From Body B's frame, Body A has kinetic energy equal to H. Now, let Body A emit light with energy L/2 in two directions, for a total of L energy, directly opposite of each other so that there is no acceleration of A. Body B will see Body A as having less kinetic energy after emission than before, with A's new kinetic energy equal to H-L. Since A has not accelerated, the only way for A to have less kinetic energy from B's frame of reference is for its mass to change. The difference in mass is equal to L/c2.

Now, this may seem like it supports the idea that mass can be converted into energy. But let's look at another example.

Let there be three bodies, with A inside of B and both stationary with respect to a coordinate system (x,y,z), while body C is moving with respect to the coordinate system. In other words, Body B is a spherical shell surrounding Body A, which is stationary inside it. Let A emit light with energy L/2 in two opposite directions, just as above. This time Body B absorbs the light, so it gains energy equal to L and mass equal to L/c2 while A loses energy equal to L and mass equal to L/c2. Now, suppose that from Body C's frame the total kinetic energy of A and B prior to the emission of light is H. After emission and absorption of the light the total kinetic energy of A and B is still H. Therefore the total mass of A and B is still the same as well. To simplify things we say that A and B (and the light emitted from A) form a single system, and the mass of the system doesn't change, regardless of what happens inside it.

The final piece is to look at the situation between the time of emission and the time of absorption. It turns out that the mass and kinetic energy of the system is the same prior to the emission of light, during propagation of the light, and after absorption of the light. As I said above, the key idea is that energy has mass, so when you transfer energy from one object to another you also transfer mass. No mass is ever converted to energy, it is simply moved around.

DEvens