# Energy<>Mass conversion

1. Jul 22, 2007

### jobyts

Can energy be converted to mass as per the E=mc^2 equation? Theoretically, how to convert energy to mass? Does it happen anywhere in the universe?

Another related question, why do we need to do nuclear fission or fusion to convert the mass to energy? Does physics have an explanation why mass and energy are not freely interchangable?

2. Jul 22, 2007

### meopemuk

Yes. Most commonly this occurs in particle accelerators. You can take two light particles, e.g., an electron and a positron, accelerate them to high kinetic energies, and collide. The products of such an collision many include much heavier particles, like protons and neutrons.

The conversions mass->energy and energy->mass occur around us all the time. For example, when light is emitted by an atom, the atom experiences a transition from a high mass state to a low mass state. However the mass differences are normally too small to be visible, because electromagnetic forces are relatively weak. Nuclear forces are much stronger. This is the reason why mass changes and energies released in nuclear reactions are so much higher.

Eugene.

3. Jul 22, 2007

### xez

Yes, it happens all the time in
matter-antimatter reactions, natural and artificial
nuclear reactions, ordinary chemical reactions, etc.

Everywhere there's a change in energy there's a change in
mass.

The "binding energy" of nucleons is converted to mass
when the nucleons disassemble from the nucleus.

Energy itself, via the equivalence relationship, has
mass, so in some senses there isn't a distinction except
when you specify the form and type of energy --
rest mass of particles, energy contained in rest-massless
particles like photons, potential energy of bound nucleons,
chemical bond energy, energy in gravitational fields,
energy in electromagnetic fields, etc.

So you don't "need" a particular kind of reaction
(nuclear or antimatter) to convert mass to energy, but
to convery substantial amounts of one to the other
quickly, those are noteworthy possibilities.

4. Jul 22, 2007

### xez

As to why they're not "freely" interchanged, well they
are, to a point.

As you study particle physics, quantum physics, chemistry,
et. al. you learn that there are specific possible reactions
or transitions, emissions, absorbtions, conversions,
et. al. that can occur.

There are also specific states or events that can be
observed to exist, for instance, there's a possibility that
an electron positron pair can materialize from the
vacuum field and exist for a while, then come together
and annihilate into high energy photons. Energy
shifts from field energy to mass energy back to field energy.

There can be assigned specific probabilities that such
conversions/events/transitions will occur depending on
the involved energies, momenta, fields, temperature,
et. al.

Sometimes such events are highly probably and occur
frequently, such as the explosion of a firecracker in a
fire, or the melting of an ice cube on a hot day.

Other times such events are improbable to occur at
low temperatures / energies, such as the break-up of an
iron nucleus into individual nucleons, or a piece of rock
catching fire on a cold day spontaneously. It's *possible*,
but very unlikely without a lot of added energy to help
the process occur.

It's like the reaction probability and rate and equilibrium
in chemistry, and also it's similar to the consideration
of the activation energy of a process -- without the right
energy input, even a process that will release a lot of
energy may be unlikely to occur. Thus the stored energy
in a firecracker takes added heat/energy in the form
of lighting the fuse before it'll become released with any
likelihood.

So you can say that the probability of a system *not*
undergoing a given conversion between mass/energy
is a measure of its stability.

In just a few minutes free neutrons will probably
'spontaneously' convert (decay) into a proton, electron,
and added energy. Whereas a neutron inside a nucleus
is usually quite stable and will probably stay there without
decay for a long time in most (non-radioactive) nuclei.

In contrast a free proton at normal energies will
probably not decay or change into anything else even if
you waited billions of years.

If bound neutrons or protons were *not* so stable, we'd
not be here discussing this topic now, because billions of
years ago all the normal matter that makes up our
bodies / planet / solar system / galaxy would have decayed
into other kinds of matter/energy and we'd never have
existed.

So the reason the mass and energy doesn't seem so
freely interchangable is that the universe we're familiar
with in ordinary conditions is a 'cold' fairly low-energy
place where in ordinary circumstances on earth matter
is stable in the chemical and atomic states it exists in,
and large scale changes of energy/mass do not occur due
to the stability of matter at low temperatures/energies.
Were that not the case, the planet would've "burned up"
and we (being fragile creatures that can live only in
very delicately balanced environmental conditions)
wouldn't exist.

5. Jul 22, 2007

### xez

Whereas at the beginning stages of the universe things
were at very high energies and temperatures, and
there was a large scale shift of kinds of particles,
photons, etc. back and forth to various other kinds of
energies/particles. As the universe cooled, normal
matter like the protons/neutrons/photons/electrons
that make up most of the universe today came into
existance and their stability increased so
that interconversions became less and less likely in most
places other than inside stars or similar high energy
high temperature places.

6. Aug 23, 2007

### Karthikthe

i have heard that E=mc^2 has some defalts in some situations.is it true and how?

7. Aug 23, 2007

### Danger

I've never heard of that. Can you cite a source? As far as I know, it's an immutable formula. It is very seldom, however, that full conversion is achieved. An H-bomb, for instance, converts only about 1% of the mass to energy. Perhaps it's an efficiency issue that you're thinking of?

8. Aug 23, 2007

### Parlyne

Any physical process that occurs must satisfy a whole slew of conservation laws. These are what allow certain states to be stable, and what prevents large-scale mass => energy conversion from being too common.

All known processes obey the conservation of: energy, momentum, angular momentum, electric charge, color charge, baryon number, and lepton number (and quark and lepton flavors are mostly, but not always, conserved as well); although it is generally accepted that baryon and lepton numbers should not be conserved at higher energies than we've been able to probe.

The application of these conservation laws is actually sufficient to predict exactly what kinds of interactions can occur and what cannot. For example, the conservation of electric and color charges, together with baryon and lepton numbers suggests that a proton might be able to decay into a neutron a positron and an electron neutrino. However, energy conservation will not allow it, as the mass of a neutron is larger than that of a proton.

9. Aug 23, 2007

### cesiumfrog

Energy is always equivalent to relativistic mass, but for moving particles it is more common to express energy in terms of rest mass, in which context this formula is just a special (stationary) case.

10. Aug 23, 2007

### SpitfireAce

well, its possible to change an objects rest mass isn't it...

11. Jan 30, 2010

### nevenante

Reading some of the responses to energy mass conversion question, has prompted me to ask the experts in this forum the following question:
What would be the length of time that visible light would be emitting from a very efficient process of converting enough energy into a body of mass of 6.0Ã—(10 to the 24th power) KG ?