Mass defect and conservation
A topic in science concepts and learners' conceptions and thinking
"The most important upshot of the special theory of relativity concerned the inert masses of corporeal systems. It turned out that the inertia of a system necessarily depends on its energy-content, and this led straight to the notion that inert mass is simply latent energy. The principle of the conservation of mass lost its independence and became fused with that of the conservation of energy."
Einstein, 1919
Two principles that are often considered to be universal in science, that is, to always apply in any process in the universe are
- conservation of mass
- conservation of energy
This means that in any process, if we are able to carefully account for everything present before and after some process, we would find that
- the total masses of products are the same as the total masses of 'reactants', and
- a calculation of the total energy before and after the process would also show the sum to be be unchanged.
Read about conceptions of energy
Einstein’s principle of mass-energy equivalence
Albert Einstein's development of his theories of 'relativity' led him to conclude:
"…mass is not a constant quantity but depends on (indeed it is equivalent to the energy content."
"The inertial mass of a system of bodies can even be regarded as a measure of its energy. The law of conservation of the mass of a system becomes identical with the law of conservation of energy, and is only valid provided that the system neither takes up nor sends out energy."
Einstein, 1927; Einstein, 1916
This idea is sometimes known as Einstein's principle of mass-energy equivalence.
Note that Einstein was not suggesting that either the law of conservation of mass, nor the law of conservation of energy, needed to be modified. Rather he was suggesting that as there was a kind of equivalence between mass and energy
- whenever there is energy, there is mass, and
- the amount of energy is proportional to the amount of mass
that in a sense these two conservation principles were different facets of the same underlying feature of the world.
A common misconception
It is, however, sometimes suggested that Einstein's principle of mass-energy equivalence (represented by his iconic equation E=mc2) modified this understanding.
This is an alternative conception (misconception) along the lines:
- mass can be converted into energy or vice versa
- the difference in mass before and after the event reflects an overall difference in energy (energy has become mass, or vice versa) – the effect is normally only large enough to be measurable in nuclear processes
- conservation of energy still applies, but only if mass is considered a form of energy and included into any calculation
Read about alternative conceptions
The mass defect
In nuclear processes there is a 'mass defect' * which is the difference between the total rest masses of the entities present before and after the event. It is often said that this 'missing' mass * has been converted to energy.
rest mass (also known as the intrinsic mass, invariant mass, proper mass) is the mass an object or system has regardless of its motion – if an object is moving (in the reference frame being considered) the measured (inertial) mass will be more than this
A relatively large amount of energy is given out in nuclear processes*, but this is not newly created energy, but rather a reduction in potential energy balanced by kinetic energy imparted to the subatomic products of the reaction. The total energy is conserved.
The total mass only appears to have changed if the calculation is done with rest masses, whereas at least some of the objects involved will be moving and so have measured masses greater than the rest mass.
For example, a (free) neutron will decay into a proton, an electron, and a neutrino. If one considers only the rest masses of these entities, and ignores their relative motion after the decay, it seems that there has been a change of total mass from 1.674 93 ╳ 10-27 kg to 'only' 1.673 53 ╳ 10-27 kg.
Read: How much damage can eight neutrons do?
* Of course, in some nuclear processes, energy can be 'taken in' – as when elements heavier than iron are formed during supernovae explosions. But most of the more familiar nuclear processes – radioactivity, fusion in the sun, fission in a nuclear reactor – are exothermic.
E=mc2
Einstein's equation actually tells us that mass can be considered as a measure of energy, and vice-versa.
We can see that the idea that 'conservation of energy still applies, but only if mass is considered a form of energy and added into any calculation' would be a form of double counting.
This would be like someone with five pounds claiming to have five pounds and five hundred pence to spend. There is a subtlety to how we use language here: the person has five pounds to spend; and has five hundred pence to spend (i.e., alternative ways of saying the same thing) but does not have five pounds and five hundred pence to spend (double counting).
Mass and energy only can be 'inter-converted' in the sense that units can be inter-converted (pounds to pence) rather than how currency is exchanged (euros to dollars).
That is, if you sell your euros to buy dollars, you no longer have the euros, but you have dollars instead. What you have has changed, even if its worth has not.
But if you work out
- the equivalence in electron-volts of an energy in joules, or
- convert a distance in astronomical units to a distance in kilometres, or
- you convert between temperatures in Kelvin and Celsius
nothing changes!
If the temperature is, say, 300K, then it is 27˚C.
A room at a temperature of 27˚C is still, at the same time, a room at a temperature of 300K – there is just a change in the way of describing it.
If you are 20 years old, you can consider yourself to be 240 months old, without having to lose any years.
What E=mc2 tells us is that if you change the energy of a system, you change its mass. If 'the system' is a hot cup of coffee and it cools down then its mass will drop (ever so slightly) as well.
When the system cools the heat is transferred to its environment (energy overall is conserved) which gets (ever so slightly) heavier (so mass is also conserved).
That is what was revolutionary about the idea:
- if something accelerates and so moves faster – it gets more massive
- if something is lifted up above the ground – it gets more massive
- if something is heated – it gets more massive.
Usually these differences are much, much too small to notice, or even measure (though we can calculate them). In nuclear process they are often measurable.
Mass defect in chemical change
In chemistry, it is usually assumed that there is a conservation of mass in any chemical reaction. However, most reactions are endothermic or exothermic. If energy is released (or absorbed) then mass must have decreased (or increased) – with a corresponding change of the mass (and energy) of the surroundings.
Yet the mas defect is much smaller than can be measured, so for practical purposes we can assume mass is conserved in chemical reactions – this is approximately and practically the case, even if in principle wrong. Or as the physicist/philosopher Mario Bunge explains it, "mass is physically (objectively) nonadditive though empirically additive…"
"If atomic masses were strictly additive there would be be no stable compounds: every combination would result from a chance encounter of indifferent atoms and would therefore be unstable; as it is, there are binding forces to which binding energies correspond."
Bunge, 1967/1988
The mass of the photon?
Often in nuclear processes some energy is given out as high energy photons. Although photons have no rest mass, they do have an associated energy and therefore an associated mass.** Some of the mass of nuclear processes is often 'lost' as radiation, but only in the sense that this component of the mass has quickly left the scenes of the event. If all the masses involved are taken into account, we still have conservation of mass, as well as conservation of energy.
** It had been known before Einstein that light could exert a pressure and so must carry momentum. Einstein argued that photons should therefore be considered to have mass. In general Einstein's equation is expanded for objects that are moving to:
E2 = p2c2 + m2c4
Where p is the momentum. Electromagnetic radiation such as light is always considered to be moving at the speed of light regardless of the reference frame adopted. This was a counter-intuitive feature introduced in special relativity – the speed of light is invariant, it is measured to be the same by different observers even if they are in relative motion to each other.
Why is this such a common misconception?
The idea that in nuclear processes some mass is converted to energy seems very common. It is not surprising if students sometimes think this, as popular accounts of science often seem to suggest this.
Why? Perhaps: scientists/science writers and journalists
- are using language imprecisely?
- are actually confused or have misconceptions themselves?
- think that 'mass to energy conversion' is a suitable simplification of otherwise too difficult science – a kind of teaching model?
It is certainly possible that this is sometimes adopted as a form of words because the idea is considered a useful simplification in presenting abstract ideas, and those talking of mass changing into energy (or vice versa) do not actually think this way themselves.
Misleading accounts in popular science discourse
Unfortunately, it is common to hear or read references to mass being converted into energy in nuclear reactions.
Some examples of the misconception in everyday science discourse
Consider the following text:
"In fission what happens is that a heavy nucleus is split into two medium-weight nuclei and some neutrons – somewhere between two and three [this presumably refers to an average for a specific nuclear reaction – each fusion event produces a whole number of neutrons]. In the experiment of Hahn and Strassmann, for example, a U235 nucleus was split into barium and krypton along with neutrons. If one compares the masses of the U235 nucleus and the neutron that initiates the process to the masses produced, one finds that the final masses are smaller. This mass difference is related to an energy by Einstein's formula E=mc2, where m is the mass differences. This energy goes mainly into the kinetic energy of the fission fragments.
Fusion…works at the opposite end of the nuclear mass scale. Two light nuclei are fused together to make even lighter nuclei, with the mass difference once again released as kinetic energy."
Bernstein, 2004
Strictly this does not say mass is converted to energy. Someone who understood the scientific model, could certainly read this along the lines, perhaps, of,
If one compares the [rest] masses of the U235 nucleus and the neutron that initiates the process to the [rest] masses produced, one finds that the final [rest] masses are smaller. This mass difference is related to an energy by Einstein's formula E=mc2, where m is the mass differences. [This mass defect reflects a change in potential energy of the system.] This energy goes mainly into the kinetic energy of the fission fragments [which means their inertial masses are greater than their rest masses].
Fusion…works at the opposite end of the nuclear mass scale. Two light nuclei are fused together to make a [nucleus which is] even lighter [than the sum of the rest masses of the two original nuclei]…, with the mass difference once again [due to a decrease in potential energy] released as kinetic energy [which has an equivalent mass to balance the decrease in rest masses] .
However, someone who thought that mass could be converted into energy, can much more easily read this text as suggesting the mass difference reflects some of the original mass changing into energy.
Other examples, more explicitly state the alternative conception that mass is converted to energy.
Nuclear fission is the process of splitting apart nuclei (usually large nuclei). When large nuclei, such as uranium-235, fissions, energy is released. So much energy is released that there is a measurable decrease in mass, from the mass-energy equivalence. This means that some of the mass is converted to energy.
'Nuclear fission', University of Calgary webpage (accessed 21/03/2023)
"He [Lavoisier] summarised findings such as these into a statement that became known as the law of conservation of matter: Matter is neither created nor destroyed but is simply changed from one form to another. (We now know this law must be modified to accommodate the conversions of matter into energy, thanks to Einstein and other modern scientists.)"
Royston M. Roberts (1989) Serendipity. Accidental discoveries in science
| "Nuclear fusion is when you combine nuclei of elements to form heavier elements, and when you do this there is a loss of mass, which is converted to energy which provides the thermal pressure and that is what counteracts the gravity and stalls the gravitational collapse." | Prof. Carolin Crawford talking on a radio programme Read: The passing of stars: Birth, death, and afterlife in the universe) |
| "if we take an electron and the positron, and you put them together, they would annihilate. And they would annihilate not into nothingness, because they both had mass, so they both had energy from E=mc2 that tells us if you have mass you have energy. So, they would annihilate into energy" | Prof. Victoria Martin talking on a radio programme Read: The missing mass of the electron: Annihilating mass in communicating science |
Sources cited:
- Bernstein, J. (2004) Oppenheimer. Portrait of an enigma. London: Duckworth
- Bunge, M. (1998). Philosophy of Science. Volume 2: From explanation to justification (Revised ed.). Routledge. (1967)
- Einstein, A. (1916/2004). Relativity. The special and the general theory. (R. W. Lawson, Trans.). The Folio Society. (1916)
- Einstein, Albert (1919/1994), What is the theory of relativity? In Ideas and Opinions, New York: The Modern Library.
- Einstein, Albert (1927/1994), The mechanics of Newton and their influence on the development of theoretical physics. In Ideas and Opinions, New York: The Modern Library.
