Exploring Energy-Mass Equivalence: Converting Energy to Matter in Everyday Life?

[Ebi Rogha]

a) Can we convert energy to mass (matter) in every day life?

b) When we charge a phone battery, its mass (weight) increases according to E=mc2 . Does it mean we convert energy to matter? If not, how its mass increases?

 

[PeroK]

a) Can we convert energy to mass (matter) in every day life?

b) When we charge a phone battery, its mass (weight) increases according to E=mc2 . Does it mean we convert energy to matter? If not, how its mass increases?

Yes, energy stored in a system contributes to its mass. Whether there is any conversion going on is a matter of terminology.

 

[Dale]

a) Can we convert energy to mass (matter) in every day life?

Mass and matter are different things. Mass is a property of matter, but matter also has many other properties, such as spin and charge.

When we charge a phone battery, its mass (weight) increases according to E=mc2 . Does it mean we convert energy to matter? If not, how its mass increases?

Charging a battery does not involve converting energy into matter. The mass of the battery is increased by rearranging the existing particles into a different internal configuration. The mass of the battery is not merely the sum of the masses of the particles but also depends on their configuration, so the mass of the battery changes without adding or removing particles (ideally) but simply by changing their configuration.

 

[mitochan]

a) Can we convert energy to mass (matter) in every day life?

b) When we charge a phone battery, its mass (weight) increases according to E=mc2 . Does it mean we convert energy to matter? If not, how its mass increases?

Mass is defined as energy measured in COM frame of reference where total momentum is zero. If such COM system does not exist, there is no defined mass but energy, e.g. a photon.

An electron and a positron pair, we may say they are matter, is generated from two photons. These photons have energy and also mass because two photon have their COM frame of reference. Mass keep existing before and after the reaction. So we know when the final state has material, both energy and mass are conserved before and after. I do not think chemists would admit two photons are material.

When you charge battery chemical state of the battery changes. When you warm battery its molecules do more thermal motion.
Energy and mass increase in both. Although molecular configuration or motion change, the number of molecules do not change.
I do not think chemists say material increase in both the cases.

[EDIT]
> If such COM system does not exist, there is no defined mass but energy, e.g. a photon.
Though there is no such COM frame of reference, zero mass is assigned to a photon particle because its dispersion relation $E=pc$ is included in general relation $E^2=p^2c^2+m^2c^4$.

 

[PeroK]

Mass is defined as energy measured in COM frame of reference where total momentum is zero. If such COM system does not exist, there is no defined mass but energy, e.g. a photon.

That's rest mass. There is also invariant mass of a system, which is conserved generally - e.g. where the system consists of a material object and a photon, which is absorbed.

 

[AdvaitDhingra]

a) Can we convert energy to mass (matter) in every day life?

b) When we charge a phone battery, its mass (weight) increases according to E=mc2 . Does it mean we convert energy to matter? If not, how its mass increases?

You need a lot of energy to create a significant amount of mass. You need very little mass to create a very large amount of energy (as evidenced by the atomic bombs). When measuring the mass of a system, for extremely accurate measurements it is necessary to take the energy into account.

Fun fact: Most of the mass in your body is just energy stored in the quarks in the protons and neutrons in the atoms that make you up. Most of your mass does not originate from the Higgs Field. Veritasium made a video about this.

 

[vanhees71]

That's rest mass. There is also invariant mass of a system, which is conserved generally - e.g. where the system consists of a material object and a photon, which is absorbed.

I think that's formulated not very clearly and it may give rise to misunderstandings. What do you consider as the "invariant mass of the material object and a photon" other than the total energy in the center-of-mass frame (devided by $c^2$), i.e., $\sqrt{s}/c^2$, where $s$ is the Mandelstam variable. This COM energy is of course conserved in the absorption process. So what you call "conservation of invariant mass" is in fact nothing else than the conservation of energy.

In contradistinction to Newtonian physics there's no additional mass conservation law in relativistic physics. This is due to the different structure of the Poincare group in comparison to the Galileo group. While the Galileo group's Lie algebra has non-trivial central extensions, and only these non-trivial central extensions lead to a useful physical dynamics in non-relativistic quantum theory, mass is conserved non-relativistic quantum mechanics due to a superselection rule. The Poincare Lie algebra has no non-trivial central extensions and thus there's no mass superselection rule, and from the space-time symmetries you thus have only the 10 conserved quantities from the Noether theorem (energy, momentum, angular momentum, center-of-energy velocity from symmetry under temporal translations, spatial translations, rotations, and Lorentz boosts, respectively as the corresponding one-parameter subgroups).