Perhaps a dumb question but I don't have an answer.

Why is c2 in the equation? What part does the speed of light play in it? I understand that c2 gives the equation a huge energy value even for a small mass. That is a simple enough sum.

I tried looking at this; https://en.wikipedia.org/wiki/Mass%E2%8 ... l_examples but I couldn't find what I was looking for. It must be somewhere in there.

Another question; are there other ways of releasing the energy within a mass besides through nuclear reaction methods? A 1kg mass of any material,e.g. a rock, potentially has 21500kg equivalent of TNT energy within it. (according to the above Wiki article, unless I'm not understanding it correctly). If so, how can it be released/harnessed?

Because energy is defined as the ability to do work - the ability to make a mass move over a distance in a period of time. C provides the distance and time elements of the equation.

Set c = 1* then E = m and the units for both are the electron-Volt, eV (see, e.g Fermilab, Tevatron, CERN & LHC).

* Also set h = 1 and 8 π G = 1, for completeness.

If so, how can it be released/harnessed?

Fission and fusion both rely on that yield equation but through different mechanisms ( atomic bomb ( fission ) versus hydrogen bomb ( fusion > )

Regular atomic reactors do a controlled release of energy via fission. ( there is a whole raft of approaches )

The holy grail is controlled fusion ( Iter and others )

Very good question.

Because c is universal constant and relation between mass and energy is also universal ;)

I've written a mini crash course in special relativity, hope this helps:

Pulsar wrote:I've written a mini crash course in special relativity, hope this helps:

emc.pdf

Thanks for that. I'll keep it for future reference.

It's not like the equation plays no part in chemical reactions, the energies/masses involved are just much much smaller. But it's there in chemical reactions nonetheless. For all of the reactions, it's really binding energy differences that is the source of the energies released. Most of the mass of atoms is in binding energy, not due to the particles, the up and down quarks, electrons have insignificant mass compared to the nucleons.

newolder wrote:Set c = 1* then E = m and the units for both are the electron-Volt, eV (see, e.g Fermilab, Tevatron, CERN & LHC).

I see that setting c=1 gives an eV but it doesn't help me understand any better.

* Also set h = 1 and 8 π G = 1, for completeness.

I'm not sure where this fits.

Treat me as a complete layperson. I do have a bit of insight into technical issues but I get lost easily if I skip an important stage.

tuco wrote:Very good question.

Because c is universal constant and relation between mass and energy is also universal

I accept that there are constants and relationships and the theories have been proven. I just want more info as to why c is there and what role does it play. I see that e is the work that gets done. I see that m is the "fuel" that is used up. What I don't see is why c is needed.

Pulsar wrote:I've written a mini crash course in special relativity, hope this helps:

emc.pdf

Thanks for that. I guess the paragraphs between formula (11) and (13) is the crux of my question? There must be a Youtube video that shows that in simple form.

Nice formulas by the way. That would make a cool print to put on a wall.

Adco wrote:

newolder wrote:Set c = 1* then E = m and the units for both are the electron-Volt, eV (see, e.g Fermilab, Tevatron, CERN & LHC).

I see that setting c=1 gives an eV but it doesn't help me understand any better.

* Also set h = 1 and 8 π G = 1, for completeness.

I'm not sure where this fits.

Treat me as a complete layperson. I do have a bit of insight into technical issues but I get lost easily if I skip an important stage.

The SI unit of energy is the Joule (kilogram metre squared per second squared). The SI unit of mass is the kilogram. In the equation E = m c2 the c2 makes the units match - it can be considered the constant of proportionality relating mass and energy. If, instead, we choose to work in units where c=1 then the units for mass and energy become equivalent and eV (electron charge (Coulomb) x Volt (Joule per Coulomb)) is the unit chosen by physicists.

The treatment of special relativity posted by Pulsar shows how the equation is derived from the postulates of that theory and is, I feel, a better aid to understanding your initial question than my crude shortcut.

You are right that setting other constants to unity doesn't really fit here - I just added that for completeness (it's a mathematical trick frequently adopted by theorists that surfaces anytime I re-read my notes).

ETA
Found this at Quora that might help further...
Where-does-c-2-come-from-in-E-mc-2

Energy used is a function of mass times distance moved.

Distance is a measure of time travelled at speed x.

C is invariant, in a vacuum it is always the same and is independent of reference frame. That makes c a useful constant for speed x in this instance.

Turns out that when speed is constant and invatiant energy used and distance moved essentially cancel out.


*that could all be rong, i iz not a physicist but i haz vague memories from high school, what were long ago.

crank wrote:It's not like the equation plays no part in chemical reactions, the energies/masses involved are just much much smaller. But it's there in chemical reactions nonetheless. For all of the reactions, it's really binding energy differences that is the source of the energies released. Most of the mass of atoms is in binding energy, not due to the particles, the up and down quarks, electrons have insignificant mass compared to the nucleons.

From what I've read, a 1kg mass can produce about 21500kg equivalent of TNT in energy when subjected to a certain process like fission etc. Now take that 1kg to be a piece of wood and burn it in a fire. The energy released is nowhere near 21500kg of energy. I know I'm looking at it incorrectly but that is something that can really boggle a brain. I'm just rambling on.

Adco wrote:

crank wrote:It's not like the equation plays no part in chemical reactions, the energies/masses involved are just much much smaller. But it's there in chemical reactions nonetheless. For all of the reactions, it's really binding energy differences that is the source of the energies released. Most of the mass of atoms is in binding energy, not due to the particles, the up and down quarks, electrons have insignificant mass compared to the nucleons.

From what I've read, a 1kg mass can produce about 21500kg equivalent of TNT in energy when subjected to a certain process like fission etc. Now take that 1kg to be a piece of wood and burn it in a fire. The energy released is nowhere near 21500kg of energy. I know I'm looking at it incorrectly but that is something that can really boggle a brain. I'm just rambling on.

That is because, in a fire, only chemical bonds are being broken, not nuclear bonds. No mass is actually being converted to energy. The energy release in a chemical reaction is massively smaller than that in a nuclear reaction.

Fenrir wrote:Energy used is a function of mass times distance moved.

Distance is a measure of time travelled at speed x.

C is invariant, in a vacuum it is always the same and is independent of reference frame. That makes c a useful constant for speed x in this instance.

Turns out that when speed is constant and invatiant energy used and distance moved essentially cancel out.


*that could all be rong, i iz not a physicist but i haz vague memories from high school, what were long ago.

I believe, because I said it already :), its the in-pub answer OP was looking for. Otherwise one needs to go further, like Pulsar's pdf or here.

1/2mv2 does not cut it in relativity and is not universal.

Adco wrote:

crank wrote:It's not like the equation plays no part in chemical reactions, the energies/masses involved are just much much smaller. But it's there in chemical reactions nonetheless. For all of the reactions, it's really binding energy differences that is the source of the energies released. Most of the mass of atoms is in binding energy, not due to the particles, the up and down quarks, electrons have insignificant mass compared to the nucleons.

From what I've read, a 1kg mass can produce about 21500kg equivalent of TNT in energy when subjected to a certain process like fission etc. Now take that 1kg to be a piece of wood and burn it in a fire. The energy released is nowhere near 21500kg of energy. I know I'm looking at it incorrectly but that is something that can really boggle a brain. I'm just rambling on.

**Weaver said it. One way to look at it is that chemical processes involve shuffling of electrons/electron orbits, the binding energy differences are quite small, and electrons readily hop off-ionization. Nuclear binding energies are huge in comparisons, the differences in binding energies are therefore also huge. So nuclear processes result in far higher energy releases.

crank wrote:

Adco wrote:

crank wrote:It's not like the equation plays no part in chemical reactions, the energies/masses involved are just much much smaller. But it's there in chemical reactions nonetheless. For all of the reactions, it's really binding energy differences that is the source of the energies released. Most of the mass of atoms is in binding energy, not due to the particles, the up and down quarks, electrons have insignificant mass compared to the nucleons.

From what I've read, a 1kg mass can produce about 21500kg equivalent of TNT in energy when subjected to a certain process like fission etc. Now take that 1kg to be a piece of wood and burn it in a fire. The energy released is nowhere near 21500kg of energy. I know I'm looking at it incorrectly but that is something that can really boggle a brain. I'm just rambling on.

**Weaver said it. One way to look at it is that chemical processes involve shuffling of electrons/electron orbits, the binding energy differences are quite small, and electrons readily hop off-ionization. Nuclear binding energies are huge in comparisons, the differences in binding energies are therefore also huge. So nuclear processes result in far higher energy releases.

Echoing Weaver and Crank, it's impressive that almost nothing that happens naturally close to us, at the surface of the Earth, involves one kind of atom changing to another kind of atom. For example, wood consists of carbon, oxygen and hydrogen (plus small quantities of other elements) arranged in long linked chains, and air has a certain amount of oxygen in it, arranged in 2-atom molecules buzzing around. After the wood has completely burned, there are exactly as many carbon, oxygen and hydrogen atoms as before, but rearranged, with the carbon in 3-atom molecules of carbon dioxide buzzing around and contributing to global warming, and the hydrogen in 3-atom molecules of water. This conservation of elements isn't at all obvious, it was worked out by chemists like Dalton and Berzelius in the early nineteenth century, building on earlier discoveries. It wasn't until the end of the nineteenth century that it was discovered that atoms (the word comes from Greek for "cannot be split") can in fact be split and changed in radioactivity. While elements stay unchanged in ordinary chemical reactions like wood burning or the chemistry of living things, there's so very little mass/energy exchange that it's almost impossible to measure. It's only when atoms are split or fused to make new elements that noticeably large quantities of energy appear, transformed from matter.

How was the energy-mass equation deduced? e = mc2

zoon wrote:

crank wrote:

Adco wrote:

crank wrote:It's not like the equation plays no part in chemical reactions, the energies/masses involved are just much much smaller. But it's there in chemical reactions nonetheless. For all of the reactions, it's really binding energy differences that is the source of the energies released. Most of the mass of atoms is in binding energy, not due to the particles, the up and down quarks, electrons have insignificant mass compared to the nucleons.

From what I've read, a 1kg mass can produce about 21500kg equivalent of TNT in energy when subjected to a certain process like fission etc. Now take that 1kg to be a piece of wood and burn it in a fire. The energy released is nowhere near 21500kg of energy. I know I'm looking at it incorrectly but that is something that can really boggle a brain. I'm just rambling on.

**Weaver said it. One way to look at it is that chemical processes involve shuffling of electrons/electron orbits, the binding energy differences are quite small, and electrons readily hop off-ionization. Nuclear binding energies are huge in comparisons, the differences in binding energies are therefore also huge. So nuclear processes result in far higher energy releases.

Echoing Weaver and Crank, it's impressive that almost nothing that happens naturally close to us, at the surface of the Earth, involves one kind of atom changing to another kind of atom. For example, wood consists of carbon, oxygen and hydrogen (plus small quantities of other elements) arranged in long linked chains, and air has a certain amount of oxygen in it, arranged in 2-atom molecules buzzing around. After the wood has completely burned, there are exactly as many carbon, oxygen and hydrogen atoms as before, but rearranged, with the carbon in 3-atom molecules of carbon dioxide buzzing around and contributing to global warming, and the hydrogen in 3-atom molecules of water. This conservation of elements isn't at all obvious, it was worked out by chemists like Dalton and Berzelius in the early nineteenth century, building on earlier discoveries. It wasn't until the end of the nineteenth century that it was discovered that atoms (the word comes from Greek for "cannot be split") can in fact be split and changed in radioactivity. While elements stay unchanged in ordinary chemical reactions like wood burning or the chemistry of living things, there's so very little mass/energy exchange that it's almost impossible to measure. It's only when atoms are split or fused to make new elements that noticeably large quantities of energy appear, transformed from matter.

And I guess that is when c comes into play.

I have a lot to think about. It is making more sense to me now. However, there is still a lot more sense to be made. I'll keep looking and learning.