# Transforming mass and energy

1. Aug 6, 2004

### da_willem

Are there any other examples of converting mass into energy or vice versa besides bringing together a particle and its anti particle? Or is this the only one allowed by conservation laws?

By mass I mean the Lorentz-invariant quantity often called 'rest mass'. So the example of a nuclear reaction does not count, for it is actually the binding energy (wich is initially included in the 'mass' of the atom) that is converted into other forms of energy.

So I do not mean the 'transformation' of energy and mass by changing your perspective, but the actual physical process of transforming energy into mass or vice versa.

Thanks

2. Aug 6, 2004

I think particle/antiparticle pairing is the only way to do it. You can get massless particles to release energy, such as photon pair production.

3. Aug 7, 2004

### pervect

Staff Emeritus
Dumping matter into black holes seems to produce some spectacular high-energy displays in astronomy, and seems to meet your qualifications. I gather the process is currently theorized to be fairly efficient at converting matter into energy, though I don't have any specific figures.

4. Aug 7, 2004

### da_willem

When matter falls into a black hole, isn't it just it's gravitational potential energy that is converted into other forms of energy like radiation? And inside a black hole, I guess nobody can say anything reasonable about if the original matter is still matter or converted into some form of energy.

5. Aug 7, 2004

### pmb_phy

Yes. See - http://www.geocities.com/physics_world/sr/nuclear_energy.htm

You'll notice that the decrease in the sum of rest masses of the nuclei yields an increase in the sum of kinetic energy of fission products which may include photons. There is a definite change in mass which is an important thing to realize when you're thinking that this is just binding energy changing into kinetic energy. Loosley speaking - Binding energy is also a form of mass.

This is a change in the form of energy. While you think that this is not a case of mass-energy conversion I want you to consider that the only think that the term "conversion" means is "change in forum of energy" and nothing else. In particle/anti-particle anihilation you've change rest mass energy into electromagnetic energy.

6. Aug 7, 2004

### jtolliver

Yes; if particle types are changed, and there aren't just massless particles involved you're pretty much guaranteed to get a change in the mass

7. Aug 8, 2004

### pervect

Staff Emeritus
I did some googling, and found
http://www.pas.rochester.edu/~dmw/ast102/Lectures/Lect_14b.pdf [Broken]

which mentions on page 3 that about 10% of the rest mass of matter falling into black holes can be turned into energy.

http://www.nap.edu/nap-cgi/morehits.cgi?display=text&isbn=0309038413&term=black+holes&file=8-20.htm [Broken]

also mentions that "up to 10%" of the infalling rest mass is converted into energy, and that black holes are the "most efficient converters of rest mass to energy posited in nature", comparing this to fusion, which releases

http://zebu.uoregon.edu/~imamura/123/lecture-4/lecture-4.html [Broken]

mentions much the same figure, and points out that this is 10-100x as efficient as fusion.

Last edited by a moderator: May 1, 2017
8. Aug 8, 2004

### da_willem

If you weigh an atom and compare this with the mass calculated by summing the masses of it's constituent particles you get a discrepancy. This is because mass is not additive!! If you per se want the mass of a system like an atom you have to also add the binding energy divided by c^2.

But my point is that a particle like a proton always has the same mass (I mean it's L-invariant rest mass), it's a constant of nature, and no nuclear reaction can do anything about that.

So you should bear in mind the difference between rest mass, wich my question is about, and 'energy-mass' wich can even be changed by just moving with a different speed.

9. Aug 8, 2004

### reilly

There are many examples of 'energy->mass' or vica versa -- or, as PMB notes, energy->energy modulo form.

Virtually all nulear reactions, including fission as PMB notes, involve mass-energy conversions -- many nuclear reactions including alpha and beta decay in which the final nuclear protagonists are different the initial ones -- neutron->proton, electron, antineutrino. Then there's the world of particle physics with reactions like photoproduction of particles -- gamma+proton-> neutron +_ pi+meson, decays like
pi0-> 2 gammas, creation of particle showers and forests by cosmic rays, and accelerator beams. (I don't have access to my physics books right now, so i'll leave it up da willem to dig out the info on nulear reactions and so on. Also, a look at relativistic field theory shows that such conversions, particle->particle' and similar things, are built into the theory at the most fundamental level. )

This conversion is such a basic fact of physics life that it's the sort of thing that one virtually never thinks about -- familiarity can certainly kill amazement.
Regards,
Reilly Atkinson

Regards,
Reilly Atkinson

10. Aug 8, 2004

### rjhollingsworth

What about in high energy collisions? When two protons collide, the energy required to break apart the bonds between quarks (color force) is less than the energy required to produce quark-antiquark pairs, so you get a bunch of particles with very short lives coming out of the collision but, don't you also get energy in the form of light?

Last edited: Aug 8, 2004
11. Aug 9, 2004

### pervect

Staff Emeritus
Figuring out how to explain this took me some time, but I think I've thought of the way to do it.

Calculating the potential energy in General Relativity is a lot more difficult than it is in Newtonian theory, and is not always possible. We can assign the system a definite energy in this case, as long as we make the usual assumption of an asymptotically flat space time.

Forutnately, we don't have to actually compute the potential energy in this case, all we have to do is argue that the potential energy of an object "at infinity", i.e. one far away from a black hole, is zero, and that the potential energy becomes negative as the object approaches the black hole.

Note that in non-relativistic physics we are allowed to set the potential energy at infinity to whatever we want, however, in relativity we don't have the same degree of freedom to add a scalar to the energy. (This is true in special as well as General relativity , E^2 - (pc)^2 = (mc^2)^2 doesn't work right unless the zero point of the energy is set propertly, for instance).

So getting back to the original problem, if we have a black hole of mass M, and a small mass of mass m at infinity, we can write the total mass of the system as M+m. Thus the system mass is the sum of the individual masses.

Now, when we allow the small mass m to start falling into the larger mass M, we can say that the total energy of the system must remain constant. The mass m picks up kinetic energy, and loses potential energy.

If the small mass m did not interact with anything, but went right into the black hole, we could say that the total mass of the black hole increases from M to M+m after the smaller mass fell into the black hole. This is necessary because the total mass must remain conserved, and after the mass falls into the black hole the entire mass of the system is now in the black hole.

But in actual astrophysical situations, the mass m tends to bump inot other masses on the way in, releasing radiant energy. According to the references I found, about 10% of the total energy winds up being released as radiation.

So the black hole winds up with some mass M' that's about equal to M+.9m, and around .1m*c^2 is released in the form of radiant energy.

Thus the black hole does in fact meet your specifications for converting rest mass into energy.

12. Aug 9, 2004

### da_willem

Look at the example of e.g. a neutron falling into a black hole. You say it is rest mass it is gradually loosing while moving closer to the black hole. This cannot be correct, for the mass of a neutron is a constant of nature independent of it's speed or position in a gravitational field (just look it up, it's the same everywhere). So something else must be converted into radiation...

Couldn't it be the potential energy wich is converted into kinetic energy when the particle approaches the black hole wich is converted into radiation? So when the particle bumps into other masses it slows down and release energy in the form of radiation.

Using the nonrelativistic potential U=-GMm/r and by using the Swarschild radius of a black hole r=2GM/c^2 we see that the particle can loose a maximum of .5mc^2 of potential energy by moving from infinity to the event horizon of the black hole.

So if you count this potential energy as mass the statement quoted above can be correct. The total relativistic mass of a particle at infinity would be mc^2+.5mc^2=1.5mc^yielding a 'mass' of 1,5m. So the particle can loose 2/3 of it's mass in the process of falling in the black hole. The actual number is about 10% because the particle still has some kinetic energy (wich is added to the mass of the black hole) when it falls into the black hole.

This concept (not the details) looks plausible to me. Let me know what you think about this.

13. Aug 9, 2004

### pervect

Staff Emeritus
That's not what I'm saying at all. I'm saying that you can't add the mass of the neutron to the mass of the black hole to get the total mass.

More to the point, neither can you add the energy of the neutron to the energy of the black hole to get the total energy of the system (except for the special case where the neutron is at infinity). The reason you can't do this is because of the gravitational binding energy has to be included.

Well as I mentioned before in GR you have to be a bit careful about assuming that a potential energy even exists, but in this case I think it does. (I'm open to corrections on this point - while I think it probably exisits, I can't write down an expression for it). For more on where I'm coming from see

http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html

If we assume that the potential energy exists, you can say that the potential energy, which starts out as zero, becomes negative as the neutron approaches the black hole, and that the sum of the potential energy and the kinetic energy remains constant, at least until the neutron bumps into stuff on the way down, at which point some of the kinetic energy is converted to radiation

I'm fairly sure that the Newtonian potential is not going to give the correct answer for a relativistic problem like this.

Even if you use the Newtonian potenital, -GmM/r is zero at r=infinity, which is what I previously assumed.

It's worthwhile to try and clear up a few points of terminology. I used the overloaded term "mass of the system", which caused some unfortunate confusion. I really meant the energy of the system. The energy of the system is what an observer at infinity can measure, and find to be constant.

Using this more accurate terminology gives me an idea - it might actually be helpful to consider the issue of dropping a photon of energy E into a black hole instead of dropping a neutron.

IF you have an observer close to the black hole, the energy E of the photon just before it crosses the event horizon is going to appear to be larger, it will appear blueshifted, due to gravitational blue-shift. But that's not the observer we are interested in. We are interested in the observer at infinity. If we let that same photon climb out to infinity again, and measured it's energy, the photon would be red-shifted again, and we would get the same v alue E that we started out with. So, for the observer at infinity, E is the energy of the photon, it doesn't matter that it got blueshifted going in.

Something roughly similar happens when we drop a neutron in. If you look at the neutron from the viewpoint of someone close to the black hole, you can argue that it's total energy must be E>= m_0*c^2, where m_0 is the invariant rest mass of the neutron.

But if we convert the neutron to a photon of equivalent total energy (i.e. a photon of energy m_0*c^2 + kinetic energy terms), we see that the observer at infinity will assign a different, lower, energy to it. And he's the observer that we are interested in when computing the total system energy.

14. Aug 10, 2004

### da_willem

I agree, but sometimes you can get a rough idea of a process by using a not entirely accurate theory. But I made the mistake of using a positive potential energy for a particle at infinity. But although this is allowed because you can always add a constant to potential, this is not correct because it yields an energy above m_0c^2...

Thank you for explaining your point about the black hole. I think I understand what you mean.

But I think my point still stands that the 10% of the 'mass' of an object that is converted into energy is actually kinetic energy. So it is not the rest mass of the particle that is converted but it's kinetic energy.

15. Aug 10, 2004

### pmb_phy

My appologies. I should have been clearer in my response. Let me clarify what I posted above. Below I use the term "mass" to mean "relativistic mass" and I use the term "proper mass" to refer to "rest mass" for reasons I can explain if you'd like

There is a finite proper mass associated with binding energy. Once you add that in, the masses do add (since mass is a conserved quantity). I believe I understand why you wish to leave it out/ignore it/call it something else. People seem to want to associate proper mass with a particle or an object and not with something like binding energy. While I can understand the desire to do so I don't think I could justify that position if someone were to press me on the matter, hence my choice. However it seems to me that, from your comments here, that you're not thinking of proper mass as in the m0 in

$$E^2 - p^2c^2 = m_0^2c^4$$

but that you're thinking of the proper mass of a particle/object. What precisley do you mean when you say "converting mass into energy "? The reason I'm saying that binding energy proper mass is that it is common in relativity to refer to energy with zero momentum as having a finite proper mass as evidenced in the expression above. However I doubt that everyone would agree on this point.
I was bearing that in mind. You've chosen to look at the proper mass associated with binding energy as something else. However once one realize the semantics on this then it simply turns into a matter of semantics.

Although I disagree with the naming conventions used by Taylor and Wheeler, I do agree with there description of what it means to convert mass to energy. See the bottom of

http://www.geocities.com/physics_world/stp/pg_248.htm
http://www.geocities.com/physics_world/stp/pg_249.htm

Those pages are there with the permission of the author. The entire section starting at http://www.geocities.com/physics_world/stp/pg_246.htm
is pretty nice. Its called Use and Abuse of the Concept of Mass

Pete

Last edited: Aug 11, 2004
16. Aug 10, 2004

### da_willem

Thanks for the link to that terrific page! I'll read it, because it seems to clarify a lot of my questions about the concept of mass.

17. Aug 11, 2004

### pmb_phy

You're welcome. By the way. Those pages are from Spacetime Physics - Second Edition, Taylor and Wheeler.

I'm not sure if I posted this before but this is an example of what they're speaking of regarding mass-energy conversion using nuclear energy as an example -
http://www.geocities.com/physics_world/sr/nuclear_energy.htm

Pete

Last edited: Aug 11, 2004
18. Aug 11, 2004

### da_willem

After reading Taylor and Wheeler I think my question was about "amount of matter" instead of mass. But according to the text "Nature does not offer us any concept as "amount of matter"".

But it is comforting to know that mass as in m^2=E^2-p^2 is a conserved quantity independent of movement, wich makes it (for me) more fundamental than energy wich is not even Lorentz invariant. I guess energy is a form of mass and not the other way around...

19. Aug 11, 2004

### pmb_phy

I highly agree with the authors about "amount of matter". Its a concept which is best avoided in trying to define it in physics. But its useful to use when you don't need to be precise.
Keep in mind that this applies to a closed system in an inertial frame.

I made a web page covering all the pitfalls one can get into with that concept if one isn't careful. See

http://www.geocities.com/physics_world/sr/invariant_mass.htm

Pete

20. Aug 15, 2004

### bettysfetish

"Are there any examples of converting mass into energy or vice versa besides bringing together a particle and its anti particle? Or is this the only one allowed by conservation laws? So I do not mean the 'transformation' of energy and mass by changing your perspective, but the actual physical process of transforming energy into mass or vice versa."
Hey, does anti-matter count? We have produced about a thimblefull right here on good old Earth. Thats E=m isn't it? And how 'bout burnin' down the house? Isn't that m=E?
Oh well, just a thought.
L8R