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Is Mass Really Condensed Energy

  1. Jun 17, 2006 #1
    A. Einstein contended that (E=mc2) energy was equal to mass X velocity of light squared.

    Does is it not follow that M=e/c2 or that mass is really condensed energy?

    If mass is truly energy, then what is it that we observe from our mind's point of reference?

    Finally what is energy?
  2. jcsd
  3. Jun 17, 2006 #2


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    In physics, energy is the ability of a system to do work.


    Work is defined by force * distance (in an inertial frame)

    If you consider particle / antiparticle reactions (say an electron and an anti-electron), you can see examples of how mass can be converted into energy. This does not mean, however, that the energy contained in a mass M is necessarily fully accessible to us. Generally, it is not accessible, unless we have access to a supply of antimatter of equal mass.

    Anti-matter does not occur naturally (as far as we know) and has to be artifically produced. The amount of energy it takes to produce anti-matter is much more than the energy which it actually liberates.

    As far as whether matter is "really" condensed energy, that's a bit philosophical. What experimental tests would convince you that it was? What experimental tests would convince you that it wasn't?
  4. Jun 17, 2006 #3
    onchyo, in simple terms:

    Mass is a property of a thing. Imagine thing A is moving, and you want to slow it down. If it's massive then even if it's going slow, it has a lot of Mass, so you have to work real hard to slow it down.

    Energy is also a property of a thing. Imagine thing B is moving, and you want to slow it down. If it ain't massive but it's going real fast, it has a lot of Kinetic Energy, so you have to work real hard to slow it down.

    A and B have different properties, but these properties can sometimes look like one another. And they can be actually translated into one another for real. But I wouldn't say mass is condensed energy. Energy isn't a thing, it isn't something you can condense. It's just a property of a thing. It's like colour. It can't exist on its own. The thing exists. The motion exists. The energy does not. That's why it can't be created or destroyed. Because it doesn't exist in the first place.

    What is energy? It's just a measure of how much change in motion the thing can achieve on another thing.
  5. Jun 19, 2006 #4
    E = mc2 is a relationship between the energy supplied to a closed system and the quantity of mass increase of the system due to the added energy. It is also the maximum amount of energy a system can transfer to other systems, e.g. like the amount of rest energy possesed by a pion. The pion can disintegrate into two particles, the sum of the energies of the two particles adding up to the rest energy of the pion. Mass is not "frrozen energy."

    What is energy? Nobody knows. This is a complicated question which deserves a complete answer. Unfortunately the answer is too long to post here. For that reason I made a web page to address this question. Please see


    Note the comment by Feynman
  6. Jun 19, 2006 #5
    I don't believe this question belongs in a relativity forum. "What is mass" and "What is energy" are questions which should be discussed in general physics.

    After those discussions are held, we can then ask - "now how does relativity affect these concepts". Relativity does little to shed light on the nature of mass and energy.
  7. Jun 20, 2006 #6
    The OT asked a question about the relationship between mass and energy, i.e. E = mc2 which is a relationship derived using tghe principles of special relativity. Hence this forum is the right forum to post this question.

  8. Jun 20, 2006 #7
    I know, but I wasn't trying to shut down the discussion. The big giant font
    at the end of the question gave me the impression that the original poster was searching relativity for clues about the nature of energy. I was only pointing out that there was none to be found.
  9. Jun 21, 2006 #8
    For me, energy makes sense only if you can define an energy invariant conservation law. Better, the energy conservation law is what define energy.
  10. Jun 23, 2006 #9
    I would say that there are clues in that there are properties of energy, but energy itself is quite undefinable as far as we know.

  11. Jun 23, 2006 #10
    Ditto for mass!
  12. Jun 24, 2006 #11
    Why? Mass is a well defined quantity.

  13. Jun 24, 2006 #12
    How mass can be a well defined quantity in GR if there is not a mass conservation law?
  14. Jun 24, 2006 #13
    Who says that there is no mass conservation law?? he conservation law for mass is identical to the conservation law of energy, i.e. Tuv;u = 0.

    Last edited: Jun 24, 2006
  15. Jun 24, 2006 #14
    Pete, first of all we are now talking of energy and not only mass anymore; second Tuv;u = 0 is not a proper conservation law (that the reason for the energy pseudo-tensor and all the relevant discussion).

  16. Jun 24, 2006 #15
    Huh? This is a thread on mass is it not? In anycase I was addressing you're assertion that mass can't be defined.
    I don't see how you arrived at this assumption. Please clarify as to how you arrived at this assertion.

    The equation I posted is standard GR stuff. Its actually called the conservation of energy-momentum (i.e. energy is conserved and momentum is conserved). Its called the Law of local energy-momentum conservation. See MTW page 386 if you have that text.


  17. Jun 24, 2006 #16


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    Actually Pete Tuv;u = 0, the conservation of energy-momentum does not generally imply the conservation of energy and the conservation of momentum; those are frame dependent concepts and in a freely falling frame the separate total energy and momentum of another object, freely falling in a different part of the gravitational field will not themselves individually appear conserved.

    The (-+++) nature of the metric means that the 3-momentum component is vector subtracted from the total energy to obtain the 4-momentum or energy-momentum of the object, and it is this resultant, which is the rest mass, that is conserved in GR.

    This has the result that rulers remain of fixed length and clocks remain regular.

    Last edited: Jun 25, 2006
  18. Jun 25, 2006 #17
    Probably I was unclear: in GR you can only speak of energy conservation and not mass conservation...and also energy conservation in my opinion is not well defined.

    Yes I do have MTW; pls check page 466ff: in GR you can't localize the energy of gravitational fields... that means in general: no proper energy conservation law available and without a proper energy conservation law you can't define energy properly.

    Last edited: Jun 25, 2006
  19. Jun 25, 2006 #18
    Since relativity considers energy and mass to be the same thing then I ask you on what do you base this assertion?
    That is the energy of the gravitational field. I was speaking about the energy/mass of matter.

    In any case I was responding to your comment
    When I posted my assertion that mass is a well defined quantity I had in mind the mass of a particle (i.e. inertial mass), not a general definition of mass which encompasses all of GR (i.e. active and passive gravitational mass.

    In any case I now understand what you meant when you said that mass is not conserved and I therefore have no more questions to ask you so I will bow out here so that this thread doesn't drone on about mass/energy conservation. Seems like many threads get sidetracked with conversations like this and end up donminating a thread. I don't wish to contribute to that in any threads, hence my bowing out. Thanks.

    Garth - If you recall, we discussed your comments in the past ad nauseum and I understand that you have a different opinion on that point so I see no reason to go over the same discusssion again. Thanks.

    Last edited: Jun 25, 2006
  20. Jun 25, 2006 #19
    Probably we say the same things in different words. Let me rephrase: you can't actually distinguish in GR between mass, energy, energy of gravitational fields. That why you can't have in GR a proper energy conservation law... so mass and energy can't be well defined in GR.
  21. Jun 26, 2006 #20
    I would be interested in learning the definition of mass. Please post it.
  22. Jun 27, 2006 #21
    It depends on what you mean by "mass." There are several meanings to the term: inertial mass (aka relativistic mass), proper mass, active gravitational mass and passive gravitational mass.

    Inertial mass - The quantity m such that mv is a conserved quantity in elastic collisions. m is a function of speed, i.e. m = m(v).

    Proper mass - For a tardyon m0 = m(0). For a luxon m0 = 0.

    Active gravitational mass - That which is the source of a gravitational field.

    Passive Gravitational mass - That which a gravitational field acts on.

    For a detailed definition please see


  23. Jun 27, 2006 #22


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    I am basically with gijeqkeij and Garth on this issue, as long-time posters will probably be aware.

    The way I describe mass in GR is not that there is no defintion, it is rather that there is no single definition. There are many different defintions of mass in GR, some of the more comon are

    ADM mass, Bondi mass, and Komar mass. The first two are applicable in asymptotically flat space-times, and differ on how they handle energy in gravitational radiation. The last is applicable in any static space-time.

    Other posters have talked briefly about other sorts of mass (such as Dixon mass), which I want to learn more about someday.



    for some past discussion.

    If the space-time is neither static nor asymptotically flat, there is no general definition of mass in GR, just as there is no general definition of energy.
  24. Jul 2, 2006 #23
    I was speaking about conservation of energy, not momentum. One would never assume that a quantity such as momentum is a constant of motion when it is moving in a gravitational field. The law of conservation of momentum applies only to those particles on which no force is acting. I.e. in Newtonian gravity a particle falling in the Earth's gravitational field (as observed by someone sitting on its surface) will measure the energy to be constant and yet the momentum will constantly changing when in free-fall. However since this is a static field then the energy of such a falling particle will be zero.
    Actually its a geometric property when external 4-forces are zero. The equation div T = 0 is a geometric statement, i.e. independant of spacetime coordinates. It is easily found by calculating in a locally Lorentzian frame. So while its true that energy is frame dependant it is not true that the Law of conservation is frame dependant. Its sort of like measuring proper mass. It is measured when the particle is at rest in a locally Lorentzian field. If one is evaluating the energy from a freely-falling frame in a curved spacetime then the field will be time independant and such a field is non-conservative.

    Its not as if the GR community calls this "local" energy-momentum conservation for nothing Garth. They state it that way for a reason.
    3-momentum is not vector subtracted from energy since one is a tensor of rank zero while the other is a tensor of rank one. The meaning of the equation you speak of (i.e. the T^0u_u = 0 equation) is a conservation equation which states that energy entering a small enclosed surface will equal the rate at which energy passes through the surface which is the rate at which energy decreases from external to the surface. Plus you can't add 4-vectors which are located at different events in spacetime. That is a violation of the rule for adding vectors. In any case, when the energy for a single particle in free-fall in a static g-field is calculated then the energy (E ~ P 0) it will be a constant of motion, i.e. conserved.

    When one speaks of conservation laws one must take into account the specific example and see if it matches the condition postulated in the law. I.e. in that case "momentum" is rarely conserved since the law states that "The momentum of a free particle is conserved" and therefore you must take into account forces acting on a particle. Likewise the energy of a particle in a field is not constant unless the potential is time-independant, i.e. a conservative field.

  25. Mar 24, 2011 #24
    How would you explain black holes? I would like to think of mass and energy as states of existence which are not binary and rather a spectrum therefore providing the possibility of having a state that has both mass and energy.
    Interestingly there is a Sanskrit verse "aapOHO vaa idhagum sarvam viswaa bhuthaanyApa". Sarvam viswaa means entire universe and aapoho means water. The gist of it roughly tries to suggest that entire universe is made of water. I found the meaning quite curious and happened to have a study at the literature. I was surprised to find what the folks were hinting at. The verse tries to suggest that entire universe existed in a liquid state. This liquid was churned and and from it arose time. I am assuming here the entire energy was churned to a single point of infinite energy to create a big bang which created time too.

    I am astonished at the quality of thought that existed in these folks from the BCs with absolutely no equipments to verify even their basic theories.

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