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How does energy differ from mass?

  1. Jul 21, 2003 #1
    I wonder if anyone here can help me with this, i am refreshing my physics knowledge ( long lost ). I re-read Steven Hawkins Brief History of Time, and a many many issues jumped out of me, but lets start with the one titled in the the thread - how does energy differ from mass?

    Let me state the issue more clearly, as i understand it ( i maybe wrong)
    a. E=mc2 implies that energy and mass are interchangeable. Thus a photon has 'effective mass' - and therefore is acted upon by gravity to curve its trajectory in space

    If mass and energy are interchangeable - how do we know when to call energy just 'energy' and other times call it 'mass'?

    Hawkins says there is 'intrinsic mass' which is limited to less than speed of light, because as speed increases, its energy incrases to infinity - whereas 'energy' is said to have 'effective mass'.

    So why is a photon not subject to the same effect? i.e. what is 'intrinsic mass' that is different to 'energy effective mass' of say a photon

    In summary - what exactly is 'mass' - all matter is simply 'energy', so i cannot fathom it. IS is that energy in a particular arrangement is called mass? if so, what arrangement? and why?
  2. jcsd
  3. Jul 21, 2003 #2

    Energy is related to the ability to do work against a force, while mass (inertia) is related to the change of velocity with the change of momentum. Because an object moves with the quantum mechanical group velocity of a wavegroup the inertia differs by a factor of C2.

    Here is a short and not very complete description I put up.

  4. Jul 21, 2003 #3
    Thanx Tyger,
    I find it helpful to imagine replies must be understood by a 15 year old physics student ....infact, i always try to gain an understanding that allows me to explain answers to my 5 year old twins. This forces me to get down to 'axiomatic concepts' and a truer level of understanding.

    I still have no idea truly what 'mass' is. Let me try to make it clearer by building a framework we can use to discuss this.
    Some subatomic particules have 'mass', and some don't. All matter is simply a grouping of subatomic particles e.g. the largest are protons/neutrons + electrons, some of which have mass, and those particles comprise smaller ones and so on - we can keep getting smaller until presumably, one day, we discover the 'smallest unit of matter' - lets call it AxiomaticMatter

    Now, since all bigger matter units must be made from AxiomaticMatter, the question is :
    Does AxiomaticMatter have 'mass'? It must, or bigger units couldn't have mass
    Ah, but some bigger matter units have 0 mass? hmm.

    Logically, that's impossible. So, lets for the sake of this exploration, say there are 2 axiomatic units of matter - lets call them: AxiomaticMatter_WithMass & AxiomaticMatter_ZeroMass

    Now we can construct all the known bigger units from these two - some with mass, some with zero mass.
    OK - but now back to my question
    1. What is the difference between AxiomaticMatter_WithMass & AxiomaticMatter_ZeroMass?
    This would identify what 'mass' is, since this is the only difference. When i say 'what mass is', i mean, is it a still smaller unit of matter, which AxiomaticMatter_WithMass has?
    Maybe, if not, what is it? perhaps a rate of spin or some other physical property? i would love to know the answer, and how it has been proved.

    2. But Since energy can become mass ( e=mc2), it still leaves the question of HOW DOES ENERGY BECOME MASS?
    Energy is something different to matter, and mass, since it is a PROPERTY of them e.g. a photon has 0 mass, but HAS energy.

    Without knowing the answer to (1) above, its hard to answer this. I can see that if mass were infact a physical property such as rate of spin of Axiomatic matter, then energy could be interchangeable to spin rate or similar.

    I have yet to hear, read a clear explanation of this, and welcome any precise answers to 1 and 2 above.
  5. Jul 21, 2003 #4
    i found some answers here...

    I've done some research into this today - it turns out this is one of the biggest questions being debated right now - and here's a few links for anyone else who is interested in pursuing this:

    Take a look at this link first:

    So, it turns out the there is no answer to this very important question yet. Most likely, it is as i suggested that a as yet undiscovered axiomatic particle exists i.e. the 'Higgs particle'

    I also found this article very interesting:

    Although it is speculative in nature, the discussion of 'energy to mass' interconvertiability is the more in depth i've found, and exactly what i was getting at. Since everyone can only guess at this, my own guess is as this article suggests, that infact 'all matter is infact made of of axiomatic energy' i.e. energy exists independent of matter/mass, and infact matter/mass are just a special organisation of energy.
  6. Jul 21, 2003 #5
    Some more

    Energy is just proportional to the change of quantum mechanical phase with time, the constant of proprtionality being Planck's constant, so I suspect that it is the more basic quantity. And given the relationshipe between the group velocity of a state and the momentum I don't think the quality of mass (intertia) is as mysterious as some people seem to want us to beleive.

    Your original question wasn't so much about the origin of mass or rest energy, but their relationship, which is what I tried to describe.
  7. Jul 22, 2003 #6


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    Sorry to have bothered you with my inferior knowledge but I’m just curious. No 2 said that photon has 0 mass. Than why is light (consisting photons) attracted towards massive objects like blackholes? Is it because of the curvature in space time or else?
    Please explain in an easy term. hehe
  8. Jul 22, 2003 #7

    I would try this. Energy is attracted by Energy. Period. Any type of energy. They want to exchange to get equilibrium. Long range attraction is commonly called Gravitation.
  9. Jul 22, 2003 #8
    Originally posted by Dal
    Sorry to have bothered you with my inferior knowledge but I’m just curious. No 2 said that photon has 0 mass. Than why is light (consisting photons) attracted towards massive objects like blackholes? Is it because of the curvature in space time or else?
    Please explain in an easy term. hehe

    Asking questions is the foundation of science so your certainly not bothering me. I think i understand your question, so here goes in easy terms, because i try to think very simply ( to achieve Galileo's Simplicio test - An explanation to be understood by any honestly open-minded, non-credulous but relatively uninformed listener - as we all would ideally be)

    Newton defined the law of gravity Force = mass_body_1 * mass_body_2 * GravConstant / distance_between_masses ^2

    So, as you correctly say, this implies a Photon of 0 mass would experience Zero gravity.

    But then comes along - EINSTEINS's change to LAWs OF GRAVITY:
    Einstein realized that Newtons Gravity model is not complete, since it implies that if one of the masses disappeared, that gravity would instantly also disappear, and therefore gravities effect would travel faster than light, infact, gravity would need to travel at INFINITE SPEED, which is 'impossible' ( assuming the speed of light as a limit - Einstein 'special theory of relativity' defines that the speed of light is a limit )

    Einstein came up with his own gravitational model called General Relativitity( quoting from 'Brief history of Time' by Hawkins pg 29):
    "Einstein made the revolutionary suggestion that gravity is NOT a FORCE like other forces, but a consequence of the fact that SPACE-TIME is NOT FLAT, it is CURVED by the DISTRIBUTION of MASS & ENERGY in it. Bodies like earth are not make to move on curved orbits by a force called gravity, instead they follow the nearest thing to a straight path in a curved space called a GEODESIC. A geodesic the the shortest(or longest) path betwen two points..."

    And to answer your question specificially about light(photons) pg 31:
    "light too must follow geodesics in space-time, the fact that space is curved means light no longer travels in straight lines"

    These effects have been verified by experiment, so we can be as sure as science can be that this is correct.
    So, whilst thinking of gravity as a force between masses is mostly correct, it is not quite, it is really that space itself is curved by a DISTRIBUTION of MASS & ENERGY.

    What Hawkins does not discuss is why mass and energy have this effect - one theory is that gravitons exist ( the gravitational eqivalent of photons for electromagnetics), and energy/mass throw out gravitons ( presumably at the speed of light) - this is all being reseached and is yet theoretical.

    This takes us back to my original question, of the distinction between mass & energy. They both cause gravitational effects ( i.e. curving space-time), and E=mc2 shows they are interchangeable ( do not think of energy here as 'work done', it is not that here see http://www.cox-internet.com/hermital/holoprt2.htm )

    So, really, i now find it easier to consider mass & energy to be THE SAME - the question i had, was when do i know to call it mass and when energy - and the answer appears to be it is mass when a 'Higgs Boson' is present ( see the linked articles), and a photon presumably does not have this theoretical Higgs Boson present, so has 'no instrinsic mass' ( though it can be converted to mass via E=mc2, that convertion presumably requires us to mix in a Higgs Boson?).

    As i say, this is massively theoretical, and i provided links above if you want to pursue it.

    I hope i explained my limited understanding clear enough.
  10. Jul 22, 2003 #9


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    Thanks fractal. That explained alot and the link you've given is very useful.
  11. Jul 22, 2003 #10
    Mass and energy are not the same thing. In special relativity
    there's a thing called the energy momentum four vector which
    in some respects is as basic as you can get. In any case,
    energy is the time component of the four vector,
    momentum is the space component and mass is the magnitude of the four vector. This is all summed up in the equation:

    E2 = m2c4 + p2c2

    E = energy
    m = mass
    p = momentum

    I think a lot of people get hung up on this because they think mass and energy are things. But they’re not things -- they’re properties of a system. This is not to say they’re not intimately related, they are. If you study the equation:

    m2 = E2 - p2
    (c = 1)

    You can see that if the momentum is zero the mass of the system equals the energy of the system, or to put it another way -- mass is equal to the energy of the system that cannot be transformed away.

    If you wanted to, you could abandon the concept of mass altogether and just talk about the magnitude of the energy momentum four-vector, but the concept of mass is so ingrained that I doubt this will ever happen.
  12. Jul 23, 2003 #11


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    thanks Ring for contributing what is a concise and enlightening presentation of the mainsteam view. Some eminent people (IIRC like Frank Wilczek and John Wheeler) have written about the desirability of getting rid of the mass concept and doing "physics without mass". Inertia has problems as a quantity and some of the other quantities have been seen as maybe more basic. Despite its problems the mass concept is, as you say, deeply ingrained in the culture of physics. I can only concur with your post, and can think of nothing to add.
    Last edited: Jul 23, 2003
  13. Jul 23, 2003 #12


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    We have a Tower of Babel problem. I urge you to use words the way they do in mainstream physics. Use conventional meanings! (Even if you want to express non-standard ideas.)

    Otherwise--with everybody using words with his own or with unstable popular meanings---the discussion doesnt get anywhere.

    E = mc2 is not true if the object is moving. Ask your mentor about this----e.g. Tom has a special relativity textbook online that represents the mainstream view very clearly
    E = mc2 is true only in the rest frame.

    We have trolls come here with fringe views of what "mass" means that say different things but this is destructive because
    it undermines the conventional common language.

    Ring gave an absolutely fundamental equation.

    m2 = E2 - p2

    this equation is bedrock in relativity. it indicates maybe better than any other single equation what a working physicist means when he or she says mass. One thing that this equation means is that E = m only if the momentum (p) is zero. If the thing is moving, it has some momentum, and so E cannot be equal to m.

    things are cleaner if you adjust the units so c = 1, which is why c is not always written in the equation, but if you want to use metric units and put the c back into the equation then it is

    m2c4 = E2 - p2c2

    again you can see that E = mc2 only in the case where the momentum is zero.

    Dont ask me to justify the use of language in contemporary physics! My only point is that we ought to conform with the professional majority use of words (even if we want to disagree with them) because not having a common language is too confusing.

    In the professional majority usage, the mass of an object is its inertia at rest-----a ratio of force per unit acceleration: the force applied divided by the units of acceleration produced. Ultimately that is the way the mass of anything is determined---the fundamental measurement on which the concept is based.

    Using this idea of the masss m being inertia-at-rest, it then turns out in special relativity that

    m2 = E2 - p2

    Be wary of adding adjectives like "effective" or "relativistic" to the word mass. That tends to be confusing and makes the Tower of Babel problem worse. For a working physicist a photon has zero mass.

    It is not necessary for a photon to have mass in order for it to follow the geodesic (straightest possible) curves in spacetime. Gravity is geometry. Light goes in the straightest paths it can and those paths are curved because space itself is curved. What does a photon need mass for? And in fact it has no mass.
  14. Jul 23, 2003 #13


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    Yes. This is an easy answer. First off please note that the issue of how to define mass is the subject of debate right now. There are two definitions

    (1) the M in p = Mv. This implies that mass is a function of speed. For particles which travel at less that the speed of light m(v) = m_o/sqrt[1 - (v/c)^2]. m_o = m(0) is the rest mass, i.e. the mass of the particle when it is at rest in the observers frame of referance.

    some people call m relativistic mass. In this case - for a free particle of energy E then m = E/c^2. That holds for photons as well. But for non-free particles note that E does not represent the total energy but the total energy less the potential energy

    (2) The quantity M in M^2c^4 = E^2 - (pc)^2

    If M is not zero then M = m(0). M is an intrinsic property of matter

    Def #1 implies that a photon has mass
    Def #2 implies that a photon has no mass

    One puts a subscript on the m to denote that its the rest mass or what I like to call the proper mass

    And anyone who is familiar with this debate is passionate about their opinion. marcus is one of those who is strongly bound to Def 2. From his comments "mainstream physics. Use conventional meanings!" he has always given me the impression that he prefers this definition as more of going with the flow and not for any reason other that which I can recall at this time. But he has the wrong idea on this. This is not what mainstream physicists do and it's not the convention. Such notions give the false impression that most physicists use the term as he suggests. And that's not what is in the literature and it's not something that relativistist agree on. And to me its an extremely bad idea to go with the flow simply to go with the flow - especially if it's a weak position to hold on theoretical/philosophical grounds.

    The most outspoken people are the most noisiest people and those are particle physicists. And it was a particle physicist who got this ball rolling about this debate which is very hotly debated in the literature. The main task for the particle physicist is to understand the fundamental properties of matter at it's most elementary level and that means to study it's intrinsic properties. Rest mass is an intrinsic property and it's for that reason that a particle physicist thinks only on those terms.

    Let me clarify that comment: Last night someone mentioned something to me regarding something in relativistic particle dynamics and I started a discussion on it in sci.physics. A relativistic that I know put this example in his new text as a reason why it's not good to think in terms of what some people call "relativistic mass." And I thought it good to mention it since I always like new ideas - especially if they go contrary to what I might have thought. So I started to derive this relation which is a rather messy one. Not a trivial problem that I can see (or my brain is still asleep). Now in working with this problem its a pain in the ass to write things with a subscript and when doing the math you want what is easiest to use when doing the nitty gritty pencil to paper grinding. So when I do that I rarely think in terms of relativistic mass. I don't need to. The particle physics lends itself to def #2 to a certain extent. For example, some of the vectors used in relativity are 4-vectors. P = (E/c,p) is an example. This is the energy-momentum 4-vector. The magnitude of this vector is the rest mass. So people like to define mass as the value of the magniture of the 4-vector. But that can lead to terribly bogus ideas. One bogus idea that I've seen lately is one person in sc.physics whoi tried to answer a tricky question that I posed to show how one can get into a mess. And sure enough that person not only made the mistake but was unable to understand what the mistake was! When you have a system of particles which are subjected to forces then you can't add the 4-momentum of two particles and get a meaningful result - and most people don't understand that - probably because this rarely happens - i.e. the 4-vectors don't find applications in that area

    However when I'm working with gravity and continuous matter instead of particles then i think strictly in terms of m = E/c^2. In such cases one works with the stress-energy tensor. But due to Einstein than tensor can also be called the mass-momentum tensor. In defining this tensor one relies on def #1. There's no way around it. People seem to constantly miss this basic fact.

    There's a huge amount more than the above but I'm getting tired from all this typing.

  15. Jul 23, 2003 #14

    Guys, thanks, very interesting, I was unware of this semantics issue surrounding the word 'mass', I am an not a physicists , just someone with an interest due to my work in financial markets...don't ask! ( yeah, i have a physics degree 15 years ago, but the details get forgetten!!!).
    I found these article very useful on this semantics discussion:
    http://math.ucr.edu/home/baez/physics/Relativity/SR/mass.html And

    Here is a relavent quote from the links
    "There is sometimes confusion surrounding the subject of mass in relativity. This is because there are two separate uses of the term. Sometimes people say "mass" when they mean "relativistic mass", mr but at other times they say "mass" when they mean "invariant mass", m0. These two meanings are not the same. The invariant mass of a particle is independent of its velocity v, whereas relativistic mass increases with velocity and tends to infinity as the velocity approaches the speed of light c. They can be defined as follows:
    mr = E/c2
    m0 = sqrt(E2/c4 - p2/c2)
    where E is energy, p is momentum and c is the speed of light in a vacuum. The velocity dependent relation between the two is
    mr = m0 /sqrt(1 - v2/c2)
    Of the two, the definition of invariant mass is much preferred over the definition of relativistic mass. These days, when physicists talk about mass in their research, they always mean invariant mass. The symbol m for invariant mass is used without the subscript 0. Although the idea of relativistic mass is not wrong, it often leads to confusion, and is less useful in advanced applications such as quantum field theory and general relativity. Using the word "mass" unqualified to mean relativistic mass is wrong because the word on its own will usually be taken to mean invariant mass. For example, when physicists quote a value for "the mass of the electron" they mean its invariant mass.
    At zero speed, the relativistic mass is equal to the invariant mass. The invariant mass is therefore often called the "rest mass". This latter terminology reflects the fact that historically it was relativistic mass which was often regarded as the correct concept of mass in the early years of relativity. In 1905 Einstein wrote a paper entitled Does the inertia of a body depend upon its energy content?, to which his answer was "yes". The first record of the relationship of mass and energy explicitly in the form E = mc2 was written by Einstein in a review of relativity in 1907. If this formula is taken to include kinetic energy, then it is only valid for relativistic mass, but it can also be taken as valid in the rest frame for invariant mass. Einstein's conventions and interpretations were sometimes ambivalent and varied a little over the years; however an examination of his papers and books on relativity shows that he almost never used relativistic mass himself. Whenever the symbol m for mass appears in his equations it is always invariant mass. He did not introduce the notion that the mass of a body increases with velocity--just that it increases with energy content. The equation E = mc2 was only meant to be applied in the rest frame of the particle. Perhaps Einstein's only definite reference to mass increasing with kinetic energy is in his "autobiographical notes".

    My original question needs to be refined into a set of more detailed questions, and i'll be as semantically clear as i can!:
    1. What causes invariant mass at an elemental level ?
    Inertia - yes, but that is too high a level of abstraction i.e. What is inertia?

    I researched this and said the answer i found was inertia( and hence invariant mass) is the result of the Higgs fields, i have some links in previous posts, and here's an excellent article in scientific america:
    "One major ingredient in this model is a hypothetical, ubiquitous quantum field that is supposed to be responsible for giving particles their masses (this field would answer the basic question of why particles have the masses they do--or indeed, why they have any mass at all). This field is called the Higgs field. As a consequence of wave-particle duality, all quantum fields have a fundamental particle associated with them. The particle associated with the Higgs field is called the Higgs boson. "

    2. Can invariant mass be converted to energy, and energy to invariant mass?
    Yes, invariant mass to energy occurs in fission/fusion.
    Energy to invariant mass occurs in nature and forced particule accelerator experiments.

    I'm sure if i have got something incorrect someone will tell me! thanks.

    BUT - This still leaves me where i started though, and let me rephrase the question:
    What are Photons 'made of', what are 'quarks made of'. Take all the lowest level elemental particles - either 'real' or 'virtual', and ask 'what are they composed of'. They must be made of something, what is it?

    I have trouble accepting the idea that one can ever stop 'sub dividing and decomposing', since you can chop a quark in half etc or if you do that, do you get two smaller quarks?

    Whilst science cannot answer why question, we surely should be able to answer the 'what questions' as in, what is a fundamental particle made of. This gets trickier of course since really the both waves and particles - so that needs explaining too. I've read a little of string theory - but all physics seems to do is move the issue from one elemental element to another - the question remains, what these are made of too.

    My specific interest is to know if fractals behaviour shows up at an elemental level, since it shows up at higher levels everywhere in nature, but that's getting ahead of myself here. Completely unscientifically!, i propose that the elemental level must exhibit fractal properties.

    The ultimate question i'm research is the issue of determinism versus chance - i'd hoped that elemental physics would reveal some answers. I'm aware of the uncertainty principle, but thats a measurement problem - it doesn't answer whether 'randomness' is a built in feature of our universe or just a built in feature of our ability to measure it.

    Has the determinism debate been settled? Hawkings implies it has, saying that were close to having all the elemental elements etc But, then fractal behaviour must be explainable, and all other natural observable phenomena that appears to exhibit an 'element of chance' - in essense, randomness would not exists, there would be cause for all things - and of course, humans themselves would just be predicable with no free will.

    Any useful links on this appreciated, i'm sure this discussion exists somewhere i can look at.
  16. Jul 23, 2003 #15


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    I don't particularly like that page. I first came across it in the late 90's. I found it highly suspiscous. So I hit the library and looked in my favorite physics journal - "The American Journal of Physics" (AJP) and saw the use of mass just as it always had been - and even more so. Looking in other journals the usage was highly different depending on the particular field. I have several of the newer relativity texts and that use and and a few that even denfend it. I don't think that page you listed referanced much of the debate. I think they listed only one side of the debate.

    There was a paper in AJP called

    "In defense of relativistic mass," by T. R. Sandin, Am. J. Phys. 59, 1032 (1991)

    It was written as a response to that article the link you gave referanced - and the fact that it doesn't list it even more tells me that it's biased. I wrote to the person who maintains it and discussed it with him. He asked me to take crack at updating it. I'm in the process of finishing and article on this subject and have decided to wait until I was finished before I submitted any suggestions.

    However if you'd like to read that article by Sandin from the AJP then let me know. I can scan it in and e-mail it to you. Just send e an e-mail at pmb46@hotmail.com and I'll send it.

    That's one of the things that's subject to debate. Inertia os that property of matter which resists a change in momentum or that can impart momentum to matter. The larger the inertia the harder it is to change the momentum.

    The definition of inertial mass can be defined as the ratio of momentum to velocity. [E.g. see "Special Relativity," A.P. French, MIT Press, page 16]

    That's the mechanism for inertia - not the definition. That's like asking how a car 'works' as opposed to what a car 'is.'

  17. Jul 23, 2003 #16
    Nope. Fusion/fision isn't about converting mass to energy its about converting potential energy to kinetic and electromagnetic energy. In other words it's about changing one type of energy into another. The remnant of the nucleus has less internal energy and as a result of this decrease in internal energy it has less mass, not vice versa. However the mass of the entire system does not change.

    A vault that contains nuclear weapon will weigh the same both before and after the explosion.
  18. Jul 23, 2003 #17
    thanks but for the offer, but the semantics of the mass are clear enough for my limited need to know.

    I'm not sure where you believed i asked for a definition ? I clearly asked 'what causes', what is the mechanism, just like your car analogy, and that was the answer i gave - Higgs field/Boson

    Any response to the other parts of my question? i.e. what is elemental matter made of? and the issue of ramdomness/determinism?
  19. Jul 23, 2003 #18


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    There is a very specific meaning to the phrase "mass to energy conversion" and that meaning has to do with the form of the energy and the sum of the masses which is left overy.

  20. Jul 23, 2003 #19


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    You asked

    "If mass and energy are interchangeable - how do we know when to call energy just 'energy' and other times call it 'mass'?
    So why is a photon not subject to the same effect? i.e. what is 'intrinsic mass' that is different to 'energy effective mass' of say a photon

    In summary - what exactly is 'mass' - all matter is simply 'energy', so i cannot fathom it. IS is that energy in a particular arrangement is called mass? if so, what arrangement? and why?

    That was what I was responding to. And to answer that question it means to properly define what mass is. Then one can easily procedd from that. If you ask mw "what is mass" then the answer will be in the form of a description and not what it's made of or something like that.

    Perhaps I didn't understand your question properly.

    There is an online portion of a text called "Gravitation and Inertia" and one of the authors is John Wheeler whose a well known special/general relativity expert.

    Here's the link


    Hope that helps

  21. Jul 23, 2003 #20
    I don't understand what it is you're saying. Mass is a property of a system and in the center of momentum frame it's invariant--there's no conversion involved. Are you talking about the local mass deficit?
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