# How does energy differ from mass?

fractal
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 let's 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?

Tyger
Definitions

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.

fractal
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' - let's 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, let's for the sake of this exploration, say there are 2 axiomatic units of matter - let's 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.
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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.

fractal

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:
http://physics.bu.edu/ATLAS/guide/higgs.html [Broken]
Also:
http://www.pparc.ac.uk/Nw/Md/Artcl/where_does_mass_come_from.asp

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'

http://www.cox-internet.com/hermital/holoprt2.htm

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.

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Tyger
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.

Dal
Originally posted by fractal
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' - let's 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, let's for the sake of this exploration, say there are 2 axiomatic units of matter - let's 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.
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 black holes? Is it because of the curvature in space time or else?
Please explain in an easy term. hehe

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 black holes? Is it because of the curvature in space time or else?
Please explain in an easy term. hehe

Bonjour,

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.

fractal
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 black holes? Is it because of the curvature in space time or else?
Please explain in an easy term. hehe
-------------------------------------------------------

Dal,
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)

NEWTONS LAW OF GRAVITY:
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..."

"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.

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Dal
Thanks fractal. That explained a lot and the link you've given is very useful.

Ring
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.

Gold Member
Dearly Missed
Originally posted by Ring
...

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.

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.

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Gold Member
Dearly Missed
Originally posted by fractal
I wonder if anyone here can help me with this, i am refreshing my physics knowledge ...

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

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 doesn't 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.

Originally posted by fractal
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 let's 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?

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.

Pete

fractal
marcus/pete,

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
http://math.ucr.edu/home/baez/physics/Relativity/SR/light_mass.html [Broken]

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 that's 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? Hawking 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.

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Originally posted by fractal
marcus/pete,

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
http://math.ucr.edu/home/baez/physics/Relativity/SR/light_mass.html [Broken]

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.

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?

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]

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 ...

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

Pete

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Ring
Originally posted by fractal
marcus/pete,

2. Can invariant mass be converted to energy, and energy to invariant mass?

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.

fractal
Pete,
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?

Originally posted by Ring
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.

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.

Pete

Originally posted by fractal
Pete,
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 ?

"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.

http://pup.princeton.edu/sample_chapters/ciufolini/chapter3.pdf [Broken]

Hope that helps

Pete

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Ring
Originally posted by pmb
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.

Pete

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?

fractal
I guess we are falling victim to word semantics here. I have at least learned some things here - let's try and focus on this one issue of 'mass and energy conversion/equivalence'.

I find a lot of conflicting views:

Can invariant rest mass be converted into photons ( which have 0 invariant mass.) i.e. can 'mass' be converted to 'energy' which has no mass such as photons?

From what i read it can, though others here say it can't. This says E=mc2 literally says 'a bunch of matter' can be converted into photons ( and other massless particles) i.e. mass is converted to kinetic energy. Of course, we can take the view that 'no mass is lost' because these photons with velocity have equivalent relativistic mass - so were back to the semantic again, let's not do that!

I'm aware that in nuclear process, it is the binding energy of the atom that is the 'lost mass' - so, in that instance we can argue it wasnt' invariant mass conversion. But, the links below give plenty of example of rest /invariant mass conversion to energy i.e. If you weighed the 'stuff' it would weight less due to conversion of 'mass' to energy (photons) - Here are some links that say this:
http://musr.physics.ubc.ca/~jess/p200/emc2/node9.html
http://www.phys.virginia.edu/CLASSES/252/mass_and_energy.html
http://www.mathpages.com/home/albro/albro8.htm [Broken]
http://www.britannica.com/eb/print?eu=117370 [Broken]
http://library.thinkquest.org/17940/texts/binding_energy/binding_energy.html
http://fusedweb.pppl.gov/CPEP/Chart_Pages/3.HowFusionWorks.html [Broken]

I await enlightment! is it true that for example "an electron (which has mass) has been observed to collide with an anti-electron (positron) to produce only a high-energy photon (which has only energy, no mass). "

True or false - yeah or neah ?

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Originally posted by Ring
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?

Consider an electron and a positron. In the absence of a potential energy the total energy E_t is the kinetic energies plus the rest energies. Let the kinetic energy be T. Then

E_t = T_1 + E_2 + T_2 + E_2 = T_1 + T_2 + 2m_e*c^2

The sum of the rest masses is 2m_e

where m_e is the proper mass of the positron (and the electron)

If the electron/postitron pair meet and annihilate and then there will be two or three photons, the energy of which we can treat like it being kinetic energy. The total energy remains constant.

E_t = T(photons)

where T(photons) is the sum of the energies of the photons. I.e. the sum of the kinetic energies. The sum of the proper masses is now zero.

That is what is meant by mass being converted into energy - A change in form with a change in the sum of the proper masses.

Pete

Bonjour Fractal,

Ring
Originally posted by pmb

where T(photons) is the sum of the energies of the photons. I.e. the sum of the kinetic energies. The sum of the proper masses is now zero.

That is what is meant by mass being converted into energy - A change in form with a change in the sum of the proper masses.

Pete

Yes, but the mass of the system isn't the sum of masses of the photons, its m2 = E2 - p2. And in center of momentum frame p = 0 so m = E.

Ring
Originally posted by fractal

Can invariant rest mass be converted into photons

Yes

which have 0 invariant mass. i.e. can 'mass' be converted to 'energy' which has no mass such as photons?

An individual photon has no mass, but a system of photons that has a center of momentum frame has mass equal to m = E. If the system momentum is zero before the interaction it must be zero after the interaction and therefore m = E - 0. Mass cannot be converted to energy.

Gold Member
Dearly Missed
Originally posted by fractal
I guess we are falling victim to word semantics here.

Yeah

Originally posted by fractal

Can invariant rest mass be converted into photons ( which have 0 invariant mass.) i.e. can 'mass' be converted to 'energy' which has no mass such as photons?

Yeah

(but there are some rules that have to be respected, like
the conservation of momentum, not merely of energy)

Originally posted by fractal

I await enlightment! is it true that for example "an electron (which has mass) has been observed to collide with an anti-electron (positron) to produce only a high-energy photon (which has only energy, no mass). "
True or false - yeah or neah ?

suppose an electron and a positron are each going one mile per hour, coming from opposite directions, and they collide

the total momentum is initially zero----their two momentums are in opposite directions and cancel. So if they annihilate each other and produce light (which is one possible result) that light has to have zero momentum

One possibility is two photons each with the same energy and leaving in opposite directions----that way their momentums cancel and make a total of zero.

So the short answer to your question is True, yeah----except that the result could not be a single photon because that would have non-zero momentum

BTW the momentum of a photon (imagine the typical case where it is traveling in vacuum) is a vector with magnitude E/c, pointed in the direction the thing is going.

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Originally posted by Ring
Yes, but the mass of the system isn't the sum of masses of the photons, its m2 = E2 - p2. And in center of momentum frame p = 0 so m = E.

That depends on what one calls the mass of the system. That term has different meanings for different people. And the term "mass of the system" as you're using it has to be used carefully. It's only meaningful in cases such as this when there are no "external" forces acting on them (i.e. no forces external to the system). For example you can't meaningfull define a mass of a system of electrons moving in a magnetic field - at least not in the way you've used it. Or if you do then it's tricky.

However I was not referring to the mass of the system. I was describing what it means when it is said that "mass is converted into energy". And it's almost universally agreed upon that it means that the sum of the masses of the constituent particles changes.

You're referring to something else - the conservation of mass. It's a subtle point. It's the form of the composition of the system that undergoes conversion. And this goes to the notion that rest mass is a form of energy

For example: Consider the total energy of a harmonic oscillator. Both the potential and kinetic energy goes through harmonic oscillation. The kinetic energy converts to potential engery and the potential energy converts to potential energy etc. The total energy is the sum and that's what remains constant. This is shown mathematically as follows

E = T + V

So there is a changing going on where the energy shuttles back and forth, i.e. T <===> V. Potential energy is converted to kinetic energy and kinetic energy is converted to potential energy.

Now take another look at my previous post

E = "Kinetic Energy" + "Rest Mass Energy" = T_1 + T_2 + 2m_e.

Suppose that when the particles annihilate you get two photons of energy T_3 and T_4. Then let

T_i = T_1 + T_2
T_f = T_3 + T_4
E_o = "rest mass of electron" + "rest mass of positron" = 2m_e

E = T_i + E_o = T_f

This is like that shuttling of energy I described above but now

T <===> E_o

Pete

Originally posted by Ring
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.

Let's keep in mind that "invariant" means "does not change under a coordinate transformation" it does not mean "remains constant in time."

If a body's proper mass is chaning with time then the proper mass will still be invariant - it just won't be constant and therefore not conserved.

And also note that "invariant" does not mean "does not depend on the observer" either. It's quite reasonable to define an invariant energy for a photon. One simply takes the scalar product of the observers 4-velocity and the photon's 4-momentum.

Pete

Gold Member
Dearly Missed
Oops, I seem to have contradicted what Ring said!
How did that happen?
I guess Ring was speaking very carefully and is probably right
when he says mass can't be converted into energy
but I was speaking more loosely and casually.

Well let me pull up my socks and try again.

The root meaning of mass is inertia of an object at rest. this is
the primitive measurement that determines and defines mass.

inertia at rest of an object or a collection of several objects is
just too physically basic not to have a name for and "mass"
is the name given to it.

the mass of an object does indicate something else too, namely how much energy nature has invested in the existence of the object----in its sheer being as it sits there at rest in front of you.
If you can annihilate the object, you cash in the energy invested in its existence.

but strictly speaking that invested energy tied up in the things existence---that "rest energy" or "energy of being" if you want to call it that---isn't what the mass IS.

the mass is just the things inertia---a ratio of force to acceleration, the force required per unit of acceleration produced.
the mass only INDICATES how much rest energy is tied up in the thing's being.

what I am trying to do is take seriously how mass is measured. we don't measure mass by annihilating things with antimatter and measuring the calories released and dividing by two. We measure masses by determining inertia at rest----so that is what mass is at the most primitive level.

It only indicates an amount of energy that might be available---but I should not say (if I want to keep my socks pulled up) that the inertia is "converted" into that amount of energy.

Aieee! Just listen to Ring and try to talk like him and I will try not to say anything. Also Tom, as a grad student/postdoc, if he drops in, is an example of good speech habits. People need to use basic words consistently or endless confusion ensues.

Originally posted by marcus
inertia at rest of an object or a collection of several objects is
just too physically basic not to have a name for and "mass"
is the name given to it.

Unless you're discussing this with a physicist at Fermilab

http://www.fnal.gov/pub/inquiring/questions/accel_obj.html
http://www.fnal.gov/pub/inquiring/questions/angelo.html
http://www.fnal.gov/pub/inquiring/more/light/light_page16.html

what I am trying to do is take seriously how mass is measured. we don't measure mass by annihilating things with antimatter and measuring the calories released and dividing by two. We measure masses by determining inertia at rest----so that is what mass is at the most primitive level.

Not in particle physics. In particle accelerators the mass is measured by observing it's motion in a magnetic field. Besides - How would you measure the proper mass of light to have a zero value?

Pmb

Ring
Originally posted by pmb

However I was not referring to the mass of the system. I was describing what it means when it is said that "mass is converted into energy". And it's almost universally agreed upon that it means that the sum of the masses of the constituent particles changes.

I agree that many texts, for the sake of simplicity, use this definition. But according to the most universally accepted definition of mass m2= E2 - p2this is patently untrue. What this entails is the redefinition of the system in the middle of the stream. If you're consistant in defining the system then the mass does not change and it cannot be converted to energy.

You're referring to something else - the conservation of mass. It's a subtle point. It's the form of the composition of the system that undergoes conversion. And this goes to the notion that rest mass is a form of energy

I must disagree. Mass and energy are not things they're properties of a system. If you are consistant in defining your system and include all the products of the interacting particles then the mass and energy remain the same. If you don't do this then, as I said, your changing horses in the middle of the stream.

Originally posted by Ring
I agree that many texts, for the sake of simplicity, use this definition.
They don't do it for the sake of simplicity. They do it because that's what they think is the best way to explain/describe it. Entire papers get published just on that very notion.

But according to the most universally accepted definition of mass m ....

You mean the way it's used at Fermilab? See
http://www.fnal.gov/pub/inquiring/q.../accel_obj.html [Broken]
http://www.fnal.gov/pub/inquiring/questions/angelo.html
http://www.fnal.gov/pub/inquiring/m...ght_page16.html [Broken]

Can you tell me how you got the impression that what you use is the most universally accepted definition?

What this entails is the redefinition of the system in the middle of the stream. If you're consistant in defining the system then the mass does not change and it cannot be converted to energy.

I disagree. It's not even a generally meaningful definition.

I must disagree. Mass and energy are not things they're properties of a system.
Did I ever say that they were things? No. I did not. I said that the form changed. I explained all that in detail above. It basically means that the composition of a system changes. See "Spacetime Physics - Second Edition," Taylor and Wheeler, page 248-249. In particular - see the section "Use and abuse of the concept of mass" - see page 249

"Thus part of the mass of the *constituents* has been converted to energy; but the mass of the *system* has not changed."

As I said - that is the meaning of "covert mass to energy"

And I wouldn't say that Taylor and Wheeler are sloppy or that they're too lazy to be 100% precise (though I don't always agree with them - they are precise!)

Pete

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I recently posted in another forum quotation from three recent books by leading physicist each of which clearly stated that "we do not know what are mass, charge or any of the other peculiar properties of particles".
My own view is on my website and is, as far as I am aware, the only proposal that explains the origin of mass and links force, mass and radius. (According to the experts there has been no explanation for the peculiar mass/radius ratios of atomic elements).
There surely is little point in trying to explain the relationship between energy and mass unless you first define what causes mass to exist.

Originally posted by marcus
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.

On second read it seems, from our past conversations, that you think I'm one of these trolls? If so then you've misunderstood. When I see something I believe is incorrect I speak up - the fact that you repeat it all the time means I speak up all that time. That's not being a troll - that means I have a different opinion than you do and I state what I think.

Comments like you post give the false impression that everyone who is a physicists does not use the term "mass" to refer to light. Well I'm a physicist and I do so there's one data point. But it was Einstein who proved this to be true - it has to be true for the "center of mass theorem" to hold true. That was the purpose of his 1906 paper in fact.

And your comment "fringe view" is quite wrong if you're referring to relativistic mass. This is something that can be found in most relativity textbooks in one form or another. MTW is a good example.

Let me give you a better example: Wolfgang Rindler is one of the more prominent authorities in relativity today. He published another book in 2001 called

"Relativity: Special, General and Cosmological," Rindler, Oxford Univ., Press, (2001)

Rindler defines mass, for a particle with a non-zero rest mass m_o, as m = m_o/sqrt[1-(v/c)^2]. He addresses photons on page 120
According to Einstein, a photon of frequency f has energy hf, and thus (as he came to realisze several years later) a finite mass hf/c^2 and a finite momentum hf/c.

The same is true for

"Introducing Einstein’s Relativity," D’Inverno, Oxford Univ. Press, (1992)

"Basic Relativity," Mould, Springer Verlag, (1994)

Let me ask you this - would you find it surprising that the term "mass density of radiation" is used throughout cosmology? Saying that "light has no mass" without clarifying can be misleading. Especially if you don't want to give the person you're talking to a distorted view of what actually is. For example: A particle physicists might say "light has no mass" but a cosmologist will speak of the term "mass density of radiation."

Would it surprise you to find cosmologists referring to the "mass density of radiation"? Try searching the internet of that phrase.

And as Wheeler himself says in
pup.princeton.edu/sample_chapters/ciufolini/chapter3.pdf

its the active gravitational mass that generates a gravitational field - and that is not rest mass.

Then there are texts like "Classical Electrodynamics," which has a problem - find the center of mass for an EM field (second ed - page 617)

Pete

As an amateur I am aware that a theoretical mass for the photon was reported in Scientific American in the early 80's.
I am also aware that almost every book on particle physics, written for the layman; contains a statement to the effect that there is no answer to the question "what is mass or charge?"
The London 'Daily Telegraph' for Sat. 26 July 2003 carries a report on yet another conference to decide whether the impasse in Relativity (and by implication astro-physics) can be resolved by the introduction of Anti-gravity or Vacuum.
It seems that your confidence in current theory is not shared by those at the highest level (which does not mean that they are right, but merely that they dissagree).
My own support for a vacuum theory is up for discussion on a separate forum.
Surely it is time to realize that there is room for considerable improvement in our understanding of how things work and firm opinions should await solutions to current problems.