pmb

Yes, it is. Photons are a subject of quantum mechanics, not relativity

Sorry about getting back to you on this. Yes. When photons are used in relativity the quantum effects are ignored. The photon can be assigned a position, velocity and momentum, simultaneously. In relativity a photon moves on a classical trajectory. In essense in SR and GR the quantum effects are assumed to be insignificant for the purposes which it is used. When QED is brought in then one is no longer talking about classical mechanics.

 

A relavent point was suggested by the late Phillip Morrison in Taylor and Wheeler's relavent text Exploring Black Holes. In the front matter it says

Philip Morrison made several suggestions and convinced us not to invoke that weird quantum particle, the photon, in a treatment

of the classical theory of relativity (except in some exercises).

Taylor and I had several conversations about this for the above reasons, i.e. people seem to get confused when you use a quantum particle in a classical theory. That's why I prefer the term Luxon so that there will be no confusion. Nobody tries to analyze the quantum mechanics of a luxon. lol! In fact just because a particle is a luxon (a classical particle) it doesn't mean that its a photon. A photon has a spin associated with it. A luxon, again, a classical particle, need not have a spin.

 

Pete

And you can find pretty much an equal number of corrections to those statements, saying that they exhibit that behavior, not that they are these things.

This is the most basic, and thus first, thing one learns when studying quantum theory. Nobody is more correct on this point than Feynman. From his lectures V-III page 1-1

... Things on a very small scale behave like nothing that you have any direct experience about. They do not behave like waves, they do not behave like particles, they do not behave like clouds, or billiar balls, or weights on springs, or anything that you have ever seen.

Newton thoughtthat light was made up of particles, but then discovered that it behaves like a wave. Later, however (in the beginning of the twentieth century), it was found that light did indeed sometimes behaves like a particle. Historically, the electron, for example, was thought to behave like a particle, and then it was found that in many repects it behaved like a wave. So it really behaves like neither. Now we have given up. We say: "It behaves like neither."

Never try to say it better then this I say.

Nope. granpa is correct. The speed of light is locally equal to c. Using the words global and general relativity in the same sentence doesn't make sense.

The speed of light is locally c. But now consider Irwin Shapiro' work on radar ranging onf the inner plantes. The EM waves sent out from Earth and bounced off a planet or two (or whatever. I forgot the details over the years.) There was a time delay due to the path the EM wave took through the gravitational field thus making the light slow down. This is explained by saying that the speed of light varies as the light moves through a gravitational field. It is this notion in which it is said that the speed of light varies. To be exact, it's the coordinate speed of light that varies with gravity. That's the same sense in which Einstein proved that the speed of light varies in gravitational field in his 1911 paper.

 

See the derivation here - http://home.comcast.net/~peter.m.brown/gr/c_in_gfield.htm

 

Eq. (5) c' = (1 + Phi/c²)c

 

is the result that Einstein obtained in that paper. Similar derivations can be found in Ohanians GR text as mentioned above.

This sound contradictory. The specific aether theory M-M were trying to confirm is falsifiable and falsified; it made a prediction and the experiment showed that it is spectacularly wrong. The aether as a general concept is not falsifiable because the theories keeps changing, ad-hoc, to prevent falsification.

Please take a closer read of my last post

 

The ether theory is not falsifiable. Falsification means that its possible for an observation to happen which proves the theory wrong. That's not the case with the ether theory. No observation can happen which contadicts the ether theory. swansont was right on this. Early experiments showed that the value of the speed of light was independant of any frame of reference. That proves that the original theory is wrong. People have taken that theory and bastardized it into something that is not falsifiable.

Notice where I used the terms "ether theory" at the begining and the "original theory" later. I said that people have taken the original theory and bastardized it to something that is not falsifiable. I never saw anybody use different names for the two theories so I called the first one, the real one, the "original theory" and thus the bastardized one the current one, which is not falsifiable.

Has aether been disproved?

 

Were Michelson and Morley even looking in the right direction?

 

peace

ron

 

P.S.

kind and well reasoned responses are always greatly appreciated

insults not so much

No. This is a good lesson in the philosophy of physics; you can't prove something exists which doesn't exist.

 

Yes, yes you can. It's one of the basic principles of science: falsification. It relies on a logical tool called Modus Tollens.

The ether theory is not falsifiable. Falsification means that its possible for an observation to happen which proves the theory wrong. That's not the case with the ether theory. No observation can happen which contadicts the ether theory. swansont was right on this. Early experiments showed that the value of the speed of light was independant of any frame of reference. That proves that the original theory is wrong. People have taken that theory and bastardized it into something that is not falsifiable.

bolded mine

wrong excuse(*) (**).

pmb just reached the bottom of the abyss of my unconsideration.

Don't worry you are not alone there.

I don't understand. What do you mean by that?

 

I had deleted a lot of the things in your post. I was having a hard time restraining my irritation at juan's poor argument skills, i.e. all claims, no valid proofs (invalid proofs, sure). But I didn't want to let my anger get in my way and I don't want to give juan more attention that he deserves.

 

No. Bolded part does not look to me as an error of translation from paper to text. And no one goes from Eq(3) to (4) when there is an error in Eq(3).

Well, that is actually the case. I still have the papers where I derived it and the paper contains the right derivations and equations. All you need do is ask whether I made a translation or not and I'll be glad to tell you. Only I have the ability to answer that question. I have no need to lie, that's for sure.

Yes, it is. Photons are a subject of quantum mechanics, ..

This is getting carried away. One last time and then let it go, okay? I mean we have to stop somewhere and I hate debating about definitions. Its something a teenager would do.

 

When the photon is used in relativity its treated as a classical particle. It's not treated as a quantum object. This also means it has a classical trajectory and the Heisenberg Undertainty Relation is not used in non-relativistic QM. In that context its just another luxon (a particle that travels at v = c). And as I've already explained many times, in relativity its ofen useful to think of light as having mass. I won't repeat what I've already provided.

 

So let's drop the debate/ We all know what the other guy thinks. There is absolutley no reason to continue this debate on a definition.

 

@pmb

 

Bolded mine.

"The proper mass m₀ of a particle is independant of speed." except for m₀= zero.

The velocity never changes so we can't speak of the photons mass at differrent speeds. So the relationship m = gm₀ doesn't apply to photons so we can't speak of independant of speed

 

-------------

edit

from post #3

you wrote

 

then

 

Are you sure?

Isn't it

 

g=E/mc2 ?

------------------------

Correct! Thank you very much. I must have made a mistake translating from paper to text.

 

You substitution m --> m = m0 + dm changes nothing because is m --> m. Your momentum p=m gamma v is not the momentum of an electron in an electromagnetic field because its momentum receives a correction due to interaction with the field. blah blah blah...

Wrong. Read Classical Charged Particles - Third Edition by Fritz Rohrlich, World Scientific Pub. Co. 2006.

 

I won't be reading your posts again unless circumstances require it and I don't see that happening. You just have too many errors. Ever time you attempt to correct me you add an error or two in response. I don't have the time or the will to keep doing that. It's just plain silly. And remember, it makes absolutely no difference whether you think its an error or not (since you ususally reject the corretions given you). With regards to me responding to you, it only matters whether I think its an error or not. Good bye juan. I hope you take an open mind and read that book. It will do you a lot of good. It will teach you what Poincare mass is (See Feynman lectures to learn the meaning of that term).

The speed of light is constant in General relativity in the same way as the speed of a racing car can be constant on a circular race course and this is the result of the light following null geodesics (the path at right angles to null vectors in a 4D manifold).

I disagree. The speed of light in a uniformgravitational field was calculated by Einstein back in 1911. He got the result in Eq. (5) where I calculate the speed of light in such a field

http://home.comcast.net/~peter.m.brown/gr/c_in_gfield.htm

 

A modern textbook does the same thing. E.g see Gravitation and Spacetime - Second Edition by Ohanian and Ruffini page 197 Eq (47).

 

Baez doesn't make a lot of sense to me. The comment

"If general relativity is correct, then the constancy of the speed of light in inertial frames is a tautology from the geometry of spacetime.

Makes no sense. Why is it a tautology. He doesn't say as far as I can see. Of course he does bury it in math so I might have missed it. It seems to me that he says one thing, i.e. In such a frame, the speed of light can differ from c, basically because of the effect of gravity (spacetime curvature) on clocks and rulers. which is 100% right. He's only talking about the local speed of light then he's being confusing since the variation in the speed of light comes from gravty, which he omits when he says that the speed of light is constant. His most misleading statement is this

Finally, we come to the conclusion that the speed of light is not only observed to be constant; in the light of well tested theories of physics, it does not even make any sense to say that it varies.

Which is untrue. The Shapiro time delay demonstrates that the speed of light varies with gravitational potential. I see a lot of diversion in his page. That speed of light in a gravitational field iis near trivial to calculate. I do it for both the uniform gravitational field as well as the Schwarzchild spacetime. That can be made very difficult by adding in a lot of differential geometry terminology but there's no real reason for it. Make it simple I say. E.g. instead of saying The essential feature of General Relativity is that the tangent space to any point in spacetime is a 4 dimensional Minkowski Space instead say At every point in spacetime there is a locally inertial frame of reference.

 

Let's recall that a beam of light moving towards the event horizon of a black hole slows down as it gets to the horizon. If it could get there in a finite amount of time then it would stop on the horizon.

standard model does not view photons and other force carriers as matter. Matter is stuff that has mass and occupies space.

I'm not interested in the Standard Model. The standard model is not the owner of the soul of the photon. If one were to claim that matter is that which is stuff that had mass and occupies space then that depends on how the term mass is defined. To that end we have already seen how experts in the field of SR/GR (not just people who apply the field to get their work done) decide to define the term mass. There are different views, contrary to what people claim. As I've explained before this list is a list of sr/gr texts which define mass such that photons have mass

 

Introducing Einstein's Relativity by Ray D'Inverno, Clarendon Press

Basic Relativity by Richard A. Mould, Springer

Relativity: Special, General and Cosmological by Wolfgang Rindler, Oxford University Press

 

The exact quotes are here - http://home.comcast.net/~peter.m.brown/ref/relativistic_mass/relativistic_mass.htm

 

Alan H. Guth does the same thing and he's no slouch! Take notice how Schutz uses the term "inertial mass" onm [age 94 i is GR text (as well as his "Gravity From the Ground Up" text). Those are just to name a few. There is also that new sr/gr text I got written by Hans Stephani,k published not that long ago in 2004 he uses the term "inertial mass" as Schutz does.

 

juan used a logical fallicy above (which is against the rules) when he asserted that because one web page, the CERN page, uses the term matter such that photons don't have matter is the end all and be all in definitions in the particle physicist community.

 

Since we've all said our piece on this matter thing, let's let it go. We could argue this forever in the hopes to convert the other to their beliefs. If that's the case then so be it. But please leave me out of it.

 

Thanks

the light that burns the brightest burns out the fastest, and we have burn so very bright, so is life on this planet better off without humans?

Yes. This world would be better off without humans.

 

Humans are the only ones protecting earth from the real evil... asteroids and comets that would exterminate most species. It's like the other animals don't even care. They refuse to shoulder their share of the responsibility.

Asteroids etc. are not real evils. They are just falling rocks and a falling rock is not evil. For something to be evil it must have a conscious intention of doing bad. We exist only because an asteroid hit the Earth and cleared the way for the possibility of humans to arrive. Who knows. Perhaps the next asteroid which wipes out humans is one that prepares the way for a better species than ours. One that doesn't kill others of its own species.

 

Also, humans have done nothing to protect ourselves from asteroids etc. All we've done is create a very small group of people who spend time searching the sky for such asteroids. If one was found that will hit the earth in, say, 10 years, we'd be unprepared to do anything about it. There is no real program to slaughter an asteroid which could hit the Earth. Take a look at the Historic record of Near-Earth objects which have impacted the earth from 19018 (Tunguska Event) to 2009 (Indonesia Event)

 

http://en.wikipedia.org/wiki/Near-Earth_asteroid#Near-Earth_asteroids

 

Asteroid hits are chances for the Earth and evolution to start over. The Earth doesn't really get damaged. For the Earth its like its skin getting buffed off.

 

Animals are so fucking stupid. I hate them.

That's a pretty silly notion. Animals aren't stupid. Stupidity is a relative concept and applies only within a species. One can only speak of a relatively dumb dog copared to other dogs of its same species.

 

At Einstein's time most people in the world was less intelligent than Albert Einstein. How do you think he felt being around all the stupid people in the world? Einstein was smarter than 99% of the people in the world at that time (rough estimate)

For zero mass, the object should be at zero mass (tautology): that's the origin, the point A.

By definition, the inertial mass of a particle is defined by

 

m = m₀/sqrt(1 - v²/c²)

 

The derivation is here - http://home.comcast.net/~peter.m.brown/sr/inertial_mass.htm

 

When v = 0, m = m₀, not zero. That's why m₀ is refered to as the particle's proper mass, or rest mass. You have A located at the wrong value of m. You have it a zero whereas the correct position is at m = m₀.

 

But no, science tells us that for no mass, the "thing" (the photon) is closer to point B, actually infinitely far up out of the diagram, upon the C line, up, up,up to the moon.

The relationship m = m₀/sqrt(1 - v²/c²) is derived under the the assumption that the speed of the particle can change and have any value 0 <= v < c. Therefore that derivation cannot be applied to a photon. In that diagram you are plotting inertial mass versus speed. You are not plotting proper mass vs speed.

 

The derivation for the value of the proper mass of a photon is given by Post #3. At the end you simply take the limit in Eq. (15) for v --> c we find m[sub[0[/sub] = 0.

 

But not even, the photon is not infinitely up out of the diagram, the photon is down the C line, at the intersection with the horizontal zero-mass line, at point C.

And certainly not at the zero-zero origin point.

Which makes no sense to me.

Not to worry. You are simply misinterpretting your diagram. You are plotting m vs v, not m₀ vs v. The prope mass m₀ of a particle is independant of speed.

 

I highly recommend that you take a very close read of post #3. It should clear a lot of this up.

 

Note: There are zero errors in post #3.

A friend of mine gave me a copy of the text Relativity: An Introduction to Special and General Relativity by Hans Stephani, Cambridge University Press, 2004. See www.cambridge.org/9780521811859

 

Seems like a very nice text. I wanted to point this one out because it seems like a great text for the student who wants to move on from simple relativity to more advanced relativity as well as general relativity. It too uses relativistic mass instead of proper mass and its relatively new.

I decided not to post that.

But photons are not generally considered matter. D H, juanrga and ajb have all said this.

Taylor and Wheeler suggest not using the term. And I agree with them.

No, it's a very standard definition.

No, it isn't. There is no such official definition. A loose definition used is "something that has mass" and that will depend on how one defines mass. I am confused though. I can't figure out why you'd think that I'd accept a definition without proof. Do my previous posts make you believe that that is something I'm in the habit of doing?

 

Take a look at Taylor & Wheeler's SR text. Turn to page 248

Question: Does mass mean "amount of matter" "

 

Answer: Nature does not offer us any such concept as "amount of matter." History has struck down every proposal to define such a term. Even if we could count the number of atoms or by any other counting method try to evaluate amount of matter, that number would not equal mass. First, mass of a specimen changes with its temperature. Second, atoms tightly bonded in solid -- are less massive -- than the same atoms free. Third, many of natures undergo radioactive decay, with still greater changes in mass. Moreover, around us occasionally, and continually in stars, the number of atoms and number of particles themselves undergo change. How the speak honestly? Mass, yes; "amount of matter," no.

Bolding, mine.

 

 

Electrons are fermions. They are subject to the Pauli exclusion principle. They occupy space. Photons and other force carriers are bosons. They are not subject to the exclusion principle. They do not occupy space.

That's wrong. The fact that a particle follows Pauli exclusion principle doesn't tell you anything about that particle alone. It only addresses what it does it other fermions.

 

It's a well-known fact that both all point particles have zero spatial dimension. positrons are the same way as are all types of neutrinos.

 

!

Moderator Note

juanrga and pmb,

 

You're both getting caught up in a bit of off-topic discussion here, so I am going to split your posts about what mass is into a new thread and ask that you please do not continue derailing this one.

 

 

God bless ya! You can toss the other part out because I have zero interest in the subject. I'm already an expert in the matter.

No, Pete. juan is not dragging this thread off topic.

I disagree. The OPs question has been answered. You, juan and myself all agreed that whether a photon is matter depends on the definition of matter. Let that rest as is.

 

After I posted post #16 the answer was all there for the OP to see. All that needed to be said had been said. juan the added some bogus stuff. I.e. I wrote p = gamma m v. juan then replied

This is not the momentum of an electron in an electromagnetic field. Neither the momentum of Mercury near the Sun (due to general relativistic effects).

juan never backed up his claim. That's just poor form.

 

Without him being clear I'd wager that he's thinking that I was forgetting the momentum due to the the electrons field. If so then he is sorely misinformed. Let m = the proper mass of an electron. Let m₀ = bare mass of the electron, dm = electromagnetic mass of electrons field. Then m = m₀ + dm. The proper mass of an electron has the mass contribution of the electrons field built right into it. That's pretty well established.

 

A bit later through my derivation he posts "More of the same." I find that just plain rude and condescending.

 

The term "proper mass" for m...blah blah blah

I don't care. Never have and I never will. Sell it somwhere else juan. I'd wager I know this subject much much much more that you do. I get that feeling from the arguments you've provided so far.

Thank you very much for your advice and the article, although I doubt that it can be useful for me.

And that's why you won't get the answer. You're just one of those people who, when they don't get the answer right they attempt to change physics so that the do get it right.

What is your problem?

Oh man! Everybody thinks they're so unique as if they're the first one to point out the obvious, i.e. what a newbie in SR learns in the first week of relativity. What you think you're telling me for the first time I learned a quarter of a century ago. So why do you think you're different. Better yet, what makes you think I'm so ignorant?

 

My problem is that this thread is getting off topic and you are responsible for doing it. Please stop it!

 

As far as you so-called proof goes, it's not a proof at all. There's no logic to it which could be considered a proof. You really cant prover your assertion because its far from being true. All your doing is showing your igorance in these concepts.

 

All you ended up doing was to show what some people think. That's far from being an assertion. But then again you weren't rigidly clear on that either. You state only

Many textbooks give the Hamiltonian for matter plus radiation. CERN website also explain to broad audiences why an electron is a matter particle, but a photon is not a matter particle

 

http://public.web.ce...rdmodel-en.html

Which tells us only what "many" (whatever that means) textbooks say the Hamiltonian for matter plus radiation but you didn't say what that has to do with the terminology. And what was your textbook example supposed to do? You once again thought that you could argue a point without including the relavent information. E.g. quote one of those textbooks which you claim supports your assertion. I.e. show this Hamiltonian.

 

Mving on, all your link shows is something I already know, that particle physicists use the term "mass" to refer to "proper mass". If I were a particle physicist then that's what I'd use in print too. All that tells us is what particle physicists use. It says nothing about the relativistic mechanics of continuous media. Nor does it say anything about active, passive and inertial mass as used in GR, astronomy and cosmology. That's no proof at all. Then there are relativists who study relativity for itself, i.e. study its useage in all concievebale applications.

 

As far as textbooks go, relativity texts, SR and GR, the ones that use inertial mass to mean m = p/v = relativistic mass in at lese one derivation are

 

Gravitation by Misner, Thorne and Wheeler, W.H. Freeman and Company

Introducing Einstein's Relativity by Ray D'Inverno, Clarendon Press

Relativity DeMystified by David McMahon, McGraw-Hill

Basic Relativity by Richard A. Mould, Springer

Relativity: Special, General and Cosmological by Wolfgang Rindler, Oxford University Press

A First Course in General Relativity by Bernard F. Schutz, Cambridge University Press

A Short Course in General Relativity - Second Edition by J. Foster and J.D Nightingale, Springer

Special Relativity by A.P. French, The MIT Introductory Physics Series

General Theory of Relativity by P.A.M. Dirac, Princeton University Press

Introduction to the Theory of Relativity by Peter Gabriel Bergman, Dover Pub.

Space-Time Structure by Erwin Schrodinger, Cambridge University Press

Special Relativity by Albert Shadowitz, Dover Pub.

The Meaning of Relativity - Fifth Edition by Albert Einstein, Princeton University Press

Theory of Relativity by Wolfgang Pauli, Dover Pub.

Relativity, Thermodynamics and Cosmology by Richard C. Tolman, Dover Pub.

The Theory of Relativity by C.M. Möller, Oxford at the Clarendon Press

 

The ones that were published recently (i.e. after 1990) are

 

Introducing Einstein's Relativity by Ray D'Inverno, Clarendon Press

Relativity DeMystified by David McMahon, McGraw-Hill

Basic Relativity by Richard A. Mould, Springer

Relativity: Special, General and Cosmological by Wolfgang Rindler, Oxford University Press

A First Course in General Relativity by Bernard F. Schutz, Cambridge University Press

A Short Course in General Relativity - Second Edition by J. Foster and J.D Nightingale, Springer

 

Examples from the American Journal of Physics

 

Apparatus to measure relativistic mass increase, John W. Luetzelschwab, Am. J. Phys. 71(9), 878, Sept. (2003).

Relativistic mass increase at slow speeds, Gerald Gabrielse, Am. J. Phys. 63(6), 568 (1995).

In defense of relativistic mass, T. R. Sandin, Am. J. Phys. 59(11) 1032 (1991).

A simple relativistic paradox about electrostatic energy, Wolfgang Rindler and Jack Denur, Am. J. Phys. 56(9), Sept. (1988).

An elementary development of mass-energy equivalence, Daniel J. Steck, Frank Rioux, Am. J. Phys. 51(5), May (1983).

 

So please stop trying to pass of your misguided beliefs on me. I've heard them all before and have gotten into debates such as these thousands of times over the last 14 years. You're no different.

juanrga - Please stop pulling this thread off topic. Nobody cares how many people use what.

Before I continue I'd like to make one thing clear - I have no intention of ever getting into a debate regarding a definition of a term used in physics ever again on the internet. That's my goal and I might slip accidently. But I get all of you, please don't try to drag me into a discussion about a definition. I hate them and they serve no purpose. I will introduce a term to somone who has never heard of it but that'll be the extent. I might discuss it e-mail. People have much less to prove in PMs. That's why I don't mind PMs.

 

For interacting particles one merely substitutes the total energy and momentum by the kinetic energy and kinetic momentum [math]K^2 - (\pi c)^2 = m^2c^4[/math]

You didn't define what K is. If you mean E then you're using a new symbol that is rarely if ever never used to express inertial energy. And that relationship works only for particles. It doesn't hold for continuous media.

 

For fields there is no kinetic vs. non-kinetic distinction, ...

I have no idea what you mean by that. Please explain.

 

...only the total energy and momentum are defined locally for fields.

You're forgetting that a field is an example of a continuous medium. The mathematical object that used to find the mass of something is the stress-energy-momentum tensor. So far you haven't taken the stress in the magnetic field into account. Are you aware that stress has inertia?

 

I do not know what you mean by "you assume that inertial mass density equals mass density", because I do not know exactly what you mean by inertial mass (I only can guess).

You don't know what inertial mass is? The inertial mass m of a particle is the m in p = mv. The proper mass M of a particle is the M in p = Mv/sqrt(1-v^2/c^2). m and M are related by m = M/sqrt(1-v^2/c^2). Sometimes people use m for proper mass and M for inertial mass. The people who prefer to use proper mass instead of inertial mass also prefer to use the term "inertial mass" to refer to proper mass. I choose inertial mass to mean the m in p = mv.

 

I do not know why you think that I am trying to obtain an "invariant mass density". Where I said or even suggested that a density is an invariant? Nowhere I said such one thing about the density.

You have a habit sometimes of just tossing out equations and expecting everyone to know what its supposed to mean. This is one time that you can't do that. Especially since you wrote an expression that has never written in relatvity (because it's wrong for your use). You wrote rho = sqrt (energy density^2 - momentum densoity ^2) without explaining why. The M in M = sqrt(E^2 - P^2) is often called the invariant mass of a particle. You never offered an eplanation of why you were doing what you were doing. One can't just toss out equations and expect people to know why you're doing what you're doing. Especially in this case.

 

Tell you what. I don't think that it's a good idea for me to show you the solution until you learn the physics of the inertial of stress. A nice text that does this is by either Rindler or Mould. Hit the library and learn about the mechanics of continuous media. I really don't expect that you'd accept the solution because I don't think you'd accept the definitions used in the relativity community.

 

Or you could get a copy of the article The inertia of stress, Rodrigo Medina, Am. J. Phys. 74(11), November 2006

Abstract - We present a simple example in which the importance of the inertial effects is evident. The system is an insulating solid narrow disk whose faces are uniformly charged with equal charges of equal magnitude and opposite signs. The motion of the system in two different directions is considered. It is shown how the contribution of energy and momentum of the stress that develops inside the solid to balance the electromagnetic forces have to be added to the electromagnetic contributions to obtain the results predicted by the relativistic equivalence of mass and energy.

 

To others - I'll send it to you in e-mail. I've already sent it to one person.

The concept of matter given by ajb and myself is the usual in the modern Standard Model.

Yes. You can say it, but can you prove it?

PMB

Light do not have any proper mass...

But wen it travels at the speed of light "c", it gains some mass, becoming heavier than earlier.

That's incorrect. This was what I was trying to get through to you earlier.

 

Let \gamma = 1/sqrt(1 - v²/c²), b = v/c, m = mass as measured when v << c. m is also called the [/b]proper mass[/b] or rest mass. I prefer the term proper mass since the "rest mass"is for particles at rest and a photon can never be at rest. Let M = gm be the inertial mass of a particle.

 

It can be shown that the momentum of a point particle is

 

1) p = Mv = gmv

 

The energy is

 

2a) E = Mc² = gmc²

 

or

 

2b) E = Mc² = gE₀

 

where E₀ is called the proper energy of the particle

 

 

 

Eq. (2) can be rewritten to as

 

3) g = E/Mc² = E/gmc²

 

Substitue Eq.(3) into Eq. (1) to obtain

 

4) p = mvg = mv(E/Mc²) = mv(E/gmc²) = vE/c²

 

Multiply Eq(4) through by c to obtain

 

5) pc = Ev/c

 

This can be rewritten as

 

6) pc/E = v/c

 

A luxon is a particle that always travels at the speed of light. For such a particle v = c.

Substitute into Eq. (6) to obtain

 

7) pc/E = 1 ===> E = pc

 

Now substitute Eq. (2) into Eq. (1) to obtain

 

8) p = Ev/c²

 

Multiply through by c to obtain

 

9) pc = Ev/c = Eb

 

Square both sides to get

 

10) E²b² = (pc)²

 

Subtract E² from both sides

 

11) E²b² - E² = (pc)² - E²

 

or

 

12) E² - E²b² = E² - (pc)²

 

Factor E² out of the left side to get

 

13) E²(1 - b²)² = E² - (pc)²

 

Note that g² = 1/(1-b²) ==> (1 - b²) = 1/g²

 

14) E²/g²)² = E² - (pc)²

 

Note that E²/g² = m²c⁴. We finally have

 

15a) E² - (pc)² = m²c⁴ = (mc²)²

 

or

 

15b) E² - (pc)² = (E₀2[/sup])²

 

Recall that for a photon v = c. If we take the limit in Eq. (15) for v --> c we find

 

16) m = 0

 

This is what it means for a photon to have zero proper mass. People often get ride of the "proper" and say "photons have zero mass". Recall the expression for momentum in Eq. (1), p = Mv. Let v = c to get p = Mc. Therefore M = p/c. Substitute p = E/c to get M = E/c[su]2[/sup]. For a photon E = hf where h = Planck's constant and f is the frequency of the photon. We now have M = hf/c² which means that a photon has inertial mass. So the two expressions for the mass of a luxon is

 

Proper Mass: m = 0

 

Inetial Mass: M = p/c = M = E/c[su]2[/sup] = hf/c²

 

Connection between E, p and m: E² - (pc)² = (mc²)₂

 

 

Hopefully that should clear eveything up.

In my expression [math]T^{00}[/math], [math]T^{i0}[/math], and [math]T^{j0}[/math] are densities (recall I am using c=1). The energy density consists of two terms: an 'inertial' term (given by mass) plus a 'kinetic' term (associated to motion). This is the same structure that energy has for particles as electrons.

 

When there is not electric field the mass density of the EM field is

 

[math]\rho \equiv \sqrt{(T^{00})^2 - (T^{i0})^2} = T^{00}[/math]

 

which coincides with yours (when reintroducing c).

What you're doing is to use the expression [math]E^2 - (pc)^2 = m^2c^4[/math] which was derived for isolated particles. Your application to a density turns out to be invalid in general and in particular it doesn't work in this case. The reason you don't recognize your mistake is because you are operating under the assmption that what holds for an isolated single particle will also hold for a continuos medium like a magnetic field. By this I mean that you assume that inertial mass density equals mass density (c=1). That relationship doesn't hold in this scenario. Try transforming to another frame and see if your attempt yields the same result since you're trying to get an invariant mass density.

 

Try again. This time go back to the definition of mass instead of an equality that was derived for particles.

So light does not have mass..

But wen it travles at the speed of light ("c"), it gains mass and the time slows down.. (Relativity)

Right??

That have zero mass in what sense?

 

Precisely photons travel to the speed of light because have not mass (m=0). As you said above Einstein showed that a massive particle with nonzero mass cannot travel at the speed of light because its mass would become infinite (which means that you need an infinite energy to accelerate one electron up to c, and this is impossible).

Your use of the term "mass" is contrary. When you choose to say that light has zero mass then you have chosen to use the term "mass" to mean "proper mass". The proper mass of a particle does not change its value with c. Therefore the assertion that Einstein showed that a massive particle can't travel at c because its mass would become infinite is then am invalid statement.

Fair enough: it's an uncertainty relationship but not Heisenberg.

 

 

 

But that wasn't the question being addressed. The question is more along the lines of must energy be able to be measured precisely, because the OP wanted to know if something can have an irrational amount of energy. I was simply pointing out that there are states where the energy is not precisely defined.

Sorry. My mistake. I also mistakenlky said that you used it incorrectly and I'm not in a position to say such a thing. Sorry Tom.