Mass of Photon: Is 0 Rest Mass Possible?

[row]

i don't know if this is the right section for this but here goes my doubt,I read that the rest mass of a photon is 0,but how can a photon have a rest mass if speed of light is constant and about 3*10^8m/s ?i mean if light cannot be slowed how can we define mass of a photon at 0 speed?

 

[Garth]

i don't know if this is the right section for this but here goes my doubt,I read that the rest mass of a photon is 0,but how can a photon have a rest mass if speed of light is constant and about 3*10^8m/s ?i mean if light cannot be slowed how can we define mass of a photon at 0 speed?

You can't, the concept of rest mass for a photon is meaningless, that is why it doesn't have it.

If you like, it is similar to the two different situations: having a bank account with nothing in it, or not having any bank account at all.

The question of a photon's rest mass is like not having any bank account at all.

In either case you may say: "I have no money in the bank", similarly it is often said: "The photon has no rest mass."

Garth

 

[jtbell]

This is one reason why many people prefer to say "invariant mass" rather than "rest mass".

 

[pmb_phy]

i don't know if this is the right section for this but here goes my doubt,I read that the rest mass of a photon is 0,but how can a photon have a rest mass if speed of light is constant and about 3*10^8m/s ?i mean if light cannot be slowed how can we define mass of a photon at 0 speed?

The term "rest mass" is a poor term to use. The better term to use is "proper mass." The proper mass of a photon is often not measured in the same was as that of, say, an electron. The expression for proper mass m₀ in terms of energy and momentum is usually given by

$$E^2 - (pc)^2 = m_0^2 c^4$$

For a photon E = pc so you can see how the proper mass, m₀, is zero. Recall that the mass of anything is defined by the relation p = mv. If you substitute this into E = pc and arrange terms you get E = mc² or solving for mass m = E/c²

Pete

 

[Giulio B.]

If photon has an energy, (and it has...when we are exposed to sun we feel hot), it must necessarily have a rest mass...or proper mass anyway, otherwise E=mc² craps...i don't understand what you are sayng about the bank account...for me seems obviusly that it has a mass.

is possible that a photon goes to a bit less than speed of light to do that? (a matematical infinity bit less...)

 

[Hootenanny]

is possible that a photon goes to a bit less than speed of light to do that? (a matematical infinity bit less...)

Just to paraphrase what you said. You are saying that light doesn't travel at the speed of light?

~H

 

[Hootenanny]

If photon has an energy, (and it has...when we are exposed to sun we feel hot), it must necessarily have a rest mass...or proper mass anyway, otherwise E=mc² craps..

If a particle has energy, doesn't mean that it must have mass;

A general energy expression in terms of momentum is given by;

$$E = \sqrt{p^{2}c^{2} + (m_{0}c^{2})^{2}}$$

Now, if we assume that a photon has zero rest mass ($m_{0} = 0$), then the term $(m_{0}c^{2})^{2}$ drops out leaving us with;

$$E = \sqrt{p^{2}c^2{2}} = pc$$

Using a manipulation of the above equation

$$p = \frac{E}{c}$$

And Plank's relationship;

$$E = hf \Leftrightarrow E = \frac{hc}{\lambda}$$

The momentum of a photon is given by

$$p = \frac{h}{\lambda}$$

Thus, a particle with no mass can have energy.

~H

 

[jtbell]

If photon has an energy, (and it has...when we are exposed to sun we feel hot), it must necessarily have a rest mass...or proper mass anyway, otherwise E=mc² craps...

You have to be careful about how you apply $E=mc^2$, depending on whether you consider $m$ to be "invariant mass" or "relativistic mass."

If $m$ is "invariant mass", then $E$ is the "rest energy" of the particle, that is, the energy that the particle has when it's at rest. Photons don't have "rest energy", only kinetic energy, and their "invariant mass" is zero, so $E=mc^2$ reduces to 0 = 0.

If $m$ is the "relativistic mass", then $E$ is the total energy of the particle, that is, rest energy plus kinetic energy. In this case you can use $E=mc^2$ to calculate the "relativistic mass" of a photon, which is obviously not zero.

When most physicists talk about "mass", they usually mean "invariant mass." Most of these physicists prefer not to use the concept of "relativistic mass" at all. Some do use "relativistic mass", and you occasionally see arguments here about which kind of mass is "better."

The basic problem is that there is no single quantity in relativity which has all the properties of the classical "mass." People disagree on which of those properties are more important, and so they disagree on which kind of mass is more important or useful in relativity.

 

[clj4]

Here is a very nice treatment, coming from Cornell:

http://www.lassp.cornell.edu/~cew2/P209/part11.pdf

 

[pmb_phy]

If photon has an energy, (and it has...when we are exposed to sun we feel hot), it must necessarily have a rest mass...

There is absolutely no reason to make such an assumption, expecially since its wrong.

..or proper mass anyway, otherwise E=mc² craps...

E is inertial energy, not rest energy. You can have one without the other. Some people call E the total energy when it's really the energy of a free particle. If the particle has a non-zero potential V then the total energy W is W = E + V. I call E inertial energy so one doesn't fall into this trap. The term appears in the American Journal of Physics in the same year they nuked Japan.

is possible that a photon goes to a bit less than speed of light to do that? (a matematical infinity bit less...)

Not if the proper mass of the photon is exactly zero.

Pete

 

[pmb_phy]

When most physicists talk about "mass", they usually mean "invariant mass."

Take a look at MTW. At times they use "mass" to mean "relativistic mass" (references provided upon request).

Mst of these physicists prefer not to use the concept of "relativistic mass" at all. Some do use "relativistic mass", and you occasionally see arguments here about which kind of mass is "better."

One has to be careful in such arguements because taking one side might imply to others that the other side is wrong somehow. I've always argued that the correct response to the question "does mass depend on velocity" is to ask "by mass do you mean proper mass or inertial mass?" Then once that is cleared up there is no arguement. I do hold that relativistic mass has all the properties associated with the term "mass" as usually assumed and that proper mass is very important as well. If I had it my way then $\mu$ would stand for proper mass and m for inertial mass. If we use the greek symbol $\tau$ for proper time and "t" for "coordinate time" then we should use $\mu$ for proper mass and "m" for inertial mass (what one might call coordinate mass. - This is just my very humble opinion which I believe I can strongly support.

The basic problem is that there is no single quantity in relativity which has all the properties of the classical "mass."

Sure they do - relativistic mass. Why do you disagree on this point?

Pete

 

[bernhard.rothenstein]

Here is a very nice treatment, coming from Cornell:

http://www.lassp.cornell.edu/~cew2/P209/part11.pdf

as i see it is the same with what i find in Mermin It's about time.

 

[rbj]

The question of a photon's rest mass is like not having any bank account at all.

i disagree. i think that it's more like the saying that there is a bank account, but the balance is zero.

we were arguing about this before:

https://www.physicsforums.com/showpost.php?p=957440&postcount=24

and some guy, posted something about NIST specifying a non-zero upper bound for the rest mass of a photon:

https://www.physicsforums.com/showpost.php?p=957736&postcount=27

which i find very hard to swallow.

the reason why the photon (or any other "massless particle") has a concept of "rest mass", but such rest mass must be zero is that the speed of the particle is the speed of E&M propogation (light) and that the rest mass is:

$$m_0 = m \sqrt{1 - \frac{v^2}{c^2}} = \frac{h \nu}{c^2} \sqrt{1 - \frac{v^2}{c^2}}$$

plug in $v = c$ and you get $m_0 = 0$.

 

[pmb_phy]

$$m_0 = m \sqrt{1 - \frac{v^2}{c^2}} = \frac{h \nu}{c^2} \sqrt{1 - \frac{v^2}{c^2}}$$

plug in $v = c$ and you get $m_0 = 0$.

A very odd way of looking at it. Something seems wrong but I can't quite put my finger on it.

Pete

 

[quantumdude]

Just to paraphrase what you said. You are saying that light doesn't travel at the speed of light?

Cute. But the suggestion isn't necessarily as silly as it sounds. It depends on the sense in which the term "speed of light" is used.

The "speed of light" in SR need never have been identified with the "speed of light" from Maxwell's equations. That is just a leftover relic from the discovery of SR from electrodynamics. SR only requires an invariant speed, not some special one.

I think that when Giulio says, "is possible that a photon goes to a bit less than speed of light", he really means "is possible that a photon goes to a bit less than the invariant speed of SR".

 

[Hootenanny]

I think that when Giulio says, "is possible that a photon goes to a bit less than speed of light", he really means "is possible that a photon goes to a bit less than the invariant speed of SR".

Ah, I feel rather stupid now(and a bit guilty) :shy: Apologies Giulio.

~H

 

[jtbell]

The basic problem is that there is no single quantity in relativity which has all the properties of the classical "mass."

Sure they do - relativistic mass. Why do you disagree on this point?

Classical mass is an invariant property of a particle or object, leaving aside non-closed systems such as a rocket expelling fuel. Relativistic mass is not.

and some guy, posted something about NIST specifying a non-zero upper bound for the rest mass of a photon:

https://www.physicsforums.com/showpos...6&postcount=27

which i find very hard to swallow.

That upper bound is a statement about the precision of experimental data relating to the (invariant) photon mass. It means that experiments done so far cannot detect a invariant photon mass less than $6 \times 10^{-17}$ eV. Or, to put it another way, if that mass were greater than $6 \times 10^{-17}$ eV, some experiments would have seen its effects by now. It's like the upper end of an error bar on a data point on a graph.

 

[pmb_phy]

Classical mass is an invariant property of a particle or object, leaving aside non-closed systems such as a rocket expelling fuel. Relativistic mass is not.

Something being coordinate dependant is not a problem in SR. In fact that's all we are able to measure. Therefore it is not a problem.

That upper bound is a statement about the precision of experimental data relating to the (invariant) photon mass...

Yeah. Jackson covers all of that.

Thanks

Pete

 

[robphy]

Classical mass is an invariant property of a particle or object, leaving aside non-closed systems such as a rocket expelling fuel. Relativistic mass is not.

Something being coordinate dependant is not a problem in SR. In fact that's all we are able to measure. Therefore it is not a problem.

Pete

With this clarification, the correct statements are:

• "proper mass" or "rest mass" is an invariant property of a particle alone.
  
• "relativistic mass" (being an observer-dependent/coordinate-dependent quantity) is not an invariant property of the particle alone. Instead, it is a property of the "pair consisting of the particle and an observer". Both need to be specified. If you keep the qualification of "a particle and an observer", then the property is actually an invariant [since it's a scalar formed from two distinct tangent vectors (that of the particle and that of the observer) and the metric].

An analogous set of statements is:

• the "norm" or "magnitude" of a vector is an invariant property of a vector alone.
  
• the "projection of a vector onto an axis" (being an observer-dependent/coordinate-dependent quantity) is not an invariant property of the vector alone. Instead, it is a property of the "pair consisting of the vector and an axis". Both need to be specified. If you keep the qualification of "a vector and an axis", then the property is actually an invariant [since it's a scalar formed from two distinct vectors (that of the vector of interest and that of (say) a unit vector along an axis) and the metric].

 

[jtbell]

Classical mass is an invariant property of a particle or object, leaving aside non-closed systems such as a rocket expelling fuel. Relativistic mass is not.

Something being coordinate dependant is not a problem in SR. In fact that's all we are able to measure. Therefore it is not a problem.

I wasn't addressing the question of whether it is a problem or not. I was addressing the question of whether classical mass has a property that relativistic mass does not, which I thought was the point of the exchange at the bottom of posting #11, to which I was responding.

 

[rbj]

A very odd way of looking at it. Something seems wrong but I can't quite put my finger on it.

i was involved in an argument about this (at least about the pedagogy of this) in that other photon mass thread. seems as if only myself and bernhard.rothenstein look at it this way and i am convinced it is because of the time that we took our first physics courses (30 years ago for me) and something changed in what was the fashionable pedagogy since then.

it sure wasn't a very odd way of looking at it then. perhaps you can find a copy of Arthur Beiser Concepts of Modern Physics 2^nd edition, © about 1974. this was precisely the approach taken in that book. they never said that photons are massless particles, only that they have no rest mass (for the reason stated in my post). the expressions

$$E^2 = \left( m_0 c^2 \right)^2 + (p c)^2$$

nor

$$p = \frac{h \nu}{c}$$

were never stated as first principles but were derived from

$$m = \frac{m_0}{\sqrt{1 - \frac{v^2}{c^2}}}$$

$$E = m c^2$$

$$p = m v$$ (where $m$ is relativistic mass)

from these three equations, we can derive

$$E^2 = \left( m_0 c^2 \right)^2 + (p c)^2$$.

and for photons,

$$E = h \nu = \hbar \omega$$ .

from this and the 3 previous "axiomatic" equations immediately above, and from the presumption that the particles that manifest the particle-like properties of light have the same velocity as of the E&M wave, that is $v = c$ for photons, you get:

$$m_0 = 0$$

$$m = \frac{E}{c^2} = \frac{h \nu}{c^2}$$ (not rest mass)

and $$p = m v = m c = \frac{E}{c^2} c = \frac{h \nu}{c}$$ .

i would still like to see a cogent explanation, from first principles, on how to derive

$$E^2 = \left( m_0 c^2 \right)^2 + (p c)^2$$

for the general body of invariant mass $m_0$ and, for photons,

$$p = \frac{h \nu}{c}$$

without a concept differentiating rest mass from relativistic mass.

Photons with energy greater than zero are not "massless" particles, but they have no rest mass (or "invariant mass") because their velocity is (practically by definition) that of light.

 

[pervect]

Photons with energy greater than zero are not "massless" particles

False. (And why the bold text?) One will find numerous references in the literature that photons are massless particles.

One could say "when physicists say that a photon is a massless particle, they mean that its rest mass (invariant mass) is zero. They do not mean it has no relativistic mass.

This would be unobjectionable. But unfortunately, that's not what you actually said.

but they have no rest mass (or "invariant mass") because their velocity is (practically by definition) that of light.

True.

 

[pmb_phy]

One could say "when physicists say that a photon is a massless particle, they mean that its rest mass (invariant mass) is zero. They do not mean it has no relativistic mass.

If that were universally true then the authors of all the textbooks and journal articles listed here

http://www.geocities.com/physics_world/relativistic_mass.htm

would have to be rewritten so as to comply with your assumption. In particular look at all the links to particle accelerator labs listed towards the bottom. Especially this one from CERN

http://humanresources.web.cern.ch/humanresources/external/training/tech/special/AXEL2003/AXEL-2003_L02_24Feb03pm.pdf

Pete

 

[ZapperZ]

Again, as in the other thread, there seems to be a very CLEAR mismatch in the INTENTION and PURPOSE of not telling anyone who asked "does a photon have mass?" with the answer "Yes, but it is a relativistic mass".

Since people are quoting other sites and documents, then I will also play this very game even though this is something I dislike. In 1948, Einstein wrote[1]:

... no clear definition can be given [for the] mass M = m(1 - V^2/c^2)^-1/2 of a moving body. It is better to introduce no other mass than the "rest mass" m.

I would also like to point out that today, no nuclear and particle physics papers make any reference to "relativistic mass". When you look at the cited mass for the top quark, the neutrinos, etc... never, EVER was there a qualifier that these are "relativistic" or "rest" mass.

OK, so you say that these are meant for professionals in the field who know better. Fine. When Joe Schmoe asks "Does so-and-so have a mass?", what exactly is the concept of mass being asked here? I would put it to you that here, that person is asking for the "quantity of matter" or the amount of "material object" in the most naive sense of the word! For some odd reason, this issue has somehow being neglected. You cannot give an answer that somehow satisfies YOUR understanding, but neglects completely the comprehension of the RECEIVER! You are not teaching Special Relativity to physics majors here!

So then you ask "well, how are you going to explain the existence of momentum for something with no mass?". Easy! Light has E-field component, and this interacts with the electrons and ions in material! That's why light's momentum is more easily transferred to a conductive material than an insulator! Jackson didn't need to define ANY mass whatsoever to discuss radiation pressure.

Not only that, I can also play this game as well. If I am Joe Schmoe, and I understand "mass" in the naive fashion, I can then ask "well, if relativistic mass really is a form of mass, doesn't his mean that there's more matter in the object as it moves faster and faster? After all, that is what I understand mass is! So where is the additional mass appearing from for light since you said it had no rest ones?"

Questions like this is NOT about satisfying YOUR understanding. It has everything to do with giving the correct impression to the person asking the question based on the concept that he/she is familiar with, even if such concepts are based on naive pictures. That is what you have to go by and it is not something you can simply wish away or ignore!

Zz.

[1] L. Okun, Phys. Today v.42, p.32 (1989)

 

[francesca]

Okun papers

In any case...
A clear discussion on the concept of mass:

http://arxiv.org/abs/hep-ph/0602037
The Concept of Mass in the Einstein Year
L.B. Okun
19 pages, Presented at the 12th Lomonosov conference on Elementary Particle Physics, Moscow State University, August 25-31

"Various facets of the concept of mass are discussed. The masses of elementary particles and the search for higgs. The masses of hadrons. The pedagogical virus of relativistic mass."

(another by Lev Okun is http://arxiv.org/abs/hep-ph/0602036)

 

[pmb_phy]

Again, as in the other thread, there seems to be a very CLEAR mismatch in the INTENTION and PURPOSE of not telling anyone who asked "does a photon have mass?" with the answer "Yes, but it is a relativistic mass".

I quite agree with that.

Note: When someone says "everybody uses..." their intent is to take a vote to see who many people does what. Who cares on the result of a pole. What should only matter is what makes the most sense and is the most logical.

I would also like to point out that today, no nuclear and particle physics papers make any reference to "relativistic mass". When you look at the cited mass for the top quark, the neutrinos, etc... never, EVER was there a qualifier that these are "relativistic" or "rest" mass.

It would be impossible for you to check every paper to see what percentage uses it. You're also being very restrictive since you're speaking about what particle physicists like to do and you seem to ignore everyone else, such as those who work in reltivity and then publish it in Am. J. Phys. which does use it. Then there are cosmologists who write text to teach the basics as I pointed out and students in cosmology would most likely publish artilces with the ideas and views taught to them in their education depending on their taste. Then there are foreign journals to think about.

OK, so you say that these are meant for professionals in the field who know better.

I didn't say that. It was meant to show that people do this in theor texts which are widely read. E.g. MTW is usually read by students of cosmology and GR.

When Joe Schmoe asks "Does so-and-so have a mass?", what exactly is the concept of mass being asked here?

I believe that I stated above (or somewhere) that the appropriate response is "What do you mean by mass?"

Note: Okun's article had many mistakes in it.

Pete

 

[ZapperZ]

Note: When someone says "everybody uses..." their intent is to take a vote to see who many people does what. Who cares on the result of a pole. What should only matter is what makes the most sense and is the most logical.

Sorry, but I don't buy that. You are saying to hell if you understand me or not. All I care about is that I'm logical and I make sense to ME. You are forgetting that this ISN'T about YOU! It is about the person who is asking you the question. Do you talk the same way to a 12-year old as you do to a 55-year old distinguished physicist?

If you do, then we have nothing else to talk about.

Zz.

 

[bernhard.rothenstein]

Sometimes people like to say that the photon does have mass because a photon has energy E = hf where h is Planck's constant and f is the frequency of the photon. Energy, they say, is equivalent to mass according to Einstein's famous formula E = mc2. They also say that a photon has momentum and momentum is related to mass p = mv. What they are talking about is "relativistic mass", an outdated concept which is best avoided [ See Relativity FAQ article Does mass change with velocity? ] Relativistic mass is a measure of the energy E of a particle which changes with velocity. By convention relativistic mass is not usually called the mass of a particle in contemporary physics so it is wrong to say the photon has mass in this way. But you can say that the photon has relativistic mass if you really want to. In modern terminology the mass of an object is its invariant mass which is zero for a photon.
I think that is a very relativistic quotation in accordance with pmb phy
If

 

[pmb_phy]

ZapperZ - Sorry but I'm not interested in a conversation where the poster has that kind of tone.

re - " By convention relativistic mass is not usually called the mass of a particle in contemporary physics so it is wrong to say the photon has mass in this way."

I sure wish my body could handle traveling to Boston right now so I could look in a variety of journals besides AJP to see this for myself since I doubt its truth. I'd look in a very wide spectrum of journals including those which have GR and cosmology articles as well as foreign journals. Someday!

Pete

 

[ZapperZ]

ZapperZ - Sorry but I'm not interested in a conversation where the poster has that kind of tone.

Which is just as well since you refused to answer my question on if you treat those two people that I gave as examples the same way.

re - " By convention relativistic mass is not usually called the mass of a particle in contemporary physics so it is wrong to say the photon has mass in this way."

I sure wish my body could handle traveling to Boston right now so I could look in a variety of journals besides AJP to see this for myself since I doubt its truth. I'd look in a very wide spectrum of journals including those which have GR and cosmology articles as well as foreign journals. Someday!

Pete

Please note that EVEN in AJP, the issue of the use of the term "relativistic mass" has come up a few times. Check out this preprint

http://arxiv.org/abs/physics/0504110

... and keep in mind the PURPOSE and mission of journals such as AJP and EJP, and how they differ from research-front journals. And having been in a high energy physics division for the past several years and attending the seminars, I have never ONCE heard any speakers refer to a "relativistic mass". Invariant mass, yes. Relativistic mass? Never.

Just pick up papers on the two most recent discoveries of the mass of important "particles" - the top quark, and the electron neutrino. Both of them are "relativistic" particles by all indication. Do you see any mention of "relativistic mass" for ANY of them in these papers?

Zz.

 

[pmb_phy]

"relativistic mass" (being an observer-dependent/coordinate-dependent quantity) is not an invariant property of the particle alone. Instead, it is a property of the "pair consisting of the particle and an observer". Both need to be specified. If you keep the qualification of "a particle and an observer", then the property is actually an invariant [since it's a scalar formed from two distinct tangent vectors (that of the particle and that of the observer) and the metric].

Note that if you take the scalar product of observer and 4-momentum and divide by c² youi have a scalar product (tensor of rank zero = invariant) which equals the inertial mass measured by the observer.

I'd like to add a few things of my own here. First off - If someone here asks a question then we may not know who the person asking the question is. We can take a guess at their knowledge of SR by the question asked as is the case here. So it is appropriate to respond to the question as posted if we don't know the person asking and they're expertise in SR. Second off there are two ways to correctly respond to the question as asked: (1) Ask what they mean by "mass" of (2) tell them that if they mean "proper mass" then the answer is a photon has no mass. If they mean "inertial mass" (aka relativistic mass) then the answer is yes, photons do have mass. People learning SR should know this difference since in reading some very famous physics literarture (E.g. Feynman Lectures, etc) then they should know what the author means when he uses the term "mass". It can be gathered by the usage of the word in most cases. In the third case - There is a ton of SR literature out there for the beginner who needs to know the difference. And when they ask "Why?" then we also need to know how to respond. E.g. in particle physics, when it comes to proper mass then it is the subject being studied and it is a pain in the butt to keep using "proper mass" when that is all they use to study intrinsic properties. For the fourth reason ... whew! I'm too tired to go on. But this is an important issue since it comes up a lot. Hence my reason for writing this

http://www.geocities.com/physics_world/mass_paper.pdf

Problem is that its too complicated for the beginner and of no interested to those on the con-relativistic side. Only those with a truly open mind will get something out of it.

Pete

 

[robphy]

Note that if you take the scalar product of observer and 4-momentum and divide by c² youi have a scalar product (tensor of rank zero = invariant) which equals the inertial mass measured by the observer.

Yes, that is correct... and that is my point: there must be reference to the observer doing the observing to be unambiguous. So, "inertial mass" or "relativistic mass" is not a property of the particle alone... but a property of the pair: the particle and its observer... said another way, the particle and the measurement device. So, I have no problem with its use as long as the observer or measurement device is also referenced. Is that too much to ask? [When discussing the component of a vector, one needs to refer to the axes used... right?]

I'd like to add a few things of my own here. First off - If someone here asks a question then we may not know who the person asking the question is. We can take a guess at their knowledge of SR by the question asked as is the case here. So it is appropriate to respond to the question as posted if we don't know the person asking and they're expertise in SR. Second off there are two ways to correctly respond to the question as asked: (1) Ask what they mean by "mass" of (2) tell them that if they mean "proper mass" then the answer is a photon has no mass. If they mean "inertial mass" (aka relativistic mass) then the answer is yes, photons do have mass. People learning SR should know this difference since in reading some very famous physics literarture (E.g. Feynman Lectures, etc) then they should know what the author means when he uses the term "mass". It can be gathered by the usage of the word in most cases. In the third case - There is a ton of SR literature out there for the beginner who needs to know the difference. And when they ask "Why?" then we also need to know how to respond. E.g. in particle physics, when it comes to proper mass then it is the subject being studied and it is a pain in the butt to keep using "proper mass" when that is all they use to study intrinsic properties. For the fourth reason ... whew! I'm too tired to go on. But this is an important issue since it comes up a lot. Hence my reason for writing this

http://www.geocities.com/physics_world/mass_paper.pdf

Problem is that its too complicated for the beginner and of no interested to those on the con-relativistic side. Only those with a truly open mind will get something out of it.

Pete

Agreed. Likewise, there are lots of conventions, nomenclature, and "ways of thinking" that were established long ago... many of which we regret today but are forced to deal with. In some cases, one camp wins in the long run... in other cases, we have fragmented camps... and translators who can talk to the various camps. In the grand scheme of things, it of course doesn't matter as long the real physics gets learned. However, as an educator, if something looks like it could be an obstacle to learning, I try to move it out of the way... or at least alert the student to it.

By the way, in your manuscript,
before drawing your conclusion on Einstein's comment that "It is not good to introduce the mass [expression for relativistic mass]...", it might be worth checking whether there were any changes in text between the last editions of "The Meaning of Relativity". I could certainly imagine that a new edition may be merely a repackaging of an older edition... without changes in text. I also do not know whether "a full five years" is "enough time" back then to propagate changes in a book. Finally, I could also imagine that, at the time and for the audience of the book, AE could have thought... it's good enough... I have more pressing things on my mind (like my Unified Field Theory, for example). I'm not saying any of these things necessarily happened... but I think your conclusion needs more justification.

 

[bernhard.rothenstein]

In any case...
A clear discussion on the concept of mass:

http://arxiv.org/abs/hep-ph/0602037
The Concept of Mass in the Einstein Year
L.B. Okun
19 pages, Presented at the 12th Lomonosov conference on Elementary Particle Physics, Moscow State University, August 25-31

"Various facets of the concept of mass are discussed. The masses of elementary particles and the search for higgs. The masses of hadrons. The pedagogical virus of relativistic mass."

(another by Lev Okun is http://arxiv.org/abs/hep-ph/0602036)

It is interesting to compare how the same problem is presented by the author you propose and who puts the ban on the concept of relativistic mass and Kard (see Leo Karlov "Paul Kard and the Lorentz free special relativity," Phys.Educ. 24 165-168 (1989) who uses the concept of relativistic mass for photons as well.
Kard proposes the following problem. Consider the problem when electron and positron move in opposite directions with equal speeds /u/ having equal rest masses m^0. Theirs momentums are equal and opposite. As a result of their collision the two particles annihilate generating two photons of equal mass and equal but opposite momentum. What is the mass of one of the photons m^f?
Conservation of mass leads to
m^f=m^0(1-u^2/c^2)^1/2
If the annihiltion takes place in a state of rest (u=0)
m^f=m^0.
In Okun's version the same problem sounds as follows:
"Let us consider the case when electron and positron annihilate at rest. Then their total energy is E=E^0=2m^ec2 while the total momentum is equal to zero (p=0). Due to the conservation of energy and momentum the two photons will fly with opposite momenta, so that each of them will have energy equal to m^ec^2. The rest frame of e^+ and e^- will be obviously the rest frame of the two photons. Thus the rest energy of the system of two photons will be 2m^ec^2 and hence the mass of this system will be 2m^e, in spite of the fact that each of the photons is massless. We see that mass in relativity is conserved, but not additive."
Please tell me, as a student who learns or as a teacher who introduces the
students in the problem, which of the two approaches would you prefer?
I would surely prefer the first one?

 

[ZapperZ]

It is interesting to compare how the same problem is presented by the author you propose and who puts the ban on the concept of relativistic mass and Kard (see Leo Karlov "Paul Kard and the Lorentz free special relativity," Phys.Educ. 24 165-168 (1989) who uses the concept of relativistic mass for photons as well.
Kard proposes the following problem. Consider the problem when electron and positron move in opposite directions with equal speeds /u/ having equal rest masses m^0. Theirs momentums are equal and opposite. As a result of their collision the two particles annihilate generating two photons of equal mass and equal but opposite momentum. What is the mass of one of the photons m^f?
Conservation of mass leads to
m^f=m^0(1-u^2/c^2)^1/2
If the annihiltion takes place in a state of rest (u=0)
m^f=m^0.
In Okun's version the same problem sounds as follows:
"Let us consider the case when electron and positron annihilate at rest. Then their total energy is E=E^0=2m^ec2 while the total momentum is equal to zero (p=0). Due to the conservation of energy and momentum the two photons will fly with opposite momenta, so that each of them will have energy equal to m^ec^2. The rest frame of e^+ and e^- will be obviously the rest frame of the two photons. Thus the rest energy of the system of two photons will be 2m^ec^2 and hence the mass of this system will be 2m^e, in spite of the fact that each of the photons is massless. We see that mass in relativity is conserved, but not additive."
Please tell me, as a student who learns or as a teacher who introduces the
students in the problem, which of the two approaches would you prefer?
I would surely prefer the first one?

But there is a problem here in the sense that you think that there are TWO separate conservation laws. There isn't! The more general conservation law is mass+energy. In fact, in high energy physics, such distinction is meaningless since both mass and energy are often quoted in units of eV or MeV.

If you do that and apply it to this case, it really is doesn't matter what you call where. The mass+energy conservation law works!

Zz.

 

[Meir Achuz]

ZZ: I don't know you, but why waste your time on this?
People never get what they'll never get.