Mass of Photon: Is 0 Rest Mass Possible?

[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.

 

[ZapperZ]

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

I was bored out of my mind in our Control Room trying to get 60 nC of electrons to pass through a tube the size of a drinking straw!

:)

Zz.

 

[pmb_phy]

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".

That was the first thing that I did. I had an expert GR historian (Dr. John Stachel, Boston Univ., former editor of the Einstein papers project) confirm it for me just to double check. I figured that'd be the first objection someone should bhring up. But that's not the only place. He mentioned the mass of light in the book he wrote with Infeld "The Evolution of Physics."

I'm not saying any of these things necessarily happened... but I think your conclusion needs more justification.

Which ones? All of them?

Pete

 

[robphy]

That was the first thing that I did. I had an expert GR historian (Dr. John Stachel, Boston Univ., former editor of the Einstein papers project) confirm it for me just to double check. I figured that'd be the first objection someone should bhring up. But that's not the only place. He mentioned the mass of light in the book he wrote with Infeld "The Evolution of Physics."

Actually, he was one of the folks I had in mind who could check this. (Is he still at Boston U.?) From what I can tell, he's a nice guy with lots of interesting insights. Too bad I only get a brief chance to chat with him at busy conferences... and at these opportunities I don't get a chance to ask my real questions.

Which ones? All of them?

Pete

I actually didn't read your entire manuscript (although I think I read a draft a while back)... In my last post, I was specifically referring to your conclusion suggesting that Einstein's comment in the letter to Barnett (often used by advocates for emphasizing proper/rest-mass and de-emphasizing relativistic/inertial-mass ) is somehow to be dismissed regarding this issue because it isn't followed up in later publications.

Have you submitted your manuscript for publication?


You might be interested in

http://arxiv.org/abs/physics/0504110
On the Abuse and Use of Relativistic Mass
Authors: Gary Oas

http://arxiv.org/abs/physics/0504111
On the Use of Relativistic Mass in Various Published Works
Authors: Gary Oas

 

[pmb_phy]

Actually, he was one of the folks I had in mind who could check this. (Is he still at Boston U.?)

Yep. Still at BU.

From what I can tell, he's a nice guy with lots of interesting insights.

He's a very nice guy. He's helped me out on many occasions. Sometimes we just talk about life. There was a flamer who was obssesed with me at sci.physics.relativity and would post all sorts of lies and try to use the fact that I had Leukemia to tick me off. When he did that I said every four letter word I knew to him, but only when he did the Leukemia thing - too disgusting to do on a physics discussion board. In the end someone e-mailed Stachel telling him I'm a bad guy and I swear at people. I told him the whole story. It turns out that his mom passed away from Leukemia so we had some common ground. He's a great guy and fun to talk to.

I actually didn't read your entire manuscript (although I think I read a draft a while back)... In my last post, I was specifically referring to your conclusion suggesting that Einstein's comment in the letter to Barnett (often used by advocates for emphasizing proper/rest-mass and de-emphasizing relativistic/inertial-mass ) is somehow to be dismissed regarding this issue because it isn't followed up in later publications.

That was never my intention. My intention was that he used relativistic mass but he didn't use it in the form M = \gamma m_0 but he used in in other forms like "Light has mass" and in Mach's principle where he held that mass piled up near a massive particle will change the (relativistic) mass of the particle. He did emphasize that it was moving slowly but the "slow moving particle" did not have the rest mass = proper mass and that was his piont there. I made the point that proper mass does not always equal rest mass but I guess some people missed it the way I wrote it.

Have you submitted your manuscript for publication?

Yes. There is a standing rule at AJP - "Try as best you can to reject relativity articles". A friend of mine has reviewed articles there for a very long time and the editor would tell him that. I figured I'd try anyway because I think its a good article. The reviewer didn't think so. E.g. he said that nobody he knows thinks light has mass. My friend told me that the reviewer didn't know what he was talking about. My friend thought the artilce was very good. Perhaps you'd heard of him - Robert W. Brehme (as in Brehme diagram)? He wrote a relativity textbook which is awesome. Schutz recommends it (highly?) in his GR text.

You might be interested in

http://arxiv.org/abs/physics/0504110
On the Abuse and Use of Relativistic Mass
Authors: Gary Oas

http://arxiv.org/abs/physics/0504111
On the Use of Relativistic Mass in Various Published Works
Authors: Gary Oas

Thanks. I'll check them out. Much appreciated.

Pete

 

[pmb_phy]

Actually, he was one of the folks I had in mind who could check this. (Is he still at Boston U.?)

Yep. Still at BU.

From what I can tell, he's a nice guy with lots of interesting insights.

He's a very nice guy. He's helped me out on many occasions. Sometimes we just talk about life. There was a flamer who was obssesed with me at sci.physics.relativity and would post all sorts of lies and try to use the fact that I had Leukemia to tick me off. When he did that I said every four letter word I knew to him, but only when he did the Leukemia thing - too disgusting to do on a physics discussion board. In the end someone e-mailed Stachel telling him I'm a bad guy and I swear at people. I told him the whole story. It turns out that his mom passed away from Leukemia so we had some common ground. He's a great guy and fun to talk to.

I actually didn't read your entire manuscript (although I think I read a draft a while back)... In my last post, I was specifically referring to your conclusion suggesting that Einstein's comment in the letter to Barnett (often used by advocates for emphasizing proper/rest-mass and de-emphasizing relativistic/inertial-mass ) is somehow to be dismissed regarding this issue because it isn't followed up in later publications.

That was never my intention. My intention was that he used relativistic mass but he didn't use it in the form M = \gamma m_0 but he used in in other forms like "Light has mass" and in Mach's principle where he held that mass piled up near a massive particle will change the (relativistic) mass of the particle. He did emphasize that it was moving slowly but the "slow moving particle" did not have the rest mass = proper mass and that was his piont there. I made the point that proper mass does not always equal rest mass but I guess some people missed it the way I wrote it.

Have you submitted your manuscript for publication?

Yes. There is a standing rule at AJP - "Try as best you can to reject relativity articles". A friend of mine has reviewed articles there for a very long time and the editor would tell him that. I figured I'd try anyway because I think its a good article. The reviewer didn't think so. E.g. he said that nobody he knows thinks light has mass. My friend told me that the reviewer didn't know what he was talking about. My friend thought the artilce was very good. Perhaps you'd heard of him - Robert W. Brehme (as in Brehme diagram)? He wrote a relativity textbook which is awesome. Schutz recommends it (highly?) in his GR text.

You might be interested in

http://arxiv.org/abs/physics/0504110
On the Abuse and Use of Relativistic Mass
Authors: Gary Oas

http://arxiv.org/abs/physics/0504111
On the Use of Relativistic Mass in Various Published Works
Authors: Gary Oas

Thanks. I'll check them out. Much appreciated.

A friend of mine said he'd sponsor my paper for the physics archive so it will be there soon I hope. Then I'll try another journal for publishing. Any recommendations you might have as to which journal?

Pete

 

[pervect]

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

I didn't see anything objectionable in the article. The authors were making it clear that they were talking about relativistic mass.

They did not use "mass", unqualfiied, to mean relativistic mass. Nor did they say that "a photon is not a massless particle", the original statement that I objected to.

 

[Dcase]

Would there be any advantage of using inductance instead of mass?

1 - You might be wondering if there is an equivalent of the mass in the electrical domain ... ... There is indeed such an element, and it is called an inductor.
http://othello.mech.northwestern.edu/ea3/book/elec8/Inductors.htm

2 - Mass is merely the self-inductance of an electric field.
http://home.netcom.com/~heensle/phys/book/induct.html

 

[robphy]

Yes. There is a standing rule at AJP - "Try as best you can to reject relativity articles". A friend of mine has reviewed articles there for a very long time and the editor would tell him that. I figured I'd try anyway because I think its a good article. The reviewer didn't think so. E.g. he said that nobody he knows thinks light has mass. My friend told me that the reviewer didn't know what he was talking about. My friend thought the artilce was very good. Perhaps you'd heard of him - Robert W. Brehme (as in Brehme diagram)? He wrote a relativity textbook which is awesome. Schutz recommends it (highly?) in his GR text.

A friend of mine said he'd sponsor my paper for the physics archive so it will be there soon I hope. Then I'll try another journal for publishing. Any recommendations you might have as to which journal?

Pete

I can believe that such a rule exists. My first attempt was turned out a few years ago. My revised and extended version was also recently turned down. I'm convinced that there has been some resistance to "spacetime diagrams". Out of the blue, someone invited me to contribute to a special issue of another journal... so, I submitted it to them as well as put it on the arxiv. I think one strategy to help overcome that hurdle is to mingle among those in physics pedagogy (some of whom may be reviewers)... and try to get them to look at your stuff. So, I've ramped up my AAPT activity.

Yes, I know of (but don't know personally) Brehme. What has become of his diagram? Does he still use and advocate his diagram?

As for another journal, I'm not sure... EJP, maybe?

 

[pmb_phy]

I didn't see anything objectionable in the article. The authors were making it clear that they were talking about relativistic mass.

The point was that they never used the qualifier "relativistic" and write "relativistic mass." When they used the term "mass" without a qualifier it always meant "relativistic mass."

They did not use "mass", unqualfiied, to mean relativistic mass.

Page 3 reads

Then the mass of a moving particle is m = \gamma m_0.

There is no qualifier here nor elsewhere where relativistic mass is used.

Nor did they say that "a photon is not a massless particle", the original statement that I objected to.

Why would they? I was speaking about nomenclature and that page is about accelerators not photons. Whether a photon has relativistic mass is not a question of debate by those who understand relativity. There are planty of texts to back this up, i.e. any SR text that uses rel-mass states that photons have mass

Pete

 

[pmb_phy]

Yes, I know of (but don't know personally) Brehme. What has become of his diagram? Does he still use and advocate his diagram?

I'm not sure. I think he still thinks its a good idea though and its used in his own text.

I was planning on EJP as my next stop. Thanks for the reassurance.

Pete