Unraveling the Controversy: Understanding Light's Dimensions and Properties

[scott_sieger]

Ongoing long term theory development discussion

Observations of light

1. It's only seen when it is within a very narrow spectrum

2. It can not be seen except in reflection and at it's source.

3. It generates heat.

4. It doesn't appear to have mass.

5. Every thing suggests that it is 2 dimensional.

6. An awful lot of contraversy surrounds it's understanding

7. There seems to be a lot of tail chasing going on.


If light has no mass but is a particle then it would have to be 2 dimensional I would think. Actually when you look at reflected light it certainly seems to be 2 dimensional. Like it's not something you can peel away is it. It definitely appears to have no thinkness.

Another point to make is that if light was 3 dimensional particles then you would actually see it looked at from the side. Which of course we can't unless it is reflecting of something.

The laser pistol seen in the movies where a beam of light fires from a gun would be the effect of light if it was 3 dimensional.

Can anyone offer a counter argument that can be observed without getting all techo. Anything that is real and not theory that can prove light to be three dimensional?

If not then why are we chasing our tails on this one?

an apple is an apple is an apple is an apple when do we stop and say hey this is an apple

have fun

 

[Jonathan]

Light, as a particle, is supposed to be zero dimensional.

 

[pmb]

Originally posted by scott_sieger

If light has no mass but is a particle then it would have to be 2 dimensional I would think.

Light does have mass. It just doesn't have rest mass.

Pete

 

[Anton A. Ermolenko]

Originally posted by pmb
Light does have mass. It just doesn't have rest mass.

Pete

Photon doesn't have mass, it just does have a non-zero linear part of four-momentum, therefore it call a massless linear particle.

 

[Anton A. Ermolenko]

Originally posted by Jonathan
Light, as a particle, is supposed to be zero dimensional.

Because photon has both linear part of four-momentum, and helicity, therefore it needs the four-dimensional space. You can't describe a photon in space having smaller dimensionality. You can't conserve both momentum, and helicity, and spin, without four-dimensional space.

 

[Jonathan]

By zero dimensional, I mean that it has no effective size when veiwed as a particle.

 

[scott_sieger]

so we have a "particle" that is thought of as being zero dimensional, two dimensional and 4 dimensional the 4th being time I assume. hhhmmmmmmm...It just shows you that the light is in the eye of the beholder...ha...oops excuse me...

 

[Jonathan]

LOL!

 

[pmb]

Originally posted by Anton A. Ermolenko
Photon doesn't have mass, it just does have a non-zero linear part of four-momentum, therefore it call a massless linear particle.

That's rest mass. Not mass.

Some people call the "mass" in relativity "relativistic" mass. What light does not have is "rest mass."

This is nothing new by the way. Even Einstein said light has mass. It's mass is E/c^2.

The same thing can be found in the Feynman lectures since Feynman said it too. Rinlder does as well in his new relativity text as does Mould and D'Inverno etc.

'mass' is defined as the quantity m such that the quantity mv is a conserved quantity. This, along with the postulates of relativity, gives enough information to show that, for a tardyon (particle with non-zero mass) has a mass m given by

m = m(v) = m_o/sqrt[1-(v/c)^2]

where m_o = m(0) is the rest mass.

But according to the definition of mass above - anything which has a non-zero momentum has a non-zero mass. In fact if you look in the well-known text "Special Relativity," A.P. French, MIT intro series and turn to page 16 and look at the footnote you'll see this

By inertial mass we mean the ratio of linear momentum to velocity.

This text is still used at MIT by the way. See
http://web.mit.edu/8.20/820Info_2003.pdf

The following textbooks are required or strongly recommended.

And lists French and Rindler's text. Each of which define mass in exactly this way. Einstein argued that light had mass back in 1906.

I know of one new physics book by a very famous author on this subject, i.e. Max Jammer, who even labels the time component of 4-mommentum as m where

m = m_o/sqrt[1-(v/c)^2]

See
"Concepts of Mass in Contemporary Physics and Philosophy," Mass Jammer, Princeton University Press, (2000), pages 49-50


Pete

 

[Anton A. Ermolenko]

Originally posted by pmb
That's rest mass. Not mass.

That's mass, you can call it the rest energy, but not rest mass.

Originally posted by pmb
Some people call the "mass" in relativity "relativistic" mass. What light does not have is "rest mass."

This is nothing new by the way. Even Einstein said light has mass. It's mass is E/c^2.

You've made mistake. In general, E₀=mc², but total energy of particle E is equal to mc² if and only if the particle's momentum p is equal to zero, because E=p²c²+E₀²=p²c²+m²c⁴
Let c=1, then
E=p²+E₀²=p²+m².

Originally posted by pmb
The same thing can be found in the Feynman lectures since Feynman said it too. Rinlder does as well in his new relativity text as does Mould and D'Inverno etc.

'mass' is defined as the quantity m such that the quantity mv is a conserved quantity. This, along with the postulates of relativity, gives enough information to show that, for a tardyon (particle with non-zero mass) has a mass m given by

m = m(v) = m_o/sqrt[1-(v/c)^2]

where m_o = m(0) is the rest mass.

The serious scientific literature is deprived of such definition of a mass, because the mass is an invariant concerning Lorentz and Poincare transformation groups. Invariant signifies not varying, without dependence from a velocity or something else (of course, if the particle is free). A mass is a mass and it is an invariant. Be exacter.
1. Landu L., The theoretical physics. Field theory, vol 2;
2. Einstein A., Ann. d. Phys., 1905.Bd 17.S.891;
3. Ìi1ler A. I., Albert Einstein's Special Theory of Relativity: Emergence (1905) and Early Interpretation (1905-1911). -Addison-Wesley, 1981;
4. Einstein A.//Ann. d. Phys., 1905. Bd 18. S. 639;
5. Einstein A.//Ibidem. 1906. Bd 20. S. 371;
6. Einstein A.//Ibidem. 1907. Bd 23. S. 371;
7. Åinstein A.//Ibidem. 1911. Bd 35. S. 898;
8. Jammer M. Concepts of Mass in Classical and Modern Physics.- Cambridge: Harvard Univ. Press. 1961;
9. Feynman R.//Phys. Rev. 1949. V. 76. Ð. 749, 769;
10. Feynman R., Leighton R., Sands Ì. The Feynman Lectures on Physics.- Addison-Wesley, 1963, 1964. - V. 1. Chs/15, 16; V. 2. Ch. 28;
11. Fåónmàn R. P.//The reason for antiparticles//Elementary Particles and the Laws of Physics; The 1986. Dirac Memorial Lectures.- Cambridge; New York; New Rochel-le; Melbourne: Sydney: Cambridge Univ. Press, 1987 - P. 1;
12. Adler C.//Am. J. Phys. 1987. V. 55. P. 739.
Especially Adler C., because he has proved that my point is right. He also has criticized the majority of the educational literature because of presence of this erroneous definition.

 

[Anton A. Ermolenko]

Originally posted by Jonathan
By zero dimensional, I mean that it has no effective size when veiwed as a particle.

Then what is a photon's wave length?

 

[scott_sieger]

as an amatuer i find all this particle, non particle, mass , non mass very interesting.

Could it be we could agree on one thing?

That what is trying to be described is just a very small centre of attraction that has no mass, isn't a particle but definitely has intensity.

This would accommodate all approaches and make a lot more sense.

It also doesn't require dimensional definition either.

 

[Jonathan]

Intensity is a scalar dimension.

 

[pmb]

Originally posted by Anton A. Ermolenko
That's mass, you can call it the rest energy, but not rest mass.

As I said above - it depends on how the term "mass" is defined. And there is no definition that is used uniformly throught the physics literture. In special relativity there

mass = relativistic mass
mass = proper mass aka rest mass

You've made mistake.

Sorry dude but I've made no mistake.

In general, [...]

That holds true if and only if m = proper mass. If m = relativistic mass then E = mc^2 where m = m_0/sqrt[1-(v/c)^2] = re;ativistic mass

The serious scientific literature is deprived of such definition of a mass, because the mass is an invariant concerning Lorentz and Poincare transformation groups.

That too is incorrect. The following are very much serious scientific literature as are the texts used at MIT to teach relativity

"The Feynman Lectures on Physics," Vol I - III, Feynman, Leighton, and Sands, Addison Wesley, (1963)(1989)
As Feynman says (lectures V-1, page 7-11 "Gravity and Relativity")

One feature of this new law which is quite easy to understand is this: In Einstein relativity theory, anything which has energy has mass-mass in the sense that it is attracted gravitationally. Even light, which has energy, has a "mass". When a light beam, which has energy in it, comes in it, comes past the sun. Thus the light does not go straight, but it is deflected. During the eclipse of the stars which are around the sun should appear displaced from where they would be if the sun were not there and this has been observed.

"Relativity: Special, General and Cosmological," Rindler, Oxford Univ., Press, (2001). From pagte 113

Einstein's mass-energy equivalence allows us to include even particles of sero rest-mass (photons,...) into the scheme of collision mechanics. If such a particle has finite energy E (all of it being kinetic!), it has fionite mass m = E/c^2 and thus, because of (6.4), it must move at the speed of light. Formally we can regard its mass as the limit of the procuct, gamma*m_o, of which the first factor has gone to infinity and the second to zero.
In 1905 he therefore boldly suggested that

Then there are two other new texts which I know of off hand which define mass in this way. They are

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

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

Then there is the American Journal of Physics. See

"An elementary derivation of E = mc^2," Fritz Rohrlich, Am. J. Phys.58, 348 (1990)

Are you familiar with Gravitation by Misner, Thorne and Wheeler? If so then see Section 5.7 "Symmetry of Stress-Energy Tensor"

Calculate in a specific Lorentz frame. Consider first momentum density (components T^j0) and energy flux (components T^0j). They must be equal because energy = mass ("E = Mc^2 = M")

T^0j = (energy flux)

T^0j = (energy density)x(mean velocity of energy flow)^j

T^0j = (mass density)x(mean velocity of mass flow)^j

T^0j = (momentum density) = T^j0

This mass cannot be rest mass must be relativistic mass.

Are you familar with Alan Guth? I have a copy of his lecture notes for his course "The Early Universe"

We are perhaps not used to thinking of electromagnetic radiation as having mass, but it is well-known that radiation has an energy density. If the energy density is denoted by u, the special relativity implies that theelectromagnetic radiation has a mass density

(7.3) rho = u/c^2

To my knowledge nobody has ever "weighed" electromagnetic radiation in any way, but the theoretical evidence in favor of Eq. 7.3 is overwhelming - light has mass. (Nonetheless, the photon has zero rest mass, meaning that it cannot be brought to rest). The general relation for the square of four-momentum reads p^2 = -(mc)^2, and for the photon this becomes p^2 = 0. Writing out the square of the four-momentum leads to the following relation for photons:

p^2- E^2 = 0, or E = cp.

In this set of notes we will examine the role which the mass of electromagnetic radiation plays in the early stage of the universe.

All of the above are very serious.


Let me tackle a few of these.

Invariant signifies not varying, without dependence from a velocity or something else (of course, if the particle is free). A mass is a mass and it is an invariant. Be exacter.
1. Landu L., The theoretical physics. Field theory, vol 2;
2. Einstein A., Ann. d. Phys., 1905.Bd 17.S.891;
3. Ìi1ler A. I., Albert Einstein's Special Theory of Relativity: Emergence (1905) and Early Interpretation (1905-1911). -Addison-Wesley, 1981;
4. Einstein A.//Ann. d. Phys., 1905. Bd 18. S. 639;
5. Einstein A.//Ibidem. 1906. Bd 20. S. 371;
6. Einstein A.//Ibidem. 1907. Bd 23. S. 371;
7. Åinstein A.//Ibidem. 1911. Bd 35. S. 898;
8. Jammer M. Concepts of Mass in Classical and Modern Physics.- Cambridge: Harvard Univ. Press. 1961;
9. Feynman R.//Phys. Rev. 1949. V. 76. Ð. 749, 769;
10. Feynman R., Leighton R., Sands Ì. The Feynman Lectures on Physics.- Addison-Wesley, 1963, 1964. - V. 1. Chs/15, 16; V. 2. Ch. 28;
11. Fåónmàn R. P.//The reason for antiparticles//Elementary Particles and the Laws of Physics; The 1986. Dirac Memorial Lectures.- Cambridge; New York; New Rochel-le; Melbourne: Sydney: Cambridge Univ. Press, 1987 - P. 1;
12. Adler C.//Am. J. Phys. 1987. V. 55. P. 739.
Especially Adler C., because he has proved that my point is right. He also has criticized the majority of the educational literature because of presence of this erroneous definition. [/B]

1. Landau = Landau simply defines mass differently. I see no problem with anyone choosing a definition that they like

2. Einstein A., Ann. d. Phys., 1905.Bd 17.S.891;

Not sure of the referance numbers. But if you're referring to Einstein's 1905 article then that was his first paper. Not his last. He does speak of transverse and longitudinal mass which are velocity dependant. These are two different quantities. Max Planck came up with a better definition the next year and said that m = m_o/sqrt[1-(v/c)^2] is better since you can now write force as

f = dp/dt

where p = mv


3. Not familar with it. But I suspect that its just a different definition - like Landau

4. Einstein A.//Ann. d. Phys., 1905. Bd 18. S. 639;

Einstein's first derivation. Not his last

5. Einstein A.//Ibidem. 1906. Bd 20. S. 371;

If this is the paper that I think it is, i.e. the conservation of the center of mass, then I ahve to ask you if you've actually read this paper. In this paper Einstein was investigating the mass of light. It consists of two parts. The first part Einstein concludes light mass carries mass with it. In the second part he defines the mass density of light as rho = u/c^2 where u is the energy density of radiation. He also implies in the math that the mass of a particle = energy of particle/c^2

6. Einstein A.//Ibidem. 1907. Bd 23. S. 371;

I have to reread that since I don't recall that the subject arose in that paper

7. Åinstein A.//Ibidem. 1911. Bd 35. S. 898;

Again I have to ask you if you've read this? He does say that light has mass in that paper. He calls it radiation though.

8. Jammer M. Concepts of Mass in Classical and Modern Physics.- Cambridge: Harvard Univ. Press. 1961;

What about this book are you referring to? He does explain relativistic mass. However he has a new book out.

"Concepts of Mass in Contemporary Physics and Philosophy," Mass Jammer, Princeton University Press, (2000)

On pages 49-50 Jammer argues that the time component of the 4-momentum is mass m. I.e. he starts out with P^u = (cq, um, 0, 0) and shows that q = m = relativistic mass

9. Feynman R.//Phys. Rev. 1949. V. 76. Ð. 749, 769;

Sorry but I haven't read it. I've read his lectures and a few others in which he does state that mass = m_o/sqrt[1-(v/c)^2] and that light has mass. And he said that many years after this article was written.

10. Feynman R., Leighton R., Sands Ì. The Feynman Lectures on Physics.- Addison-Wesley, 1963, 1964. - V. 1. Chs/15, 16; V. 2. Ch. 28;

I don't understand your reason for citing this. They agree with my definition of mass. Not yours.


11. Fåónmàn R. P.//The reason for antiparticles//Elementary Particles and the Laws of Physics; The 1986. Dirac Memorial Lectures.- Cambridge; New York; New Rochel-le; Melbourne: Sydney: Cambridge Univ. Press, 1987 - P. 1;

Never heard of it. Sorry.

12. Adler C.//Am. J. Phys. 1987. V. 55. P. 739.

This article is loaded with errors. In fact all of his arguements are very flawed. I'll point them out one by one if you'd like.

Rindler is much better at relativity than Adler. See Rinlder's comments on this topic in Physics Today. I placed it on my web page with Rindler's permission

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


But if you're interested in the other point of view then see


"In defense of relativistic mass," T.R. Sandin, Vol. 59(11), No. 1991

For a more complete listing of articles on this debate then see
http://www.geocities.com/physics_world/mass_articles.htm


Pete

 

[pmb]

to be described is just a very small centre of attraction that has no mass, isn't a particle but definitely has intensity.

Mass (and hence energy) is the source of gravity. Not rest mass. Since light has energy then it has mass and thus creates a gravitational field. For an example of such a field see

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

Pete

 

[Anton A. Ermolenko]

Originally posted by pmb
Mass (and hence energy) is the source of gravity. Not rest mass. Since light has energy then it has mass and thus creates a gravitational field. For an example of such a field see

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

Pete

Once again, mass is an invariant concerning Lorentz and Poincare transformation groups. You can't defining mass by gravitation, because measure of attraction within dependence to both an energy and direction of moving. E.g. two photons with the same energy, but the perpendicular momentums will be differ twice by attractive force by the massive body.
However, your point - almost religion. Believe and enjoy.

 

[scott_sieger]

an example of massless intensity could be described using three magnets

Place them in a circle so that they are poled so at to be attractive...leave a gap of say 6 inches between all of them

So we have a circumferance of magnets and their attractions.

Each magnet is also attracted to each other across the diagnal or diameter.

In an appropriate center there is an intensity and if one swings a magnet across this arangement the magnet will eventually settle at this point. I call this a culminant centre of attraction where the total attractions are averaged and a point in the magnetic middle is achieved.

So the relevance is that this centre of attraction is a mass less intensity. a resultant centre of attraction.

Say apply the logic to 6 stars in any arrangement it would show an averaged centre of attraction i would think..

Theory of gravity in developement.

 

[pmb]

Originally posted by Anton A. Ermolenko
Once again, mass is an invariant concerning Lorentz and Poincare transformation groups.

Rest mass yes. Relativistic mass no.

You can't defining mass by gravitation, because measure of attraction within dependence to both an energy and direction of moving.

That is why mass is completely defined by a tensor and not a scalar.

This has nothing to do with "religion." I'm not being dogmatic about it whatsoever. I just took the time to explore every single aspect that I could about this subject and I came to the conlusion I have, not because I'm being dogmatic, and not because I learned it a long time ago and "don't know the new way." But I do so becuase I've come to understand that it is the best choice since it stands up as the one that can have the most most rigourous definition.

By the way - I see you didn't answer my questions. Is there a reason for that?

Pete

 

[pmb]

Originally posted by Anton A. Ermolenko
You can't defining mass by gravitation, because measure of attraction within dependence to both an energy and direction of moving. E.g. two photons with the same energy, but the perpendicular momentums will be differ twice by attractive force by the massive body.

Not sure what you mean by "You can't defining mass by gravitation." The soruce of gravity is mass i.e. mass-energy. The source is not rest mass.

But if you're referring to the mathematical quantity then the mass-tensor aka stress-energy-momentum tensor is the quantity which acts as the source.

Consider the EM analogy. The source of the EM field in Maxwell's equations is the 4-current. Yet one can truly say that charge is the physical entity which acts as the source. In this context - In gravity the physical entity which acts relativistic mass.

Relativistic mass is to gravitation as charge is to electromagnetism.

Pete

 

[Michael F. Dmitriyev]

Light as a basis of all.

In this list is absent the most important book. It is…. the Bible, where creation of the world is described how it was actually. All other scientific books in the sum costs nothing in comparison with one phrase from this book. This phrase says that all

OUR WORLD IS CREATED OF LIGHT!

I CAN PROVE IT!

1. The Bible, a first book of Moses, Life, chapter1.

 

[pmb]

For a derivation of what I was describing and the proof of the relations see

http://www.geocities.com/physics_world/sr/inertial_mass.htm

Pete

 

[Anton A. Ermolenko]

Originally posted by pmb
Rest mass yes. Relativistic mass no.


That is why mass is completely defined by a tensor and not a scalar.

This has nothing to do with "religion." I'm not being dogmatic about it whatsoever. I just took the time to explore every single aspect that I could about this subject and I came to the conlusion I have, not because I'm being dogmatic, and not because I learned it a long time ago and "don't know the new way." But I do so becuase I've come to understand that it is the best choice since it stands up as the one that can have the most most rigourous definition.

By the way - I see you didn't answer my questions. Is there a reason for that?

Pete

2. Einstein A., Ann. d. Phys., 1905.Bd 17.S.891;

Not sure of the referance numbers. But if you're referring to Einstein's 1905 article then that was his first paper. Not his last. He does speak of transverse and longitudinal mass which are velocity dependant. These are two different quantities. Max Planck came up with a better definition the next year and said that m = m_o/sqrt[1-(v/c)^2] is better since you can now write force as
f = dp/dt

where p = mv

Of course, not. You’ve made mistake again p=mug, where
`````____
g=1/Ö1–b<sup>2</sup>,
b=u/c.
In Einstein's first paper he really does speak of transverse and longitudinal mass, but he obtain the following equation,
``````````______
W=mV<sup>2</sup>(1/Ö1–u<sup>2</sup>/V<sup>2</sup>–1)
where m – mass, V – speed of light.


And of course, he doesn’t use the rest mass concept. That was his first paper, his second paper begin with words: «Let the system (x, y, z) with a rigid body which is in a state of rest, its energy relative to the system (x, y, z) is equal to E<sub>0</sub>.» Well, his second paper hasn’t the rest mass concept, too, but, it has the rest energy concept. And the rest energy is defined by its equivalence to the mass. Einstein’s papers never contained the rest mass concept, but papers of Planck, Lewis and Tolman did. Well, those were the papers and what about Einstein’s books? Maybe those contained the rest mass concept? And which one, maybe the first? Well, his first book («Relativity: The Special and General Theory») was written at 1916, first English was published at 1920. That has no the rest mass concept, but, it has the rest energy concept, too. Maybe his next book (Einstein A. The Meaning of Relativity: Four Lectures Delivered at Princeton Univerisity) has? Of course no, it hasn’t. Pauli was first who’s made this mistake in his book: Relativitats Theorie. And you use that artificial nomenclature. The (total) energy is a tensor, but mass is an invariant, hence, scalar.
Eventually, let c=1, then E=mc<sup>2</sup>Þ E=m and what does it mean? Only energy is a mass? Huh... really, it is very substantial equation, i.e. you’ve termed an energy as a mass...

 

[Anton A. Ermolenko]

Originally posted by pmb
Not sure what you mean by "You can't defining mass by gravitation." The soruce of gravity is mass i.e. mass-energy. The source is not rest mass.

Energy yes, mass no.

Originally posted by pmb
But if you're referring to the mathematical quantity then the mass-tensor aka stress-energy-momentum tensor is the quantity which acts as the source.

Consider the EM analogy. The source of the EM field in Maxwell's equations is the 4-current. Yet one can truly say that charge is the physical entity which acts as the source. In this context - In gravity the physical entity which acts relativistic mass.

Relativistic mass is to gravitation as charge is to electromagnetism.

Pete

What is a relativistic and rest mass or total and rest energy? What for? Moreover with c=1. Energy and mass.
In general, I think, that we already have understood each other.

 

[pmb]

Originally posted by Anton A. Ermolenko
Of course, not. You’ve made mistake again...

I've made no mistake. Do you understand what the symbol "m_o" is? It refers to the proper mass (aka rest mass) of a particle. m, as I've been using it, is defined by the relation

p = mv

In this definition, m is often referred to as 'relativistic mass.'

Do you know what relativistic mass is?

In Einstein's first paper he really does speak of transverse and longitudinal mass,

That is incorrect. I very much does speak of transverse and longitudinal mass. His 1905 paper is online at

http://www.fourmilab.ch/etexts/einstein/specrel/www/

See the part where he states

Taking the ordinary point of view we now inquire as to the ``longitudinal'' and the ``transverse'' mass of the moving electron. We write the equations (A) in the form ...

The relations follow soon after. The longitudinal mass is correct. The transverse mass is not what is used today. This is due to the way Einstein defined mass. He related force on the instanteous rest frame with the coefficient of acceleration in the frame in which the particle's instantaneous velovity is v.

And of course, he doesn’t use the rest mass concept.

The rest mass is the m in the equation of longitidual and transverse masses. But this was his first paper. Not his last. In his paper


"Elementary Derivation of the Equivalance of Mass and Energy," A. Einstein, Bulletin of the American Mathematical Society 41, 223-230 (1935)

Einstein writes

"The mG(u) is the kinetic energy, E_s the rest-energy of the material point, m the rest-mass or, simply the mass."





Which paper is his second? Please state title.


re - "And the rest energy is defined by its equivalence to the mass."

My comments on this thread are with regards to the mass of light. And in his 1906 paper Einstein clearly and specifically states that light (radiation) has mass. That was the whole point of his paper on the consdervation on the center of gravity.


re - "Of course no, it hasn’t." - His 1916 GR paper clearly states that mass = energy.

re - "Pauli was first who’s made this mistake in his book: "


Pauli made no mistake.

You're confusing mistake with definition.


Pmb

 

[Anton A. Ermolenko]

Originally posted by pmb
"Elementary Derivation of the Equivalance of Mass and Energy," A. Einstein, Bulletin of the American Mathematical Society 41, 223-230 (1935)

Einstein writes

"The mG(u) is the kinetic energy, E_s the rest-energy of the material point, m the rest-mass or, simply the mass."

I like it. After Pauli's book everyone should termed the mass... kinda "Oh! yes, of course, I quite forgot (in Pauli's terms, not Einstein) the rest mass..."
Just say me, you really use those terms when you read or use the QFT? There are no the relativistic or rest mass and total and rest energy, but there are energy and mass. Isn't it? Dude

 

[krab]

Anton A. Ermolenko is correct in my view. I should add that by "correct", I mean by Occam's Razor: it results in a simpler description of reality.

In lower level physics courses in America, relativity is usually first taught in such a way that it is easier to compare with Newtonian mechanics. However, if you carry this to solving complicated problems relating to the dynamics of relativistic particles, it is way too cumbersome. One of its results is a distinction between "longitudinal" and "transverse" mass. Another is that pesky sqrt(1-v^2/c^2) factors appear everywhere.

I now believe it is the wrong way to teach relativity. My undergraduate education left me with the impression that relativity is very tricky, with many pitfalls. My later career turned out to be at an accelerator lab where it is essential to correctly describe trajectories of relativistic particles. To my surprise, I found the equations of motion are relatively (unintended pun) simple, and simple to derive, if one begins with 4-vectors and Hamiltonians. In 4-vector form, mass is rest mass; it is in a sense the norm of the 4-momentum. It is a useful concept because it is invariant. Defining mass in such a way that it depends on momentum only complicates life.

James Smith in his text Introduction to Special Relativity (1965) derives E=mc^2/sqrt(1-v^2/c^2) and then comments: "This raises a semantic question. Here is a new quantity that is the relativistic generalization of two classical quantities. Many treatments do just what we have temporarily done and call M=m/sqrt(1-v^2/c^2) the "mass", m the rest mass, and call Mc^2 the energy. But, if energy is always just c^2 times the "mass", this is not good economy with words or concepts. Furthermore, it seems desirable to have the word mass refer to an intrinsic property of the particle, and not to refer to a property of its motion. From now on this book will follow what is becoming quite general practice. The word energy will refer to the quantity mc^2/sqrt(1-v^2/c^2) . The word mass wil refer to m, the quantity many other treatments call the "rest mass"."

I am also quite close to the field of particle physics. No one says photons have mass. Everyone says photons are massless, without qualifying this by saying they are speaking of rest mass only.

 

[pmb]

Originally posted by krab
Anton A. Ermolenko is correct in my view. I should add that by "correct", I mean by Occam's Razor: it results in a simpler description of reality.

That's not a correct application of Ockham's razor. Ockham's razor really applies to explanations/theories. Not definitions. It states that

Ockham's Razor: Of two competing theories, the simplest explanation of an entity is to be preferred.

As to what a simple definition is - that's a matter of debate.

However, if you carry this to solving complicated problems relating to the dynamics of relativistic particles, it is way too cumbersome.

Not really. First off the ddefinition of mass is simply part of theory. And if you're referring to things like the subscript in equations like p = gamma*m_o*v then one can simply drop the subscript and write p = gamma*m*v. The "m" is then the proper mass.

This is exactly what Thorne and Blanchard do in their new text. E.g. See chapter one
http://www.pma.caltech.edu/Courses/ph136/yr2002/chap01/0201.2.pdf

One of its results is a distinction between "longitudinal" and "transverse" mass. Another is that pesky sqrt(1-v^2/c^2) factors appear everywhere.

For one, that was something Einstein used at first but which he soon gave up. It was a poor definition of force, F = ma, which led to that. Physicists today do not use that definition. In fact Newton didn't even define force like that. The correct definition of force is f = dp/dt. You cannot get rid of the gamma. Its there whether we like it or not. All you can do is shift it around.

I now believe it is the wrong way to teach relativity. My undergraduate education left me with the impression that relativity is very tricky, with many pitfalls.

I got the exact opposite impression. However I did find most if not all discussions of this subject very lacking.

To my surprise, I found the equations of motion are relatively (unintended pun) simple, and simple to derive, if one begins with 4-vectors and Hamiltonians.

Some people do prefer the geometric approach to the dynamic approach. However there are some bothersome things in that approach. The most simplest thing in relativity is the velocity of light. Its magnitude being indepedand of the frame of referance. Yet there is no 4-velocity for light.

Some people love to try to define "mass" as the magnitude of 4-momentum. Problem with that is the the time component, the free-particle energy E, is defined in terms of the particle's "mass." So such a definition is circular.

Nobody can deny the usefulness of proper quantities like rest mass. But just because a property is not invariant it does not mean that it is not physically meaningful. Length, time, density etc are all of thast nature. The two should never be confused. For example: The lifetime of a free neutron is about 15 minutes. You will almost always seen this defined in this manner. However the actually physically measured lifetime of the particle is a frame-dependant quantity. The lifetime really should be called the proper lifetime - but it never is. Just like the proton mass being 938 MeV/c^2 when it really should be called the proper proton mass or proton rest mass.

However if I were writing a paper/article/text on particle physics calculations I'd say once that m is rest mass and call it mass and be done with it. The reason being that particle physics is about the inherant properties of particles. E.g. A particle physicist doesn't care about the difference between proper time and time (aka coordinate time).

Smith makes the same bogus argument that many do. Its a very poor explanation to say that there is a poor economy of words when in fact this is not "poor economy of words" but is physics.

For example: m = mass is defined such that mv is a conserved quantity. E = Free-particle energy is defined as the sum of rest energy and kinetic energy. It is then *proven* than E = mc^2.

What you later call these terms after its all fleshed out is a matter of convinience.

Furthermore, it seems desirable to have the word mass refer to an intrinsic property of the particle, and not to refer to a property of its motion.

That is purely a matter of opinion though. And it can only apply to particles. It cannot apply as a general usage. For example: the most general thing mass can be is a tensor. A second rank tensor to be exact. This tensor describes bodies which are composed of continuous matter. One should take the most general qauntity and define terms in that manner. Then specialze to simplier things like matter of a point like nature. If you recall the derivation that MTW give to show that the stress-energy tensor is symetric you will see that this is exactly what they do. The can't use rest mass in that since not all stress-energy tensors describe matter which has a non-zero rest mass so that wouldn't work.

I am also quite close to the field of particle physics. No one says photons have mass.

That is incorrect. If they say that then they are referring to proper mass. And I know of at least one particle physicist who will tell you that light has mass. And that's Alan Guth. I even have that in writing since it's in his class lecture notes.

And we haven't even touched on gravity. Do you think there should be different definitions of mass for each different use?

Besides - nobody can be sure on what "everybody" does or says unless they exact "everybody" what they think and say. And that would just take far too long! :-)

And if you work in particle physics then that is probably the only exposure that you get to physicists correct? How many cosmologists do you see on a day to day basis? And not all relativists are either particle physicits not are they all cosmologists.

Rindler had a nifty problem about the mass of a charged capacitor. If you're truly interested in this subject then I highly suggest reading it. The article is

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

Pete

 

[pmb]

Originally posted by Anton A. Ermolenko
I like it. After Pauli's book everyone should termed the mass... kinda "Oh! yes, of course, I quite forgot (in Pauli's terms, not Einstein) the rest mass..."
Just say me, you really use those terms when you read or use the QFT? There are no the relativistic or rest mass and total and rest energy, but there are energy and mass. Isn't it? Dude

I don't know QFT. But I imagine that QFT only uses invariant (and thus intrinsic) properties like proper mass and not inertial mass.

Tell me. It's said that the lifetime of a neutron is 15 minutes. That is the "proper lifetime" d(tau) i.e. the lifetime as measured in the rest frame of the neutron. As measured in a frame of referance moving relative to the neutron the lifetime is dt = gamma*d(tau). You won't see dt mentioned in tables of the lifetime or particles. Why do you think that is? Do you think this time dilation relation wrong? Or do you think that it is a matter of definition of the term "lifetime"?

Pete

 

[pmb]

Originally posted by Anton A. Ermolenko

In general, I think, that we already have understood each other.

I appoligize Anton. I didn't see this comment at first. I was unware that you didn't want to discuss this.

I had posted one last comment about lifetime but I will cease on this since you believe that we understand each other.

Pete

 

[Anton A. Ermolenko]

Originally posted by pmb
I appoligize Anton. I didn't see this comment at first. I was unware that you didn't want to discuss this.

Pete

Don't mention it, Pete. Thank's for discussion.

 

[pmb]

Originally posted by Anton A. Ermolenko
Don't mention it, Pete. Thank's for discussion.

You're welcome.

Just one last note. There are many people who claim that mass, m, always means 'rest mass' and that is what the entire physics community means when they use this term. I've composed a list of counter examples to dispel this myth. See

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

Pete