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- Thread starter merc-blue
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Originally posted by merc-blue

The problem is that there are two meanings to the term "mass" as commonly used in physics today. One usage refers to what is called "rest mass" and the other usage is what some call "relativistic mass." The former (rest mass) is the mass of a particle when it's at rest or moving slowly while the later (relativistic mass) is the mass of a moving body. This mass has been defined in two equivalent ways (1)as the "m" in the relation p = mv (i.e. momentum = mass*velocity) and (2) as the m in m = E/c^2

When you used the term "mass" above where the say that the mass of a photon is zero, what you were really doing is saying that light has zero rest mass.

In what follows I will use the term "mass" to refer to "relativistic mass."

Since light has both energy and momentum it has mass but it does have zero "rest mass." I don't care for the term "rest mass" since a photon can never be at rest so you really can't measure it to me zero. I prefer the term "proper mass" which also is used to refer to "rest mass"

In Einstein's 1916 review paper "The Foundation of the General Theory of Relativity" Einstein wrote

The special theory of relativity has led to the conclusion that inert mass is nothing more or less than energy, which finds its complete mathematical expression in a symmetrical tensor of second rank, the energy-tensor.

Since light has energy and momentum it has mass. And since mass is the source of gravity, light also generates a gravitational field. I made a web page on an example here

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

In fact Einstein stated something similar tow hat you're thinking about. In his book "The Evolution of Physics." Commenting on the observation made by an observer inside an accelerating elevator that light is ‘weightless’ he writes (page 221)

But there is, fortunately, a grave fault in the reasoning of the inside observer, which saves our previous conclusion. He said: “A beam of light is weightless and, therefore, it will not be affected by the gravitational field.” This cannot be right! A beam of light carries energy and energy has mass.

Richard Feynman stated something similar in his famous lecture text. I.e. From "The Feynman Lectures on Physics," Vol -I page 7-11 - Section entitled Gravitation and Relativity

One feature of this new law 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 gravitationaly. Even light, which has energy, has a "mass". When a light beam, which has energy in it, comes past the sun there is attraction on it by the sun.

But if it's an online source you're looking for then look at University web sites and government web sites (where scientific research is done). The URLs have a ".edu" in them. Such as

http://www.astro.washington.edu/tmurphy/phys110/faqs/AB05.05.html

But the most honest answer to your question is yes--light has mass. I say this, running against the physics grain (photons have no mass), because the photon in all respects behaves as if it has mass. It is affected by gravity (light is deflected by gravity). It carries momentum. It creates dimples in spacetime (albeit tiny), like any mass or energy does. The fact that it has no rest mass is irrelevant in many respects, because it never travels any slower than light speed!

Also try searching under the phrase "mass density of radiation."

You'll find that there are two answers to your question though. And they are exact opposites. But keep in mind that when someone says the light *does not* have mass, then they are referring to "rest mass." And if they say that light is not attracted by massive bodies, that they are moving through curved space then keep in mind that this is not quite an accurate statement - General relativity is based on the notion that gravitational mass and inertial mass are proportional to each other. And from Einstein's E = mc^2 he was led to equations which demand that light is deflected and moves throught curved spacetime *because* it has mass. If an object had no mass then it would not be effected by curved spacetime - since there are no objects that have no mass then we don't have to worry about that. So all things have energy and thus all things have mass and thus all things are deflected by gravity.

Pete

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selfAdjoint

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So modern physicists are careful to avoid the term "rest mass" and use instead the term "invariant mass". And going along with this they attribute the Lorentz change to the energy, not the mass, so the invariant mass really is invariant, not changed by Lorentz transformations.

And the bending in GR is attributed to this important fact. Energy gravitates. Indeed the mathematical expression for the real world "stuff" that bends spacetime is called the momentum-energy-stress tensor, and it has components of all those things, momentum, and energy, and stress (or change in momentum-energy). They all "gravitate", and a light beam, with no mass at all, can bend spacetime with its energy.

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Javier

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Mass in quantum field theory (the basis of our understanding about what particles are) is a "good quantum number", being an eigenvalue of the "mass-squared" operator, which commutes with the Hamiltonian operator (the generator of time translations). All of this tells us that the mass of a particular species of particle, like an electron, is a well defined notion, even if the electron speeds up, slows down, or interacts with other particles (as long as there is no interaction where the electron is no longer in the system, e.g., in interacting with a positron to form two photons). As long as the electron is present, we know what we mean by the "mass of the electron".

As for massless vs. massive particles: the fact that a particle can be massless (like a photon) is *intimately* connected with the fact that we can't go to a rest frame of the particle...in fact, a particle is massless when we can't go to its rest frame and vice versa. Therefore, via special relativity, it is quite necessary to have a notion of "massless" (using the correct definition of mass in quantum field theory that we did above).

Now, Einstein's field equations state that anything with energy gravitates. Well, photons and electrons always have some energy (even though photons are massless, they have energy E=h(frequency)). Therefore, both photons (which in large numbers can make up a ray of light) and electrons (and all matter for that matter) will be affected by a gravitational field.

In turn, anything with energy is a source of gravitational field; that is, in general relativity, energy and momentum in a region of space determine the geometry of spacetime around it, which then tell objects like photons and electrons how to move.

- #5

But really it is necessary to give the other side. If light has mass, how much mass does it have?

A photon of energy E has a mass = E/^2

That's a misuse of the mass formula. The formulaIf you naively multiply its zero "rest mass" by the infinite Lorentz factor associated with c, you get an undefined quantity.

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

is derived on the assumption that the particle can be at rest and therefore is not a photon. To derive the mass relation for light you can do what Einstein did and derive it on the basis that the center of mass of a system is conserved. You then get m = E/c^2 for the mass of the photon. In this derivation no assumption is made regarding the photon other than it has energy and momentum.

That's an inaccurate statement. Since the relation between mass and energy is E = mc^2 it makes no sense to say that one is the source and the other isn't. However if you do want to then its more precise to say that mass is the source of gravity since mass refers to a physical property whereas energy doesn't. And in fact Einstein based his derivations on the relation E = mc^2 - i.e. since he knew that mass is the source of gravity in Newtonian physics and that mass and energy are equivalent then the correct formulation will reflect this fact. So mass or energy are equivalent in their usage in the equations. If you look at Einstein's field equations you'll see that the energy-momentum tensor. T^uv, is usually explicity written down in that equation. However one can always define a tensor M^uv defined such that T^uv = M^uv c^2 and then M will be the source - makes no difference - it all comes out in the wash. Fpr more on this "mass tensor" seeAnd if you examine the actuality of the bending of light in GR, you conclude that what is "attracted" in light is not mass, but energy.

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

That's quite wrong. I'd say that most use the term rest mass. In fact take a look at Kip Thorne's (head honcho in general relativity) new text - seeSo modern physicists are careful to avoid the term "rest mass" and use instead the term "invariant mass".

http://www.pma.caltech.edu/Courses/ph136/yr2002/chap23/0223.1.pdf

http://www.pma.caltech.edu/Courses/ph136/yr2002/chap24/0224.1.pdf

I can't find the term "invariant mass" in this text. But I do find the term "rest mass" all over the place

When you say that "energy is the source, not mass" all you're doing is arguing semantics and what word to use in a sentance. They are equivalent - so it makes no difference.

Pmb

- #6

There is nothing unfortunate about it. Its the most reasonable way to define mass. And while most particle physicist might do that, the same cannot be said about cosmologists.Allow me to clarify some issues: These days, when a particle physicist says something is massive or massless, they are referring to what would formerly be known as "rest mass". This is because, decades ago, people used to talk of "relativistic mass". Unfortunately, this terminology has continued on in non-technical literature, and even basic physics texts.

As I said above it's best to call this proper mass rather than rest mass - IMHO

rest mass is a 'good quantum number' because it's an inherent property of the particle. There are also other properties of particles which are inherent such as their lifetime - those numbers are listed in tables - and those numbers **always** refer to the proper lifetime of the particle. However time is not an invariant quantity - proper time is. Mass is not an invariant property - proper mass is.Mass in quantum field theory (the basis of our understanding about what particles are) is a "good quantum number", being an eigenvalue of the "mass-squared" operator, which commutes with the Hamiltonian operator (the generator of time translations).

When someone tells you that the mean life time of a neutron is 15 mintutes do you know that it's the proper life time? Would you prefer to say that time does not slow down and that the lifetime of the particle increases withe speed? OR would you say that time slows down - not proper time?All of this tells us that the mass of a particular species of particle, like an electron, is a well defined notion, even if the electron speeds up, slows down, or interacts with other particles (as long as there is no interaction where the electron is no longer in the system, e.g., in interacting with a positron to form two photons). As long as the electron is present, we know what we mean by the "mass of the electron".

Pmb

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