# Mass of light

benzun_1999
what is the mass of light particels?

Doctor Luz
deppends on their frequency m=h&nu;/c^2

Gold Member
Photons have zero mass.

Gold Member
relativistic mass is not the same as mass and is hardly ever used.

Doctor Luz
Originally posted by jcsd
relativistic mass is not the same as mass and is hardly ever used.

Relativistic mass, mass at rest, mass... It's a question on nomenclature.

Gold Member
Originally posted by Doctor Luz
Relativistic mass, mass at rest, mass... It's a question on nomenclature.

Not really, because mass that is invariant under a Lorentz transformation is a much more useful defintion than one that isn't. The term 'mass' means invariant mass only.

Doctor Luz
Originally posted by jcsd
Not really, because mass that is invariant under a Lorentz transformation is a much more useful defintion than one that isn't. The term 'mass' means invariant mass only.

It's worthwhile to discuss about this. However I think that a definition of mass that include the term 'mass' is not very good.

Of course, in my first post, I was talking about the 'relativistic mass'.

Staff Emeritus
Gold Member
Dearly Missed
And the "relativistic mass" is wrong because it would be infinite. The invariant mass of a photon is zero, and its energy and momentum are what depend on its frequency.

Doctor Luz
And the "relativistic mass" is wrong because it would be infinite.

Gold Member
And the "relativistic mass" is wrong because it would be infinite. The invariant mass of a photon is zero, and its energy and momentum are what depend on its frequency.

No: the relativistic mass is a function of the kinetic energy and therefore frequency of a photon and the correct formula for this was given by Dr. Luz. This is obviously not invariant under a Lorentz transformation as different observers will observe different frequencies and therefore each give a different value for it's energy and relativistic mass.

Gold Member
Dearly Missed
Luz seems to be asking for a primitive definition of mass

(he says a definition of one kind of mass based on another kind of mass would not be very good----so he probably wants a definition of mass in terms of the most basic kinds of measurement)

the only one I know is this

"the mass of a body is the inertia of the body at rest"

inertia is a ratio of force to acceleration

the potential circularity of this definition is a long-recognized minor problem in the foundations of physics

it may not be a perfect definition but at least it has a clear operational meaning and removes some of the ambiguity

I agree with several of the other posters here that relativistic mass does not seem to be a very useful concept---Einstein explicitly advised against using it (there is a letter to this effect)----and it is apt to lead to confusion. Both selfadjoint and
jcsd are right although they contradict each other----defined one way the "relativistic mass" of some light would be infinite if the light had any mass to begin with and defined another way the "relativistic mass" is just a redundant jargon synonym for the energy of the light and is not infinite but simply E/c2.

So one might as well follow Einstein's advice and not use the concept. Saves endless useless discussion about terminology.

Following majority usage among working physicists, since mass is the inertia of a body measured at rest, since light cannot be at rest it has no mass.

However boxes CONTAINING light can be at rest and part of their inertia can be due to the light which they contain. The sun is soaked full of light even to its very core and that light (which has zero mass) contributes mass, inertia, gravitational attractiveness, etc. to the sun.

In other words the notion of mass prevailing in modern physics is not additive-----which is tough for some people to accept. So they have this irresistible urge to try to get people to change the way they talk so that mass can be more of an alias for energy and have the additivity that we associate with energy.

I'm for the simplest least ambiguous use of words----getting mass aligned with what most physicists mean by it.

I also appreciate when at least some types of quantity can have simple operational meanings, without a lot of theory mixed up in them.

Force can be measured purely electrically by a device called the "watt balance", which is kind of interesting. Maybe it is more primitive than mass.

Doctor Luz
Originally posted by marcus
Luz seems to be asking for a primitive definition of mass

(he says a definition of one kind of mass based on another kind of mass would not be very good----so he probably wants a definition of mass in terms of the most basic kinds of measurement)

the only one I know is this

"the mass of a body is the inertia of the body at rest"

inertia is a ratio of force to acceleration

the potential circularity of this definition is a long-recognized minor problem in the foundations of physics

it may not be a perfect definition but at least it has a clear operational meaning and removes some of the ambiguity

I agree with several of the other posters here that relativistic mass does not seem to be a very useful concept---Einstein explicitly advised against using it (there is a letter to this effect)----and it is apt to lead to confusion. Both selfadjoint and
jcsd are right although they contradict each other----defined one way the "relativistic mass" of some light would be infinite if the light had any mass to begin with and defined another way the "relativistic mass" is just a redundant jargon synonym for the energy of the light and is not infinite but simply E/c2.

So one might as well follow Einstein's advice and not use the concept. Saves endless useless discussion about terminology.

Following majority usage among working physicists, since mass is the inertia of a body measured at rest, since light cannot be at rest it has no mass.

However boxes CONTAINING light can be at rest and part of their inertia can be due to the light which they contain. The sun is soaked full of light even to its very core and that light (which has zero mass) contributes mass, inertia, gravitational attractiveness, etc. to the sun.

In other words the notion of mass prevailing in modern physics is not additive-----which is tough for some people to accept. So they have this irresistible urge to try to get people to change the way they talk so that mass can be more of an alias for energy and have the additivity that we associate with energy.

I'm for the simplest least ambiguous use of words----getting mass aligned with what most physicists mean by it.

I also appreciate when at least some types of quantity can have simple operational meanings, without a lot of theory mixed up in them.

Force can be measured purely electrically by a device called the "watt balance", which is kind of interesting. Maybe it is more primitive than mass.

Thank you for your efforts and this great explanation. Realy I did not wanted a primitive definition of mass, I only was remembering my old logic teacher when he told me that "when you are going to define the concept A you must not include the word A in the definition". Do you understand me?

From now when I read mass I will think in the "invariant mass-mass at rest"

Then answering the initial question, the mass of photons are 0

Dissident Dan
If mass is "the inertia of the body at rest", there are several problems. Firstly, there is no absolute "at rest". Motion is relative. Secondly, a photon at rest has never been observed, so how can you say that it has 0 mass?

How do we measure mass, and what purpose does the concept have, other than in inertia/momentum-qualities that a photon exhibits?

Can it be said that a photon has mass when it is localized, or briefly localized? Perhaps all mass is localized photons.

Originally posted by jcsd
Photons have zero mass.

Wrong - It has zero *proper mass*

Originally posted by jcsd
relativistic mass is not the same as mass and is hardly ever used.

Wrong. Relativistic mass is just another name for mass. When the term "mass" is used it means one of two things - "proper mass" or "relativistic mass" and the later is closed to being mass than the former since it retains all the properties associated with mass.

Pmb

Originally posted by jcsd
Not really, because mass that is invariant under a Lorentz transformation is a much more useful defintion than one that isn't. The term 'mass' means invariant mass only.

As far as proper mass being more useful - that's a matter of usage - i.e. for what problem is being solved. And even then it's a matter of point of view since different people sovle the same problem in different ways.

And "invariant mass" is not what people mean when they use mass. That's just plain wrong. In almost every case the author will simply say what he means by the word "mass" and then use it as such. If it's not exlained like that then one can tell by the context. And it
also depends on the journal. Mass means relativistic mass in almost all cases in the American Journal of Physics while in Physical Review D it means proper mass in almost all cases. If you go online to a place like FermiLab then it might mean relativistic mass. One only has to look to find counter examples to your claim. Examples are all over the place. Invariant mass is important as quite useful but does not have a well defined meaning in general. For example: th term "invariant mass" (aka rest mass aka proper mass) has liitle meaingin for several particles moving in an EM field. And its quite easy for people to make mistakes if they think strictly in terms of proper mass. For example: If you asked someone if a moving particle weighs more than the same particle at rest then they're likely to say no. And that's the wrong answer. Weight increases as a body moves faster since the mass increases (no. Not proper mass. Passive gravitational mass = relativistic mass = inertial mass = just plain 'mass')

Note: Weight W = mg is defined as the magnitude of the supporting force required to supoort a particle in a gravitational field where g is the local acceleration of gravity

Pmb

Gold Member
Originally posted by pmb
Wrong. Relativistic mass is just another name for mass. When the term "mass" is used it means one of two things - "proper mass" or "relativistic mass" and the later is closed to being mass than the former since it retains all the properties associated with mass.

Pmb

I'm afraid your very wrong, 'mass' always means invariant mass, the idea of relativistic mass as 'mass' went out the window a very long time ago.

There are reasons for this for example when talking about the Chanderskar limit, relativistic mass is a completely useless defintion.

Yes some pop-sci books do occasionally muddy the water in this way, but when a scientists says mass he means invariant/rest/proper mass.

Originally posted by jcsd
I'm afraid your very wrong, 'mass' always means invariant mass, the idea of relativistic mass as 'mass' went out the window a very long time ago.

Sorry to disappoint you but that's quite far from the truth. You've gotten the wrong idea somewhere along the line. There are many new relativity texts which clearly use the concept - some heavily. In fact one of the most prominent relativists, i.e. Wolfgang Rindler, use this concept in his new text, published in 2001. Many universities do as well. The Chanderskar limit, as I recall, is an inherent property and as such it would be incorrect to refer to is as anything other than rest mass. And just because you've never found relativistic mass to be useful - in NO way implies that everyone does - That's quite far from the truth.

And when I say that it's used I don't mean in pop-sci books. I mean at the undergraduate and graduate level texts in both special and general relativity. And I also mean recent texts too. And I aslo mean in physics journals.

Pmb

Gold Member
PMB, you must of learned your physics about 20 years ago because 'mass' these days means exclusively invariant mass, you will simply not find a recently published paper that refers to relativistic mass as 'mass'.

Gold Member
Here's an artilce discussing the use of the term 'mass':

http://www.weburbia.demon.co.uk/physics/mass.html [Broken]

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Isotope
Excuse my idiocy, but would photons, although they must go at the speed of light, were stopped or slowed, would they have mass? Since they go so fast, length-contraction would effect them alot. What I'm saying is, does length-contraction cause photons to lose all mass, or would they possibly have some while fixed in a position?

Gold Member
A photon can't be in a rest frame or indeed any frame where it's not traveling at c, so talking about photons slowing or stopping (in case someone mentions it I'm aware of the experiments but that's not photons being slowed that's a light pulse) is pointless, that said as all their energy is kinetic they have a rest mass of zero.

Length contraction doesn't cause any lose in mass and doesn't affect photons anyway.

clicky
Mass is a resistence to acceleration. Therefore everything that creates effects due to a change of its velocity, including light photons, should have a mass.

Pusshing relativity too hard leads to paradoxes - like length shrinking creates massless photons.

Gold Member
Originally posted by clicky
Mass is a resistence to acceleration. Therefore everything that creates effects due to a change of its velocity, including light photons, should have a mass.

Pusshing relativity too hard leads to paradoxes - like length shrinking creates massless photons.

Photons can't change velocity, so they can't. The big problem with relativistic mass is that it's different for different observers.

Ah... is the definition of mass really that complex? How is it not simply "how much is there"? How does a change of position alone change mass? If photons are a form of energy... wouldn't that mean they would have to have some kind of mass, because theoretically, matter and energy are interchangeable, but you simply get a lot of energy from a certain amount of matter? Basically.. If some fuel source was somehow converted into 100% light, that light it gave off would have to have mass, because the fuel it started out as also had mass.

Originally posted by jcsd

What difference does it make when I learned physics? The fact is that mass is often defined in different ways

..because 'mass' these days means exclusively invariant mass, ..

This is incorrect.

...
you will simply not find a recently published paper that refers to relativistic mass as 'mass'.

This is also incorrect.

I'd like to know how you got this impression? You don't seriously think that you actually know what all physics articles in all journals by all authors use do you?

All you have to do is to look in a physics journal to see. The American Journal of Physics is a goopd example.

For example: In the paper "An elementary derivation of E = mc^2," Fritz Rhorlich, Am. J. Phys. 58(4), April 1990 uses the term "mass" to refer to what you're calling "relativistic mass" and yet there is no use of that term. Adn Rohrlich is a well known relativist.

Pete

Originally posted by jcsd
Here's an artilce discussing the use of the term 'mass':

http://www.weburbia.demon.co.uk/physics/mass.html [Broken]

Yes. I'm well aware of this FAQ. But I don't know why you posted it. It clearly states

Sometimes people say "mass" when they mean "relativistic mass", ..

And you're saying that is 100% wrong - correct?

Here's an example of why it's useful to think in terms of this usage of mass: Suppose there is a uniform gravitational field, in frame S, parallel to the z-axis. The acceleration of gravity at z = 0 is g. A particle is sliding smoothly in the z = 0 plane with velocity v. What is the weight of the particle? Now supose that, instead of being in frame S, you're in frame S' moving relative to S where S' is the frame in which the particles is nov moving. What is the weight of that particle in S'?

Take a look at Fermi Lab's website
Some people thought, this formula is ugly, and they decided to introduce a new mass, called the dynamic mass M, defined by

M=m/sqrt(1-v^2/c^2)*c^2

and then the Einstein's formula will look nice again,

E=Mc^2.

This trick will make it easier to use many of the fundamental formulae from classical mechanics in Einstein's theory of relativity, just by simply exchanging the rest mass m for the dynamical mass M. ( Also it is easy to show, that for very low speeds, compared to the speed of light, m=M.)
http://www.fnal.gov/pub/inquiring/questions/accel_mass.html
One effect is that particles with mass acquire a "relativistic mass" equal to their mass at zero velocity (called the rest mass) divided by the square root of ( 1 minus (particle velocity/speed of light)squared ). So effectively a particle gets more and more mass and is therefore harder and harder to speed up further. So hard that you can't ever reach the speed of light. If you look at the equation, you see that if the particle velocity were to equal the speed of light, then you would compute a "relativistic mass" of the rest mass divided by zero. Something divided by zero is infinitely large.
http://www.fnal.gov/pub/inquiring/questions/accel_obj.html
To accelerate an object so its mass is increased by 1% then gamma, the "time dilation factor" will be simply 1.01. That is equivalent to accelerating the mass to a velocity of 14% of the speed of light or 42,000 km/sec.

A 10% increase in mass corresponds to a gamma of 1.10 or a velocity of 42% of the speed of light.

Pete

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Gold Member
Originally posted by pmb
What difference does it make when I learned physics? The fact is that mass is often defined in different ways
It makes a difference because relativistic mass was used years ago, now it isn't, this gives me the impression that you studied physics several decades ago.

This is incorrect.

This is also incorrect.

I'm sorry these are both correct statements, relativitic mass is an almost redunant concept these days.

I'd like to know how you got this impression? You don't seriously think that you actually know what all physics articles in all journals by all authors use do you?

All you have to do is to look in a physics journal to see. The American Journal of Physics is a goopd example.

For example: In the paper "An elementary derivation of E = mc^2," Fritz Rhorlich, Am. J. Phys. 58(4), April 1990 uses the term "mass" to refer to what you're calling "relativistic mass" and yet there is no use of that term. Adn Rohrlich is a well known relativist.

Pete

No I don't, but I do know what is standard terminology and what is not.

This question comes up in the context of wondering whether photons are really "massless," since, after all, they have nonzero energy and energy is equivalent to mass according to Einstein's equation E=mc2. The problem is simply that people are using two different definitions of mass. The overwhelming consensus among physicists today is to say that photons are massless. However, it is possible to assign a "relativistic mass" to a photon which depends upon its wavelength. This is based upon an old usage of the word "mass" which, though not strictly wrong, is not used much today. See also the Faq article Does mass change with velocity?.

The old definition of mass, called "relativistic mass," assigns a mass to a particle proportional to its total energy E, and involved the speed of light, c, in the proportionality constant:

m = E / c2. (1)

This definition gives every object a velocity-dependent mass.

The modern definition assigns every object just one mass, an invariant quantity that does not depend on velocity. This is given by

m = E0 / c2, (2)

where E0 is the total energy of that object at rest.

The first definition is often used in popularizations, and in some elementary textbooks. It was once used by practicing physicists, but for the last few decades, the vast majority of physicists have instead used the second definition. Sometimes people will use the phrase "rest mass," or "invariant mass," but this is just for emphasis: mass is mass. The "relativistic mass" is never used at all. (If you see "relativistic mass" in your first-year physics textbook, complain! There is no reason for books to teach obsolete terminology.)

http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/photon_mass.html

Gold Member
Originally posted by pmb
Yes. I'm well aware of this FAQ. But I don't know why you posted it. It clearly states

And you're saying that is 100% wrong - correct?
This is correct some basic level textbooks and popsci explanations.

Here's an example of why it's useful to think in terms of this usage of mass: Suppose there is a uniform gravitational field, in frame S, parallel to the z-axis. The acceleration of gravity at z = 0 is g. A particle is sliding smoothly in the z = 0 plane with velocity v. What is the weight of the particle? Now supose that, instead of being in frame S, you're in frame S' moving relative to S where S' is the frame in which the particles is nov moving. What is the weight of that particle in S'?
the problem is you change refernce frames the relativitic mass changes so it's not that useful, weight is diferent from mass anyhow.

These are very basic explantions aimed at the general public, not at scientists.

It makes a difference because relativistic mass was used years ago, now it isn't, this gives me the impression that you studied physics several decades ago.

Well you're incorrect. Although I started college in the early 80s I wasn' much interested in relativity until the mid 90s.

I'm sorry these are both correct statements, relativitic mass is an almost redunant concept these days.
Its not redundant at all. Its a pure fact depending on who one chooses to define mass. You can write p = gamma*m*v or you can write p = mv - in either case relativistic mass is there - its "gamma*m" in the first case and m in the second case. And you're claiming that relativistic mass is not used at all by anyone - that's just wrong. It is used. Why would you think otherwise? One only need look to see. You have an incorrect notion what is "standard" terminology. This is highly dependant on the particular person and what they find useful. Some physicists use it almost exclusively while others don't. But the relativity literature is full of this notion of mass and I'm not talking about older text as I've said.

So where did you get this impression from?

Pmb

Gold Member
Originally posted by pmb
Well you're incorrect. Although I started college in the early 80s I wasn' much interested in relativity until the mid 90s.

Its not redundant at all. Its a pure fact depending on who one chooses to define mass. You can write p = gamma*m*v or you can write p = mv - in either case relativistic mass is there - its "gamma*m" in the first case and m in the second case. And you're claiming that relativistic mass is not used at all by anyone - that's just wrong. It is used. Why would you think otherwise? One only need look to see. You have an incorrect notion what is "standard" terminology. This is highly dependant on the particular person and what they find useful. Some physicists use it almost exclusively while others don't. But the relativity literature is full of this notion of mass and I'm not talking about older text as I've said.

So where did you get this impression from?

Pmb

So do you haven't any formal training in relativity then?

'mass' is defined as rest mass these days. I'd like to know which physicists use 'relativitic mass' as a definiton for mass, I've never met one. Even the concept of relativitic mass isn't used much these days.

Originally posted by jcsd
the problem is you change refernce frames the relativitic mass changes so it's not that useful, weight is diferent from mass anyhow.
So what? That's relativity for you. Mass changes with speed. Electic and magnetic fields change with speed. Length changes with speed. The lifetime of a neutron changes with speed. The intensity of a gravitational field changes with speed etc. etc. etc.

re - weight - Weight is intimately related to mass. In fact the passive gravitational mass M is defined according to weight as W = Mg.

BTW - Why did you ingnore my question?

These are very basic explantions aimed at the general public, not at scientists.

Wrong. Why would you think they'd do that? If you wouldn't explain it that way they why would you think others would?

Gold Member
Originally posted by pmb
So what? That's relativity for you. Mass changes with speed. Electic and magnetic fields change with speed. Length changes with speed. The lifetime of a neutron changes with speed. The intensity of a gravitational field changes with speed etc. etc. etc.

re - weight - Weight is intimately related to mass. In fact the passive gravitational mass M is defined according to weight as W = Mg.

BTW - Why did you ingnore my question?

Wrong. Why would you think they'd do that? If you wouldn't explain it that way they why would you think others would?

Yes but rest mass is more useful as it tells you how to work out the relatvistic mass in a different reference frame. Weight and mass are two different things. I ignore the question, as it involves a gravitational field, which should properly be described by GR.

Imagine a simlair situation that you are traveling at a certain velocity past a neutron star, though if you measure the Chanderskar limit using relativistic mass you may find that the neutron star shoukld collapse into a balck hole, but it doesn't.

Originally posted by jcsd
So do you haven't any formal training in relativity then?
Where id you get that idea? That's not what I said. I said I wasn't much interested in it until the mid 90s. I studied relativity as an undergrad. In the late 90s I unofficially took a course in general relativity (Ed Bertchinger's course at MIT). Unofficial because it costs \$5,000 to take it and I didn't want to spend that kind of money if it was just for me learning it. But if you have the idea that I don't understand relativity in a strict formal sense - math and all - then you'd be mistaken.

'mass' is defined as rest mass these days. I'd like to know which physicists use 'relativitic mass' as a definiton for mass, I've never met one. Even the concept of relativitic mass isn't used much these days.
I already told you. Rohrlich was an example.

But I don't think anyone would ever write a term without specifically defining it first. And not everyone calls it
'relativistic mass.' Some call it 'inertial mass.'

So first - almost all authors will say what they mean by mass and then go ahead and use it as such

But here are some new relativity texts which use mass to mean relativistic mass. They use the term once to say what they mean and then simply call it mass .

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

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

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

There are others too such as "A short course in general relativity," Foster and Nightingale who write on page 135, explaining/deriving gravitational red shift
The loss in intrinsic energy h(f_E - f_R), while the gain in potential energy is

hf_E*GM/c^2(1/r_E - 1/r_R)

on assigning the mass hf_E/c^2 to the photon.

Then there's MTW who use the term on one occasion in their text "Gravitation" to mean E/c^2 to show that the energy-momentum tensor is symetric.

Take a crack at the weight question - it will illustrate why m = E/c^2 is meaningful as well as important.

Pmb