# The Naked Scientists Forum

### Author Topic: Does a photon have mass equivalent to its energy?  (Read 25204 times)

#### thedoc

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##### Does a photon have mass equivalent to its energy?
« on: 29/04/2012 11:22:01 »
Peep Toom  asked the Naked Scientists:

Hello Naked scientists,

On your recent show you said the photon carries energy but no mass.

If E =mc^2, and the photon transfers energy, how can it have no mass even if the mass is miniscule?

Thank you.

Peep Toom
Ballarat, Victoria, Australia.

What do you think?
« Last Edit: 02/05/2012 17:28:53 by chris »

#### yor_on

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##### Re: Does a proton have mass equivalent to it's energy?
« Reply #1 on: 30/04/2012 22:28:07 »
It's a equivalence to mass. Enough energy can spontaneously produce particles of rest mass and particles can become 'radiation'. In Special relativity a description of mass called its rest mass or invariant mass is used. That type of mass is what you can see and touch being 'at rest' relative it, having the exact same motion, or 'non motion', relative it. So that is 'rest mass', then you have photons. They are never 'at rest' relative anything. No matter how fast you go, or what 'gravity' you measure where you are, that radiation still will present you with the same invariant 'speed', called 'c'. It's the exact same constant no matter where you measure it. So a 'photon' has no 'rest frame' where you can be 'at rest' relative it, measuring.

But it has a 'energy' and a 'momentum'. And that 'energy' is a equivalence to a mass.
« Last Edit: 30/04/2012 22:30:50 by yor_on »

#### syhprum

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##### Re: Does a proton have mass equivalent to it's energy?
« Reply #2 on: 30/04/2012 22:33:04 »
Are we meant to be discusing Protons or Photons here.

#### JP

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##### Re: Does a photon have mass equivalent to it's energy?
« Reply #3 on: 01/05/2012 00:20:44 »
Are we meant to be discusing Protons or Photons here.

I believe the thread was mis-titled.  I've changed it to photons, as is mentioned in the first post.

#### Phractality

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##### Re: Does a photon have mass equivalent to it's energy?
« Reply #4 on: 01/05/2012 05:50:28 »
In Einstein's general relativity, GR, the old familiar parameters don't have the same meanings as those of classical physics. I believe this is a subtle result of the redefinition of space and time. Consequently, it is claimed that light has no mass, as mass is defined in GR. The concept of force is absent from GR. I am not comfortable applying GR, so I cannot dispute those claims. Instead, I shall demonstrate that, in classical physics, it is entirely consistent to attribute mass to a photon.

For a particle with rest mass, at non-relativistic speeds, force is defined by the formula, f = ma. Turning that around to m = f/a serves as a definition of mass. However, those formulas are not valid at relativistic speeds because it takes greater force to account for the increasing mass. A better definition of force is f = dp/dt, the rate of changing momentum, which is valid at all speeds. That formula is even valid for a photon at the speed of light.

A photon's momentum does change in response to gravity, so it does feel a gravitational force of attraction. To preserve the principal of conservation of momentum, it must be true that the mass which attracts the photon is also attracted to the photon. Thus, a photon has gravitational mass.

For particles with rest mass at relativistic speeds, dp = mdv + vdm, so f = d/dt(mdv + vdm), where m is the rest total mass, including relativistic mass.

For a photon, f = dp/dt = d/dt(E/c) = d/dt(mc), where m is the mass equivalent of E, as in E = mc^2. So a photon has inertial mass.

QED

#### Pmb

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##### Re: Does a photon have mass equivalent to it's energy?
« Reply #5 on: 01/05/2012 10:37:07 »
Peep Toom  asked the Naked Scientists:

Hello Naked scientists,

On your recent show you said the photon carries energy but no mass.

If E =mc^2, and the photon transfers energy, how can it have no mass even if the mass is miniscule?

Thank you.

Peep Toom
Ballarat, Victoria, Australia.

What do you think?
More often than not people get the answer to the mass of a photon wrong.

In general, let

p = |p| = momentum
v = speed = |v|
m = inertial mass = m = p/v
m_0 = proper mass
p = mv
E^2 = (pc)^2 + (m_0 c^2)^2
E = mc^2

P = 4-momentum = (mc, p_x, p_y, p_z)

P^2 = (m_0*c)^2

1) If the partice moves at speeds, v < c, the particle has positive proper mass and it's called a tardyon.

2) If the particle moves at speed v = c, the particle has zero proper mass and is called a luxon.

3) If the particle moves at speed v > c, the particle has imaginary proper mass and is called a tachyon.

Regarding, specifically, the mass of a photon:

m_0 = 0
v = c
p = mv = mc --> m = p/c

For a photon E = pc

For the online Physics FAQ please see  http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/photon_mass.html

For my private website treatment of the subject please see
On the concept of relativistic mass by Peter M. Brown located at  http://arxiv.org/abs/0709.0687
« Last Edit: 11/05/2012 08:36:55 by Pmb »

#### yor_on

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##### Re: Does a photon have mass equivalent to it's energy?
« Reply #6 on: 01/05/2012 10:57:39 »
I thought of using relativistic mass as a definition Pete, but what builds a relativistic mass?
Accelerations?

Take a relative motion, can I define that as a result from a acceleration? If I can then there must be a absolute rest frame from where all motion originates. Or else I will have to assume that accelerations has nothing to do with any uniform motion.

Take a relative motion again :) Where is its relative mass? name it A, then imagine two objects B and C, of different 'speeds' relative A. As they all are in a uniform motion there is no way you should be able to define who is 'absolutely moving'. To me it becomes relations in where you can assign yourself (A) to be 'still' with B and C being the ones moving. But their relative mass in a collision with A won't change, although the definition between B and C:s speed relative A is different. What I mean is that the outcome will be defined by both, in a outcome, not in their relative motions as such. Because assuming that you can define those from a single objects uniform motion as a 'absolute' presumes you know if they are 'absolutely moving' as I finds it.

The point is, without a way of defining A :) uniform motion as absolute, how do I define its momentum or relative mass? I can only do it as a relation between spheres (heh) as it seems to me, and then those definitions are only true in a outcome. I'm not discussing a acceleration for this btw.

And a photon has no accelerations as I understand it.
« Last Edit: 01/05/2012 11:03:15 by yor_on »

#### Pmb

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##### Re: Does a photon have mass equivalent to it's energy?
« Reply #7 on: 01/05/2012 11:18:11 »
I thought of using relativistic mass as a definition Pete, but what builds a relativistic mass?
Accelerations?
Morning yor_on!  What do you mean by "what builds relativistic mass?" If you are thinking of relativistic mass as requiring a change in velocity then that is not the way I see it. Newton defined mass in terms of velocity not acceleration. It was Euler who defined mass in terms of accelerationm bit Newton.
And a photon has no accelerations as I understand it.
Correct. In special relativity it ha no acceleration. But we only need p = mv, not f = ma. See "mass of luxon" at http://home.comcast.net/~peter.m.brown/sr/inertial_mass.htm

Notice that it needs no acceleration to define it's inertial mass.

#### yor_on

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##### Re: Does a photon have mass equivalent to it's energy?
« Reply #8 on: 01/05/2012 11:33:43 »
And no, I'm not saying that any of us did that. It's more of how I wonder about those things, and momentum comes into it too if we assume that I can assign a momentum to something uniformly moving without taking into consideration what 'frame of reference' I define it from. But I really though about if I could define it as a relative mass

#### yor_on

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##### Re: Does a photon have mass equivalent to it's energy?
« Reply #9 on: 01/05/2012 11:35:08 »
Ahh :) need to read up on how Euler thought there.

#### Pmb

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##### Re: Does a photon have mass equivalent to it's energy?
« Reply #10 on: 01/05/2012 12:35:32 »
Ahh :) need to read up on how Euler thought there.
There are two good books out there each written by Max Jammer. Very reasonably priced too. I highly recommend them.

#### lightarrow

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##### Re: Does a photon have mass equivalent to its energy?
« Reply #11 on: 07/05/2012 17:25:50 »
In Einstein's general relativity, GR, the old familiar parameters don't have the same meanings as those of classical physics. I believe this is a subtle result of the redefinition of space and time. Consequently, it is claimed that light has no mass, as mass is defined in GR. The concept of force is absent from GR. I am not comfortable applying GR, so I cannot dispute those claims. Instead, I shall demonstrate that, in classical physics, it is entirely consistent to attribute mass to a photon.
You can demonstrate nothing. A photon has no mass, period.
http://pdg.lbl.gov/2011/listings/rpp2011-list-photon.pdf

#### Pmb

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##### Re: Does a photon have mass equivalent to its energy?
« Reply #12 on: 07/05/2012 18:00:02 »
You can demonstrate nothing. A photon has no mass, period.
http://pdg.lbl.gov/2011/listings/rpp2011-list-photon.pdf
Hi lightarrow! How's if going?

Regarding your comment A photon has no mass, period. Do you recall our discussions elsewhere? If so then you would have seen me state that whether a photon has mass or zero-mass mass is a matter of taste. The PDF file you gave did not give zero proper mass for the photon but an upper limit of the photon's proper mass. It is experimentally impossible to prove that a quantity can be measured to be exactly zero. Physicists learned their lesson when it was finally proven that neutrinos have a finite mass. What Phractality posted in this thead in the part you quoted was very unclear since he didn't speak of what he was talking about i.e. inertial mass or proper mass. Between yor_on and myself we have together touched on these points. i.e. proper mass and inertial mass.

Good to see you again.
« Last Edit: 07/05/2012 19:03:20 by Pmb »

#### lightarrow

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##### Re: Does a photon have mass equivalent to its energy?
« Reply #13 on: 07/05/2012 20:10:57 »
Hi lightarrow! How's if going?
Regarding your comment A photon has no mass, period. Do you recall our discussions elsewhere?
Do you mean the century-long war of mass?    It will never finish, so, if I remember that or not, is the same

Quote
If so then you would have seen me state that whether a photon has mass or zero-mass mass is a matter of taste. The PDF file you gave did not give zero proper mass for the photon but an upper limit of the photon's proper mass. It is experimentally impossible to prove that a quantity can be measured to be exactly zero.
But when in physics something has measured to be zero within experimental limits, it means, in physics, that its value is zero. Physicists know very well that one day it could be measured as a non-zero value; that was the case when it was discovered a non-zero mass of neutrino, as you remind us. Should we say that physics was wrong when it stated, before of that discover, that neutrino's mass was zero? No. No because physics doesn't worry about what is *true* but about what we can measure.
No (prepared) physicist would say that photon's mass will be exactly zero even in the future; are we maybe able to see into the future?

Quote
Physicists learned their lesson when it was finally proven that neutrinos have a finite mass. What Phractality posted in this thead in the part you quoted was very unclear since he didn't speak of what he was talking about i.e. inertial mass or proper mass. Between yor_on and myself we have together touched on these points. i.e. proper mass and inertial mass.
Good to see you again.
Thank you, Pete, bye.

#### Pmb

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##### Re: Does a photon have mass equivalent to its energy?
« Reply #14 on: 07/05/2012 20:43:15 »
Should we say that physics was wrong when it stated, before of that discover, that neutrino's mass was zero?
To be precise, it was physicists who spoke of the neutrino's mass, not the science. Those who used to say it was zero were just plain wrong. A lot of physicists were lazy and thus never precise.

Let's be precise. From Fundamentals of Physics Extended 3rd. Ed. by Haliday and Resnick, (1988), page 1085,
Quote
...
Section 47-5 Beta Decay - The symbol v represents a neutrino, a massless, neutral, particle ..
...
Footnote - ... Finally, whether the mass of the neutrino is truly zero or not is subject under current investigation

If you were to look under a different text you'd see the neutrino's mass stated as zero but with nothing mentioned about the mass being truly zero. E.g. see Sears, Zemansky and Young, (1985) page 894.

It goes on. The wise man will keep in this kind of thing in mind if that information was made available to him.

As for the non-zero proper mass of the photon seek out the Proca Lagrangian and see what it's used for. Hint; there are two sections in Jackson's Classical Electrodynhamics - 3rd Ed. text about it. The PDF file you linked to is about the photon's proper mass upper bound, the proper mass upper bound that the PDF file you linked to spoke of.

A wise physicist would read those chapters of Jackson.
« Last Edit: 07/05/2012 21:18:36 by Pmb »

#### lightarrow

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##### Re: Does a photon have mass equivalent to its energy?
« Reply #15 on: 08/05/2012 07:49:20 »
...
If you were to look under a different text you'd see the neutrino's mass stated as zero but with nothing mentioned about the mass being truly zero. E.g. see Sears, Zemansky and Young, (1985) page 894.
As I wrote, the term "truly" is meaningless in physics. What counts is what we measure and nothing else.

Quote

As for the non-zero proper mass of the photon seek out the Proca Lagrangian and see what it's used for. Hint; there are two sections in Jackson's Classical Electrodynhamics - 3rd Ed. text about it. The PDF file you linked to is about the photon's proper mass upper bound, the proper mass upper bound that the PDF file you linked to spoke of.

A wise physicist would read those chapters of Jackson.
I already know about Proca equations and I've discussed a lot of times about what would happen if photon's mass were non-zero. But physics is not phylosophy, you cannot say "this is zero but perhaps not"; either you say is zero, or you say is not. If you measure it as zero, how can you reasonably say that it's not? Do you have more demonstrations about the fact is zero or about the fact it's not? In the second case, physics (= what is more accepted among all the physicists community) would say that it's not...

--
lightarrow.
« Last Edit: 08/05/2012 07:53:28 by lightarrow »

#### Pmb

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##### Re: Does a photon have mass equivalent to its energy?
« Reply #16 on: 08/05/2012 09:41:29 »
If you measure it as zero, how can you reasonably say that it's not?
Because nothing can ever be measured to have a given value with zero experimental error in the measurement.

#### MikeS

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##### Re: Does a photon have mass equivalent to its energy?
« Reply #17 on: 08/05/2012 09:52:14 »
It is easy to account for why a seemingly mass-less particle can have momentum but I am not allowed to answer it in this thread.

http://www.thenakedscientists.com/forum/index.php?topic=44008.0

Original post 2nd. para. from end.
"A photon has no mass but does have momentum."

#### Pmb

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##### Re: Does a photon have mass equivalent to its energy?
« Reply #18 on: 08/05/2012 12:27:39 »
But physics is not phylosophy, ....
Yipes! :o If you're not doing philosophy then you're not doing physics. - Fritz Rohrlich
« Last Edit: 08/05/2012 12:29:21 by Pmb »

#### lightarrow

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##### Re: Does a photon have mass equivalent to its energy?
« Reply #19 on: 08/05/2012 13:44:30 »
If you measure it as zero, how can you reasonably say that it's not?
Because nothing can ever be measured to have a given value with zero experimental error in the measurement.
But zero experimental error is mathematics or phylosophy, not physics. In physics it's zero by definition.
« Last Edit: 08/05/2012 13:46:10 by lightarrow »

#### Pmb

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##### Re: Does a photon have mass equivalent to its energy?
« Reply #20 on: 08/05/2012 13:52:23 »
Sorry but I'm bowing out at this point since the topic is gong off from the purpose of this thread.

#### lightarrow

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##### Re: Does a photon have mass equivalent to its energy?
« Reply #21 on: 08/05/2012 20:01:13 »
It is easy to account for why a seemingly mass-less particle can have momentum but I am not allowed to answer it in this thread.

http://www.thenakedscientists.com/forum/index.php?topic=44008.0

Original post 2nd. para. from end.
"A photon has no mass but does have momentum."
It is even easier: light has no mass but momentum even classically, it comes from Maxwell's equations. Momentum is not m*v, in general.

#### Pmb

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##### Re: Does a photon have mass equivalent to its energy?
« Reply #22 on: 08/05/2012 22:10:41 »
Since this is right on target for the OP's opening question it makes sense to respond to this post.

It is even easier: light has no mass but momentum even classically, it comes from Maxwell's equations. Momentum is not m*v, in general.
That's completely a matter of taste. I.e. actually p = mv is general. In fact the prominence of this is easy to find a GR/SR texts. E.g. see Gravitation by Thorne and Wheeler, W.H. Freeman & Co., (1973), page 141.
Quote
Proof that stress-energy tensor is symmetric

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

T^j0 = (energy flux)

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

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

= (momentum density) = T^0j
Notice that, since MTW use units where c = 1, the authors use the general relation E = M to obtain energy density = mass density. A comprehensive list of textual examples can found under my website under Relativistic Mass at http://home.comcast.net/~peter.m.brown/ref/relativistic_mass/relativistic_mass.htm. This list demonstrates that GR and texts , mostly published in the last 10-15 years, uses the definition p = mv. The list also provides a list of notes used at university SR and GR courses.

Question to OP: Peep Tom. Are you still following this thread? I'll assume that a lack of response means that you're happy with your answer and you have no further needs on this subject.
« Last Edit: 08/05/2012 22:12:53 by Pmb »

#### Pmb

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##### Re: Does a photon have mass equivalent to its energy?
« Reply #23 on: 08/05/2012 22:27:03 »
Peep Toom  asked the Naked Scientists:

Hello Naked scientists,

On your recent show you said the photon carries energy but no mass.

If E =mc^2, and the photon transfers energy, how can it have no mass even if the mass is miniscule?

Thank you.

Peep Toom
Ballarat, Victoria, Australia.

What do you think?
During the decade 2000 to 2008 Don Koks and myself had a discussion about this topic. Don is the person who maintains the online Physics FAQ for this topic as well as others. This long discussion resulted in a change the the old FAQ resulting in the new FAQ which is at http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/photon_mass.html

It gives a clear discussion on the subject. He left a lot out but the details he left out require an extensive knowledge of tensor calculus.

#### MikeS

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##### Re: Does a photon have mass equivalent to its energy?
« Reply #24 on: 10/05/2012 05:22:56 »
A massive object has mass.  An object traveling backward in time has negative mass.  Therefor time is a necessary component for mass to have any meaning.  Anything traveling at c does not experience time therefore it cannot have mass.

"In physics, mass (from Greek μᾶζα "barley cake, lump (of dough)"), more specifically inertial mass, can be defined as a quantitative measure of an object's resistance to the change of its speed."
http://en.wikipedia.org/wiki/Mass

You can't change lights speed therefore you cannot measure its resistance to change in speed.  Therefore by definition light cannot have mass.

#### The Naked Scientists Forum

##### Re: Does a photon have mass equivalent to its energy?
« Reply #24 on: 10/05/2012 05:22:56 »