Does a photon have mass equivalent to its energy?

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Offline thedoc

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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 »

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Offline 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 »
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Offline 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.
syhprum

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Offline 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.

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Offline 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
Imagination is more important than knowledge. Einstein

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Offline 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
See also http://home.comcast.net/~peter.m.brown/sr/inertial_mass.htm
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 »

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Offline 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 »
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Offline 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.

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Offline 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
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Offline 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.
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Offline 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.

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Offline 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

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Offline 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 »

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Offline 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.

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Offline 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 »

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Offline 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 »

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Offline 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.

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Offline 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.

Please see
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."

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Offline 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 »

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Offline 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 »

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Offline 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.

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Offline 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.

Please see
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.

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Offline 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 »

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Offline 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.

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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.

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Offline Pmb

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Re: Does a photon have mass equivalent to its energy?
« Reply #25 on: 11/05/2012 02:36:34 »
A massive object has mass.  An object traveling backward in time has negative mass. 
I'm curious. Where did you get this idea that a particle traveling backward in time has negative mass? I've decided to study Tachyon's in parallel to my study of Dark Matter. The dynamics relations are given by

E = m_0c^2/sqrt( 1 - b^2), p = m_0v/sqrt( 1 - b^2 )

If the particle is moving superluminally then b>c and therefore sqrt(b^2 - 1) is real. This can be written as

E = uc^2/sqrt( b^2 - 1), p = uv/sqrt( b^2 - 1)

where m_0 = iu. In the above equations we have the follow identities; b = v/c, m = iu where i = sqrt(-1), m_0 and u are real numbers where the magnitude is the proper mass of the particle.

The source article that I'm learning about tacyhon's is the following is the famous article
Quote
Possibility of Faster-Than-Light Particles, G. Feinberg, Phys. Rev. 159(5), 25 July 1967
We consider the possibility of describing, within the special theory of relativity, particles with spacelike four-momentum, which therefore have velocities greater than that of light in vacuum. The usual objections to such particles are discussed, and they are found to be unconvincing within the framework of relativistic quantum theory. A quantum field theory of noninteracting, spinless, faster-than-light particles is described. The field theory is Lorentz invariant, but must be quantized with Fermi statistics. The associated particle theory has the property that the particle number is not Lorentz-invariant, and the no-particle state is not Lorentz-invariant either. Never the less, the principle of relativity is satisfied. The Lorentz invariance implies a relation between emission and absorption processes, in contradiction to the usual case. Some comments are made about the problem of introducing interactions into the field theory. The limiting velocity is c, but a limit has two sides.
There is no room for the mass of the particle to be negative.

You can't change lights speed therefore you cannot measure its resistance to change in speed.  Therefore by definition light cannot have mass.
You have incorrectly used the flawed definition of mass wherein mas is supposed to be related to force and acceleration, i.e. mass is not defined as the m in F = ma. The m as defined here is known as the Euler definition of mass. The correct definition of mass is the m in p = mv. This is how Newton defined it in his Principia and how most SR texts have it right (e.g. p = mv and F = dp/dt). The correct definition of mass is that uised by Newton, of course, but also by Weyl. See

http://home.comcast.net/~peter.m.brown/sr/inertial_mass.htm

Notice Figure #1.

This definition is found throughout all of the well written, scholarly, articles in Newtonian and relativistic articles. i.e.

http://home.comcast.net/~peter.m.brown/ref/mass_articles/mass_articles.htm

See references under References to Journal Articles on the Concept of Mass in Relativity in web page
http://home.comcast.net/~peter.m.brown/sr/sr.htm

As I keep saying , this is how mass is properly defined throughout the classical physics literature (classical physics by definition includes Newtonian physics as welll as relativity. Merely disagreeing with me by stating that I'm wrong cannot be considered a logical proof of any sort.
« Last Edit: 11/05/2012 14:29:57 by Pmb »

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Re: Does a photon have mass equivalent to its energy?
« Reply #26 on: 11/05/2012 08:38:49 »
I thought of using relativistic mass as a definition Pete, but what builds a relativistic mass?
Accelerations?
No. I rewrote my first response to this thread. Please check it out.

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 is 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 acceleration for this btw.

A photon can accelerate by the way. It does so by scattering off, say, an electron  as in Compton Scattering. The magnitude of the photon's velocity remains constant. It's the change in direction that changes, which means that velocity changes, i.e. the photon accelerates.
« Last Edit: 11/05/2012 13:56:45 by Pmb »

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Re: Does a photon have mass equivalent to its energy?
« Reply #27 on: 11/05/2012 08:46:55 »
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.
In relativity space and time are not redefined. Phractality has mentioned "old familiar parameters" but has not defined. I no of no familiar parameter in GR that has changed.
...old familiar parameters don't have the same meanings as those of classical physics.
Both SR and GR are considered to be part of classical physics so this claim cannot be true. What is not classical physics is quantum physics and herein defines the divide.

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Offline Pmb

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Re: Does a photon have mass equivalent to its energy?
« Reply #28 on: 11/05/2012 09:13:14 »
In Einstein's general relativity, GR, the old familiar parameters don't have the same meanings as those of classical physics.
Classical Physics consists of Newtonian Mechanics, Special Relativity (SR) and General R elativity (GR). In either SR or GR neither space nor time are redefined. There is no distinction between "old parameters" and anything else since there is no distinction between Newtonian mechanics and relativistic mechanics when it comes to any parameters.

...old familiar parameters don't have the same meanings as those of classical physics.
Both SR and GR are considered to be part of classical physics so this claim cannot be true. What is not classical physics is quantum physics and herein defines the divide.

Consequently, it is claimed that light has no mass, as mass is defined in GR.
The definition of mass didn't change when SR & GR came along.

The concept of force is absent from GR.
This is an invalent assertion. The only thing that happened to gravitational force when GR came along was that it was postulated that gravitational force and inertial force have the same character.
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.
[/quote]
If I recall correctly the notion of the mass of light was already around before relativity made its apperance.

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.
That relation forms what is known as Euler's definition of mass. It was not Newton's definition of mass. Newton's definition, as we;; as Weyl's definition of mass is defined through the relation p = mv. For more on this please see my posts above.

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.
F = dp/dt has always been the definition. f = dp/dt can only be said to be consistent for relativity because p = constant making f = 0 which is consistent.

A photon's momentum does change in response to gravity, ...
That is not true. The momentum of a photon changes as it travel throughs the gravitational field.

For particles with rest mass at relativistic speeds, ...
A better term is proper mass. The term "rest mass" can't be applied to a photon because a photon is never at rest. That's why the more appropriate term is proper 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.
A photon has inertial mass through its definition p = mv = mc or m = p/c = E/c^2 since E = pc for particles with zero proper mass.

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Offline MikeS

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Re: Does a photon have mass equivalent to its energy?
« Reply #29 on: 11/05/2012 09:34:38 »
A massive object has mass.  An object traveling backward in time has negative mass. 
I'm curious. Where did you get this idea that a particle traveling backward in time has negative mass?.

Perhaps I should have said that "an object traveling backward in time has negative mass" relative our perspective or time frame.

If matter and antimatter should prove to be gravitationally repulsive (the jury is still out on that one) then mass can be considered to have positive mass and antimatter to have negative mass.  This is the same as them existing in reversed time frames.  They both have positive mass in their own time frame but negative relative each other.

Positive gravity (mass) exist for objects that share the same time frame.  Their futures lie together.
Negative gravity (mass) exists for objects that exist in reversed time frames.  Their futures lie apart.
« Last Edit: 11/05/2012 10:11:49 by MikeS »

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Offline MikeS

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Re: Does a photon have mass equivalent to its energy?
« Reply #30 on: 11/05/2012 10:42:14 »
A massive object has mass.  An object traveling backward in time has negative mass. 
I'm curious. Where did you get this idea that a particle traveling backward in time has negative mass?
You can't change lights speed therefore you cannot measure its resistance to change in speed.  Therefore by definition light cannot have mass.
You have incorrectly used the flawed definition of mass wherein mas is supposed to be related to force and acceleration, i.e. mass is not defined as the m in F = ma. The m as defined here is known as the Euler definition of mass. The correct definition of mass is the m in p = mv. This is how Newton defined it in his Principia and how most SR texts have it right (e.g. p = mv and F = dp/dt). The correct definition of mass is that uised by Newton, of course, but also by Weyl. See

http://home.comcast.net/~peter.m.brown/sr/inertial_mass.htm

Notice Figure #1.

This definition is found throughout all of the well written, scholarly, articles in Newtonian and relativistic articles. i.e.

http://home.comcast.net/~peter.m.brown/ref/mass_articles/mass_articles.htm

See references under References to Journal Articles on the Concept of Mass in Relativity in web page
http://home.comcast.net/~peter.m.brown/sr/sr.htm

As I keep saying , this is how mass is properly defined throughout the classical physics literature (classical physics by definition includes Newtonian physics as welll as relativity. Merely disagreeing with me by stating that I'm wrong cannot be considered a logical proof of any sort.

p = mv

If you reverse time, then velocity becomes negative.  If velocity is negative then mass is negative (from our perspective).


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Offline lightarrow

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Re: Does a photon have mass equivalent to its energy?
« Reply #31 on: 11/05/2012 11:17:01 »
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.
An electron has mass m = 9*10-31 kg; it moves at v = 299,792,457.99 m/s. How much is it its momentum?

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Offline Pmb

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Re: Does a photon have mass equivalent to its energy?
« Reply #32 on: 11/05/2012 12:30:28 »
p = mv

If you reverse time, then velocity becomes negative.  If velocity is negative then mass is negative (from our perspective).
So what? Change in direction of velocity is always interpreted as change in direction of momentum. Why should this be any different?

The v in the expression p = mv is not velocity. It's speed. The p in that expression is not the particle's momentum, it is the magnitude of the particle's momentum.

If you take v out of equation p = mv and plop in -v it means that you'ved changed the direction of the particle with the expected change in change in direction of the particle's momentum. When I write the equation p = mv it is assumed that the reader understands that the real meaning is

|p| = m|v|

where m is inertial mass, not proper mass. Changing the direction of velocity results in m|-v| = m|v| = mv and therefore

p = mv

An electron has mass m = 9*10-31 kg; it moves at v = 299,792,457.99 m/s. How much is it its momentum?
The velocity you gave is faster than light (FTL). I know that no tachyon has ever been observed and thus know that an electron has never been observed traveling FTL. I'm just refreshing myself on tachyons (it's been close to 15 ytears since I've first studied them- I need a refresher!) by the way, if an electron is created traveling v > c then the following follows.

Let b = v/c and u = proper mass of electron = 9*10-31 kg. Plug into

p = uv/sqrt( b^2 - 1) = magnitude of momentum

where u = proper mass. You now have your answer. I'm curious. May I ask why you asked?
« Last Edit: 11/05/2012 14:35:43 by Pmb »

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Offline lightarrow

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Re: Does a photon have mass equivalent to its energy?
« Reply #33 on: 11/05/2012 21:20:02 »

An electron has mass m = 9*10-31 kg; it moves at v = 299,792,457.99 m/s. How much is it its momentum?
The velocity you gave is faster than light (FTL).
What do you mean? c = 299,792,458 m/s.

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Offline Pmb

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Re: Does a photon have mass equivalent to its energy?
« Reply #34 on: 11/05/2012 21:33:29 »
Lightarrow. What was the purpose of asking the electrons's momentum since that's basic relativity?

The reason for my mistake must be some sort of problem causing my ADD in effect making me see the speed of the electron being less than light rather than it being greater than the speed of light. I'm guessing here of course. One has to expect that when one is asking a person why they made a particular mistake.
« Last Edit: 11/05/2012 23:55:10 by Pmb »

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Offline Phractality

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Re: Does a photon have mass equivalent to its energy?
« Reply #35 on: 11/05/2012 22:14:27 »

An electron has mass m = 9*10-31 kg; it moves at v = 299,792,457.99 m/s. How much is it its momentum?
The velocity you gave is faster than light (FTL).
What do you mean? c = 299,792,458 m/s.
Correct. We no longer measure the speed of light because meters and seconds are defined by the speed of light, which is now exactly 299,792,458 m/s by definition. That number came about as a result of older definitions of meters and seconds, which are no longer valid.
299,792,457.99 m/s / 299,792,458 m/s = 0.9999999999666 c
That makes the relativistic gamma = 122432
So the electron's inertial mass,
m 1.22 * 105) * (9*10-31) kg 1.1 * 10-25 kg, and its momentum is
mv (1.1 * 10-25 kg) * (2.998 * 108 m/s)  3.3 * 10-17 kgm/s.
Imagination is more important than knowledge. Einstein

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Offline Pmb

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Re: Does a photon have mass equivalent to its energy?
« Reply #36 on: 11/05/2012 23:48:04 »

An electron has mass m = 9*10-31 kg; it moves at v = 299,792,457.99 m/s. How much is it its momentum?
The velocity you gave is faster than light (FTL).
What do you mean? c = 299,792,458 m/s.
Correct. We no longer measure the speed of light because meters and seconds are defined by the speed of light, which is now exactly 299,792,458 m/s by definition. That number came about as a result of older definitions of meters and seconds, which are no longer valid.
299,792,457.99 m/s / 299,792,458 m/s = 0.9999999999666 c
That makes the relativistic gamma = 122432
So the electron's inertial mass,
m 1.22 * 105) * (9*10-31) kg 1.1 * 10-25 kg, and its momentum is
mv (1.1 * 10-25 kg) * (2.998 * 108 m/s)  3.3 * 10-17 kgm/s.
Good show sir!

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Offline Pmb

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Re: Does a photon have mass equivalent to its energy?
« Reply #37 on: 12/05/2012 00:05:05 »
299,792,457.99 m/s / 299,792,458 m/s = 0.9999999999666 c
That makes the relativistic gamma = 122432
What method did you use to calculate gamma? My calculator does not have that many significant places. Do you have a better calculator? Used another method of calculation than the calculators basic functions?

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Offline Phractality

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Re: Does a photon have mass equivalent to its energy?
« Reply #38 on: 12/05/2012 06:20:53 »
299,792,457.99 m/s / 299,792,458 m/s = 0.9999999999666 c
That makes the relativistic gamma = 122432
What method did you use to calculate gamma? My calculator does not have that many significant places. Do you have a better calculator? Used another method of calculation than the calculators basic functions?
I used Wolframalpha.com. You have to learn a few tricks, like adding .0000000001 to a number to force higher precision, and don't use commas within a number. The syntax takes some learning.
 
Imagination is more important than knowledge. Einstein

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Offline Pmb

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Re: Does a photon have mass equivalent to its energy?
« Reply #39 on: 12/05/2012 13:54:08 »
You have to learn a few tricks, ....
Can you show me exactly what you did in this particular case? It would be of great help. I'm going to be doing a lot of relativity and will be dpoing a lot of gama function calculations and would like to know how to do it. It would be greately appreciated.

I see lightarrow never answered my question.

Yo! lightarrow. You out there? I'm still curious as to why you asked that question.
Pete
« Last Edit: 12/05/2012 14:28:23 by Pmb »

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Offline Phractality

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Re: Does a photon have mass equivalent to its energy?
« Reply #40 on: 12/05/2012 18:32:29 »
Can you show me exactly what you did in this particular case? It would be of great help. I'm going to be doing a lot of relativity and will be dpoing a lot of gama function calculations and would like to know how to do it. It would be greately appreciated.
When you click on the link I gave you, note the input box near the top of the page. I typed in "relativistic gamma (299792457.99000000001 m/s)" and clicked "enter". Then I copied the url from my address window and pasted it into the hyperlink with the title "Wolframalpha.com". Most of the stuff on that page is irrelevant. The answer I was looking for is near the bottom.
Quote

Lorentz factor γ:

 
Input value:

 
velocity | 2.9979245799×10^8 m/s  (meters per second)

 
Result:

 
relativistic gamma 122432.116
With your mouse over the result box, click the "A" icon to get copyable plain text.
 
Until recently, Wolframalpha was totally free. They now offer a professional version for a fee, and they frequently remind you that you don't have it.
EDIT: In this case, I didn't have to tack on the extra zeros and one. I've gotten into that habit because I frequently get a result of "0" or "1". For example:
An input of "299792457.99 m/s"
yields "1 c".
An input of "299792457.99000001 m/s"
yields "0.9999999999666436 c", as well as
"Relativistic factor gamma from gamma = (1-v^2/c^2)^(-1/2):
 | 122432".
Have fun playing with this new toy. It's a scientific calculator on steroids!
Relativity is just one of its many uses.
In many cases, you can enter the name of a parameter instead of the value. For example: You can enter "population of New York City / surface area of Earth"; it returns "0.01603 people per square kilometer".
Another thing you need to know: Use the notation "1.3e7", rather than "1.3 * 10^7".
P.S.: I just did some exploring at Wolframalpha and found a shortcut to the problem at hand. I could have input
"relativistic momentum electron, 299792457.99 m/s".
It returns
"momentum | 3.344×10^-17 kg m/s  (kilogram meters per second)".
« Last Edit: 12/05/2012 19:13:59 by Phractality »
Imagination is more important than knowledge. Einstein

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Offline lightarrow

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Re: Does a photon have mass equivalent to its energy?
« Reply #41 on: 12/05/2012 20:46:52 »

An electron has mass m = 9*10-31 kg; it moves at v = 299,792,457.99 m/s. How much is it its momentum?
The velocity you gave is faster than light (FTL).
What do you mean? c = 299,792,458 m/s.
Correct. We no longer measure the speed of light because meters and seconds are defined by the speed of light, which is now exactly 299,792,458 m/s by definition. That number came about as a result of older definitions of meters and seconds, which are no longer valid.
299,792,457.99 m/s / 299,792,458 m/s = 0.9999999999666 c
That makes the relativistic gamma = 122432
So the electron's inertial mass,
m 1.22 * 105) * (9*10-31) kg 1.1 * 10-25 kg, and its momentum is
mv (1.1 * 10-25 kg) * (2.998 * 108 m/s)  3.3 * 10-17 kgm/s.
Wrong. Electron's mass = 9.1*10-31 kg.
Your mass is no longer used by most of the physicist community. When we say "mass" it means "invariant mass" (or "proper mass").

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Offline lightarrow

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Re: Does a photon have mass equivalent to its energy?
« Reply #42 on: 12/05/2012 20:52:14 »
Lightarrow. What was the purpose of asking the electrons's momentum since that's basic relativity?
To show the readers that momentum is not m*v, because in that example the result is much greater than that.
Of course m is the mass.
(The term "mass" means invariant mass only, no ambiguity).

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Offline lightarrow

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Re: Does a photon have mass equivalent to its energy?
« Reply #43 on: 12/05/2012 20:59:18 »
I see lightarrow never answered my question.
[:)]
Pete, I have a private life. You are not 24 hours in front of the computer, are you? [;)]

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Offline Pmb

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Re: Does a photon have mass equivalent to its energy?
« Reply #44 on: 12/05/2012 23:17:57 »
Quote from: lightarrow
Pete, I have a private life. You are not 24 hours in front of the computer, are you? [;)]
This is one of those questions which serve no real purpose other than to entertain the poster. Sorry la, not interested in that kind of ow brow humor.

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Offline Pmb

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Re: Does a photon have mass equivalent to its energy?
« Reply #45 on: 12/05/2012 23:37:08 »
Wrong. Electron's mass = 9.1*10-31 kg.
Your mass is no longer used by most of the physicist community. When we say "mass" it means "invariant mass" (or "proper mass").

Phractality - lightarrow doesn't know what he's talking about on this point. I happened to have stopped by MIT to visit someone whose class I was hoping to sit in that semester. He wasn't going to teach it that semester. However I have a copy of his class notes. The notes area as follows
Quote
Lecture Notes 7
Black-Body Radiation And the Early Universe
...
We are perhaps not used to thinking of electromagnetic radiation as having mass, but it is well-known that radiation has energy density. If the energy density is denoted u, then special-relativity implies that the electromagnetic radiation has a mass density rho given by

(7.3)     rho = u/c^2

To my knowledge nobody has ever actually "weighed" electromagnetic radiation in any way, but the theoretial evidence in favor of (7.3) is overwhelming - light does have mass.
The author of these notes is Dr. Alan H. Guth. Guth is right. I am right. etc, etc, etc. You, lightarrow, are not right. When you come back and repeat that you're right and the world agrees with is simply an ignorant response. Feel free to keep making tis claim world over. But please stop badgering me with it. What do I have to do or say to convince you to stop it?

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Offline Geezer

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Re: Does a photon have mass equivalent to its energy?
« Reply #46 on: 13/05/2012 00:51:42 »
Pmb - In this forum it is unacceptable to say that a member "doesn't know what he's talking about". That is a personal attack.

Please do not do that again.

There ain'ta no sanity clause, and there ain'ta no centrifugal force ćther.

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Offline Pmb

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Re: Does a photon have mass equivalent to its energy?
« Reply #47 on: 13/05/2012 04:21:11 »
Pmb - In this forum it is unacceptable to say that a member "doesn't know what he's talking about". That is a personal attack.
I'll refrain from speaking of him at all in the future if he stops harassing me and those like me. Otherwise it is so much better to leave an injust forum rather than live in the midst of injustice.

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Offline Geezer

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Re: Does a photon have mass equivalent to its energy?
« Reply #48 on: 13/05/2012 05:01:42 »
Well yes, but then again, no.
There ain'ta no sanity clause, and there ain'ta no centrifugal force ćther.

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Offline MikeS

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Re: Does a photon have mass equivalent to its energy?
« Reply #49 on: 13/05/2012 08:16:51 »
 rho = u/c^2

Vacuum energy is explained by this article.
http://www.astro.ucla.edu/~wright/cosmo_constant.html

The article uses the analogy of evacuating a cylinder.  Evacuating the cylinder costs energy.  This seems to be only true if the cylinder has air pressure on the outside pushing the piston in.  If the same experiment were to be done in a vacuum, the only energy required would be to overcome the apparatus friction.  As a demonstration of vacuum energy, it seems to be totally lacking.