[stevewillie (OP)]

Special Relativity (SR)says that the mass of a particle will increase with its velocity according to the Lorentz transformation. Photons have no rest mass but photons always travel at light speed. General Relativity (GR)states that gravity can bend a light beam, and this has been observed. GR explains this in terms of the geometry of spacetime. Quantum mechanics (QM) proposes the graviton as the carrier of the gravitational force. As such, it interacts with particles with mass. However it's clear from E=mc^2, it seems that if m=0, photons have no 'energy' at light speed or energy equivalent mass. If rest mass is zero, it seems photons cannot acquire mass by virtue of moving.       

[labview1958]

Photons seldom travel at light speed. The c in Einstein equation is an impossibility. There is no 100% vacuum. For example photons travel slower in glass in comparison with space.

[stevewillie (OP)]

Photons seldom travel at light speed. The c in Einstein equation is an impossibility. There is no 100% vacuum. For example photons travel slower in glass in comparison with space.

I've argued this point myself with others and lost. The reason, which I accept, is that in the near vacuum of deep space, there is macroscopic distance between atoms and light travels at c in the intervals. Also photons in deep space have a small probability of interacting with a free atom, ion or alpha particle over long distances.

My question was the equation E=mc^2 would seem to indicate that photons have no energy at  light speed because m is zero at any speed. This does not prevent light from being affected by gravity under GR, but it does raise the question of how photons interact with the gravitons of the Standard Model.

[lightarrow]

Special Relativity (SR)says that the mass of a particle will increase with its velocity according to the Lorentz transformation. Photons have no rest mass but photons always travel at light speed. General Relativity (GR)states that gravity can bend a light beam, and this has been observed. GR explains this in terms of the geometry of spacetime. Quantum mechanics (QM) proposes the graviton as the carrier of the gravitational force. As such, it interacts with particles with mass. However it's clear from E=mc^2, it seems that if m=0, photons have no 'energy' at light speed or energy equivalent mass. If rest mass is zero, it seems photons cannot acquire mass by virtue of moving.       

1. Mass doesn't vary with speed.
2. Not only general relativity says that gravity bends a light beam, newtonian mechanics does it too.
3. Gravitons don't exist yet, since an accepted quantum theory of gravity doesn't exist yet.
4. Photons do have energy, regardless of the fact they have mass or not.
5. GR says that gravity acts on energy too, not only mass, and that energy too generates gravity.

[stevewillie (OP)]

       
1. Mass doesn't vary with speed.

[/quote]

OK. Let's say total energy varies with velocity. Nevertheless if you substitute '0' for mass in the equation E=mc^2, you get 0 energy. How should we interpret this result? 

[lightarrow]

1. Mass doesn't vary with speed.

OK. Let's say total energy varies with velocity. Nevertheless if you substitute '0' for mass in the equation E=mc^2, you get 0 energy. How should we interpret this result? 

Simple: because that equation is valid ONLY at zero velocity.
You have to use this one:

E² = (cp)² + (mc²)².

if m = 0 (e.g., photons) then E = cp; photons do have momentum (even classical light) so they have energy.

[stevewillie (OP)]

Lightarrow,

Ok. But the classical definition of momentum is p=mv. So how do we deal with mass in this equation? Do we take 'm' as equal to the mass equivalent of the photon's energy which is given a priori?

[lyner]

Lightarrow,

Ok. But the classical definition of momentum is p=mv. So how do we deal with mass in this equation? Do we take 'm' as equal to the mass equivalent of the photon's energy which is given a priori?

Your 'classical' definition of mv of momentum refers to objects with mass. For an electromagnetic wave, the momentum of a photon is h/λ where λ is the wavelength and h is the Planck constant.

Using these two definitions describes accurately what happens when photons run into objects - so it works. (Light pressure etc).)

[stevewillie (OP)]

Lightarrow,

Ok. But the classical definition of momentum is p=mv. So how do we deal with mass in this equation? Do we take 'm' as equal to the mass equivalent of the photon's energy which is given a priori?

Your 'classical' definition of mv of momentum refers to objects with mass. For an electromagnetic wave, the momentum of a photon is h/λ where λ is the wavelength and h is the Planck constant.

Using these two definitions describes accurately what happens when photons run into objects - so it works. (Light pressure etc).)

sophiecentaur

Yes. I thought there needed to be a way to derive instead of measure the energy equivalent of mass for a photon: so in a classical Length, Mass, Time dimensional system:

Energy: (L^2)(M)(T^-2)
Action: (L^2)(M)(T^-1)
Wave length: (L)

(L^2)(M)(T^-1)(L^-1)= (L)(M)(T^-1) which are dimensions of classical momentum. So like you say, it works when you translate energy to mass equivalent.

Thanks

[labview1958]

Does the compton effect prove that light behaves like a particle? Thus photons have mass.

[lightarrow]

Does the compton effect prove that light behaves like a particle? Thus photons have mass.

Compton effect shows that light behaves as particles (and, however, about this I will have discovered a very interesting thing, but it's too long to post here, now). This has nothing to do with particle's mass.

[labview1958]

A particle must have mass. Thus photons have mass.

[lightarrow]

A particle must have mass.

The red colour means mistake.

[Physics Dilettante]

Not only general relativity says that gravity bends a light beam, newtonian mechanics does it too.

Apologies for coming late to the table, but would you elaborate? I thought Newtonian mechanics predicts no bending, and that's why Campbell's solar-eclipse measurements in 1922 were such an important confirmation of GR.

[lightarrow]

Not only general relativity says that gravity bends a light beam, newtonian mechanics does it too.

Apologies for coming late to the table, but would you elaborate? I thought Newtonian mechanics predicts no bending, and that's why Campbell's solar-eclipse measurements in 1922 were such an important confirmation of GR.

The bending depends on the field, not on the mass; so, regardless of the mass, all other factors being equal, the bending is the same; it means that you can put m = 0 in the equations and the amount of bending doesn't vary. It turns out that General Relativity predicts a bending which is double the one predicted by newtonian mechanichs, and this is exactly what they discovered in 1922.
(Don't ask me why is exactly 2 times, this is a mistery I still haven't unveiled, because I don't have much knowledge of GR).

[Physics Dilettante]

The bending depends on the field, not on the mass; so, regardless of the mass, all other factors being equal, the bending is the same

So in this respect, Newtonian mechanics and GR are in agreement.

It turns out that General Relativity predicts a bending which is double the one predicted by newtonian mechanichs, and this is exactly what they discovered in 1922.

That's really interesting because Einstein revised GR shortly before the 1922 eclipse when he realized an earlier version's prediction was off by 1/2. So it turns out that earlier prediction would have matched Newtonian mechanics' and, had he not made the change, the eclipse results would have resolved nothing. (They would have embarassed Einstein, though.)

Apparently, this Newtonian prediction wasn't recognized at the time, i.e., the thinking then was that any bending at all would be a violation. So it's a more recent refinement (?)

[lightarrow]

The bending depends on the field, not on the mass; so, regardless of the mass, all other factors being equal, the bending is the same

So in this respect, Newtonian mechanics and GR are in agreement.

It turns out that General Relativity predicts a bending which is double the one predicted by newtonian mechanichs, and this is exactly what they discovered in 1922.

That's really interesting because Einstein revised GR shortly before the 1922 eclipse when he realized an earlier version's prediction was off by 1/2. So it turns out that earlier prediction would have matched Newtonian mechanics' and, had he not made the change, the eclipse results would have resolved nothing. (They would have embarassed Einstein, though.)

Apparently, this Newtonian prediction wasn't recognized at the time, i.e., the thinking then was that any bending at all would be a violation. So it's a more recent refinement (?)

History of Gravitational Lensing:
http://relativity.livingreviews.org/open?pubNo=lrr-1998-12&page=node2.html

<<In the year 1911 - more than a century later - Albert Einstein [50]directly addressed the influence of gravity on light (``Über den Einfluß der Schwerkraft auf die Ausbreitung des Lichtes'' (``On the Influence of Gravity on the Propagation of Light'')). At this time, the General Theory of Relativity was not fully developed. This is the reason why Einstein obtained - unaware of the earlier result - the same value for the deflection angle as Soldner had calculated with Newtonian physics. In this paper, Einstein found

α = 2GM/c²R = 0.83  arcsec

for the deflection angle of a ray grazing the sun (here M and R are the mass and the radius of the sun, c  and G  are the velocity of light and the gravitational constant, respectively)

...

With the completion of the General Theory of Relativity, Einstein was the first to derive the correct deflection angle α  of a light ray passing at a distance r  from an object of mass M  as

α = 4GM/c² *1/r

where G is the constant of gravity and c is the velocity of light. The additional factor of two (compared to the ``Newtonian'' value) reflects the spatial curvature (which is missed if photons are just treated as particles). With the solar values for radius and mass Einstein obtained [51, 52]:

α = 1.74 arcsec

It is common wisdom now that the determination of this value to within 20% during the solar eclipse in 1919 by Arthur Eddington and his group was the second observational confirmation of General Relativity [47] and the basis of Einstein's huge popularity starting in the 1920s. (The first one had been the explanation of Mercury's perihelion shift.) Recently, the value predicted by Einstein was confirmed to an accuracy better than 0.02%>>

[Physics Dilettante]

This is all even more interesting than the "bending vs. no bending" version of the story I've always heard before.

I think it's a stretch for the text to call the Mercury shift an "observational confirmation" because Einstein was aware of it. The agreement he found was a major reason he believed his final equations were correct. If we accept this characterization of the shift, any data he considered would have to be added to the list.

Thanks very much for the lesson and the pointer to the article, lightarrow!

[lightarrow]

This is all even more interesting than the "bending vs. no bending" version of the story I've always heard before.

I think it's a stretch for the text to call the Mercury shift an "observational confirmation" because Einstein was aware of it. The agreement he found was a major reason he believed his final equations were correct. If we accept this characterization of the shift, any data he considered would have to be added to the list.

Thanks very much for the lesson and the pointer to the article, lightarrow!

Yes, it is really very interesting. For example:
<<There actually were plans to test Einstein's wrong prediction of the deflection angle during a solar eclipse in 1914 on the Russian Crimea peninsula. However, when the observers were already in Russia, World War I broke out and they were captured by Russian soldiers [32]. So, fortunately for Einstein, the measurement of the deflection angle at the solar limb had to be postponed for a few years.>>
He was even lucky!

[yor_on]

You are all very knowledgeable here.
How do you look at QFT:s view of the photon?
http://en.wikipedia.org/wiki/Quantum_field_theory

" in QFT, the photon does not have any concept of classical momentum - it only has an 'interaction in the field theory.' The interesting thing, in QFT, of the graviton interaction is that the fermion recoils along the incoming vector of the graviton - a mirror reversal of the photon interaction. The graviton interaction in that way is the opposite of the photon interaction. These particles only 'interact within the quantum fields,' and NOT according to any classical concepts like momentum, and they are 'field communicators.'"

I wonder as I believe that the photon do have a momentum:)
Can both ideas coexist?