Photon Mass: Debunking the Myth of Zero Mass in SR Equation

[yu_wing_sin]

Photon's mass is zero?
-----------------------------------

According to the SR's equation : m=m0/√(1-v2/c2), if the photon's velocity is the speed of light, then the photon's mass should be zero in value, but recently scientists have measured the photon having mass, but I forget the very long value of the photon mass.

 

[yu_wing_sin]

But I think maybe the extreme speed of cosmos is not the speed of light, is a bit faster, thus the photon's mass just not be zero. Or the equation always has error, the actual result is a bit higher than or different to the calculation, but how can modify this equation with slight factor?

 

[yu_wing_sin]

More clear explanation,

From m=m0/√(1-v2/c2),

If we don't let the photon's mass be zero, we must have a higher speed than the speed of light to replace the c2.

.
.. therefore is,

m=m0/√(1-c2/x2)

*x is an unknown value.

 

[yu_wing_sin]

Or any other possible corrections?

 

[εllipse]

It doesn't make sense to make "the extreme speed of cosmos" something other than the speed of light because then the speed of light wouldn't be a constant. Where did you read that a photon's mass isn't zero? My guess is that either it was a crackpot website or they were talking about relativistic mass (photons have zero invariant mass). Many at this forum are against the use of "relativistic mass", and I guess this is one more example of why it shouldn't be used.

 

[yu_wing_sin]

It doesn't make sense to make "the extreme speed of cosmos" something other than the speed of light because then the speed of light wouldn't be a constant. Where did you read that a photon's mass isn't zero? My guess is that either it was a crackpot website or they were talking about relativistic mass (photons have zero invariant mass). Many at this forum are against the use of "relativistic mass", and I guess this is one more example of why it shouldn't be used.

But this link pointed out the photons have mass...
http://www.aip.org/pnu/2003/split/625-2.html

-------------------------------------------------
The content is:
Number 625 #2, February 19, 2003 by Phil Schewe, James Riordon, and Ben Stein
A New Limit on Photon Mass

A new limit on photon mass, less than 10-51 grams or 7 x 10-19 electron volts, has been established by an experiment in which light is aimed at a sensitive torsion balance; if light had mass, the rotating balance would suffer an additional tiny torque. This represents a 20-fold improvement over previous limits on photon mass.

Photon mass is expected to be zero by most physicists, but this is an assumption which must be checked experimentally. A nonzero mass would make trouble for special relativity, Maxwell's equations, and for Coulomb's inverse-square law for electrical attraction.

The work was carried out by Jun Luo and his colleagues at Huazhong University of Science and Technology in Wuhan, China (junluo@mail.hust.edu.cn, 86-27-8755-6653). They have also carried out a measurement of the universal gravitational constant G (Luo et al., Physical Review D, 15 February 1999) and are currently measuring the force of gravity at the sub-millimeter range (a departure from Newton's inverse-square law might suggest the existence of extra spatial dimensions) and are studying the Casimir force, a quantum effect in which nearby parallel plates are drawn together. (Luo et al., Physical Review Letters, 28 February 2003)
-------------------------------------------------------------

 

[cefarix]

... A new limit on photon mass, less than 10-51 grams or 7 x 10-19 electron volts, has been established by an experiment in which light is aimed at a sensitive torsion balance; if light had mass, the rotating balance would suffer an additional tiny torque. This represents a 20-fold improvement over previous limits on photon mass.

Photon mass is expected to be zero by most physicists, but this is an assumption which must be checked experimentally. A nonzero mass would make trouble for special relativity, Maxwell's equations, and for Coulomb's inverse-square law for electrical attraction. ...

That does not mean the photon has mass. The experiment was conducted to confirm that the photon indeed has zero mass. The 10-51 grams figure cited above is the accuracy of the experiment, suggesting that IF the photon did have mass, it would have to be less than 10-51 grams, otherwise the experiment would have given different results.

 

[DaTario]

Nice explanation by cefarix.

I, in turn, think that a physical entity which is able to transmit momentum (Einstein's gedanken experiment with the box) and also has energy, and also get attracted by gravitational fields deserves be interpreted as having mass. Our impossibility to measure mass in its own referential seems to be somewhat independent from the mass notion.

What is the current interpretation to the expression:

Planck's constant x frequency / c^2 ??

 

[IAN STINE]

Pair production. Positrons and electrons are often spoken of as having mass. So a photon having no mass becomes a produced pair having mass which turn into photons having no mass...! I'm getting swim-headed!

 

[EL]

Energy is conserved, not mass. Mass is just a form of energy (E=mc^2).

 

[yu_wing_sin]

That does not mean the photon has mass. The experiment was conducted to confirm that the photon indeed has zero mass. The 10-51 grams figure cited above is the accuracy of the experiment, suggesting that IF the photon did have mass, it would have to be less than 10-51 grams, otherwise the experiment would have given different results.

Quote:
"if light had mass, the rotating balance would suffer an additional tiny torque"

They set this hypothesis, but I don't know whether they had detected this, the abstract had not told. I think the limit of the experimental accuracy is not the main matter. So I am hard to judge your view on the matter photons are zero mass.

 

[Doc Al]

Quote:
"if light had mass, the rotating balance would suffer an additional tiny torque"

They set this hypothesis, but I don't know whether they had detected this, the abstract had not told. I think the limit of the experimental accuracy is not the main matter. So I am hard to judge your view on the matter photons are zero mass.

Please read the abstract that you yourself had quoted. And reread cefarix's comments. This experiment puts a lower bound on the possible mass of light than ever before, thus confirming (so far) expectations of light having zero mass.

 

[LURCH]

It may seem strange, Yu Wing Sun, but for experiments that attempt to measure the mass of light, the limit of experimental accuracy really is the main point. The reason for this can be explained historically. You see, all the best theories and models of physical law predict the mass of light to be zero. But how does one measure "zero"? All measurements so far have confirmed a result of Zero, but does that really prove anything? A sceptic could say, "the photon has mass, it's just such a small amount of mass that our current methods of measurement can't detect it".

So the problem facing the experimental researcher is that this is a valid argument, and one that is extremely hard to disprove. About the only thing they can do is to come up with more and more accurate ways of trying to measure the mass of the photon, with more and more sensitive equipment, and show that the result still comes up "Zero". Then they publish their results by saying, "I've got a new method that can detect a mass as little as x. I used it to try to measure the mass of a photon, and got no reading. Therefore, if a photon has mass, that mass must be less than x. The point that researchers are trying to verify is that we could put any number for the value of that "x", and the statement would still be true. The simple logic being that the statement:

"the mass of a photon is <x, no matter what x is"

can only be true if the mass of the photon is zero.

 

[nmondal]

Photons has momentum!

Photons has momentum!
Common misconception is that, as it has momentum, it must be having a mass.
That is untrue, as we know that any wave has a momentum!

 

[pmb_phy]

Photons has momentum!
Common misconception is that, as it has momentum, it must be having a mass.
That is untrue, as we know that any wave has a momentum!

Oy! Here we get yet once more!

It is not a "common misconception." What is a common misconception is that there are too many people who use the term "mass" to mean "proper mas."

A photon as a non-zero "relativistic mas" an zero "proper mass."

Pete

 

[Chronos]

Momentum without mass seems to be a difficult concept. If photons are not massless [in the relativistic sense], theoretical physics is in serious trouble.

 

[yu_wing_sin]

Logical view, every matter has mass, otherwise they are non-existence! Maybe in our now technologies are still unable to detect the photons' mass, but without doubts, photons were from the big bang (all mass were concentrated at it), since that, photons should be having mass.

 

[Ich]

Photons exist and have no mass.
And don´t be so quick with "logic" - example:
A system of 2 similar parallel moving photons has no mass.
A system of 2 similar antiparallel moving photons has mass 2hf.
Maybe You should first read about the meaning of "mass" in modern physics before You draw any conclusions.

 

[Juan R.]

Energy is conserved, not mass. Mass is just a form of energy (E=mc^2).

This is a common misconception.

If E=mc^2 and E is conserved (dE/dt = 0), then m is also conserved because c is just a constant => dm/dt = 0

The idea of that mass is just a form of energy "arises" from E=mc^2

but rewrite it like m = E/c^2, then energy is just a form of mass. Our current knowledge is about matter and the study of changes of energy on matter. Matter is more "fundamental" than energy.

As was admited by Feynman the more powerful idea of science is that universe is done of "atoms".

 

[pmb_phy]

Photons exist and have no mass.
And don´t be so quick with "logic" - example:
A system of 2 similar parallel moving photons has no mass.
A system of 2 similar antiparallel moving photons has mass 2hf.
Maybe You should first read about the meaning of "mass" in modern physics before You draw any conclusions.

Oh no! Not another one!. That's just a bunch of horse hockey! You learned the concept of mass wrong in "modern" physics. That's rest mass you're speakin of and not relativistic mass. When we speak of mass here some (most - hard to tell anymore) mean proper mass and some mean inertial mass, relativistic mass, etc. There's a reason you learned ir wrong but that's another story.

In you're case you're referring to the concept of the magnitude of free objects or an object which can be considered as a particle or a system which is isolated.

The more general case falls to hell if you want to define mass in the most general sense. See

http://www.geocities.com/physics_world/misc/relativistic_mass.htm

No selecctive reading please, i.e. don't skip the part which is from MTW's text that discusses it.

Notice how Argonne National Laboratory defines "mass."


http://www.neutron.anl.gov/hyper-physics/inertia.html

Massive Pete

 

[pmb_phy]

This is a common misconception.

If E=mc^2 and E is conserved (dE/dt = 0), then m is also conserved because c is just a constant => dm/dt = 0

The idea of that mass is just a form of energy "arises" from E=mc^2

but rewrite it like m = E/c^2, then energy is just a form of mass. Our current knowledge is about matter and the study of changes of energy on matter. Matter is more "fundamental" than energy.

As was admited by Feynman the more powerful idea of science is that universe is done of "atoms".

Writing mass as m = E/c² is just bad juju! Einstein showed that this expression is not generally valid in On the inertia of energy required by the relativity principle. A. Einstein, Annalen der Physik 23 (1907): 371-384.

For a much much simpler derivation please see Energy vs. Mass located at - http://www.geocities.com/physics_world/sr/inertial_energy_vs_mass.htm

and written by me. But this is standard stuff. It can be found in Rindler's 1982 Intro to SR text as well as Tolman's tex.

Pete

 

[Ich]

There's a reason you learned ir wrong but that's another story.

I don´t remember exactly where I got this from, but I´m quite sure it was Taylor/Wheeler "Spacetime Physics", 1992 ( I read the german "Physik der Raumzeit"). There they told me that one should say "mass" instead of "rest mass", because
a) that´s the only invariant quantity about mass and
b) the concept of "relativistic mass" is of little or no use.
They also declared this to be the view point of "modern physics".

In you're case you're referring to the concept of the magnitude of free objects or an object which can be considered as a particle or a system which is isolated.

Yes, I explicitly did. That was the most enlightening point of the whole book to me: m is invariant, but m(particle1+particle2) != m(particle1)+m(particle2). So eg thermal energy increases mass.

The more general case falls to hell if you want to define mass in the most general sense. See
http://www.geocities.com/physics_world/misc/relativistic_mass.htm
No selecctive reading please, i.e. don't skip the part which is from MTW's text that discusses it.

Yes, there he talks differently. I´m not too much into GR, so unfortunately I can´t judge what concept is of more use there.

Notice how Argonne National Laboratory defines "mass."
http://www.neutron.anl.gov/hyper-physics/inertia.html

I notice.
To clear things up, just replace every "mass" in my post by "rest mass". If this whole thing is about semantics, I have no problem with calling rest mass "mass", "Ruhemasse", or "not the mass pete means but the one Ich means".
If not, I´m looking forward to gain insight by understanding or even adopting Your point of view.

btw, in this thread yu_wing_sin quoted an article where they put an upper bound to the "mass" of the photon. This could hardly mean m=E/c². So my terminology is at least consistent.

Massive Pete [/QUOTE]

 

[russ_watters]

Logical view, every matter has mass, otherwise they are non-existence!

That's true, but photons are not matter!

 

[pmb_phy]

That's true, but photons are not matter!

Who says so? It certainly wasn't Einstein that said that!

Pete

 

[pervect]

Writing mass as m = E/c² is just bad juju! Einstein showed that this expression is not generally valid in On the inertia of energy required by the relativity principle. A. Einstein, Annalen der Physik 23 (1907): 371-384.

For a much much simpler derivation please see Energy vs. Mass located at - http://www.geocities.com/physics_world/sr/inertial_energy_vs_mass.htm

and written by me. But this is standard stuff. It can be found in Rindler's 1982 Intro to SR text as well as Tolman's tex.

Pete

A short comment:

m = E/c^2 can be fully and logically justified if p=0. (This is of course invariant mass, not relativistic mass). Before you get too ambitious in correcting other people's usage, remember that there are a lot of people who do NOT use "relativistic" mass and who prefer invariant mass.

 

[TheAntiRelative]

Nice explanation by cefarix.

I, in turn, think that a physical entity which is able to transmit momentum (Einstein's gedanken experiment with the box) and also has energy, and also get attracted by gravitational fields deserves be interpreted as having mass. Our impossibility to measure mass in its own referential seems to be somewhat independent from the mass notion.

What is the current interpretation to the expression:

Planck's constant x frequency / c^2 ??

Photons certainly behave like they have mass. The compton effect is probably the best example. The path of a photon is actually deviated by collision with an electron if I remember correctly. It's a billiard-ball like effect.

 

[EL]

This is a common misconception.

If E=mc^2 and E is conserved (dE/dt = 0), then m is also conserved because c is just a constant => dm/dt = 0

What I wanted to say is that the total energy of a free particle comes from both it's kinetic motion and from it's mass. In E=mc^2 I'm of course talking about the invariant rest mass (I thought everyone by this time had abandoned the ugly and easlily confusing use of relativistic mass), and E is not ment to be the total energy, just the part coming from the (invariant rest) mass of the particle.

 

[Juan R.]

Writing mass as m = E/c² is just bad juju! Einstein showed that this expression is not generally valid

If E=mc^2 is valid (WHICH WAS A PREMISE OF MY POST) then m=E/c^2 is also!

 

[Juan R.]

What I wanted to say is that the total energy of a free particle comes from both it's kinetic motion and from it's mass. In E=mc^2 I'm of course talking about the invariant rest mass (I thought everyone by this time had abandoned the ugly and easlily confusing use of relativistic mass), and E is not ment to be the total energy, just the part coming from the (invariant rest) mass of the particle.

E = mc^2 in SR, where m =/= m0, the rest mass, in general.

If E is conserved, it is, then mass is also because the proportionality.

Mass is always conserved, In fact there is no violation of mass conservation in nuclear phenomena, for example, because mass is transformed to energy, that is also a form of matter via inverse Einstein relationship.

 

[pervect]

Photons certainly behave like they have mass. The compton effect is probably the best example. The path of a photon is actually deviated by collision with an electron if I remember correctly. It's a billiard-ball like effect.

Photons have energy and momentum, but their invariant mass is zero, i.e. E^2 - (pc)^2 = 0, or E = pc.

This is usually shortened to say that photons have no mass, that they are massless particles (because their invariant mass is zero).

This is widely known, I have no idea why the question keeps popping up repeadetdly and endlessly.

 

[EL]

E = mc^2 in SR, where m =/= m0, the rest mass, in general.

If E is conserved, it is, then mass is also because the proportionality.

But the total energy of a free particle is not just mc^2 (where "m" is the rest mass, a convention I will stick to). That's unless you're in it's rest frame of course.
It is the total energy which is conserved, not mc^2.

Mass is always conserved, In fact there is no violation of mass conservation in nuclear phenomena, for example, because mass is transformed to energy, that is also a form of matter via inverse Einstein relationship.

Again, if we are talking about rest mass there are plenty of processes where mass is not conserved. Take electron-positron annihilation into photons for example.

 

[EL]

Who says so? It certainly wasn't Einstein that said that!

Pete

http://en.wikipedia.org/wiki/Matter

 

[pmb_phy]

A short comment:

m = E/c^2 can be fully and logically justified if p=0.

What is "p"? If its pressure/stress then that's correct. However you're beihng vauge about your terms. If you use E to mean inertial energy then E = K + E₀, not E = E₀ unless you're making the unstated assumption that K is always zero.

If the object is extended object then its more commplicated.

Note Pressure contributes to inertia. E.g. see Shutz's new text Gravity from the ground up. Especially at the bottom of page 192 in the section entitled The extra inertia of pressure.

Before you get too ambitious in correcting other people's usage, ..

Sorry lad but I didn't correct anybody in this thread. I stated my opinion that writing m = E/c^2 is bad juju.

... remember that there are a lot of people who do NOT use "relativistic" mass and who prefer invariant mass.

There's no accounting for taste. Most peole learned SR wrong.

Pete

 

[pmb_phy]

http://en.wikipedia.org/wiki/Matter

That's their opinion. And my opinion of them decreases evertime its referenced. Look at Einstein's 1916 GR paper

 

[pervect]

If the object is extended object then its more commplicated.

Note Pressure contributes to inertia. E.g. see Shutz's new text Gravity from the ground up. Especially at the bottom of page 192 in the section entitled The extra inertia of pressure.

I don't have the text (though I hear it's quite good) - but you are right that pressure contributes to the stress energy tensor and hence the mass of a system.

Defining the mass of an extended system as the response to an external force is however an extremely bad idea, just because of the very fact that the mass of the system does depend on the distribution of the stresses. This means that different force distributions give different masses, an unsavory state of affairs. Fortunately, there are MUCH better ways of defining the mass of an extended system than considering the response of a system to an external force. More on this later.

Sorry lad but I didn't correct anybody in this thread. I stated my opinion that writing m = E/c^2 is bad juju.

There's no accounting for taste. Most peole learned SR wrong.

Pete

E = mc^2 is perfectly fine as long as p (momentum!) is zero, and m is invariant mass. (Apparently you did nor realize that p was momentum? Or were you pulling my leg? I think you were pulling my leg - though I doubt you'll admit it.)

Thus there's no reason for people to un-learn E=mc^2, all they have to do is realize that that equation only works when p=0, and that the real equation is more like E^2 - (pc)^2 = (mc^2)^2, (when p is not zero), which can be further simplfied by using geometric units to E^2 - p^2 = m^2. And they need to know that the m in this equation is the "invariant mass".

In addition, people eventually have to learn that the total energy E of a system is not the intergal of the energy density term of the stress-energy tensor (T_00), but also does includes contribution from the pressure terms as you state.

However, given that one has the necessary condtions - an isolated system and an asymptotically flat space-time will do, the resulting system has a well defined energy E in GR, and a well defined momentum p, as well. One confusing thing is that the energy of the extended system is not just the intergal of the energy density, but includes the intergal of some of the pressure terms as well. Note well that with these (standard!) defintions of energy and momentum, in geometric units E^2 - p^2 = m^2 works for both point particles AND extended systems.

Given that a system has an energy E and a momentum P, and that these quantities transform as a 4-vectors in the appropriate asymptotically flat space-time (which they do), it's trivial to compute the invariant mass 'm' of the system, usually just called the mass. If one needs to be especially precise, the mass of a system can be sub-categorized into at least two types of mass - the ADM mass, and the Bondi mass. The ADM mass is mathematically based on the behavior of the system at space-like infinity, and includes gravitational radiation terms. The Bondi mass is mathematically based on the behavior of the system at null infinity, and does not include gravitational radiation contributions.

Usually such detail is not needed or even wanted at the introductory level. The best source for information on mass in GR is probably Wald's "General Relativity", which is not an introductory book.

 

[pmb_phy]

Defining the mass of an extended system as the response to an external force is however an extremely bad idea, just because of the very fact that the mass of the system does depend on the distribution of the stresses.

So what? This is based on your wishing to define mass as an intrinsic property of an object where there is no need to do so. In fact in general its impossible to do so. Mass is that which defines momentum an

This means that different force distributions give different masses,...

Absolutely correct.

.. an unsavory state of affairs.

The elite say that beluga caviar is quite savory ubut I find that al caviar are quite unsavory.

Fortunately, there are MUCH better ways of defining the mass of an extended system than considering the response of a system to an external force.

This I got to hear. Please keep in mind that those who have defined mass in such a way have done so as he definer of momtum. The momentum of an object is dependant of the environment its in and the details of the object.

E = mc^2 is perfectly fine as long as p (momentum!) is zero, and m is
invariant mass.

At first I did but upon reflection I realize that the statement is incorrect as it stands but correct if p = pressure. Upon further reflection I see that is wrong too. Since you're not one to make such a glaring error I assumed it was pressure. But once you read Schutz you'll see why that is incorrect. He gives an example where he calculates kinetic energy as being the definer of mass. He ends up, with (for v << c) {Note: Schutz uses E}

K = \frav{1}{2}(\rho + \frac{p}{c^2})v^2 v

This gives an inertial mass densit of \rho + p/c^2

re - " (Apparently you did nor realize that p was momentum? Or were you pulling my leg? I think you were pulling my leg - though I doubt you'll admit it.)" - Shame on you. Whenever I note an error of mine I make it my highest priority to make sure I correct myself. My response is sxplained above.

Thus there's no reason for people to un-learn E=mc^2,...

I don't see how you got from my response that this was something to be unlearned. Its place should never be forgotten since all currect appliccations I'm aware of that is 100% correct. But current applictions is not 100% of its possible concievable uses.

A hile bal I wrote an article on this entire subject. The pupose being so I woudn't have to keep getting into the same ole disucssions. Here's the article fof the topic at hand - http://www.geocities.com/physics_world/mass_paper.pdf

It'd be incorrect to dissmiss this debnate as mere semantic since the concepts and words we use detemine our thoughts and thoutht paterns.

Pete

 

[EL]

That's their opinion. And my opinion of them decreases evertime its referenced. Look at Einstein's 1916 GR paper

Well, it's just a definition. You are of course free to define "matter" however you want, but I think it is convenient to define it in the way most people do nowadays.

 

[pmb_phy]

Well, it's just a definition. You are of course free to define "matter" however you want, but I think it is convenient to define it in the way most people do nowadays.

I never chose to define it myself. It always fails at a definition. E.g. if you have Taylor and Wheeler's text read the section on mass.

Pete

 

[EL]

I never chose to define it myself. It always fails at a definition. E.g. if you have Taylor and Wheeler's text read the section on mass.

Pete

Maybe we should put up a poll about this!

 

[Sam Owen]

just a thought and no doubt many have had it before but...

...can you isolate light from Einsteins equation to show that everything is made from it by making breaking c down to distance over time ?

if not why not and if so would the answer be something like 42

 

[Ich]

after knowing the answer, please try to remember the question. "...can you isolate light from Einsteins equation to show that everything is made from it by making breaking c down to distance over time ?" certainly doesn´t make sense.

 

[Sam Owen]

sure it does...

...the only difference is you aren't me

frames and terms of reference aren't my strong points as you may have guessed...

...I'm more of a visual type of guy, pictures in my head, that sort of thing

Can you really not get the gist of what I'm asking ?

 

[Ich]

sorry, no.
Maybe later, I´m going to drink some beer :)

 

[pmb_phy]

Maybe we should put up a poll about this!

Why? It'd be a huge waste of time. Stop worrying who calls things what. Concentrate only what is measurable

 

[EL]

Why? It'd be a huge waste of time. Stop worrying who calls things what. Concentrate only what is measurable

Que? I'm worried?
I have to remind you that you were in fact the one who started worrying about the definition of "matter".
Relax for god's sake. Did you see the smiley at the end of my post?

 

[Juan R.]

But the total energy of a free particle is not just mc^2 (where "m" is the rest mass, a convention I will stick to). That's unless you're in it's rest frame of course.
It is the total energy which is conserved, not mc^2.

Again, if we are talking about rest mass there are plenty of processes where mass is not conserved. Take electron-positron annihilation into photons for example.

From special relativity

E^2 = (pc)^2 + (m₀c^2)^2

and

E = mc^2

The total energy E is conserved <=> the total mass m is also conserved because c is a constant.

As said m =/= m₀. You may be wrong about what mass is entering on general formula E = mc^2. (Your "m" is my m₀)

The formula E = m₀c^2 that you claim in some of your posts is valid only when p is zero as pervect already said.

In a pair annihilation process, precisely rest mass is transformed on energy (which is another form of mass). Total mass -or total energy- continues being constant. Precisely photons have mass (equal to total mass of initial pair annihilated), this is the reason of light bending around Sun computed from Newtonian mechanics. Since photons have mass they feel gravitation. Of course, rest mass m₀ of photons is (at least today) zero but m =/= 0 because photons travel to light velocity.

 

[Redfox]

Photon's mass is zero?
-----------------------------------

According to the SR's equation : m=m0/√(1-v2/c2), if the photon's velocity is the speed of light, then the photon's mass should be zero in value, but recently scientists have measured the photon having mass, but I forget the very long value of the photon mass.

you never know. photons are supposed to have only impuls mass (pressure of light) however lightwaves still change direction in a strong gravitational field.
I am very doubtful about relativistic formulas anyway...

 

[inha]

I am very doubtful about relativistic formulas anyway...

You mean the formulae that give results validated by thousands of experiments?

 

[EL]

As said m =/= m₀.

As I said before I am only using the invariant mass (you call it m₀, I call it m). You are unfortunately stuck in that you believe I mean relativistic mass by m.
The reason why I only use the invariant mass, and never speak about any relativistic mass is because all (ok at least all) modern texts adopt this convention. The concept of relativstic mass is an easily confusing one, and should in my opinion (and many others) not be used.
I stress it again: I am always talking about the invariant (rest) mass, and I call it just m.

By this convention photons are massless, and mass is not (in general) conserved in interactions.

 

[Sojourner01]

Does this thread need to keep banging on?