Different Speaker Cable Lengths

[MrPeabody]

Given that this thread has turned into Gravity Science Review, I feel free to join the party.

The use of the term relativistic mass is quite misleading, as indeed it may iduce to think that particles do have two types of mass, what intuitively we call mass, like a stone. However, a lot of texts use simply relativistic energy and invariant mass to refer to both phenomena. As you have pointed out, Einstein established a relation between energy and mass, which is a relation between both, but this is mainly useful in the direction from mass to energy, no the inverse. I mean, you can say that a mass is equivalent to certain amount of energy, so one can determine the amount of energy that would result in the process of a mass converting into energy, like in the atomic bomb. This has the result of being able to treat both mass and energy like energy (physicists like energy). However, a certain amount of energy can't be interpreted as invariant mass in any case. They are different physical phenomena, and therefore classical physics models can't be applied to them.

Mixing different models can look interesting but it leads to unsolvable inconsistencies. This can be very instructive though, so they are worth considering. Newton's models don't have any explanation for what a photon is, it was of course unknown at that time, and there is no way to describe its motion using Newtons laws. Lets' try to follow the conjecture you propose of a photon in a Newtonian model. If a photon is a massive particle moving at the speed of light, which we assume is not a limit speed as in relativity but some very high speed, a gravitational field would exert a force to the particle, changing its trajectory and eventually reducing its speed. That however does not happen, as photons travel always at the same speed. That even could lead to the photon to stop, which again, doesn't happen. Furthermore, in this Newtonian model, the gravitational potential energy of a photon escaping from the sun would increase very quickly, but then, since the photon doesn't stop nor reduce its speed, the total amount of energy, kinetic plus potential, would be increasing overtime, which violates the energy conservation principle, unless you start adding more and more esoteric conjectures. Therefore, to keep Newton's laws alive in this conjecture, one has to admit that photons do not obey them or that photons aren't affected by the Newtons notion of gravity.

As a summary, you can regard the relativistic mass as the hypothetical mass that a massive particle should have to have the same amount of energy-mass as the photon. Also, models overlap each other, as relativity explains things that Newton's laws can't. However, it does so by completely changing the basis to interpret the natural phenomena and only keeping some very basic principles: conservation, causality, etc. Think of poor Maxwell being completely unable to explain why electrons in an atom don't lose energy by radiation and collapse, and yet his equations describe most of the electrical phenomena discussed here at ASR.

Of course, this fundamental subjects are very tricky, and I'm not an expert, so don't take my word for granted. Hope however that this encourages you to keep researching. Have fun.

Rest assured that I will not take your word for granted, or anything a little bit like that.

Instead of speaking of the "relativistic mass" of a photon, I should have used the common descriptive "effective mass". This is neither here nor there. I like the term "relativistic mass" because while Planck's equation gives the energy of a photon, it is by way of the 1905 Theory of Relativity (now known as the "Special Theory") that we know the mass equivalent for the energy. Your notion that the mass-energy equivalence is a one-way equivalence is silly.

Photons absolutely do possess mass, and the mass is exactly as I explained via the equation I obtained by the simple combination of Einstein's most famous equation with Planck's equation. The combining of these two simple equations is perfectly obvious and there is nothing the least bit incorrect about it.

As for the question of whether Newtonian gravity applies to the photon, this question is not as simple as it may seem or as we might prefer. The best answer is that it does, notwithstanding that the predicted acceleration is not correct (and notwithstanding that even though Newton had proposed the corpuscular theory of light, he wouldn't likely have thought that light would be affected by gravity because he had no understanding of the mass of corpuscles of light). The 1915 Theory of General Relativity and Newtonian theory both say that the curvature for a particle or object moving through a gravitational field does not depend on the mass of the particle or object. The curvature predicted by Newtonian gravitational theory is intrinsically incorrect for any object, not particularly so for photons. And with respect to photons, the reason that it is incorrect is unrelated to the fact that photons do not have rest mass. It is not readily apparent that the gravitational acceleration predicted by Newtonian theory applies to all objects; the reason that this is not readily apparent is that the error is only significant when the speed of the particle or object is very great. For particles moving at very high velocity, General Relativity predicts the correct curvature whereas Newtonian gravitational theory does not. It is appropriate to note that Newtonian gravitational theory is incorrect for Mercury (as I previously mentioned), as had been known for some time before Einstein came along, and which discrepancy between theory and observation was the primary impetus for Einstein's development of the General Theory. Perhaps it would make sense to say that Newtonian gravitational theory does not apply to Mercury.

 

[escksu]

Note also that photons do not always move at the same fixed speed. The constant c is the speed of light in a vacuum. If anyone ever comes up with an explanation for why photons in a vacuum move at this particular speed, that person is assured to win a Nobel Prize.

Some corrections for this. Photons do move at same fixed speed everywhere. Yes, I know light slows down in air and in mediums like glass or in water etc... But this is the effective speed.

What happens when light moves through a medium is that the photon is absorbed by an electron, the electron becomes excited state and release the photon. There is a small delay in absorbing and relasing the photon. This cycle is repeated till photon leaves the medium. This is why the photon appears to slow down. When the photon is released by the electron, its traveling at exact speed till its absorbed by another electron.

This is why I say speed is light is constant and fixed everywhere.

 

[MaxBuck]

I don't think that relativity has sweet FA to do with the original topic of this thread.

 

[xaviescacs]

Rest assured that I will not take your word for granted, or anything a little bit like that.

Instead of speaking of the "relativistic mass" of a photon, I should have used the common descriptive "effective mass". This is neither here nor there. I like the term "relativistic mass" because while Planck's equation gives the energy of a photon, it is by way of the 1905 Theory of Relativity (now known as the "Special Theory") that we know the mass equivalent for the energy. Your notion that the mass-energy equivalence is a one-way equivalence is silly.

Photons absolutely do possess mass, and the mass is exactly as I explained via the equation I obtained by the simple combination of Einstein's most famous equation with Planck's equation. The combining of these two simple equations is perfectly obvious and there is nothing the least bit incorrect about it.

As for the question of whether Newtonian gravity applies to the photon, this question is not as simple as it may seem or as we might prefer. The best answer is that it does, notwithstanding that the predicted acceleration is not correct (and notwithstanding that even though Newton had proposed the corpuscular theory of light, he wouldn't likely have thought that light would be affected by gravity because he had no understanding of the mass of corpuscles of light). The 1915 Theory of General Relativity and Newtonian theory both say that the curvature for a particle or object moving through a gravitational field does not depend on the mass of the particle or object. The curvature predicted by Newtonian gravitational theory is intrinsically incorrect for any object, not particularly so for photons. And with respect to photons, the reason that it is incorrect is unrelated to the fact that photons do not have rest mass. It is not readily apparent that the gravitational acceleration predicted by Newtonian theory applies to all objects; the reason that this is not readily apparent is that the error is only significant when the speed of the particle or object is very great. For particles moving at very high velocity, General Relativity predicts the correct curvature whereas Newtonian gravitational theory does not. It is appropriate to note that Newtonian gravitational theory is incorrect for Mercury (as I previously mentioned), as had been known for some time before Einstein came along, and which discrepancy between theory and observation was the primary impetus for Einstein's development of the General Theory. Perhaps it would make sense to say that Newtonian gravitational theory does not apply to Mercury.

Apologies for following this off topic pissing contest (quoting someone wiser than me). This is my last post on this and then I will apply myself a severe regime of abstinence. Apologies for quitting here too.

@MrPeabody, just to make sure I'm following you. You state that you can calculate the mass (m) of the photon if you know its frequency (v), in the following way:

m = h*v/c²

and then we can use Newton's laws to describe the movement of this massive photons, something like this (F = m*a):

dp/dt = h*v/c²*(d²x/dt²)

(bold means vector)

Is that what you mean? If this is so, nothing stops you from calculating the trajectory (curvature if you like) of this photons under Newton's laws (see Marion and Thornton linked below). That will allow you to eventually fill the gap in your knowledge that you explained in your first post, as you would be able to compare the Newtonian prediction vs Einstein's prediction, which is of course far more complicated to obtain analytically. I think you can use this solution and use this as a theoretical reference.

General Relativity and Newtonian theory both say that the curvature for a particle or object moving through a gravitational field does not depend on the mass of the particle

To invoke a classic, Marion and Thornton, page 182 (190 in the pdf), 2nd paragraph, and all Chapter 8 (from page 287 in the pdf). You will see that there is a mu in all deduced movement equations (section 8.4) which corresponds to the reduced mass of the two particle system, which means that the movement depends on the mass of the two particles, of course.

While the strength of the gravitational force acting on an object depends on the mass of the object, the resulting acceleration of the object is not dependent on its own mass. This is something that most everyone knows in the context of falling apples and balls dropped from the famous leaning tower. But it also applies to science demonstrations using Galileo's inclined plane, and to ballistic trajectories (which are the same for projectiles with large mass as for projectiles with small mass except for aerodynamic drag effect),

Although this is correct, it's also an approximation and one has to be careful making generalizations (the comet example). First of all because that assumes that the gravitational field is constant, which only happens in apples and trees experiments, but not in large distances with massive moving objects, like when a particle travels through space near a planet. Secondly because the masses of the two particles affect the movement, as they attract each other, and therefore this is an approximation when the mass of one of them is very small. Projectile problems on earth are described with the earth as the reference, because what we care about is only the movement of the projectile with respect to earth, but in a two particle problem in space, as the case of a massive particle deflected by a gravitational field, the reference frame is a bit more tricky, and then the masses of both particles matter, as you can see in the referenced book. Yes, you can show the mass center falls in the center of the more massive body if the other is very light in comparison, but that will be a particular approximation useful in some cases, but one can't turn this into a general statement.

Well @MrPeabody, as I promised, this passionate, ridiculous and completely out of place discussion ends up here for me, whether I'm right or wrong, whether it's fair or not, whether that means I'm out of my mind or not. Of course, you have the right and the privilege of the last word (and I assume the moderator has the right of expunging me from this land). I can't promise I'm reading it in the following days, accordingly the abstinence commitment. I can promise though that I'm not going to answer it.

It has been and it will always be a pleasure squandering my time in pointless arguments.