May be?

How this change should be done?

The next problem is that according to Newton's gravity law a body could attracts unlimited other objects and it grows to infinity, this is also unrealistic, because it is not compatible with experience. In addition, in relativistic Newton second law the infinite speed of classical mechanics is replaced by the infinite mass. This review should solve both of these problems that have been done in the following article.

Dear Thierry

Thank you for interesting comment and your mention about c'=c(1+-GM/r)

Please see following links, then correct me if I am wrong on page 31

http://www.speed-light.info/speed_of_light_variable.htm

page 7 of:

http://myweb.rz.uni-augsburg.de/~eckern/adp/history/einstein-papers/1911_35_898-908.pdf

Dear Thierry

I appreciate your attention and trying on this issue, thank you so much.

Hi Hossein, what an impressive paper! I made this same comment following the paper.

It would take an entire course to do justice to the paper, so I have only two points:

1. Yes, I do think that relativity changes Newton's second law, and I'll take a short stab at it further down, but without involving subatomic particles!

2. I have a problem with the energy equivalence you make in the paper, and possible ramifications on the mass of a photon.

Start with number 2.

E = mc² is the equivalence of mass and energy, for particles that have mass. If that mass is completely converted to energy, you get E amount of energy.

E = hf (sorry, can't create the right Greek letters in this) is the energy of a massless photon, and it depends on frequency rather than mass.

This is the part that bothers me:

mc² = hf, so therefore it must follow that m of photon = hf/c²

My interpretation is quite different. My interpretation of that equivalence is simply that IF a photon with a certain energy E were instead a particle with mass, THEN the mass of that particle would have to be m. But this does not mean that the photon's mass is m.

You can make similar arguments in classical physics. For example, you can equate the potential energy of an object at height above ground of h, E = mgh, with the potential energy of a compressed spring, E = 1/2 kx². But that does not mean that the spring must have a particular mass, governed by solving m = 1/2 kx² / gh. No. It simply says that the energy in that compressed spring WOULD BE equivalent to the energy of such a mass, so many meters above ground. "Would be" is not the same as "is." In fact, no telling what the mass of that spring might be. Spring constant is not governed by mass. It depends on the material the spring is made of.

However I don't think that changes anything materially in your paper. All the same considerations seem to apply regardless. It's just a matter of interpreting whether anything suggests that photons really do have mass.

On the matter of Newton's second law, F = ma, yes, that must be changed to accommodate relativity. Clearly, since F = ma would easily move the mass m at speeds greater than c.

Mass is now a function of speed, so you rewrite the equation to show this, and to incorporate the Lorentz transformation. Using mr to mean mass at rest,

F = ma = m(v) dv/dt = mr * (1 /sqr(1 - v²/c²)) * dv/dt

Correcting my previous answer, which was going to computing momentum, this equation suggests that as v tends to c, the force required to accelerate this mass tends to ∞.

That is, for a massive particle.

Dear Albert

Thank you for interesting and useful detail, I appreciate your attention on this issue.

The great problem is which you have concluded " Suggesting that as v2 tends to c, the force required tends to ∞. "

As you wrote, in quantum mechanics, only moving photon has mass as follows from the Einstein formula E=mc^2.

Consider that massless particle is an assumption.

David J. Griffishs. (1987). Introduction to Elementary Particles. Wiley-VCH Verlag GmbH, online available, https://notendur.hi.is/~ath68/griffiths.pdf, page 90.

Physicists have not stopped on assumption of massless. There are more attempts were made to clarify the photon masslees in theoretical and experimental physics. There are good theoretical reasons to believe that the photon mass should be exactly zero, there is no experimental proof of this belief.

S. A. Hojman, et. at. (2013). Closing a Window for Massive Photons. Hindawi Publishing Corporation, Volume 2013, Article ID 967805 .

These efforts show there is an upper bound on the photon mass, although the amount is very small, but not zero. The tight experimental upper bound of the photon mass restricts the kinematically allowed final states of photon decay to the lightest neutrino and/or particles beyond the Standard Model.

J. Heeck. (2013). How Stable is the Photon? arXiv:1304.2821v2 .

Theories and experiments have not limited to photons and graviton will also be included. For gravity there have been vigorous debates about even the concept of graviton rest mass.

A. S. Goldhaber, et. at. (2010). Photon and Graviton Mass Limits. arXiv:0809.1003v5

Let's close this window and open new window on concept of particles mass. There are two kinds of particles in physics;

1- Some particles like the photon move only with the speed of light c, in all inertial reference frames. Let’s call these kinds of particles as Never at Rest condition particles (NR-particles).

2- Other particles like the electron always move with the speed v

As it was shown the photon has a mass. See the link

Article The substantial model of the photon

Dear Sergey

Thank you for interesting link.

I hope more success for you.

Let me add out of context that the global-c Schwarzschild metric changes the depth of Einstein's cloth around a gravitating body.

Accelerator physics has done a very large amount of high energy testing and discovered energy momentum relationships that are not in doubt among the majority of researchers.

Newton laws are not relativistic and cannot be modified empirically in a satisfactory way.

Relativistic mass is a obsolete concept not supported by main stream scientists in recent times, because the gravity of high energy particles did not increase in accelerators or their exit beams. The modern concept is non linear momentum which comes from the accelerator equations of energy and momentum.

Dear Jerry

Of the first I must thank you that remind me "Relativistic mass is a obsolete concept not supported by main stream scientists in recent times"

Secondary, " the gravity of high energy particles did not increase in accelerators or their exit beams." Surely, it means we need to review our understanding of acceleration that is the reason why we should reconsider the relativistic Newton's second law.

Dear Jerry and Hossein:

One should not believe too easily in new "experimental facts."

I would be very skeptical about the claimed violations of special relativity.

Dear Otto

Sure, you are right that new experimental facts take very time to be accepted.

In addition, reconsidering relativistic Newton's second does not violate to special relativity, in fact it is a step to develop relativity.

Hossein, another point. If we put in doubt the massless nature of photons, then we also put in doubt the Lorentz transformation. And if we accept the possibility that photons have some mass, however small, then we also allow for matter to travel faster than c, however little faster than c.

I thought time dilation had been experimentally demonstrated. A massive proton would really complicate these matters. Of course, nothing mandates that an equation as simple as the Lorentz transformation HAS to be correct always. Just as Newton's equations have been shown not to be correct always (even if they are very close at lower speeds).

Dear Albert

You have mentioned a considerable point, but consider that " Lorentz transformation" has formulated for observable phenomena, There are two other spaces in nature, one is virtual space-time and another is non-obvious space. For detail see:

https://www.researchgate.net/publication/270276224_Interactions_Between_Real_and_Virtual_Spacetimes?ev=prf_pub

Article Interactions Between Real and Virtual Spacetimes

I prudently withhold judgment until told the simplest example.

Dear Otto

Your caution is logical and understandable. Thank you.

Dear Hossein Javadi and other debaters,

I agree that Newton's second law in the SR needs explore. The question is whether in SR the second law of dynamics changes significantly or cosmetically. I have already met with extremely different opinions. On the one hand, it can be said that in the notation of four-vectors, the equation is similar. However, in three-dimensional terms, the current form of this equation is getting really complicated.

You wrote an important sentence:

"Surely, it means we need to review our understanding of acceleration that is the reason why we should reconsider the relativistic Newton's second law." (Hossein Javadi)

Indeed, based on the definition of acceleration, I managed to unify the three-dimensional second law in the Newton version and in the Einstein version. Details are described in the preprint:

Preprint Defining of three-dimensional acceleration and inertial mass...

Greetings to all physicists who still ask questions.

Dear Grzegorz

Thank you for comment and interesting mentions.

In my opinion, according to the structure of the particle, it must review.

The +/- sign in formula (61) of Yours article seems unnecessary. The standard sign is +, and the derivative dE/dt knows when it is positive and when it is negative. With the + sign, Yours formula is equivalent to the derivative form (rate form) of Newton's second law F = dp/dt.

Is equation (61) Yours reinterpretation of Newton's second law of dynamics?

I understand that the use of the minus sign (-) is for negative frequency particles. However, it is not clear why this sign does not appear in the mass multiplied by acceleration?

There is no answer regarding formula (61), so I will develop my statement yet.

A minus sign (-) in equation (61), assuming relativistic energy E, leads to a longitudinal mass equal to gamma*(2-gamma^2)*m. This means that the mass of the particle is zero at 0.71c and its negativity above this speed.

Therefore, it is not known what is happening above this speed and whether the equation makes sense. Nevertheless, the search for the classical Dirac/Hawking/Unruh particle equation with a negative frequency is interesting.