As far as this equation can describe real physical phenomena it must be called real and not only a pure mathematical concept. But I´m afraid that this discussion will again divide maths and physics. Phycisists use mathematical algorithms with great benefit.

BTW: The variation of mass (often called relativistic mass) with velocity of a particle has been left in theoretical physics. In the moment the description of particles with energy and momentum is preferred. The dependence on velocity is described with the Lorentz factor, the only mass is the rest mass m0. But there are a lot of applications where the conventional concept with increasing mass is working. Why should we leave it?

Both!

Period!

It's a physical reality. It can be measured with charged particles at relativistic velocities in magnetic fields. It would also be taken into account in the design of particle accelerators. This url describes a beautiful experiment where it was measured:

http://www.dickinson.edu/download/downloads/id/55/apparatusmeasuremass

Dear Marzouk Lajili,

Mainstream claims that the inertial increase of mass with velocity is a physical reality. But in fact, there exist extremely fast spinning stars in the universe that don't fall apart. If the inertial mass would really augment with velocity, these stars would immediately fall apart.

The accelerations in particle accelerators are provided by static electromagnetic fields. It is not the increase of inertial mass, but the difficulties to make accelerate a particle with EM fields in the same inertial frame that cause the limitation of accelerating the particles. In fact, the EM fields are retarded with the speed of light themselves...

In fact, the Lorentz Transformations can only account for an increase of the kinetic energy, not for the physical mass increase.

Reference: Oleg Jefimenko: see link

http://www.amazon.com/Electromagnetic-Retardation-Theory-Relativity-Classical/dp/0917406257/ref=asap_bc?ie=UTF8

As far as this equation can describe real physical phenomena it must be called real and not only a pure mathematical concept. But I´m afraid that this discussion will again divide maths and physics. Phycisists use mathematical algorithms with great benefit.

BTW: The variation of mass (often called relativistic mass) with velocity of a particle has been left in theoretical physics. In the moment the description of particles with energy and momentum is preferred. The dependence on velocity is described with the Lorentz factor, the only mass is the rest mass m0. But there are a lot of applications where the conventional concept with increasing mass is working. Why should we leave it?

Dear Dr. Marzouk Lajili,

as dr.Olsen suggests, there are experimental aspects. To evaluate the interrelationships between theory and experiment I suggest to have a look at:

http://en.wikipedia.org/wiki/Kaufmann%E2%80%93Bucherer%E2%80%93Neumann_experiments

This is an interesting question and it can lead to discussions between mathematicians and physics.

Roughly speaking, it seems that someone can ask more generally: whether Special relativity is a pure mathematical concept?;

What is relation between Special relativity and the flat spacetime known as Minkowski space?

I read in the literature that ''Special relativity implies a wide range of consequences, which have been experimentally verified, including length contraction, time dilation, relativistic mass, mass–energy equivalence, a universal speed limit, and relativity of simultaneity. It has replaced the conventional notion of an absolute universal time with the notion of a time that is dependent on reference frame and spatial position. Rather than an invariant time interval between two events, there is an invariant spacetime interval.

As Galilean relativity is now considered an approximation of special relativity that is valid for low speeds, special relativity is considered an approximation of general relativity that is valid for weak gravitational fields, i.e. at a sufficiently small scale and in conditions of free fall''. General relativity incorporates noneuclidean geometry in order to represent gravitational effects as the geometric curvature of spacetime, special relativity is restricted to the flat spacetime known as Minkowski space. A locally Lorentz-invariant frame that abides by special relativity can be defined at sufficiently small scales, even in curved spacetime.

In mathematics definitions and axioms have a special role. It seems that a mathematician can have difficulties with definitions of concepts like mass, the rest mass, time etc .

In further discussions, I will tray to contribute with more details.

Mass variation with velocity is a physical theory described by a mathematical equation. The particular equation was derived mathematically, but followed a physical interpretation that depends upon the constancy of the speed of light.

The claim is made that Einstein proved Newton wrong. Really? Newton's equations of motion are not reality, because they cannot correctly predict physical behavior at low velocity. Nevertheless, they are theoretically correct over a very wide range of velocities. Einstein's corrections at high velocity closely predict observation velocities approaching the speed of light. Are Newton's and Einstein's equations reality at appropriate velocities? They are very good theoretical descriptors. 

Mathematics is a powerful method for expressing theoretical concepts, in particular, as it allows calculation under differing circumstances. The equation is purely mathematical and contains physical units. The equation reflects the theory. Reality is experimental or observational results. There is always the possibility of altering the theory and equation. There is always a matter of interpretation. See the discussion "Is the speed of light constant."

Dera eminent researchers,

Thank you for you all for these fruitful interactions.

May be I joint my idea to our colleague J. L. Alvarez and to ask the question: Is the speed of light is the absolute velocity?

Of course it is well known that for example the phasis velocity (the group velocity of a train waves) can exceed the velocity of light, but what is the physical meaning of this?

The postulats of relavitity must they remain the same? concerning:

- the abosolute veclocity of lignt

- the fact that all mechanic lois take always the same forms in all galilen references.

The theory of relativity is based on the speed of light as the absolute velocity. There have been objections to an absolute velocity on theoretical and philosophical grounds. There are no observations that dispute an absolute velocity. Phase velocity of a wave packet is calculated to exceed the speed of light in a given medium. Tunneling events appear to be faster than light.  Nevertheless, there is no demonstration that information is transferred faster than light.

There are no incontrovertible experiments that demonstrate relativity and none that disprove relativity. It seems a good path is to accept relativity as the best description and keep a skeptical eye on everything.

"There are no incontrovertible experiments that demonstrate relativity and none that disprove relativity. It seems a good path is to accept relativity as the best description and keep a skeptical eye on everything."

This is a contradictio in se. You cannot prove that my sister has blue eyes. You cannot disprove it. So, let us accept that she has blue eyes and be skeptical about any other opinion!

Of course, SR has not been proven. Its sole application is the Compton effect which don't even require the postulates! Sagnac, the GPS and the several paradoxes are extremely incriminating!

So, the SR interpretation must be abandoned! The Lorentz Transformation must be reinterpreted in a real physical environment, and not in a pure mathematical environment.

@Thierry De Mees

SR has been proven millions of times - not only in the GPS system (why that should be incriminating I don't know) but also in simple TV sets (the old ones with the cathode tube) - without taking relativistic effects into account --> blurry picture on the TV, with relativistic effects --> sharp picture (as the electrons with up to several tens of keV, they are already relativistic). Furthermore time dilatation was measured during high speed flights with high precision atomic clocks.

Then in the life time of muons reaching the earth from outer space - only with relativistic effects you can explain the measured data and so forth...

So, there is a vast number of experiments, which prove SR.

@ Johannes

"they are already relativistic"

"Being relativistic" is just saying: they go fast. That isn't a proof of SR.

"time dilatation was measured during high speed flights"

In fact, the Hafele–Keating experiment has proven nothing about SR, since the two clocks flying in different directions didn't retard the same way. With SR it should be identical but it wasn't.

"the life time of muons"

The muon life time explanation is a speculation, a guess, not a proof, because it can perfectly be explained differently.

So, where is the proof and where is the use of SR?

@ Hanno

"As far as this equation can describe real physical phenomena it must be called real and not only a pure mathematical concept."

That is not correct. SR is described as a purely geometrical concept without real physical events. If it described the observation of an electomagnetic event at a certain velocity from a distance, that would allow to get a physical handhold.

As a matter of fact, such a calculus results in the Lorentz Transformations, but avoids paradoxes and wrong conclusions. This exercice has been made by the genius Prof. Oleg Jefimenko in his book on electromagnetism and relativity.

In this book is describes how different kinds of electromagnetic events result in different time retardations, depending from the electromagnetic device. With SR, there is only one type of time retardation, which is obviously wrong.

It also shows that the mass increase is not real.

Indeed there exist very fast spinning stars. If their mass would increase with velocity, they would immediately fall apart. That is not happening.

@Thierry,

I´m not so convinced like you. I know a lot of physical examples for the application of SR, which show perfect results and agreement. Try to ask a CERN colleques about his opinion to SR and GR. Or try to construct a relativistic cyclotron without taking the Lorentzfactor increase of momentum, or try to understand the gravitational effect on light which you can observe during special astronomic events. And, and, and...

BTW: I don´t worry to differentiate "mathematical concept", mathematical method, physical formula so long as these ideas help to solve and describe physical problems.

Dear Johannes Gruenwald,

Absolutely there isn't any doubt concerning the two manifestations of SR : time dilatation and the length contaction. But, with mass variation we need more clarifications. The mass definition contains two main physical meanings: the inertia and the abundance/ scarcity of material in a given body.  How these intrinsic physical characteristics could be affected by velocity?

Shall we when dealing with SR or GR problems introduce the graviton as a quasi particle related to the gravitational feild as it is the case of the photon for the light wave, the phonon for the vibration wave, the magneton and so on...?

@ Hanno

I understand your position: we can manage with what we have. However, you get an amalgam of bits and pieces: SR, GR, Minkowski, Schwarzschild, Kerr, Perturbation Theory,... and you use one or more or combined to get proven what you want.

But still you get stuck with the disc galaxies and the too high temperature of clusters and need to invent dark matter.

Still, there is no explanation for very fast spinning stars that don't fall apart, spites the alleged mass increase with velocity, And, and, and.

What about a gravity theory for which the Lorentz Transformations and a true, physically founded SR are just an application, the disc galaxies and the too high temperature of clusters are just an application, very fast spinning stars are just an application? And, and, and?

Would such a theory interest you?

Dear Marzouk,

my I post a question to your last remark. Why don´t you accept the change in modern theoretical physics, where mass increase is avoided, the phycicists use instead the Lorentzfactor? By this method they can avoid problems with the inertia and as you name it "abundance/scarcity"  ie gravity. Indeed you find the mass-energy relation in many places. Have a look on the binding energies of nuclei where the mass of the single particles is always higher then the mass of the final nucleus.

Of course Thierry, I´m highly interested, but there is only a little hope to find quick solutions. And in order not to leave undone the rest of practable applications, I believe the results of SR and GR.

Dear dr. Lajili,

your interesting question entails the meaning of the term “mass”. As dr. Krieger points out, Einstein's theories of relativity are not well suited to handle the problem of abundance/scarcity of matter. To explain, if that problem is related to Archimedes' law of buoyancy (statics of macroscopic solid bodies,) it arises that the molar mass is not proportional to the molar volume, but depends in a non-linear way on the structure of chemical compounds – at constant temperature and pressure. In my opinion, the position is not to manage with what we have, but rather to discuss what one can manage within a given theoretical framework. The following paper is just to give an example.

http://philosophy.unc.edu/files/2013/10/PofSconservlawspaper.pdf

@ Marzouk Lajili:

Without being an expert in particle and accelerator physics but the relativistic increase of mass should be easy to prove/disprove: When you let two particles collide (both with a certain velocity) and you know the stopping potential (say, for two protons), you can calculate the stopping force from that and from the force the impulse (via simple integration).

So, if there is no mass increase at high velocities it should give different results as if there is a relativistc mass increase, as:

Fclass = ma = m dv/dt = m d²x/dt²

or Frel = d(mv)/dt = dm/dt v + m dv/dt = ...