Seriously, I think there is a problem in our understanding of space-time. However, I have no answer, the paper I just pre-published contains only questions.
You can be sure that our understanding of the reality is very incomplete and all the present theories are not the last word of wisdom par example the so called 'space-time'.
The increasing mass whereas is mandatory and logical: If you accelerate an object with rest mass it accumulates energy. You have to accelerate on further accelerating the rest mass and also the accumulated energy resp. its mass equivalence. The calculation is possible by using an integral equation with zero as lower limit and c as upper limit.
There is no need for Einsteins equations resp. Lorentz-transformations. This is very cumbersome and obviously not factual (in German I would say: nicht tatsachenorientiert).
In this paper, I explained why the increasing mass and the wavelength reduction have nothing to do with the acceleration of the object. The development here is purely relativistic and that of the study of the wavelength of a particle located in a space-time more and more curved.
I do not know if you've read it, but it would have been better for me to understand what you're talking about in the rest of your message (which must surely make sense).
So, apart from "hors sujet", I do not know what to say, sorry.
Aha x) But I have no idea what it could be. And then it may become very quickly difficult to found a model on the basis of such a paradox. But if you have any ideas to solve it, you would do me a favor.
The fist thing to know is: what is the ground for the claim of a space-time realm?
Therefore we need to look at Einstein's SRT 1905 paper.
I agree for the kinematic part of the 1905 paper under conditions: it is the observation of a moving system by another system (observer), hence an optical communication *between* frames, provided that the event is strictly local. It means that light is deformed by motion and that one can "engineer back" what the velocity of the frame is. There is no change whatsoever *in* the systems (frames) themselves.
What is observed are an optical (fictive) change of the length ruler and 'time' measurement, as well as a fictive transverse and longitudinal mass.
I don't agree with the "Electrodynamic" part. Also there, the electromagnetic fields are treated as if they were kinematic systems, that is: *observed*, i.e. by light. That is not how electromagnetism works. There is an electrical field and an inducing magnetic field, and the "observation" will be: forces upon charges.
Hence, SRT has nothing to do with electromagnetism, and accounting for covariance is fraud, as well for kinematics as for electromagnetism, hence for every physics.
Hence, it is clear that no physical alteration whatsoever occurs due to SRT.
Planck invented that mass would really augment with velocity in order to "explain" ad hoc Kaufman's experiments with charges.
This is incorrect since electromagnetism is the theory that complies with charges and electromagnetism. Not an invented 'new' theory.
As a matter of fact, Oliver Heaviside has explained around 1890 that fast moving charges get a deformed field about them, because the conjunction of the immediately 'emitted' fields at the moments t0, t1, t2,... will result in an augmentation of the transverse field and a decrease of the longitudinal field with respect to the actual position of the particle.
So, also here, it is found that electromagnetism supplants any invented 'new' theory, hence, there is no mass increase.
Consequently, it is wise to consider in your analysis, that only energy really augments, never mass.
I wish it were so simple. But, based solely on General Relativity, we obtain this result. And Relativity is a model that works. I do not understand how to solve this paradox (which must surely have a solution).
If you follow carefully the logic and very simple math derivation described in Sections 2 and 3 of this paper (pages 1057 to 1060), and verify the calculations with a simple scientific handheld calculator, you may get some understanding of how mass increase can be understood from the electromagnetic perspective:
https://doi.org/10.4236/jmp.2018.95067
One question. Have you verified the soundness of your equations with known values?
Your equations are not numbered, wich makes it hard to discuss you paper.
Please remind that the equivalence principle is valid for any theory that respects the conservation of energies. It is not specifically GRT.
You wrote : "Relativity is a model that works." Only in apparence. As I explained, there is no space-time realm, it is fictive.
It has been clearly stated by Louis de Broglie in his analysis, explained in his 1937 book “La Physique Nouvelle et les Quanta”: He wrote :
"There is, however, one essential difference between Lorentz-Fitzgerald's contraction and that which, according to Einstein, results from the transformation of Lorentz: the first, indeed, was supposed to be a real contraction provoked by the absolute movement of the body. in the ether, while the second is an apparent contraction relative to the second observer: it derives solely from the way in which the various observers measure their distances and durations, and from the Lorentz transformation, which mathematically expresses the relationship between the measurements. Thus, the apparent contraction of the lengths is complemented by the apparent slowing down of the clocks."
He continued:
"In particular, we can perfectly justify the paradoxical fact that the contraction of the rules and the slowing down of the clocks are reciprocal appearances, that is to say that if two observers in uniform relative motion are each equipped with a rule and a clock, the two rulers and the two clocks being of identical construction, each of the observers finds that the rule of the other is shorter than his own, and that the clock of the other retires on his own. Surprising as this reproach may seem at first sight, it is easy to explain when one examines the theory carefully."
Hence, de Broglie clearly speaks of a fictive result of SRT, limited to the deformation of the measurement signals, in accordance with Einstein's thoughts.
Even in the electrodynamical part of his 1905 paper, Einstein treats the fields as if they could be "observed" at a distance by using light! That is not what happens with electromagnetism! So, electromagnetism cannot be treated by SRT, and there is no Lorentz covariance.
Once this is understood, it will be clear that masses don't change, only the content of energies and momentum, as compared with other frames.
"you may get some understanding of how mass increase can be understood from the electromagnetic perspective:"
I'm sorry, but I do not understand the connection you make between a mass relating to the deformation of the geometry of space-time in which it is ... and electromagnetism. And I do not think I'm able to understand the meaning of this link.
And you said:
"One question. Have you verified the soundness of your equations with known values?"
I do not understand what would be the use of it. Maybe you'll explain it to me.
Indeed, the equations are not numbered. But for a preprint I admit that I was a bit too lazy to do it.
Dear Thierry,
You said:
"You wrote : "Relativity is a model that works." Only in apparence. As I explained, there is no space-time realm, it is fictive."
I think that if you consider that General Relativity does not work (which I do not really understand), my paper will not be of interest to you, since I have relied entirely on General Relativity for this work.
Let's say that General Relativity is incomplete, why not ... But General Relativity works and gives results of a very high precision (LIGO, Gravity Probe B, Pound-Rebka Experiment, etc ...).
Sorry for the misunderstanding, I thought you wanted to understand how mass physically increases with velocity at the general level.
Withing the theory of GR, you will find no answer to your question because this concept does not exist either in SR on which GR is grounded nor in GR itself.
There is no real paradox in reality, because this issue is meaningless in GR. It is however meaningful in electromagnetism, which is why I offered your this link.
About the question as to whether you had verified the soundness of your equations with known values, this is due to the same misunderstanding. I thought you wanted to verify if your development matches physical reality.
It seems to me that your approach to mass is too formal. Everyone understands the term "mass" in its own way. Therefore we must call things by their proper names. You did not give a definition of mass. What mass are you talking about: the amount of a substance, energy, etc.?
You are considering increasing mass depending on defomation of the geometry of space-time. But space-time is not a material object, it is a mathematical abstraction. The energy and mass of material bodies cannot depend on the play of our mind.
We will not be able to solve the mass problems until we create a visual physical model of particles and bodies. But also within the framework of the substance system, the causes of phenomena will be incomprehensible. You need to go to the super system. Such a supersystem is the electromagnetic field environment.
If you find some free time, please look at the book ""Electromagnetic Gravity.Part1" in my profile. Take your attention at figure 4.4 ( The scheme of the gravitational interaction of active and passive masses) in the book ""Electromagnetic Gravity.Part2" in my profile.
First, Relativity provides highly precise predictions confirmed by observation (Pound-Rebka experiment, Gravity Probe B, gravitational wave detection, ... ... ...). It takes more than a simple affirmation to pretend otherwise.
This is not the first time I have received a paper claiming to show that Relativity is wrong. Nor is it the first time that I find that what is sent to me makes no sense.
Then I'm sorry, but I do not understand the difference between what you call "inertial mass" and "gravitational mass". To the extent that this difference has no mathematical meaning (in classical mechanics as in relativistic mechanics), I do not think it is my fault.
If anyone has proof that Relativity is wrong, I invite him to publish this proof in Physical Review D or Physical Review Letters (they are quite open to this kind of questioning). In the meantime, I can not waste my time reading papers that make no sense, as soon as they are introduced. I no longer hope to find gold nugget in the river of unconsidered papers.
Finally, I am not philosopher and too much physicist to have this kind of conversation (or maybe the French that I am needs too much wine for that). I am looking for a possible mistake in my paper, not to reinvent what we know about the world.
I have only skimmed your paper so what I say may not be correct. Your initial equation uses the non-relativistic equation p=mv while I think you should be considering the relativistic equivalent shown here:
As a small body is pulled towards a larger, it gains both momentum and energy but mass is invariant when derived using the energy-momentum relation:
(mc2)2 = E2 - (pc)2
My suspicion is that you are inadvertently calculating the so-called "relativistic mass" by using the low-speed approximation for momentum and that will increase due to the added kinetic energy.
Just after the first expression of the De Broglie's thesis equation, I explain that by default I include the Lorentz factor in the wavelength, which is therefore from the beginning relative to the speed. I let you consult the explanation. This was to really distinguish the applications of SR and GR.
1. Logic of the Second Law of Thermodynamics: Subjectivism, Logical Jump, Interdisciplinary Argumentation.
2. New thermodynamics pursues universality, two theoretical cornerstones:
2.1 Boltzmann formula: ro=A*exp(-Mgh/RT) - Isotope centrifugal separation experiments show that it is suitable for gases and liquids.
2.2. Hydrostatic equilibrium: applicable to gases and liquids.
3. The second and third sonic virial coefficients of R143a derived from the new thermodynamics are in agreement with the experimental results.
3.1. The third velocity Virial coefficient derived is in agreement with the experimental data, which shows that the theory is still correct when the critical density is reached.
4. See Appendix Pictures and Documents for details.