First, allow me to clarify that invariance and symmetry are often used as synonyms: for instance, we may say that a ball is spherically symmetric, or that it is invariant under the three-dimensional rotation group. These mean the same thing.

Also, symmetries aren't conserved (not in the usual meaning of the term). However, symmetries can lead to conservation laws. Specifically, when you have a Lagrangian theory that is invariant under some transformation (i.e., it has some symmetry), there is a conservation law associated with that symmetry. (This is the essence of Noether's theorem, named after the remarkable German mathematician Emmy Noether.)

Having said that, I think the gist of your question is whether or not in physics, Lorentz invariance is exact or approximate. As far as we know (notwithstanding speculative theories) it is exact. That is, our best classical theories, special and general relativity, are built on the notion of exact Lorentz invariance (at least in infinitesimal neighborhoods, i.e., "local" Lorentz invariance). Similarly, quantum field theory, being a relativistic theory, is manifestly Lorentz invariant.

There are other theories that break Lorentz invariance. These theories are often proposed to address important questions, e.g., in cosmology. However, as of yet they have no experimental support.

First, allow me to clarify that invariance and symmetry are often used as synonyms: for instance, we may say that a ball is spherically symmetric, or that it is invariant under the three-dimensional rotation group. These mean the same thing.

Also, symmetries aren't conserved (not in the usual meaning of the term). However, symmetries can lead to conservation laws. Specifically, when you have a Lagrangian theory that is invariant under some transformation (i.e., it has some symmetry), there is a conservation law associated with that symmetry. (This is the essence of Noether's theorem, named after the remarkable German mathematician Emmy Noether.)

Having said that, I think the gist of your question is whether or not in physics, Lorentz invariance is exact or approximate. As far as we know (notwithstanding speculative theories) it is exact. That is, our best classical theories, special and general relativity, are built on the notion of exact Lorentz invariance (at least in infinitesimal neighborhoods, i.e., "local" Lorentz invariance). Similarly, quantum field theory, being a relativistic theory, is manifestly Lorentz invariant.

There are other theories that break Lorentz invariance. These theories are often proposed to address important questions, e.g., in cosmology. However, as of yet they have no experimental support.

So far the answer is Yes. Here ``velocity range'' is, in fact, controlled by the energy of the particles. At the LHC, on the one hand and in the study of cosmic ray showers-that can go to much higher energies-the properties of the particles are consistent with Lorentz invariance being a global symmetry. 

These deal with what might happen when gravitational effects become relevant, beyond general relativity. Here the framework is what happens when gravitational effects can be neglected. 

Thanks to all;

Actually the reason for this question is; There are certain theories that assumed the violation of Lorentz invariance and others that assume Lorentz symmetry violation; which most of times assumes Lorentz invariance violation. Usually these theoreis are intended to interpret certain phenomena that the Lorentz transformations or special relativity can't explain, like the vacuum Cherenkov radiation and others. I want to know is there any theory that assumes Lorentz invariance conservation while at the same time assumes Lorentz symmetry violation?

Thank you for your cooperation.

The question has been clarified. It can be restated as : "are the formulas giving the transformation rules for the components of vectors, as measured in the frames of two different observers in relative motion, valid even when the motion is at a high spatial speed?"

These formulas can be proven with the usual assumptions of General Relativity, for any two observers (gravity or curvature has nothing to do in this). As for an experimental check,they have been tested at small speed, and at high speed the verification is indirect.

As mentioned by Prof. V. T. Toth, special and general relativity, are built on the notion of exact Lorentz invariance (at least in infinitesimal neighborhoods, i.e., "local" Lorentz invariance). At galactic distances of the order of few Kpc the theory fails. The following article shows that introducing a deviation factor "n" which is a ratio of Newtonian gravitational acceleration to the measured acceleration (eqs.2.27 and 3.11), Lorentz invariance can be redefined and can be applied at any distance. This provides solution for the rotation curves of galaxies, which does not exist in general relativity.

http://ptep-online.com/index_files/2015/PP-40-11.PDF

The problem is the following : we have two observers, located at the same point, each of them uses an orthonormal frame to measure vectors, these measures are done in the same vector space, which is the common tangent space to the manifold (representing the 4 dimensional niverse) at this point. One goes from one frame to the other by a matrix of the Lorentz group (becaause the bases areorthonormal), and the formulas explicit this matrix.

The key points are the following :

1. The group and the matrix act on vectors, and not coordinates of points. Only in the context of special relativity is it possible to consider coordinates.

2. The two observers must be located at the same point. if not their tangent spaces (where vectors live) are not the same. Only in special relativity is it possible to consider two distant observers.

The bad habit of physicists to consider only affine spaces, frames, coordinates, and the weak demonstration of the transformations formulas (repeated word for word for a century) muddle everything. Actually it is more illuminating in the General Relativity context, but one must be very precise in stating the basic assumptions. The key assumptions are :

i) the existence of a Lorentz metric

ii) all observers travel on world lines, and their velocity (derivative with respect to their proper time) has the same length as expressed in the Lorentz metric (which assure that their clock run at the same rate)

iii) in the choice of their 4 dimensional frames, the 4th vector (the time vector) is oriented along their velocity (another choice would be difficult to conceive)

Add the generalmathematical expression of a matrix of the Lorentz group andyou have the solution.

Of course this is a mathematical proof. It has been checked experimentally, and this validates the assumptions.

As for the motion of distant stars this is a totally different story. First it is necessary to introduce a tool to compare vectors in different tangent spaces, this is a connection, linked to the gravitational field. Second one needs an adequate representation of rotations of material bodies in a 4 dimensional space,which is not given simply by a Lorentz matrix (this is where spinors enter). Third of course one needs a general theory of interacting material bodies.

Dear Johan,

Actually this is the simplest proof in General Relativity.

To locate (spatially) a point you need three scalars (or any similar data), in any chart (this can be postal address, or geographic coordinates, or astronomical coordinates,...).

To locate an event in time you need another parameter. For millenia people use the position of stars and this is good. Clocks are more complicated : they measure the time elapsed, not the time proper, so you need both an origin of time and the same clock.

So say "see you at Stonehenge at the spring equinox" and you will be understood.

When you have charts which are compatible with each other (you can translate the data use to locate the same point) you have a manifold structure. Mathematically this is nothing more.  You need 4 data, so you have a 4 dimensional manifold.

The problem is that physicists use to speak of coordinates in orthogonal frames, but I have never seen any pilot of a plane, or captain of a ship, use them. They use coordinates systems adapted to a manifold. Free yourself from the cartesian frames !

The Lorentz invariance is defined by the transformations group that is valid in Special Relativity. It has been proved largely in contemporary physics that it is wrong even though post-modern physicists continue to believe. Anyway then the Lorentz invariance does not generate symmetry, on the contrary it generates many asymmetries: the difference between transversal mass and longitudinal mass that post-modern physicists don't know or neglect, the confusion between Lorentz's invariance and covariance, the time asymmetry, the velocity asymmetry, the space asymmetry for which a symmetrical sphere at rest becomes an ellipsoid when it is moving. Instead in SR the existence of a symmetry relative to the Doppler effect is proved and this symmetry is certainly exact even if by different  formulas.

I fully agree with V. Toth's answer. He says to what extent the symmetry and the invariance are identical and to what extent they are distinct. And all theories of physics that are well experimentally established are based on Lorentz invariance. There are various attempts to investigate possible consequences of violating Lorentz invariance in order to get new physics, particularly to construct a quantum theory of gravitation, but they are all speculative - in the sense of being not based on a clear positive (not ,,violation'')  physical idea - incomplete and devoid of experimental support.

To Johan

Wa have had this discussion before on another thread. I am first a mathematician and Mathematics are pehaps perfectible, but they give clear definitions. So there is no need to go further.

To Johan

The Lorentz formulas come from a well specified set of assumptions.

You mix coordinates (what are they .), information, Doppler effect, inertial frames, waves, a cartesian metric, which have no clear definition. With this kind of narrative, that is too common in Physics, you can prove anything.

I would prefer decent conversation, so since Johan's contributions include frequent use of the word "bullshit" I I politely ask him to leave this thread.

Questions are interesting when different viewpoints are represented. It is manifest that a few scientists are inclined to defend pre-existent theories while others support new scientific ideas. The hystory of science, and of physics in particular, has been ever a fiery confrontation between old and new ideas. I think everyone feels strongly that he is right and therefore it would be convenient  to eliminate verbal extremes. A fact is certain: the scientific thought is going through a sticky path like the transition from the classical physics to the modern physics straddling the 19th and 20th centuries. The modern physics is represented by a few fundamental theories (SR, GR, QM, SM) and current scientists support  two different views: a few accept fully the modern physics and look positively at some new emergent theories that derive from ( for example UT, ST, QG, etc..), it represents the new way of the "post-modern physics". Others instead criticize strongly the modern physics and think new useful ideas may come only from that scientific criticism. I support the second view that represents the "contemporary physics".  We are unable to understand which viewpoint is right actually and only the historical judgement will be able to decide between the two views. In the meantime we can only support our ideas in a civil manner removing verbal extremes and respecting other people's ideas.

Best wishes to all for the New Year.

Johan, I can subscribe your opinion on the modern and post-modern physics and I can also understand your anger for one second but it doesn't justifies your involvement in offensive comments.  Let you go others are offensive and let you answer with the strength of your ideas and let you don't reply when discussiion takes that way. Insults certainly are not the best way in order to demonstrate the cogency of his own arguments. Again my best wishes.

Symmetry is important for the Lorentz invariance which lead to the laws of physics to be the same for all observeers in the case of Einstein's interpretation to the Lorentz transformation equations depending on the concept of objectivity which adopted by the classical physics. Objectivity means event occurs, then it must occur for all observers. Reinterpretation of the Lorentz transformation according to the Copenhagen school by refusing objectivity will lead to removing the importance symmetry in the Lorentz invariance. And thus that lead also to remove the reciprocity principle which leads to disappearing all the paradoxes in the SRT; the Twin paradox, Ehrenfest paradox, Ladder paradox and Bell's spaceship paradox. Removing objectivity required to  multiply the y-axis and z-axis in the Lorentz transformation by the Lorentz factor to interpret the negative result of the Michelson-Morely experiment. In this case the Light speed remains locally constant and equals to the light speed in vacuum. and the Lorentz factor is equivalent to the refractive index in optics, and the Lorentz transformation equations is vacuum energy dependent not on the relative velocity. According to that there is no spacetime continuum, it is only time responsible for measuring a decrease or increase in the speed depending on observation only, but not locally. And this transformation will lead to the wave-particle duality and Heisenberg uncertainty principle and the observed decrease or increase is not only in the light speed but also in the speed of particles of mass and thus interpreting the red-shift of free falling objects in gravity and solving the momentum energy problem in gravity, and that leading to measuring a faster than light without violation the Lorentz transformation Locally. in each quantum state the Lorentz transformation is linear. Furthermore, according to this interpretation I could reconcile and interpret the experimental results of quantum tunneling and entanglement (spooky action), —Casimir effect, Hartman effect. When we generalize we get there is no curved space-time, it is only time responsible for measuring a decrease in the speed of light in gravity and that leads the universe is flat. Reviiew my paper "The Quantization of General Relativity: Photon Mediates Gravitation" http://dx.doi.org/10.14299/ijser.2014.10.002 Also after that review my paper about "The Exact Solution of The Pioneer Anomaly According to The General Theory of Relativity and The Hubble's Law" http://vixra.org/abs/1109.0058

Dear Azzam,

There is no new physics associated with the 'Pioneer anomaly', it has already been explained as an instrumental effect on board the Pioneer spacecraft.

I have read your paper http://dx.doi.org/10.14299/ijser.2014.10.002. It does not lead to any new insights in gravitation or General Relativity. Your approach to quantum mechanics avoids completely operators that do not commute. This is a central problem in the search for quantum gravity.

Dear Matts,

My paper does not avoids operators that do not not commute. My transformation equations leads to the commutations relations exactly by breaking the Lorentz symmetry and the reciprocity principle in SRT which lead to disappearing all the paradoxes in SRT. According to my transformation Lorentz symmetry is not required to the Lorentz invariance, and that agreed with all the experimental results. It interpreted the wave-particle duality, and the Heisenberg uncertainty principle. I do not know how you concluded that? If you have any experiment that contradicts with my model I hope to inform me it. 

I give you this research paper and you can understand how this paper results agreed exactly with my model http://www.sciencedaily.com/releases/2014/12/141219085153.htm?utm_source=feedburner this paper Furthermore http://physicsworld.com/cws/article/news/2014/jul/28/new-correction-to-speed-of-light-could-explain-sn1987-neutrino-burst How the calculations of Franson reached to the observed decrease in the speed of light by gravity depends on the Potential no on the the strength of gravity as adopted by Einstein's equivalence principle, which predicted by my model exactly. Relative to the Pioneer anomaly read my paper  http://vixra.org/abs/1109.0058 and see how that can solve also the energy momentum problem in gravity. Relative to the thermal origin of the Pioneer anomaly read my paper http://vixra.org/abs/1205.0006 Can you explain to me the Pond-Rebka experiment according to Einstein's equivalence principle??? See my equivalence principle and compare it with Einstein's equivalence principle and all the experimental results. Can explain to me how the universe are flat according to Einstein GR? 

Dear Matts,

The Problem in quantum theory and the Relativity theory is not completely math. It is philosophy and who read the discussions between Einstein and the Copenhagen school he will understand that. Reinterpretation of the Lorentz transformation according to the Copenhagen school will lead to motion is illusion, and this the core of the idealism philosophy. This will be understood when you review the Zeno's paradox and compare it with my reinterpretation of the Lorentz transformation equations according to Copenhagen school and how that will lead to the wave-particle duality and the Heisenberg uncertainty principle. in Zeno's paradox In his Achilles Paradox, Achilles races to catch a slower runner–for example, a tortoise that is crawling away from him. The tortoise has a head start, so if Achilles hopes to overtake it, he must run at least to the place where the tortoise presently is, but by the time he arrives there, it will have crawled to a new place, so then Achilles must run to this new place, but the tortoise meanwhile will have crawled on, and so forth. Achilles will never catch the tortoise, says Zeno. Therefore, good reasoning shows that fast runners never can catch slow ones. So much the worse for the claim that motion really occurs, Zeno says in defense of his mentor Parmenides who had argued that motion is an illusion. Now it becomes clear why physicists do not like to reach to the unified theory by modification of relativity. Relativity theory is keeping on objectivity and then the deterministic and causality and continuity which is the core of materialistic philosophy.The unified theory will lead to proof materialistic is wrong!

Dear Viktor T. Toth,

I liked your statement (; (at least in infinitesimal neighborhoods, i.e., "local" Lorentz invariance). Why you said "in infinitesimal neighborhoods" Do you know why? because of the concept of Space-time continuum in Einstein's interpretation of the Lorentz transformation equations basis on objectivity in classical physics. and thus that required to the Lorentz symmetry basis on the reciprocity principle in order to keep on the Lorentz invariance. Dear Viktor, Why do not you consider the "local" Lorentz invariance in a point in space of a free falling object, which at that point the Lorentz factor depends on the relativistic escape velocity. It is well known now in a free fall object in gravity a part of the mass of the object will change to photons and these photons will let the particle to move in a speed equivalent to the escape velocity. The Pond-Rebka experiment illustrated that; The time dilation of gravity resulted as the free falling object to move in a escape velocity. Proponents of the theory of General Relativity offer three different conflicting explanations of the results of the The Pound-Rebka experiment that are said to be equivalent to each other and therefore all equally correct. All make the claim that the results of the Pound-Rebka Experiment are “proof” of the Equivalence Principle even though nothing in these measurements suggests any need for the Equivalence Principle. In strong gravitational field there is a huge amount of the rest mass change to photons which required to define the escape velocity as a relativistic, not classical as in Einstein GR. Also in the Franson's calculations in J D Franson 2014 New J. Phys. 16 065008 doi:10.1088/1367-2630/16/6/065008  treating light as a quantum object, the change in a photon's velocity depends not on the strength of the gravitational field, but on the gravitational potential itself. However, this leads to a violation of Einstein's equivalence principle – that gravity and acceleration are indistinguishable – because, in a gravitational field, the gravitational potential is created along with mass, whereas in a frame of reference accelerating in free fall, it is not. Therefore, one could distinguish gravity from acceleration by whether a photon slows down or not when it undergoes particle–antiparticle creation. Now everything becomes clear and very simple. Symmetry is keeping only on the space-time-continuum, not on the Lorentz invariance. Lorentz invariance can be described also by removing objectivity and thus that leading to time is only responsible to observe the redshift in gravity for the speed of light or  for the particles of mass (The Pioneer anomaly, and the Hubble's law). The laws of physics are the same locally, and also the speed of light is same also locally and equals to the speed of light in vacuum. The none locality of quantum theory depends only on observation and it is not happened locally. And this will be very clear and very simple to be understood by reinterpretation the Lorentz transformation according to the Copenhagen school and thus refusing the concept of Space-time continuum in SRT, and thus the concept of curved space-time in GR. Now I answered this question "Is Loretnz symmetry conserved for all velocity ranges?" in a very simple way! a student in a high school will understand it, it is very simple! Do you remember when I told you General Relativity is not completely relativistic!!!

Dear Johan,

Lorentz invariance is keeping the laws of physics to be the same for all inertial frames of reference How?. In a simple meaning, suppose a moving train with constant speed V. Now here the moving train in a constant speed V, that means the train has a kinetic energy E which is equivalent to the train to move in speed V. Now when the train moves in a constant speed V, it must pass a distance x, and in this case x/t must be equal to V which is equivalent to the kinetic energy E. In order to the laws of physics to be the same both the observer on the ground and the observer in the moving train must agree at measured kinetic energy of the moving train and thus the measured speed V of the moving train which equivalent to the kinetic energy of the moving train. Since the observer on the ground and the observer on the moving train each one has his coordinates system S(x.t), and S'(x',t') which are related to each other by the Lorentz transformation equations. Now the problem is how to define the velocity V which is equivalent to the kinetic energy E according to the coordinates systems S(x,t) and S'(x',t'). Lorentz transformation by its manner is leading to keep the laws of physics is the same for S(x,t) and S'(x’,t’) when squaring the coordinates system, but the problem is how to understand the Lorentz transformation equations. Einstein interpreted the Lorentz transformation by his SRT, and then he generalized his interpretation in the case of gravity. By math Lorentz invariance achieves the condition -for example- for the light beam which is considered as a null vector we get

c^2t^2-x^2=0=c^2t’^2-x’^2 that means the line element is the same for the observer on the ground and the observer on the moving train.

Dear Johan Frans Prins,

Great! Now you  understand my theory exactly http://dx.doi.org/10.14299/ijser.2014.10.002

when you said "There is thus NO point-to-point coordinate transformation possible within ANY manifold" you are right! The problem here is Lorentz transformation was formulated basis on objectivity...This is objectivity! when Einstein built his interpretation to the Lorentz transformation equation, he built his interpretation basis on objectivity also, and basis on objectivity he researched to the concept of space-time continuum. Because of objectivity in the Lorentz transformation, it is resulted the contradictions between quantum theory and relativity theory. Tills now none can solve this problem, but I did! review my paper above.

The Lorentz transformation is a mathematical concept. Only the interpretation of this concept makes it a physical transformation. It divides the behavior of moving objects into three categories. One delivers Galileo invariance, the second delivers the Lorentz invariance and is based on a maximum speed of information transfer and the third is considered as non-physical.

http://en.wikipedia.org/wiki/Derivations_of_the_Lorentz_transformations#From_group_postulates

Einstein used the Maxwell's form of the wave equation in order to determine the speed of information transfer. That version uses coordinate time as the fourth dimension.

Other kinds of wave equations exist. For example quaternionic differential calculus offers a wave equation that uses pure progression (proper time) as the fourth dimension.

Maxwell-Minkowski based approach versus Hamilton-Euclidean based approach.

The difference between the Maxwell-Minkowski based approach and the Hamilton-Euclidean based approach will become clear when the difference between the coordinate time t and the proper time τ is investigated. This becomes difficult when space is curved, but for infinitesimal steps space can be considered flat. In that situation holds:

Coordinate time step vector = proper time step vector + spatial step vector

Or in Pythagoras format:

(∆t)² = (∆τ)² + (∆x)² + (∆y)² + (∆z)²

This influence is easily recognizable in the corresponding wave equations:

In Maxell-Minkowski format the wave equation uses coordinate time t. It runs as:

∂²ψ/∂t²−∂²ψ/∂x²−∂²ψ/∂y²−∂²ψ/∂z²=0

Papers on Huygens principle work with this formula or it uses the version with polar coordinates.

For 3D the general solution runs:

ψ =f(r−ct)/r, where c=±1; f is real

For 1D the general solution runs:

ψ =f(x−ct), where c=±1; f is real

For the Hamilton-Euclidean version, which uses proper time τ, we use the quaternionic nabla ∇:

∇={∂/∂τ, ∂/∂x, ∂/∂y, ∂/∂z}=∇₀+▽; ∇*=∇₀−▽

∇ψ = ∇₀ ψ₀ – (▽,Ψ) + ∇₀ Ψ + ▽ ψ₀ ± ▽ × Ψ

The ± sign reflects the choice between right handed and left handed quaternions.

In this way the Hamilton-Euclidean format of the wave equation runs:

∇*∇ψ = ∇₀∇₀ψ +(▽,▽)ψ =0

∂²ψ/∂τ²+∂²ψ/∂x²+∂²ψ/∂y²+∂²ψ/∂z²=0

Where ψ= ψ₀+Ψ

For the general solution holds: f= f₀+F

For the real part ψ₀ of ψ:

ψ₀ =f₀ (î r−c τ)/r, where c=±1 and î is an imaginary base vector in radial direction

For the imaginary part Ψ of ψ:

Ψ = F(î z−c τ), where c=±1 and î= î(z) is an imaginary base vector in the x,y plane

The orientation θ(z) of î(z) in the x,y plane determines the polarization of the 1D wave front.

Quaternionic coordinate data, which are based on proper time τ, fit as eigenvalues in Hilbert spaces. This is not the case for the spacetime coordinates that are based on coordinate time t. These data must be dismantled into real numbers before Hilbert space can handle them.

Hilbert spaces require that their eigenvalues are members of a division ring. Only three suitable division rings exist: real numbers, complex numbers and quaternions.

The formula:

(∆t)² = (∆τ)² + (∆x)² + (∆y)² + (∆z)²

indicates that the coordinate time step corresponds to the step of a full quaternion, which is a superposition of a proper time step and a spatial step.

An infinitesimal spacetime step ∆s is usually presented as an infinitesimal proper time step ∆τ.

(∆s)² = (∆t)² - (∆x)² - (∆y)² - (∆z)², with signature + - - - .

Above it is indicated that the coordinate time step ∆t corresponds to a quaternionic step. It mixes progression and 3D space. Proper time corresponds to pure progression.

The issue lies with the  use of the word symmetry in Physics.

Some quantities are geometric, in nature and in mathematics. In mathematics they are geometric when they have an existence independant of any coordinates or basis. A vector, a tensor, a linear map are geometric objects. Their existence does not depend on a frame, but their measure in a frame, or a coordinate system, varies with the choice of the basis or the coordinate systems, according to precise rules defined by their mathematical nature.

Some quantities are geometric in nature, when they represent phenomena which, we assume, do not depend on the observer, according to the general principle of relativity. This is more subtle to identify these phenomena, and the related assumptions form the base of the Geometry used in the Physical Theory. For instance in Galilean 3 dimensional geometry the universe is assumed to be an affine 3 dimensional space, and time is totally separate. In special relativity it is a 4 dimensional affine space, with a special relation between space and time, that translates, after some elaboration, into the Lorentz formulas. But these formulas do not mean a symmetry : they express only the fact that some physical quantities (such as the velocity of a material boddy) are geometric in the theory.

True symmetries are different. They express a specific characteristic of an object, both in Mathematics and in Physics. A Sphere is symmetric, because it is invariant by a rotation. This holds also in Physics. But not all objects, physical or mathematical, have a symmetry. And the symmetry is not necessarily the same (a cube has not the same symmetries than a sphere).

So to come back to the question : Lorentz invariance (or more precisely equivariance) is a general property of physical quantities represented by geometric objects. The rules are then universal for these objects. Physical symmetries depend on the object, the rules are not universal,but specific.

A fact that is not familiar to many scientist is that due to their four dimensions, quaternionic number systems exist in sixteen versions that only differ in their symmetry flavors. For example right handed quaternions exist that use a different external vector product than left handed quaternions use.  Nature appears to use this diversity in order to create a diversity of elementary particle types.

Quaternions are also the real Clifford algebra Cl(3) and they can represent rotations in the 3 dimensional space. Their generalisation to R4 give the real Clifford algebras Cl(3,1),Cl(1,3) (they are not isomorphic) with the Lorentz scalar product. Dirac Spinors are a representation of these Clifford algebras on a 4 dimensional complex vector space.

Clifford algebras are a bit disconcerting at the beginning, but provide a very powerful tool in Relativity, in junction with QM.

For velocities vc one can break the Lorentz symmetry, however preserving covariance. This is related to a different scheme of clock synchronisation and existence of a hypothetical preferred frame. If tachyons were found, that would be the case in our Universe. Until then, we comfortably live with the exact Lorentz symmetry for all velocities that we have observed in Nature. 

Yes Lorentz symmetry is preserved in IRFs, but as soon as IRFs exchange radiation they are not anymore IRFs so Lorentz symmetry is gone... 

Yes Stefano  you are right!  as soon as IRF exchange radiation they are not anymore IRFs, That is because it is become non-inertial frame, because in the case of exchange radiation it is leading to acceleration or deceleration. Here is the question, What is the concept of acceleration or deceleration according to quantum? 

If we consider the concept of acceleration or deceleration in classical motion or relativistic motion  is changing velocity which means gaining or loosing energy of hf, where h is Planck's constant and f is frequency which that is quantized. So, what is the concept of acceleration or deceleration according to quantum theory? And then if energy is quantized, how the accelerated particle in a uniform acceleration will moved in a continuous path 1/2at^2? 

Depending on the Einstein's interpretation to the Lorentz transformation in SRT. He adopted the concept of objectivity in the Lorentz transformation which was adopted in the classical laws of physics. From objectivity, it is resulted the continuity. So, in order to keep on the Lorentz invariance basis on objectivity and continuity, you must keep on Lorentz symmetry. This is the main problem in physics between quantum theory and relativity theory. Because of that Einstein was hating the Heisenberg uncertainty principle and quantum theory. According to my theory there is no Lorentz symmetry. Lorentz symmetry is only to keep on objectivity, and then on continuity, but not on the Lorentz invariance. In exchange radiation, it is transition from quantum state to other quantum state.  In each quantum state the Lorentz transformation is linear. As I informed you before Review the Pond-Rebka experiment and you will understand my equivalence principle, and how it is agreed completely with all the experimental results. By refusing objectivity in Lorentz transformation, it is resulted the Lorentz transformation is vacuum energy depending, and the concept of acceleration or deceleration by exchange radiation is vacuum fluctuations.

http://dx.doi.org/10.14299/ijser.2014.10.002

The Lorentz transformation is a pure mathematical concept that gets a physical interpretation by interpreting the variables v, t and c.

See for example: http://en.wikipedia.org/wiki/Derivations_of_the_Lorentz_transformations#From_group_postulates

Einstein used coordinate time for variable t and the speed of photons in free space as c. v is the observed speed of a moving object.

This choice places the Lorentz transformation in a spacetime model that features a Minkowski signature.

According to this choice photons obey the Huygens/Kirchhoff wave equation. The solutions of this equation for an odd number of participating dimensions are wave fronts.

See:http://www.mathpages.com/home/kmath242/kmath242.htm

If another wave equation is used, for example the wave equation of the quaternionic differential calculus, then photons become solutions of this equation and the parameter t becomes pure progression. pure progression is close to the notion of proper time.

The solutions of the quaternionic wave equation equation for an odd number of participating dimensions are also wave fronts. The mathematical description of these wave fronts slightly differ from the descriptions of the wave fronts that are produced by the Huygens/Kirchhoff wave equation.

The corresponding space-progression model has a Eucldean signature.

Physical reality does not change by these choices. The choices offer two different views of the same phenomenon.

The Lorentz transform works in both views.

Quaternions are an interesting subject

Once quaternions were very popular in the nineteenth century. Gibbs changed that by introducing differential geometry and vector calculus. It is a pity because with quaternions you are enforced to keep terms together that naturally belong together.

What few physicists know is that Hilbert spaces can only handle number systems that are division rings. The quaternionic number system forms a division ring and all other division rings (real numbers and complex numbers) are contained in that number system.

Due to their four dimensions quaternions number systems and continuous quaternionic functions exist in 16 versions that differ only in their discrete symmetry sets.

Quaternions and quaternionic functions are excellent in modelling fields that have Euclidean or Riemannian structure and show how fields belong together. 

For example the quaternionic nabla shows that when it is applicable it couples several fields. 

∇={∂/∂τ, ∂/∂x, ∂/∂y, ∂/∂z}=∇₀+▽; ∇*=∇₀−▽ 

∇ψ = ∇₀ ψ₀ – (▽,Ψ) + ∇₀ Ψ + ▽ ψ₀ ± ▽ × Ψ 

Where ψ= ψ₀+Ψ 

The ± sign reflects the choice between right handed and left handed quaternions. 

Each term in the above definition of ∇ψ specifies a scalar field or vector field. 

The homogeneous quaternionic wave equation has special solutions for odd numbers of participating dimensions when c=±1 . 

∇*∇ψ = ∇₀∇₀ψ +(▽,▽)ψ =0 

∂²ψ/∂τ²+∂²ψ/∂x²+∂²ψ/∂y²+∂²ψ/∂z²=0 

Where ψ= ψ₀+Ψ 

For the general solution holds: f= f₀+F 

For the real part ψ₀ of ψ in 3D: 

ψ₀ =f₀ (î r−c τ)/r, where c=±1 and î is an imaginary base vector in radial direction 

For the imaginary part Ψ of ψ in 1D: 

Ψ = F(î z−c τ), where c=±1 and î= î(z) is an imaginary base vector in the x,y plane 

The orientation θ(z) of î(z) in the x,y plane determines the polarization of the 1D wave front. 

These solutions are wave fronts and transport information. 

The inhomogeneous wave equation can be split into continuity equations: 

∇*∇ψ= ρ 

ϕ=∇ψ 

∇*ϕ=ρ

Interesting is the relation if the functions ψ and φ are normalized and m is a real factor :

||ψ||=||φ||=1

ϕ=∇ψ=m φ

Dear Hans,

Maxwell wrote his equations in Quaternionic format. Heavyside sadly transformed into vectors....

I will ask you about these numbers because I think Hamilton didn't invent them in 1843 for nothing...

Dear Stefano, Dear Hans,

According to my transforms by removing objectivity, there is no space-time continuum, it is only time and space is invariant because of that the universe is Euclidean. According to Einstein's SRT according to objectivity, the massive object must be defined according to space-time continuum. Since in exchanging radiation it is related to frequency which is reciprocal of time. Now according to my transforms massive objects can be defined by time only and space is invariant  and that leading to the wave-particle duality and Heisenberg uncertainty principle and it is related to time only; time dilation in case of decreasing the speed of light but not locally, and time contraction which leading to measuring faster than light but not locally. Locally speed of light is constant and equals to the speed of light in vacuum. According to SRT, it is impossible measuring a massive object to be faster than light because the massive object in SRT is governed by the space-time continuum. According to SRT it is impossible to interpret the quantum entanglement  or tunnelling according to the space-time continuum which is related to objectivity. Review the discussion here which is related to the topic we discuss. According to my transforms each observer, the moving observer and the stationary observer each clock is measuring the proper time during the motion and thus each observer registers according to his clock the proper time, the proper length and then the proper velocity. Here we must forget symmetry. Dingle was right!!!

https://www.researchgate.net/post/When_it_comes_to_simultaneity_is_Einstein_correct_or_is_Dingle_correct

Dear Hans, 

Paul Dirac gave an interesting general argument for a much stronger version of Huygens' Principle in the context of quantum mechanics. In his "Principles of Quantum Mechanics" he noted that a measurement of a component of the instantaneous velocity of a free electron must give the value ±c, which implies that electrons (and massive particles in general) always propagate along null intervals, i.e., on the local light cone. At first this may seem to contradict the fact that we observe massive objects to move at speeds much less than the speed of light, but Dirac points out that observed velocities are always average velocities over appreciable time intervals, whereas the equations of motion of the particle show that its velocity oscillates between +c and -c in such a way that the mean value agrees with the average value.

Review eq. (5.1.15) in page 463 in my paper  http://dx.doi.org/10.14299/ijser.2014.10.002 to understand how the equations of motion of the particle show that its velocity oscillates between +c and -c in such a way that the mean value agrees with the average value. My quantization gravity completely agreed with QFT.

http://dx.doi.org/10.14299/ijser.2014.10.002

Dear Azzam,

I don't really think Dingle was correct. It is the SR which is not complete, that does not take care of masses properly. Maybe now with the Higgs Field action (De Broglie frequency) it is possible to account correctly for mass and inertia of bodies and to see that the curvature of the space-time is there Always, a flat space-time does not exist except a homogeneous GALILEAN in deep space, where IRFs exist.

The fairy tale of free falling IRFs has to be wiped out because it is totally unphisical. I'm afraid we will see soon that for certain collective quantum physical phenomena objects do not fall in the same way...then the unification with gravity can be attempted..

Dear Stefano,

In fact Dingle is completely correct. What about the Sagnac effect?  https://www.researchgate.net/post/Absolute_space-time_vs_SRT_GR_How_does_it_come_that_c_is_a_constant

All the problems in physics can be solved from Higgs to Galaxies if objectivity is removed from the interpretation of Lorentz transformation. Let's be honest one time... At first I would like to say for all "Happy Easter"!

Physicists refuse removing objectivity in the Lorentz transformation, and they will remain to fixing data according to SRT, and thus SRT always must be right. That is because, if objectivity removed, then all the world will understand there is God governs everything in the universe, and also motion that we thought before governed by the laws of physics, then we understand it is completely governed by God willing.

Do you know why physicists refusing the idea of photon mediates gravitation? Because in this case everything in the universe is created from light. And God said in all the holly books, I'm the light of the sky and Earth. So the war is against God. And all the world must see everything in "one eye"! Because of that physicists hate quantum theory , and they refuse quantum theory to be a theory describes the macro world. We have two eyes, and the two eyes give us one picture for the world. So, if we want to understand the world in a real picture,  we must look at the macro and micro world by the two eyes; relativity and quantum as one theory. I'm not religious, but I'm honest! I hate to be a lier or cheater. Read the "man of straw", and then you will understand what is the SRT?

Dear Azzam,

"Do you know why physicists refusing the idea of photon mediates gravitation? Because in this case everything in the universe is created from light. And God said in all the holly books, I'm the light of the sky and Earth"

I agree at least for all the matter which weights but is not directly made of elementary particles like quarks and leptons...

Lorentz transformations are an approximation because the reality is Quantistic, is HOLISITC...

HAPPY EASTER...

P.s. when Fermi talks....everybody else has to shut up

Dear Stefano,

"whether or not in physics, Lorentz invariance is exact or approximate"

Classical theories, special and general relativity, are built on the notion of exact Lorentz invariance (at least in infinitesimal neighborhoods, i.e., "local" Lorentz invariance).  That all in order to keep on objectivity...believe me; "fixing data to keep on objectivity in the laws of physics" and then defining the massive objects by the concept of space-time continuum.

Why you proposed symmetry is lost in a finite number of short interval? Is not Bond and Rebka illustrated that the time dilation in gravitational field is equivalent to the particle as moving with speed equals to the escape velocity at any point in space depending on the potential at any point in space? This was proved also in Franson's calculations in http://physicsworld.com/cws/article/news/2014/jul/28/new-correction-to-speed-of-light-could-explain-sn1987-neutrino-burst

If you connect the Pond and Rebka experiment with Franson's calculations, that means Lorentz transformation must depend on the escape velocity at any point in space depending on the potential energy of gravitational at any point in space for the free fall object. Thus Lorentz transformation is linear at any point in space for a free fall object, and it depends on the escape velocity in space depending on the potential depends on time only (time dilation, and space is invariant. That means there is no space time continuum, it is only time. And that leads to violate symmetry, and it is produced by removing symmetry in the Lorentz transformation. Review my transforms and my equivalence principle. 

The measured decrease in the speed of light in gravity depends on time dilation same as in the refractive index in optics. By removing symmetry, it is resulted the massive particle of free fall object in gravity, its escape velocity will measured as decreased same as the light beam, that is because of the wave-particle duality. This proved by the Pioneer anomaly, which leads to solve the energy momentum problem in gravity. Review my paper regarded to the exact solution of the Pioneer anomaly. http://vixra.org/abs/1109.0058 Also my comments on the Thermal Origin of the Pioneer Anomaly http://vixra.org/abs/1205.0006 

Now we can answer all the questions below by one answer, and they are related to each others, why we separate the answers of theses questions...only to keep on objectivity in SRT!!!

1- Aether field rejected by Michelson Morley experiment in 20th century, but now in 21st century Higgs field is accepted. Why is that?

Are the aether and Higgs fields equivalent? If yes, how can we accept it in the light of Michelson-Morely experiment? If not, in which manner are these two fields different?

Aether field rejected by Michelson Morley experiment in 20th century, but now in 21st century Higgs field is accepted. Why is that?

2- Is Loretnz symmetry conserved for all velocity ranges?

I want to know whether Lorentz symmetry is conserved for all the velocity ranges or not? Is the Lorentz invariance completely related to Lorentz symmetry; i.e. if Lorentz symmetry conserved then Lorentz invariance is also conserved or there are certain conditions where the Lorentz invariance conserved while Lorentz symmetry is not? what are they if there are such conditions.

3- Can zero point energy explain the rotation curve of a typical spiral galaxy: the 'flat' appearance of the velocity curve out to a large radius?

If Lorentz transformation equations is vacuum energy dependent which lead to the wave-particle duality and Heisenberg uncertainty principle, and then photon mediates gravitation according to this transformation and the new equivalence principle in which acceleration equivalent to vacuum fluctuations. The uncertainty principle requires every physical system to have a zero-point energy greater than the minimum of its classical potential well. Thus the zero point energy explains the rotation curve of a typical spiral galaxy: the 'flat' appearance of the velocity curve out to a large radius. And how that is related to Higgs field.

There are more and more.

Dear Azzam,

In another thread I just added the following comment:

With all respect for your opinion [about the role of God in science], I don't find any relation between science and religion. Religion has been developed by humans and for humans on a small planet circulating an average-sized star ,of which there are 10 billions in our average-sized galaxy, among billions of similar galaxies in our Universe. Why should the period of rotation of the binary pulsar system PSR 1913+16 be 7.751 939 337 hours? I do not see the need for a God or Allah creating a Universe in all its infinity of details which in no way affect the humans on that lttle planet.

Dear Azzam,

"Classical theories, special and general relativity, are built on the notion of exact Lorentz invariance (at least in infinitesimal neighborhoods, i.e., "local" Lorentz invariance).  "

What is the problem? LT are a good approximations of what is happening, but they have limits. The one, who thinks they don't, is like Einstein who struggled against QM  for 30 years refusing it with his sentece "God does not play dice". He was the one who put God in place,  in a quite inopportune and silly way.

Werner Hesiemberg: "The first sip from the glass of the natural sciences makes you an atheist, but at the bottom of the glass you find God" this is much better...

Maxwell equations have limits too, because LT are derived from the Maxwell equations. Quantum electrodynamics has to cope with the limts of Maxwell equations.

Dear Matt,

Thank you for your reply. 

At the time I studied physics I thought the problems in physics is physics. So I dealt with the problems related  to quantum and relativity as  physical problems. At the end I found SRT must be always right because of objectivity in the Lorentz transformation. Why objectivity? because materialism was built basis on objectivity. If objectivity lost in Lorentz transformation, then it is the death of materialism, and then the death of Atheism. So physicists now fighting to not SRT to be changed, and they make a policy in all the journals of physics to not publish or accept any paper for review against SRT. SRT is the only theory in physics now keep on objectivity.

Review the comments of Dingle in the discussion https://www.researchgate.net/post/When_it_comes_to_simultaneity_is_Einstein_correct_or_is_Dingle_correct and see the video. I solved this problem according to my transforms in my paper http://dx.doi.org/10.14299/ijser.2014.10.002 

Now, quantum and relativity is impossible to be unified under the concept of objectivity in SRT. If you want to unify between quantum and relativity, it is very simple. Just reinterpret the Lorentz transformation equations by removing objectivity, and then all the problems in physics will be solved from Higgs to Galaxies. Physicists do not like that and they hate quantum theory and Heisenberg uncertainty principle.... why?

Because according to quantum theory and Heisenberg uncertainty principle, motion in the present for micro and macro world  will be defined by collapsing the wave function. In this case each part of motion is carried by the wave function, Also the motion of clocks (time) are controlled by collapsing the wave function...thus it is periodic. Same you display the pictures of the motion of the moving train on the cinema screen , and then you see the train is moving on the screen. Each picture that display in the screen is considered as the part of the motion of the train.

and since these wave functions are unrelated. Thus motion as we see now is an illusion! So if motion is an illusion, thus who govern the motion as I see now. Thus it is God willing. The plane flies because of God willing, and the train moves because of God willing. Also I walk and I move by God willing. This is exactly what Zeno's said in his paradoxes. Zeno's paradox solved by the unified theory. He was talking exactly by the reinterpretation of the Lorentz transformation by removing objectivity, and thus Lorentz transformation will lead to the wave-particle duality and Heisenberg uncertainty principle and it is vacuum dependent by removing Lorentz symmetry instead of the relative velocity. Read my paper Related to the philosophy of the unified theory http://vixra.org/abs/1206.0002.

My paper http://dx.doi.org/10.14299/ijser.2014.10.002  related to quantization of gravity was endorsed three times to be posted in arxiv. Proponents of relativity fought for my paper not to be published in arxiv, and they sent  many emails to arxiv moderators to not publish my paper in arxiv. And all of these emails are with me now. They told me 99.99% of the published papers in arxiv are wrong. And we understand your paper is right and you succeeded in quantization of gravity, but we refuse to announce about your paper in arxiv.... They did their best to not publish my paper in arxiv....why? because a student in high school will understand I'm right, and Einstein is wrong. If 99.99% of the published paper in arxiv are wrong and meaningless as they said, why they fought to not publish my paper in arxiv? If my paper is wrong then it is one of 99.99% of the wrong papers in arxiv. But they understand the reality well.

So the problem now is not physics.

There is one thing strange relative to quantization of gravity. God said I'm 1, and I'm the light of the sky and earth. Photon has spin 1 while graviton has spin 2. Now by quantization of gravity, photon mediates gravitation photon has spin 1. And God is 1, and everything is created by one God.

Dear Stefano Quattrini,

I'm talking by physics, So, I hope to reply to me by physics.

Galilean transformation was built basis on objectivity before Lorentz transformation equations. Lorentz transformation was built basis on objectivity too basis on  objectivity in Galilean transformation. Objectivity means according to classical physics, both the observer on the moving frame and the observer on the ground are agreed at the location of the moving train on any point x0 at the ground at the same time, that is by considering t=t'. If we talking about objectivity according to SRT, that means if we take the front of the moving train thus if the observer on the moving train sees the front of his moving train arrives pylon  B on the ground, then for the observer on the ground the front of the moving train arrives pylon B too. Here if you want to talk about Dingle, then Dingle is completely right because we can't say they agree that the front of the moving train arrives pylon B at the same time during the motion...why? Because according to the twin paradox, we do not know which clock is moving slower the other during the motion. So according to objectivity we understand arriving the front of the moving to pylon B is independent on the two observers. Thus to keep on objectivity, we must adopt the Lorentz symmetry in order to keep on the Lorentz invariance. Einstein proposed implicitly that the front of the moving train arrives pylon B for the observer on the ground and for the observer on the moving train, and then in order to keep on the constancy of the speed of light for all inertial frames of reference, he proposed the concept of the relative simultaneity. 

Now why objectivity is important? By objectivity it is resulted the continuity as in the classical physics. From objectivity and continuity materialism and Atheism was proposed. Review the history of materialism and Atheism basis on Newton's laws.

Because of that it is impossible to unify between quantum theory and relativity theory in case of non-inertial frames. If energy is quantized, and in case of acceleration or deceleration is changing energy. Now according to SRT the change in the velocity must be continuous, while changing velocity required exchanging radiation which is quantized. That is the problem. Massive objects must be defined according to objectivity in SRT according to the space-time continuum, while radiation according to time only which is related to the frequency.

if LT are a good approximations of what is happening, but they have limits. Then SRT is not complete theory. Thus why you refusing any modification in SRT? Or you accept any theory that keep on objectivity in Lorentz transformation or in the natural laws?

I have a question; Is there any experiment in physics proves objectivity in classical physics or in SRT???? How Einstein adopted objectivity in classical physics in his SRT? Basis on what??? it is implicitly

Do you know if we refusing objectivity and then symmetry in Lorentz transformations, that will lead to the wave-particle duality and Heisenberg uncertainty principle? In this case it is impossible that the observer on the ground and the moving observer  agree that  the front of the moving train arrives pylon B at the same time because of time dilation and length contraction, and this is the core of Heisenberg uncertainty principle when we deal with the four vector and then deriving the relativistic mass the equivalence of mass and energy.

That means Dingle was completely right!!

Now I want to till you why you say Lorentz transformations are good approximation?

In high velocities near the speed of light because of length contraction and time dilation, that will lead to Heisenberg uncertainty principle and the wave-particle duality, where relativistic motion will lead to quantum theory. That means refusing objectivity. While in case of low velocities as in classical motion, the length contraction and time dilation are negligible, not appeared, so objectivity and continuity will be appeared as an approximation to time dilation and length contraction. Not Lorentz transformation is an approximation, but objectivity is approximation.  So quantum theory and relativity theory are one theory, each theory will lead to the other. 

Dear Azzam

I agree that space-progression can be put in an Euclidean view. In that case the notion of time is proper time. In the view that Einstein and his friends have introduced the notion of time is based on coordinate time. Both views are compatible and describe physical reality. The Euclidean view is far simpler and is based on the quaternionic wave equation, which is part of quaternionic differential calculus. The other view is based on the Huygens/Kirchhoff wave equation and the two wave equations deliver a different description of photons. For odd numbers of participating dimensions both wave equations deliver solutions that are wave fronts. However the mathematical formulation of these wave fronts differ.

The difference between the Maxwell-Minkowski based approach and the Hamilton-Euclidean based approach will become clear when the difference between the coordinate time t and the proper time τ is investigated. This becomes difficult when space is curved, but for infinitesimal steps space can be considered flat. In that situation holds:

Coordinate time step vector = proper time step vector + spatial step vector

Or in Pythagoras format:

(∆t)² = (∆τ)² + (∆x)² + (∆y)² + (∆z)²

This influence is easily recognizable in the corresponding wave equations:

In Maxell-Minkowski format the wave equation uses coordinate time t. It runs as:

∂²ψ/∂t²−∂²ψ/∂x²−∂²ψ/∂y²−∂²ψ/∂z²=ρ

Papers on Huygens principle work with this formula or it uses the version with polar coordinates.

For 3D the general solution runs:

ψ =f(r−ct)/r, where c=±1; f is real

For 1D the general solution runs:

ψ =f(x−ct), where c=±1; f is real

For the Hamilton-Euclidean version, which uses proper time τ, we use the quaternionic nabla ∇:

∇={∂/∂τ, ∂/∂x, ∂/∂y, ∂/∂z}=∇₀+▽; ∇*=∇₀−▽

∇ψ = ∇₀ ψ₀ – (▽,Ψ) + ∇₀ Ψ + ▽ ψ₀ ± ▽ × Ψ

The ± sign reflects the choice between right handed and left handed quaternions.

In this way the Hamilton-Euclidean format of the wave equation runs:

∇*∇ψ = ∇₀∇₀ψ +(▽,▽)ψ =0

∂²ψ/∂τ²+∂²ψ/∂x²+∂²ψ/∂y²+∂²ψ/∂z²=0

Where ψ= ψ₀+Ψ

For the general solution holds: f= f₀+F

For the real part ψ₀ of ψ in 3D:

ψ₀ =f₀ (î r−c τ)/r, where c=±1 and î is an imaginary base vector in radial direction

For the imaginary part Ψ of ψ in 1D:

Ψ = F(î z−c τ), where c=±1 and î= î(z) is an imaginary base vector in the x,y plane

The orientation θ(z) of î(z) in the x,y plane determines the polarization of the 1D wave front.

Hilbert spaces require that their eigenvalues are members of a division ring. Only three suitable division rings exist: real numbers, complex numbers and quaternions. 

Quaternionic coordinate data, which are based on proper time τ, fit as eigenvalues in Hilbert spaces. This is not the case for the spacetime coordinates that are based on coordinate time t. These data must be dismantled into real numbers before Hilbert space can handle them.

The formula: 

(∆t)² = (∆τ)² + (∆x)² + (∆y)² + (∆z)² 

indicates that the coordinate time step corresponds to the step of a full quaternion, which is a superposition of a proper time step and a spatial step.

An infinitesimal spacetime step ∆s is usually presented as an infinitesimal proper time step ∆τ. 

(∆s)² = (∆t)² - (∆x)² - (∆y)² - (∆z)², with signature + - - - . 

Above it is indicated that the coordinate time step ∆t corresponds to a quaternionic step. It mixes progression and 3D space. Proper time corresponds to pure progression. 

Dear Azzam,

"Galilean transformation was built basis on objectivity before Lorentz transformation equations. Lorentz transformation was built basis on objectivity too basis on  objectivity in Galilean transformation."

Lorentz transformations were built because there was no way to make the match between Maxwell equations and Galilean transformations. The only way to make Maxwell equations pass coherently from different IRFs was throught the LT.

At the time when the LT were put in place (end of 1800) there was no Planck and  the Aether was quite in vogue also thanks to Henry Poincarè which remains the best mathematician in the late 1800 and first 1900.

I better say that more than "objectivity" here we are going to talk about Determinins, Mechanicism in place from the movement of the Positivism culminating in 1905 the annus mirabilis of Einstein and continuing after 1915 the year of GRT.

The way the LT are put in place and followed by Einstein was a mechanicistic conception. He presumed that such LT were infinitely accurate. This is against the physics which does state that any relation is an approximation, an approximation of something more significative, yet to be found.

Einstein made the biggest mistake ever, having thought that his theory was the definitive answer.

Planck, maybe brought in physics the biggest contribution in 1900, he was about to choose medicine before choosing Physics. He liked Physics and before choosing it he met one important professor of Physics,  in order to get advices for his future. This guy told him in the 1890's :" well, by now in Physics there is little more to be discovered, there are just a few things that I can say will be solved in a matter of some years,  some scientists are already tanking care of . So it is Worth to choose some other promising fields".  Planck was about to become a medic..

This was basically the results of the positivism of the last years of 1800, "superbia", presumptuousness of the man in that period.

Dear Hans,

"Hamilton-Euclidean based approach will become clear when the difference between the coordinate time t and the proper time τ is investigated."

Why you proposing There is coordinate time and proper time. Coordinate time proposed by Einstein in order to keep on objectivity. That is clear in the Einstein interpretation of the Lorentz transformation equations. Einstein proposed the relative simultaneity basis on objectivity. Why do not you propose each observer during the motion measures according to his clock the proper time, then the proper length and proper velocity. This is really what happened!! But in order to keep on objectivity, Einstein proposed the coordinates time. When we propose each observer during the motion measures according to his clock the proper time, then the proper length and proper velocity. Then quantum theory, the wave-particle duality and Heisenberg uncertainty principle will be applied in micro and macro world, and thus it is very simple to quantization of gravity. 

If objectivity is right as adopted by Einstein interpretation of the Lorentz transformation. According to objectivity Einstein proposed when he proposed the relative simultaneity during the motion both the observer on the ground and the observer on the moving are agreed at the location of the moving train at any point in space on the ground at the same time. ...that means at the same coordinate time....not proper time he meant. So, Please can you inform me if they have different coordinates time according to the reciprocity principle, how can we say at the same time, which time? Objectivity many be convinced according to Galilean transformation when t=t'. But according to relativity it is not true.  Review Dingle!!!!! https://www.researchgate.net/post/When_it_comes_to_simultaneity_is_Einstein_correct_or_is_Dingle_correct

Thus Heisenberg uncertainty principle is completely right and if we considering the proper time and proper length for the moving observer and the stationary observer, it is impossible that the two observers are agreed at the location of the moving train at the same point in space at the same time because of time dilation and length contraction. Thus relativistic motion will lead to quantum theory and quantum theory will lead to relativity. They are one theory.

Dear Stefano,

"Lorentz transformations were built because there was no way to make the match between Maxwell equations and Galilean transformations. The only way to make Maxwell equations pass coherently from different IRFs was throught the LT."

I do not discuss you  the history of relativity!

I discuss you how Einstein derived his SRT basis on objectivity. The main problem between quantum and relativity is objectivity! So why you hide objectivity in the interpretation of Lorentz transformation? Why don't you need people to understand how Einstein derived his SRT? basis on what?

Relativity theory is very simple, but you do not want people to understand it. 

So why do not you tell people about objectivity in Lorentz transformation equations? Why you hide it? and why you do not want to discuss it?

Dear Azzam

My personal model of physical reality uses a model wide clock. This model is compatible with proper time and with the usage of quaternions as storage of the combination of progression and space.

It is not compatible with the usage of coordinate time without assuming a carrier of information, such as a photon.

See the link.

http://vixra.org/abs/1502.0186

Dear Hans,

As I understand you. Here you will face a problem with SRT interpretation of the Lorentz transformation in the y and z coordinates. That is if you considering each observer during the motion registers the proper time, proper length and proper velocity. If the direction of the velocity in the x coordinates, in this case y and z coordinates must be multiplied by the Lorentz factor in case of interpreting the negative result of the Michelson-Moorely experiment. In this case the Lorentz transformation will lead to the wave-particle duality and Heisenberg uncertainty principle. Thus your model is working very good. And you reach to the same theory I reach in my paper below. There is no any contradiction between what I reach and what you reach. The problem is how to understand relativity by refusing objectivity. In fact your theory is The mathematical form of my transforms of my paper below

http://dx.doi.org/10.14299/ijser.2014.10.002

Dear Azzam,

"So why do not you tell people about objectivity in Lorentz transformation equations? Why you hide it? and why you do not want to discuss it?"

I don't hide that LT are an approximation, and Maxwell equations too are valid under certain approximations.

How can people can think of the opposite? This is my question.

It is like the "king is naked"...it is evident

GRT and SRT are based on determinism  on the math of LT which is a model falsified by Quantum mechanical behaviour or reality.

I don't know if you can define it as "objectivity" but anyway the LT are just an approximation of what happens, and if they were not as such nothing would move at all.

Azzam,

In my paper space is not quantized, but progression steps. The step size is rather constant, but may smoothly vary with progression. Elementary particles are represented by stochastic location swarms. These swarms are not quantized in any regular way. They are completely characterized by their statistical properties and by their discrete symmetry set. The embedding continuum is a mostly continuous function that at some locations features vibrations that can be quantized. These locations represent higher order modules, such as atoms.

The features of the Lorentz transformation, such as observed space contraction and observed progression dilatation, depend on the properties of the transporter of observed information. In my model that transporter is quantized with respect to the number of contained wave fronts. The relevant parameters transporter speed c, observe object speed v and progression t are not quantized.

Dear Hans,

Also, in my paper space is not quantized, space is invariant.  That is clear by reinterpretation of the Lorentz transformation by removing objectivity. That is resulted each observer during the motion registers proper time, proper length and proper velocity. Lorentz transformation is transformation between these two measurements of the two observers without the reciprocity principle in space and time. That leads to the Lorentz transformation is vacuum dependent and it leads to the wave-particle duality, and Heisenberg uncertainty principle. Now when we talking about changing the velocity(non-inertial frame), then we are talking about exchanging radiation which is quantized. In this case that leading to vacuum fluctuation. Where the moving train changes from quantum state to another quantum state. Here in each quantum state the Lorentz transformation is linear. So in all ranges of the velocities from 0 to c there is no Lorentz symmetry, by there is Lorentz invariance. That means there is no space-time continuum, but it is only time, and space is invariant.

Also by the equivalence principle, the escape velocity of freely falling object in gravity must be defined as relativistic escape velocity. In case of weak gravitational field, it is approximated to classical escape velocity. And thus at any point in space for the free fall object in the gravitational field, the Lorentz transformation is depended on the relativistic gravitational escape velocity at any point in space locally. which depended on the gravitational potential at that point in space. Because of the gravitational time dilation, there must be a red shift for the measured relativistic escape velocity globally for the freely falling object. Where according to my transforms, there is no space-time continuum, it is only time and space is invariant, and because of that the universe is flat and Euclidean. Thus according to my equivalence principle, in all ranges of the escape velocity from 0 to c in the Schwarzschild radius there is no symmetry, but there is Lorentz invariance.

Dear Hans,

Dear Stefano,

Review the paper attached ....It is good proof that the space is invariant as I predicted in my transforms. I succeeded in quantization of gravity. I hope to hear from you about this paper. I told you I solved all problems in physics according to my transforms!!!

http://arxiv.org/abs/1405.5174v1

Please read the paper, may be helpful for you.  A new approach to the correction of

Galilean transformation.