Yes, special relativity is experimentally checked to be a correct description of natural phenomena, at speeds close to the speed of light. From cosmic rays to LHC events and, in its extension to account for gravitational effects, to GPS measurements. It's not the point of being ``against'' a theory-this isn't a question of metaphysical argument. The point is that any new description of natural phenomena must, also, explain what is known in the appropriate limit. So focusing on one quantity, like the speed of light isn't useful. If one does want to understand how the idea of the speed of light as some limit can be generalized, one should study general relatvity, which does, precisely, that.

Yes, special relativity is experimentally checked to be a correct description of natural phenomena, at speeds close to the speed of light. From cosmic rays to LHC events and, in its extension to account for gravitational effects, to GPS measurements. It's not the point of being ``against'' a theory-this isn't a question of metaphysical argument. The point is that any new description of natural phenomena must, also, explain what is known in the appropriate limit. So focusing on one quantity, like the speed of light isn't useful. If one does want to understand how the idea of the speed of light as some limit can be generalized, one should study general relatvity, which does, precisely, that.

The question is different. Special relativity is correct and describes well for particles below speed of light. How did we verify whether it describes well the particles above speed of light because it generates a imaginary transformation? Why can't an extension of relativity above the speed of light as described in above papers be correct as they do not violate relativity below the speed of light?

It does-such particles are called tachyons and they describe excitations around maxima of the potential energy. So they decay as the physical system settles in the minima of the potential energy. That's why they're not observed.

One of above papers gives a method using existing lab equipment and technology to push particles above speed of light based on the theory of both papers. Wouldn't trying it resolve the mechanics for tachyons once for all?

No, because using the way described, in fact, doesn't achieve the stated goal-and can't. To claim that some apparatus ``pushes'' a particle, whose speed is below the speed of light to a speed above the speed of light means making that particle unstable: particles that move below the speed of light have real masses, particles that move above the speed of light have imaginary masses. So it's not possible to speed up an electron, because the election is a stable particle, for instance. On the other hand, it is known how to describe unstable particles within special relativity.

And it is known how to describe tachyons. There's nothing to resolve. The physics is understood and the mathematical description, too. And if the apparatus is based on using electric and magnetic fields, then Maxwell's equations imply that it can't work as imagined. One needs a model for the detector, in order to interpret its response-and one needs to test the detector, that it works as it should, where the answer is known. Of course it's possible to have a speed greater than the speed of light, e.g. the phase velocity of electromagnetic waves in a waveguide is greater than the speed of light in vacuum-but electromagnetic energy is transported at another speed, that's lower than the speed of light (in this case Lorentz invariance is explicitly broken by the boundary conditions).. it is possible for charged particles to move in a medium at a speed greater than the speed of light in the medium-then they radiate and this effect, known as Cerenkov radiation, is used in particle detectors.

Physics and mathematical descriptions are already understood does not mean that there is nohing more to be discovered. We cannot become functionally blind by the existing knowledge and thus never try to discover things which break existing theories. In fact there is no lab evidence of real tachyons yet and all theories like Hill & Cox 2012 royal society of physics paper is a valid theory unless proven wrong by experiment. Their theoey is same as Einstein's relativity below the speed of light so no contradiction with already observed experiments.

On the Maxwell theory -- it extended to speed above light in the other paper and I agree that it may not work exactly as given in paper due to lab difficulties but it is indeed a good portal towards thinking about push for faster than light. From stablility point of view and QFT point of view even positron is a electron moving back in time. Because it moves back in time it is observed as unstable but none the less it exists. If you look at Hill and Cox Lorentz transformation (or the one other paper), the time transformation is negative, which means a particle moving above the speed of light is also observed moving back in time. So an electron moving faster than light will be observed as a positron. For the charge and quantum point and the dual outcome described in the above paper an electron pushed above light will be seen as anhealing and generating 2 electrons and a positron. None the less because it is indeed moving faster than one should be able detect it reaching a pre-specific detector earlier than light.

I have invited Hill and Cox to the forum to share their thoughts on their theory. Let us wait for them to come and share.

Positrons aren't unstable-they can annihilate into photons, when encountering electrons, but they don't decay, since there don't exist any particles they can decay to:  a positron is the lightest, positively electrically charged, lepton. How antiparticles are described consistently is known since Feynman's work in the 1940s and is taught in all courses on relativistic quantum mechanics and has been checked by countless experiments since.   A positron doesn't arrive at any detector faster than light and has the same mass as the electron.

What Cox and Hill propose is a different parametrization of putative superluminal propagation scenaria-and this doesn't have anything to do with accelerating particles from subluminal to superluminal velocities.

The method in the paper does not talk about accelerating the particles above the speed of light but if you carefully read the Hill & Cox paper there is a speed of a particle c > v > 0.7 c where the particle has same momentum of a particle going above the speed of light (momentum in same direction, path in opposite direction). by first taking the electron above 0.7c and then reversing the field we create a situation where the better/least action path for the electron is to smoothly tunnel over the speed of light rather than deceleration. The result is a natural deduction from Hill & Cox paper.

About positron, as per Feynman it is a electron going back in time. If you look at the Hill & Cox transformations, the particle above the speed of light appears to be moving back in time. This implies an electron above the speed of light will appear as an positron and vice a versa. Our current accelerator measurements are not geared to measure particles moving back in time as measuring them moving above the speed of light. Prof Guy who is a accelerator experimentalist at Columbia University is already looking into a method to realize this theory and test it out. The Hill & Cox paper and the other paper cannot be trashed without a attempt to experimentally counter it.

If star-ship's velocity v>c, then exists observer, for whom v' = infinity of this ship.Thus, the ship is omnipresent. The ship is not God. Thus, such ship does not exist.

Actually at v = infinity using Hill & Cox equation and some mathematics I conjecture that matter will convert to space-time trajectory (omni-present). The energy of a particle at v = infinity is E = 0 but momentum is P = mc. Conversely you can also deduce that space-time is made from E = 0 energy moving at infinite speeds.

One can always make mathematical transformations, the question is, whether such transformations reveal new insight (about known effects)  not whether they, only, express known effects in other ways.  What is, definitely true, however, is that there's an abundance of experimental data concerning positrons in all kinds of energy ranges: at LEP positrons were accelerated to energies of more than 100 GeV, which corresponfs to a velocity so close to the speed of light that talking of something special occurring at 0.7 c is irrelevant to the issue. And this doesn't have anything to do with any specific article. Incidentally, electrons can't ``appear as positrons'', in any physically meaningful way, due to charge conservation, that, also, has been abundantly tested experimentally. 

If an electron going into past is a positron then the charge conservation does not hold with reversal of time frame of reference. With time reversal, the charge reverses. BUT the process of creation of positron DOES conserve charge, which means that a gamma photon which generates a positron also generates as electron. As per QFT the photon wave function degenerates/time evolves into a electron and positron under a specific condition.

Similarly the process of tunneling electron above the speed of light with carefully time changing field will degenerate (time evolves) into 3 wave functions -- 2 electrons and a positron. Of course the electrons have been accelerated to speed much closer to light than 0.7 C but there has been NO calibrated experiment to tunnel the electron above the speed of light with time and space varying field where the field reverses at a zero crossing when the electron is above 0.7c. As you can see in the paper for a clean push, the field has to reverse as a smooth function and it has to be manipulated in a way that the field at the electron position has to vary smoothly with time with positive half enough to push electron above 0.7c and then cross to the negative zone. As it is also mentioned in the paper NO static configuration of fields like smashing them to a tungsten wall can do it. The field has to vary with time.

Of course there have been such studies, in great detail, since they are crucial for all electron-positron colliders, e.g. http://www.hep.princeton.edu/~mcdonald/e166/nim/alexander_nim_a_09.pdf where *real* electrons and positrons are produced, accelerated, collided in controlled circumstances. These are all well known facts. Once more, one shouldn't confuse the many different *mathematical* parametrizations of the *same* physical phenomena with different *physical* phenomena.

Stam> BTW thanks for a very good discussion.

About mathematical model and real physics> At the level of nano-scales it is mathematical model and the observable predictions from it, which are used to verify the model as a "Real physics model". There may be multiple different models which can correctly predict the same thing like "Casimir effect".

Another important thing is whether a model can be used to conduct a experiment or build a device, which not only agrees with the model but is also useful. An example is quantum mechanics for building semi-conductor devices. Even newton mechanics model is good enough to build mechanical or civil engineering things. 

Einstein's model is very useful and is very important to build things for space travel. For example if Mangalyaan did not consider the solar radiation drift, it would be off the course by thousands of miles.

The question here is whether a direct experiment can be used to verify a model. The paper "Extended principle of relativity beyond speed of light and a method to push particles beyond the speed of light" is NOT JUST A CONJECTURE of model of space-time beyond the speed of light, it validly proposes an experiment based on a peer reviewed paper in Royal Journal Of Physics from Hill and Cox.

So saying that the experiment will not work has to either refute the basis of the proposed experiment directly in the way Hill and Cox or the other paper proposes it OR a easier way is to conduct the experiment and validate/invalidate it for ever. In fact a negative result will not only invalidate Hill and Cox and other paper but a lot of other papers proposing extension of relativity beyond the speed of light. 

If there has been existing experiment in common knowledge which directly refute Hill & Cox theory then paper should not have gone through the peer review process of the Royal Physics Society. So the experiment has to be designed and conducted to invalidate it.

Dear Singh, because I have shown (using God), that super-luminal ships do not exist, your unsupported theory "E=0, if v = infinity" is wrong.

The relativity principle (Galieli-Poincaré-Einstein) per se does not exclude the existence of particles traveling faster than light. They can exist without any violation of the Lorentz invariance. As a matter of fact there are specific theoretical studies of the properties of these objects in the literature since decades. Back in 1967 Gerald Feinberg gave even them a name, tachyons.

The fundamental relationship between energy E, momentum p and mass m of a free particle (a real one not a virtual one) is E2–(pc)2 =(mc2)2 (called dispersion relation). Contrarily to what is still found in the literature, Lorentz invariance requires mass tobe an invariant, namely it does not depend on the speed. However, it can have any value

A "normal" massive particle has real mass, namely m2>0. Hence, it is always E>pc . The speed of these particle is always smaller than c, including being zero. Photons (and gravitons) have zero mass, meaning that in any case for them E=pc.Their speed can be only c. Tachyons have pc>E, hence their squared mass is negative, their mass is imaginary. Their speed can have any value >c, not incuding c, but including infinite. To many the latter looks as an absurdity (see Dmitri)

However, the main logical problem with tachyons is causality. A signal faster than light is able to produce the effect of a cause before the cause happened. Some theorists believe that the causality problem can be solved by interpreting a particle going back in time as its antiparticle going forward. This is similar to what we are normally doing with virtual particles in the Feynman diagram we use to calculate cross sections etc.

Tachyons and tachyonic effects have been searched for experimentally. No evidence at all was found (not considering mistakes). However, the searches have been, obviously, done up to the maximum available energies. The possibility exists that at higher energies the above mentioned dispersion relation cheases to be valid. Tis is the case, for example, of "hidden dimensions". Space might have morre than three dimensions, the further ones being still "hidden" at the energies of LEP and LHC, but possibly not at larger ones. More generally, if the space has a granularity, like a crysthal, speeds larger than c are possible

Alessandro Bettini > Thanks for an amazing answer: "However, the main logical problem with tachyons is causality. A signal faster than light is able to produce the effect of a cause before the cause happened. Some theorists believe that the causality problem can be solved by interpreting a particle going back in time as its antiparticle going forward. This is similar to what we are normally doing with virtual particles in the Feynman diagram we use to calculate cross sections etc."

I agree with the above. I have proposed a principle of half-space in my paper based on a logical thought experiment. What I propose is that if a tachyon is beyond the a space-time point for a stationary observer and moving away, it cannot observe the space it has left behind by using light. This is because light can never reach it from the point it is moving away. It solves a part of the problem of causality but I agree there are many unresolved other causality problems.

What I have also proposed through a well explained thought experiment is that in 1D + 1D if a reference frame is travelling faster than light then a single event in your frame will appear as two distinct event for a observer in it. This because if the event occurred at (x,t) = (0,0) before the faster than light frame reaches origin, an observer in that reference frame can not only pick up photons transmitted towards it but also the photon moving away from it.

The paper is: https://www.researchgate.net/publication/265643274_Extended_principle_of_relativity_beyond_speed_of_light_and_a_method_to_push_particles_beyond_the_speed_of_light

The most important thing I have proposed in the paper is a method based on energy/momentum proposed by Hill & Cox and by me to tunnel particles above the speed of light. It might not be accurate but if Hill & Cox theory & my theory is correct then it will allow us to understand the nature of Tachyons and problems related to it like causality. As it might turn out to be a big discovery and it does not take building anything new, I think it is important enough to try and test.

Article Extended principle of relativity beyond speed of light and a...

Shalender

thanks for your explanations.

Let me just stress that physics is an experimental science, based on the Galilei method. And that the concept of "thought experiment" is just a contradiction in terms. I am not referring specifically to your work, but it is true in general that theories cannot be considered to be true only on the basis of logic. Any theory must have experimentally testable predictions. If not, it is not useful for physics. Experiments are designed to ask nature what is the theory she has chosen. Cannot be only "thought".

Dear Shalender. I can recommend an interesting article on this topic "The Speed of Gravity What the Experiments Say"

Tom Van Flandern, Meta Research [as published in Physics Letters A 250:1-11 (1998)]http://metaresearch.org/cosmology/speed_of_gravity.asp, and my article "Manifesto. Galactic Internet" http://vixra.org/abs/1306.0079     http://metagalactic.net/galanet/index_en.html

Alessandro Bettini > I completely agree with you. That is why in my paper https://www.researchgate.net/publication/265643274_Extended_principle_of_relativity_beyond_speed_of_light_and_a_method_to_push_particles_beyond_the_speed_of_light I have proposed a lab testable method to tunnel/push electron above the speed of light using existing technology. As it can be a very important discovery, it is worth to test and check whether it agrees or refutes my and Hill & Cox theory.

Article Extended principle of relativity beyond speed of light and a...

Alexander M. Ilyanok> Thanks for it.

As far as I know the special relativity theory mathematically is as valid below the speed of ligh c as above it. Below c all experiments agree so far. Above c, the so called tachyons, are mathematically OK but they have not been observed. I remember that an experiment was performed to detect them in case they were charged, (a type of Cherenkov radiation was predicted), but the result was null. 

In parallel with the referenced work of Tom Van Flandern, ""The Speed of Gravity What the Experiments Say", I have in arXix and here in RG my work ""The Speed of Gravity What e a Theory Says" . The theoretical possibility is there. But no experimental evidence is available , so far.

Both theories of relativity are incompatible with a flow of time - past, present and future already exist.    Tine is therefore only a timescape in which objects and events are laid out.  What we perceive as a flow of time is an illusion created by our brains to allow us to make sense of the world.  If this is true then cause-and-effect is a human invention to account for what we observe.  Speed (dx/dt) is simply a measure of spatial separation in space in relation to a time interval. 

Charles> Thanks for an answer. Actually NASA is working on developing FTL warp drive and they also have a small scale experiment to prove it: http://www.nasa.gov/centers/glenn/technology/warp/warpstat_prt.htm

Chales> Thanks.

Remi: It seems to me that the transmission of pure information, the quantum state, certainly requires transmission of mass-energy. You may see some of my papers here that imply that information, the bit, has energy. Then, the result is that information transfer, as any transfer of energy, should obey the same laws as are well known for these transferences.

Antonio> I agree that information has to be carried by some sort of energy or negative energy -- leading to change of state of detector of information (quantum entanglement?). It does not mean that energy cannot be transferred faster than light.

The biggest problem with FTL communication/energy transfer is causality and if a FTL generator is generating a EM wave towards an observer, it will appear to be reversed in time. But that will happen only when the generator is approaching the observer and not receding it. When the generator is approaching the the observer, the EM wave will appear as a Left hand EM wave in vacuum where there direction of wave is opposite to the energy. Does it mean a problem with causality? It does not because when the generator is approaching the observer A, another observer B stationary with respect to A at a different location will still see EM starting from the generator and not the receiver.

However if there is a retractable wire connecting the generator antenna and the observer in stationary frame then the oscilloscope of the observer will show the wave pattern of received EM wave earlier than the transmitted one. That does not mean that the receiving antenna has become the cause. It happens only because the observer is matching 2 observations across FTL frames.

Causality will only be violated if somehow observer A in the stationary frame can send information back to the another observer C in the FTL reference frame predicting what kind of wave pattern the generator is going to transmit and the observer C decides not to transmit it. In that case I predict following:

Assume that FTL generator is generating pulses which are received by the stationary observer A. Assume that the generator generates N pulses suddenly stops generating those pulses. The observer A will observer N pulses will full amplitude and a few more pulses with exponentially dying amplitude. So a causality disruption transmits as a decaying noise.

Mathematics is the language of physics. Sometimes a constrained choice of mathematical construct can lead of restrictions that do not exist. One such thing is mistaking a point singularity with a region. For example 0K temperature cannot be achieved but negative absolute can be achieved. So 0 K is a singularity and not a limit and Physicist have been able to side step it to achieve negative absolute temperature.

Similarly for a particle carrying mass V = C is a singularity not a limit. The problem is that because the singularity exists between the two sides velocity we cannot accelerate any particle to first C and then beyond. But one can side step it. Another problem with 1/sqrt(1 - v^2/c^2) is that it assumes a single event will appear as a single event even to the observer in a FTL reference frame, which makes it imaginary. If one looks logically a single event occurring in a reference frame A ( v = 0) when seen by a reference frame B( v > c) will appear as multiple events OR zero events. This is because if a observer is moving faster than light it will not only catch photons coming towards it but also the photons moving away from it at different space-time points. On the other hand if the observer is moving away from the source of event, the photons from the event can never catch it.

So in my paper: https://www.researchgate.net/publication/265643274_Extended_principle_of_relativity_beyond_speed_of_light_and_a_method_to_push_particles_beyond_the_speed_of_light we have presented a Extended principle of relativity as: “If there are 2 inertial reference frames A and B, the set of measurements from frame A for a single event observed in the frame B is the same as the set of measurements from frame B for a single event observed in the frame A under the same conditions. Similarly the single measurement from frame of reference A for a set of events observed in B is same as the single measurement from frame of reference B for a set of events observed in A under the same conditions”.

We have proposed a extended Lorentz transform in the paper, which is one event to many event and many event to one event. This transformation satisfied following:

A) Symmetric. -- Direct transformation represent transform from reference frame A -> B and the matrix Inverse transformation represents B -> A.

B) Speed of light remains constant and the direction also remains the same.

C) The origin of the reference frames are correct with the observation, which means x = 0 in the reference frame moving faster than light is at X = VT for reference frame at 0 speed and vice-a-versa.

D) For speed below light it becomes the ordinary Lorentz Transformation.

A important result of the paper is that we have proposed a method to push electrons above the speed of light using existing lab equipment and technology. This method is based on the energy and momentum formulation above the speed of light.

Article Extended principle of relativity beyond speed of light and a...

Charles> I am amazed by your answer and it seems that you do are not abreast with the latest developments in the Thermodynamics for last 30 years. Kindly refer to http://en.wikipedia.org/wiki/Negative_temperature, http://en.wikipedia.org/wiki/Thermodynamic_temperature . The temperature of a thermodynamic system is defined as T = dQ/dS, which means change energy with entropy. In case of solids the entropy is determined by the number of states the physical system allows given an energy. If the energy is lowest, the system takes only one state where all the components of the system at their minimum energy state. This is 0 K temperature. Similarly at the highest energy system allows only one state, where all the components of the system are highest energy. So when a solid state system moves from lowest energy to the highest energy state it maximizes entropy in-between and then starts reducing it with the energy. This is the negative absolute temperature zone. In fact second law of thermodynamics gets reversed in the negative absolute temperature range. Incidentally for gases and liquids the temperature at low and medium energies is almost directly proportional to the square of average velocity of molecules. This means dQ/dS ~ K V2avg . If you take discrete and finite system of gas molecules, given a energy you can find the number allowed states taking minimum quanta of energy as planck's constant. Given the number of allowed states you can compute entropy (which is equivalent to the Shanon's entropy as used in electrical engineering) as: http://en.wikipedia.org/wiki/Entropy_(statistical_thermodynamics). Given this entropy you can find dQ/dS, which is equal to  K V2avg when the number of molecules are very large (tend to infinity).

To resolve the mathematical ambiguity of thermodynamics a different measure of temperature is taken as t = -1/T = -dS/dQ so the 0 K temperature becomes positive and negative infinity. 

The earlier answer was to say that mathematics can sometimes pose artificial constrains to the understanding a physical system. It does not mean that we should discard mathematics as a tool for physics BUT mathematics cannot be the Summum bonum for understanding of physics. If a mathematical apparatus is constraining physics then one has to find more generic and better apparatus instead of harping onto the existing apparatus and assuming the constrains as absolute truth.

Now a days information theory, computation theory and physics are converging as we see as a resolution of entropy of Maxwell Daemon.This also means that sometimes mathematics may not even be able to capture the essence of physics. One may require a more generic computational paradigm, which means a model may not be described in terms of equations but a solution to a NP hard problem or intractable problem.The only solutions to these intractable problems is guesswork OR actually a physics computer, which solves them as a matter of physics phenomena. Eventually we will hit this boundary of physics defined in terms of non-computable problems because the existence of consciousness/free will does not allow determinism even at the probabilistic level.

I am writing a paper on it and here is the abstract:

There are so many situations in real universe and physics those are impossible to map as input-output in a finite time and no model based on finite observations can be accurate on them. It is like Gödel incompleteness. Physicist sometimes chose to ignore the infinite nature of universe while modeling it as mathematics but it is a fact that we can never model the universe completely in terms of mathematics. Still all the physics we make is in terms of mathematics and all our computational machines are also in the same form. Comparing with this in this paper we present another paradigm of physics computers. Let us consider a physical system, which cannot be modeled in more details because of the sheer un-predictability of its responses. The system we consider cannot be modeled accurately as perfect or probabilistic input-output using finite responses. But given two exactly same systems, their responses to an input are in high agreement. Then the correct way of predicting response of a remote system is by measuring the response of a replica system in lab by giving the same input to the system in lab. We conjecture that there are a set of such fundamental physical computers in universe, which can be used as a basis to generate the model and response of more complex things. These are not driven by mathematics but are just black boxes, which can replicated the un-predictability as well as the predictability of the universe. We propose the next generation of physics and computing to be modeled as such real physical systems and not just mathematics.

Charles> Actually thermodynamic temperature is exactly equal to the historic temperature but it also allows the definition of negative absolute temperature. Negative absolute temperature has been attained in the lab at the macro level. Not all systems can achieve negative absolute temperature but that does not mean NO system can achieve negative absolute temperature. Similarly not all systems can achieve FLT communication/motion but that does not mean NO system can achieve FTL communication/motion.

Charles/Bose/Remi> If we go through the original derivation of Einstein, he never considered a option where a single event may be measured as multiple events in another reference frame. So his theory is incomplete and not correct for speed greater than light. As I responded in another response if a indeed a observer is going above the speed of light, he will not only catch photons coming towards it but also photons going away from it. That is why we have extended relativity in our paper and find perfectly consistent results: https://www.researchgate.net/publication/265643274_Extended_principle_of_relativity_beyond_speed_of_light_and_a_method_to_push_particles_beyond_the_speed_of_light

Einstein defines the coordinates as absolute, which means that for 1D + 1D all points in the coordinates (x, t) from (-Infinity,0) to (Infinity, 0) exists at t = 0. If an observer takes birth at (x,t) = (0,0), it does not mean that at time t = T the universe for him only exists for (-cT, T) --> (cT, T). The whole infinite universe for him still exists independent of whether he has the capability to explore it farther than (-cT, T) --> (cT, T).

In fact if you can take light path as the coordinate system then it easier to define FTL coordinates. In the case of 1D + 1D if we define two dimensions in terms of light path as (x + ct, x - ct) instead of (x, ict) we will not need any imaginary dimensions and the Lorentz transformation can be simply calculated equal Doppler dilation and compression of the light paths. Furthermore a negative dilation and positive compression of light paths will lead to faster than light transformation.

A negative compression of light path is simply the reversal of the observed wave. 

Article Extended principle of relativity beyond speed of light and a...

Remi> in my paper I have proposed a method to push particles beyond the speed of light using existing equipment and technology. The measurement of speed can simply be made by tracking the time taken by the electron to move a fixed length of distance using a detection sheet in the reverse path. The experiment itself may need to be carefully designed so that electric field indeed reverses at when electron reaches > 0.7c. For surety we can do it when electron is at 0.8c. The field has to smoothly vary over time and > 0.7c should achieved at zero crossing.

It is not a difficult experiment so we can just conduct it and we might be able to either discover and validate new physics or disprove mine and Hill & Cox theory. 

The square wave question is unrelated to this discussion.

===== About 10x experiment and DQ/dt thing I do not want to discuss it publicly unless I have a iron clad experiment, so kindly do not discuss it here. =======

1. Cordinates are relative to a observer but they are still infinite and always existence in his reference frame. The coordinates themselves are not dependent on speed of light but the transformation of coordinates across inertial frames is dependent on constancy of speed of light.

2. Pushing in this context does not mean accelerating but jumping from speed below light to speed above light. So there is no question of intermediate infinite energy state. Kindly read the paper again and you can find it there.

3. No emperical law is broken. In fact Hill & Cox paper also went through a peer review process and there is no emperical evidence contradicting it. My eqns & Hill & Cox eqns are normal relativity below the speed of light so only emperical evidence against it will be a negative result of my proposed method to push particles above the speed of light. Do the experiment and prove us and many others wrong by a negative result.

4. I do not know what you mean by "Maximum" is the law of physics. There is no maximum for speed as derived as fundamental knowledge from universe. In fact as a mathematician you will agree that universe and existence imply non-finiteness of everything (remember definition of natural numbers starting from a null set?)

The emperical observation is the constancy of speed of light and not it being a maximum. My eqns satisfy constancy of speed of light as well everything else Einstein took as mathematical constraints in his derivation. The only difference is one event occuring as many events when observed from a frame faster than light. I have not used anything fancy other than this. One to many is very logical because FTL observer can catch not only those photons which come towards it but also going always from it thus recording same event mutilple number of times.

The only way to emperically disprove us is to conduct the experiment and get the negative results.

Charles> "there is no evidence": That is why my method is there to do it and have a evidence. There are always firsts in technology.

: Can you prove it with mathematics or is it just your conjecture? Einstein never said that and it is not even a postulate/inference of relativity.

You statement "Different law in different frames" means that there is no uniform law. Do you think Science before 1905 was in that state and only after 1905 we started having uniform laws?

Charles> A strong word as Tautology is never used in Physics and any experimental science because that itself means end of all possibilities to extend, challenge or improve. Even the most important and most verified principles of science, which are called "Universal Laws" imply "Universally accepted" and not tautologies.

"Science is a collection of explanations about objective reality that is based on observed or predicted phenomena. In addition, the explanation must be verified repeatedly to confirm that it correctly models reality. As our technical ability to observe reality improves, we are able to increase the quality and quantity of our observations. Better-observed data challenge our explanations, some of which will no longer fit the observed facts. New theories are then formed and either verified or falsified."

Charles> So are you saying that the limit of speed of light is true by definition? Are you saying that limit of speed of light needs no empirical evidence and no experiment should ever be conducted to try and break the speed of light because it is a fundamental truth?

Charles> Can you substantiate your claim of "the defined quantities and equations which we use to describe physics would be inconsistent with observation." with a specific example or derivation? If yes then you can probably publish it as a counter to Hill & Cox paper and many other papers including the NASA warp drive project. In fact then you can also disprove existence of worm hole. That itself is a big thing.

Charles> Can you substantiate your claim of "the defined quantities and equations which we use to describe physics would be inconsistent with observation." with a specific example or derivation? 

Charles> Thanks. I will look into it.

Shalender, I will offer a somewhat different take which perhaps you may find more satisfying (or not).  The other posters here will not like it, and it is not a proven theory, although many luminaries from de Broglie to Bell have held this view.  It is somewhat related to Charles' answer, but goes much deeper in understanding, and it that respect extends to what is strongly suspected rather than what is proven.

Most likely, anything you would consider matter, or material, is made of light.  Some people, perhaps most prominently my friend Asif, have put forward speculative theories of how this might be, such as electrons which are composed of a photon trapped in a circle from which spin arises, with the positive vector of the E field bound to the center, giving the appearance of a negative charge and resolving the problem of an extra force needed to confine charge which stopped the "electromagnetic theory of everything" back when Lorentz and Poincare were working on it.

Since then, we (humanity) first developed theories of 4 fundamental forces.  But by now all but 1 of them are suspected to be derived from one grand unified force, the electro-weak-strong force.  So this supports the idea that all matter is made of one kind of energy.  We do know, from experience, that matter is readily converted into EM energy, and vice versa (photons under certain conditions will decay into a particle and antiparticle, always oppositely charged).  So it is plausible everything is made of light.

Now consider what you are saying when you ask for a theory in which something travels faster than light.  If everything is light, it cannot travel faster than itself.  QED.

Robert> I can write a good counter but would you like to listen?

Shalender, I doubt it.  I'm just offering an idea to you for what it is worth.  It is not a theory I am defending, and I'm not seeking a debate.  It cannot be proven at the moment that everything is made of light, so I will not defend it.

Robert> Thanks. Duality: All energy and matter is composed of light but all light is also composed of matter. There is my paper about duality in progress here: https://www.researchgate.net/publication/266143448_Matter-light_duality_and_speed_greater_than_light. It needs a lot more details and refinement but the basic idea is there.

I am currently working extending the Klein Gordon Equation above the speed of light and solving that for Hydrogen Atom. I have almost completed it and I have been able to show that there exist a "negative excited states", which have lower energy than the ground state but they lower probability and less stable than the ground state. A electron in an atom goes into that state only if it absorbs a Left hand negative energy photon .An atom in negative excited state will spontaneously emit a left hand negative energy photon and goes to ground state.

Coming back to the question: If matter is composed of photons, how can it travel faster than photons> One important relation of any system/composition of particles to go above speed of light is E/P < c, which means energy and momentum ratio is less than the speed of light. This can happen if the system/composition contains negative energy constituents. The question whether negative energy can exist is same as question whether Left hand EM wave can exist. Left hand EM wave have been made in meta material and nothing stops it to exist in vacuum.

As I wrote earlier the question of violation of causality and ability to influence past is resolved if we consider energy/information transfer across causality breaking reference frames as not perfect but correlated one. The effect of change of existing decision will result in it's effect dying down and blending into new decision. For example if there is a observe A who predicts/sees B's future and transfers that information to B and B decides to change it then for A the effect of the earlier decision will dying down and blend into the new decision from the point of time contact of A from B. There might still be residual effects of it. In case A decided to make a video of it, it will have already overwritten it. This is just a rough sketch and I should be able to do a more authentic and mathematically rigorous model soon.

P.S. All attractive forces are negative energy and in fact Dirac's solution to energy of a electron in hydrogen atom is lower than the mc^2. In QFT, the attractive virtual photons travel back in time, which means negative energy.

Article Matter-light duality and speed greater than light

Sorry, I thought you were asking a question, not proposing a sophisticated theory.  I would not have responded at that level.

Remi> No problem. As there is no experimental proof of my proposed experiment, the theory is refutable. E/P < c for faster than light is a correct argument but my proposed Lorentz transformations are just proposal unless proven by experiment. They are not conceptually wrong but they have no proof.

The answer to the question - in my opinion, mainly because of psychological reasons.  I have some experience regarding this issue. I have given about 20 talks on the preferred synchronisation and description of tachyons.  First remark is such that people are so much attached to the Einstein's relativity that they  are probably not interested in other synchronisations and following consequences.  Second -  many people think that introducing a new synchronisation means overthrowing Einstein's relativity as false, while it has been confirmed in thousands of measurements.  The latter follows from ignorance that synchronisation of clocks  is only a convention in the Einstein's relativity.  Third - existence of a preferred frame, necessary for incorporating  tachyons, contradicts  the relativity principle which brings us to the previous point. Again ignorance, because  the relativity principle is an assumption sufficient for slower than light motion and not a  general law of Nature. Fourth - at the moment  there are no unexplained phenomena  that would obviously require reaching for   superluminal physics.   I do not want to offend anyone but  in my opinion, the Einstein's relativity of a kind of religion in physics and people in general  are reluctant to search  beyond it. 

Jacek> Einstein relativity is correct defined for speed slower than light but is not defined for speed greater than light. Relativity does not deal with the possibility of one event appearing as multiple events because it cannot happen below the speed of light. Above the speed of light an observer can pick up many photons generated from same event in different directions at different times OR it may not pick any at all. For example in the 1D direction an observer above speed of light will pick photons arising from an event in V = 0 reference frame coming towards itself and also the ones going away from it because it always wins the race. If it is moving away from the source of event in V = 0 reference frame then it can never pickup photons from it because it is already ahead and moving faster.

So for V > C one event occurring in V = 0 maps to multiple events and based on that definition we can satisfy all requirements of relativity including symmetry. Look at the derivation at: https://www.researchgate.net/publication/265643274_Extended_principle_of_relativity_beyond_speed_of_light_and_a_method_to_push_particles_beyond_the_speed_of_light

Old relativity is not compatible with one to many and many to one possibility, which is simple to deduce from the argument I have given above. The philosophical problems of "instantaneous transmission" seems to be deeper than what we think. As we can see in the above equations an infinite speed particle has zero energy but non-zero momentum. We have to re-think and deeply analyze the information transformation and instantaneous information transfer at superluminal speeds instead of rejecting the theory because of that.

Moreover I have proven a simple problem with conservation of relativistic momentum and energy using existing equation with a scenario of continuum of observers. Furthermore if any interaction needs to take place by converting potential energy to kinetic energy then the potential energy should also have momentum. It also shows that we can derive infinite linearly independent conservation equations. This also implies that normal day phenomena like elastic collision will not take place unless somehow space-time compensates for the deficit in the infinite conservation equations. https://www.researchgate.net/publication/265643349_Problem_in_the_relativistic_energy_and_momentum_conservation . It is under consideration from a Journal and till now no one has been able to disprove the derivation pointing out any specific physics or mathematical mistake.

As you can find in the above paper the concept of energy and conservation and space-time itself it inconsistent and needs changes. So people challenging the superluminal physics based on it are already on a shaky ground.

Article Extended principle of relativity beyond speed of light and a...

Article Problem in the relativistic energy and momentum conservation

Charles> Good point. Even in my equations if a particle is at infinite speed it's energy becomes zero but the momentum is not zero. I think the question of information transfer is deeper than what we can directly deduce from my paper. We will need to consider entropy, information theory and QM at superluminal speeds and explain the problem of zero energy non-zero momentum and speed of communication.

I have been working on Klein Gordon equation for superluminal speeds and have some interesting results about zero energy but non-zero probability particles in a box of length L. It can occur when mass is nh/(2cL) and momentum comes out to be mc, which is precisely what we get for infinite speed particle. In the case of particle in a box a zero energy particle exhibits a stationary wave with the frequency of oscillation itself being zero. This is like space itself! I think that the deducted non-zero momentum of empty space with zero energy can also fix the problem with conservation of relativistic energy and momentum I have found in my paper: https://www.researchgate.net/publication/265643349_Problem_in_the_relativistic_energy_and_momentum_conservation.

This can also mean that the zero point energy might of vacuum may turn out to be zero point momentum and this momentum can itself cause Casimir effect.

Article Problem in the relativistic energy and momentum conservation

Charles> Synchronisation is a convention in Einstein's relativity. In this sense one may say that  Einstein's relativity does not depend on snychronisation.  What does it mean " but on the maximum speed of communication between observers"? In Einstein's relativity this maximum velocity is c. This is not the law of Nature but a universal constant.  Superluminal motion is not excluded by Einstein's relativity  but it is not properly described. Superluminal motion can be described using a distinguished synchronisation procedure with a preferred frame and information can be transmitted with velocities v>c  without violation of causality. This scheme is equivalent to Einstein's for subluminal motion but not necessary  unless we discover tachyons. Can you prove your statement "  That such a thing exists is indeed a fundamental law of Nature"?  I agree that this is true in Einstein's relativity but not in general.

Charles, all you are talking about is the Einstein's relativity. All you write is true within this framework.  You cannot prove  nor disprove superluminal motion using this framework. The velocity c is a limiting velocity but Einstein's relativity does not state anything about the hypothetical motion that is always faster than c.  Nothing is proved in that website but the Einstein's relativity. If you insist that superluminal motion is disproved, please indicate me  the  underlying argument.  

Charles, you quoted the  link to a kind of a lecture on Einstein's relativity and I do not question the content.   One can find the same  in dozens of textbooks.  I repeat: where is the proof that superluminal motion is forbidden? Btw, please  avoid argumentum   ad personam. 

To the original question: I think the answer should consist of two parts:  Special relativity is, today, for those who study physics, an early experience.  Part of the childhood. And it is the fascination of these space-time mystics which are probably a decisive part of the decision to study physics.  So, the same psychological mechanisms, which prevent people from changing their religions, even if the ratio later tells them that there is not much difference between the different religions, works here too.  Those who try to return to a pre-Einstein metaphysics are - emotionally - rejected as heretics. 

The other point is modern organization of science. You have grants for one/two years, and you have to look, after this, for a new job.  This is much less job security than in every other domain, where a possibility to loose the job exists, if you or the firm fail miserably, but there is no necessity to look for other jobs. It is, therefore, the thing one should not do if one wants independence of science. For scientist to be independent, their jobs should be extremely safe. 

The consequence is predictable: Scientist have to follow the actual mainstream fashion, whatever this is. Once ether theory is not a mainstream fashion, it is completely out. 

Charles: "So long as distance is defined as it is (and note that its definition is empirical), special relativity is a tautology"

Sorry, no. There are no empirical definitions.  There are definitions, which are meaningful only if a given theory about physics is correct.  In a Newtonian world, the actual definition of the SI units would simply be meaningless, and lead to very different results about length measurements in dependence on the speed of the laboratory.  Once there is no such dependence, this type of definition is possible and meaningful, and, what is the important point, may appear to be the most accurate way to meausre lenght. 

So, SR is not a tautology, but presupposed as correct by those who propose the definition. 

"Consequently negative absolute temperature would means that the square of velocity is negative."

If you would have really learned thermodynamics, you would have learned also that systems with negative temperature are imaginable.  All you need is a system where the number of possible states does not, as usual, increase with energy, but (say,, for energies higher than a critical one) decreases.  Then in this region of energies the temperature will be negative. 

Not that such systems are somehow important, just a consequence of the definitions.

Extension does not mean refutal. Einstein's derivation did not consider a case of one event appearing as many event and vice versa. As I already pointed out, if matter at infinte speed looses a dimension, energy and time then its entropy and information is not as straightforward as it may seems. One may need to reconsider and expand these definitions as well. 

Charles, your empiricist position that there is something following from observation and logic alone is nonsensical.  Read Popper to understand this.  Observations are always theory-laden, what is the observation of a few worthless stones for somebody without any theoretical interests may be the observation of a prehistoric fossil for an archeolog. 

And, by the way, the possibility of negative temperatures for some systems follows from the actual standard definition of temperature by the energy-dependence of entropy. If entropy decreases with increasing energy, the temperature will be negative.