A physical reality of our universe is that the speed of light is always the same, irrespective of the speed of the source of light or the speed of the observer. This special status regarding the speed of light violated Galilean-Newtonian physics (which for short we will call Newtonian physics or classical physics) and necessitated a revision of physics. Albert Einstein provided a revision. Classical physics was consistent with the “common sense” or intuitive notion that objects would be seen to move at changed speeds by observers, depending on speed of the observer and its direction. For observers looking at moving mass, the speed they measure is affected by their own motion. How or why does light behave differently, in that an observer’s own speed does not matter when looking at light and measuring its speed? How did Einstein explain this strange reality? Einstein had no direct explanation, no mechanism, and no details of what makes this happen. We do!

We visit Albert Einstein’s famous 1905 Special Theory of Relativity which modified the space, time and equations of Newtonian physics. Modern physics has since been built to be consistent with special relativity. We solve the mystery of the motion of light and from this solution a new theory emerges that challenges Einstein’s. Our theory also serves to show that Einstein’s arguments, using which he derived his major physics conclusions, were based on unstated assumptions and therefore not a valid path to his conclusions.

Most importantly, our theory is urgently needed at this time because of recent experimental failures of special relativity in certain cases. We explained in our paper titled “Space is discrete for mass and continuous for light,”  which is attached as Appendix A, that special relativity would fail this specific set of tests. The results of these experimental observations are a failure for special relativity but are in line with our theory, and confirm its predictions. The reader who wants to know all the technical details of our theory can view the Appendix.

Let us begin with some basic physics, and then quickly get to the mystery of motion of light.

In physics, for any observer, we can assign a frame of reference. As an example, for a person standing on the ground by the side of a road, the road is the frame of reference and the person will make measurements relative to the road. For a person in a car moving on the road, the car will be the frame of reference and the person standing on the road will be moving in the car’s frame of reference but persons sitting in the car will be at rest in the car’s frame.

Special Relativity considers two observers who are at rest in their inertial frames of reference. Inertial frames move at constant velocity with respect to each other. If there was acceleration between these frames they would not be inertial frames of reference. We take the term inertial frames exactly as defined in special relativity.

Special relativity dramatically broke from classical physics because of the below postulate.

Light postulate: The speed of light has the same value in space in all (inertial) frames of reference.

The other postulate of special relativity is: The laws of physics are the same in all (inertial) frames of reference. This postulate is largely consistent with what was already known from Galilean-Newtonian physics; in chapter 3, we address the question of arguable fine differences between it and what was before.

The experimental evidence for the light postulate is overwhelming, and there are no credible experimental results against it. Our theory agrees with both the postulates and thus all the experimental evidence in favor of the postulates also supports our theory. (The experimental failures of special relativity that we referred to above are not of the postulates but of other parts, where our theory diverges from special relativity).

Let us first review classical physics, which was so dramatically contradicted by the light postulate. As we know, velocity is just speed with direction specified, thus for our purposes of discussion we can interchange one for other.

We consider two cars moving on the road. Commonly, when we say a car is moving at a certain speed we refer to its speed relative to the road, and that is what we mean here. We can skip the units of speed. One car is moving at 20 and the other at 30 in the same direction as shown. We refer to the occupants of the cars as You and Other.

u and v are commonly used as symbols in physics to denote speed or velocity. You are going to the right at u=20. Other is going to right at v=30.

According to classical physics, You will see Other going to the right at v’= v – u = 30 – 20 = 10 relative to you. And, of course, this classical velocity addition makes perfect sense from experience because Other is 10 faster than You. But to make the light postulate hold true, it can be shown that all velocity additions have to change, so this answer of 10 is not perfectly accurate, but at speeds much slower than light the error is miniscule.

Now suppose You are going to the right at 0.9 times the speed of light, u = 0.9c, and the Other you are observing is Light, v=c.

Then by classical physics, You would see Light going at v’ = v – u = 1c – 0.9c = 0.1c relative to you i.e. light will be faster than you by 0.1 c. But according to above light postulate of special relativity, all observers always see the speed of light to be the same. That means, no matter what speed You are moving at, you will see light to be moving to the right at 1c. Thus classical physics and the “common sense” expectation that you would be catching up to light and therefore would see light at 0.1c is wrong! Even if You increase your speed to, say, 0.999999c, you will observe light to be traveling at 1c.

We provide below a simple explanation for the constancy of speed of light. Einstein simply assumed this constancy of speed of light and called it a postulate. It often is the situation in physics that we have discovered something we can experimentally confirm, and that is where the physics of the situation ends. If one could answer further “how” and “why” something holds true then that could be new physics.

We actually give below the “how” and “why” which Einstein was not able to provide, and that does lead to new physics; in fact, it leads to new equations which are different from and contradict those that Einstein found. To understand our answer to the “how” and “why” of the light postulate let us detour back to classical physics, forgetting about special relativity – for a moment only.

Light has long been known to have a high but finite speed. Special relativity also says (correctly) that no mass can travel faster than the speed of light.

However, in classical physics mass could be made to travel with there being no maximum limit. We are taking a momentary hypothetical detour from special relativity only for the purpose of visiting the concept of infinity (∞). We are only illustrating a mathematical concept and do not suggest that any mass would actually travel with infinite speed in classical physics, and thus do not need to go into what such actual travel at infinity would physically mean.

In mathematics, when you add or subtract a finite number from ∞ you still get ∞. For example, ∞ – 4700000 = ∞ and ∞ + 99999999999999 = ∞.

Then applying this rule of mathematics to below diagram, no matter how fast a finite speed You have, you will always see Other travel at ∞.

In above v’ = v – u= ∞ – 9000000= ∞. The answer from rules of classical physics would be ∞ whether you had u = 9000000 or u = 99999999999999 or any other finite value.

Einstein’s approach has taught physicists to look primarily at distance-time analysis but we are looking at velocity as the starting point of analysis. Trained in Einstein’s ways, Nobel Prize winner Gerard ‘t Hooft reacted to this conceptual case by this email in May 2017: “Didn’t you ask yourself what infinite velocity means? It means that two different points in space are passed by that object at the same time, that is, simultaneously.” Again, we are only illustrating the mathematical concept of infinity, and from it drawing a key parallel below between velocity in classical physics and special relativity. We are emphasizing this point to make it clear to those who are looking to raise objections. And of course, in our theory as in relativity, mass cannot travel faster than light. Since no mass is actually going at infinite speed no time-based objection arises. Gerard ‘t Hooft’s Nobel Prize lecture was titled “A Confrontation with Infinity”^[1] and dealt with particle physics and a process called renormalization, which has no connection with the matter of equations of motion. Our theory has no problem incorporating infinity.

In classical physics: If You, the observer, were looking at an object traveling at infinity (∞), your own (finite) speed would not matter. You would always see that object travel at ∞.

Compare to special relativity: When You, the observer, are looking at light, which travels at c in empty space, your own (less than c) speed does not matter. You will always see light travel at c.

Light, in having this property of its speed being constant, is behaving the way an object moving at infinite velocity would in classical physics, in that the speed of the observer would not matter. For light to behave this way there should, in our view, be a hidden infinity in the mathematics of relativity which corresponds to the speed of light. We parted from Einstein and actually found this hidden infinity in the mathematics of velocity addition.

In physics we have the famous notions of “quantum jump” and “discreteness.” These come from quantum mechanics, where at small scales things are not continuous but “granular.” Many physicists have been suggesting a lattice structure for space, or some other way whereby space takes on a discrete character. But giving space such structures would not explain “how” and “why” of the light postulate and tell us where the hidden infinity in the mathematics of the motion of light is which causes the speed of the observer to not matter.

In classical physics and in the theory of relativity all motion is continuous. In our theory we abandon continuous motion for mass and thereby unite relativity with the discrete nature of quantum mechanics. However, very importantly, we hold on to light (or massless particles) having continuous motion. Mass moves through space discretely, “jumping” from one point to another without passing through the points in between. On the other hand, the motion of light through space is continuous.

The book cover design is an illustration of this. The continuous lines at the top represent motion of light and the lines at the bottom depict discrete motion of mass.

For mass traveling at constant velocity, the “length jumped” is constant. The higher the velocity the more the number of jumps per unit time and the smaller the jump length. Note that these jump lengths are all very small. They match the length scales we see in quantum mechanics, which are of atomic length and smaller. At the quantum scale, a fundamental length is called the Planck length, after physicist Max Planck, and it is 10^-35 m (which is a decimal point followed by 34 zeros and then 1).

Now let us look at a stretch of space that mass and light are moving through. In a unit time a discretely moving point mass particle will be at a finite number of points and will have made a finite number of jumps; in this time light will travel continuously over all points in its path. Continuous motion is not discrete motion, as the latter has number of jumps per time and length of jumps. However, we can consider the number of jumps in continuous motion to be infinite, with the jump length being zero. By thus using infinity and zero, continuous motion mathematically parallels discrete. Therefore light will effectively have made an infinite number of jumps.

Thus we have the hidden infinity we were looking for.

In our theory, addition of velocities depends on adding (or subtracting) the number of jumps per unit time. The number of jumps per unit time is infinite (∞) for light and finite for an observer having mass. When an observer looks at light, addition and subtraction will involve adding or subtracting a finite number from ∞ and the result will still be ∞. Thus the speed of the observer will not matter and that is what explains the light postulate.

Let us actually go further into the mathematics – all of which is elementary – and show how this works. We will show precisely why the light postulate holds true. Given what we are achieving do follow the simple math. (If you want to not join us in this then skip the below paragraphs having mathematical notations and continue reading after that. Understanding of this mathematics is not needed to read the rest).

In a unit time a mass particle with constant velocity would have made N jumps. N need not, of course, be a whole number (for example, if a particle makes 10 jumps in 4 seconds then we say N=2.5 jumps per second, but the particle makes whole jumps only). Each jump length is Ld where L is a length that is a constant for space and d is a function of N. (A function is a formula; the actual formula is given in the paper in the appendix). We can think of d as a function that causes “shrinkage” of the jump length. The distance the particle travels in unit time is v = NLd, which comes from multiplying the jumps per unit time N by the length of each jump Ld. For simplicity we can take L = 1 and have v=Nd (but if we use the shorter formula for v must keep in mind the L=1 or we will be missing the distance unit from the formula). Note that since d is a function of N it would mean v itself is a function of N. Every velocity v corresponds to a N. Our formula for velocity v is such that as v of the mass particle increases, N gets larger, but d decreases in such a way that v approaches speed of light, c, but never crosses c. That also explains why no mass can travel faster than c.

For light, as explained above, continuous motion means N = ∞, and we have jump length d=0.

Mathematically, the actual product of ∞ and 0 is deemed to be indeterminate, which means it can be any number. However, for motion in space this indeterminate is fixed and we have ∞ • 0 = c. All continuous motion in space is at this speed.

In our theory, addition of velocities depends on converting the velocities to number of jumps per unit time, adding (or subtracting) these number of jumps per unit time, and then converting the result back to velocity. All this is done using the formulas we have found. Let us apply the method to You as an observer viewing Light. As in earlier example, we again take Your speed to be u = 0.9c and for Light we have v = c. Corresponding to them we have jumps per unit time N_u and N_v, where N_u would be a “finite value” (which we can calculate using our formula) whereas N_v = ∞. In classical physics we add or subtract velocities v and u directly. Here we add or subtract the N’s. For the case when You are observing light we have N_v‘= N_v – N_u = ∞ – “finite value” = ∞. From N_v‘ = ∞ we will get d’= 0 and from our formula, with these values of N_v‘ and d’ we get velocity v’ = N_v‘• d’= ∞ • 0 = c. This explains the light postulate.

The full set of three-dimensional velocity addition and distance-time formulas that would replace those of special relativity are in the paper in the Appendix.

Infinity “naturally” occurs in many places in physics and we have embraced it and gotten the light postulate. However, infinity has traditionally been considered an enemy by physicists. Physics dogma teaches that infinity should be avoided, and if that is not possible, then it is to be confronted and eliminated. So physicists would never do what we did above by seeking out and working with ∞. Thus they could never explain the light postulate and simply assumed it. Modern physics has been avoiding or fighting infinity for a hundred years, and the methodologies that have been laid out in modern physics seem to have put physics on course to continue avoiding infinity. Avoiding infinity in physics has, in fact, been a doctrine that goes back to Aristotle.

Another long-standing dogma in physics is to put distance and time as primary physical quantities, with velocity (speed) derived from them. This comes from dimensional analysis which is taught to students as a classical physics foundation. In line with this, Einstein was focusing on obtaining distance and time equations. But the fundamental reality of physics is that all observers see light at the same speed, no matter what the observers’ own speed. Given that this physics truth, which forms the starting point of relativity, is about velocity we found it natural to examine velocity directly.

Starting with velocity is our deliberate approach for another reason too. When looking at moving objects we can directly observe velocity and directly observe distance traveled. We can actually see how fast something is going and from which point to which point it is moving. Time, however, is subtle and elusive in that time “flow” cannot be directly observed, unlike velocity and distance. For us, in that sense too we would rather have velocity and not time as the quantity we prefer to work with as a starting point. This simple realization worked wonders. By going directly to velocity we have above shown how and why it is that all observers measure the same speed of light, and thus we never needed to assume the light postulate. Having gotten equations for velocity we use them to get equations for distance and time.

However, for momentum we get the same effective formula as Einstein’s. So that part is common between the theories. Using his interpretation of special relativity, physicist Stephen Hawking writes, in A Brief History Of Time: “As an object approaches the speed of light, its mass rises ever more quickly.”^[2] Physicist Brian Greene similarly states in The Elegant Universe that mass of a particle “increases without limit as its speed approaches that of light.”^[3] We never agreed with such interpretations of Einstein’s formula. We note that for momentum we get the “same effective formula as Einstein’s,” the “effective” word being important because the formula is not exactly the same. We are glad that, unlike Einstein’s formula, there is no possibility of interpreting our formula to suggest that mass is actually changing with velocity. If you view our momentum formula in Appendix A, p. 6 you will see why. Having the same momentum formula also results in the same energy formulas, and E=mc² is thus preserved.

Special relativity is Einstein’s theory. However, the term “Lorentz transformations” is associated with it and we use that term frequently in this book. Let us go into what these Lorentz transformations are. Newtonian physics has distance-time equations, and equations for velocity addition. These equations are not consistent with the physical reality that all observers will see the speed of light to be the same; thus there was need to replace these. Using the constancy of speed of light as a postulate, along with incorporating the older classical physics postulate about the laws of motion being the same in all frames, Einstein’s special relativity derives a set of replacement distance-time equations. These equations are called the Lorentz transformations, after physicist Hendrik Lorentz who first stated them. In high school one first learns the equations of Newtonian physics. Then in advanced high school courses or in college physics one learns the Lorentz transformations. 

Time dilation and length contraction are two major results from the Lorentz transformations, but our distance-time equations do not have these physical effects. Thus we can test and see if our equations or the Lorentz transformations are the correct equations of nature.

Lorentz noted that “Einstein simply postulates”^[4] the constancy of speed of light, which he and others had been trying to explain. Lorentz was also trying to find a physical explanation, involving electrons, for length contraction, and was struggling with a theory of time. The name Lorentz transformations was given by Henri Poincaré, who interacted with Lorentz, and was ahead of Lorentz in aspects of time.

However, Lorentz praised Einstein’s approach and became a supporter. Indeed, the whole of physics came to greatly admire special relativity. We were not happy with the postulate approach and actually found the explanation for the constancy of the speed of light that Lorentz and others had been seeking, before Einstein appeared. Our explanation formed the basis for our velocity addition equations; from these equations we derive distance-time equations. We got the correct equations using velocity as a starting point. Einstein got the Lorentz transformations by going directly to distance and time, and then from those equations coming to equations of velocity addition. Both our distance-time equations and the Lorentz transformations have the equations of Newtonian physics as a limiting case, which means that at speeds much slower than light, both our equations and Lorentz transformations give physics results close to those given by the equations of Newtonian physics. And the higher the speed the greater the deviation from the results given by the equations of Newtonian physics.

Physics books and papers repeatedly state that time dilation has been experimentally confirmed. Despite what physicists think and claim, time dilation – that time itself dilates – has never been shown to be true; to show it to be true we need to simultaneously test it across multiple clock mechanisms and that has not been done. Clocks are mechanisms that are affected by motion, and by gravity and various forces, so they show different times when these differ. Our equations also lead to different time measurements by observers. However, unlike special relativity, in our theory, the ratio between the time measured by the two observers takes into account the mechanics of the event being measured. To illustrate special relativity’s time dilation many textbooks and popular books give the example of the “light clock,” whose mechanism we detail in chapter 3. In this case our equations yield the same time factor as special relativity. But in our theory different clock mechanisms observed by the same two observers could give different time ratios. Special relativity has a time dilation formula that applies between the inertial frames of the two observers. Using this formula, the ratio of time rates between clocks in the two inertial frames is computed from the relative velocity between the frames. This formula has been tested multiple times using atomic clocks. In special relativity the ratio between the time measured by observers in these two frames will have this same computed value, no matter what the clock mechanism or the event being measured. So to confirm this we need to simultaneously test with different clock mechanisms and show that time dilation remains the same irrespective of clock mechanism. Unfortunately for special relativity, as we discuss below and in full detail in chapter 3, it has already been shown that natural cosmic clocks – quasars being an example of a such a clock – behave differently than atomic clocks when it comes to time dilation. Special relativity has failed this test involving different clock mechanisms!

Length contraction has not been experimentally tested at all. In our theory length of an object remains invariant, and there is no length contraction. Many in physics look only at the mathematics of a physics theory and they can correctly point out that, mathematically, there is no problem with length contraction. However, we are talking physics, and we doubted it was physical reality. What is special relativity’s length contraction? From the Lorentz transformations it follows that length of an object moving relative to you contracts parallel to the direction of motion. Suppose Other and You both have a measuring stick of the same length. Other gets into a very fast vehicle and zooms past You; assume that both sticks are aligned parallel to Other’s direction of motion. As Other passes You, you will notice that Other’s stick is shorter. At v = 0.866c Other’s stick would have contracted to half the length of your stick. It is not just the stick, Other’s vehicle and everything in it will all contract parallel to the direction of motion. And, of course, this happens all the time as people move relative to each other, except that the contraction is so small at everyday speeds that you cannot observe it. We consider length contraction to be one of the strangest claims in the history of physics, and we have always felt that special relativity came with a clear expiry date because the day length contraction claim is experimentally tested would be the day this theory falls. However, giving a rigid body enough speed would be a technological challenge. We also always felt that time itself does not dilate and that properly testing time dilation, by using diverse clock mechanisms, would experimentally topple special relativity before failure of its length contraction does. Where we did agree with Einstein was that the two postulates of special relativity were physical reality.

We have noted that in the path to the Lorentz transformations Einstein made unstated assumptions by choosing to avoid infinity and choosing to start with distance and time. Einstein followed two other paths which we consider erroneous and based on unstated assumptions. These two other erroneous paths were adopting the linear thinking of Newtonian physics and also adopting the wrong philosophy of time based on a seeming lack of realization that, within Newtonian physics itself, two interpretations of time are possible. We discuss these further in the next two chapters.

By our equations, have we shown Einstein’s relativity equations to be wrong? No, only experiments can do that, and they have done so. Independent of experiments, what we have theoretically done, using simple mathematics, is to give a counterexample to Einstein’s “derivation” that special relativity’s two postulates necessarily lead only to a certain set of equations, namely the Lorentz transformations. Einstein’s derivation of the Lorentz transformations from the postulates was based on unstated assumptions, and thus was not a derivation at all. That derivation is widely accepted and celebrated. Following Einstein’s thinking, various derivations of the Lorentz transformations have since been published, and this link between the postulates and the transformations is a cornerstone of relativity. This derivation is taught as part of a standard college course in modern physics. Reputable physics textbooks derive the Lorentz transformations, in a claimed mathematically rigorous manner. Numerous physics papers that review or discuss relativity similarly accept that the Lorentz transformations can be derived from the postulates; popular books and articles on the subject repeat this claim.

Einstein’s derivation meant that it has been mathematically and rigorously shown that A (the postulates) necessarily implies B (the Lorentz transformations). Physicists have studied and checked this derivation thoroughly for over a 100 years. However, as philosopher Thomas Kuhn noted in The Structure of Scientific Revolutions, the general aim of physicists is to preserve rather than try to refute their foundational theories. Therefore, it should not be generally surprising that all of them would find the derivation to be correct, and we go into more specifics on this matter in the next chapter. It is this “derivation” that we have shown to have been based on unstated assumptions and thus not a valid derivation. We have achieved this because we found a counterexample C (our new equations) that shows that A does not necessarily imply B but can equally well imply C.

We are not questioning that the postulates of special relativity are correct and, in fact, we are in full agreement with them, having actually explained the light postulate. We are questioning the Lorentz transformations. There are two issues to be decided:
(1) Whether, by having a counterexample, we have shown that Einstein’s derivation was invalid. Three physics Nobel Prize winners and others have reviewed this counterexample and none have been able to state that we do not have a counterexample.
(2) Whether B (Lorentz transformations) or C (the Equations we found) are the correct space and time equations. These two sets of equations make different experimental predictions and experiments are the way to show that relativity is wrong and that the Lorentz transformations are not reality. Lorentz transformations have failed the test involving different clock mechanisms.

We have shown that Einstein did not have a derivation of the Lorentz transformations, and we believe physics professors should therefore stop teaching that “derivation” as part of their standard modern physics course.

. . . 

We continue the discussion in the previous chapter of Einstein’s path to the equations of special relativity, called Lorentz transformations. And we discuss in more detail some of the related philosophical matters. Again, the Lorentz transformations of special relativity replaced the equations of Newtonian physics. Since we have a counterexample to Einstein’s derivation that special relativity’s two postulates necessarily lead to the Lorentz transformations, we already know that his claimed derivation of the Lorentz transformations cannot be correct.

There are other books and websites devoted to attacks on special relativity. We do not make a frivolous or amateurish attack. In most attacks on special relativity, the light postulate speed limit is the one questioned; most such attacks are by amateurs who are looking to remove the speed limit but do not offer equations of their own. Many people want a future where we can zoom across the universe as fast as we want. After all, even at the speed of light travel to the nearest star would take years, which means we are not going anywhere in a hurry and are effectively restricted to lifetime travel to a very small region of the vast universe. In science fiction they have the concept of warped space or hyperspace, without which the Star Trek crew would reach nowhere in their five year missions. In fact, as we see below, even mainstream scientists having a need to modify special relativity’s equations would modify the constancy of the speed of light – though only slightly. A potential replacement of special relativity, we felt, would involve one that offers equations explaining the constancy of the speed of light, not one that in some way alters the constancy. Our equations keep the two postulates perfectly intact and, by explaining the light postulate and thus making it not a postulate, completely rule out the faster than light travel for mass that is proposed by many amateurs and mainstream scientists.

In May 2017, Nobel Prize winner Gerard ‘t Hooft replied to us regarding our forming alternative equations to special relativity that also preserved the postulates and thus were a counterexample to Einstein’s derivation: “[T]hink can outsmart more than a century of theoretical physicists … Please be assured that this is elementary physics, taught to freshmen students in a few weeks time.” (This was part of the same email that we quote from in chapter 1, regarding infinity).

Gerard ‘t Hooft’s absolute confidence and blind faith that special relativity’s foundations cannot be toppled has been the problem with special relativity, with students being indoctrinated into accepting their professors’ faith. What fool will question the foundational derivation of what is today deemed “elementary physics”? Students swiftly and faithfully memorize the Lorentz transformations along with Einstein’s derivation that shows no other equations consistent with the two postulates are possible; in such pursuit they follow the same scientific tradition and practice by which much of Aristotelian scientific reasoning was uncritically memorized. Professors who today are the experts in charge, including ‘t Hooft, are products of this ongoing system of deep faith in special relativity. 

We share technical specifics of comments from physicists in chapter 4, and there we give ‘t Hooft’s and other editors and referees review of our paper, “Space is discrete for mass and continuous for light.” Physicists have not attempted to rebut our proper and rigorous scientific counterexample to the foundational derivation of special relativity using reason and intelligence; instead, anger, evasion and refusal to address the specifics have been the general reaction of relativity worshipping physics authorities.

. . .

Let us recap Einstein’s unstated assumptions in concluding that the Lorentz transformations were the only ones consistent with the postulates. In chapter 1 we discussed how Einstein chose to avoid infinity and chose to start with distance and time, rather than velocity directly. These choices were seemingly born out of the physics prejudices of Einstein’s time and these prejudices are even stronger today, being firmly cemented into modern physics by special relativity. These were choices made by Einstein regarding what path to follow or not follow in getting to new equations of space and time. By not considering, or not being aware of, alternative paths he had already made unstated assumptions about what paths are available. A derivation based on such unstated assumptions is not a valid derivation. Einstein followed the standard interpretations of Newtonian physics in the matter of time, and reached certain conclusions, as we discuss in the next chapter. However, we do not follow this standard interpretation of time in Newtonian physics and do not reach the same conclusions. Another methodology Einstein followed from Newtonian physics is regarding how to add velocities, which we discuss later in the chapter.

Was it not wise of Einstein to stick closely to Newtonian physics which was so well verified until the matter of constancy of speed of light arose? Well, what Einstein did not realize is that there were other available choices on how to modify Newtonian physics. Our equations also limit down to those of Newtonian physics. However, we retain the three-dimensional space of Newtonian physics, with time being separate, and we also retain constancy of length of objects. Just because all observers see light at the same speed does not necessitate, though Einstein’s derivation concludes that it does, that one must give these up. As noted in chapter 1 and discussed further below, length contraction to us was a strange and unwanted phenomenon that would not survive experimentation. Also, we have explained the constancy of the speed of light rather than postulated it, and an unexplained postulate was the door Einstein left open for us to topple his derivation of the Lorentz transformations and get alternative equations.

Let us pause here to review this task of finding unstated assumptions made by Einstein that we have taken on. Is this how theoretical physics functions? Further, are we out to also prove that even prior to the matter of constancy of the speed of light, Newtonian physics, by itself, was wrong in its conclusions? Answering the first question, looking for unstated assumptions in foundational theories is not how theoretical physics functions today because today’s physicists normally never attempt to refute foundational theories (and later in this chapter we explain in detail why we qualified our answer by adding today). In particular, Einstein’s reasoning on which the equations of special relativity are founded has been declared by physics experts and authorities to be beyond question. Addressing the second question, while we can argue about interpretations of speed and time in Newtonian physics, such arguments remain philosophical and do not attempt to change the laws and equations of Newtonian physics. However, carrying over conclusions about speed and time from Newtonian physics has serious implications for the new situation regarding what set of equations follow from the constancy of the speed of light.

By following the standard interpretations of Newtonian physics in matters of speed and time, Einstein reached certain conclusions. We stress the word interpretations because that is where philosophy comes into physics, and only through philosophical analysis were we able to counter Einstein’s derivation. (Of course, philosophical interpretation is the start and not the end of physics analysis, and we had to change the mathematical Newtonian velocity addition).

Different philosophical thinking can actually lead to different physics equations, as we have shown, and that should be reason enough to be very conscious of possible differences in philosophical interpretations in the foundations of physics. However, the importance accorded to the role of philosophy in physics by Einstein and many of his predecessors is not shared by most physicists today. Einstein’s quotes below from 1936 and 1949 respectively give a glimpse of his views:

The physicist cannot simply surrender to the philosopher the critical contemplation of the theoretical foundations; for, he himself knows best, and feels more surely where the shoe pinches. In looking for a new foundation, he must try to make clear in his own mind just how far the concepts which he uses are justified, and are necessities (italics mine).^[12]

A knowledge of the historic and philosophical background gives that kind of independence from prejudices of his generation from which most scientists are suffering. This independence created by philosophical insight is – in my opinion – the mark of distinction between a mere artisan or specialist and a real seeker after truth (italics mine).^[13]

The value given to philosophical thinking in the physics of space, motion and time has so dramatically declined in the decades after Einstein’s death that even the possibility of different philosophical thinking from that of relativity leading to new foundations would be mocked and dismissed.

Steven Weinberg has a chapter titled Against Philosophy^[14] in one of his books and Stephen Hawking announces on the first page of one of his books that “philosophy is dead.”^[15] Physicists Lawrence Krauss and Neil deGrasse Tyson also piled on in loudly dismissing the role of philosophy. Skepticism regarding the foundations can arise from philosophical questioning; such philosophical contemplation, which poses the greatest danger to relativity dogma, has been entirely banished from physics. It is not physics alone that pays the price, and these banishers of philosophy can personally pay a heavy price. The life work of Stephen Hawking is almost entirely based on the spacetime and equations of relativity, and not much will survive of his work if these are not reality. And as for his famous book on time, that too is based on the concept of time in relativity.

In chapter 1 we quoted a top relativity expert, who being philosophically inclined was glad that we were removing the need for a postulate – which we did by explaining the constancy of the speed of light. But while we also had other problems with the foundations of special relativity, as we have specified, we saw the concept of postulate as an invitation to provide a missing explanation. However, those who decide to reflect on the philosophical foundations of relativity seemingly memorize the philosophy as it follows from the foundations of the theory, rather than think critically about philosophical foundations as the above professor was inclined to. Thus almost all physicists now love Einstein’s postulate style. Weinberg tells us how, like almost all others, he adopted himself to admire the postulate concept as a philosophy:

We learn about the philosophy of science by doing science, not the other way around … A favorite example of mine, one much closer to home, is presented by Albert Einstein’s development of the Special Theory of Relativity in 1905. For some years before 1905 a number of physicists had been worrying about why it seemed to be impossible to detect any effect on the speed of light of the earth’s motion through the ether … He took as a fundamental hypothesis the principle [postulate] of relativity, that it is not possible to detect the effects of uniform motion on the speed of light … In this work Einstein set the tone of the twentieth century by taking a principle of symmetry, or invariance – a principle that says that some changes in point of view cannot be detected – as a fundamental part of scientific knowledge, a hypothesis at the very roots of science, rather than something that is unsatisfactory until it can be deduced from a specific dynamical theory. In other words, Einstein had changed the way that we score our theories (italics mine).^[16]

The title of a public speech by Frank Wilczek exclaims, Symmetry: How Einstein Changed the Way We See Everything^[17] and his book adds: “These big ideas – relativity, symmetry, invariance, … form the heart of modern physics. They should be, though they are not yet, central to modern philosophy and religion (italics mine).”^[18] Relativity hyperbole seems to have replaced philosophy as the new path, whereby a principle such as symmetry that was already part of physics and can be associated with many past physics theories, including Newtonian space and time equations, is suggested to be a unique philosophy of relativity. Weinberg reiterates: “Symmetry principles made their appearance in twentieth century physics in 1905 with Einstein’s identification of the invariance group of space and time … expressions of the simplicity of nature at its deepest level.”^[19] The “deepest level” actually would be explaining why a postulate is true. What is the great new Einsteinian philosophical style that Weinberg, Wilczek and others admire? Is it that a particular principle of symmetry or invariance was postulated by Einstein rather than explained? Is that failure to provide an explanation better than to explain why something is true? Would explaining the constancy of the speed of light ruin the symmetry? Physicists, in their new version of philosophy, confuse postulate with the beauty of symmetry. Weinberg, Wilczek and others assume that Einstein’s postulate cannot be deduced from anything else and no explanation of why the postulate is true can be possible. Symmetry is a mathematical property founded on equations. The special relativity symmetry is called Lorentz symmetry. That and other much hyped symmetries or invariances would be wrong if the equations called Lorentz transformations are not reality. Starting in 2005, leading physicists saw our explanation for the constancy of the speed of light, as detailed in chapter 4 and, matching with the behavior of the worst of church authorities when faced with science that goes against their dogma, evaded the matter. These physics leaders have been peddling relativity and symmetry hyperbole to their colleagues, students and the public. What are you going to do admire about a favorite physics symmetry if it is not a reality of nature!

(We have not discussed ether, which is mentioned in above quote, because our explanation of the constancy of the speed of light is such that there is no need to discuss the nature of any possible ether; in chapter 1 we explained the constancy of the speed of light without ether coming in. Unlike Einstein’s special relativity where a postulate is employed to make ether superfluous, our explanation of constancy of speed of light makes ether superfluous to our theory. However, though entirely superfluous to our theory, we do visit ether again in chapter 5 and discuss its relevance and renewed general status.)

 . . . 

However, there are some in physics today who express the belief, common among philosophical physicists of the pre-WWII era, that determinedly looking for wrong or unstated assumptions in foundational theories – special relativity included, they say – should be part of what physicists do. Einstein himself was one such philosophically inclined physicist till the end of his life, and his above comments do not make relativity worshipping physicists happy. But, as we see, even for today’s few philosophically inclined, there are boundaries, and examining the foundations of Einstein’s special relativity derivation has been off limits. Who are these other philosophers, even though they live in a box that restricts them from truly foundationally challenging special relativity? Physicist Lee Smolin is one who has a weakness for philosophy and hidden assumptions, and in his book, The Trouble with Physics, suggests that there might be “some wrong assumption we are all making”^[26] and someone “needs to find that unexamined assumption.”^[27] Lee Smolin and his research partner Carlo Rovelli have become the public face of loop quantum gravity; as noted in chapter 1 loop quantum gravity is one of the two major approaches attempting to unite general relativity (gravity) with quantum mechanics, with string theory being the other path. The Trouble with Physics was an attack on the then runaway public relations victory – within physics departments – of string theory. Anti-string theory blogger Peter Woit followed with his book. Rovelli later joined the public relations battle with his books. String theory holds special relativity’s Lorentz transformations absolutely sacrosanct, with their leader Ed Witten and others sharing this common faith.

What attracted us to loop quantum gravity was that people within it were, like us, interested in discrete motion and were boldly trying to modify special relativity. These rebels, who would modify special relativity, are mainly from Europe and Smolin (who is an American living in Canada) suggests that such pursuit would not have earned them a position in American physics, though that has been changing slowly, particularly with quantum gravity competitor string theory not living up to early hopes. What was of most interest to us was that these loop quantum gravity folks were looking to modify special relativity’s length contraction, by having observers measure equal lengths at small scales. We certainly shared their desire to modify length contraction and our theory entirely removes length contraction. But our theory does not share the fundamental principle of loop quantum gravity that space itself has a discrete structure with a minimum length. As we saw in chapter 1, in our theory light moves continuously through space and, for mass, the discrete motion has jump lengths that become smaller as speed increases and get infinitesimally (i.e. arbitrarily) close to zero. Further, our mathematical explanation of “how” and “why” of the light postulate will not allow any violation of the constancy of the speed of light, whereas the discrete structure of loop quantum gravity and other such suggested modifications of special relativity involve slight violations of the postulates. Their proposed equations that would replace the Lorentz transformations are mathematically complicated, and we believe this results from these theorists putting on themselves the restriction that their equations must have the Lorentz transformations a limiting case. Our alternative simple equations, which form a counterexample to Einstein’s derivation of the Lorentz transformations, have discrete motion while perfectly preserving the postulates. Again, we do not have discrete space in our theory, since light travels continuously and there is no minimum jump length for mass. In loop quantum gravity discrete space causes the speed of light to be slightly different for different frequencies of light, thus causing slight violations of the constancy of speed of light. In our theory the discrete motion of mass is used to explain why light will always be seen to always travel exactly at the same speed. Thus discrete motion, in the way we propose, becomes the unexplained cause of the constancy of speed of light and not a cause of slight deviation from that constancy.

Another group that was of interest to us had Alan Kostelecký as its major proponent, and these comprised mainly experimentalists that were looking for “Lorentz violations,” as a means to extend what is known as the Standard Model of particle physics. But what they called a search for “Lorentz violations” was mainly a search for violations of the postulates of special relativity and not a test of the equations which comprise the Lorentz transformations; however, for them both were the same since they believed that testing the postulates is equivalent to testing the Lorentz transformations. Our theory states that the two postulates hold true but that the Lorentz transformations do not.

Both the quantum gravity and the standard model extension folks had learnt and accepted the foundational reasoning of Einstein’s derivation, as had the world, that the two postulates necessarily imply the Lorentz transformations. Thus they worked under the restriction that having new equations would need a modification of the postulates.

João Magueijo, in his book Faster Than The Speed Of Light, rails against the sacrosanct status accorded to special relativity, arguing for the need to modify its equations:

Lee [Smolin] and I discussed these paradoxes at great length for many months, starting in January 2001 … The root of all the evil was clearly special relativity. All these paradoxes resulted from well-known effects such as length contraction, time dilation … The implications were unavoidable: To set up a consistent quantum gravity theory, whatever that might be, we first needed to abandon special relativity. We realized that many of the known inconsistencies of proposed quantum gravity theories probably also resulted from religiously assuming special relativity. Our reasoning was therefore that before doing anything clever, special relativity should be replaced by something else that rendered at least one of E_p [energy], L_p [length], and t_p [time] the same for all observers [at small scales] … But as we have seen before, special relativity results from just two independent principles [postulates]. One is the relativity of motion, and the other the constancy of the speed of light … solution to our puzzle could be to drop the relativity of motion … or the speed of light would no longer be constant (italics mine).^[28]

As the above book title states, Magueijo suggests modifying the constancy of the speed of light postulate through what are called varying speed of light (VSL) theories. Unlike loop quantum gravity where slight variations of speed of light come in because of the discrete nature of their proposed space, VSL, or at least Magueijo, revels in intentionally rejecting the light postulate as a starting point, and does this for reasons not originally related to formulating a theory of quantum gravity. Magueijo the VSL theorist met up with Smolin the loop quantum gravity (LQG) theorist; together they combined their pursuits and got complicated new equations that limit down to the Lorentz transformations. But the postulates are, in our view, good and beautiful principles and do not need to be changed to remove the “evil” of length contraction and time dilation. Again, the Appendix contains our theory’s simple equations that remove length contraction and time dilation while holding on to the constancy of the speed of light and to clocks showing different times. All suggestions by LQG and VSL theorists that in the near future certain types of experiments may show a variation in the speed of light, with the speed being based on frequency of light, have not panned out and speed of light continues to stay perfectly constant. Einstein simply postulated it, leaving a door open for LQG and VSL speculation, but we explain why the speed of light will always be constant and close that door.

Smolin, Rovelli, Magueijo and all others believed that the postulates would need to be modified in order to keep a certain physical quantity (or quantities) the same for all observers. Our alternative equations, which we were looking to replace the Lorentz transformations with, would topple this dogmatic belief. We were happily alone in looking for a possible new theory whose equations would have Newtonian physics as a limiting case (and also maintain the Newtonian constancy of length), and that would entirely replace the Lorentz transformations rather than continue to maintain them as the foundation of the new equations must link to. Further, to repeat, we believe both the postulates of special relativity are physical reality and were looking to get new equations that would be consistent with both postulates i.e. without modifying the postulates in any way. If we succeeded, what would get the theory immediate recognition (we expected and hoped) was that, by finding such new equations which are consistent with the two postulates, we would have a counterexample to Einstein’s derivation. Existence of a counterexample would be immediate proof – no experiments needed – that Einstein’s reasoning that the two postulates necessarily imply the Lorentz transformations, was, in fact, wrong. We did succeed in finding a counterexample to Einstein’s derivation, exactly as we hoped. But then began a science vs. religion struggle against the blind worship of Einstein’s derivation, with the authorities of the church of physics employing evasion and suppression methodologies against the scientific reality of a counterexample.

The task we had taken on was to show that the link between the two postulates and the Lorentz transformations is not a valid one. Accepting Einstein’s derivation of the Lorentz transformations from the postulates, and not finding the unstated assumptions that form its basis, is where modern physics went wrong!

This book goes beyond physics and relativity into philosophy of science and sociology of science, and into comparison of scientific and religious dogma. Our interest in these developed as we interacted with physicists. We go into these matters for much of this remaining chapter, coming back to relativity specifics near its end and in the following chapters.

. . . 

Yet, while noting that the nature of authorities is primary in what determines whether scientific dogma is greater in practice, there are other factors worth examining regarding the nature of scientific dogma vs. religious dogma. We will stick primarily to physics in the comparison below and sometimes use the case of special relativity to illustrate our comparison, though other science fields could also replicate such a situation. Planck is paraphrased as saying, “Science progresses from funeral to funeral.” Indeed, it is very hard for scientists to leave the foundational dogmas they have believed in, and they tend to become opponents of truths that are against their dogmas. This view of Planck does not go well with the public relations narrative that scientists are objective and priests are dogmatic. Yet Planck stated it openly, illustrating how he was the philosophically inclined pursuer of truth who could say potential truth that his colleagues would not like to hear. Indeed, as is widely noted by Einstein biographers, it was Planck, more than any other person, who quickly supported dissemination and discussion of Einstein’s 1905 paper.  . . .

. . . 

Carlo Rovelli, among the greatest admirers of general relativity, talks of both special and general relativity in his books, noting that “Special relativity is a subtle and conceptually difficult theory. It is more difficult to digest than general relativity (italics mine)”.^[34] Special relativity is “subtle,” in our view, in that the physics question of what equations follow from the constancy of speed of light is subtle. And for us special relativity is “difficult to digest” because of its lack of rigor in providing the answer, thus allowing a counterexample to its derivation and, additionally, because of its lack of explanation for constancy of speed of light. Einstein stuck to the great dogma, seemingly started by Aristotle, of avoiding infinity in physics. Subtle is the Lord, as the title of Einstein’s acclaimed biography by Abraham Pais proclaims and, as we have shown, infinity is God’s subtle number that provides the explanation for the constancy of the speed of light.

 . . .

 Wilczek further notes in his Nobel Prize lecture^[41]:

Quantum mechanics and special relativity are two great theories of twentieth-century physics. Both are very successful. But these two theories are based on entirely different ideas, which are not easy to reconcile. In particular, special relativity puts space and time on the same footing, but quantum mechanics treats them very differently. This leads to a creative tension, whose resolution has led to three previous Nobel Prizes (and ours is another).

And Wilczek notes the theoretical foundations of particle physics: “combining quantum mechanics and special relativity seemed to lead inevitably to quantum field theory [QFT].”

Wilczek spent many years staying in the house where Einstein lived; it might have been wise for him to also spend some years at Newton’s old house pondering how his physics did not have a space and time that was so dramatically incompatible with quantum mechanics, and whether special relativity was the only possible way to resolve the matter of speed of light.

 . . .

We differed philosophically regarding infinity and the physical world, and went back to 1905 and actually incorporated infinity as the means of explaining the constancy of speed of light, leading to new equations that would replace those of special relativity. Our theory has discrete motion for mass, but not discrete space with a minimum length; such minimum length is a path away from infinite divisibility, and we were not looking to escape the reality of the infinite in the physical world. And our path leads to the constancy of length and not having time itself dilating, thus avoiding these troubling incompatibilities with quantum mechanics.

 . . .

In founding special relativity, Einstein continued thinking along the ‘linear’ foundations of Newtonian physics and made the unstated assumption that velocity must be added the way Newton added them. We see that Einstein’s velocity addition is also ‘linear’ just as Newton’s was. Einstein failed to abandon this ‘linear’ thinking in Newton’s equations and thus failed to get the right equations. Newton did not have any information that would suggest that light is not obeying the common sense classical velocity addition, so there was no reason for him to think beyond the simple linear classical velocity addition and look for a new theory of velocity that would explain the constancy of speed of light. Einstein had the facts about the behavior of light but was unable to abandon the ‘linear’ velocity addition of classical physics, and built relativity on this continued ‘linear’ thinking. Einstein did not have a theory of velocity different from Newtonian and simply postulated the constancy of speed of light. As explained in chapter 1, we have a theory of velocity that abandons the ‘linear’ velocity addition of Newtonian physics and relativistic physics. For us, this abandonment of Newtonian velocity addition was key in explaining the constancy of speed of light.

You can skip the below technical paragraph if you wish, since following it is not necessary for continued reading.

There is a (u_x ± v) term denoting simple ‘linear’ velocity addition that appears in both Newtonian physics and relativity. Let us look at the typical setup which considers two observers, You and Other, who are looking at a moving object. Other is moving at velocity v is the positive x-direction relative to You. If You see an object moving at velocity u how does Other see that object moving? In chapter 1 we looked at motion in a single line for simplicity but, of course, objects move in three dimensions. Velocity is a vector with a magnitude (value) and a direction, and a vector can be broken into components along x, y and z directions. u_x represents x-component of the velocity u. Vector components are numbers with signs, and the sign given to individual components comes from the vector’s direction. Breaking vectors into components is a way to add or subtract vectors. It is the x-component, u_x, from which v is added or subtracted, because v was assumed to also be in the x direction. Given that we took v to be in the positive x-direction, according to Newtonian physics (ignoring relativity) Other will see the x-component of velocity of the object to be u’_x = (u_x – v). In relativity this (u_x – v) term also appears in its formula for u’_x. In relativity (u_x – v) itself is not the x-component of velocity as seen by Other but is still a linear velocity addition. In our theory velocity addition is not linear because from u_x and v we get jumps per unit time N and those are what we add, as explained in the previous chapter. Thus we abandon the ‘linear’ velocity addition of Newtonian and relativistic physics.

 . . .

The philosophy of time has an increasing number of books, articles, and video lectures about it nowadays, discussing the evolution of time from Newton to Einstein and their respective “time flow” and “time flow affected by motion.” Both these “time flow” concepts can be brought down using clock experiments; finally, emerging experimental reality is at hand to bring an end to centuries of mistaken philosophy. This wrong “time flow” philosophy, which states time to be an independent physical entity, came from Newtonian physics and then was built upon – not repudiated as philosophers and physicists say – by Einstein. Our focus is on the common Newton-Einstein philosophy regarding there being “time flow” and on the further Einsteinian modification that time itself dilates. Our time philosophy aligns back with the ancient pre-Newtonian philosophy that time does not flow as an independent physical entity; we agree with the philosophy that time is a measure of change and thus there needs to be some physical change for time to exist. We unite this ancient philosophy of time with the modern reality of the constancy of speed of light.

A favorite description by authors narrating the path from Newton to Einstein is that Einstein freed us from the “absolute time” of Newtonian physics. We would agree that this is true. But things are not that simple. While the Lorentz transformations, the equations of special relativity, do remove the “absolute time” flow of Newtonian physics, they preserve the concept of time flowing as an independent physical quantity. (We will address the matter of relativity’s spacetime later in the chapter.) Physicists summarize special relativity’s modification of Newtonian time flow with phrases such as, “Motion affects the flow of time.”^[52]

As discussed in chapter 1, special relativity addresses clocks in inertial frames (which are reference frames moving at constant velocity relative to each other). Einstein’s derivation claims to show that constancy of speed of light necessitates that all clocks in a frame, irrespective of clock mechanism, will show the exact same time dilation. This happens because Einstein’s derivation reasoned that time itself must dilate if the speed of light were to be constant for all observers; however, we have overturned that derivation. We have now shown that Einstein’s derivation that time itself must dilate and therefore the exact same time effect should hold for all clocks in a frame is not correct since, as explained previously, we have a counterexample to the derivation. Our alternative new equations, while incorporating the same constancy of light, show that for some clocks there will be the precise time dilation predicted by special relativity while for other clocks there will be no time dilation whatsoever. And it is not one or the other; depending on clock mechanisms you can have various magnitudes of time effects. This is because, in our theory, time itself does not dilate, and time does not even itself “flow” as an independent physical quantity; in our theory it is a clock’s mechanism that determines the observed time effect on a clock. Quasars are a type of clock that will see no time effect based on their motion, according to our equations, and this is now emerging as telescope-observed reality that violates the time dilation of special relativity.

Let us now examine Einstein’s reasoning connecting velocity and time, from which he made the conclusion that “Motion affects the flow of time.” This conclusion about time has two parts. To analyze the possible cause and effect in “motion affects” we look at the philosophical and logical connections between time and speed; further, the Newtonian physics concept of “flow of time” itself needs examination.

Einstein followed this seemingly infallible logic: since speed=distance/time the only way speed of light would remain the same when measured by different moving observers is if there existed formulas by which distance and time measurements changed between the reference frames of these observers. We quote from the book The Evolution of Physics by Albert Einstein and Leopold Infeld^[53] pp. 195-6: “If the velocity of light is the same in all [coordinate systems], then moving rods must change their length, moving clocks must change their rhythm, and the laws governing these changes are rigorously determined … there is no other way.” The “laws” are the Lorentz transformations and Einstein’s derivation purported to show these equations to be “rigorously determined” and show that “there is no other way.” At the church of physics the believers sing in chorus that the “law” regarding length contraction and time dilation has been “rigorously determined” and “there is no other way.” Einstein’s conclusion and logic is unanimously accepted by physicists to be correct, and through popular books they teach this conclusion and logic to the general public. Lee Smolin discusses this logic in his book, The Trouble with Physics:

The key is that we do not measure speed directly. Speed is a ratio: It is a certain distance per a certain time. The central realization of Einstein is that different observers measure a photon [light] to have the same speed, even if they are moving with respect to each other, because they measure space and time differently. Their measurements of time and distance vary from each other in such a way that one speed, that of light, is universal.^[54]

Einstein’s above conclusion that for different observers to measure light to have the same speed it is necessary that observers measure lengths in space differently and measure time differently was wrong. We can argue that if we rearrange and put time=distance/speed then speed is no longer a ratio and time becomes the ratio, and then it is time and not speed that we can supposedly claim to not measure directly. The relationship between time and speed and whether one, and which one, should be considered the primary physical quantity is an interesting philosophical question. Time, and not speed, being a primary quantity is a dogma that we explicitly rejected in chapter 1. There we gave our simple reasons why, in our theory, we “have velocity and not time as the quantity we prefer to work with as a starting point.” Philosophically, we believe that change (such as that represented by velocity) is associated with the very existence of time rather than time flowing independently of anything else, and that philosophy affected our choice of what we start with: velocity (change) or time. And this different philosophy yielded different equations! The physics reality is that through our theory’s equations, we are able to explain the constancy of speed of light without observers measuring length of objects differently and without time itself dilating. The reasoning about the necessary implications of speed=distance/time is thus shown to be wrong. This unstated and wrong assumption about speed and time was central to Einstein’s thinking.

 . . .

  . . .  In fact, no equation of Newtonian physics necessitates that time is an independent quantity that “flows” at a constant pace. This statement would be surprising to many readers, since it contradicts what they have read in textbooks and popular science books that detail the path from Newtonian physics to special relativity.

. . .

There is no doubt that t’ = t equation holds true in classical physics and we have different observers measuring the same time for the same event. But our interpretation does not take the absolute time of Newtonian physics to have meant that time itself “flows” as an independent physical quantity. We could attempt to make a similar statement about observers in different frames and relativity’s relative time flow; however, in relativity time necessarily is an independent physical quantity and we have actual time dilation.

Our alternative interpretation of time in Newtonian physics, which goes against the conclusory Principia statement regarding time, is a philosophical interpretation that is fully consistent with the equations of Newtonian physics. One can either simply go with the Principia statement from Newton or one can try to understand the physics of time through possible interpretations that Newton’s equations allow. Physics authors have unanimously chosen the former when it comes to classical physics and time.

 . . .

 . . . In physics classrooms professors write out Einstein’s derivation, which is based on flawed logic, to show that it necessarily follows from constancy of light that time itself dilates, and the light clock is their illustration. Our equations which form a counterexample to this taught derivation are definitive proof of its flawed logic and its wrong claim that it is necessary that time itself must dilate! 

If it was time itself that was dilating, as it does in special relativity, then all clocks being compared between the observers’ frames would necessarily record the same dilation. Again, in our theory time itself does not dilate.  . . . 

. . .

Our paper was completed in January 2005 and was rejected by journal editors, mostly without comments on specifics, with our final attempts being in 2018. This is a history of that evasion and rejection, with some renowned names involved.

Peer review is the process by which the editor of a journal sends the paper to referees (with names of referees not publicly revealed). The referee would typically be a professor specializing in the topic. The editor can also make a decision on his or her own, without sending the paper to referees; in practice, this is often done when the decision is a negative one.

Many times a famous name can become involved in a publication decision. Albert Einstein was known for having supported the publication of potentially revolutionary papers by unknown authors, as was Max Planck who published Einstein’s special relativity paper. Addressing facts and reason was the working methodology in physics before WWII, and a recommendation by famous physicists to reject a paper would be for stated reasons. Evasion of the kind we encountered from famous names has not been standard physics practice; traditionally, scientists would give a reason. The nature of a field of science, as we have discussed earlier, varies with the nature of the authorities in charge.

 . . .

Most of the people mentioned below have great expertise with special relativity; these include the three Nobel Prize winners we quote below – whose expertise partly comes from quantum field theory (QFT) which is built to be consistent with special relativity. Others included those who had themselves had been working on possible modifications of special relativity as part of their pursuit of quantum gravity (uniting relativity with quantum mechanics).

. . .

Our paper was then submitted to Annals of Physics Editor and physics Nobel Prize winner Frank Wilczek on May 2, 2005:

Dear Esteemed Professor Wilczek:

… I share your great admiration for the works of Albert Einstein. However, Einstein wrongly thought that his equations are the only ones that can be shown to follow from his two postulates. My theory presents an interesting alternative …

We got this intermediate email from journal administrator:

Submissions are normally made through our publisher, Elsevier, via the submission tool at their site: http://www.elsevier.com/locate/aop and I look forward to receiving your paper through that site. I will log your ms. and assign a number, however, so that if you prefer to wait to do this until Prof. Wilczek had made a decision regarding publication, you may do so.

Cordially,

Eve Sullivan for ANNALS OF PHYSICS

And then Sullivan sent the rejection decision on May 21:

The editor has reviewed your paper and finds it to be too speculative. Thank you for having given us the opportunity of considering it. There is no further report.

“Too speculative” is seemingly a term available to editors looking to reject potentially revolutionary papers that they do not like, without sending them to referees. Again, looking at our argument above regarding Einstein publishing his arguably more speculative paper, what has changed in physics?

A 2020 Wall Street Journal article by Wilczek has as the title the question, Could Einstein Get Published Today?^[71] Wilczek answers: “[I]t probably wouldn’t be publishable in a scientific journal today … It might not even get past the first editors to be sent out to referees.” He elaborates: “Scientific journals and institutions have become more professionalized … an all-but-inevitable consequence of the explosive growth of modern science … and outsiders face entry barriers at every turn.”

We believe that the nature of a field of science can vary dramatically in different periods, and physics today is far more dogmatic than it was in Einstein’s time. Political and social power and interests centered around relativity have a big role in physics today. In Einstein’s time pursuit of scientific truth was paramount in professional physics. On the other hand, physics today is a relativity worshipping church that evades facts and reason that are against special relativity and wants to hide these.

Wilczek goes on to explain that the physics peer review system is still fine and Einstein would eventually have successfully published. But in which journal?  . . .  Physics now has a system where journals and media hide experimental and theoretical problems with special relativity: its time dilation and its central derivation.

. . .

Wilczek cites books by Sabine Hossenfelder, John Horgan and others and counter-argues:

I get asked about these books and their dismal messages frequently … For theoretical physicists they are a kind of reproach, since they argue that today’s physics has gotten itself into a dead-end … What’s going on here? Opinions may differ about the current health of physics, but … 20th-century breakthroughs … relativity … our theoretical understanding reached a very high plateau … a pinnacle of human achievement …When you have reached a high plateau, ascending still higher gets more difficult … Really, the plateau we’ve reached is a good place to be (italics mine).^[75]

We certainly appreciate many points made in the writings of Sabine Hossenfelder, John Horgan, Alexander Unzicker and Martín López Corredoira. Too bad that physics authorities don’t.

. . .

The dramatic problem with modern physics has been that its two main theories – relativity and quantum mechanics – are incompatible with each other. That itself should have been cause for caution regarding the extraordinary confidence in relativity. Special relativity, in our view, needs to be foundationally replaced and we have the replacement. 

 . . .

 Another referee hit us on experimentation in April 2005: 

The author derives velocity transformation laws that differ from those of special relativity. These laws have been precisely tested in a number of experiments and found to be correct. The author does not identify circumstances where his rules would be an improvement on special relativity. Since the authors notions have not been shown to have anything to do with reality, they are not relevant for a physics journal. 

The referee claims that the velocity transformation laws – where our theory begins its separate path from that taken by Einstein’s special relativity – have been verified in favor of special relativity in multiple experiments. Unfortunately, the referee was making these experiments up. We wrote to the editor: 

Could you please ask the referee to provide specific citations about these various experiments. 
… 
The experiments the referee refers to do not exist. 

Of course, the editor could not get us specifics about these non-existent experiments but, in reply, simply affirmed that “the decision for not publishing it is final.”

We got a couple of referee/editor objections regarding our use of infinity and zero, such as below: infinity x zero = c is mathematically undefined – one is not allowed, with reason, such equations in Physics, or for that matter in Mathematics. The referee uses the terms “undefined” and “not allowed.” These two terms are used in school math along with a third term, indeterminate, and taken to mean the same thing. But they are not the same. At a bygone time many would say 1/0 is “not allowed” or is undefined because that would be actual infinity and they would say there is no actual infinity and infinity exists only as a limit; however, today that would be a wrong statement given that actual infinity has been accepted since the time of Georg Cantor to be part of math. 0/0 is formally defined in math to be indeterminate which is different from “not allowed” or undefined. In math “indeterminate” is an accepted term and one sees a list of indeterminate forms. 

In math 0/0 is an indeterminate and can be equal to any (finite) number (crossing the zero over would show this). Another known indeterminate is ∞ • 0. What is new is that the indeterminate from math actually appears in our paper as an equation in the physics world. The equation ∞ • 0 = c did not dawn on us easily, and was a dramatically surprising breakthrough. But this was not due to any questions regarding its mathematical validity. We, however, thought more physicists would fight us on the mathematical validity of ∞ • 0 = c. However, pleasantly, was not the case with most referees and editors, many of whom were looking to attack or dismiss in any way possible. Whatever their surprise at the equation ∞ • 0 = c, the three Nobel Prize winners and the other big name editors did absorb it.

 . . .

Telescopes and their observations were in news. While browsing about telescope observations of celestial bodies in 2014, we discovered that quasars had failed special relativity’s time dilation all the way back in 2001! . . . 

. . .

The paper was submitted to Foundations of Physics in November 2014, with a letter addressed to ‘t Hooft.

We got the below rejection email:

… I regret to inform you that the editors had to conclude that this work is not suitable for publication in Foundations of Physics.

Gerard ‘t Hooft, Editor in Chief

Specific comments from a member of the Editorial Board:

The author of this manuscript fails to make clear how his/her work relates to current discussions in the foundations of physics. Regrettably, this fact places the current submission outside the scope of Foundations of Physics.

This is displayed by a lack of references to recent literature.

We responded:

Professor ‘t Hooft – The most recent reference mentioned in my submitted paper was the 2010 Quasars paper, where quasars are not showing Time Dilation. There should have been vigorous discussion of this experimental failure of Special Relativity in physics journals. But since today’s editors and authors are relativity-worshippers there is no such discussion.

From later correspondence with ‘t Hooft it seemed that the “editorial board” had entirely handled the submission and ‘t Hooft was not personally involved, though he seemed to have looked at the issue after we connected by email. These later emails were about the physics matter itself and were not regarding the submission to his journal. A couple of ‘t Hooft emails are mentioned in early chapters, and we quote further here from the times ‘t Hooft engaged with us on some technical matters regarding the paper.

. . .

As part of continued correspondence, we got this thoughtful email from ‘t Hooft on Nov 25, 2017:

… check the group property: L1 . L2 = L3, or, what happens when you add 3 velocities …

PS My arguments for not accepting the paper would still be as they were.

He thought he now had a technical victory punch against our alternative and thus added the PS regarding the 2014 paper rejection. Again, his name had been signed in the rejection but they were likely not his arguments to begin with because the paper rejection statement (above) was, frankly, too stupid to have been written by him; further, there were no technical points there whatsoever.

Our reply:

You point to group property regarding three velocities as a comparison. But please note that relativistic velocity addition is NOT a group operation because it is not associative. While all textbooks on relativity give the three-dimensional relativistic velocity addition, they almost never point out that these formulas – except when velocities are collinear – are neither associative nor commutative. This fact about relativistic velocity addition is not widely known, for details see …

We pointed to two references showing the above statement – a common online article on finer details of special relativity’s velocity addition formula^[77] and a book titled Analytic Hyperbolic Geometry and Albert Einstein’s Special Theory of Relativity^[78] – and noted:

Our velocity addition formulas also satisfy the properties of closure, identity and inverse that relativistic velocity addition does.

‘t Hooft seems to have conceded that objection, and in any case our reply can be checked to be correct.

The last email we received from ‘t Hooft was on Dec 9, 2017 where he said: “[Y]ou shouldn’t formulate the laws of relativity by guessing velocity addition rules.” We replied: “You ignore the advantages of my equations that I listed. You can call my equations a ‘guess’ since there is no derivation, but I would rather have a correct guess than have a mistaken derivation, to which a counterexample exists, as the foundation.”

. . . Foundations of Physics . . . editorial board had three names who had themselves been looking to modify special relativity: Carlo Rovelli who was editor in chief, Lee Smolin and Alan Kostelecký. In chapters 2 and 3, we have discussed our work and compared it with theirs.

Rovelli and Smolin were highly conversant with the matter of discrete versus continuous and the need to modify properties of special relativity such as its length contraction. They were also experts on the matter of time, having written entire books on it.

. . .

We wrote again on May 15:

Rejecting the paper without addressing the specifics is not acceptable peer review methodology, particularly given the multiple editorial board members with expertise in modifications of special relativity. Why are your papers – and that of your colleagues – on possible modifications on special relativity publishable but not mine? It certainly is not a matter of experimental testability because my paper is clearly superior in that respect. Why does the editorial policy of “severe restraint” regarding “relativity” not disallow these other publications?

. . .

Our final email regarding the submission was sent on Jun 3, 2018:

I appeal to the Editorial Board of Foundations of Physics …

Your journal describes itself to be the “leading journal for controversial issues concerning the foundations of modern physics” which “welcomes papers on issues such as the foundations of special and general relativity.”

We have a contradiction between the journal mission statement and the “severe restraint” rejection concerning special relativity.

Carlo Rovelli: You are an expert on possible modifications on special relativity, and my paper cites your papers on the topic. You note that “The worst enemies of knowledge are … those who would never accept their certainties to be questioned” and “the credibility that science enjoys rely on the intellectual honesty of the scientists.” I urge you to publish the paper, or give a reason for rejection. 

 . . .

For how many more decades will physicists waste their lives dogmatically building on what is not reality by refusing to replace special relativity?

Special relativity is the foundation upon which general relativity is built. Since the Lorentz transformations of special relativity are not reality, Minkowski spacetime reformulation of these cannot be reality and, in turn, the curved spacetime of general relativity, which is founded on this, cannot be reality.

We have toppled general relativity by taking out its special relativity foundations. However, we do not have a new theory of gravity. A theory of gravity to replace Newtonian gravitational theory was needed because Newtonian theory makes wrong predictions even within our solar system. A further theoretical problem with Newtonian gravity was that gravity was instantaneous whereas we have a speed of light limit in special relativity (and in our theory.) That Newtonian gravity can be reinterpreted to have the speed of gravity be equal to the speed of light is, arguably, a possibility (though some would challenge that and say it cannot be done without substantial problems arising). However, the key victory of general relativity over Newtonian gravity was in making the right predictions within our solar system.

Many Popular versions paraphrase physicist John Wheeler to give a short essence of general relativity: “Matter tells space how to curve, and curved space tells matter how to move.” (Wheeler properly used the rigorous term “spacetime,” rather than space.) Physically general relativity has been pictured in popular versions by a rubber sheet which represents space and a mass that curves the sheet.

The showdown between Newtonian gravity and general relativity occurred during a solar eclipse in 1919, and media coverage of that result made Einstein a celebrity overnight. Newtonian gravity had light bending by half the amount that was predicted by general relativity. Simply having differences in the amount of bending would be too boring a story for the public; the press skipped that key detail and even today many, if not most, physicists and media skip that detail when they transmit the 1919 history to the public. They suggest “mass bending light,” was an extraordinary and revolutionary Einsteinian idea, rather than state that only the degree of bending of light differed in Newtonian gravity. That the sun bends space would indeed be extraordinary and revolutionary, and that was taken to have been “indirectly” confirmed in 1919. However, there is actually nothing about light bending that requires mass to curve space, since Newtonian gravity gave a bending of light too.

There was another key victory for general relativity within the solar system. The perihelion (which means the orbital point closest to the Sun) of Mercury was not behaving in a way consistent with Newtonian gravity. The existence of a planet, Vulcan, between the sun and mercury was theorized to explain this. Such is the power of belief that, from time to time, observers kept reporting telescopic sightings of Vulcan. But it does not exist. General relativity was able to precisely explain the observations 

. . .

 Let us critically examine the experimental status of general relativity by itself, forgetting, for a moment, about problems with the correctness of the Lorentz transformations of special relativity, which problems alone would topple general relativity. We particularly examine the common repeat claims in books and articles written by physicists that general relativity has passed all experimental tests. We concentrate on two wide aspects: dark matter and curvature of space (or spacetime).

. . .

If there is no dark matter then general relativity is a wrong theory and all those additional bells and whistles in its favor will not save it. No number of experiments can prove a theory right but a single contradiction to its key foundations or predictions can prove it wrong.

. . .

After the first detection of gravitational waves, LIGO pointed to methodologies used to ensure that what was detected was not noise, including:

[LIGO’s inbuilt] PEM sensor network would easily detect any electromagnetic signal … external observatories were also checked for natural or human-generated electromagnetic signals … Although cosmic ray events are not expected to produce coincidences between detectors … cosmic ray rates at the LIGO-Hanford site and external detectors around the world were low and exhibited no unusual fluctuations at the time of the event.[91]

However, LIGO is a unique and extraordinarily sensitive detector that can seemingly detect all types of waves and particles, while these other detectors would only notify of electromagnetic ranges and particles they were designed to detect.

A further LIGO claim is regarding events such as that in August 2017 which was supposed to be a neutron star merger that produced both gravitational and electromagnetic waves. This event with two types of waves would be a confirmation that what LIGO detected was not noise but an actual event that can be independently confirmed. In this event, LIGO detected gravitational waves while simultaneously, 2 seconds later, independent telescopes detected electromagnetic waves. But how do we know what LIGO detected were also not electromagnetic waves or noise, as LIGO would term such? Again, telescopes only detect the electromagnetic ranges they are designed to but LIGO, on the other hand, can seemingly detect all ranges of electromagnetic noise. Further, over the following weeks, this merger kept producing various ranges of electromagnetic waves, which were detected by observatories designed for different ranges; thus diverse electromagnetic radiation seems to be a possible feature of such events. We believe it quite likely that for the first 2 seconds the merger produced electromagnetic waves outside the range of other observatories. There were other problems too with the August 2017 event.

Sabine Hossenfelder notes . . . Alexander Unzicker similarly writes regarding that event . . .

. . .

Gravitational waves are weakly interacting and comparing space and Earth detections of these would not produce the kind of differences that electromagnetic waves and other particles incident on the Earth would, in space vs. Earth detection comparisons. Thus by comparing space vs. Earth detections of supposed gravitational wave detections we can confirm that electromagnetic and particle noise is not what is being detected. Also, with a detector in space, the possibility of Earth-based coincidental noise at detectors will be gone.

Laser Interferometer Space Antenna (LISA) is a proposed European Space Agency space probe to detect gravitational waves. It is not over yet regarding gravitational waves, and the conclusion made regarding LIGO having measured gravitational waves may have been premature.

 . . .

General relativity has a curved spacetime based on a 4-dimensional geometry. This curvature of space (or spacetime) should be measurable. How do we directly measure the curvature of space?  . . . light rays in flat space would remain parallel, whereas in curved space (or spacetime) they would diverge away from each other or converge towards one another. By focussing on light reaching us from very far away objects we can make a determination  . . .

The cosmic microwave background (CMB) has visible distant “patches” or “spots” and their size has been measured to determine flatness. Physicists now largely accept, based on experimental data from high precision measurements by Wilkinson Microwave Anisotropy Probe (WMAP) and by the Planck satellite, that the universe is flat within a 0.4% margin of error. Parallel light rays in our universe stay parallel, and there is no hint of the exotic geometry of general relativity being reality.

Publicly, physics professors will confidently preach that general relativity has experimentally passed all tests. But where is the curvature of space? Privately, with the assurance that their name will not be divulged, general relativity experts can give a clear unequivocal view that lack of curvature is a serious negative for the theory. A professor from a top university, quoted in chapter 1, whose life-long specialty has been general relativity emailed regarding this clash of its curved spacetime with reality: “There is no experimental evidence, I believe, that our space-time is not conformally flat.” Being objective in addressing the zero curvature reality and being a traditionalist on options that need to be pursued, he was himself inclined to suggest the need for a replacement theory.

 . . .