**Infinity x Zero = c Explains the Constancy of the Speed of Light and Topples Einstein’s Special Relativity**

## “Annihilation” by Infinity that Aristotle Used to Argue Against its Existence is Actual Physical Reality

# Table of Contents

· Overview

· The Speed of Light is Constant But Einstein’s Special Relativity is Wrong

· ∞ • 0 = c Explains the Constancy of Speed of Light and Leads to New Equations

· “Annihilation” by the Infinite that Aristotle Used to Argue Against its Existence is Actual Physical Reality

· Einstein’s Special Relativity Derivation Has Been Toppled via our Counterexample

· Special Relativity is Wrong on the Philosophy of Time and Fails Experiment: No Time Dilation Observed in Certain Cosmic Bodies

# Overview

There have been a long list of attacks on special relativity, which have all failed because the speed of light continues to stay perfectly constant. (For those who do not know special relativity foundations, we will explain these after this paragraph, so do keep reading). Our technical physics paper titled “Space is discrete for mass and continuous for light,” is different from these failed attacks on special relativity in that it fully accepts both the postulates of special relativity as physical reality (without modifying them in any way), actually explains the light postulate (which Einstein couldn’t) and gives full replacement equations which form a counterexample to Einstein’s derivation that only one set of equations could be consistent with both postulates. Since we keep the postulates exactly as they are, all the experimental evidence in favor of the postulates also supports our theory. Most importantly, our theory is urgently needed at this time because of recent experimental failures of special relativity in certain cases. (The experimental failures of special relativity are not of the postulates but of other parts, where our theory diverges from special relativity). The results of these experimental observations are a failure for special relativity but are as predicted by our theory, and these observations should be further tested and confirmed. No alternative to special relativity has ever come close to having these verifiable qualifications. The open discussion of these details is being opposed by authorities of (what we call) the relativity-worshipping “Church of Physics.” The physics paper is included in our recent book as an Appendix and also available free at our website. In pursuit of scientific truth, refutation has always been sought and welcome, but evasion has been the methodology we have encountered.

# The Speed of Light is Constant But Einstein’s Special Relativity is Wrong

A physical reality of our universe is that the speed of light (in empty space), c, 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!

Albert Einstein’s famous 1905 Special Theory of Relativity 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.

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 experimental evidence for the light postulate is overwhelming, and there are no credible experimental results against it.

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 classical physics.

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.

# ∞ • 0 = c Explains the Constancy of Speed of Light and Leads to New Equations

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, c.

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. 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. And of course, in our theory as in relativity, mass cannot travel faster than light.

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, speed c, 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 the “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.

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.

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.

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 our paper). 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 Nu and Nv, where Nu would be a “finite value” (which we can calculate using our formula) whereas Nv = ∞. 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 Nv'= Nv — Nu = ∞ — “finite value” = ∞. From Nv'= ∞ we will get d'= 0 and from our formula, with these values of Nv' and d' we get velocity v' = Nv' • 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 physics paper.

# “Annihilation” by the Infinite that Aristotle Used to Argue Against its Existence is Actual Physical Reality

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.

Georg Cantor fought the authorities and dogmas of his time and brought *actual infinity* into mathematics. (Potential infinity or infinity as a limit was previously accepted, but not the concept of an actual infinite). Cantor biographer Joseph Dauben explains in *Georg Cantor: His Mathematics and Philosophy of the Infinite*, p. 122 the Aristotelian challenges to infinity faced by Cantor:

As the inspiration for centuries’ worth of opposition to the actual infinite, Aristotle required explicit confrontation … A typical argument used by Aristotle and by the scholastics involved the‘annihilation of number.’Were the infinite admitted, it was said that finite numbers would be swallowed up by any infinite number or magnitude. For example … their sum a + b … if b were infinite, no matter what finite value a might assume, a + ∞= ∞ … It was in this sense that anyinfinite number was thought to ‘annihilate’ any finite number(italics mine).

Was Aristotle wrong in claiming such *annihilation* would be caused by actual infinity? No. His *annihilation* argument is perfectly valid. Aristotle particularly pointed to such annihilation as being physically “absurd.” But such annihilation actually happens in the physical world! What Aristotle notes about infinity actually forms our explanation for the constancy of speed of light. We explain above the* addition* of *infinite* number of jumps associated with light and *finite* number of jumps that the observer makes: “For the case when You are observing light we have… ∞ — ‘finite value’ = ∞” (note that + or — work the same way). *No matter what the finite value, the infinite annihilates the finite number.* The speed of light *annihilates* the speed of the observer in that the speed of the observer does not matter when looking at light.

# Einstein’s Special Relativity Derivation Has Been Toppled via our Counterexample

Our equations, founded on ∞ • 0 = c, form an alternative to Einstein’s equations of special relativity (called the Lorentz transformations). Our equations are consistent with both of Einstein’s special relativity postulates, and are a counterexample to Einstein’s claimed derivation — taught in college-level textbooks — that Einstein’s two postulates necessarily imply the Lorentz transformations.

Our explanation for the constancy of speed of light, and the equations that follow from it, prove devastating for the *logic *of Einstein’s derivation of the equations of special relativity, which derivation claims to show that there are no alternative equations possible.

Another major difference in prediction between our theory and Einstein’s special relativity is that lengths remain constant in our theory; we do not have the special relativity *length contraction,*** **whereby different observers measure different lengths of objects.

*The Evolution of Physics* by Albert Einstein and Leopold Infeld* pp. 195–6 *states:

If the velocity of light is the same in all [reference frames], 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.”

The physics reality is that we are able to explain the constancy of speed of light without observers measuring length of objects differently and without time *itself* dilating.

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*, p. 228:

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.

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 reject. 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 time equations! Again, 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.

Brian Greene teaches the same “logic” of Einstein in his book *The Fabric of the Cosmos, pp. 46–47*:

Einstein figured it out, and the answer he found islogical yet profound… Since speed is nothing but distance divided by time, there is no other way … When we move relative to one another clocks do not agree … yardsticks do not agree.If space and time did not behave this way, the speed of light would not be constant and would depend on the observer’s state of motion.… Space and time adjust themselves in an exactly compensating manner so that observations of light’s speed yield the same result, regardless of the observer’s velocity … He was able to show precisely how one person’s measurements of distances and durations must differ from those of another in order to ensure that each measures an identical value for the speed of light (italics mine).

Our explanation for the constancy of speed of light refutes the claim — which originates from Einstein’s special relativity derivation — that “*If space and time did not behave this way, the speed of light would not be constant and would depend on the observer’s state of motion*.” Physicists today are great admirers of Einstein’s spacetime. However, just because all observers see light at the same speed does not *necessitat*e that one must give up our familiar 3-dimensional space of Newtonian physics, with time being separate, and move to a strange new 4-dimensional spacetime. We can all observe our physical 3-dimensional world, so why should we look for theories with more dimensions?

# Special Relativity is Wrong on the Philosophy of Time and Fails Experiment: No Time Dilation Observed in Certain Cosmic Bodies

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. Einstein modified Newtonian “*time flow*” by bringing in time dilation between reference frames. Many would counter that Einstein freed us from the “absolute time” of Newtonian physics. We would agree that this is true. But things are not that simple.

Our time philosophy aligns back with the ancient pre-Newtonian philosophy that time does not flow as an independent physical entity; we agree with this 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. 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; depending on clock mechanism you can have various magnitudes of time effects, including no effect.

Again, Newtonian “flow of time” was replaced in Einstein’s special relativity with “time flow affected by motion” whereby all clocks in the same (inertial) frame of reference would show the same time dilation. In the case of the “light clock”, which is widely used to illustrate special relativity’s time dilation, our equations yield the exact same time dilation. 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. However, clocks not being equally affected by motion and not giving the same time dilation is the emerging experimental reality, with certain moving cosmic clocks showing no time dilation whatsoever. 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. However, these facts have been hidden from physicists and the public, with physics texts, most science publications and popular science writers not covering them.

Let us look at the commendably honest time dilation failure coverage of the two science publications that are known for boldly and objectively reporting results that science authorities may not want disseminated.

*New Scientist* reported in a 2010 article titled *Time waits for no quasar — even though it should*, https://www.newscientist.com/article/mg20627554-200-time-waits-for-no-quasar-even-though-it-should:

Using observations of nearly 900 quasars made over periods of up to 28 years, Hawkins compared patterns in the light between quasars about 6 billion light years from us with those at 10 billion light years away.

All quasars are broadly similar … So one would expect that a brightness variation on the scale of, say, a month in the closer group would be stretched to two months in the more distant group.

[Article quotes Hawkins:] “To my amazement, the [light signatures] were exactly the same … There was no time dilation in the more distant objects.”

Phys.org, in a 2010 article titled *Discovery that quasars don’t show time dilation mystifies astronomers*, https://phys.org/news/2010-04-discovery-quasars-dont-dilation-mystifies.html, notes:

“This quasar conundrum doesn’t seem to have an obvious explanation.”

Beyond quasars, experimental failures of the time dilation equation of relativity’s Lorentz transformations have now begun piling up across space in gamma-ray bursts and even supernovae explosions; supernovae were thought to obey relativity’s time dilation but it is now being realized that this was possibly because of potential bias that caused a methodology whose aim seems to have been to prove relativity right. Thus there are possibly conflicting telescopic observations regarding celestial bodies and time dilation.

Peer review has failed and physics authorities have been evading our alternative. The physics paper, which now stands published as an Appendix to our book, is available free at ashishsirohi.com; breakthrough physics has often been historically published as part of a book. Even today, a book can turn out to be the only available option. *The Trouble With Physics*, p. 323, mentions this advice regarding peer review rejecting publication of papers challenging foundations: “[P]apers on this were rejected by the physics journals … for someone whose work focused on foundational problems … should write a book about them.”

The persistence of the physics dogma of running away from pursuing and incorporating the physical nature of the actual infinite, and never even suspecting a similar significance of zero, has led modern physics on this dark path away from light and its truth.

Physics history shows that intelligent and objective outsiders can help push for the pursuit of truth that dogmatic physics authorities are trying to evade. We are therefore reaching out to such a wider audience.