A Viable Alternative to Einstein's Special Relativity Theory


The essential features of Einstein's special relativity theory are often illustrated for the case of one spatial dimension. I too will focus on the basics. I will explain my alternative to Einstein's SR in the easy case of one spatial dimension.

In my theory, when the universe is viewed in one spatial dimension, the space part of spacetime is just a great circle.

To do relativity on a circle, you'll need to learn how to use the following transformation equations:

x'=Y(v)(x-vt)
t'=t/Y(v)

Y(v)=1/sqrt(1-v^2/c^2)

I call the unprimed coordinates the absolute frame of reference.

With these equations and the following rules you'll see that my system is free of contradictions.

Length Expansion
Let d be the distance around the universe in the absolute frame of reference. Let d' be the distance around the universe according to a "stationary" observer in a moving frame of reference. Then d'=Y(v)d

The Law of Light Propagation
To track the motion of light rays in a moving frame of reference, use the equation, distance =rate*time; understand that the speed of light is a function of an observer's motion with respect to the absolute frame of reference.

C(v) is the velocity of light in the direction of motion.
->

C(v) is the velocity of light opposite the direction of motion.
<-

C(v)= (Y(v)^2)(c-v)
->

C(v)= (Y(v)^2)(c+v)
<-

There is An Absolute Time Order
You know what this means instinctively.

Those are the basics.

The essential feature of this theory is the existence of an absolute past, present and future. There is also a physically distinguished, absolute frame of reference but it's very difficult to detect.

The essential difference between this theory and Einstein's is that in SR, motion faster than light results in some observer interpreting the motion as time-travel into the past. This contradiction doesn't exist in my theory.

The similarity to Einstein's SR is pretty much all-around experimental indistinguishability. In any moving frame of reference, the average back-and-forth speed of light is c. Also, if measuring the one-way speed of light in the following manner, in any moving frame of reference, you will also get c.

This is a delightful curiosity. If you use my transformation equations and have two synchronized clocks side-by-side and slowly transport one of them to any convenient distance D and then measure the speed of light, i.e., D/(t2-t1), then the measured value will be c. (t1 is the time on the stationary clock when the light pulse is sent. t2 is the time when the light arrives as measured by the slowly transported clock. Take the limit of ultraslow transport for a perfect answer of c).

Exercise 2: Detecting Absolute Motion

Let an observer in the circle universe be at rest in her own "inertial frame of reference." Let her pick a positive and negative direction. Suppose she has a nice watch on her wrist to note the time. Other than just looking nice and being able to see how old she's getting, let her do experiments. Let t1 be the time she measures for a photon to circumnavigate the universe in the positive direction. Let t2 be the time she measures for a photon to circumnavigate the universe in the negative direction. Being only a one-dimensional creature, she is still smart enough to realize the impossibility of all frames agreeing on a frame independent law of light propagation. Consequently, if t1 doesn't equal t2, then she is moving at some velocity v with respect to an absolute frame of reference. Isn't it obvious, based on the global theorem, that the velocity v is given by the equation: t1/t2 = (c+v)/(c-v) ?

Correct. But it's more accurate to say that the speed of light depends on the system of coordinates. An inertial frame of reference is just a platform that moves at a fixed velocity with an observer attached. This observer is free to synchronize her clocks in any way she likes. In other words, an inertial frame of reference can have more than one system of coordinates. It turns out that the speed of light does depend on the definition she chooses.


Thank you for that delightfully perceptive question. You made me see that I wasn't speaking as clearly as I thought. My aim is to answer as clearly as possible. Thanks for keeping me on the straight and narrow. Permit me to try again.

I will give you a picture that represents my equations. You may forget about the visualization just a soon as you understand it. The ancients called this model that I'm about to recite "the luminiferous aether." They really believed in it. I do not. To us it will serve as a naïve illustration of the physics and math, useful only for teaching purposes.

Imagine all of space being filled with an invisible fluid. If you're at rest with respect to this fluid, then the speed of light is c in all directions. Now imagine that you're moving through this "luminiferous ether" in a specific direction. For this illustration, let's say that you send out a pulse of light in both the fore and aft directions. I'm calling the direction that you're traveling toward, the positive direction. The direction you're leaving (moving away from) I call the negative direction. The equations say that the measured speed of light, in my moving coordinate system, is

C(v) for the light pulse moving directly ahead and in front of you and
->

C(v) for the light pulse directed toward where you come from.
<-

So the system is symmetric.

The axiom of (S^3)xR topology has staggering consequences. It compels the appearance of an absolute frame of reference and establishes an absolute time order. I believe that elevates my insights to a category C scientific theory. See J. L. Synge, Relativity: The Special Theory, 2nd ed., North-Holland Publishing Company, 1965, p. 1. Please notice the line about "fruitful excursions;" and "critical scrutiny."

"A scientific theory may be divided into three parts: (a) foundations, (b) accepted dogma, (c) excursions. The foundations are axioms, principles or laws (e.g. Newton's laws of motion or the first and second laws of thermodynamics). The accepted dogma consists of deductions from the foundations confirmed by observation and experiment, linking reason with nature in a satisfying way (e.g. Newtonian mechanics as it stood before relativity was thought of). The excursions wander out of the domain of accepted dogma, sometimes arousing in cautious minds a feeling that they have more imagination than solid fact in them (e.g. Maxwell's electromagnetic theory of light at the time when he put it forward --- all excursions are not so successful!). A scientific theory is a living thing which grows and changes; fruitful excursions extend the body of accepted dogma and critical scrutiny of the foundations clarifies and sometimes modifies them."


I accept your wonderful admission and feel vindicated by its extraordinary transparence. It's so obvious that SxR has an "absolute time order" that you have no mathematical argument to prove that it isn't so.

Also... If you believe that an absolute time order is essentially semantics and not physics or mathematics, then please explain all the hoopla and religious fervor about the non-science of relative simultaneity in a universe with a presumed (S^3)xR topology?


Likewise for the claim of absence of an absolute time order, an absolute frame of reference, and motion faster than light: The evidence of absence is not the absence of evidence.

I hereby happily accept winning this debate by the clear and forceful arguments already presented by me, and by default, because my opposers are speechless.


If you were interested in communicating physics, you would explain the expert opinion or the mathematical proof of why the spacetime SxR doesn't really have an absolute time order when all obvious appearances indicates that it does.

Regarding the implications of time order: please note that you have cowardly bowed out of answering the question BEFORE I claimed to have won a debate.

Somebody call Stephen Hawking and ask if he has the ability to defend dominant pseudo-scientific beliefs and answer my challenge with actual, meaningful statements. Unlike the wusses that I've been conversing with recently, Stephen Hawking should be interested in SxR and in the next level of SxR generalization: The consequences of an absolute time order on FRW manifolds and the complete death of black hole fantasy.

Time order is inextricably tied to the globally-valid frame-dependent speed of light in SxR, which is inextricably tied to an absolute frame of reference. No one has contested my global law of light propagation for SxR. Do you wish to do that now?

If you have the might, try to apply Einstein's criterion for absolute time order from Einstein's famous train and embankment gedanken experiment to SxR. Do you realize that trying to repeat Einstein's demonstration of relative simultaneity derails itself immediately in SxR?

If you mean by your babbling that clocks could be reset to foil or obfuscate the obvious physically-based, reality-grounded, global synchronization of events in SxR, I say, that's a wonderful deception. I have used the same trick to make it appear that I have derived the Lorentz transformation from the Galilean transformation. I have confounded professional physicists with it. The problem is any mathematically literate person can see that my math-based magic is superior to your feeble attempts at trickery.

Dear Gregory L. Hansen,

Please forgive my writing in the elaborate language of mathematicians. I understand that it's not terribly meaningful to most physicists. I really do mean to write for the largest audience possible.

S is a circle, S^2 is a sphere and S^3 is a hypersphere. R is the real line.

In mathematics (point set topology) there is a topological product for topological spaces. The topological product of S and R is SxR, a cylinder. As a model of spacetime, I specified that S is the space part of spacetime. The time part is R so every event of the spacetime SxR is a point (x,t) where x is a point of S and time t is a point of R. As you can imagine, all of this formalism is really unessential. I will get right to the point.

You wrote:

I will prove that your argument is unreliable by repeating your logic in another coordinate system and arriving at directly opposite conclusions. The riddle is 'which coordinate system is physically meaningful and which is spurious?' I claim that the Lorentz transformation does a poor job of coordinatizing all of SxR. The synchronization scheme that I propose works globally for SxR and means precisely the same as the Lorentz transformation equations locally if you reset all local clocks.

According to my coordinates:

x'=Y(v)(x-vt)
t'=t/Y(v)

Y(v)=1/sqrt(1-v^2/c^2)

Now let's repeat your argument in the coordinate system of SxR.

If events E1 (x1, t1) and E2 (x2, t2) are simultaneous in one inertial frame, then t1=t2 and the events are simultaneous in all inertial frames. If event E1 precedes event E2 in one inertial frame, then t1<t2 and event E1 precedes event E2 in all inertial frames. Consequently, the spacetime SxR has an absolute time order.

Now that you realize that your former beliefs were tied to the peculiarities of a single coordinate system, how do you resolve the paradox?

Your very imaginative accusation that I assume a flat spatial metric is without foundation. Why not post an incriminating excerpt?


My coordinates apply to Einstein's hyperspherical spacetime (S^3)xR but there's no point in considering the non-static case, i.e., the FRW's model, if you don't understand the implications of the static case.


Your seeming inability to grasp the restrictions imposed by my global theorem stems from your reluctance to understand SxR in one spatial dimension and to openly declare a right judgment about it.


I have posted direct challenges to your belief that an "absolute time order" is just semantics.


And some of your attempts to refute what I say are clear. In this instance, what you say is obviously just totally empty obscurantism.


My argument for an "global time order" is based on the straightforward, overwhelmingly conclusive and easy to see constraint that topology imposes on definitions of simultaneity. Without the restrictions imposed by a global topology, I see no valid or analogous proof that may be generalized to Schwarzschild spacetime.


That's not a quote from me nor does it embrace all that I have specified in my view of an absolute time order.


OK. Let's see your coordinate independent definition of "global time order" for Galilean spacetime (S^3)xR in wacky coordinates. I remind you that any two inertial frames of reference in an ordinary Newtonian universe, governed by Galilean spacetime, have an Einsteinian synchronization.

http://www.everythingimportant.org/relativity


I don't even believe that Galilean spacetime has the property, as you would define it.

Whose fault is that? The crackpots aim to overthrow relativity at the most fundamental level. Responsible physicists and educated students cater to the crackpots. When truly respectable arguments are asserted that shakeup informed, mainstream, conventional thinking—such as my argument for the existence of an absolute time order in a closed and bounded universe—responsible experts go into hiding. Only Tom Roberts has been honest enough to admit openly that he's not interested in debating my thesis because the contention and refutation, he claims, is essentially linguistic.

Assume that Tom Roberts is right: Relative time order is pure semantics. How does that not justify an absolute time order to dissident mathematicians who assert their perfect liberty to use positive language and opposing semantics? How is Roberts' admission not a half-hearted confession? What's modern science doing trumpeting poorly stated conclusions and misleading rhetoric?

It's logically consistent to believe in the homogeneity of time and therefore the Lorentz transformation yet divide all physical law into those laws which are independent of all inertial frames of reference and those which are not. Conceivably, the second category may be the empty set but no harm is done to science if mathematicians were permitted to speculate about the set of all mathematically conceivable universes.