The following is a quick summary of a new model that I've advanced: The Dominium

The model begins with the same set of premises and conditions that were originally set forward and given the moniker, the "Swiss Cheese" model. In other words, at Big Bang creation, matter and antimatter were created equally, however, distribution was slightly random. Statistically, some areas would have greater concentration of one type over an other ("perturbations" or "imperfections" depending on which author you follow).

The Dominium model takes this core idea and adds one truly new hypothesis: matter/antimatter repulsion. As a result of like attracts like/opposites repel forces, the once heterogeneous mixture would be expected to undergo the process of "Self assembly"--as commonly noted in hydrophobic/hydrophilic extremely heterogeneous mixtures. As a result of self-assembly, the original matrix of the Universe became more organized rather than heading towards more chaotic (as is the case of self-assembly heterogeneous mixtures at the nano and atomic level)--in other words, this model assumes that classic understanding of entropy is flawed. Not all systems become more chaotic. This has been shown over and over again at the atomic, molecular, and nano levels, why couldn't this also apply at the galactic? With this solution, we achieve results consistence to observable phenomena: a uniform distribution of mass and flat event horizon.

The actual model is quite long. For a free download of the abridged version (91 pgs) go to http://www.hasanuddin.org/viewtopic.php?t=3&sid=6709b63831e91b0f6d8a4b99be6570c1

Or if you're really interested, the full book is at online bookstores.

PS: Two words of caution. 1) It's written in lay language in the tradition of Sagan & 2) There is a truly ominous implication: mini black-holes are predicted to be stable... right now LHC at CERN is a hair's breath away from creating a mini black-hole

Hi Hasanuddin.

Thanks for being the first to utilize the "Alternative Relativity" thread on my blog. Actually, from the looks of it, it may have been better placed in my "Alternative Cosmologies" thread. I can't shift it, so would you mind re-posting this one there as well? It can stay here too, no problem.

I haven't had a chance to look at your proposal yet, but I will...

Jorrie

E-gads! In reply to: Dominium Hypothesis: If what you say is true, re LHC and creating a mini-black hole, isn't that a rather foolish undertaking? How does one restrain the "laboratory" mini-BH from absorbing all the Earth's atmosphere, as well as any container that one may use to try to enclose the mini-BH, followed by the Earth in general. Ultimately, the new, growing BH will merge with the massive BH at the center of our galaxy, while absorbing a good portion of the stars and and planetary systems in its path. Or is the assumption that the mini-BH will readiate away it's energy and "evaporate"?

Hi Cardio-2.

IMO, the chances of creating a mini/micro black hole in the laboratory is extremely small. The required energy densities are very far above what's feasible today. Take note: it is density that causes gravitational collapse, not total energy.

I checked out the "Dominium Hypothesis" and was not very impressed!

Jorrie

Dear Jorrie,

There are two points that need to be discussed. First, you state that the required energy densities are very far above what's feasible today. How can you make such a statement? I realize that there are equations that are used under current theories that seem to suggest this, however, the new model suggests that current theories are fundamentally flawed. Therefore, if current models are indeed flawed, then the equations you site could also be flawed. Existing flaws, as put forward by the Dominium model:

1) The assertion that only matter exists in the Universe; the Dominium maintains that there is a 50:50 balance to this day

2) The assertion that entropy always brings systems to increasing levels of chaos; the Dominium aligns with more current understandings that "entropy-defying" self-assembly is a documented fact/phenomenon

On the first account, the old models and the new Dominium are completely incompatible with one another. Only one can be right. To use arguments from one incompatible theory against its rival's projections will not prove anything. I agree that what you site is projected by the old models, but I disagree that it proves any evidence against the Dominium's implication on this matter.

On the second account: entropy understanding is wrong. The process of "Self-assembly," which is an important nanotechnology tool, proves that systems can and do predictably move from chaotic to organized. The original Big Bang matrix would have been extremely mixed (just like a mixture used by a nanotechnologist prior to initiating self-assembly), the jump that galactic structure could self-assemble is not a large one.

The last point is this: you state that you were not impressed when you checked out the Dominium Hypothesis, yet you supplied no reason to refute it. I agree that it is not a normal paper: the writing is designed for the lay audience, and the method is qualitative deduction rather than quantitative induction. Assuming you overlooked the lay language, I realize that qualitative deduction is not usually applied to the scientific process. However, formal deduction is the tightest form of logic there is. I tried to present the deduction as formalized as possible, in the tradition of Aristotle, as standard syllogisms. Though this method may seem archaic, it is much more defensible than any form of induction. Please have another look. Honestly, I don't mind if you find an error or even prove the entire model wrong, just give me a reason and a chance to explain myself to avoid miscommunication

Hi Hasanuddin.

I'm afraid that I stand with my decision not to discuss your Dominium Hypothesis on this forum. Other's are welcome to do so, but I will not debate it any further, except perhaps to make a remark on scientific inaccuracies that are posted. Whenever the statement "... the new model suggests that current theories are fundamentally flawed ...", is made, this is my standard reaction, so nothing personal!

Jorrie

Dear Jorrie,

I meant no disrespect. And the statement was not meant to be uppity and it is not baseless. Let us consider "entropy" for a moment:

Standard/current understanding of "entropy" states that "all systems degrade and become increasingly disorderly."

However, the tool of self-assembly which is utilized by the nanotechnologist is a clear example of where system moves from a state of extreme disorder to a state of order.

How can "Self-assembly" be possible if current theories are correct? Yet, self-assembly is not only possible, it is a cornerstone of nano-engineering.

Entropy is a fundamental principle of current theories. If self-assembly exists, doesn't that mean current theories are fundamentally flawed?

Again, no disrespect, I'm being serious, impartial, and earnest.

Hi Hasanuddin. "How can "Self-assembly" be possible if current theories are correct? Yet, self-assembly is not only possible, it is a cornerstone of nano-engineering."

Self-assembly is nothing new; cells in living organisms do it continuously. However, it is done at the expense of entropy increase of the the system or systems around them. The whole universe is continuously increasing its entropy.

Jorrie

Hello Jorrie,

I think there needs to be a clarification: there are two distinct definitions for "self-assembly:"

1) the process by which viruses self-repilcate using the mechanisms existing within a cell

2) the process underwhich an extremely hetrogeneous matrix self-organizes into a more uniform pattern. This process occurs most easily in extremely heterogeneous mixtures where there are two types of particles with distinctly different properties, e.g., oil & water.

I was referring to the second definition. Now, you are right that there are several theories to account for self-assembly. In one of the most common, it is explained that it occurrs as a result of free-energy drivers at the expense of entropy.

Regardless of the definition:

A: Given the hypothesis that gravitational likes-attract and opposites-repel (matter/antimatter), this would be a case of two particles w/ distinctly different properties.

B: And given that the original Big Bang fireball was an extremely hetrogeneous matrix of matter and antimatter

C: Therefore, the system would be expected to self-organize

This conclusion is reached whether you believe that self-assembly occurs because of internal energy drivers or that the theories regarding entropy are flawed.

After the initial self-assembly occurs, I agree with you, from then on the Universe is continuously increasing its entropy. However, I would maintain that initially the Big Bang fireball decreased in entropy as a result of self-assembly. This assertion is a shift away from commonly held assumptions, yet is totally justifiable.

Hi Jorrie, It's been a long time since I conversed with you. Thought you'd be interested that the discussions of the Dominium model have moved to http://www.scientificconcerns.com/Forums/viewtopic.php?f=32&t=776 Also, if you wish to skip the banter of a thread like that it is more smoothly laid out at http://www.hasanuddin.org

Hi Hasanuddin, yes I've been off the relativity and cosmology topics for a while...

I've read the three threads of your "Dominium hypothesis" at http://www.hasanuddin.org. Although I've not (yet) formed a strong opinion one way or the other, the following struck me as slightly strange:

1. "... pair production is the standard occurrence and manifestation of Einstein's famous equation, E=mc2. In this standard occurrence of high-energy experiments, the scenario is always the same: equivalent charges, equivalent masses, and one the antiparticle of the other."

AFAIK, antiparticles have opposite charges and the same masses, hence they attract, as is shown in particles accelerators - or at least no repulsion has ever been observed.

2. "This is the first and only model that can span the entire timeline from Big Bang to present and then onto how the Universe is moving to the next Big Bang without anomalous contradiction from the established physical experimental and observational data record."

The standard Big Bang (BB) has at a starting condition a rapid expansion at BB-time zero and does not include the inflationary epoch. Guth's inflationary hypothesis gives one scanario for the rapid (exponential) expansion before BB-time zero and what we can observe in the aftermath is compatible with Guth's ideas. The standard cosmological model encompasses both BB and inflation.

I'm not convinced that your model can explain all the observed phenomena, but not being a scientist, I cannot go into that. You must remember that the present cosmology is a numerical model of great complexity and all the math ties up with a large set of observations. The fact that we do not understand all of it does not detract from the scientific merits of the model.

I fail to see where your model makes a different prediction than the standard cosmological model.

-J

Hi again Hasanuddin. In my previous post I wrote: "I fail to see where your model makes a different prediction than the standard cosmological model."

As a matter of fact, I can think of one: in a ~50:50 distribution of matter and antimatter galaxies that repel each other, but attract the same polarity, the overall net gravitation effect will be zero. Hence, such a universe should have a steady expansion rate over time - no acceleration or deceleration. This is not observed.

During the first 5 Gy or so, the expansion rate dropped markedly, then it changed over smoothly to an increasing expansion rate up to the present. The standard ΛCDM model fits this observation, but I fail to see how your idea can account for it.

-J

Hi Jorrie,

I'll do what I can to address the points you bring up.

1: The gravitational relationship between matter and antimatter cannot be determined experimentally at this time for a variety of reasons. Essentially it boils down to the fact that under lab conditions gravity is approx 10e23 times weaker than electrostatic forces. Also, the machines used to guide, corral, and accelerate particles utilize extremely strong electric and/or magnetic fields. Combine these two factors and the disparity becomes so great that detector technology simply doesn't exist to read such subtleties.

From this observation many individuals falsely conclude that gravity is therefore the weakest player in all cases and can therefore always be ignored. Such a conclusion is actually based on a false premise because we do not have data for "all cases." Specifically, we do not have data for cases of absolute chaos and where proportions of matter and antimatter present are near the 50:50 level (as would be expected to have existed at the moment of the Big Bang.)

I'll cut to the final conclusion of the Dominium model to save space & time. The final conclusion of the Dominium model is that gravitational stability is the first order requirement of a system at absolute chaos. Once gravitational stability is met, the importance/affect of this force drastically decreases. The Earth is an all matter object and therefore it is a system that has already met the prerequisites of gravitational stability, hence the measured "importance" of gravity appears small under lab conditions. However, the Big Bang would have been a case of maximum chaos, therefore leading to the self-assembly which resulting in gravitational equilibrium/stability

2: The Deductive method

I do apologize for the lack of numbers, but that is unavoidable because the methodology used to create this model was deduction, not the more commonly used induction. However, it can easily be argued that the rules of deduction are much more tight/precise than those used for induction. Also, with the more familiar inductive method, there is always a margin of error. That is not true for deduction; so long as the premises are 100% categorically correct, then the conclusions are 100% categorically sound.

When deduction is used to consider every-day issues, the resulting conclusions have the resulting feel of obviousness. This leads some to wrongly conclude that deduction is not useful to scientific inquiry, because it concludes things that we already know. This generalization is both unfair and incorrect. The true strength of the deductive method comes when it is applied to areas/issues where there is very little understanding. In very young or poorly understood areas, deduction is actually the best way to proceed. I liken this aspect of the scientific process to the art of sculpting. You begin with a large amorphous blob of fact. The first moves are to whack of giant chunks to give the structure (deduction); after that is done, the art is to bring out the fine-tuning tools to achieve perfection (induction and formulaic applications.) The problem in the past is that those approaching these problems have attempted to do so using the fine tools first, and as a result they either over-simplified or made unjustifiable assumptions without truly realizing it.

The fact is that deduction was used to carve out the major over-arching relationships in all of the classic sciences. However, once the deductive steps have been taken, this application becomes obsolete. Consider again sculpting, once the major chunks of the slab have been removed, the use of the sledgehammer is no longer. Because the initial steps of the classic sciences were taken centuries ago, many forget how important they were to set inquiry in the right direction. There is a more current example from which this process can be shown. Consider the field of genetics. Just twenty years or so ago, genetics was in its infancy. During this time deduction was the main tool of exploration. Because of this, folks who worked in the more mature classic disciplines often derided the geneticist as a pseudo-scientist because of the lack of numbers used to form many of the conclusions of that day. Today, genetics has matured. The initial shape has been hewn by deduction, therefore applications that are more fine-tuned are more and more appropriate. To look at a genetics paper today, you will find a much greater application of both numbers and formulae. Although cosmology was one of the first fields considered by the ancient Aristotle via his deductive syllogisms, there simply was not enough information for him, or anyone else, to assert anything categorical. The real data concerning the cosmos has only recently come available. As a result, deduction has never been applied to it.

There are many differences between the status quo models based on the idea of universal attraction and the Dominium's notion of gravitational repulsion between matter and antimatter. The most important difference is the amount of verifiable and concrete natural and empirical phenomena explained by the Dominium, but considered "anomalous" under current theories, e.g., the solar wind, supermassive central galactic black-hole, twisting magnetic fields of the heliosphere, ever accelerating expansion, flatness of the event horizon, near uniform distribution of mass…etc. All of these known and measurable phenomena conflict with the understandings resulting from universal attraction. As a result, separate theories with only-in-this-case assumptions are needed to come close to accounting for them. Such special case maneuvers, extra-assumptions, and new (and unexperimented-with) forms of matter/energy are not required for the Dominium.

"The grand aim of all science is to cover the greatest number of empirical facts by logical deduction from the smallest number of hypotheses or axioms"
—Albert Einstein (1879-1955)

In fact, it is arguable that the Dominium aligns better with the standard model because unlike popular-bias "solutions" the Dominium embraces the notion of symmetry, rather than be dependent of asymmetric CP Violation magically causing all of the antimatter formed at the time of the Big Bang to "vanish" resulting in an all matter Universe.

Hi Hasanuddin, it seems to me that you are very good at philosophy, which unfortunately does not really interest me. I'm not too sure about your science, though, e.g., you wrote:

"The most important difference is the amount of verifiable and concrete natural and empirical phenomena explained by the Dominium, but considered "anomalous" under current theories, e.g., the solar wind, , twisting magnetic fields of the heliosphere, ever accelerating expansion, flatness of the event horizon, near uniform distribution of mass…etc. All of these known and measurable phenomena conflict with the understandings resulting from universal attraction."

I know little about the first two phenomena, but the ones that I do know about, I think you have things very wrong.

1. "Supermassive central galactic black-holes" are fully explained by the current models, contra to what you stated. See e.g. http://adsabs.harvard.edu/abs/2000ApJ...539L...9F|.

2. The near-uniform distribution of matter at the largest scales are part and parcel of the ΛCDM cosmic model and so is ever-increasing rates of cosmic expansion. Stock-standard textbook stuff!

3. I do not know what you mean by "flatness of the event horizon", because spacetime is certainly NOT flat at black hole event horizons.

I would also like to hear your response to my post #56 on the observed expansion rate changes over the age of the universe. Without an explanation for that, the rest of your premise becomes pretty meaningless...

-J

Alan Guth has discussed how it might be possible to create a universe. " Now we have the mathematical tools to allow us to seriously discuss the prospects for creating a universe in your basement" ........ compress 10 kg of particles at energy 10¹⁵ GEV to the size of a black hole.

Hello Jorrie: I thought I might post this and see if this is something you you would consider an alternate reality. You're probably already familiar with this theory, I didn't learn about until a year ago so I'm behind the times. Though I've just skimmed some of the information available there are some pretty profound implications. The many worlds theory, which seems to go in and out of favor would certainly be more plausible. It also impacts Einstein's theories of relativity. The way I understand this theory ,even time or at least what we consider time would have to be rethought. My personal definition of time is a relationship between matter and motion. May not make sense to you or anybody else, using my own definition it was easy to accept Thomas Aquinas definition of time being a creature (that is created along with the universe) which obviously would make a question of how long the universe didn't exist moot. My understanding of one of the implications of this theory is the ability to peer beyond the big bang singularity, thus beyond the beginning of time.
Thought this might be of interest, so let me know if you think it's worth pursuing.
PS do you think my 200 amp service will be adequate to test this theory? Just kidding. YW

Sorry I missed a correction, I can see my voice dictation needs some work, obviously (reality) should've been relativity. Also my reasoning may need some explanation, since this theory is able to extend beyond the singularity were relativity breaks down it would seem to imply that relativity's rules could be local. If true what now call the universe is no more the universe than our galaxy was before Hubble. The existence of parallel universes is nothing new, however to my understanding there was never any mathematical way to connect parallel universes, conventional physics ignores anything that can't be proved defined and measured, it must. My reasoning maybe flawed, but this would seem to move parallel universes back from metaphysics into physics necessitating a redefining of relativity, and time.

Hi YWROADRUNNER,. "... compress 10 kg of particles at energy 10¹⁵ GEV to the size of a black hole."

You have to press that 10 kg of particles into a diameter of about 10^{-26} meter. That's 10^{-11] times the size of a proton!

"My understanding of one of the implications of this theory is the ability to peer beyond the big bang singularity, thus beyond the beginning of time."

I think it is only the 'bounce' theories that can possibly peep to before the BB, or beginning of our time, because there might have been a 'collapse' before the bang.

Jorrie

HI Jorrie,. The numbers are right, but that may be the only thing. As yet I have been unable to locate where I read that the mathematics extended through the singularity. So I apologize to jumping the gun here. I am going to look for further documentation, as well as a towel to wipe the egg off of my face.

Dear Cardio-2

You are right on several levels, though I believe the sequencing is different than you put forward.

First you are right: if they succeed in creating a stable black-hole the consequence would be apocalyptic.

However, I believe the atmosphere would be the last thing to go. Also, there would be no chance of the synthetic black-hole merging with the supermassive black-hole at the galaxy center.

If a stable black-hole is generated, then it will sink to the core of the Earth (because of normal gravity) and then once there it would consume the entire planet. The process would not but "quick" however, because you would have an hour-glass effect where all the matter is trying to squeeze through a small opening.

The resulting Earth-black-hole, would continue to rotate around the Sun (as if nothing ever happened). The Moon would also expected to be "unaffected," continuing to dance around the center of gravity of the Earth-BH as if it were the same Earth. Even the satelites and space station would continue their orbits. After all, the momentum, mass, and position of the Earth would not be expected to change...only its volume.

You also bring up the "evaporation" hypothesis, via Hawking radiation. Perhaps. But do you want to gamble?

Check out the new model. It explains all the anomalies the old models couldn't. It shows that current assumptions regarding entropy are wrong. It is seamless and matches all known data. Before you consider which theory you'd lay your life on (possibly literally), read the new one

Hi Jorrie et al:

Here is a description of the basic elements of the "stopwatch" physics I have previously referred to. As always, I would appreciate your and other's comments!

Introduction

It is now assumed that Lorentz' transforms (LT) accurately reflect Einstein's two principles of special relativity—spatial isotropy and the fixed finite speed of light—(SR)—and that a violation of the former implies a flaw in the latter. However, to derive the LT from his two principles Einstein assumed that Newtonian concepts for distance and time apply to electromagnetic (EM) events just as they do to material events. Now, of course, radiolocation tools, e.g. the GPS and "spy" satellites derive kinematic features of EM events from their own signals. One such method patented by Lee de Forest in 1904 (U.S. #771818) one year prior to Einstein's 1905 paper [1] derives positions and times of EM events from differences in arrival times of their signals at separate receivers. As shown here, applying Einstein's principles of SR to a simple dual-stopwatch (SW) version of de Forest's idea leads to relativistic definitions for distance, time, and motion different from Newton's (except in just two symmetrical cases) and relationships for these non-Newtonian values between observers of the same events different from the LT. While differences between these physics are small, initial analysis suggests they are consistent with the Pioneer blueshift and cosmic redshift acceleration anomalies.

Stopwatch Measurement Physics

The Dual-Stopwatch Tool: Consider a version of de Forest's tool where rate-synchronized stopwatches collocated with two EM events are turned "on" and "off" by signals from those events, and let resulting SW values, C₀ and C₁, be positive if turned "on" by the local event, otherwise negative. It is clear that Einstein's two principles of SR are satisfied in two cases: simultaneous (space-like) events and collocated (time-like) events. In the first case, spatial isotropy requires that propagation times, P₀ and P₁, of signals from events to opposite clocks are equal, i.e.: P₀ = P₁ = C₀ = C₁ = D/c; D/c = (C₀+C₁)/2; and T = (C₀-C₁)/2 = 0. And, for collocated (time-like) events: P₀ = P₁ = 0 and C₀ = -C₁ = T = (C₀-C₁)/2; and D/c = (C₀+C₁)/2 = 0. As described below, these two "proper" cases serve as unambiguous references for deriving one-way signal propagation times, SW values, and thus relativistic distance, time, and motion in the general case.

Stopwatch Electrodynamics: It is clear that collocated events (D=0) separated by time T in one frame are separated in distance (D'>0) in a second moving frame; less obvious is what causes the time T' between these events to exceed T as SR demands. Similarly, SR requires distance and time between simultaneous events increase in a second moving frame. While Einstein assigned these effects to changes in the observer's tools, SW measurements depend directly on signal propagation distances, and thus times, from observed events to those clocks. The question in this case is then: while these propagation times are unambiguous for collocated and simultaneous events, what are they in the general relativistic case?

Minkowski's spacetime geometry suggests one possibility: In his geometry, the "proper" interval between two EM events is the minimum "time" for two time-like events, and the minimum "distance" for two space-like events, values that are not only the same for all observers of the same events, but are derivable by those observers from their own measurements. The dual-SW tool described above is, in effect, an embodiment of Minkowski's geometry. That is, those frames with simultaneous or collocated events, where Minkowski's interval is measured directly, serve as zero-velocity unambiguous references for all other observers of these same events. In contrast to ST physics, observer motion in SW physics is between observers and EM events (i.e., the proper frame defined by those events); measurement differences between observers come from differences in their speeds relative to the proper frame for those events; and relativistic effects come from asymmetries in signal propagation times to clocks of observers moving relative to those proper frames. In contrast to Minkowski's abstract geometry, the proper separation of two events in SW physics is their fixed physical "real" separation in time or distance in time-like and space-like domains separated by a border of light-like events.

The SW Hypothesis: Extrapolating unambiguous features of "proper" frames to the general relativistic case relies on three assumptions: (1) The above SW definitions for time and distance hold in all inertial frames [i.e., T_sw' = (C₀'-C₁')/2 and D_sw'/c = (C₀'+C₁')/2]. (2) Motion is between observers and "proper" frames of observed events. And (3), Einstein's two principles are universally valid. As shown below, this "Stopwatch Hypothesis" provides relativistic values for distance, time and motion different from Newton's and relationships between observers of the same events different from both the LT and Minkowski's spacetime interval. (Unprimed values here are Newtonian in proper frames; "sw" subscripts represent relativistic non-Newtonian values in non-proper frames.)

SW Relativity: Time-Like Domain: Let collocated EM events separated by time T in their proper frame be observed by a second frame moving at V_sw' relative to that frame. The two clocks collocated with these same events in the second frame are separated by V_sw'T. From the first frame, signal propagation times in the second frame, P₀' and P₁', are, clearly, both finite and asymmetrical. That is, following the first event, the clock collocated with that event is seen moving away from the second event, the source of its "off" signal, while the second clock is approaching its "on" signal from the first event. Given the finite speed of light: P₀' = T/(1-V_sw'/c) -T and P₁' = -T/(1+V_sw'/c)+T. Then, assuming clock rates are the same in both frames: C₀' = P₀'+T = T/(1-V_sw'/c) and C₁' = P₁'-T' = -T/(1+V_sw'/c). Note that V_sw' is a function of relativistic values, C₀' and C₁', (e.g., V_sw' = 1-T/C₀') and differs from Newtonian motion, v. This leads to the following definitions for any observer of any two time-like EM events whose raw SW measurements are C₀' and C₁':

T_sw' = (C₀'-C₁')/2 = T/[1- (V_sw'/c)²]

D_sw'/c = (C₀'+C₁')/2 = T(V_sw'/c)/[1- (V_sw'/c)²]

V_sw'/c = D_sw'/cT_sw' = (C₀'+C₁')/(C₀'-C₁')

These SW relativistic definitions clearly differ from the LT (which, for collocated events are D'/c = T(v/c)/[1- (v/c)²]^1/2, T'= T/[1- (v/c)²]^1/2 and v/c = D'/cT'). Also, for any observer of any pair of time-like events with SW values C₀' and C₁', the above relationships show that Minkowski's interval T in this physics equals - 2C₀'C₁'/(C₀'- C₁'), which in SW relativistic definitions for distance, time, and motion are represented in either of two ways:

T = T_sw'- (V_sw'/c)(D_sw'/c) = [(T_sw')²- (D_sw'/c)²]/(T_sw')

While these functions equal Minkowski's interval in value, both are "real" rather than "imaginary" and differ in form from Minkowski's: [(D'/c)² – T'²]^1/2 = (–T²)^1/2.

SW Relativity: Space-Like Domain: Applying the SW Hypothesis to simultaneous space-like EM events separated by D/c in their proper frames shows one-way signal propagation times, P₀' and P₁' in any other moving frame are P₀'= C₀' = (D/c)/(1- V_sw'/c) and P₁'= C₁' = (D/c)/(1- V_sw'/c) respectively. These SW relationships define, in turn, time, distance, and motion between space-like events as:

T_sw' = (C₀'- C₁')/2 = (D/c)(V_sw'/c)/[1- (V_sw'/c)²]

D_sw'/c = (C₀'+ C₁')/2 = (D/c)/[1- (V_sw'/c)²]

V_sw'/c = cT_sw'/D_sw' = (C₀'- C₁')/(C₀'+ C₁')

D/c = C₀'C₁'/(C₀'- C₁') = (D_sw'/c)- (V'/c)T_sw' = [(D_sw'/c)²- (T_sw')²]/(D_sw'/c)

Relationships between Newtonian and SW Variables: The above expressions show that SW and Newtonian definitions for motion, V_sw and v are related as follows:

V_sw'/c = 1- [(1- v/c)/(1+v/c)]^1/2

Note that, unlike V_sw, which is derived from SW values and thus relativistic, non-relativistic Newtonian velocity (D/T) is based on values defined independent of the speed of light. It is clear that V_sw'/c = v/c at v = 0 and 1. Otherwise v> V_sw, v reaching a maximum of ~1.207V_sw at v/c = 2^-1/2. (As described later, this "bubble" between ST SW definitions for velocity, plus differences in Doppler-velocity transforms shown in Table 1 below, is surprisingly consistent with the yet-to-be explained cosmic "jerk" observed for SNe Ia supernovae in the 0.1<z<2.0 redshift regime.)

While time (and distance) dilation exists in both physics, and while v/c = V_sw/c at "0" and "1", otherwise the SW function, 1/[1- (V_sw/c)²], exceeds the ST version, 1/[1- (v/c)²]^1/2. Although this difference is less than 0.02% below ~0.02 c, (v = ~6000 kms^-1) a peak of 8.0% is reached at v/c = 0.8 (v = ~240,000 kms^-1.) Given the above relationship between V_sw and v, then [1- (v/c)²]^1/2/[1- (V_sw'/c)²] = (1+v/c)/(1+V_sw'/c), and for any observer of any two time-like EM events:

T_sw' = T'(1+v/c)/(1+V_sw'/c)

D_sw' = D'(V_sw'/v)(1+v/c)/(1+V_sw'/c)

Similarly, for any observer of any two space-like events:

T_sw' = T'(V_sw'/v)(1+v/c)/(1+V_sw'/c)

D_sw' = D'(1+v/c)/(1+V_sw'/c)

Relativistic Doppler Relationships: In SW physics, Doppler shift is the ratio of stopwatch values in the proper (rest) frame to those in the moving frame, i.e., f_R/f₀ = C₀/C₀' = (1- V_sw'/c), and f_A/f₀ = C₁/C₁' = (1+V_sw'/c).

Table 1. Doppler transforms in Lorentzian, spacetime, and stopwatch physics

Lorentzian Physics:

Motion v between objects: <infinity

Motion of EM signals: c (re an ether)

Motion of objects re EM events: undefined

Doppler redshift (f_R/f₀): 1/(1+v/c)

Doppler blueshift (f_A/f₀): 1/(1-v/c)

Spacetime Physics:

Motion v between objects: <c

Motion of EM signals: c

Motion of objects re EM events: undefined

Doppler redshift (f_R/f₀): [(1-v/c)/(1+v/c)]^1/2

Doppler blueshift (f_A/f₀): [(1+v/c)/(1-v/c)]^1/2

Stopwatch Physics:

Motion v between objects: (undefined) v<c (?)

Motion of EM signals re objects: V_sw= v = c

Motion of objects re EM events: V_sw = 0 to c

Doppler redshift (f_R/f₀): 1- V_sw'/c

Doppler blueshift (f_A/f₀): 1+V_sw'/c

Assumptions of ST and SW Physics

While both ST and SW physics assume the validity of Einstein's principles of SR, they rely on different assumptions to interpret these principles. Einstein assumed that classical concepts for distance and time based on synchronized clocks and rigid rods applied to EM as well as material events. In fact, to ensure synchronized clocks do measure time between EM events independent of distance, he made the following assumption in his 1905 paper: ''We have not defined a common "time'' for A and B, for the latter cannot be defined at all unless we establish by definition that the "time'' required by light to travel from A to B equals the"time'' it requires to travel from B to A." [1]. (No such assumption needed for rigid rods since, by design, they measure distance independent of time!) Einstein made this assumption despite his own theory that showed distance and time between EM events to be dependent variables. In contrast, these variables in SW physics are non-Newtonian dependent functions of more elemental SW values.

Also, while Einstein assumed motion is between observers of the same EM events (i.e., Newtonian, where v = D/T), motion in SW physics is between observers and observed events. (Einstein made his assumption despite his 1905 statement that electrodynamic theories like his: "…have to do with relationships between rigid bodies (systems of co-ordinates), clocks and electrodynamic processes". [1]) This SW assumption leads to a non-Newtonian relativistic definition for motion, V_sw, which, for time-like events is D_sw/T_sw, and for space-like events is T_sw/D_sw. It also offers a simple physical explanation for dependencies that SR shows exist between distance and time between EM events and observer motion, one that avoids the imaginary time and paradoxical effects of ST physics.

However, ST and SW interpretations of Einstein's two principles of SR rely on different assumptions, the validity of which, in either case, depends solely on how accurately their predicted effects match real-world processes.

Theory versus Reality

Past tests, such as those for time dilation by Frisch-Smith in 1963 and transverse Doppler shift Ives-Stillwell in 1938,accurately reflect the LT. Initial analyses below show, however, that effects predicted by SW relationships described above also fall within error bounds of these past tests. There may be others.

While these tests are not definitive, other differences between these physics, may have already been observed. Three such effects are: the small acceleration anomaly of the Pioneer deep-space probes; the much larger unexpected cosmic acceleration of SNe Ia supernovae; and a puzzling blueshift limit of 2f₀ found in ultra-intense femtosecond laser-plasma interactions. Given their disparate features, that all three might come from the same source is surprising. The Pioneer anomaly is very small (~8.7x10^-8 cm/s²), towards the Sun, and at vehicle speeds below 40 km/s [2]. In contrast, the cosmic "jerk" is orders of magnitude greater, away from the Sun, at source velocities of ~10⁴ km/s [3], while the blueshift limit occurs at c [4]. This latter limit is of special interest since physical evidence confirming that it can, or has in fact been exceeded, would disprove this SW theory for SR. Note that ST physics predicts this will occur for at v>0.6c. (While I am unaware of any evidence in this regard, I would certainly like to know of such.)

My initial analysis shows that differences in velocity definitions and Doppler-velocity transforms in these two physics (Table 1) do accurately model both the Pioneer and cosmic "jerk" anomalies. (Though my analyses alone guarantee little, I will post both later. However, for anyone interested, the above relationships should be sufficient to explore how differences between ST and SW relativistic Doppler-velocity transforms might affect our view of these two fundamental problems of contemporary physics and cosmology.)

Time Dilation: The existence of time dilation at relativistic speeds was first demonstrated by Rossi and Hoag in 1940 [5]; subsequently by Durkin, Loar, and Havens in 1952 [6]; and by Frisch and Smith again in 1963 [7]. All did so by showing that decay times of high-velocity atomic particles exceeded their rest decay times. In the first and third tests, experimenters compared mean decay times of muons generated by cosmic rays with their known rest value t₀, of 2.2 us. In the last test, Frisch and Smith observed a time dilation factor of 8.8+0.8 for muons traveling at a mean speed v of ~0.9929 c, a value consistent with the ST prediction of 8.4067… at this speed.

In SW physics, decay time is that between generation and decay of these muons measured by a clock collocated with those events, i.e., D = 0 and T = t₀ (the rest or "proper" decay time). Thus, in this physics the laboratory is considered to be moving at V_sw' relative to muon proper frames, which, for the mean observed muon velocity v of 0.9929c, is 0.9403c. In this case, SW time dilation function, 1/[1-(V_sw'/c)²], is ~8.633…, a value within Frisch-Smith test error limits and actually closer to the measured value of 8.8+0.8 than the ST prediction.

Transverse Doppler Shift: Both classical and ST physics predict infinite Doppler frequency shifts—and thus infinite energies—for EM sources approaching at c (Table 1). In contrast, the SW transform predicts energy integrated over a sphere for a uniformly radiating EM source is fixed for all observers, but with a distribution that depends on motion between observer and source. When this motion equals c, approaching and receding frequencies are 2f₀ and "0" respectively.

The difference between classical and ST Doppler transforms was first demonstrated by Ives and Stillwell at Bell Labs in 1938 who showed that the average of approaching and receding wavelengths of EM signals from ionized hydrogen atoms at a velocity of ~0.01c [8] was close to that between classical and ST Doppler transforms of ~0.5f₀(v/c)², or ~0.00005f₀. It is generally accepted that this and subsequent tests (e.g., Saathoff et al [9] who measured this effect to an accuracy of ~8x10^-7 at 0.064c) validate the LT.

While SW transforms (Table 1) predict finite rather than infinite transverse Doppler shifts, surprisingly they seem to pass these same tests. For example, in the Ives-Stillwell tests at 0.01c, mean approaching and receding velocities predicted by classical, ST, and SW Doppler transforms relative to the rest frequency are, respectively, 1.00010001, 1.000050004, and 1.000000000. Thus, the expected test result, assuming the ST Doppler transform is valid, is 1.0000050006. Note, however, if in fact the SW transform, instead of the classical version, accurately fits reality, then the measured value would be 1.000050004, a small difference of 2x10-9 between these two predictions, which appears to me to be within estimated error bounds for these tests.

This small difference questions the long-accepted view that the Ives-Stillwell and subsequent similar tests verify the existence of finite transverse Doppler shifts as well as time dilation predicted by ST physics. It suggests instead, that if SW physics more accurately represents reality than ST physics, then the Ives-Stillwell tests would validate the existence of time dilation but would also validate a zero transverse Doppler shift contrary to ST physics.

Conclusion

The above "engineering" interpretation for Einstein's two principles of SR relies on a simple radiolocation measurement concept used in a wide range of engineering applications before World War II, a concept that depends solely on propagation times of signals from EM events to clocks (rate-synchronized only). As described, this physics leads to relativistic definitions for distance, time, and motion for electrodynamic processes different from Newton's (though the latter remains applicable to material processes as well as collocated and simultaneous EM events). This assignment of relativistic effects to a derivable physical process (one-way propagation times of EM signals) avoids the mysterious physical paradoxes, imaginary time, etc. of ST physics. While this physics seems —at least from this engineer's perspective—the more logical of the two, its validity, as does that of ST physics, depends solely on how accurately either mirrors real world processes.

References

[1] Einstein A 1905 Zur elektrodynamik bewegter korper Ann. D. Phys. 17 891

[2] Anderson J D, Laing P A, Lau E L, Liu A S, Neito M M and Turyshev S G 2002 Study of the anomalous acceleration of Pioneer 10 and 11 Phys. Rev. D 65, 082004/1-50 (Preprint gr-qc/0104064)

[3] Riess A G et al Feb. 2004 Type Ia supernovae discoveries at z>1 from the Hubble space telescope: evidence for past deceleration and constraints on dark energy evolution arXiv.org.astro-phy/0402512

[4] Galimberti M, Giulietti A, Giulietti D, Gizzi L A, Balcou PH, Rousse A, and J PH Rousseau 2001 Laser and Particle Beams 19 47-53

[5] Rossi B, Hilberry N and Hoag J B 1940 The variation of the hard component of cosmic rays with height and the disintegration of mesotrons Phys. Rev. 57 46

[6] Durkin R P, Loar H H and Havens Jr. W W 1952 The lifetimes of the pi+ and pi- mesons Phys. Rev. 88 179

[7] Frisch D and Smith J 1963 Measurement of the relativistic time dilation using u-mesons Am. J. Phys. 31 342

[8] Ives N E and Stillwell G R 1938 An experimental study of the rate of a moving atomic clock J. Opt. Soc. Am. 28 215

[9] Saathoff G et al 2003 Improved test of time dilation in special relativity Phys. Rev. Let. 91 19

Hi Mac.

Thanks for posting this lengthy and fairly complete overview of your SW relativity.

It will take some time for us to work through it and comment, so please be patient!

Jorrie

Hi Mac, before replying to details of your post, can we please clarify some definitions of yours that seem to be non-standard (for the benefit of other readers and myself).

1. "Spatial isotropy". If it is not the isotropy of the speed of light in every inertial frame, please define accurately.

2. "However, to derive the LT from his two principles Einstein assumed that Newtonian concepts for distance and time apply to electromagnetic (EM) events just as they do to material events."

Please define what you mean by "electromagnetic (EM) events" and "material events" and how they differ. As far as I know, an event is something that happens at a specific time at a specific place. It can be the onset of the emission of a radio signal or it can be me clapping my hands and hence emitting an audio signal. The space and time coordinates of events can differ in different inertial frames, but essentially, an event is an event in physics.

3. "Now, of course, radiolocation tools, e.g. the GPS and "spy" satellites derive kinematic features of EM events from their own signals."

What are these "kinematic features of EM events"? I suppose it depends on your definition of EM events.

4. "... while these propagation times are unambiguous for collocated and simultaneous events, what are they in the general relativistic case?"

If by 'general relativistic case' you mean general relativity, this is misplaced here. If you mean something else, please change the term to avoid utter confusion.

Lastly (for now), can you provide the Table 1 that you refer to in your post?

Jorrie

Hi Jorrie

Thanks for your excellent questions! They point to issues key to understanding relativistic concepts, agreement being essential to successful discussion of the latter.

(1) To me, spatial isotropy (sans gravity) requires all laws of physics to be the same in all inertial frames independent of direction; one such law being the fixed speed of light which Einstein raised to that status with a separate postulate.

(2) I agree that a generic "event"—e.g., a radar pulse or cannon shot—defines a point fixed in space and time in every inertial frame. However, as Maxwell showed and as Einstein captured so elegantly with his two principles of SR, distance and time between these two kinds of events are, in general, different. Thus, while as you say "an event is an event in physics", you also agree I am sure with Maxwell and Einstein that distance and time between EM events are not, in general, the same for two material events collocated with those events. Like spacetime physics, the stopwatch physics I describe addresses this latter relativistic effect.

(3) My statement "kinematic features of EM events" refers solely to the concepts of distance, time, and motion associated with pairs of EM events measured from inertial frames sans gravitational fields. (I assume my definition for an EM event: a short pulse of EM energy that expands at c in a perfect sphere in all inertial frames, is identical to yours and spacetime physics. If not, please let me know.)

(4) I agree that my reference to "general relativistic case" is confusing and will refrain from using the term general. (Note, while I do not address implications of SW physics for general relativity, since it differs from ST physics not only in form but also in its quantized versions for distance, time, and motion, it might wiell provide a different perspective for this physics.)

Sorry about Table 1: The format was destroyed when I posted it. However, I did list my understanding of relationships for motion and associated Doppler shifts in classical (ether-based) and spacetime physics, plus the same in stopwatch physics. (These are under the heading "Relativistic Doppler Relationships".) Let me know if you have any issues re these relationships.

I also attempted to include several x-y plots comparing these physics, but was rejected by your software. I generated these using a "DPlot" program and I tried several file formats but unsuccessful. Can you help here?

Thanks, Mac

Hi Mac.

Before replying to your technical answers, some comments about inserting tables and figures into CR4's editor.

I copy and paste my tables and figures from the original software individually into a graphics editor and then save them as .gif or .jpg graphics files. From there it is a simple operation to insert them with the CR4 editor (the green camera of the editor task bar). Give it a try - I would like to see your graphs and tables!

It does not always work well to copy and paste directly from an application like Word, Exel or Dplot into CR4.

Jorrie

Thanks Jorrie--I will post an addendum w/plots, hopefully shortly.

Mac

Hi again, Mac.

1. "Thus, while as you say "an event is an event in physics", you also agree I am sure with Maxwell and Einstein that distance and time between EM events are not, in general, the same for two material events collocated with those events."

This makes little sense. SR does not distinguish between "EM events" and "material events". They are the same thing. What are you trying to say here?

2. "My statement "kinematic features of EM events" refers solely to the concepts of distance, time, and motion associated with pairs of EM events measured from inertial frames sans gravitational fields."

Again, it seems as if you are allocating motion to events! Events are static in every inertial frame, so there can be no motions between events, or between observers and events at all.

3. "I assume my definition for an EM event: a short pulse of EM energy that expands at c in a perfect sphere in all inertial frames, is identical to yours and spacetime physics."

OK, I suppose one can have a subclass of the class "event" that you label an EM event. Just remember that it inherits all the attributes of the class "event", hence you cannot talk about an EM event being propagated at c in all directions. The EM event is just the emission of the EM radiation, at some fixed place and time in very inertial frame.

Please consider points 1 and 2 above, so that we can try and agree on a common terminology. Without that, there will be little progress and lots of miscommunication.

Jorrie

Hi Jorrie:

I agree we need to get on the same page with some of these basic relativistic concepts, especially when exploring alternative explanations for these concepts.

Re my statement (1):

Ah, events, points, distance, time, and motion—seemingly simple, obvious, unambiguous concepts until Maxwell and Einstein came along. We do agree, I believe, that each material and EM event defines a unique fixed point in every inertial frame in position and time, and I assume in addition that separations between pairs of such points differ in different inertial frames. Thus, while I agree that your statement, "SR does not distinguish between "EM events" and "material" events." holds for individual events, I cannot agree it holds for pairs of such events. (E.g., let a cannon that fires two shots separated by time T in one frame be observed from a second frame moving at v relative to the first. My understanding is that the cannon and its "bangs" (material events) will be separated by vT in the second frame while its "flashes" (EM events) will be separated by vT/[1-(v/c)²]^1/2. Or am I missing something?

Re my paragraph 2: I agree with your statement, "events are static in every inertial frame, so there can be no motion between events…", but disagree, as described above, with the rest of that sentence: "or between observers and events at all." My understanding is that distance and time between events, whether material or EM, differ in different inertial frames as a function of motion. (While Einstein derived the LT by assuming this motion is between observers, in SW physics, it is assumed that motion is between inertial frames and EM events as defined by measurements within those frames.) So am not sure what you mean here.

Re my paragraph 3: I guess we more or less agree on this point.

Thanks again for your stimulating inputs!

Mac

Hi Mac, maybe we are getting closer to agreement!

You wrote: "...that each material and EM event defines a unique fixed point in every inertial frame in position and time, and I assume in addition that separations between pairs of such points differ in different inertial frames."

SR also says that, so I do not think you that you have to "assume in addition" that separations between pairs of such points differ in different inertial frames." That's standard SR.

"My understanding is that the cannon and its "bangs" (material events) will be separated by vT in the second frame while its "flashes" (EM events) will be separated by vT/[1-(v/c)²]^1/2. Or am I missing something?"

Ah, I eventually see what you mean by a "material event" and also that you are misstating the SR position completely. Two cannon shots, co-located and separated by a time interval T in one (proper) inertial frame are observed exactly as any "flash" event in SR in all inertial frames. In the reference frame you can time it with one clock. In all frames moving relative to the cannon, you need two synchronized clocks in each frame, one present at the first shot and one present at the second shot. You then use the LT to find the temporal and spatial separations of the two events. The time interval will obviously differ for various inertial frames of reference, but it does not matter if they are "flashes" or "shots" - they are treated exactly the same. Events are events in SR!

"I agree with your statement, "events are static in every inertial frame, so there can be no motion between events…", but disagree, as described above, with the rest of that sentence: "or between observers and events at all." "

Events do not move (in space) in any inertial frame, so how can there be spatial movement between an event and an observer? More technically, an event cannot have a spacetime worldline and it is the angles between spacetime worldlines that represent movement. An event is a dot (a set of coordinates) in every inertial frame.

What we can say about two events is that relative to their proper frame, as you defined it, observers can be in motion. This proper frame is equivalent to an observer static in that frame. I recommend you use this (proper frame) qualifier every time and never talk about observers moving relative to events, because that is absolutely false and leads to all sorts of confusion.

Food for thought...

Jorrie

Hi again Jorrie:

Thanks for clarifying the accepted interpretation for Special Relativity! My view is that understanding any "alternative relativity"—e.g. "Stopwatch Physics"—requires precise definitions for differences and similarities re accepted physics, which neither I nor anyone else can change (it is what it is!)—though I find the latter is a little tricky to tie down. After all, however, words describing any physics are pretty much fluff compared to how accurately its predicted values match measured effects.

The principal similarity between SW and ST physics is that both assume the validity of Einstein's two principles of special relativity: spatial isotropy and the fixed finite speed of light. Below is a stab at describing their primary differences.

Measurement concepts: In ST physics, rigid rods and synchronized clocks measure distances and times between EM events separately, motion being that between observers of the same events. In SW physics, distances and times are derived from differences in arrival times of signals from two EM events measured by stopwatches collocated with those events, motion being that between these clocks and the "proper" frame for those events. (I.e., those frames wherein time-like events are collocated and space-like events are simultaneous, and with values that equal Minkowski's interval, are Newtonian but also satisfy Einstein's two principles of SR.)

Illustrative Example: Let collocated (time-like) EM events separated by time T in one frame be observed by a second frame moving relative to the first at v = 0.5c. In ST physics, the time T' and distance D' between the two events in the second frame are T/[1– (v/c)²]^1/2 and T(v/c)/[1– (v/c)²]^1/2, (values in this case being T' = 1.1547…T and D'/c = 0.57735…T). In this physics, the "proper" Minkowski interval for these events, i.e., [(D'/c)² – (T')²]^1/2 = [–(T²)]^1/2, is an "imaginary" abstract geometric feature fixed for all observers of those events.

In SW physics, propagation times of signals to stopwatches in the second frame are T(V_sw'/c)/(1– V_sw'/c) and T(V_sw'/c)/(1+ V_sw'/c), giving SW values, C₀' and C₁', of T/(1– V_sw'/c) and –T/(1+ V_sw'/c) respectively. As a result, D_sw'/c = (C₀'+C₁')/2 = T(V_sw'/c)/[1 – (V_sw'/c)²] and T_sw' = (C₀'-C₁')/2 = T/[1 – (V_sw'/c)²]. Since V_sw' = D_sw'/T_sw' and V_sw'/c = 1– [(1–v/c)/(1+v/c)]^1/2 (from my analysis) then T_sw' and D_sw' in the above example are 1.21748…T and 0.51457…T respectively.

The principle difference: The small differences in values predicted by ST and SW physics mask a large difference between these two physics: i.e. motion in ST physics is between any two observers of the same pair of events; in SW physics motion is between individual observers and specific proper frames for the observed events. EM events, and thus pars of such events, are fixed forever in space-time; while inertial frames are forever in motion. In the above example, observers moving in different directions but at the same speed relative to collocated events must measure the same separation for those events (to satisfy Einstein's two principles of SR) independent of their own relative motions. In this example, D_sw' and T_sw' range from zero and T in the proper frame, while approaching infinity as observer speed approaches c. These increasing values come solely from increases in signal propagation times from zero, at zero speed, to T/2 and infinity at a speed of c, where D_sw' and T_sw' are both infinite, but D_sw'/T_sw' = V_sw'= c. While Minkowski's proper interval T is measured directly in the proper frame, otherwise T = [(T_sw')² – (D_sw'/c)²]/T_sw' = T_sw'– (V_sw'/c)( D_sw'/c), functions that, unlike the ST versions, are mathematically "real", instead of "imaginary", and that define physically "real" values, rather than abstract geometric concepts. That is, T is the intrinsic irreducible separation of the two events, while values for D_sw', T_sw', and V_sw' in other moving frames come from increased signal propagation times from the observed EM events to measurement clocks derivable from Einstein's two principles of SR.

More food for thought!

Mac

Hi Mac, you wrote:

1. "In this physics, the "proper" Minkowski interval for these events, i.e., [(D'/c)² – (T')²]^1/2 = [–(T²)]^1/2, is an "imaginary" abstract geometric feature fixed for all observers of those events."

The modern way of defining the Minkowski spacetime interval is:

S² = (cT)² - D² for cT > D (timelike interval)

S² = 0 for cT = D (lightlike interval)

S² = D² - (cT)² for D > cT (spacelike interval)

Nothing goes imaginary if the square roots are taken. Time and distances are never "imaginary abstract geometric features".

2. "The in values predicted by ST and SW physics mask a large difference between these two physics:"

The 'small differences' are getting the biggest at 0.9c. For this relative velocity, I get:

SR: T' = 2.29416…T and D/c = 2.06474…T, retaining the ST interval as exactly T.

SW: T' = 2.41050…T and D/c = 2.16945…T, both of which are about 5% higher than the SR values and not retaining the ST interval at T (it's also 5% higher than T).

Don't you think such a difference would have been detected by now? After all, 0.9c is easy stuff in particle accelerators. Although this is very interesting, I think any physics based on non-synchronized clocks are fatally flawed and will fail to predict many observations that are indisputable. Will get to that later.

Jorrie

Hi Jorrie:

I was relying on some old text books! Your "modern way" definition for Minkowski's spacetime interval is—at least from this old engineer's perspective—much more logical! The fact that "time and distance are not imaginary abstract geometric features" also fits with the SW perspective. (I am throwing out my old books!)

Still, I have difficulty with a couple of points. We agree, I believe, that every event defines a fixed point in spacetime but that distance and time between two such points/events differ in different inertial frames. In SW physics, such differences come from derivable differences in signal propagation times from events to clocks in those frames. While this "engineering" explanation for relativistic effects seems clear to me, I have never understood how such effects are created by motion alone between observers of EM events, and felt that my text-book assignment of these effects to shifting clock rates and rod lengths was hokum. (What is your concept of the "modern" interpretation; it must make more sense!)

While my reference to "small differences" between ST and SW physics hold in general, as you show, these differences can be significant. (FYI this difference in time dilation reaches a maximum 8% (exactly!) at v = 0.8c. Also, since motion V_sw in SW physics = 1-[(1-v/c)/(1+v/c)]^1/2, v being Newtonian, values for T' and D'/c are actually somewhat larger, i.e., 2.46184…T and 2.215656…T. However, these differences in time and distance dilation become very small at low and high speeds, extremely small at speeds generated by particle accelerators.)

Interestingly, classical tests for time dilation like those by Frisch and Smith based on decay times of comic-ray generated muons, actually give results closer to values predicted by SW physics. For example, in 1963 they measured mean time dilations for muons traveling at an average velocity ~0.9929c of 8.8+0.8, while ST and SW derived values at this speed are ~8.4 and 8.6 respectively. [1]

Nevertheless, a resounding "YES" to your question: "Don't you think such a difference would have been detected by now?" In fact, I believe three such differences between ST and SW physics may have already been observed, but not recognized as such. My initial analyses show that the Pioneer blueshift anomaly, the cosmic redshift acceleration, and a puzzling blueshift cut-off at 2f₀ in ultra-intense laser plasma reactions reflect these differences [2]. The first two effects come from a mix of differences in definitions for velocity and Doppler shifts; the peak difference in velocities at 0.707c corresponding to the anomalous cosmic redshift "jerk" at z of 0.46+ 0.13 reported by Riess [3] and Shapiro [4] for high-z SNe Ia supernovae.

Moreover, the huge difference between Doppler blueshifts in these two physics at high velocity offers a definitive test for their relative validity. While SW physics limits blueshifts to 2f₀ for sources approaching at c, ST physics predicts these blueshifts approach infinity (there being a huge difference between 2 and infinity!). Yet, I have found no evidence—cosmological, experimental, etc.—that blueshifts can exceed 2f₀, even though such should occur above the relatively low speed of 0.6c. However, this lack of evidence for the ST version plus just one bit of evidence for the SW version proves little. Are you aware of any evidence either way?

I see I need to clarify the role of clock synchronization in SW physics! I agree with your statement: "…I think any physics based on non-synchronized clocks are fatally flawed…" In fact, basic relationships in SW physics hold only if clocks in all frames are synchronized and remain so independent of their relative motions (a feature also required by spatial isotropy). In SW physics, clocks need be synchronized in rate only. While time-synchronized clocks are useful in many applications, such clocks rely on an artifice that not only ensures time measured between separated events is independent of distance, but forces the separate independent measurement of the latter. This, it seems to me, contradicts Maxwell and Einstein's theories that show time and distance in electrodynamic processes are dependent variables.

Hope this helps. Mac

[1] Frisch D and Smith J 1963 Measurement of the relativistic time dilation using u mesons Am. J. Phys. 31 342

[2] Galimberti M, et al 2001 Laser and Particle Beams 19 47-53

[3] Riess A G et al Feb. 2004 Type Ia supernovae discoveries at z>1 from the Hubble space telescope: evidence for past deceleration and constraints on dark energy evolution arXiv.org.astro-phy/0402512

[4] Shapiro CA and Turner MS 2005 What do we really know about cosmic acceleration arXiv:astro-ph/0512586 v1

Hi Mac.

I still have to chew some more on your reply, but this part is at least easy to answer:

"I have never understood how such effects are created by motion alone between observers of EM events, and felt that my text-book assignment of these effects to shifting clock rates and rod lengths was hokum. (What is your concept of the "modern" interpretation; it must make more sense!)"

The "modern" explanation in SR is simply the way clocks are synchronized in different inertial frames. As I have illustrated before (to the right), with the X,CT frame, Pam and Jim all using Einstein's clock synchro method, they do not agree on what is simultaneous and even what time it is when events happen. Although their clocks all run at the same rate, they do not even agree on that fact!

I know there are relativists that will disagree with my "their clocks all run at the same rate", but it is true in purely inertial systems, where it is impossible to detect absolute clock rates. The synchronization differences result in different times and hence different distances measured between the two events (the black dots, which are co-located in the black frame).

It so happens that Pam and Jim, if their speeds are identical, but in opposite directions as indicated, will measure the same space- and time intervals between the events, despite them moving relative to each other. They will just not agree with the black frame. The issues are resolved by clock synchronizations that differ.

Observed distances between events (length contraction and the like) are also resolved by clock synchronization differences. I this sense, length contraction is not real, but just a measurement problem. To measure the length of a moving rod, one must read the coordinates of it's front and rear simultaneously. Different observers with different definitions of simultaneity (clock synchronizations) will obviously not agree on the length of the moving rod.

I hope that clears some of the "old" misconceptions about SR.

Jorrie

Thanks Jorrie--I will also need to chew on this a little!!

Mac

Thanks Jorrie!

Your explanation makes a great deal more sense than the "old" view of ST physics. It is also clarifies key differences re the radiolocation alternative.

The latter supports your conclusion that "…clocks all run at the same rate"; a result for identical clocks as well as rigid rods that, it seems, is required by spatial isotropy. This leads to your seemingly unavoidable conclusion that differences between observers of the same events must come from "…the way clocks are synchronized in different inertial frames". But, what specific physics or asymmetries between inertial observers is responsible for these "clock synchronization differences"?

SW physics offers one possibility. In this physics, the time and rate synchronized clocks of ST physics are replaced by stopwatches that measure differences in arrival times of signals from the observed events. Resulting relationships hold only if clocks do remain rate-synchronous in all frames. This suggests that differences beween observers come not from clock synchronization differences, but rather from Einstein's more fundamental assumption that time between EM events can be measured by synchronized clocks. I would argue that this violates both Einstein and Maxwell's theories that show time and distance in electrodynamic processes are dependent variables. Note also, SW physics assigns differences between observers to differences in signal propagation times from events to clocks, not to observed events themselves (with separations fixed forever in time or distance), or to changes in observer motions or clock rates fixed forever in all inertial frames. This SW perspective, it seems to me, is consistent with your view that relativistic effects (at least length contraction) reflect measurement distortions rather than physical changes in either the measurement tools or observed events.

Thanks for your description of the modern view of spacetime physics. It was very helpful, especially in exposing the core difference between these two physics: the reliance on clocks synchronized in both time and rate on the one hand, and in rate alone on the other.

Mac

Hi again Mac.

I'm looking at your "evidence": "... the peak difference in velocities at 0.707c corresponding to the anomalous cosmic redshift "jerk" at z of 0.46+ 0.13 reported by Riess [3] and Shapiro [4] for high-z SNe Ia supernovae" and have a question.

Where do you get the 0.707c from? According to cosmological equations, the recession speed giving z=0.46 is v=0.36c. This is not calculated by using Doppler shift, but rather expansion factors.

As a cross-check, if I calculate the SR Doppler shift from the v=0.36c, I indeed get z=0.46. This does however only hold for relatively low redshifts. If you go to redshift 6 and above, SR and the cosmological redshifts do not agree at all.

Jorrie

Hi Jorrie:

Re your question: "Where do you get the 0.707c from?": This speed is where the Newtonian speed v of a receding source derived from its relativistic Doppler shift, v/c = [1- (f_R/f₀)²]/[ 1+ (f_R/f₀)²], is a maximum relative to the SW transform: V_sw/c= 1- f_R/f₀. It turns out that this peak occurs at v/c = 2^-1/2 (exactly), where v is ~1.207V_sw. (While these redshift relationships equal those between these variables independent of the Doppler transforms, i.e., V_sw/c = 1- [1-v/c)/1+v/c)]^1/2, interestingly, the same does not hold for approaching sources.)

My understanding is that the relationship v/c = [1- (f_R/f₀)²]/[1+ (f_R/f₀)²] holds at all velocities for receding sources. To address your two statements: "This is not calculated by using Doppler shift, but rather expansion factors.", and "If you go to redshift 6 and above, SR and the cosmological redshifts do not agree at all." I need to get your definitions for "expansion factors" and "cosmological redshifts.". (My analysis is restricted solely to relationships between frequency shifts of known elements and source radial speed, independent of the mechanism responsible for that motion. I suspect you may be mixing the two.)

Hope this helps.

Mac

Hi again Mac. You wrote:

"Re your question: "Where do you get the 0.707c from?": This speed is where the Newtonian speed v of a receding source derived from its relativistic Doppler shift, v/c = [1- (f_R/f₀)²]/[ 1+ (f_R/f₀)²], is a maximum relative to the SW transform: V_sw/c= 1- f_R/f₀."

Ah, so it has nothing to do with the "cosmic jerk", which surely does not happen at an apparent recession speed of 0.707c.

"My understanding is that the relationship v/c = [1- (f_R/f₀)²]/[1+ (f_R/f₀)²] holds at all velocities for receding sources."

This is true in the flat spacetime of SR, but not generally true for cosmological redshift. It holds only approximately for low z. One needs to study cosmology^[1] quite deeply to be able to wrap your head around this, but as an example: the area where the present microwave background originated has an observed cosmological redshift of z ~ 1100 (or f_R/f₀ ~ 1/1100). If you put that into the SR formula, you would get an apparent recession speed of 0.999998...c. This is the speed at which a nearby object, moving away from you through free space, will give Doppler ratio of f_R/f₀ ~ 1/1100, but is not true for objects at cosmological distances.

In cosmological reality, there are two recession speeds involved: (i) when that light was transmitted, the apparent recession speed (due to expanding space) was ~66c, and (ii), presently, the recession speed if that area is ~3.3c. Sounds absurd? It fits the concordance model, which in turn fits ~99% of all observable data.

Jorrie

[1] A good starting point is my web-site's downloads available from here => Cosmology and the Engineer.

Hi Jorrie:

In referring to the velocity "bubble" created by the ST Doppler transform relative to the SW transform which peaks at 0.707c, you stated: "Ah, so it has nothing to do with the "cosmic jerk", which surely does not happen at an apparent recession speed of 0.707c." Your statement is understandable, given that 0.707c (v = ~212,100 km/s) is well above the peak cosmic "jerk" reported by Riess et al as z= 0.46+0.13 (v= ~108,000 km/s). This, however, is only part of the story: The reported cosmic "jerk" comes also not only from differences between Doppler transforms in these two physics, but also that this "jerk" represents the rate of change of velocities for SNe Ia supernovae derived from these higher velocities.

(Note, the following analysis addresses only differences between values derived by ST and SW Doppler transforms from measured redshifts, f_R/f₀, independent of how those redshift were generated and the cosmological models used to explain such effects, which as you know, can get pretty knotty.)

Consider first, relativistic transforms used to derive source velocities from observed Doppler shifts, f_R/f₀, in these two physics, i.e.: v/c = [1-(f_R/f₀)²]/[1+(f_R/f₀)²] and V_sw/c = 1- f_R/f₀. Since z = f₀/f_R, z = [(1+v/c)/(1-v/c)]^1/2 and z = (V_sw/c)/(1-V_sw/c) in ST and SW physics respectively. The difference between these transforms, v/c-Vsw/c = z²/[(z+1)³+z+1] a function that peaks at z=2.38 (where v/c = 0.83903…, and V/c= 0.77169...). The derivative of this function, z(-z³+4z+4)/[(z+1)(z²+2z+2)]², is surprisingly consistent with the cosmic jerk reported by Reiss and others. That is, this function peaks at z=0.37 at 12.56…% above the ST value , compared to the reported peak at 0.46+0.13 at a value 10 to 15% above the expected value as shown below. (Jorrie, I assume that the above relativistic relationships are in fact used to derive raw speeds of receding cosmic objects. Do you agree, and are you aware of any "corrections" etc. normally used with these transforms?)

Acceleration "Jerk" between ST and SW Doppler transforms and that observed for high-velocity supernovae

While this similarity to the anomalous cosmic "jerk" could be coincidental, the possibility that it is not just coincidence is supported by the accuracy to which these same transforms match the Pioneer spacecraft anomaly. This as-yet unexplained small fixed acceleration towards the sun of 8.74 +1.33x10^-8 cm/s², is surprisingly consistent with the difference between SW and ST Doppler transforms, that, based on a simple first-order model, gives a value of 8.2 x10^-8 cm/s². (Now that I have learned how to include plots I will provide more in the future for your perusal.)

Mac

Hi Mac. Some cosmological comments to your last post. You wrote:

"The reported cosmic "jerk" comes also not only from differences between Doppler transforms in these two physics, but also that this "jerk" represents the rate of change of velocities for SNe Ia supernovae derived from these higher velocities."

Firstly, the "jerk" is a bit of a confusing term. One tends to think of it as a sudden change in acceleration. There is no sudden change in cosmic acceleration. It very smoothly changed from a deceleration to acceleration over billions of years. The cosmic deceleration got less and less until it was about zero some 5.6 billion years ago. Then it stayed immeasurably close to zero for 2 billion years, until at some 3.6 billion years ago, it started to show a tiny acceleration. That acceleration has grown somewhat over the last 3.5 billion years. Not your usual "jerk", although the technical definition of "jerk" is simply a change in acceleration.

The SN1Ae used to detect the "jerk" was at distances ranging from 9 to 11 billion light years away, with redshift (z) ranging from 1.4 to 2.5, with respective proper recession velocities from 0.88c to 1.4c (obviously not Doppler, but cosmological). The v/c values from the normal Doppler shift agree roughly with the cosmological values up to z ~1, where the difference is ~10%. At z=1.4, the respective speeds are 0.7c and 0.88c and at z=2.5 it is 0.85c and 1.4c. If we go to the farthest galaxies ever observed (z~6.5), the two values are: 0.97c and 2.92c. The CMB radiation, at a redshift of z~1100, yields the largest difference that we can observe, i.e., apparent recession speed ~c, proper recession speed ~66c.

These differences stem from the fact that Doppler shift represents a movement through space, while cosmological redshift represents the expansion of space. Some of the confusion does perhaps come from a common practice of stating that a cosmological redshift of (say) 2.5 is the same as the Doppler shift of an object that recedes from us at 0.85c through space. This is however just an apparent velocity, because that object does not move through space at that sort of speed (peculiar speeds are tiny by comparison). Your hypothesis as to the source of the "jerk" is thus suspect.

You graph is an interesting mathematical exercise, but in the light of the above, it probably has very little cosmological meaning. Those SN1Ae did not sit at z~0.46, as explained above.

I will comment on the Pioneer anomaly next time around.

Jorrie

Hi again Mac. Here's another issue that I need clarified on the "evidence". You wrote:

"Interestingly, classical tests for time dilation like those by Frisch and Smith based on decay times of comic-ray generated muons, actually give results closer to values predicted by SW physics. For example, in 1963 they measured mean time dilations for muons traveling at an average velocity ~0.9929c of 8.8+0.8, while ST and SW derived values at this speed are ~8.4 and 8.6 respectively. [1]"

If I read correctly, there was a huge uncertainty in the effective average speed of the muons. Quote: "... with the effective time dilation factor calculated for mesons of these speeds in our detection geometry 1/(1 – v²/c²)^½ = 8.4 ± 2." This gives an effective speed range of 0.9877 < v/c < 0.9954, which can hardly be used to indicate a preference for SW physics.

BTW, how do you calculate the Lorentz factor γ in your SW relativity?

Still working on-and-off on the rest...

Jorrie

Hi Jorrie

I agree that these results do not imply that the SW version is more likely valid, especially given the relatively large estimated error. However, for the reported mean muon velocity (v) of 0.9929c, the ST dilatation, 1/[1-(v/c)²]^1/2 and SW version, 1/[1-(V/c)²] (where V/c = 1-[1-v/c)/1+v/c)]^1/2), give time dilations of 8.407… and 8.633… respectively, versus the reported mean measurement of 8.8. The fact that the SW version is closer to the mean reported value is of only passing interest, unless of course test errors are overstated.

The dilation factor in SW physics is as shown above.

Jorrie: I appreciate your close scrutiny, and will be tackling your next questions shortly.

Mac

Hi Mac. Sorry, I had a bit of a hectic week, hence the delay...

Your V_sw looks like a Doppler shift. Can you please explain how you get to that again?

I have a suspicion that your SW time dilation is the same as SR with a few higher order terms added. Will look at that a bit more.

Jorrie

Hi again Jorrie:

Glad your back, but no apologies needed—you are always quicker to reply than I!

Your words: "Your V_sw looks like a Doppler shift." are perceptive. Motion, V_sw/c equals (C₀'+C₁')/(C₀'-C₁'), SW values that depend on propagation times of signals from EM events, and thus intrinsically relativistic. As a result, V_sw/c is linearly related to Doppler shift, i.e., V_sw/c = 1-f_M/f₀ (f_M being the observed frequency, f₀ the rest frequency). In contrast, these relativistic relationships in ST physics are non-linear: i.e., v/c = [1-(f_M/f₀)²]/[1+(f_M/f₀)²].

Re your question as to how I derived V_sw: In SW physics, motion is relative to "proper" frames wherein time-like events are collocated; space-like events simultaneous. As in Newtonian physics, V_sw is a function of measured values for the "distance" and "time" between events; i.e., V_sw'/c = D_sw'/cT_sw' for time-like events, and, unlike Newton's definition, V_sw'/c = cT_sw'/D_sw' for space-like events. Thus, in both cases V_sw'/c = 0 for observers stationary relative to the proper frames for the observed events.

While I agree that time dilation in SW and ST physics refers to the same effect—i.e., the increase in measured time due to motion—otherwise they differ significantly in physical origin and also slightly in value. That is, in SW physics motion is between observers and specific inertial frames (i.e. proper frames), time dilation coming directly from increases in propagation times of signals from observed events imposed by SR. While this effect in ST physics is assigned to motion between observers of the same events, I must admit I have yet to grasp the physics responsible. However, the latter is relatively unimportant since, whatever the source, the objective relationships between time dilation in these two physics are precise, i.e. 1/[1-(V_sw/c)²) = 1/[1-(v/c)²]^1/2, where V_sw/c = 1- [(1-v/c)/(1+v/c)]^1/2.

Hope this helps, Mac

Hi Mac.

Before trying to reply fully, just an observation on the final sentence of your reply: "... the objective relationships between time dilation in these two physics are precise, i.e. 1/[1-(V_sw/c)²) = 1/[1-(v/c)²]^1/2, where V_sw/c = 1- [(1-v/c)/(1+v/c)]^1/2."

These values are only approximately equal. There is exactly 8% difference at v/c=0.8.

I still have difficulty to comprehend your V_sw, which is not really a velocity, but a function of Doppler shift. Propagation times are surely related to Doppler shifts. In SR, we do not measure velocities dependent upon propagation times of signals. We actually subtract the propagation times of signals to get the proper observed times.

I'm still very uncomfortable about the theoretical basis of your SW theory and I've not seen anything that eases that 'discomfort'! A difference of 8% is huge and I still hold that if SR was out by that much, it would have been verifiably detected long ago. The examples that you quoted before do not quite qualify as "verified deviations".

Jorrie

Have been working on responses to your other critiques, but want to reply to this one first.

I agree with your observation on my last sentence. My error was that the "equal" sign should have been an "and". Still, these definitions are unambiguous, directly related, and do differ (as you say) by up to 8%.

Relative to your comment: "I still have difficulty to comprehend your V_sw, which is not really a velocity, but a function of Doppler shift.": I think of V_sw as motion of one inertial frame relative to another (as in classical and ST physics) but with two major differences. One is that V_sw applies only to motion between measurement frames and proper frames of observed EM events; the other is that it is defined differently. That is, for time-like events, V_sw/c = (C₀'+C₁')/(C₀'-C₁') = D_sw'/T_sw'c, and for space-like events, (C₀'-C₁')/(C₀'+C₁') = T_sw'c /D_sw'. (Note, for time-like and only time-like events, C₁' is always negative, (C₀'-C₁') always positive.) In these definitions, V_sw/c ranges from "0" in the proper frame for any two events to "1" in frames moving at c relative to that proper frame. (Thus, V_sw applies only to electrodynamic processes, i.e., between material frames and proper frames of EM events; motion between material frames and objects remains Newtonian.)

All variables in SW physics (unlike ST physics) are derived from SW values (e.g., C₀' and C₁') that are intrinsically relativistic, i.e., depend directly on propagation times of EM signals. This, leads to simpler Doppler-velocity relationships in SW physics, i.e., V_sw/c = 1-f_R/f₀ and f_A/f₀-1 for receding and approaching sources respectively.

Let me briefly address your two very reasonable concerns: "the theoretical basis of your SW theory", and "A difference of 8% is huge… would have been verifiably detected long ago…". Both SW and ST physics recognize the validity of Einstein's two principles of SR. Hence, I assume that your "theoretical basis" here refers to assumptions used to explain how real-world effects reflect these two principles. Einstein derived the LT between distance, time, motion, and c by assuming that Newtonian concepts for distance, time, and motion applied to electrodynamic as well as material processes, and that measurement differences between observers of the same events (imposed by his and Maxwell's theories) depend on their own relative motion. SW physics assumes, instead, that distances and times between EM events are derivable directly from differences in arrival times of their own signals at separated clocks. In contrast to ST physics, distance, time, and motion are derived by applying Einstein's two principles of SR to this simple proven electrodynamic measurement concept instead of assuming classical Newtonian concepts for distance, time, and motion for material objects can also be used to explain electrodynamic processes.

I agree, an 8% difference in predicted value is huge. But how about the almost 13% difference in Doppler-derived receding velocities at z of ~2.4, and the near infinite spread between the 2f₀ blue-shift limit predicted by SW physics versus unlimited shifts in ST physics! It seems, as you say, these differences should have been discovered long ago. However, without an alternative reference this is difficult. For example, past time dilation tests like those by Frisch and Smith were at high speed, ~0.9929c, to maximize difference re classical physics. If conducted instead at 0.8c, where SW time dilatation is 8% higher than ST physics, their results might have been different. In fact, an initial search suggests that three such differences between ST and SW physics have already been observed: the Pioneer and the cosmic acceleration anomalies, and the blue-shift cut-off discovered in high-intensity laser-plasma reactions. Such chance "discoveries" like these are, at present, simply unexplained anomalies. (I will try post my findings in this area in the near future.)

As always, I welcome your comments.

Mac

Hi Mac. You wrote:

"In contrast to ST physics, distance, time, and motion are derived by applying Einstein's two principles of SR to this simple proven electrodynamic measurement concept instead of assuming classical Newtonian concepts for distance, time, and motion for material objects can also be used to explain electrodynamic processes."

I disagree completely with these statements. To me it seems like the inverse is true. Your SW physics assume classical Newtonian/Galilean concepts and disagrees with Einstein's two principles of relativity. It is a little ridiculous to state that Einstein's SR disagrees with his own principles and uses Newtonian concepts of space and time!

"I agree, an 8% difference in predicted value is huge. But how I agree, an 8% difference in predicted value is huge. But how about the almost 13% difference in Doppler-derived receding velocities at z of ~2.4, ..."

You state this z~2.4 case often. I don't know what the significance of that value is and I'm not sure if you understand that cosmological redshifts of that magnitude are not Doppler shifts at all. The recession velocity of a galaxy with z=2.4 is 1.36c. (From the Cosmo Calculator that I referenced before). If you use the Doppler formula, you get 0.84c, which has nothing to do with cosmological recession rates. The cosmological redshift-velocity relationship has no exact equation and is obtained by numerical integration of the expansion formula of the universe.

Can you perhaps give more information/references to the "blue-shift cut-off discovered in high-intensity laser-plasma reactions"?

Sorry the be ultra-critical, but your SW relativity is rather radical, not very convincing and the evidence is quite skimpy. It will be a tough road ahead for you...

Jorrie

Hi Jorrie—

I don't mind you being critical—it gives me a chance to clarify issues that I have apparently explained poorly.

Let me briefly "review the bidding": Einstein, in his 1905 paper, presented his two principles of SR as follows:"…the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good." And: "that light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body." He stated in the first paragraph of his paper that these postulates addressed the Michelson-Morley tests and Maxwell's theory which showed "observable phenomena depend only on relative motion". Einstein made two key assumptions to explain these principles: that distance and time between EM events are measured by synchronized clocks rigid rods and depend on motion between observers of the same events. The rest (i.e., ST physics) as they say, is history.

SW physics is based on two quite different assumptions: that motion is between observers and proper frames of observed EM events, and that distances and times between those events are functions of time-differences between signals received from those events. These assumptions and resulting physics reflect that of GPS, spy satellites, and other such tools that derive positions and times of EM events directly from their signals, independent of other observers of the same events, a proven physics that employs neither time-synchronized clocks nor rigid rods. Applying Einstein's two principles to this physics leads to definitions for distance, time, and motion different from Newton's and relationships between these variables different from the LT. Moreover, it predicts physical effects, e.g., time/distance dilation and Doppler-velocity transforms, that differ slightly, in general, from ST physics.

Time-synchronization is a simple, useful artifice that ensures time between EM events measured by such clocks is independent of distance between those events (rigid rods, of course, do measure distance independent of time). In contrast, Einstein's two principles of SR show distance and time between EM events are dependent variables, which, it seems, questions whether this time is consistent with his own principles. SW physics avoids this issue since distance and time are dependent functions of more elemental SW values.

In this context, I do not grasp what you mean by the following: "To me it seems like the inverse is true. Your SW physics assume classical Newtonian/Galilean concepts and disagrees with Einstein's two principles of relativity. It is a little ridiculous to state that Einstein's SR disagrees with his own principles and uses Newtonian concepts of space and time!"

Re your words: "You state this z~2.4 case often. I don't know what the significance of that value is and I'm not sure if you understand that cosmological redshifts of that magnitude are not Doppler shifts at all. The recession velocity of a galaxy with z=2.4 is 1.36c." At z=2.4 the difference between Doppler-derived velocities in ST and SW physics, (v/c-V_sw/c) peaks at ~0.13488c falling below 0.01c for 0.2>z>200. This velocity "bubble" is significant since its derivative fits the cosmic "jerk" discovered by Riess and others. My analyses are based solely on relativistic transforms between velocity and the observed (measured) Doppler shifts (f_R/f₀) where z = f₀/f_R-1, v/c = [(f₀/f_R)²-1]/[(f₀/f_R)²+1], and V_sw/c = 1-f_R/f₀. (I do not address subsequent modeling corrections such as you describe, since (I assume) all must start from observed Doppler shifts and thus any error in derived velocity would be retained.)

You asked about the observed blue-shift cut-off at 2f₀: This effect was reported by M. Galimberti et al in Laser and Particle Beams 19 47-53 in 2001, "Investigation of ultra-intense femtosecond laser-plasma interactions through w and 2w imaging and spectroscopy". Figs. 3 and 5b in this paper show the observed spectrum of the second harmonic of the laser beam along with the calculated "pure" 2w spectrum. Unlike the red-side of the spectrum, which extends "many tens of nanometers" the "2w light shows a blue-shift limit very close to l₀/2." This result was apparently a surprise to the authors who offered no explanation.

Re your last words: I am not concerned about being radical—any theory that replaces ST physics would have to be—and I am sure that convincing those emotionally attached to a theory over 100 years old is likely hopeless. However, the proof of any such theory depends only on how well its objective expressions explain observable effects. Since SW physics provides objective relationships different from ST physics, it would be more fruitful to assess which best accomplishes the latter. (After, all, after 100 years there are those who still argue over the infinities, apparent paradoxes, etc. associated with ST physics. However its ability to accurately—maybe perfectly!—predict observed effects relative to classical physics trumps such arguments.) Hence, I would like to compare how well these two physics pass past tests (e.g., time dilation, transverse Doppler shift, etc.) plus establish whether significant differences between these physics (Doppler-velocity transforms, blueshift limit in SW physics) are consistent with observed effects. (E.g., just one example of a Doppler blueshift >2f₀ would disprove SW physics and help confirm ST physics.)

Jorrie, are you aware of any other tests, observations, etc. that might be useful in this task? I have briefly described some initial results and will post more details shortly.

Thanks, Mac

Hi Mac. Another "installment" of comments.

You wrote: "While SW physics limits blueshifts to 2f₀ for sources approaching at c, ST physics predicts these blueshifts approach infinity (there being a huge difference between 2 and infinity!). Yet, I have found no evidence—cosmological, experimental, etc.—that blueshifts can exceed 2f₀, even though such should occur above the relatively low speed of 0.6c. "

Just one small terminology correction: redhifts and blueshifts are not expressed as f/f₀ or such. This is the Doppler factor. Red- and blueshifts are relativistically expressed as fractional wavelength change: Δλ/λ₀ = (λ-λ₀)/λ₀ = [(1+v/c)/(1-v/c)]^½ - 1. This value approaches infinity for v → c (redshift) and -1 for v → -c (blueshift). It does still mean that frequencies tend to infinity in the case of extreme blueshift though (λ approaches zero).

"However, this lack of evidence for the ST version plus just one bit of evidence for the SW version proves little. Are you aware of any evidence either way?"

There are no physical celestial bodies that I know of that move through space as fast as 0.6c. The expansion of the universe gives distant galaxies apparent recession speeds above that, but not closing speeds. The plasma jets from AGNs are thought to travel near the speed of light and some of them do come our way. Unfortunately, they seem to be 'featureless', i.e., there are no telltale signatures of known elements that can be used to determine their amounts of blueshift (it's a plasma after all).

I would think that it must be possible to measure blueshifts in particle accelerators, because electrons being accelerated radiate. Will look for possible evidence.

Jorrie

Hi Jorrie:

I agree with your terminology. I often do use (mistakenly, I suppose) use "blueshift" and "redshift" to refer to approaching and receding Doppler shift, and include "z" when in that form. (I will try to change my ways, but at my age it may prove difficult!)

Note that the SW Doppler limit of 2f₀ and the SW prediction of a zero transverse Doppler shift are directly related. The Ives-Stillwell tests at Bell Labs in 1938 have long been evidence for the existence of a finite transverse Doppler shift, a shift that approaches infinity as source speeds approach c. Recently, however, evidence (found by radio engineers!) suggests that transverse Doppler shifts of microwave sources are not consistent with the ST prediction. (I found >200,000 hits for "absence of transverse Doppler shift" on Google.) While particle accelerators do operate at speeds very near c, measurement of Doppler shift requires an EM source radiating at known frequency, which may be impractical.

To me, the most striking and strongest evidence for a hard Doppler blueshift limit at 2f₀ is that shown to exist in ultra high-intensity laser-plasma interactions such as by Galimberti ea al, f₀ in this case being the laser frequency. (Thus far I have made only a cursory search in this area.)

Mac

Mac, you wrote: "Recently, however, evidence (found by radio engineers!) suggests that transverse Doppler shifts of microwave sources are not consistent with the ST prediction."

Those type of results are disputed. Read e.g.: http://www.physicsforums.com/showthread.php?t=181719

I have not studied the "ultra high-intensity laser-plasma interactions such as by Galimberti ea al ..." either. I am not aware of any verified (peer reviewed over a lengthy period and/or duplicated) test that has shown deviations from the SR prediction of redshift. That surely does not rule it out and it would be very interesting if a verified experiment could find a deviation...

Jorrie

Hi Jorrie,

The poster of that thread (lalbatros) disagrees with the IEEE paper's conclusion (see paragraph 3).

S

Hi S. You wrote:

"The poster of that thread (lalbatros) disagrees with the IEEE paper's conclusion. ..."

That's what I meant with my: "Those type of results are disputed. Read e.g.: ......"

Jorrie

Hi Mac.

There is another definition problem in you opening post on "Radiolocation Relativity", i.e.:

"Transverse Doppler Shift: Both classical and ST physics predict infinite Doppler frequency shifts—and thus infinite energies—for EM sources approaching at c (Table 1). "

What you describe here is not "Transverse Doppler Shift". What you described is normal relativistic Doppler shift of approaching or receding sources. Transverse Doppler means relative radial velocity is zero and there is only a transverse component, where Newton would have predicted zero Doppler shift, but SR predicts a finite redshift because of time dilation of the transmitter. I know it is sometimes used in the older literature as meaning "the relativistic part of the radial Doppler shift", but is is so confusing that it should be avoided.

It's also wrong to say that SR (your 'ST physics') predicts infinite Doppler frequency shifts. The Lorentz transformations are not applicable to material objects that move at c relative to any reference frame, because it explicitly forbids that speed for material objects. One can say that as a closing speed of a material objects approaches c, the Doppler shift will start to diverge - but infinite energy, nah!

"This small difference questions the long-accepted view that the Ives-Stillwell and subsequent similar tests verify the existence of finite transverse Doppler shifts as well as time dilation predicted by ST physics."

I think those tests at 0.01c can distinguish between Newtonian and relativistic physics, but not between SR and possible rival theories of relativity. There are many other tests that validated SR at high relative velocities in particle accelerators. I'm not aware of the error bands of those theories, but AFAIK, until SR fails (predictions outside the error bands), nobody will seriously question its validity. Many people have tried and failed so far...

Jorrie

Hi again, Jorrie:

The validity of any physical theory depends, of course, on how well it predicts real-world processes. As indicated in my original post, differences between physical effects predicted by Radiolocation and Spacetime physics are generally slight though might be observable in some situations. I compare how these two physics treat four effects reported in the literature that appear to reflect such observable differences. Any comments you or others care to offer re these analyses are welcome.

Mac

Radiolocation Relativity versus Reality

While both SW physics--based on radiolocation concepts--and ST physics--based on classical clocks and rods--rely on Einstein's two principles of SR, differences in their measurement physics leads to different definitions for, and relationships between, distance, time, and motion in electrodynamic processes. While differences in their predicted physical effects are generally small, evidence suggests that four such differences may have already been observed.

Two of these—the acceleration anomaly of Pioneer spacecraft and an unexpected cosmic "jerk" observed for a certain class of very remote supernovae—are now widely recognized as anomalies unexplainable by known physics. Two others—an apparent Doppler-shift limit at 2f₀ observed in high-intensity laser plasma experiments, and the inability to detect a transverse Doppler shifts at microwave frequencies—are of special interest here since they address fundamental differences that exist between these two physics.

The Radiolocation View: Radiolocation physics suggests that all four of these anomalies come from the same source: differences in Doppler-velocity transforms in these two physics. As shown in my original post, velocities of EM sources in classical, ST, and SW physics are related to observed Doppler shift, f_R/f₀ and f_A/f₀ for receding and approaching sources respectively, as shown below and Fig. 1.

Table 1: Doppler-Velocity Relationships;

Redshift = (f_R/f₀) Blueshift = (f_A/f₀)

Classical physics: f_R/f₀ = 1/(1+v/c) f _A/f₀= 1/(1+v/c)

ST physics: f_R/f₀ [(1-v/c)/(1+v/c)]^1/2 f_A/f₀= [(1+v/c)/(1-v/c)]

SW physics: f_R/f₀=1-V_sw/c f_A/f₀=1+V_sw/c

Figure 1. Relationships between Doppler shift and source velocity in Classical, ST, and SW physics

Thus for any observed Doppler shift, f_D/f₀, the ST transform gives a source velocity, v/c, of [(f_D/f₀)²-1]/[1+(f_D/f₀)²]; SW physics, V_sw/c = (f_D/f₀)²-1 (negative values for receding sources). These transforms show for approaching and receding sources, v/c = [(1+V/c)²-1)]/[(1+V/c)²+1)] and [1-(1-V/c)²]/[1+(1-V/c)²].

In SW physics, motion (V_sw), distance (D_sw), and time (T_sw) depend directly on c, i.e., on time-difference ("stopwatch") values based on propagation times of EM signals. These values differ from ST values except in perfectly symmetrical "proper" frames for time- and space-like events where distance or time is zero and all values are Newtonian. However, values in the two physics in electrodynamic processes are always related as follows (D', T', and v being ST values as defined by the LT):

V_sw/c = 1-[(1-v/c)/(1+v/c)]^1/2

T_sw' + D_sw'/c = T' + D'/c

The Pioneer Blueshift Anomaly: Pioneer 10 and 11 deep-space probes, launched in March 1972 and December 1973 respectively, were designed to measure small forces within the solar system, e.g. solar wind, radiation, and gravitational effects. In 1980, about two billion miles from Earth, analysts found that both were experiencing an unpredicted acceleration towards the sun by a small but apparently fixed rate of ~8x10^-8 cms^-2. Observations over 20 years since have refined this value to 8.74+1.33x10^-8 cms^-2 [1]. Engineers at JPL and Los Alamos National Laboratory analyzed all potential sources external and internal to the spacecraft, software errors, tracking station effects, gravitational, solar wind and radiation models, spacecraft dynamics, out-gassing, etc., etc. without locating its origin. This mystery, unexplained to this day, is exacerbated by its independence of distance—and thus could not be gravitational—and includes small unexplainable annual and diurnal components. Program analysts concluded: "Currently we find no mechanism or theory that explains this anomalous acceleration, the most likely cause of the effect being an unknown systematic, likely a gas leak or heat radiation" [2].

DSN (Deep Space Network) tracking stations derive Pioneer spacecraft velocities from Doppler shifts of their coherent two-way S-band signals. As shown in Fig. 1, ST Doppler transforms derive slightly lower receding and slightly higher approaching velocities than SW transforms. Thus, if SW transforms do in fact give true spacecraft velocities, this asymmetry would mimic an acceleration of the Pioneer spacecraft towards DSN stations. A first-order model for this effect is given below.

Table 2. SW Model for the Pioneer Anomaly

Pioneer 10 speed re barycenter (v_sc): 12.5 kms^-1

Pioneer 10 celestial latitude (Θ_cl): 4^o

Pioneer 11 speed re barycenter (v_sc): 11.4 kms^-1

Pioneer 11 celestial latitude (Θ_cl): 18^o

Earth orbital rate (v_e): 29.7 kms^-1

Conjunction angle (Θ) 0 to 360^o

Annual velocity profile (v_a): v_ecos(Θ_cl)sin(Θ) + v_sc

Pioneer RF wavelength (λ₀): 13.6 cm

Annual acceleration profile: λ₀(v_a/c)² cms^-2

Figure 2. Spacecraft-to-Earth velocity profiles (a) Acceleration mimicked by ST Doppler-to-velocity transforms in this velocity regime (b)

Velocity profiles for Pioneer 10 and 11 spacecraft relative to Earth are shown in Fig. 2(a), and the acceleration mimicked by the difference between SW and ST Doppler-to-velocity transforms in this velocity regime, based on Table-2 assumptions, is given in Fig. 2(b). These two functions lead to the annual SW "acceleration" profiles for the Pioneer spacecraft in Fig. 3(a), integration of which gives SW predictions for Pioneer 10 and 11 long-term acceleration anomalies. (Note, acceleration here is in quotes because it comes solely from differences in vehicle velocities given by SW and ST Doppler transforms.) These values, 8.98x10^-8 and 8.01x10^-8 cms^-2 respectively, correspond to measured values of 7.84x10^-8 and 8.55x10^-8 cms^-2 (the lower value predicted for Pioneer 11 coming from its slightly lower velocity and higher celestial latitude). As shown in Fig. 3(a), this SW model predicts a long-term acceleration anomaly well within the estimated error of +1.33x10^-8 cms^-2 for the observed anomaly 8.74 cms^-2 [1].

Figure 3. Pioneer annual acceleration profile predicted by SW physics plus long-term values measured values, (a). Annual and semi-annual components and their mean contributions predicted by the SW model, (b).

This simple model explains other puzzling aspects of the Pioneer data as well. Program analysts concluded, after examining a variety of potential sources, that annual and diurnal components in the Pioneer data "…are very likely different manifestations of the same modeling problem", and "…that the source of the annual and diurnal terms are (sic) both Earth related." As shown in Fig. 3, these terms are not only intrinsic to the SW model but are very close to observed values. For example, annual acceleration profiles predicted by this model, Fig. 3(a), consist of in-phase semi-annual and annual components, which as shown in Fig. 3(b) for Pioneer 10 produce peak values of 11.193 x10^-8 cms^-2 and 6.6325x10^-8 cms^-2 and means of 6.614x10^-8 and 2.361x10^-8 cms^-2 (their sum equaling the long-term anomaly). The annual component in the measured data [1] is very similar to that in Fig. 3(a). While analysts did not mention a semi-annual component, measurement noise and the larger annual component would have likely masked its presence.

The effect of Earth's rotation was not included in the SW model because its contribution to the long-term anomaly is small (~0.03x10^-8 cms^-2) and depends largely on unavailable tracking protocols and records. However, given that it exists only in the east-west direction at low elevations to DSN stations it should be in the range of ~1% and 10% of Earth's equatorial rotation rate (~0.5 kms^-1). For a spacecraft-to-Earth velocity of 20 kms^-1, Fig. 3(a), Earth's rotation generates peak-to-peak diurnal accelerations between ~0.013 and 0.06x10^-8 cms^-2, versus the observed value of ~0.03x10^-8 cms^-2. This SW model is also consistent with two other unexplained features of the Pioneer anomaly: its independence of distance and its absence in planetary orbits. The first is because the SW model depends solely on spacecraft motion relative to DSN ground stations; the second, because planetary orbits are based on directional measurements, not Doppler-derived velocities.

The Universe's Anomalous Comic "Jerk" Hubble discovered the universe's expansion by observing cosmic sources at speeds less than ~300 kms^-1, an effect now confirmed up to ~300,000 kms^-1. However, over the past ten years, observations at higher speeds appear to question not only Hubble's discovery but also the standard Einstein-de Sitter "big-bang" model of the universe, a model that predicts this expansion will slow and the universe will eventually collapse in a "big crunch". In 1999, Filippenko and Riess [2] found that a new class of distant supernovae—SNe Ia—were receding at ~10% to 15% higher than Hubble's rate. They reported that "---the light curves of high redshift (z = 0.3-1) SNe Ia are stretched in a manner consistent with the expansion of space; similarly, their spectra exhibit slower temporal evolution (by a factor 1+z) than those of nearby SNe Ia." [3]. This "accelerating acceleration" or "cosmic jerk" became more puzzling when subsequent observations showed this expansion to be temporary. Shapiro et al [5] concluded in 2005 that "A fair summary of the present state of affairs is that there is little understanding of why the Universe is accelerating."

While, like the Pioneer anomaly, this anomaly involves acceleration derived from EM signals, unlike the former, which involves man-made objects moving at ~12 kms^-1 relative to our sun, this cosmic anomaly involves objects receding at >30,000 kms^-1. Moreover, while the former appears as an acceleration towards the sun, cosmic acceleration is away from the sun.

Figure 4. Redshift Transforms (a) Differences between transforms (b)

Still, source speeds in both cases come from ST relativistic formulas. The redshift (z) of a signal from a receding source is λ_R/λ₀, or, f₀/f_R -1. From Table 1, source velocity in classical, ST, and SW physics for a given z are, respectively, v/c = z; v/c = [(z+1)² -1]/[(z+1)² +1]; and V/c = z/(z+1), Fig. 4(a). These functions diverge above ~0.1c, although both return to "1" at v = c. While source velocities derived by ST transforms exceed SW values only slightly at low velocities (i.e., where the Pioneer anomaly is observed), this difference becomes significant at z >~ 0.1 where the "cosmic jerk" is observed.

Cosmologists have extracted an amazingly detailed permanent record of the first few minutes of "big bang" from the cosmic microwave background (CMB) at z of ~1090 (v= ~0.9991c). Although an observation gap exists between redshifts ~10, and that of the CMB, the cosmic "jerk" occurs in the range ~0.1<z<~1. As shown in Fig. 4, while SW and ST Doppler transforms above the CMB redshift differ by less than ~0.1%, for 0.2 <z<100 they differ by up to13.49% at z = 2.4.

Figure 5. A comparison of the cosmic "jerk" predicted by SW physics (blue) with the observer "jerk" (red)

The derivative of the difference between ST and SW Doppler-to-velocity transforms for receding sources defines a change in acceleration (i.e., "jerk") which, as shown in Fig. 5, falls in the regime ~0.01<z<2.0 (solid blue). During the past two years the shape of the anomalous acceleration of SNe Ia supernovae has, as described above, become clearer, the key features of which, shown in Fig. 8 in red, are consistent with that predicted by SW physics. Specifically, as described by Riess [4] and Shapiro [5], the observed jerk peaks between 10 to 15% above the expected value at a z of 0.46+1.3, whereas the SW predicted peak occurs at a z of 0.37 at 12.93% above the expected value, both clearly within error estimates for the observed values. This predicted bubble is also consistent with observations suggesting this acceleration occurred above z = 1.25 and that the universe has been decelerating below z ~0.3. Recent analysis by Ghirlanda et al [6] suggest that gamma ray bursts (GRB) (used as standard candles to extend observations to z >6) confirm the temporary nature of this cosmic anomaly, an observation consistent with both the cosmic expansion observed for SNe Ia supernovae and that predicted by SW physics.

Relationships between the Pioneer and Supernova Anomalies. The Pioneer and SNe-Ia anomalies were both exposed at Doppler and velocity measurement accuracies considerably higher than in the past. SWP offers explanations for both anomalies based solely on the difference in source velocity derived by SW and ST Doppler-to-velocity transforms (Fig. 2), even though the Pioneer anomaly appears as acceleration towards the sun, while the SNe Ia acceleration is away from the sun. This seemingly contradictory situation is explained as follows.

In the Pioneer program, spacecraft trajectories are predicted using astrophysical models of gravitational and other forces, plus spacecraft distance and velocity measurements derived from two-way coherent S-band links. While vehicle distances obtained by radar ranging are the same in both ST and SW, vehicle velocities, derived from S-band Doppler shifts, differ. Thus, if the SW version is valid, spacecraft positions predicted by the ST transform will exceed their observed positions, a result that mimics acceleration towards the sun. (Pioneer analysts did recognize, however, that this anomaly might not represent acceleration, stating: "In actual fact it (the Doppler shift) is a cycle count. We interpret this as an apparent acceleration experienced by the spacecraft. However, it is possible that the Pioneer effect is not due to a real acceleration." [1]. This is consistent with the SW prediction that this anomaly comes from the Doppler-velocity transforms.

Different conditions lead to the conclusion that SNe Ia are accelerating away from the sun. While the Pioneer anomaly occurs between zero and 40 kms^-1 (where ST and SW Doppler-velocity transforms differ by an average of ~3x10^-4 cms^-1) the SNe Ia anomaly occurs for z >~ 0.01 (v/c ~3000 kms^-1), peaking at a z ~0.37 (Fig. 5) at a velocity difference of ~10,420 kms^-1. SW physics suggests the observed Pioneer anomaly comes from higher than actual spacecraft speeds introduced by a flawed ST algorithm, which, if true, would mimic acceleration towards the sun as described. In contrast, receding velocities for SNe Ia supernovae derived from this same ST Doppler algorithm exceed values given by the SW algorithm mimicking acceleration away from the sun. If by some remote possibility the SW transform rather that the ST version gives the "true" velocity of these receding sources then this acceleration anomaly would disappear and cosmic acceleration would again fit the "standard" cosmological model

Blueshift transforms: From Table 1, blueshifts of approaching EM sources in classical, ST, and SW physics are v/c = z/(z+1); v/c = [(1+v/c)²-1]/[(1+v/c)²+1]; and V_sw/c = z, respectively. While classical and ST transforms predict infinite Doppler shifts for sources approaching at c, SWP limits this shift to 2f₀ (Fig. 2). Thus, any evidence that this blueshift limit can or has been exceeded would invalidate this physics. Conversely, evidence that source velocities greater than 0.6c generate Doppler shifts less than 2f₀ would disprove ST physics. While I have thus far found no hard evidence for either case, some limited evidence does support the existence of this limit. In particular, Galimberti et al [7] measured spectra of ultra-intense femtosecond laser-plasma interactions at f₀ and 2f₀ (f₀ being the laser frequency). They found, that while there was a broadening of the blue side of the spectrum at f₀, the spectra at 2f₀ "…show a blueshift limit very close to λ₀/2, while they extend towards the red for many tens of nanoseconds." This unexpected result is of course consistent with the SW predicted limit at 2f₀. (I would appreciate any evidence showing that this predicted limit can or cannot be violated, since such would, respectively, either disprove or strongly support the validity of this SW physics)

Transverse Doppler Shift: Both classical and ST physics predict infinite Doppler shifts—and thus in the limit, infinite energies—for EM sources approaching at c (Table 1 and Fig. 2). In contrast, the SW transform predicts the integrated energy of a uniformly radiating EM source in its inertial frame is fixed for all observers, though its distribution depends on motion between observer and source. As this motion approaches c, approaching and receding signal frequencies approach 2f₀ and "0" respectively; a redistribution of radiated energy with no change in total energy.

In 1938, Ives and Stillwell at Bell Labs demonstrated that Doppler shifts of signals from material sources are in fact closer to values predicted by ST physics than classical physics. They showed that the mean of approaching and receding wavelengths of EM signals from ionized hydrogen atoms at a velocity of ~0.01c [8] was close to the difference between values predicted by ST and classical Doppler transforms of ~0.5f₀(v/c)², or ~0.00005f₀. It is generally accepted that this and subsequent tests (e.g., Saathoff et al [9] who measured this effect to an accuracy of ~8x10^-7 at 0.064c) validate the LT.

However: since V_sw/c = 1-[(1-v/c)/(1+v/c)]^1/2, for v/c= 0.01 in the Ives-Stillwell tests, V_sw/c = 0.009950496. Then from Table 1, mean approaching and receding wavelengths and frequencies in classical, ST, and SW physics, given a rest value of "1", are as follows:

Mean Wavelength:

Classical physics: 1.000000000

ST physics: 1.000050004

SW physics: 1.000099022

Mean Frequency:

Classical physics: 1.000100010

ST physics: 1.000050004

SW physics: 1.000000000

Ives-Stillwell showed that the mean of approaching and receding wavelengths of an EM source moving at ~0.01c was ~1.00005, a difference consistent with that predicted by ST physics of 1.000050004, but inconsistent with the classical value of 1.000000000. While this test shows that real-world processes do violate classical physics, it is generally presumed that it also validates ST physics.

However, consider the following. While wavelength is inversely proportional to frequency, inverting the mean of two wavelengths does not define the mean frequency of those two signals (as is shown by the values above.) Moreover, the observable of primary interest here is signal energy, a value proportional to frequency but inversely proportional to wavelength.

Recognizing this suggests a quite different interpretation for this class of tests. SW physics predicts a transverse Doppler shift equal to the rest frequency (f₀), i.e. "1" (Table 1). If this physics accurately reflects real-world effects, then the result expected in the Ives-Stillwell test, i.e., the difference between mean frequencies predicted by classical and SW physics, would be 0.000050006, a difference of 2x10^-9 relative to the 0.000050004 predicted for ST physics (Fig. 6); a difference well within the measurement accuracies of such tests.

Figure 6. Differences between means of approaching and receding frequencies of EM sources

This suggests that the Ives-Stillwell tests would validate both SW and ST physics, even though at a source speed of c the latter predicts a zero transverse Doppler shift, while the former predicts an infinite shift. While direct measurement of transverse Doppler shift of moving sources is difficult, some tests suggest the lack of such a shift, e.g., "Absence of the relativistic transverse Doppler shift at microwave frequencies" [10]. I am unaware of any tests to the contrary, and as indicated above, evidence for existence of finite transverse Doppler shifts is questionable.

References:

[1] Anderson J D, Laing P A, Lau E L, Liu A S, Neito M M and Turyshev S G 2002 Study of the anomalous acceleration of Pioneer 10 and 11 Phys. Rev. D 65, 082004/1-50 (Preprint gr-qc/0104064)

[2] Nieto M M, Turyshev S G and Anderson J D 2004 The Pioneer anomaly: the data, its meaning, and a future test (Preprint gr-qc/0411077 v2)

[3] Filippenko A V, and Riess A G May 1999 Type Ia supernovae and their cosmological implications arXiv.astro-ph/9905049 v1

[4] Riess A G et al Feb. 2004 Type Ia supernovae discoveries at z>1 from the Hubble space telescope: evidence for past deceleration and constraints on dark energy evolution arXiv.org.astro-phy/0402512

[5] Shapiro C A, and Turner M S 2005 What do we really know about cosmic acceleration arXiv:astro-ph/0512586 v1

[6] Ghirlanda G, Ghisellini G, and Firmani C 2006 Gamma ray bursts as standard candles to constrain the cosmological parameters New J. Phys. 08 12

[7] Galimberti M, Giulietti A, Giulietti D, Gizzi L A, Balcou PH, Rousse A, and J PH Rousseau 2001 Laser and Particle Beams 19 47-53

[8] Ives N E and Stillwell G R 1938 An experimental study of the rate of a moving atomic clock J. Opt. Soc. Am. 28 215

[9] Saathoff G et al 2003 Improved test of time dilation in special relativity Phys. Rev. Let. 91 19

[10] Thim H W 2003 Absence of the relativistic transverse Doppler shift at microwave frequencies IEEE Trans. on Inst. and Meas. 52 5

Hi Mac, I've been away from this thread for about a year. I haven't replied to your final post because it was a (good) summary of what you wrote before. Returning to it, there are a few things that I did write before that I have to repeat in order not to let things appear to hang in the air.

1. The problem with your "supernova anomaly" (the "jerk") discussion is that you treat the cosmological redshift as if it is a Doppler shift. You wrote: "Cosmologists have extracted an amazingly detailed permanent record of the first few minutes of "big bang" from the cosmic microwave background (CMB) at z of ~1090 (v= ~0.9991c)."

The cosmological recession speed when the light left the CMB region was ~66c and that region is now receding at ~3.3c. There is absolutely no correlation with Doppler shift, which gives the ~0.9991c that you mentioned. The cosmological redshift is not caused by objects moving through space, but by the expansion of space itself. The cosmological calculator encompasses the ΛCDM model, giving the above (correct) conversions.

2. You wrote: "While direct measurement of transverse Doppler shift of moving sources is difficult, some tests suggest the lack of such a shift, e.g., "Absence of the relativistic transverse Doppler shift at microwave frequencies" [10]. I am unaware of any tests to the contrary, and as indicated above, evidence for existence of finite transverse Doppler shifts is questionable."

The transverse Doppler shift has been well established experimentally (see e.g. http://mysite.du.edu/~jcalvert/phys/doppler.htm#Tran), while the Thim H W 2003 paper "Absence of the relativistic transverse Doppler shift at microwave frequencies" has been well refuted as not measuring transverse Doppler shift at all. The source and receiver were not in relative motion and SR predicts zero Doppler shift in such a case.

Finally, transverse Doppler shift is required (proven) every time you get an accurate fix of position with your GPS!

AFAIK, the jury is still out on the Pioneer anomaly - it is simply not known whether it is a systematic phenomenon or a gravitational one.

-J

http://www.geocities.com/sciliterature/RelativityDebates.htm