Explain an apparent violation of spatial isotropy by Lorentz' transform

Hi Mac,

"Spatial isotropy requires all such moving frames observe the same distance and time between these collocated events"

I believe this statement is incorrect. Check the definition in wikipedia. When something is approaching the speed of light, measurements change, but space is not altered. Electromagnetic waves move at the speed of light. You are talking about measuring one from the others position - an absurd idea, because time does not exist for light.

If you were to measure the distance from a 'fixed' object in space from 2 rockets moving away in opposite directions at the same speed, they would agree on the distance, which would support isotropy.

S

The topic is way beyond my expertise, however, concerning your statement: "an absurd idea, because time does not exist for light."

If this is true then how can we assign it a speed? velocity = distance * time, or v = dt. Time is definitely in the equation as far as I can see. If we eliminate time from it we have velocity = distance, which also is absurd.

-John

Hi S: Thanks for your input. It suggests, however, that my question was not sufficiently clear, so let me expand a little.

In my expressions for D' and T', I assume motion v is the same magnitude for observers moving in different directions relative to the frame with collocated events. (This "proper" frame is unique in that it is the one and only frame wherein two time-like events are collocated; their separation in time T is both Newtonian and relativistically correct; their separation equals the proper interval as defined by Minkowsk; and the distance and time between these events are minimized.) To satisfy spatial isotropy and the constant speed of light, measued values for D' and T' must be the same for all observers moving at the same velocity relative to the same collocated events. Meaning, I believe, either that Einstein's principles of SR are flawed or that the Lorentz transforms (LT) hold only in a limited subset of situations.

I vote for the latter. Based on additional considerations not addressed here, I believe it can be shown that the LT do hold only between observers and proper frames for those events (i.e., for collocated and simultaneous events).

Hi Mac, I've noticed that you actually answered my previous question here: "To satisfy spatial isotropy and the constant speed of light, measured values for D' and T' must be the same for all observers moving at the same velocity relative to the same collocated events."

So 'spatial isotropy' is not 'light isotropy' and hence I still do not know what its characteristics must be. Apart from that, the statement is correct and it is precisely in line with special relativity, so I do not see the problem, unless 'spatial isotropy' has some funny meaning!

I think you must refrain from saying "relative to the same collocated events" and rather use "relative to the frame in which the events are collocated", or, usable but less precise, "relative to the proper frame for the events". Nothing can move relative to an event, because the event "moves" with every frame you wish to choose. Before it happens, it does not exist and once it has happened, it has fixed spacetime coordinates in every inertial frame.

Jorrie

JohnJohn,

When I said that time does not exist for light, I was paraphrasing Paul Davies from one of his books. It means that when an object travels at the speed of light, then time does not pass (from it's own point of view). Time still exists for us as we observe it. There is much confusing about special relativity, and I don't consider myself an expert.

Mac,

Welcome to CR4! You picked a big subject for your first post. I think you're going above my head, but given the 2 choices you gave, I would choose as you did.

Jorrie,

Do you want to jump in here?

S

"It means that when an object travels at the speed of light, then time does not pass (from it's own point of view)."

If I understand you S, that means that the speed of light is a fundamental standard by which we establish all other speeds and velocities. In other words, without light as a speed constant, there could be no time (v = dt would have no meaning). This would seem to be somewhat of a circular logic situation though. Am I totally off base here?

-John

Hi JohnJohn,

Regarding the speed of light as a constant, it is or once was the basis of the length standard: The meter was once defined as 1,650,763.73 wavelengths in vacuum of the red light of the element krypton-86.

"without light as a speed constant, there could be no time (v = dt would have no meaning)."

I'm not sure where you came up with this conclusion, but it is an interesting speculation.

S

Hi S,

I thnk I got it from your post #1: "- an absurd idea, because time does not exist for light."

Lets suppose I'm Photon, a free-spirit photon, hurrying(?) along because I'm running late(?) for my 7:00 PM date with Photonette. But if time does not exist for me, how can I get there (she lives in Andromeda and I live in the Milky Way)? By v = dt, v = d0 hence v = 0! No, that's not right. t ≠ 0, t just simply does not exist. Then does v = d? That can't be either. I (Photon) have no way to tell if I can make it by 7:00 PM. But then, OTOH, she won't know if I'm late or not either.

You said "The meter was once defined as 1,650,763.73 wavelengths in vacuum..."

"Wavelength λ is inversely proportional with the frequency ν (Greek "nu"), the number of wave periods per time unit passing a given point." (Wiki)

Okay, I get it (?), time just doesn't exist for me, the photon, and me only. For an outside observer time exists, right? How can time not exist for light? When discussing light, it seems a lot of arguments wind up being circular. Reminds me of another thread concerning the nature of time. It's almost(?) impossible to define time in terms of anything other than itself.

-John

red-faced erratum to post #9:

"By v = dt, v = d0 hence v = 0! No, that's not right. t ≠ 0, t just simply does not exist. Then does v = d?"

Again, as in my erratum to post #5, this should have read: By v = d/t, v = d/0, hence v is undefined! No, that's not right. t ≠ 0, t just simply does not exist. Then does v = d/null?

-John

erratum:

(v = dt would have no meaning).

Indeed it doesn't! That should have read (v = d/t would have no meaning).

Sorry,

-John

Thanks to you both for your comments--as an old radio engineer my experience re special relativity is based on real-world applications rather than theory, hence any help with the latter is appreciated.

Re your comments: Based on my work with radiolocation systems I view light speed as the distance from an EM event to an inertial body--e.g., a clock--divided by the time to travel that distance. However, this electrodynamic definition for c differs from the usual view. Einstein, for example, assumed that to ensure synchronized clocks do in fact measure time between any two EM events indpendent of their separation in distance, that the time for a light signal to travel between material clocks collocated with those events are the same in both directions. While it appears that this view remains accepted by physicists to this day, it seems to me that it violates Einstein's own SR that shows time and distance between electromagnetic events are dependent variables.

Re my other issue. It seems that observers moving at the same speed in different directions relative to two collocated events must, if space is in fact isotropic, measure the same time between those events and will do so only if their clock rates are idependent of their own relative motions. If true, this would question the validity of the Lorentz transform (LT). Hence the conundrum: Either there is a well hidden flaw in my simple argument, or a flaw in the LT has escaped scrutiny by armies of physicsts for over a century. Neither, it seems, being very likely!

However, my experience with systems such as the GPS and electronic reconnaissance "spy" satellites raises questions in my mind re Einstein's use of classical Newtonian concepts to explain his SR. Such tools, which derive locations and times of EM events from differences in the arrival times of signals from those events at separate receivers, depend on observer motion relative to observed events but not on either time-synchronized clocks or motion relative to other observers of the same events. Recent examination of this physics hints that the above conundrum might well come from the assumptions Einstein used to derive the LR.

Mac

Hi Mac,

If I understand your original post, this may be of help:

Originally Posted by yogi To get the temporal difference equation for Δt', one subtracts the event transforms for t1' and t2', i.e., so when this is done, the term (vΔx/c2) that appears in both t1' and t2' is eliminated. Once eliminated, it cannot be recovered from the time differentials:

Δt' = t2' - t1' = (t2 - t1)(1-B^2)^-1/2

"So? The fact remains that you can:

1. Start with the coordinate transformations for t' and x' for two different events.
2. Subtract them.
3. Conclude that the speed of light is the same in every frame.

This procedure accomplishes exactly what I said it does: Starting from the LT for individual events (which you said could be arrived at by not assuming a Lorentz-invariant speed of light), you can derive the constancy of the speed of light in one direction." Tom Mattson

Mac, the above post is one of many posts on the Physics Forums website concerning this topic.

Hope this helps,

-John

JJ: I agree that the speed of light is the same in all inertial frames. My point is simply that the distances light signals travel are from EM events to observers rather than between material objects collocated with those events as Einstein assumed in his 1905 paper with his statement: "We have not defined a common "time" for A and B, for the latter cannnot be defined al 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. We assume that this definition of synchronism is free from contradictions and possible for any number of points."

I believe that Einstein violated his own theory with this statement. That is, while spatial isotropy requires that this assumption holds for simultaneous events, it seems to me that in the general case it violates Einstein's other principle that the speed of light is a universal constant. This principle ensures that, except for simultaneous events, that distance and time are dependent not independent.

Hi again Mac, a last comment before X-Mas.

You wrote: "I believe that Einstein violated his own theory with this statement. That is, while spatial isotropy requires that this assumption holds for simultaneous events, it seems to me that in the general case it violates Einstein's other principle that the speed of light is a universal constant."

I think you are forgetting Einstein's method for the synchronization of clocks, which ensures that neither of Einstein's principles of relativity are violated. BTW, there are other ways of synchronizing clocks, but there is no other way that can give results consistent with all observations so far!

Jorrie

Hi Mac, sorry, I missed this one until I Googled "spatial isotropy"!

I'm not sure what you mean by "spatial isotropy". In cosmology, that is usually taken as large scale isotropy of matter/energy density, in line with the cosmological principle.

Other references I found on Google do not seem to be from accepted journals or books, so I still don't know what it means.

In special relativity, reference is often made to "isotropy of the speed of light" or sometimes just "light isotropy". Is this what you meant?

Jorrie

Hi Lorrie--Thanks for your input and Merry Christmas!

I assume the validity of Einstein's postulate in his 1905 paper that: ....the laws of electrodynamics and optics will be valid for all frames of reference for which the laws of mechanical hold good." I assume this means that relationships between material observers and electromagnetic events (i.e., electrodynamic processes) in free (empty)-space and symmetrical conditions are direction independent. Einstein postulated his other principle of SR separatly, i.e.: ... 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.

I believe this simple example exposes a fundamental disconnect between Einstein's two principles of SR and the Lorentz transform (LT) based thereon, despte the now universal assumption that SR and the LT are synomous and that any violation of the the latter would reflect a flaw in the former. Note, however, Einstein used Newtonian concepts to derive the LT. In particular, I believe the above example questions his assumption that differences between observers of the same EM events depend on thier own relative motion, an assumption that seems to contradict his own statement in the introduction to his 1905 paper, i.e., ...that the assersions of any such (electrodynamic) theory have to do with relationships between rigid bodies (clocks) and EM events". Moreover, my engineerin experience clearly shows measurements by radiolocation systems depend on motion relative to the observed EM events, not on motion relative to other observers of the same events. All of this suggests that the LT may, even likely, do not accurately reflect Einstein's own two principles of SR.

Hi Mac.

While waiting for a clearer 'thought experiment with sketch' from you, some (hopefully ) useful remarks on your last post regarding Einstein's two postulates.

"I assume this means that relationships between material observers and electromagnetic events (i.e., electrodynamic processes) in free (empty)-space and symmetrical conditions are direction independent."

Correct, although I do not think this is all that Einstein tried to say with his statement. It had to so with all the laws of physics. You must just remember that you cannot have a velocity relative to an event, as I tried to point out before. An event can merely have a set of spacetime coordinates in your own frame of reference and a different set of spacetime coordinates in another inertial frame. It does mean that the event can be located in any direction relative to you and that direction does not matter, but you cannot move relative to the event!

One common misconception that I've encountered is this: "One can measure the Doppler shift of an electromagnetic radiation event, hence you know your radial velocity relative to the event." Not true, since all you know is the your radial velocity relative to the inertial frame of the emitter of that event, not the event. That event forever has fixed spacetime coordinates in every inertial frame. To make this even clearer, I usually add: a differently moving emitter could have 'emitted the event' in the exact same spot in your inertial frame, giving you a different Doppler shift for the same event. So what's your speed relative to the event?

Your second quote is incomplete and hence dangerous if viewed out of context: "... 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."

Looking at it in isolation, it seems that Einstein said that there is an 'absolute space' in which light propagates at c, independent of the state of motion of the emitting body through that 'absolute space'. In context, Einstein said (paraphrased) that every inertial frame will measure the speed of light as c, independent of the relative movement between it and the source and not dependent upon any movement relative to 'absolute space'.

Your: "I believe this simple example exposes a fundamental disconnect between Einstein's two principles of SR and the Lorentz transform (LT) based thereon, despite the now universal assumption that SR and the LT are synonymous and that any violation of the the latter would reflect a flaw in the former."

hints at some misapplication of Einstein's postulates that I mentioned above. The two postulates are completely in alignment with each other and also with the Lorentz transformations. However, both require that the Einstein synchronization of clocks principle is followed for every inertial frame.

I'll be very interested to know what principle of clock synchronization your 'de Forest relativity' follows. I'm pretty sure it cannot be Einstein's.

Jorrie

Hi again Jorrie—You are just too speedy for me! I apologize for not getting back to you with a good description/picture of de Forest's stopwatch physics. I will do so in my next message.

However, I do believe your above comments identify core differences between de Forest's and spacetime physics. I agree that Einstein's two principles of SR require the laws of physics to be the same in all inertial frames, and that motion between individual EM events and inertial frames is indeterminate and unrelated to Doppler shift. (This, however, is not true for a single observer of two EM events, the basis of Einstein's derivation of the LT.) I also agree with you that c is independent of observer motion relative to the source of an EM event and is not relative to any "ether". We both agree, I believe, that any supposed relativistic physics must accurately reflect Einstein's two elegantly simple principles of SR.

Here, however, is where we part company a bit. In particular, it seems to me that De Forest's physics, proven by >50 years in real-world engineering applications, does raise questions re your last comment that Einstein's: "two postulates are completely in alignment with each other and also with the Lorentz transformations. However, both require the Einstein synchronization of clocks principle is followed for every inertial frame." However, de Forest's physics suggests to me that the Newtonian concepts Einstein used to derive the LT may be incompatible with his own SR. In which case, the LT and spacetime physics based thereon would not be synonymous with his own SR. For example, while SR shows that distance and time between EM events are dependent variables, Newtonian time-synchronized clocks by design measure time independent of distance. In fact, to ensure that such clocks do measure time between two separated EM events in every inertial frame independent of distance, he assumed that the speed of light is the same in both directions between those events and clocks. In contrast, distances and times between EM events in de Forest's physics are dependent functions of SW values (no time-synchronization required!), and measurements by different inertial observers of the same events reflect the SR only if their clock rates are synchronous (which, to satisfy SR, must be the same for similar clocks!).

De Forest's physics suggests that the Newtonian concepts Einstein used to derive the LT may be inconsistent with his own two principles of SR, i.e., that the LT and SR may not be in total alignment. Hope this helps define the specific differences between these two physics.

Hi again Mac, no rush this time of the year!

You keep on referring to Einstein's derivation of the Lorentz transformations using Newtonian concepts, or something like that. I'm not quite in agreement with this view.

Firstly, Einstein did not derive the Lorentz transformations, Joseph Larmor discovered them in 1897 and they were later named after Hendrik Lorentz because he published them in their final form in 1904. Einstein actually just found that they agree fully with his special theory of relativity and used them. In some of his writings, he did show how they could be derived from his two postulates: Lorentz covariance and the constancy of the speed of light in any inertial reference frame.

Secondly, I do not understand where he used Newton's concepts in such a way that it may violate any of the two postulates! Are you perhaps referring to Einstein's "photon clock" by which demonstrated time dilation, or more generally, that either time or space or both must be relative?

You wrote: "In fact, to ensure that such clocks do measure time between two separated EM events in every inertial frame independent of distance, he assumed that the speed of light is the same in both directions between those events and clocks. In contrast, distances and times between EM events in de Forest's physics are dependent functions of SW values (no time-synchronization required!), ..."

Ah, I see. Not very clearly stated, but I presume that de Forest physics will not maintain the spatial isotropy of the speed of light then, right? If this is so, it may be just an aether theory in disguise! I still would like to know how spatially separated clocks are synchronized (by which I mean set to the same time reading at some instant) in de Forest physics. Perhaps clocks are all set to "absolute de Forest time".

Jorrie

Hi Again Jorrie:

First, some short answers to your questions, and then a more thorough treatment. By Newtonian concepts I mean Einstein's use of synchronized clocks and rigid rod to define time and distance between EM events as observed by material observers. These definitions are fine for material objects and events, but as described below, from the perspective of de Forest's physics, may not be applicable to distances and times between electromagnetic events. Basically, Newton defined distance and time as independent variables while Einstein's two principle of SR show these variables to be dependent. The same is true for Newton's definition for motion as that between material frames, a definition also used by Einstein, whereas his theory addresses electrodynamic relationships between material frames and EM events. I believe de Forest's physics, as described below, answers you questions re spatial isotropy and the universal fixed speed of light sans an ether--which I believe are firm requirements for any viable explanation of Einstein's principles of SR.

In de Forest's physics, features of individual EM events, e.g. relative directions, locations, and times, are derived from sets of time-difference (stopwatch) measurements. For example, the time difference of a pulse from a remote EM event at two separate receivers defines a hyperbolic surface in 3-space (de Forest's 1904 direction-finding patent), a third antenna gives a second such surface, a fourth antenna, a third. These surfaces intersect at the event, defining its location relative to those receivers. This, plus a fourth time-difference re a local clock defines its original transmission time. This technique has been used for decades in a variety of forms from "spy" satellites to, in inverse form, the GPS. While clocks in such systems must be synchronized in rate, raw SW values depend on neither time-synchronization nor motion relative to other observers that may or may not be observing the same events.

While quite familiar with this physics—I pioneered development of several "spy" satellite systems during the Cold War—only recently did I realize that it may be used to derive relativistic definitions for distance, time, and motion lead to relationships different from the LT. My analysis suggests that puzzling aspects of spacetime physics come from Einstein's use of Newtonian concepts and tools to derive the LT. (You might ask: "O.K., smarty pants, so what are these so-called non-Newtonian relativistic de Forest concepts for distance, time and motion??' You might also be thinking: "Sounds to me like crackpot physics.")

Glad you asked. This is where some fun new physics comes in!: Let collocated time-like events separated by time T in one frame be observed by a second frame moving at velocity v relative to the first. To satisfy his two principles of SR, Einstein showed (as you know!) that time T' and distance D' in the second frame are T'= T/ [1-(v/c) ²]^1/2 and D'/c = T (v/c)/[1-(v/c)²]^1/2. However, he based these results on two key assumptions: T' is measured by time-synchronized clocks, D' by rigid rods; and v is between observers of the same events. In the above example, it is clear that values in the first frame, D and T, are Newtonian, while D' and T' are relativistic and non-Newtonian. Also, to ensure separated clocks do measure T', Einstein assumed in his 1905 paper that: "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." A and B being clock locations.

Now consider this case using a version de Forest's physics wherein these two synchronized clocks are replaced by stopwatches (SW) triggered "on" and "off" by signals from the two events. Also, let resulting SW values, C₀ and C₁, be positive if turned "on" by the event assigned to that clock and "off" by the signal from the other, otherwise negative in sign. In the first frame, clocks and events are collocated, both signal propagation times are zero, and, with the above "sign" convention, C₀ = -C₁ = T. As a result, T = (C₀-C₁)/2 and D/c = (C₀+C₁)/2 = 0. While these values are clearly Newtonian and equal values in the spacetime example, relativistic values based on de Forest's physics in the second frame do not equal spacetime values in the second frame.

Unlike in the first frame, C₀' and C₁' in the second frame depend on propagation times of signals from EM events to clocks. While Einstein simply assumed they are equal, from the first frame they do not appear so: i.e., after the first clock in the second frame is turned "on" by the first event, this signal propagates towards the approaching clock to turn that clock "on". And, when this clock is turned "off" by the second event, the signal from this event must then "catch" the receding clock to turn it "off". Since values in the first frame are known, this frame serves as a natural reference for deriving signal propagation distances, and thus times, in the second frame. This gives P₀ = T/(1-V_sw/c)–T and P₁ = T/(1+V_sw/c)+T, where P₀ and P₁ are signal propagation times from the second and first events to clocks C₀' and C₁' respectively. Since C₀'= P₀+T and C₁'= P₁-T, and assuming relationships for distance and time in SW values in the first frame also hold in the second, then: T_sw' = (C₀'-C₁')/2 = T/[1-(V_sw/c)²] and D_sw'/c = (C₀'-C₁')/2 = T(V_sw/c)/[1- (V_sw/c)²]. These functions clearly parallel relationships between Newtonian values as defined by the LT. They lead, as well, to relationships between the proper separation between time-like events, T in this case, that parallels Minkowski's spacetime interval. I.e.: T_sw'- (V_sw'/c)(D_sw'/c) = [(T_sw')² - (D_sw'/c)²]/(T_sw') = -2C₀'C₁'/(C₀'-C₁') = T. (Though these relationships are "real" not "imaginary".)

Note that the three terms, T_sw', D_sw', and V_sw', are non-Newtonian relativistic values derived, as shown above, using the proper frame for time-like events as a natural reference, i.e. that inertial frame where distance and time are both Newtonian and satisfy SR; distance and time are minimum relative to all other inertial observers; signal propagation times from events to clocks are zero, as is V_sw; and their separation in time equals Minkowski's spacetime interval. Only one inertial frame out of the infinity of such frames exists for every pair of time-like events. As in spacetime physics, both T_sw' and D_sw'/c approach infinity as V_sw'/c approaches "1", not because of changing clock rates or rod lengths, but rather because of increasing propagation times of signals from the two events to the rapidly moving clocks. Thus, in this physics relativistic effects are assigned solely to electrodynamic processes, i.e., relationships between material frames and electromagnetic events (or what is the same, the proper frame for those events). For example, in the above case clock rates remain the same in both frames (to satisfy spatial isotropy) and the two clocks in the second frame are separated by the Newtonian vT (giving a maximum separation of cT) while both T_sw' and D_sw' are infinite at V_sw'/c = 1.

Note that this SW physics differs from that Einstein used to derive the LT, leading to a quite different explanation relativistic effects (e.g. no time-synchronized clocks). However, my objective was to explore how de Forest's measurement physics, which derives kinematic features of EM events using a non-Newtonian physics, would explain relativistic processes within the constraints of Einstein's two principles of SR. In fact, differences between this and the corresponding spacetime physics from a theoretical perspective are significant. And, while differences in their predicted physical effects are small, they are potentially testable. Of course, if both are logically sound, ultimate validity can be determined only by which best predicts/fits real-world effects.

I much appreciate you constructive critiques of my sometimes confusing words and thoughts, and hope this provides at least partial answers to your questions/concerns.

Thanks, Mac

Hi Mac, still no sketch and still some confusion on my part! I'll try and clear it up with two sketches of my own: first, the standard relativistic view.

You wrote: "Let collocated time-like events separated by time T in one frame be observed by a second frame moving at velocity v relative to the first. To satisfy his two principles of SR, Einstein showed (as you know!) that time T' and distance D' in the second frame are T'= T/ [1-(v/c) ²]^1/2 and D'/c = T (v/c)/[1-(v/c)²]^1/2. However, he based these results on two key assumptions: T' is measured by time-synchronized clocks, D' by rigid rods; and v is between observers of the same events."

In the sketch, the two black bullets are the clock (Ca) at the co-located events, separated by time T. The red bullets are two different clocks (C'a and C'b), synchronized in the red frame, which moves relative to the black frame. At the origin, Ca and C'a pass and can read each other's clocks directly. After T seconds in the black frame, Ca and C'b pass and can read each other's clocks directly. The read clock will read T' (> T) seconds, as you calculated above because of Einstein synchronization. So far, so good.

Now let me try and picture your "stopwatch" scenario from your (in my view, slightly confusing description).

C₀ and C₁ are now the black stopwatch start and stop times at the two events. C'₀ and C'₁ are the start and stop times of the first red stopwatch. C'₂ and C'₃ are the start and stop times of the second red stopwatch. The magenta dotted lines are EM signals sent from the events towards the respective red stopwatches, where they were not co-located with the events.

Have I got it right so far? I would like to know before I spend more time on your theory. There is one piece that I do not understand the significance of, where you wrote: " ... C₀ = -C₁ = T. As a result, T = (C₀-C₁)/2 ". It's like saying x = (x+x)/2.

Jorrie

PS: I must say that the whole idea still seams absolute time, absolute space to me, but let me not jump to conclusions!

Happy New Year to you, Jorrie:

You wrote: "Have I got it right so far? I would like to know before I spend more time on your theory. There is one piece that I do not understand the significance of, where you wrote: " ... C₀ = -C₁ = T. As a result, T = (C₀-C₁)/2 ". It's like saying x = (x+x)/2."

Thanks for the picture (better than what I would have done!), it seems to me to be correct. Your statement "It's like saying x = (x+x)/2." is also correct; a tautology only for collocated time-like events (and for simultaneous space-like events). Those frames wherein two time-like events are collocated (signal propagation times are zero, T is Newtonian and measured by a single clock) serve as reference frames for deriving signal propagation times, and thus SW values, in all other moving frames. In these frames, corresponding values for C₀' and C₁' are, as in the reference frame, but opposite in sign and finite and unequal. However, the same orthoghonal functions that define T and D=0 in the reference frame also define derive relativistic values for distance and time in these latter moving frames.

I understand why you find my description confusing. I took me several years, after realizing that radiolocation tools required neither synchronized clocks nor rigid rods to make their measurements, to discover how Einstein's two principles of SR might be appliec to this physics. Confusing the issue was that while SW measurements depend on motion relative to observed events, Einstein assigned motion to that between observers rather than between observers and events. It was also clear, as you are aware, that such motion is undefined for individual EM events (though given the finite speed of light, such a dependency it seems to me, must exist). Like I say, all very confusing. Also, Einstein relied on Newton's independent definitions for distance and time between material objects and events, even though his own and Maxwell's theories showed distance and time between EM events are dependent not independent variables. Of couse, it seemed clear to me that values for distance and time derived from common sets of SW values measured by radiolocation tools are intrinsically dependent variables.

As far as I can determine, the SW physics I describe is logically consistent, violates no known physics, and avoids the puzzling paradoxes, imaginary time, etc. implicit in the LT and spacetime physics based thereon. However, which best predicts real-world effects can only be established by direct test.

Thanks again Jorrie for "keeping me honest". Mac

Hi Mac, and Happy New Year to you too!

I'm afraid the mental exercise to understand your "de Forest Relativity" is a bit much for the last day of the old year!

Trying to go further, it looked to me as if my second diagram above does not reflect your nomenclature, because you do not have a c'₂ and c'₃, yet you do refer to the 'left-hand' clock in your text.

Another issue: since you talk "stopwatch" physics, there is only one reading per stopwatch, right? If so, my diagram' labels are wrong for your scenario.

Please tell me what I must change in the diagram to be according to your text.

Jorrie

Hi Mac,

I had another look and the frustration is growing, without a correct diagram at least (I'm missing that 1000 words!)

Here is another attempted diagram that are perhaps a bit closer, bit still there are confusing aspects in your text. I took C'₀ to be the time reading of the right-hand stopwatch being turned off as the second event's signal arrived there. Likewise, C'₁ as the reading of the left-hand stopwatch, which was turned on as the first event's signal reached it and turned of as it passed the second event.

Then I calculated the signal delay times (not total times) to the two stopwatches as follows: to the left-hand sw, P₁ = vT/(c+v). The signal delay to the right-hand sw, P₀= vT/(c-v). Neither of these two quite agree with your P₀ and P₁ of reply #19, most likely because I still do not understand what you are computing! Also, check your units in the calcs!

Jorrie

PS: I'm going through the pain because I'm always interested in a more engineering-like presentation of relativity! Besides that, I've also worked on passive radio-location techniques in the past...

Hi again Mac.

Before you answer my previous one, read this. I discovered that your equations for P₀ and P₁ have the right units and are just different stages of calculation than mine. When I worked through to the end, I got the same answers than you got.

What you have is effectively the algebraic mean of two stopwatch readings, which includes signal propagation times in opposite directions, for two co-located events in your "proper frame". I do however think it is all Newtonian and not 'relativistic', as you claim. I will look at it further, but it reminds about the fact that the full Newtonian two-way Doppler shift equation is the same as the relativistic equation, where one takes the geometric mean of two relativistic one-way Doppler shifts.

However, there may be more to it than what meets the eye. I'm still very interested...

Jorrie

Hi Jorrie--I really do appreciate your assessment of these ideas--I've convinced myself that they may have some value to theoretical physics and could provide simple solutions to other puzzling issues such as the Pioneer and cosmic acceleration anomalies. I had finished a response to some of your previous concerns (showing that you diagram accuratly reflected my ideas) then noticed you two later inputs--so need to review the former to address the latter. Will respond later today (while watching a little football!)

Mac

Hi Mac, when you reply, pse also consider the following. You wrote (reply #20):

"They lead, as well, to relationships between the proper separation between time-like events, T in this case, that parallels Minkowski's spacetime interval. I.e.: T_sw'- (V_sw'/c)(D_sw'/c) = [(T_sw')² - (D_sw'/c)²]/(T_sw') = -2C₀'C₁'/(C₀'-C₁') = T."

I do not follow where you get these relationships from. There also seems to be an error in the first of the three manipulations (T_sw'- (V_sw'/c)(D_sw'/c)), since it does not yield T if I put values in.

I'm still puzzling on what it all means and will have to work a few examples to look at the differences in results.

Jorrie

Hi Jorrie—I apologize, your frustration is likely all my fault! I dropped a minus sign my expressions in #19 in my sentence: "Since values in the first frame are known, this frame serves as a natural reference for deriving signal propagation distances, and thus times, in the second frame. This gives P₀ = T/(1-V_sw/c)–T and P₁ = T/(1+V_sw/c)+T, where P₀ and P₁ are signal propagation times from the second and first events to clocks C₀' and C₁' respectively.", P₁ = T/(1+V_sw/c)+T should have been: P₁ = -T/(1+V_sw/c)+T! Your expressions for these two propagation times are correct, or, at least, they are identical to functions for distance, time, and motion that I derive.

In your missive # xxx, you questioned whether values for distance, time, and motion are not Newtonian in this physics. It is clear that in fact they are Newtonian in those perfectly symmetrical cases when events are simultaneous or collocated and where V_sw is zero. Otherwise I believe I can show that in the general case that these values not only differ slightly from Newton's, differences that, in turn, lead to slightly different but testable relativistic effects for time-dilation, transverse Doppler shift, and Doppler-to-velocity transforms. I found the latter, in turn, to be surprisingly consistent with the anomalous accelerations associated with the Pioneer spacecraft below 40 km/s and the cosmic "jerk" at much higher velocities.

I wanted to let you know about my error right away, but have some more ideas I will get back to shortly. But hope this reduces at least some of your frustrations.

Mac

Hi Mac. How did the football go?

I think I understand your scheme well enough now. I've corrected the 'offending' piece of derivation that I mentioned before: "I do not follow where you get these relationships from. There also seems to be an error in the first of the three manipulations (T_sw'- (V_sw'/c)(D_sw'/c)), since it does not yield T if I put values in."

Should be: Tsw'- (Vsw'/c)² Tsw' = Tsw' (1-(Vsw'/c)²)

If I'm right, it exposed a weakness in the whole scheme. Dsw' is simply defined as the distance that the clock frame travels in Tsw' seconds relative to the proper frame, or:
Dsw' = Vsw'Tsw' = Vsw'T/(1-Vsw²/c²). It is then not surprising to find that Tsw'(1-Vsw²/c²) = T. I do not think this justifies the assertion that the Minkowskian ST interval is invariant under the change of coordinates.

A second issue that I spotted is that the speed of light is not invariant under coordinate transformations. I do not see any way how the primed (moving) observers can observe the speed of light as isotropic in your scheme. It will be c-v in one direction and c+v in the opposite direction, violating the most important relativistic principle.

Jorrie

Hi Jorrie and Mac.

You guys are way beyond me, but I just wanted to let you both know that I'm following along to the best of my ability.

-John

John: It will all eventually become clear--one way or another.

Mac

Hi Jorrie: The football did not go well! But this is a new year and I am still here—that's more important when you get to my age!!

I agree with all of your expressions, but also stand by mine: T_sw'- (V_sw'/c)(D_sw'/c) = T. Since we agree that D_sw' = V_sw'T_sw', (V_sw'/c)² in your expression = (V_sw'/c)(D_sw'/c)/T_sw', which, I believe (???), changes your's to mine.

Your statement: "Dsw' is simply defined as the distance that the clock frame travels in Tsw' seconds relative to the proper frame, or: Dsw' = Vsw'Tsw' = Vsw'T/(1-Vsw²/c²). It is then not surprising to find that Tsw'(1-Vsw²/c²) = T." exposes a fundamental difference between de Forest's and spacetime physics, i.e., that the distance (and time) between EM events does not always equal that between clocks collocated with those events. I.e., Maxwell and Einstein showed that relationships between material frames differ from those between material frames and electromagnetic processes. After Einstein derived the LT using Newtonian concepts he assumed they also held for material events. SW physics suggests, however, that while the latter is true in some cases, e.g., collocated and simultaneous EM events, it is a stretch to conclude it holds in all cases. For example, two collocated EM events in one frame observed by a second frame moving at v are separated by D = vT, or at the speed of light, by cT. So which is it? Is it cT, or is it infinity as Einstein concluded (it can't be both can it?). SW physics suggests an engineering (i.e., logical?) solution, i.e., that D_sw' between the two EM events in the second frame come from the infinite distance created by motion of clock C₀' at c relative to the source of its "off" signal, while the Newtonian distance D between it and clock C₁' in that frame is measured either by rigid rods, or by the time (cT) for clocks in the first frame to travel from C₀' to C₁'. This is in fact the distance between the two moving clocks measured from the first frame. This engineering solution seems to me much more logical than Einstein's.

If you can understand this, maybe you can explain it all to me!

Happy thinking! Mac

"For example, two collocated EM events in one frame observed by a second frame moving at v are separated by D = vT, or at the speed of light, by cT. So which is it? Is it cT, or is it infinity as Einstein concluded (it can't be both can it?)."

May I interject a naive question here?

Suppose an object at an arbitrary inertial reference frame at x = 0, y = 0, could somehow be attached to an object by a rigid rod of length 186,000 miles, say in the x direction. If a beam of light attached at (x,y),were projected toward the object would an observer at the object detect the photon 1 second later, or instantaneously? Oops! I just answered my own question! x = 186,000, y = 1. (Should have called y = t for time).

Anyway, the point I'm getting at is there are no separate locations (events) involved. It's two events occuring within the same reference frame, since they are attached. How does this impact the resolution of time/distance?

Hi Johnjohn, I'm afraid that your question is not very clear. It seems that you are asking about the time it would take a photon to travel the length of a one light-second long rod that is moving inertially, i.e. unaccelerated in free space. You are moving with the rod, I presume?

The answer will depend somewhat on how one would measure it. Einstein would have told you that you must first ensure that you have clocks at each end of the rod that are synchronized. Einstein's synchronization meant that you had to measure the length of the rod with your standard yardsticks, getting 186,000 miles, as near as dammit. Then, at t = 0, you had to send a signal from the one end to the other and the receiving end would add the propagation delay (one second) and set the receiving clock to one second. Whenever you like, you can now send a photon from either end to the other, and you will always find that the photon takes one second - direction independent! That's roughly the meaning of the isotropy of the speed of light!

I do not think Mac's scheme handles this very well, but I'll leave him to tell us the details of an equivalent test.

Jorrie

That makes sense Jorrie. Thanks the response. Now off to ponder some more.

-John

Hi Mac. Yep, your equation: T_sw'- (V_sw'/c)(D_sw'/c) = T is right; I read a divide in the last term which screwed it up! This does not remove my critique that your algebra does not prove invariance of the spacetime interval. It can actually only be proven in a scheme where the speed of light is isotropic. I still want to know how speed of light measurements will yield isotropic results in your SW relativity!

You wrote: "After Einstein derived the LT using Newtonian concepts he assumed they also held for material events. "

I disagree that Einstein took such a path. He postulated his two principles of relativity and then time dilation and length contraction followed. He was not the one that derived the LT using Newtonian principles. He found that the LT satisfies his principles, but without requiring an aether, as Lorentz and others postulated.

"SW physics suggests, however, that while the latter is true in some cases, e.g., collocated and simultaneous EM events, it is a stretch to conclude it holds in all cases. For example, two collocated EM events in one frame observed by a second frame moving at v are separated by D = vT, or at the speed of light, by cT. So which is it? Is it cT, or is it infinity as Einstein concluded (it can't be both can it?)."

Einstein's view (infinity), what else! The high speed world is certainly not Newtonian, that we know for sure!

"SW physics suggests an engineering (i.e., logical?) solution, i.e., that D_sw' between the two EM events in the second frame come from the infinite distance created by motion of clock C₀' at c relative to the source of its "off" signal,..."

You must keep in mind that in Einstein's relativity, one can also measure the time interval between events by reading a stopwatch and then subtracting the propagation delay as viewed by the 'moving frame'. It is just more secure/clear/whatever when using two synchronized clocks to do so. And the distance interval between the events are then always the physical (proper) distance between the two clocks, measured in the "moving frame". No funnies involved!

Finally, it is invalid to use a clock "moving at c" relative to any frame, so there is never an infinite distance involved. One can postulate clocks approaching c relative to your "proper frame", with the time and distance intervals tending to infinity, while still retaining the absolute spacetime interval between the events.

Assuming that you can show that your "SW relativity" does not contain inconsistencies, you will also have to show that it agrees with every experiment that has conformed to Einstein's SR, starting with the isotropy of the speed of light and possibly ending with the particle accelerator experiments. Only then can you move onto some so-called "anomalies" that are not explained yet. A tough ask!

Jorrie

Hi again, Jorrie:

I see I still have some explaining to do: I stated the following "After Einstein derived the LT using Newtonian concepts he assumed they also held for material events." By Newtonian concepts, I am referring to Einstein's use of synchronized clocks to measure time T between events, rigid rods to measure distance D, and defining velocity as D/T. Synchronized clocks, by design, measure time between events independent of light speed and independent of distance. In Section 3 of his 1905 paper: "§3. Theory of the Transformation of Co-ordinates and Times from a Stationary System to another System in Uniform Motion of Translation Relatively to the Former", he derived the LT by applying his two principles of SR to Newton's concepts, which interestingly, equalled Lorentz' expressions. Of course, Lorentz' earlier derivation was also based on Newton's concepts.

My argument is that Einstein's two principles show distance and time are dependent variables in electrodynamic processes, and that the resulting LT in Newtonian concepts fail to fully capture the implications of Einstein's SR. (This is hinted at by the fact that Lorentz derived the same relationships assuming the existence of an aether!) Moreover, Einstein in his 1905 paper blinded his analysis to this dependency when he stated that: "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." While it is easy to show that this holds for material events/points in every inertial frame, Einstein assumed it held as well between EM events and clocks collocated at these points.

While spatial isotropy does require the propagation times of signals between clocks collocated with simultaneous and collocated events be equal, otherwise this assumption may be overly restrictive. This possibility is suggested by de Forest's physics which suggests that clock synchronization is, like the aether, an artifice that ensures time is measured independent of distance, a feature that masks the dependencies between these variables intrinsic to both Maxwell and Einstein's theories.

You showed that the distance and time between two EM events derived by a dual-clock SW tool depend on asymmetries in signal propagation times between EM events and clocks. These times, in turn, are based on distances between EM events and stopwatches, assuming a fixed speed of light. It seems to me that this physics better reflects the isotropy of light in electrodynamic processes than Einstein's assumption that the propagation times of signals from EM to clocks are always the same in all inertial frames. Otherwise, I am not sure I understand your question: "I still want to know how speed of light measurements will yield isotropic results in your SW relativity!"

Of course the validity of any theory can be established only experimentally. My analysis shows that these SW-derived values for distance and time equal Newtonian values for simultaneous and collocated EM events, they otherwise differ, though very slightly, from relativistic values defined by the LT (so slightly, in fact, that time dilation and tranverse Doppler shifts effects in both pass previous tests for these effects).

Hope this helps, and thanks again for your valuable critiques!

Mac

Hi Mac, yea, I think we are a long way from reaching some form of common understanding!

Instead of going around in circles arguing the points that you mentioned, let us construct a simple experiment and let you and Einstein slog it out.

Let's take John's 1 light-second (ls) long rod, floating in free space at some considerable velocity in a length-wise direction relative to one of your "proper frames", for which you can choose any two events, as long as the rod is moving relative to the proper frame. These two events have nothing further to do with the test.

At the ends of the rod are two observers L and R, with synchronized clocks and a radar set each. They use the radars to confirm the distance between them as exactly 1 ls (no need for meter-sticks, although they could have used them as well). Now let the two observers perform a one-way speed of light test in each direction, by sending EM signals to one another at an agreed common time and then reading the arrival times of the signals on their respective clocks (all strictly EM). Hence, they can calculate the speed of light.

We know what Einstein's prediction would have been. What is your SW prediction for the outcome of the one-way speed of light tests and how would you get to it? Obviously, you are not allowed to assume that the 'rod clocks' are synchronized.

In the interest of reaching some conclusion, skip the previous points (which tends to go in circles) and let's concentrate on this test.

Jorrie

Hi to you both: Good question! One I believe exposes key differences between Einstein's spacetime (ST) physics and de Forest's stopwatch (SW) physics.

First, some electrodynamic facts that, I assume, we can all agree hold in both physics: Einstein's two principles of SR (spatial isotropy and the fixed speed of light) are valid; and, while individual EM events define single points in every inertial frame, separations between such events differ in different inertial frames. It is clear as well that one "proper" frame exists for every pair of events where this separation is minimized and equals Minkowski's ST interval. (E.g, one and only one frame exists wherein two time-like events are collocated and separated by their proper time T.) In all other frames these events are separated in distance D'/c and time T' greater than T and directly related to motion relative to the proper frame, a frame defined by the events themselves. A similar situation exists for space-like events which are simultaneous in their proper frames.

In de Forest's physics, motion is between observers and events (defined by their proper frame). Hence, in your example, since the two events are simultaneous, the rod defines their proper frame. Also, as you state, radar distances are Newtonian and signal propagation times between two events and collocated clocks are equal. In this situation, distance and time are not only the same whether measured by rigid rods or stopwatches but also Newtonian and satisfy SR. In contrast, the LT are based on two very different assumptions, i.e., that motion is between any two observers of any two events, and that time and distance between events are defined by synchronized clocks and rigid rods.

While your example is Newtonian it does allow comparison of ST and SW physics in the general relativistic case. Since these events are separated by D = 1s, the LT show that an observer moving at Newtonian velocity v parallel to the rod will measure time T' and distance D' equal to 1s(v/c)[1-(v/c)²]^-1/2 and 1s[1-(v/c)²]^-1/2 respectively. In SW physics, time and distance, T_sw' and D_sw', equal 1s(V_sw'/c)[1-(V_sw'/c)²]^-1, and 1s[1-(V_sw'/c)²]^-1 respectively, where V_sw'/c = T_sw'/D_sw'. Analogous expressions for time-like events are obtained by interchanging distance and time in these functions.

It is clear that these relativistic functions differ in form between SW and ST physics; less clear is that definitions for distance, time, and velocity also differ. These differences arises because values in SW physics depend on signal propagation times from events to clocks, whereas LT relationships between Newtonian variables come from the assumption that time and distance between EM events equal values between material events as defined by synchronized clocks and rigid rods.

Hope this helps! Mac

Hi Mac, you wrote: "Hope this helps!"

Well, I'm afraid not.

Unless you are willing to answer the direct question that I posted last time: "What is your SW prediction for the outcome of the one-way speed of light tests and how would you get to it? Obviously, you are not allowed to assume that the 'rod clocks' are synchronized.", I'm not willing to discuss "de Forest physics" further. A simple question, just answer it, then we can talk again.

I am reasonably convinced that your brand of relativity does not preserve isotropy of the speed of light for all inertial frames. You seemed to have replaced that concept with a principle of "spatial isotropy", whatever that may mean.

But don't worry about defining "spatial isotropy", just come up with a prediction and rationale for the one-way speed of light, when tested in both directions in a 'moving frame', as I defined it before. It will become necessary later to also explain the Michelson-Morley experiments (orthogonal vs. parallel propagation) and a number of particles accelerator results...

Sorry...

Jorrie

Sorry Jorrie: I seem to have missed your key question--much simpler than I presumed.

In Forest's physics, stopwatches (C₀ and C₁) collocated with two EM events are triggered "on" by the first signal to arrive , "off" by the second, with the convention that resulting values are positive in sign if turned "on" by the local event, otherwise negative. Distance D and time T between any two events are then given by (C₀+C₁)/2 and (C₀-C₁)/2. Hence, for simultaneous events, where both clock values are positive and each clock measures one-way signal propagation time, D equals that measured by radar as well as synchronized clocks.

Of course, in more interesting relativistic cases where time, distance, and motion are all finite, signal propagation times are asymmetrical (given c) and relativistic values differ slightly from those defined by the LT.

Does this help? Again, I hope so!

Mac

Sorry Mac, but you did not answer the question! So let me restate it.

"At the ends of the rod are two observers L and R, with synchronized clocks and a radar set each. They use the radars to confirm the distance between them as exactly 1 ls (no need for meter-sticks, although they could have used them as well). Now let the two observers perform a one-way speed of light test in each direction, by sending EM signals to one another at an agreed common time and then reading the arrival times of the signals on their respective clocks (all strictly EM). Hence, they can calculate the speed of light."

Remember that the rod is moving "at some considerable velocity in a length-wise direction relative to one of your "proper frames", for which you can choose any two events, as long as the rod is moving relative to the proper frame."

The reason I posed this question is that you have to have a definition of simultaneity to be able answer it at all. From our previous discussions, it appears as if your scheme has Galilean simultaneity, i.e. absolute time. If you do that, you will get two different (Galilean) answers: the speed of light will be c+v in the rearward direction and c-v in the forward direction. I modified the original picture to show this simultaneity and the propagation times C'₁ and C'₀, which will differ from each other. Remember it is now the light propagation time from the two ends of the rod, separated by length d on the X-axis, to the opposite stopwatch, moving at speed v. The stopwatches are started at a common time t₀, when the light signals are sent (simultaneously) and stopped as the light signals arrive at the other end.

If you take the algebraic mean of C'₁ and C'₀ and divide it by the distance d, you will get c, but this constitutes a 2-way speed of light test, which always gives c in Galilean relativity. So, my conclusion is that your SW relativity is pure Galilean and not special relativistic at all! Isotropy of the speed of light in every inertial frame is a cornerstone of all science today and AFAIK, only Einstein's special relativity guarantees that. By your own admission, your SW relativity is not concordant with special relativity...

OK, I've answered the question as I see it in your SW relativity. You may differ from me, of course, but then please describe the one-way speed of light test in your scheme as you see it. My guess is that if you do not have a definition of simultaneity, you cannot answer the question sensibly - and there are some others that you may then not be able to answer either.

Jorrie

Jorrie: I do appreciate your hanging-in on these frustrating ideas.

I too was frustrated for over a decade trying to grasp the relativistic implications of the unique physics used by spy satellites, one that not only depends on motion relative to EM events, rather than other observers of the same events, but also depend on neither time-synchronized clocks nor rigid rods. It was only recently that I found that the simple dual-clock "stopwatch" tool based on de Forest's ideas exposes core differences between these two measurement physics. (Hence this is still a "work in progress".)

But back to your question re speed-of-light measurements: My answer to your original question "We know what Einstein's prediction would have been. What is your SW prediction for the outcome of the one-way speed of light tests and how would you get to it?" is that it is the same as that measured by synchronized clocks and rigid rods if the two events at rod ends are simultaneous. This restriction is, however, not due any change in c itself but rather differences in propagation distances--and thus signal propagation times-- from events to clocks necessary to satisfy Einstein's two principles of SR.

Intrinsic to this physics is that, as for spy satellites, motion is between clocks and EM events, rather than between observers of the same events as Einstein assumed. Key to this definition is the concept of a "proper frame", one of which exists for every pair of EM events where distance and time are minimimal, one being "0", the other equaling Minkowski's spacetime interval. Observed from their proper frame, time-like events are collocated (signal propagation times are zero) and space-like events are simultaneous (equal signal propagation times). Such frames serve as unambiguous references for deriving one-way signal propagation times from events to clocks in other moving frames. This results, unlike in ST physics, increases in distance and time due solely to asymmetrical increases in propagation distances, and thus signal propagation times from events to clocks.

Back to your question again: With simultaneous events at the ends of your rod, this frame becomes the proper frame for these events where SW values C₀ and C₁ are equal. Distances from these events to clocks in a second moving frame are D/(1-V/c) and D/(1+V/c) respectively, resulting in one-way signal propagation times and associated clock values, C₀' and C₁', equal to (D/c)/(1-V/c) and (D/c)/(1+V/c) respectively, giving a distance D'/c = (C₀'+C₁')/2= (D/c)/[1-(V/c)²], and time T' = (C₀'+C₁')/2 = (D/c)(V/c)/[1-(V/c)²] respectively. In this physics, these relativistic increases in distance and time come solely from signal propagation times from events to clocks based on distances imposed by Einstein's two principles of SR.

Note, the two events in this frame can, of course, be separated by any time from zero to infinity without changing the length D of the rod. Nor, of course, do other moving frames affect this length. Differences between any two observers of these events depend on their speed relative to the two events in their "proper" frame (conceptual or real) where they are simultaneous and separated by D. (A simple corresponding "engineering-friendly" analysis holds for time-like events.)

Would appreciate your critique and questions! Mac

Hi Mac.

Ok, I've changed my ST diagram for two simultaneous events, as you described it, which BTW, means that you have chosen a simultaneity scheme!

I agree with your calculations, but it supports my position, i.e., the speed of light is not isotropic in your SW physics. Relative to the moving (red) frame, it is c+v in the left-bound direction and c-v in the right-bound direction. If I take your D' and divide it by T', get v/c, which is correct, but it has nothing to do with isotropic light-speed.

Finally, the answers you get is not relativistic. It is the values Galileo and Newton would have calculated for the absolute frame of reference (the aether). What is novel in your approach is that you choose an 'aether' where the two events are simultaneous and then you use Newton to calculate an algebraic average of two anti-parallel propagation times. This is essentially Galilean relativity. Einstein would not have agreed...

Having "failed" this test (one-way isotropy of light-speed), how about explaining the Michelson-Morley null result for two-way isotropy of light-speed in two orthogonal directions, using your SW relativity?

Jorrie

Hi Jorrie

I think we are making progress, but not quite there yet. It is clear that any physics claiming to explain Einstein's principles of SR must be consistent with those principles. Unlike classical clocks and rods, measurements by spy satellite systems depend directly on both principles, i.e., on propagation times of signals from those events, which depend on motion relative to those events. You claim that the form of this physics I describe does not satisfy "isotropic light speed". While I have not seen yours, my definition, in the generic sense, is that for any given distance D, the time for an EM signal to travel that distance in any inertial frame in any direction will always be D/c, D being measured by rigid rods (or radar) and time by synchronized clocks. This simple definition, I believe holds for any EM signal between any two fixed (static) points within individual inertial frames.

Einstein's LT, however, define dynamic relationships between material frames and EM events, processes differ fundamentally from classical Newtonian kinematics. For example, collocated events in one frame separated in time by T will be separated in both distance and time in all other inertial frames, a result applicable to material and EM events. Einstein, however, showed that unlike classical physics, where T' = T, and D'= vT in the second frame, for EM events these relationships are T/[1-(v/c)²]^1/2 and T(v/c)/[1-(v/c)²]^1/2 respectively. Einstein derived these relationships (the LT) by assuming that signal propagation times between the two clocks in the second frame are the same in both directions.

As you showed, the dual-SW tool based on de Forest's physics questions this assumption, suggesting in turn that distances between EM events and clocks in frames moving relative to two collocated events, and thus signal propagation times from those events to those clocks, are unequal. This, of course, contradicts Einstein's assumption in his 1905 paper that the two one-way signal propagation times between any two events and clocks collocated with those events are equal in all inertial frames. This assumption is necessary to ensure that time between any two EM events can be measured by synchronized clocks independent of their separation in distance. (Even though his own theory showed time and distance between EM events are dependent variables.)

In de Forest's physics, distance in the above definition for light-speed isotropy is that between EM events and clocks in different inertial frames, an electrodynamic value that for time-like events defined by motion relative to their proper frame where in those events are collocated, and for space-like events, that frame where those events are simultaneous.

Must finish these thoughts latter, as I must leave now and will be away for a couple of days. But hope this helps.

Mac

Hi Mac, no, I'm afraid we are not making any progress!

You wrote: "It is clear that any physics claiming to explain Einstein's principles of SR must be consistent with those principles."

Yet, as I've shown, your SW physics are pure Newtonian and does not satisfy Einstein's isotropy of light-speed principle.

You wrote: "You claim that the form of this physics I describe does not satisfy "isotropic light speed". While I have not seen yours, my definition, in the generic sense, is that for any given distance D, the time for an EM signal to travel that distance in any inertial frame in any direction will always be D/c, D being measured by rigid rods (or radar) and time by synchronized clocks."

But your own "thought experiment" that we discussed does not comply to this definition! It gives Newtonian speeds of light in the moving frame...

I have started to work on the orthogonal propagation of two light signals (Michelson Morley interferometer) a-la your SW theory, and my first result is that your theory fails that crucial test as well. It gives identical results to what Newton/Galileo would have given and which was disproved many, many times in practice.

I still have to write it up properly, but I'm afraid we are close to the end of this line of discussion, because it is going nowhere and my experience in such cases is that it soon becomes circular.

Jorrie

Hi Jorrie: I'm baaaack! I agree we need to quit running in circles on these ideas. I was pleased to get your following explanation of my original question, which may help break this circle. So let me address the latter first.

Mac

Hi again Mac. I don't think anyone has fully answered your opening post. I jumped in too late and then queried your definitions. Here I just want to provide the relativistic answer to you request: "Explain an apparent violation of spatial isotropy by Lorentz' transform."

The confusion comes in when one tries to attribute difference in the 'real rate' of time passage to two inertial frames that are in relative movement. Because these apparent time rate differences are reciprocal, it should be clear that it cannot be 'real'. In fact it is impossible to compare two clocks in relative inertial motion, because they can be co-located only once in all eternity! They need be either accelerated or in orbits in a gravitational field to be co-located more than once.

You wrote: "...Einstein showed are defined by the Lorentz transform, i.e., T' = T/[1-(v/c)²]^1/2 and D'/c = T(v/c)/[1-(v/c)²]^1/2. However, this same transform also shows that any pair of these second frames moving at a finite relative velocity do not measure the same distance and time between these events, a result that would, its seems to me, violate spatial isotropy.
"

The Minkowski diagram shows your two co-located events as black bullets. Jim and Pam are two inertial observers moving in opposite directions at equal speeds relative to proper frame. They could just as well have moved orthogonally, but it is easier to picture this way. It is clear that they both measure the same space intervals and time intervals and hence the same spacetime interval for the two events.

This proves unequivocally that there are no violations of spatial isotropy in Einstein's special relativity or in Minkowskian spacetime (or in the Lorentz transformations, for that matter).

Usually there comes a comment at this point, something like: Yea, but from Pam's point of view, Jim's clock must be running slower than hers. The answer to that is in the second paragraph above. If you make Pam's frame the "proper frame", i.e., define two different events that are co-located in her frame, then Jim would measure different spatial and temporal intervals, but they would still agree on the spacetime new interval.

The bottom line is: all inertially moving clocks measure "proper time", which is defined only between events that are co-located in their respective inertial frames.

Jorrie

Hi Jorrie,

Good answer! You certainly have more understanding, more interest, and a lot more patience than me.

Regards,

S

Hi Jorrie again:

Excellent!! Your answer to my initial question not only exposes common ground underlying spacetime (ST) and radiolocation (SW) physics but also where and how they differ. Your statement is 100% consistent with my perception of the spacetime explanation for Einstein's two principles. Your diagram demonstrates, as you say, that for Pam and Jim to measure the same time between the same events in this perfectly symmetrical case, their clock rates must be the same despite their own relative motion. But if relativistic effects cannot be assigned to physical changes in measurement tools, where do they come from? (Wherever, ST physics hides it well!)

Your diagram also exposes the key difference between ST and SW physics: that motion, v, in the former is between observers of the same events; in the latter, it is between observers and the proper frame for those events (that single frame wherein time-like events are collocated and space-like events are simultaneous). Hence, in your diagram, Pam and Jim are moving at the same speed v relative to the two events, where they measure identical values (if their clock rates are identical!) independent of their own relative speed (which can range from 0 to ~2v).

Of course, while the diagram shows observers and events as separate entities, in fact each observer measures features of the two events wholly from measurements within his own frame, i.e., independent of all other frames. While the LT explain Pam and Jim's individual measurements, I do not understand how the LT explain P and J's identical values, given that their own relative motion can range from 0 to ~2v.

Your diagram not only offers a simple reason for this seemingly (to me anyway!) glaring violation of the LT but also a physical explanation for differences between observers of the same events—experimentally validated physical effects with origins unexplained by the LT or ST physics. Minkowski, of course, showed that every pair of EM events has an intrinsic "proper" interval identical for, and derivable by, any observer of those events from his own measurements. SW tools are, in effect, real-world embodiments of Minkowski's abstract geometry: i.e., one and only one inertial frame exists for two time-like events wherein those events are collocated, both signal propagation times are zero, and one clock measures their separation in time, T (Newtonian since no synchronization required!). In all other frames moving relative to this proper frame these events are separated by T'>T and D'>0, and in SW physics, motion of any observer relative to this proper frame is D'/T'. Thus, in your diagram, while the collocated events are the same in both ST and SW physics, the SW reason why Pam and Jim measuring the same values is that their motions relative those events are the same. Moreover, values for distance and time derived from their SW values depend solely on one-way signal propagation times from the collocated events.

I believe this SW alternative explanation is not only more consistent with Einstein's two principles of SR than the ST version based on classical clocks and rods, but also gives a simple physical explanation for relativistic effects sans the puzzling paradoxes, imaginary time, etc. intrinsic to the latter. I realize you will not agree, however I most appreciate any proof re the error of my ways since I'd rather be skiing than wrestling with flawed physics!

Thanks much, Mac

Hi Mac, welcome back!

You wrote: "Your diagram also exposes the key difference between ST and SW physics: that motion, v, in the former is between observers of the same events; in the latter, it is between observers and the proper frame for those events (that single frame wherein time-like events are collocated and space-like events are simultaneous)"

But Pam and Jim are moving at +v and -v respectively relative to the proper frame X, CT - no difference in that respect between ST and SW physics!

"While the LT explain Pam and Jim's individual measurements, I do not understand how the LT explain P and J's identical values, given that their own relative motion can range from 0 to ~2v."

This seems to be a problem with your understanding of special relativity (SR), not a problem with the theory. And BTW, in SR it's not 0 to 2v, it's 0 to 2v/(1+v²/c²), which ranges between 0 and c. As long as it is symmetrical relative to the reference frame, they will measure the temporal and spatial intervals as the same.

"Your diagram not only offers a simple reason for this seemingly (to me anyway!) glaring violation of the LT but also a physical explanation for differences between observers of the same events—experimentally validated physical effects with origins unexplained by the LT or ST physics."

No violation - this is standard SR, pure and simple, totally consistent! What are these unexplained "experimentally validated physical effects"? I know of no validated observation that is not explained by SR. If you refer to the "Pioneer Anomaly" or the "Gravity Assist Anomaly", these are not SR effects, but perhaps point to a problem in gravitation theory...

Jorrie