Silly Einstein

[Goldminer]

Einstein loved his "Train Gedankens" didn't he? He used several of them. For the sake of those occupied with the idea that the platform/embankment/station is "fixed," Albert should have used a example of trains moving in opposite directions, no? Then the third frame of reference, the tracks, would be better visualized. Then Aardwolf could see that his arc is in the third frame, the track frame.

I have no problem with the arc being in its own frame as this will be the one that is stationary with respect to the ether. I only had one ship as stationary with it for simplification but I have no problem with the ships passing each other at some speed relative to ether; it just means that neither of their frames will be at the centre of the light sphere, they will just both be moving towards opposite sides of it. Makes no difference to absolute space theory.

You don't have a problem because there are some things which are unknown to you. No experiment has ever found a speed relative to the aether! If you know of one please cite the reference! The speed is relative to the spaceships. It can also be relative to the point between the spaceships. The speed of the ships relative to the point is one half the speed of the ships to each other. Get it? The point and the spaceships have no way of knowing their relative speed to the aether. I am sure that nothing makes any difference to "absolute space theory." It's definitely a spacey theory!

It just means that neither of their frames will be at the centre of the light sphere, they will just both be moving towards opposite sides of it

Now you are confusing the frames each ship occupies with the ships themselves. Yes, the expanding sphere will be centered upon the point which you claim in error to be at rest with the aether! Congratulations!

The frames are imaginary. They are useless, since each spaceship has no companions to be at rest with either ship. That is all frames do is keep those objects at rest with each other organized when discussing relative motion. All that an origin within a frame does is provide a common point from which distances to all objects within that frame can be measured. I know this explanation is useless to you. Maybe others will understand!

But, hey! Somehow in all your confusion you did get it right about the spaceships receding from the point where the light sphere was emitted. The flash from your arc has already passed the spaceships since they are going slower than the light sphere is expanding.

[Goldminer]

Origins are fixed by definition, they cannot move.

So, Aarwolf, if you read through Mathis's latest stuff on relativity, you will find that he has wisely dropped his reference as to how "origins cannot move." Those references are no longer in his work concerning relativity. He writes of coordinate systems moving in relation to other coordinate systems. In fact, at one point he has three or four moving systems in the same paragraph! An origin in a Cartesian coordinate system is merely where the coordinates meet and usually where the number lines start (usually at zero with the negative numbers running to the left and positive numbers to the right for the x axis; positive up for the y axis; and positive towards the viewer for the z axis.)

If the coordinate systems move (and one may have them move according to what ever way the author needs to have them move in relation to each other,) the origins of each respective system move with it. You have no choice. The coordinate systems represent abstractions of reality. Nothing defies any logic but yours.

The next proposition is that every set of coordinates (which describe distances from the origin) do not move in relation to the origin. This does not mean that “motion” cannot be depicted on a coordinate system.

How is that done, Mr. Smartypants Goldminer?

Here is how I plot a car moving at 60 miles an hour moving away from the origin in the positive direction:

-2_____-1_____0_____1_____2_____3_____4_____5_____6_____

Each number represents one mile or one minute. After the passage of the first minute, the car has gone one mile. That is the instantaneous time and distance for the car that is traveling at 60 mph.

After six minutes, the instantaneous elapsed time and distance is 6 minutes and 6 miles.

Come back tomorrow and look at the chart. It will have not changed. Nothing on the chart has changed position, and yet I have plotted “motion” on this single axis ordinate system.

If you don't understand this, go to your room and just think about it.

[Goldminer]

So, now we have our number-line designated with each successive whole number representing one additional mile, and concurrently, one additional minute of elapsed time:

-6____-5_____-4_____-3_____-2_____-1_____0_____1_____2_____3_____4_____5_____6

If I wish to represent a car that has traveled from the origin for 2 minutes @ 60 mph, I can mark it on the chart as a red “2.”

-6____-5_____-4_____-3_____-2_____-1_____0_____1_____2_____3_____4_____5_____6


If I wish to add another car that has gone 2 minutes @ 60 mph in the opposite direction from the origin (at 0) I can do that:

-6____-5_____-4_____-3_____-2_____-1_____0_____1_____2_____3_____4_____5_____6
__________________________ a _______________________b________________________ .
(The negative numbers have no meaning other than “opposite direction.” The elapsed time in the negative direction can be added in disregard to the “-” sign. |-2|+ |+2| = 4. There is no “going backwards in time.)

If I wish to add another car that has gone 2 minutes in the opposite direction @ 30 mph from the origin (at 0) I can do that:

-6____-5_____-4_____-3_____-2_____-1_____0_____1_____2_____3_____4_____5_____6
__________________________ a _____c_________________b________________________ .

The above line represents the distance and the elapsed time for three cars that have traveled for two minutes: two going in opposite directions from the origin @ 60 mph, and one going in the negative direction @ 30 mph (denoted in italic.) Big deal, right? Way too simple, Huh?

There are actually several things shown on the simple line above:

1. The elapsed time from the origin (2 minutes) is in red for all the cars, the distance for each car is the distance from the origin, for all three cars.
2. The car traveling @ ½ of 60 mph is shown as italic, and has only traveled one mile from the origin in the two minutes.
3. The relative time and distance between the two cars “a” and “b” is 4 miles and 4 minutes, i.e. it would take car “a” four minutes to get to car “b's” position; traveling @ 60 mph.
4. Car “c” is now one mile from car “a,” three miles from car “b,” and half way between car “a” and the origin.

The number-line below represents two instantaneous (stop-motion, if you will) situations:

-6____-5_____-4_____-3_____-2_____-1_____0_____1_____2_____3_____4_____5_____6
_a__________________c_____a ______c_________________b_______________________b .

The red time lapse and now, the blue. The blue color represents where the cars are located after 6 minutes; cars “a” and “b” traveling @ 60 mph from the origin, and “c” traveling @ 30 mph from the origin.

1. The elapsed time from the origin (6 minutes) is in blue for all the cars, the distance is the distance from the origin, for all three cars.
2. The car traveling @ ½ of 60 mph is shown as italic, and has now traveled 3 miles from the origin in the 6 minutes.
3. The relative time and distance between the two blue cars “a” and “b” is 12 miles and 12 minutes, i.e. it would take car “a” twelve minutes to get to car “b's” position; traveling @ 60 mph.
4. Car “c” is now 3 miles from car “a,” and 9 miles from car “b,” and still half way between car “a” and the origin.

Since, in reality the scene would be stretched over 12 miles, and the “stop-motion” abstraction would be hard to visualize, IMHO, the diagram here seems a simple enough “abstraction” of said reality, don't you agree, my friend Mr. Aardwolf?

Arguendo, I have not considered the curvature of the Earth; the acceleration needed to attain the said constant speeds of the cars, the temperature of the air; the sex of the drivers; the location of any observers. These are inconsequential to the understanding here, anyway. Can you think of any other assumptions that I have overlooked, that would irreparably alter this diagram from reality?

[Goldminer]

The number-line below represents two instantaneous (stop-motion, if you will) situations. This is just a re post of the last text/graphic from my last post. The number line here is called the abscissa in a Cartesian coordinate system, otherwise known as the "x" axis. You may be asking where crazy Goldminer is going with the simplistic stuff. Please follow my reasoning to another level of abstraction.

-6____-5_____-4_____-3_____-2_____-1_____0_____1_____2_____3_____4_____5_____6
_a__________________c_____a ______c_________________b_______________________b .

The graph stays the same, but we (you and me if you are following) are going to change a few of the parameters:

1. The "a" and "b" letters are now the leading edge of a light pulse expanding from a strobe light placed at the origin.
2. The scale along the number line is now units of foot/nanosecond; rather than mile/minute, since light has the latency of a foot per nanosecond.
3. The third letter, "c" is the origin of another coordinate system, or number line "moving" at ½ the speed of light.

The red time lapse (representing 2 nanoseconds of elapsed time) and now, the blue. The blue color represents where the expanding wave fronts are located after 6 nanoseconds; wave fronts “a” and “b” traveling @the speed of light from the origin, and “c, another origin,” traveling @1/2 the speed of light from the origin.

1. The elapsed time from the origin (6 nanoseconds) is in blue for the wave fronts and the additional origin, the distance is the distance from the origin, for the wave fronts and the additional origin.
2. The origin traveling @ ½ the speed of light is shown as italic, and has now traveled 3 feet from the origin in the 6 nanoseconds.
3. The relative time and distance between the two blue wave fronts “a” and “b” is 12 feet and 12 nanoseconds, i.e. it would take the wave front “a” twelve nanoseconds to get to wave front “b's” position; traveling @ the speed of light. (It can't do that, I'm just emphasizing the distance between the two separating wave fronts.)
4. origin “c” is now 3 feet from wave front “a,” and 9 feet from wave front “b,” and still half way between wave front “a” and the original origin.

Summary:
1. By using the "unit" scale of foot/nanosecond, I have incorporated the latency of light and distance all on the abscissa. There is no need to represent time on its own axis!
2. The origin of a second, moving abscissa is being diagrammed concurrently with the expanding edges of the wave front. (It looks like two wave fronts since the light from the strobe actually travels both ways from the strobe.) The second origin is the "moving frame" coordinate system where moving observers traveling in unison at ½ the speed of light are to be diagrammed. (in this example)
3. This is the way Woldemar Voigt and A. Einstein should have diagrammed the so called "Galilean Transform." IMHO, Their diagram only has the strobe itself in the diagram; they do not consider the expanding wave fronts; which is supposed to be the whole purpose of the exercise!

[Goldminer]

A little detour here from demonstrating the relationships between coordinate systems whose origins are undergoing unaccelerated motion. From the previous post:

The second origin is the "moving frame" coordinate system where moving observers traveling in unison at ½ the speed of light are to be diagrammed.

[The last diagram in my previous post] is the way Woldemar Voigt and A. Einstein should have diagrammed the so called "Galilean Transform." IMHO, Their diagram only has the strobe itself in the diagram; they do not consider the expanding wave fronts; which is supposed to be the whole purpose of the exercise!

Concerning consensus theorists; most of the diagrams I have seen discussing the "Galilean Transform" have the "source," usually labeled as the "event" in their "moving coordinate system," and they picture the opposite coordinate system as their "stationary" system.

Apparently the idea has never dawned upon consensus theorists, including professors and the like, that their initial diagram does not include the expanding wave front sphere. Their "event" (the emitter) just sits there in the "moving system" doing nothing while they "let this moving system approach the speed of light."

Do you see how silly this is?

My next bitch is that they never admit that their "stationary system" only has the observers in it. People all the time seem to assume that the source/emitter can be both "at rest" and "moving" concurrently! What you "know" that just ain't so . . .

Since relativity is the principle that either coordinate system can be taken as "stationary," or both systems assumed to be approaching or separating, I choose to diagram the source/event coordinate system as the primary, stationary system. This is because there is more happening in this system: We have the source (which is actually not an "event") and the continuously expanding light sphere (which is the event, and to my knowledge can only be diagrammed in some stop motion successive way.) (The consensus method is to put "time" on one axis and distance on the other, which is overcome by simply choosing unit measures for the main subject of consideration; the expanding sphere.)

By having the observers in the moving frame, and the "stop motion expanding sphere" in the stationary frame, we can readily diagram where a moving observer meets the wave front in the stationary frame, at a given elapsed time and place of said wave front.

Why the consensus professors do not diagram the expanding sphere, and always show the source (their so called "event") as the "moving" portion of their picture, I suppose, is that they cannot imagine a wave front that is both moving toward their observer and away from their observer. (BTW opposite sides of this wave front are separating at twice the speed of light.) Further, they do not comprehend that it takes two separate observers on opposite sides of the expanding sphere to observe both sides of said sphere!

I have overcome this problem by devoting the "moving coordinate system," the origin of which is centered on "c" in the diagram, to a fleet of observers. Each of said observers are a fixed distance from the moving origin.


-6____-5_____-4_____-3_____-2_____-1_____0_____1_____2_____3_____4_____5_____6
_a__________________c_____a ______c_________________b_______________________b .

[Aardwolf]

Let's just suppose for giggles that there is another point in relative motion with this point. Now let's suppose that there are two additional spaceships which happen to pass each other at this new point. Which of the points is at absolute rest with the aether?

Please don't tell me that both points are at rest with the aether.

Of course they are. If this second point is in relative motion with the original point and the original point is stationary with regard to the ether, then yes both are stationary relative to the ether.

You originated in your mother's womb. You are telling me that your mother can't move? Your father must have been a very frustrated individual!

Yet again you are trying to place an absolute point in space inside/attached to a moving object. Bad example like your last with the paper (which by the way you still havent explained with one shared origin).

[Aardwolf]

The number-line below represents two instantaneous (stop-motion, if you will) situations. This is just a re post of the last text/graphic from my last post. The number line here is called the abscissa in a Cartesian coordinate system, otherwise known as the "x" axis. You may be asking where crazy Goldminer is going with the simplistic stuff. Please follow my reasoning to another level of abstraction.

-6____-5_____-4_____-3_____-2_____-1_____0_____1_____2_____3_____4_____5_____6
_a__________________c_____a ______c_________________b_______________________b .

The graph stays the same, but we (you and me if you are following) are going to change a few of the parameters:

1. The "a" and "b" letters are now the leading edge of a light pulse expanding from a strobe light placed at the origin.
2. The scale along the number line is now units of foot/nanosecond; rather than mile/minute, since light has the latency of a foot per nanosecond.
3. The third letter, "c" is the origin of another coordinate system, or number line "moving" at ½ the speed of light.

The red time lapse (representing 2 nanoseconds of elapsed time) and now, the blue. The blue color represents where the expanding wave fronts are located after 6 nanoseconds; wave fronts “a” and “b” traveling @the speed of light from the origin, and “c, another origin,” traveling @1/2 the speed of light from the origin.

1. The elapsed time from the origin (6 nanoseconds) is in blue for the wave fronts and the additional origin, the distance is the distance from the origin, for the wave fronts and the additional origin.
2. The origin traveling @ ½ the speed of light is shown as italic, and has now traveled 3 feet from the origin in the 6 nanoseconds.
3. The relative time and distance between the two blue wave fronts “a” and “b” is 12 feet and 12 nanoseconds, i.e. it would take the wave front “a” twelve nanoseconds to get to wave front “b's” position; traveling @ the speed of light. (It can't do that, I'm just emphasizing the distance between the two separating wave fronts.)
4. origin “c” is now 3 feet from wave front “a,” and 9 feet from wave front “b,” and still half way between wave front “a” and the original origin.

Summary:
1. By using the "unit" scale of foot/nanosecond, I have incorporated the latency of light and distance all on the abscissa. There is no need to represent time on its own axis!
2. The origin of a second, moving abscissa is being diagrammed concurrently with the expanding edges of the wave front. (It looks like two wave fronts since the light from the strobe actually travels both ways from the strobe.) The second origin is the "moving frame" coordinate system where moving observers traveling in unison at ½ the speed of light are to be diagrammed. (in this example)
3. This is the way Woldemar Voigt and A. Einstein should have diagrammed the so called "Galilean Transform." IMHO, Their diagram only has the strobe itself in the diagram; they do not consider the expanding wave fronts; which is supposed to be the whole purpose of the exercise!

I don't disagree with any of this. It just demonstrates, as I have stated all along, that c (the ship) is not at the centre of the light sphere after an elapsed period of time.

You could easily add d which had the same origin at 0 at the same time as c but travelling in the opposite direction at 1/2 the speed of light. After 6 nanoseconds it would be positioned at 3. Neither ship c or d is at the centre of the light sphere created by their passing at 0.

[Goldminer]

Let's just suppose for giggles that there is another point in relative motion with this point. Now let's suppose that there are two additional spaceships which happen to pass each other at this new point. Which of the points is at absolute rest with the aether?

Please don't tell me that both points are at rest with the aether.

Of course they are. If this second point is in relative motion with the original point and the original point is stationary with regard to the ether, then yes both are stationary relative to the ether.

Your logic is impeccable! I cannot argue with that!!! I give up!!!! USI*

Aardwolf, please Google "logic," select which fallacy I have committed. I believe there are several that your above statement matches.

* (Ultimate Sarcasm Intended)

You originated in your mother's womb. You are telling me that your mother can't move? Your father must have been a very frustrated individual!

Yet again you are trying to place an absolute point in space inside/attached to a moving object. Bad example like your last with the paper (which by the way you still havent[sic] explained with one shared origin).

Either there are quite a number of people viewing this thread, or someone keeps clicking the topic, since the view count has risen very fast recently! If it be the former case, I plead that some of you join this discussion. From my humble point of view, I cannot follow Aardwolf's logic! Please join us on one side or the other, or add your special understanding to the mix!

One last time, Aardwolf, just for you: In one coordinate system, there is a strobe light that emits one pulse. I can imagine an observer right there beside it who sees the flash immediately. Now, think real slow, so you don't miss anything. Another coordinate system with an observer standing right on the origin of this other coordinate system, passes right over the original origin, just as the strobe pulses. The aim of this system is off just enough so the two observers don't get hurt. This second system doesn't stop, it just keeps going on its unaccelerated way. Please observe that the two origins only "share" the same place in space for an instant! They don't "share" the same origin! There are two of them. They just happen to be at the same place in space at the same time for a tiny instant. You keep insisting that I can't do it. I just did it! You are trying to make what I mean be what you think I should mean in your world. I'm not going there.

northing easting

[Goldminer]

The number-line below represents two instantaneous (stop-motion, if you will) situations. This is just a re post of the last text/graphic from my last post. The number line here is called the abscissa in a Cartesian coordinate system, otherwise known as the "x" axis. You may be asking where crazy Goldminer is going with the simplistic stuff. Please follow my reasoning to another level of abstraction.

-6____-5_____-4_____-3_____-2_____-1_____0_____1_____2_____3_____4_____5_____6
_a__________________c_____a ______c_________________b_______________________b .

The graph stays the same, but we (you and me if you are following) are going to change a few of the parameters:

1. The "a" and "b" letters are now the leading edge of a light pulse expanding from a strobe light placed at the origin.
2. The scale along the number line is now units of foot/nanosecond; rather than mile/minute, since light has the latency of a foot per nanosecond.
3. The third letter, "c" is the origin of another coordinate system, or number line "moving" at ½ the speed of light.

The red time lapse (representing 2 nanoseconds of elapsed time) and now, the blue. The blue color represents where the expanding wave fronts are located after 6 nanoseconds; wave fronts “a” and “b” traveling @the speed of light from the origin, and “c, another origin,” traveling @1/2 the speed of light from the origin.

1. The elapsed time from the origin (6 nanoseconds) is in blue for the wave fronts and the additional origin, the distance is the distance from the origin, for the wave fronts and the additional origin.
2. The origin traveling @ ½ the speed of light is shown as italic, and has now traveled 3 feet from the origin in the 6 nanoseconds.
3. The relative time and distance between the two blue wave fronts “a” and “b” is 12 feet and 12 nanoseconds, i.e. it would take the wave front “a” twelve nanoseconds to get to wave front “b's” position; traveling @ the speed of light. (It can't do that, I'm just emphasizing the distance between the two separating wave fronts.)
4. origin “c” is now 3 feet from wave front “a,” and 9 feet from wave front “b,” and still half way between wave front “a” and the original origin.

Summary:
1. By using the "unit" scale of foot/nanosecond, I have incorporated the latency of light and distance all on the abscissa. There is no need to represent time on its own axis!
2. The origin of a second, moving abscissa is being diagrammed concurrently with the expanding edges of the wave front. (It looks like two wave fronts since the light from the strobe actually travels both ways from the strobe.) The second origin is the "moving frame" coordinate system where moving observers traveling in unison at ½ the speed of light are to be diagrammed. (in this example)
3. This is the way Woldemar Voigt and A. Einstein should have diagrammed the so called "Galilean Transform." IMHO, Their diagram only has the strobe itself in the diagram; they do not consider the expanding wave fronts; which is supposed to be the whole purpose of the exercise!

I don't disagree with any of this. It just demonstrates, as I have stated all along, that c (the ship) is not at the centre of the light sphere after an elapsed period of time.

You could easily add d which had the same origin at 0 at the same time as c but travelling (sic) in the opposite direction at 1/2 the speed of light. After 6 nanoseconds it would be positioned at 3. Neither ship c or d is at the centre of the light sphere created by their passing at 0.

!!! Hooray!!! Exactly! Except that they only see the flash right when they pass. They are going too slow to keep up with the expanding sphere. If they were keeping up they would each have to go at the speed of light. But then, they would see nothing because the light would not vibrate.

I'm soo glad you understand this! Do you know how hard it is to get all those letters and numbers to line up using just text?

[Aardwolf]

The number-line below represents two instantaneous (stop-motion, if you will) situations. This is just a re post of the last text/graphic from my last post. The number line here is called the abscissa in a Cartesian coordinate system, otherwise known as the "x" axis. You may be asking where crazy Goldminer is going with the simplistic stuff. Please follow my reasoning to another level of abstraction.

-6____-5_____-4_____-3_____-2_____-1_____0_____1_____2_____3_____4_____5_____6
_a__________________c_____a ______c_________________b_______________________b .

The graph stays the same, but we (you and me if you are following) are going to change a few of the parameters:

1. The "a" and "b" letters are now the leading edge of a light pulse expanding from a strobe light placed at the origin.
2. The scale along the number line is now units of foot/nanosecond; rather than mile/minute, since light has the latency of a foot per nanosecond.
3. The third letter, "c" is the origin of another coordinate system, or number line "moving" at ½ the speed of light.

The red time lapse (representing 2 nanoseconds of elapsed time) and now, the blue. The blue color represents where the expanding wave fronts are located after 6 nanoseconds; wave fronts “a” and “b” traveling @the speed of light from the origin, and “c, another origin,” traveling @1/2 the speed of light from the origin.

1. The elapsed time from the origin (6 nanoseconds) is in blue for the wave fronts and the additional origin, the distance is the distance from the origin, for the wave fronts and the additional origin.
2. The origin traveling @ ½ the speed of light is shown as italic, and has now traveled 3 feet from the origin in the 6 nanoseconds.
3. The relative time and distance between the two blue wave fronts “a” and “b” is 12 feet and 12 nanoseconds, i.e. it would take the wave front “a” twelve nanoseconds to get to wave front “b's” position; traveling @ the speed of light. (It can't do that, I'm just emphasizing the distance between the two separating wave fronts.)
4. origin “c” is now 3 feet from wave front “a,” and 9 feet from wave front “b,” and still half way between wave front “a” and the original origin.

Summary:
1. By using the "unit" scale of foot/nanosecond, I have incorporated the latency of light and distance all on the abscissa. There is no need to represent time on its own axis!
2. The origin of a second, moving abscissa is being diagrammed concurrently with the expanding edges of the wave front. (It looks like two wave fronts since the light from the strobe actually travels both ways from the strobe.) The second origin is the "moving frame" coordinate system where moving observers traveling in unison at ½ the speed of light are to be diagrammed. (in this example)
3. This is the way Woldemar Voigt and A. Einstein should have diagrammed the so called "Galilean Transform." IMHO, Their diagram only has the strobe itself in the diagram; they do not consider the expanding wave fronts; which is supposed to be the whole purpose of the exercise!

I don't disagree with any of this. It just demonstrates, as I have stated all along, that c (the ship) is not at the centre of the light sphere after an elapsed period of time.

You could easily add d which had the same origin at 0 at the same time as c but travelling (sic) in the opposite direction at 1/2 the speed of light. After 6 nanoseconds it would be positioned at 3. Neither ship c or d is at the centre of the light sphere created by their passing at 0.

!!! Hooray!!! Exactly! Except that they only see the flash right when they pass. They are going too slow to keep up with the expanding sphere. If they were keeping up they would each have to go at the speed of light. But then, they would see nothing because the light would not vibrate.

I'm soo glad you understand this! Do you know how hard it is to get all those letters and numbers to line up using just text?

So I assume you agree there is only one single shared origin.

[Aardwolf]

In addition, if I were to introduce c into its own inertial reference frame, xcy, with x placed 2 ft in front of c and y placed 2 ft behind, all moving in the same direction, then after 2 ns from origin you can see from your updated diagram below, that y is within the ab sphere and has already observed the strobe, while x is outside the ab sphere and is yet to observe it.

-6____-5_____-4_____-3_____-2_____-1_____0_____1_____2_____3_____4_____5_____6
_a__________________c_____a ______c_________________b_______________________b
_a_____x____________x ____________y___________y_____________________________b

This is in contradiction to your sentence from page 3 of this thread;

However, all observers in the source inertial frame, fixed at a given distance from the source, will all see the flash at the same time.

[Goldminer]

I'm soo glad you understand this! Do you know how hard it is to get all those letters and numbers to line up using just text?

So I assume you agree there is only one single shared origin.

Your assumption is wrong. The two origins share the same place and time in space; for an instant. If you insist upon another origin where the pulse flashed, but this origin measures each of the other two receding origins' recession velocity at ¼ the speed of light, from that origin I'll grant you that. Now you have three origins. At least in my world!

[Goldminer]

In addition, if I were to introduce c into its own inertial reference frame, xcy, with x placed 2 ft in front of c and y placed 2 ft behind, all moving in the same direction, then after 2 ns from origin you can see from your updated diagram below, that y is within the ab sphere and has already observed the strobe, while x is outside the ab sphere and is yet to observe it.

-6____-5_____-4_____-3_____-2_____-1_____0_____1_____2_____3_____4_____5_____6
_a__________________c_____a ______c_________________b_______________________b
_a_____x____________x ____________y___________y_____________________________b

This is in contradiction to your sentence from page 3 of this thread;

However, all observers in the source inertial frame, fixed at a given distance from the source, will all see the flash at the same time.

I am sorry everyone, sorry Aardwolf: I have been ambiguous with my lettering. There should be a black "c" under the original origin. The blue observers should not be labeled "a" and "b," since they are all together different observers. If you are cursing me for not making sense, I can not blame you.

This scheme makes better sense:

-6____-5_____-4_____-3_____-2_____-1_____0_____1_____2_____3_____4_____5_____6
-b__________________c_____-a _____c______c__________+a______________________+b.

The top line depicts the rays of light expanding each direction from the strobe at 0. Imagine observers at each whole number. Each pair ("-" and "+") are equal distances from the origin, and both at that point in the expansion see the pulse at the same time. As the two directions of the pulse leave these observers, the pulse reaches the next pair of observers in line. The wave fronts of the pulse are traveling away from each other at 2 times the speed of light.

The bottom line represents the second origin (moving @ ½ the speed of light) at three positions in time, color coded. Black is t=0 nanoseconds, Red is t= 2nanoseconds, Blue is t=6 nanoseconds. Moving origin "c" was at +½ foot, at one nanosecond before the flash.

Observers +a and -a are not symmetrical around the origin in "c," Aardwolf. That is the whole point. If you look at the two axis lines they are symmetrical around the original origin. At six nanoseconds "-b" and "+b" are symmetrical around the original origin, but again not around the "c" origin. There is no source in the moving coordinate system for the observers in that system to see.

You have to keep in mind that the "c" coordinate system is moving to the left while the wave fronts are expanding (both to the left and right) in the original coordinate system. This is what the "Galilean Transform" does not consider.

If one does not examine one single light pulse one has no idea where it is in relation to other points of interest. The at rest with the strobe observers at a given distance will always have the same light latency. Moving observers have varying latencies since their distances are continually changing. If one does not understand that separate observers are required in ether/both systems, at each moment, to observe the single pulse, confusion reigns.

If one cobbles up one's own diagram confusion reigns! Hopefully you will forgive the faux pas.

[Goldminer]

I am editing two sentences in the previous post for more clarity and to remove some ambiguity:

In addition, if I were to introduce c into its own inertial reference frame, xcy, with x placed 2 ft in front of c and y placed 2 ft behind, all moving in the same direction, then after 2 ns from origin you can see from your updated diagram below, that y is within the ab sphere and has already observed the strobe, while x is outside the ab sphere and is yet to observe it.

-6____-5_____-4_____-3_____-2_____-1_____0_____1_____2_____3_____4_____5_____6
_a__________________c_____a ______c_________________b_______________________b
_a_____x____________x ____________y___________y_____________________________b

This is in contradiction to your sentence from page 3 of this thread;

However, all observers in the source inertial frame, fixed at a given distance from the source, will all see the flash at the same time.

I am sorry everyone, sorry Aardwolf: I have been ambiguous with my lettering. There should be a black "c" under the original origin. The blue observers should not be labeled "a" and "b," since they are all together different observers. If you are cursing me for not making sense, I can not blame you.

This scheme makes better sense:

-6____-5_____-4_____-3_____-2_____-1_____0_____1_____2_____3_____4_____5_____6
-b__________________c_____-a _____c______c__________+a______________________+b.

The top line depicts the rays of light expanding each direction from the strobe at 0. Imagine observers at each whole number. Each pair ("-" and "+") are equal distances from the origin, and both [ unique pairs of observers regardless which system] at that point in the expansion see the pulse at the same time. As the two directions of the pulse leave these observers, the pulse reaches the next pair of observers in line. The wave fronts of the pulse are traveling away from each other at 2 times the speed of light.

The bottom line represents the second origin (moving @ ½ the speed of light) at three positions in time, color coded. Black is t=0 nanoseconds, Red is t= 2nanoseconds, Blue is t=6 nanoseconds. Moving origin "c" was at +½ foot, at one nanosecond before the flash.

Observers +a and -a are not symmetrical around the origin in "c," Aardwolf. That is the whole point. If you look at the two axis lines they are symmetrical around the original origin. ["they" is referring to the observers in both systems: both the fixed with the source observers; and the "moving observers" except the moving observers see the duration of the pulse being shorter on the right side of the source: longer on the left side. Both sets of observers at a given point in nanosecond time are looking at the same wavefront edge in the source system]

At six nanoseconds "-b" and "+b" are symmetrical around the original origin, but again not around the "c" origin. There is no source in the moving coordinate system for the observers in that system to see. The "c" origin becomes a ghost point after the flash.

You have to keep in mind that the "c" coordinate system is moving to the left while the wave fronts are expanding (both to the left and right) in the original coordinate system. This is what the "Galilean Transform" does not consider.

If one does not examine one single light pulse one has no idea where it is in relation to other points of interest. The at rest with the strobe observers at a given distance will always have the same light latency. Moving observers have varying latencies since their distances are continually changing. If one does not understand that separate observers are required in ether/both systems, at each moment, to observe the single pulse, confusion reigns.

If one cobbles up one's own diagram confusion reigns! Hopefully you will forgive the faux pas.

Aardwolf: I assume your added observers are "in" the moving system. If so, the blue "x" on the left will see the flash at 5 nanoseconds from the initial pulse; the red "x" will see the pulse at 3 nanoseconds from the initial pulse; both of your "y" observers will see the pulse at 1 nanosecond from the initial pulse. None of the observers in either system get to see the pulse more that once.

[Goldminer]

I am editing two sentences in the previous post for more clarity and to remove some ambiguity:

In addition, if I were to introduce c into its own inertial reference frame, xcy, with x placed 2 ft in front of c and y placed 2 ft behind, all moving in the same direction, then after 2 ns from origin you can see from your updated diagram below, that y is within the ab sphere and has already observed the strobe, while x is outside the ab sphere and is yet to observe it.

-6____-5_____-4_____-3_____-2_____-1_____0_____1_____2_____3_____4_____5_____6
_a__________________c_____a ______c_________________b_______________________b
_a_____x____________x ____________y___________y_____________________________b


This is in contradiction to your sentence from page 3 of this thread;

However, all observers in the source inertial frame, fixed at a given distance from the source, will all see the flash at the same time.

I am sorry everyone, sorry Aardwolf: I have been ambiguous with my lettering. There should be a black "c" under the original origin. The blue observers should not be labeled "a" and "b," since they are all together different observers. If you are cursing me for not making sense, I can not blame you.

This scheme makes better sense:

-6____-5_____-4_____-3_____-2_____-1_____0_____1_____2_____3_____4_____5_____6
-b__________________c_____-a _____c______c__________+a______________________+b.

The top line depicts the rays of light expanding each direction from the strobe at 0. Imagine observers at each whole number. Each pair ("-" and "+") are equal distances from the origin, and both [ unique pairs of observers regardless which system] at that point in the expansion see the pulse at the same time. As the two directions of the pulse leave these observers, the pulse reaches the next pair of observers in line. The wave fronts of the pulse are traveling away from each other at 2 times the speed of light.

The bottom line represents the second origin (moving @ ½ the speed of light) at three positions in time, color coded. Black is t=0 nanoseconds, Red is t= 2nanoseconds, Blue is t=6 nanoseconds. Moving origin "c" was at +½ foot, at one nanosecond before the flash.

Observers +a and -a are not symmetrical around the origin in "c," Aardwolf. That is the whole point. If you look at the two axis lines they are symmetrical around the original origin. ["they" is referring to the observers in both systems: both the fixed with the source observers; and the "moving observers" except the moving observers see the duration of the pulse being shorter on the right side of the source: longer on the left side. Both sets of observers at a given point in nanosecond time are looking at the same wavefront edge in the source system]

At six nanoseconds "-b" and "+b" are symmetrical around the original origin, but again not around the "c" origin. There is no source in the moving coordinate system for the observers in that system to see. The "c" origin becomes a ghost point after the flash.

You have to keep in mind that the "c" coordinate system is moving to the left while the wave fronts are expanding (both to the left and right) in the original coordinate system. This is what the "Galilean Transform" does not consider.

If one does not examine one single light pulse one has no idea where it is in relation to other points of interest. The at rest with the strobe observers at a given distance will always have the same light latency. Moving observers have varying latencies since their distances are continually changing. If one does not understand that separate observers are required in ether/both systems, at each moment, to observe the single pulse, confusion reigns.

If one cobbles up one's own diagram confusion reigns! Hopefully you will forgive the faux pas.

Aardwolf: I assume your added observers are "in" the moving system. If so, the blue "x" on the left will see the flash at 5 nanoseconds from the initial pulse; the red "x" will see the pulse at 3 nanoseconds from the initial pulse; both of your "y" observers will see the pulse at 1 nanosecond from the initial pulse. None of the observers in either system get to see the pulse more that once.

So, Aardwolf, where is your condescending question asking: "WTF Goldie, where is the "c" origin if the blue "x" on the left is seeing the left going pulse at 5 nanoseconds, etc? Well Aardwolf, I am going to put my words in your mouf and change your diagram a little bit for clarity:

I am assuming that your new line is still moving at ½ the speed of light towards the left:

-6____-5_____-4_____-3_-2½_-2_-1½_-1_-½__0_____1_____2_____3_____4_____5_____6
-b__________________c_____-a ______c_____c__________+a______________________+b
-b____-z____________-x __c______c___-y_c__c_____y__________+x__________+z_____+b

Your "-x" is seeing the edge of the pulse at 3 feet and 3 nanoseconds from the strobe. This just happens to be where the origin "c" is when the two "b" observers see the edge of the pulse at 6 feet and 6 nanoseconds from the strobe. The blue origin "c" moves to position -3 . . . 3 nanoseconds after "-x" sees the light flash. The blue origin "c" does not see the light flash; none of the successive "c's" see the light flash except when "c" is at the 0 origin with the strobe. As "c" moves left, for odd numbered observers, it lands on the ½ intervals between the integers of the number-line, which is why I was trying to use just even integers. Less congestion.