apples and apples

[Goldminer]

Don't want to put words in any other mouth, but I think Mr. Waterman is demanding that before one applies Mathematics to reality, since it is merely a language, one must make sure the language's syntax and order are proper. Computer programing is done with "programing languages." The assembler or compiler is ruthless when it comes to running the program. So it is with math and reality.

[woldemar]

Goldminer,

Yes, I would agree with your words. I had hoped to prep others with this discussion in order to broach this more important issue ...
http://watermanpolyhedron.com/G1W1c.html

I wonder if anyone would care to respond....with their opinion...regarding any or all of the following...

1 - can a coordinate transformation be done with just one coordinate system ?

2 - does it matter if a representative point, say as a marker, on a coordinate system, is placed either on the line
( represented as a ruler ) or beside the actual line, in order to portrait the actual location of the point on that line ?

3 - is it possible to have coincident coordinate systems with a point in one but not the other ?

steve waterman ( woldemar )

[Goldminer]

Woldemar asks:

"I wonder if anyone would care to respond....with their opinion...regarding any or all of the following..."

"1 - Can a coordinate transformation be done with just one coordinate system?"
Goldminer: Yes, within the coordinate system, I suppose.

"2 - Does it matter if a representative point, say as a marker, on a coordinate system, is placed either on the line
( represented as a ruler ) or beside the actual line, in order to portrait [portray?] the actual location of the point on that line?" Goldminer: Not sure what your point is, but this is still a fairly free country. (How is it in Canada?) Besides, nobody is watching. So I'll go on record with "yes."

"3 - Is it possible to have coincident coordinate systems with a point in one but not the other?"
Goldminer: Obviously I do. (see my posts at "Silly Einstein" in this same "Future of Science" thread here) By the way, I would very much respect your criticism of my thoughts on that thread.

[Goldminer]

I have an unsolicited admiration and respect for Mr. Waterman. He is one of the world's great polymaths. However, he will probably not be remembered in history, as was his avatar, Woldemar Voigt. Voigt should go down as the perpetrator of the faulty "Galilean Transform" that is the basis of Einstein's "relativistic triangle."

One idea that you should obtain from Waterman's "Challenge" is this: If the origin of a given coordinate system moves to the right in the opposite system, in the opposite system, the original system moves to the left. Now, someone thinking this through might conclude that the two systems are actually moving relative to each other at twice the given speed, especially if both systems are drawn statically in one diagram. Of course that is not the case. Another is that the pairs of coordinates defining "points" fixed in one system, when properly transformed, will appear as fixed point coordinate pairs in the other system at varying distances from the origin there. The very purpose of the transform is to match corresponding points in each system, thereby doing away with Einstein's "simultaneity" problem. (simplifying the problem, both axes should be denominated in something like light-nanoseconds per foot,) rather than placing time on an axes that actually duplicates one of the existing three axes. (distance and time are actually only two ideas, not four. Space is denominated with three parameters, time with varying parameters depending upon the definition with which one is working. Google time and see how many definitions there actually are!

At first glance, one might think that there is no simultaneity between systems, but it is exactly this simultaneity that places those points in the opposite system. (I'm stressing the point twice, since it is overlooked) The apparent stretching of some of the coordinate pair positions is not the stretching of space or changing the passage of time. The perpendicularity of the system's axes needn't and shouldn't be skewed with respect to the opposite system. Einstein's insistence that there is a diagonal going pulse of light that does not appear in the original system, and further requiring the imagined pulse be limited to the "speed of light," simply enhances the mystery he wants to produce.

[Goldminer]

The last post of mine was getting a bit unwieldy. Anyhow, another point I wish to expose is that the source/origin can never observe the expanding light pulse emitted there. Only observers/detectors at various distances in that system have a one time opportunity to do so.

The same is true for the opposite system's origin. It cannot observe anything but the initial flash of light before it expands. Any observer that wishes to see the pulse expanding in the direction of motion of the origin, must locate further ahead of the origin in the direction of motion. This has nothing to do with being in the future of anything. The detector/observer is just seeing the light pulse from the receding source, just as detectors/ observers on the other side of this origin are seeing the pulse from the approaching source. Einsteinians interpret these facts as future/past events. Duh!

[Goldminer]

As I have pointed out in the Silly Einstein thread and the Re: Relativity Linear Thread:

The "source," that is, the emitter, or transmitter (something like a strobe tube) of the light pulse, can actually exist in only one or the other "frame." It cannot actually be at a given distance from the origin in both frames, the origins of which are separating, unless it is very elastic; in which it will be stretched very thin!

What does the source do? When it pulses, it starts an expanding sphere light wave front, centered upon the source, which is located in the source frame.

When can observers see the pulse? Only when the pulse arrives at the observer. It matters not whether the observer is moving in relation to the source, or at a fixed distance from the source. (A "moving observer," and a "fixed with the source observer" can simultaneously observe the same wave front, at the same time and place in space, just as the two origins can be coincident at the time of the initial pulse . . . Well, let's say almost the same place, otherwise they would crash!)

What is your point? My point is that in the Galilean Transform, the one that incorporates the expanding wave front, there is no "reverse transform." It is a one way, source to detector situation.

Then why do "Einsteinian relativity deniers" keep insisting that what happens in one frame is true for the other frame too? Because the highlighted portion of the post above is true for any source in any frame. All of the "clock" and "elastic rod" buggabo is just Einstein's side show; a distraction.

So, all the discussion about whether the "event" can be "transformed" from one frame into another or many others, is just a bunch of clatter; a bunch of empty cans trailing the just married limousine leaving the wedding with Einstein and his newly wedded Harem of Happy Followers.

.

[Goldminer]

Mathematicians can make all the rules concerning their constructs that they wish, the caveat being that said constructs must be applicable to observations, evidence, and logic of real physical existence. If "x" represents an "event" the cause of the event matters as to whether "x" is going to further the match of the mathematical construct to reality.

The physical object that produces the "event" cannot be transformed, as in being in two physical places at once. The expanding light sphere centered upon the light bulb, arc or strobe cannot magically appear simultaneously centered in two or more places either.

Trying to extract mathematical formulas from diagrams that do not diagram the expanding sphere of light cannot accurately relate anything about the finite speed of light in said formulas.

[Goldminer]

with due respect to the author of this post

I am going to show some common errors of reasoning with respect to the "Galilean Transform:"

Physical observers are considered to be surrounded by a reference frame which is a set of coordinate axes in terms of which position or movement may be specified or with reference to which physical laws may be mathematically stated.
An event is something that happens independently of the reference frame that might be used to describe it. Turning on a light or the collision of two objects would constitute an event.

In order to make Einstein's postulates work, (They are unworkable) most people trying to explain how to understand the theory by attempting to illustrate the "event" as not belonging to a "frame of reference," as in the above quote.

Secondly, the Special Theory of Relativity is concerned with the finite speed of light. Thus his inclusion of "or the collision of two objects" is a rabbit trail.

1) Inertial system:
they are systems which are in a uniform motion relative one to another.

2)The proper system:
An inertial system which contains the observer at rest.

3)An event:
it is an occurrence at certain position and certain time. (x,y,z,t)

4) the invariance property:
it's invariant under transformation between s & s'.
f(x',y',z',t')=0
after transformation
f(x,y,z,t)=0

The error in reasoning is in his definition of "Proper System" (#2):

"An inertial system which contains the observer at rest." The error: At rest to what? IMHO, his only choice is that the said observer is at rest with the "event."

the definition of "an event" (#3)

"It is an occurrence at certain position and certain time." (x,y,z,t)" The error: He doesn't explicitly state to which frame of reference said occurrence belongs. From his choice of coordinates; he implies that the "event" belongs to the un-primed coordinates "(x,y,z,t)," which according to his diagram would be frame O.

and #4) the invariance property:

Suppose there is a small event, such as a light being turned on

He recognizes that the subject is a "light being turned on," but ignores the expanding wavefront centered upon the light bulb; which is the actual subject that the Special Theory of Relativity should explore.

Transforming one frame to another while ignoring the nebulous "light bulb event" and its expanding wavefront accomplish nothing except silliness.

[Goldminer]

Mathematicians can make all the rules concerning their constructs that they wish, the caveat being that said constructs must be applicable to observations, evidence, and logic of real physical existence. If "x" represents an "event" the cause of the event matters as to whether "x" is going to further the match of the mathematical construct to reality.

The physical object that produces the "event" cannot be transformed, as in being in two physical places at once. The expanding light sphere centered upon the light bulb, arc or strobe cannot magically appear simultaneously centered in two or more places either.

Trying to extract mathematical formulas from diagrams that do not diagram the expanding sphere of light cannot accurately relate anything about the finite speed of light in said formulas.

When transforming a "point" fixed to the origin of a coordinate system into another coordinate system in relative motion with said system, the "point" becomes a line (that is, the "point" becomes a series of points.). If the motion is rectilinear, the line is straight; if the vector of said coordinate system motion is changing, the line tracking the point in the opposite coordinate system is no longer straight.

If we postulate that the second coordinate system also has a point fixed to the origin in it, this second "point," when transformed into the first coordinate system; will become a line of points in the first coordinate system.

If both transforms are done with the same time period, both transformed lines will be the same length, regardless of how fast said motion between coordinate systems is postulated to be. Sorry, Einstein!

[Goldminer]

Mathematicians can make all the rules concerning their constructs that they wish, the caveat being that said constructs must be applicable to observations, evidence, and logic of real physical existence. If "x" represents an "event" the cause of the event matters as to whether "x" is going to further the match of the mathematical construct to reality.

The physical object that produces the "event" cannot be transformed, as in being in two physical places at once. The expanding light sphere centered upon the light bulb, arc or strobe cannot magically appear simultaneously centered in two or more places either.

Trying to extract mathematical formulas from diagrams that do not diagram the expanding sphere of light cannot accurately relate anything about the finite speed of light in said formulas.

When transforming a "point" fixed to the origin of a coordinate system into another coordinate system in relative motion with said system, the "point" becomes a line (that is, the "point" becomes a series of points.). If the motion is rectilinear, the line is straight; if the vector of said coordinate system motion is changing, the line tracking the point in the opposite coordinate system is no longer straight.

If we postulate that the second coordinate system also has a point fixed to the origin in it, this second "point," when transformed into the first coordinate system; will become a line of points in the first coordinate system.

If both transforms are done with the same time period, both transformed lines will be the same length, regardless of how fast said motion between coordinate systems is postulated to be. Sorry, Einstein!

These "transformations" can be done with a pair of regular photographic cameras. The setup for one coordinate system to the other is to have a light source at rest with the camera and in the center of the camera's view. This light source will be the "event" in the un-primed coordinate system (the un-primed event.)

The other camera will photograph the opposite, primed coordinate system. This coordinate system will have a light source at rest with this camera and in the center of this camera's view. This light source will be the "event" in the primed coordinate system.

To make the setup seem more relative, both systems should be moveable. For those who can think a bit more abstractly, only one system need be mobile (be able to move past the other camera and "event," in a straight line.)

In a dark room, the "camera coordinate systems" move past each other. Each camera's shutter is open. At t=0. both sources turn on. At some later time both the sources turn off, and then the shutters close.

The picture taken in this manner will show a point of light for the "at rest with the camera" event; and a line of light for the "event" in the opposite coordinate system.

The scenario is a bit simplified, but hopefully those interested will follow the substance of the demonstration.

The event and the observation of the event are not interchangeable, the camera doesn't emit light, and the source doesn't take the picture. One source cannot exist in both coordinate systems (be both fixed in one system and the other system at the same time.) Each source can however, be seen in both pictures; each picture will show the "at rest source" as a point, and the "moving source" as a line.

Many ideas can be extracted from this demonstration. For now, I'll leave it at this: the whole idea of relativity is really just this simple. For those who didn't think the "Galilean Transformation" made much sense, this is where "Einstein's Train" leaves the tracks. For those of you who thoroughly understand his presentation, I think you are bluffing.

[Goldminer]

If you do your own research on Galileo's transform, I believe you will find the various authors (there are thousands of them published on the internet) have a real problem with "point P" or "the event." Usually one ambiguous sentence is devoted to it, or sometimes it is not even mentioned. Sometimes it is not even included in the diagram of the coordinate systems!

The reality is that the point (representing a source) must remain a fixed distance from the origin in one of the coordinate systems. It then becomes a series of points in the opposite system, as time (and motion) separate the two coordinate systems. Further, the "point" is not the subject of relativity, since Relativity is mainly about the finite speed of light. The real subject is the expanding sphere of light, centered upon the source! This subject is never even anticipated in any of the said "transformation diagrams."

Ask yourself why the subject of "Relativity" fails to make common sense!

Herbert Dingle (Do a search) vaguely understood the point I have made clear (I hope). Dingle's argument became sidetracked by trying to use Einstein's clocks. The argument is moot in Dingle's favor, when one realizes that observers, whether in motion or not relative a given source, if only momentarily, can be at the same place in space (or very close by, to avoid collision) at the same time (simultaneously). In this manner, both observers observe the same spherical wave front, centered upon the same source, at the same time.(No latency between observers, no clocks necessary.)

[Goldminer]

Rather than the Voigt/Einstein "Galilean Transform," the expanding sphere of radiation must be considered in the transform diagram, before drawing any mathematical conclusions. With the sphere added to the diagram, Einstein's diagonal going "photon" disappears; leaving no Pythagorean triangle with which to construct his fantasy.

With the expanding sphere added, one can see how to construct relatively simple experiments to prove exactly where the said expanding sphere exists in both the "at rest with the source frame", and any "moving frame."

[303vegas]

braeburns are my favourite apple.

maybe you should all get out more.

i notice that the manchester museum has an alan turing exhibition. do you think they sell toffee apples in the gift shop?

[Goldminer]

Braeburns are my favourite apple.

Maybe you should all get out more.

I notice that the Manchester Museum has an Alan Turing exhibition. Do you think they sell toffee apples in the gift shop?

Do you place yourself in the "at rest with the source frame," or one of the "moving frames?" After all, it was your fellow patriot Newton that got the conversation started by sitting under the apple tree!

Get out? How about thrown out?

The mention of Alan Turing (does he appear waxed or stuffed?) takes me back to my several readings of Gödel, Escher, Bach: An Eternal Golden Braid by Douglas R. Hofstadter. You might enjoy the read.

Braeburn's not a bad apple, but I'm the Red Cinnamon Candy Apple kind a guy. Doan'cha'no?

[Goldminer]

Rather than the Voigt/Einstein "Galilean Transform," the expanding sphere of radiation must be considered in the transform diagram, before drawing any mathematical conclusions. With the sphere added to the diagram, Einstein's diagonal going "photon" disappears; leaving no Pythagorean triangle with which to construct his fantasy.

With the expanding sphere added, one can see how to construct relatively simple experiments to prove exactly where the said expanding sphere exists in both the "at rest with the source frame", and any "moving frame."

Read the entry at FQXI A Logical Analysis of Albert Einstein's Mirror-Light-Clock Gedankin

The mirror gedanken is such an experiment, and allows both approaching and receding detectors to be graphed in a small space. My original spherical diagrams are available via a PM to me.

I would post the diagrams here but they are to scale and too big for the forum format.