Galileo Transform:
10/3/2008 9:52 AM
Curt Youngs

Steve Waterman has pointed out that the Galileo transform is a transform of a point to a line segment. http://www.network54.com/Forum/304711/thread/1222694974/last-1222983038/x+%27++-+x+-+vt+is+challenged+on+a+mathematical+basis Apparently this is hard to digest.

He suggested to me that I put his idea into my own words. Doing so will demonstrate whether I have grasped his idea or not. So, here goes:

Steve approaches things from a mathematical viewpoint. I have to get the physical understanding down, then the math dawns on me.

Here is my understanding: you see the Galileo Transform in action everyday all a round you. The print head in your printer is the moving frame point. The stationary stationery (play on words-paper) is the fixed frame. A time duration distance of a point in the printer head ejecting ink transforms a point into a line segment on the paper as it moves in the stationary frame.

The road striper machine is the moving point in the moving frame, converting or transforming a pot of paint into the line segment down the middle of the stationary road.

Again: the stationery (do you suppose there is a connection in the similarity of the two words?) just lays there as you pick up your ball point pen in the moving frame and transform a point into a line segment on the stationery.

From my train Gedankin:

“A femto pulse laser can produce a very short pulse of light. This experiment requires a short pulse, since at relativity speed, the spot normally thought to be produced, will instead be detected as a line: Shorter pulse; shorter line.”

I have had the understanding for quite a while. Mentioned it several times. Like Steve’s more rigorous approach, the idea passes notice. Hey, it has to be more complicated than that, Its in the physics books.

I'm sitting in my living room.


The TV is 11 feet away from me.

I move from the couch to the recliner.

The TV is 4 feet away from me.

4 = 11 - vt.

I moved roughly 1 foot per second for 7 seconds.

4 feet = 11 feet - (1 fps*7 s).


Physics doesn't have to be complicated.

So you moved your couch, or was it the divan? Or the sofa, or the Chesterfield? Is it better now?

Look at a photograph time exposure. All the stationary things look just fine, all the moving things are lines.

Now look at a photograph of a bird flying. It looks like a bird. everything else is blurred into lines.

Why would Galileo go to the trouble of writing some thing as complicated as you propose, and what is the purpose for doing so?

He is describing how a point turns into a line. Duh!

If you transform a point into another point what have you accomplished?

I moved.

I moved from the couch to the chair.


I transformed my coordinates in a Gallilean manner.

Ignorance is bliss for ya, I surmise, not being in that state myself.

Simple understanding is bliss.

:P

Just to attempt to reiterate, because I so hate having a point left misunderstood.

I am translating the stationary coordinates around me, from my original frame of reference, to my new frame of reference.

They are not moving.

I am.


You can, if you so choose, describe the transformation from the point of view of the TV, but since the TV and the couch and the chair remain in the same orientation, it would look the same.

"That guy who watches me moved from the couch to the chair."


I described a rotation of the universe about my location, I went from the couch.

Couch: S= 0,0

Then I moved to the Chair.

Chair: S'= 0,0


I related this motion to the TV, as it was stationary relative to the couch and the chair.

When I was sitting on the Couch.

TV: S= 11,0

When I moved to the Chair.

TV: S'= 4,0


Now I compared the coordinates I described the TV with.

S' 4,0 = S 11,0 - the speed I moved times how long I moved.

I moved 1 foot per second for 7 seconds.


S' 4,0 = S 11,0 - 1 fps * 7 s

I related my movement to a point which was stationary in the two frames I translated between.

I don't know why this is so confusing.

It isn't about the TV, or the Chair, or the Couch.

It is about my movement, and the new relations I describe based on that movement.

Curt: Look at a photograph time exposure. All the stationary things look just fine, all the moving things are lines.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

I am the line.

I am the moving thing.

I moved at v rate for t time.

I can now relate how I described any point in x to any point in x'.

Max, If you are the line you may be in the stationary frame. If you are, the point that makes the line is in the moving frame.

Or the reciprocal: If you are the line in the moving frame, the line is stationary in the moving frame, except the end with the moving point. The point that seems to be moving is in the stationary frame.

In either frame, the length of the line is the distance moved. If you were watching the line form in which ever frame, and clocked it's progress, you could determine it's rate of progress.

Your v rate for t time is a distance. It is the length of the line.

The Galileo transform transforms a point into a line, just like Mr. Waterman has tried to explain to you in oh so many ways.

I'VE BEEN EXPLAINING IT TO HIM THAT THE PURPOSE OF THE TRANSFORM IS FROM ONE ORIGIN TO ANOTHER.

Your talk about a point to a line is redundant.

It is a point translated to another point, the line is the length of the translation.

The point remains a point.


Just because you misunderstand that, don't assume everyone does.

Steve isn't explaining anything to me, other than what he mistakenly thought it meant.

I've been explaining to him what the purpose of the transformation is, and why his assumption has no meaning.


Describe the TV after I've moved to the chair.

It is 4,0, 4 feet away in the x' coordinate system.

It is 11 feet in the x coordinate system to the couch.

I AM NOT AT THE COUCH THOUGH.

I AM AT THE CHAIR.

THAT IS WHY HIS ARGUMENT ABOUT IT BEING WRONG IS INVALID.

RAAARRRRRGGHHH!

lol

Sorry, just had a rant building up after your matter-of-fact statement assuming I've misunderstood the transformation.

Steve was wrong about the purpose of the transformation, he overlooked that once you transform it with vt, arguing about a -vt retransform is silly.

Yes, the TV is 11 feet away from the couch.

I am not there any longer, I have moved.

If you want to treat it as two observers, then the person on the couch will describe it as 11,0 to the TV.

The person on the chair will describe it as 4,0 to the TV.

If you cannot understand why the person on the chair won't claim it is 4,0 and 11,0 from the chair to the TV, then perhaps you shouldn't be arguing about the rightness or wrongness of a physical theory.

Velocity times time is a distance. DO THE MATH. YOU can call it a velocity. It ain't. Galileo didn't have a TV.

Yes, it's a distance.

The distance from the Couch to the Chair.


Galileo had a Telescope, a Bed, and a Desk.


From his Bed, it is 11 feet to the Telescope.

he moves 1 foot per second for 7 seconds towards the Telescope and reaches his Desk.

It is 4 feet from his Desk to his Telescope.

4 = 11 - (1*7)
x' = x - vt


When he is at his Desk, he isn't going to give two absicca for his Telescope. The telescope is at (4,0) in the S' frame at his Desk.

He wouldn't then claim that his Telescope was also (11,0), except to say that from his Bed, the origin of the S frame, it is (11,0) to the telescope.


Steve was arguing that the Telescope had two absiccal (x) values (4 and 11) in the S frame.

That is where he made a mistake, and what I've been trying to explain ever since.

Do you not see why that is wrong?

The telescope isn't 4 feet away AND 11 feet away from the Bed.

The movement is a line. Did he mysteriously disappear at one place and reappear at another? Mathematically, the transform is from a point to a line. Doesn't matter what you want it to be. It is a line. Heads I win, tails you lose.

The movement is a line. Did he mysteriously disappear at one place and reappear at another? Mathematically, the transform is from a point to a line. Doesn't matter what you want it to be. It is a line. Heads I win, tails you lose.

...


The transform is from Frame S, to Frame S'.

Yes, there is a line between those two frames, good observation.

The line is not the reason for the transformation.


When he moved from Frame S, his Bed, to Frame S', his Desk, did he turn into Spaghettalileo?


Doesn't matter that you misunderstood what it is meant to be. Galileo is not a line. It isn't a matter of winning or losing, I'm trying to win by helping you learn something, and I can only lose by failing at it.

He Was Italian, NO?

Well played.

That still doesn't change the question, when he moved from Frame S to Frame S', does he become a line?

When he stops in Frame S', is he better described as a line, or a point?


Think about what the transformation is describing, and the math turns into a window.

that a point in one frame leaves a line in another is eye-opening for me. Too bad you can't enjoy the scene.

When two points join they become a "line" and they are no longer "points" they become the "ends" of the line; are there "points" on that "line"? Yes, but they are a "point" between the "ends", the new "point" can designate a position on the original "line" or, it can be place at the end of the "line" which would make it the new "end" of the now longer "line"............

bob s

Since we're discussing motion (not necessarily relativistic,) its nice to see "from whence" and "to whence." When there is motion, the point at the moving end of the line does not stop.

I suppose I should have asked Max: Where is the motion in his graph? He thinks it removes motion from the Galilean transform to simplify vt to d. The laser equipment that I sell uses a rotating beam of laser light. Do you know what? the rotating point of laser light becomes a line of laser light around the room. Imagine that.

I can picture Max continuously pushing his couch around the room, to prove My point.

His is a "spherical" room no doubt, that way it would follow his "line" of reasoning if you get my "point", and I think that you do! Anybody care to add their "point"?

bob s

My motion was explained, you must have missed it.

Galileo walked at 1 foot per second for 7 seconds from his Bed to his Desk.

Curt: I suppose I should have asked Max: Where is the motion in his graph? He thinks it removes motion from the Galilean transform to simplify vt to d. The laser equipment that I sell uses a rotating beam of laser light. Do you know what? the rotating point of laser light becomes a line of laser light around the room. Imagine that.


Ah, I never said to simplify vt to d, I was arguing that it loses a key portion of the utility of the transformation.

Without the time order, you sit there thinking "hell, I can just reverse this, and it doesn't make sense."

With the time order, you sit there thinking "hell, if I reverse this, it doesn't make sense."

Max™ said:

"Without the time order, you sit there thinking "hell, I can just reverse this, and it doesn't make sense."

"With the time order, you sit there thinking "hell, if I reverse this, it doesn't make sense."

Curt said:

"Hell, Max™ doesn't make sense. Max™, go wash your face."

Very funny, do you have an actual objection to my logic though?

:P

Max™ said: "Very funny, do you have an actual objection to my logic though?

:P"

Curt said: I don' understand the ":P". Colon has to do with the intestinal tract, and P has to do with the urinary tract. Two different things. Do you have a transform you wish to unveil?

Max™ said:

"Without the time order, you sit there thinking "hell, I can just reverse this, and it doesn't make sense."

"With the time order, you sit there thinking "hell, if I reverse this, it doesn't make sense."

Curt said: I don't know what to think of the above. Maybe you made a typo. Maybe you just like to type, to hear yourself type.

I was stating that if you ignore the fact that S > S' is a transformation including time (S is in the past relative to S'), you can make it very confusing by reversing parts of it.

Curt: Here is my understanding: you see the Galileo Transform in action everyday all a round you.

cinci: Well you have better eyes than most. Since most of the things around you don't travel at much more than 100mph, then you apparently can see the difference 1 X (the length of a car) and .9999999614975 X (the length of a car). Is that with glasses or without them?
****************************

Actually Cinci you're a little confused.

He's just talking about the flat Galilean.


TECHNICALLY, the Galilean IS wrong... DUN DUN DUN!


It isn't wrong for the reasons claimed here though.


It is wrong because you have to apply the Lorentz transformations to make it totally accurate.

I believe the Curt guy was talking about the Galileo Transform, if I am not mistaken. What has that to do with .999999999 c ???????

You must have a hair trigger. Try shaving with Ocam's razor, for a really close shave!