Search found 1602 matches

by steve waterman
Sun Jul 28, 2013 1:34 pm UTC
Forum: General
Topic: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x-d?
Replies: 908
Views: 172371

Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

What the hell is M(x,y,z)? Manifolds aren't functions; they get mapped to , they aren't maps themselves. M(x,y,z) are the inherent coordinates from S(x,y,z) mapped to P in the manifold. M'(x',y',z') are the inherent coordinates from S'(x',y',z') mapped to P in the manifold. This is meaningless. MEA...
by steve waterman
Sun Jul 28, 2013 12:22 pm UTC
Forum: General
Topic: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x-d?
Replies: 908
Views: 172371

Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

What the hell is M(x,y,z)? Manifolds aren't functions; they get mapped to , they aren't maps themselves. M(x,y,z) are the inherent coordinates from S(x,y,z) mapped to P in the manifold. M'(x',y',z') are the inherent coordinates from S'(x',y',z') mapped to P in the manifold. added - Thanks to all th...
by steve waterman
Sun Jul 28, 2013 12:04 pm UTC
Forum: General
Topic: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x-d?
Replies: 908
Views: 172371

Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Image

added -
ucim - real nice feedback on my list of questions. Thank you so much for the nice clear answers.

Since we are given S(x,y,z), then z generically, ( the third coordinate ) is mathematically called the applicate.
by steve waterman
Sat Jul 27, 2013 10:36 pm UTC
Forum: General
Topic: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x-d?
Replies: 908
Views: 172371

Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Just checking to see if these group of statements below are correct... In a Cartesian coordinate system, given S(x,y,z), the x axis, y axis, and z axis intersect at S(0,0,0). given S(x,y,z)....Physics takes x, by itself, to mean the x axis. given S(x,y,z)....Mathematics traditionally takes x, by its...
by steve waterman
Sat Jul 27, 2013 5:00 pm UTC
Forum: General
Topic: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x-d?
Replies: 908
Views: 172371

Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

it remains true that x = x', even if the two systems are no longer spatially coincident ( CASE 2). No. That's the whole point. Also, the purpley dashed lines are not axes . They are simply visual aids to help people locate the value of the coordinates in different systems. Follow a purpley dashed l...
by steve waterman
Sat Jul 27, 2013 2:58 pm UTC
Forum: General
Topic: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x-d?
Replies: 908
Views: 172371

Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

http://watermanpolyhedron.com/images/coordinates11.png ADDED- GIVEN S(x,y,z) spatially coincident with S'(x',y',z') and x = x', y = y', z = z', ( CASE 1) where x can mean either the abscissa x or the x axis, it remains true that x = x', even if the two systems are no longer spatially coincident ( C...
by steve waterman
Sat Jul 27, 2013 2:39 pm UTC
Forum: General
Topic: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x-d?
Replies: 908
Views: 172371

Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

GIVEN S(x,y,z) spatially coincident with S'(x',y',z') and x = x', y = y', z = z', where x can mean either the abscissa x or the x axis, it remains true that x = x', even if the two systems are no longer spatially coincident. If x and x' are the coordinates in two systems of the same point, then thi...
by steve waterman
Sat Jul 27, 2013 2:27 pm UTC
Forum: General
Topic: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x-d?
Replies: 908
Views: 172371

Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

x' =x -vt refers to the space and time coordinates of A SINGLE EVENT. NOT A POINT IN SPACE OVER TIME. Also, steve. Suppose I said that when y = 0, then x = x'. Does that always mean that the x and x' axis are in the same place.? I do not seem to be making this clear. MY CHALLENGE... NO EVENTS. NO T...
by steve waterman
Sat Jul 27, 2013 1:44 pm UTC
Forum: General
Topic: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x-d?
Replies: 908
Views: 172371

Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

AGAIN. NO time, no physics, just case 1 and case 2... http://watermanpolyhedron.com/images/coordinates7.png CASE 1 spatially coincident* x = the x axis? or abscissa x? CASE 2 spatially non-coincident* your initial depiction displays a common x/x' axis... so x axis = x' axis in case 2? * http://www.t...
by steve waterman
Fri Jul 26, 2013 11:09 pm UTC
Forum: General
Topic: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x-d?
Replies: 908
Views: 172371

Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

http://mathworld.wolfram.com/Abscissa.html The x- (horizontal) coordinate of a point in a two dimensional coordinate system. Physicists and astronomers sometimes use the term to refer to the axis itself instead of the distance along it. That is big part of the problem , your x sometimes means the x...
by steve waterman
Fri Jul 26, 2013 7:09 pm UTC
Forum: General
Topic: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x-d?
Replies: 908
Views: 172371

Re: We're on the road to nowhere

PLEASE. just x and x', and no u, PLEASE. There is no u in x' = x. This is about what x means, not about what u means. And if this isn't a microcosm of what's going wrong: an insistence that the symbol x is somehow different from other symbols and an unwillingness to consider that this might not be t...
by steve waterman
Fri Jul 26, 2013 6:22 pm UTC
Forum: General
Topic: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x-d?
Replies: 908
Views: 172371

Re: We're on the road to nowhere

Steve, I think it would be easier for you not to think of the Galilean transform etc. in terms of coordinate systems, but in terms of vectors relative to defined origins. This would allow you to use the intuitive notion of something "moving" that you seem so fond of. Not that I don't appr...
by steve waterman
Fri Jul 26, 2013 5:56 pm UTC
Forum: General
Topic: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x-d?
Replies: 908
Views: 172371

Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

I ignore the manifold. That's your problem right there. x is meaningless in this context without the manifold. There is no x axis without the manifold. There is no distance without the manifold (and a metric). Without the manifold, x is just (conventionally) a variable which stands for a real numbe...
by steve waterman
Fri Jul 26, 2013 5:34 pm UTC
Forum: General
Topic: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x-d?
Replies: 908
Views: 172371

Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

eSOANEM wrote:Those systems aren't coincident though.

Which systems?...please be specific about what you exactly mean by "those".

case 1
S and S' are coincident
case 2
S and S' are not coincident
by steve waterman
Fri Jul 26, 2013 5:29 pm UTC
Forum: General
Topic: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x-d?
Replies: 908
Views: 172371

Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Suppose you have a point (called Peter) in the mainfold, and apply two cartesian coordinate systems arranged the way you like to do. We'll call them R and B Suppose Peter is on the x axis of both systems. Suppose the origins of the two systems are not coincident, but the red system is offset 3 unit...
by steve waterman
Fri Jul 26, 2013 4:07 pm UTC
Forum: General
Topic: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x-d?
Replies: 908
Views: 172371

Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

http://watermanpolyhedron.com/images/coordinates4.png edit...the previous depiction....added some labels. added - Given S(x,y,z), x, the abscissa of S is ALWAYS measured along the x axis from S(0,0,0). the x axis is infinite length, whereas x is finite length. x and x', are in mathematical truth, t...
by steve waterman
Fri Jul 26, 2013 3:14 pm UTC
Forum: General
Topic: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x-d?
Replies: 908
Views: 172371

Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

...wait, the fuck else would x have been referring to other than the unknown point along the x axis (aka the entire x axis)? x does not refer to a point, nor is x a point. x can be an axis, iff, we use the entire term "x axis". Given S(x,y,z), x by itself, means the distance and direction...
by steve waterman
Fri Jul 26, 2013 2:27 pm UTC
Forum: General
Topic: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x-d?
Replies: 908
Views: 172371

Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Thanks for the posting your recent depiction, Pfhorrest. From inspecting your depiction, I will make this observation. For you, x by itself, means the x axis, not the abscissa of S, hence, not the first coordinate. I would never have guessed that this was how you were envisioning x. btw, the formula...
by steve waterman
Thu Jul 25, 2013 10:05 pm UTC
Forum: General
Topic: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x-d?
Replies: 908
Views: 172371

Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

NB: x is not a "vector distance". I'd suggest reviewing what a vector is. It may be helpful if you then come back and post, in your own words, a definition / short explanation of what a vector is. https://en.wikipedia.org/wiki/Euclidean_vector In mathematics, physics, and engineering, a E...
by steve waterman
Thu Jul 25, 2013 8:52 pm UTC
Forum: General
Topic: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x-d?
Replies: 908
Views: 172371

Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

If at some point in the future you decide that you'd actually like to know what the rest of us mean when we say "x' = x - vt", let me know. But this time, you'll actually have to do the exercises. Until then, ciao. Yes, you are quite correct. Schrollini had just stated that until I do his...
by steve waterman
Thu Jul 25, 2013 8:10 pm UTC
Forum: General
Topic: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x-d?
Replies: 908
Views: 172371

Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

once given S(x,y,z) . x is the abscissa of S: the vector distance from S(0,0,0) to S(x,0,0). x, as a coordinate, is ONLY INHERENT to S. x', as a coordinate, is ONLY INHERENT to S'. Given Cartesian system S(x,y,z), x is one thing and only one thing, mathematically, x is the abscissa of/in/wrt S(0,0,0...
by steve waterman
Thu Jul 25, 2013 6:40 pm UTC
Forum: General
Topic: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x-d?
Replies: 908
Views: 172371

Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

the Galilean transformations equations given states S(x,y,z) = S'(x',y',z') where the spatial parts are coincident at t = 0, and where x = x', y = y', z = z' If at some point in the future you decide that you'd actually like to know what the rest of us mean when we say "x' = x - vt", let m...
by steve waterman
Thu Jul 25, 2013 5:25 pm UTC
Forum: General
Topic: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x-d?
Replies: 908
Views: 172371

Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

I find it quite a surprise, that only very very recently, did I find out that Schrollini was unaware that the Galilean transformations equations given states 1 S and S' are coincident at t = 0 2 x = x' at t = 0 3 vt is applied to one of the coincident systems Given two coincident Cartesian systems S...
by steve waterman
Wed Jul 24, 2013 5:38 pm UTC
Forum: General
Topic: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x-d?
Replies: 908
Views: 172371

Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

I posted this once before and then deleted it because I thought it wasn't a very good exercise, but all the mathematical rigor in the world doesn't seem to convince Steve that a manifold isn't something physicists invented to pull the wool over his eyes. So here goes; I'll be using some of Steve's ...
by steve waterman
Wed Jul 24, 2013 4:38 pm UTC
Forum: General
Topic: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x-d?
Replies: 908
Views: 172371

Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Given two coincident Cartesian coordinate systems, S(x,y,z) and S'(x',y',z') with x = x' and y = y' and z = z', regardless of either system rotating or if any system is in motion or not, it is still true that x' = x . added - Which as the first coordinate means that S(0,0,0) to S(x,0,0) = S'(0,0,0) ...
by steve waterman
Wed Jul 24, 2013 4:07 pm UTC
Forum: General
Topic: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x-d?
Replies: 908
Views: 172371

Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

the above coincident S and S' subsequently repositioned and now, are no longer coincident Coordinate systems do not move! If you're talking about repositioning a coordinate system, you're doing it wrong. This has been explained and re-explained many times, so I won't bother to repeat it again. So w...
by steve waterman
Wed Jul 24, 2013 3:39 pm UTC
Forum: General
Topic: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x-d?
Replies: 908
Views: 172371

Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

If you have no manifold, and hence no points, you also don't have coordinates or coordinate systems or coordinate transformations, and x' = x - d is just an equation containing three variables, none of which are defined. Edit: Just noting, S and S' are also now undefined. Yes, thanks for reminding ...
by steve waterman
Wed Jul 24, 2013 3:19 pm UTC
Forum: General
Topic: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x-d?
Replies: 908
Views: 172371

Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Allow me to not discuss points or manifolds any more. Hey, you're allowed to discuss whatever you'd like. Just don't pretend that what you're talking about has a durned thing to do with coordinate transformations in general or the Galilean transformation specifically if you're taking points and man...
by steve waterman
Wed Jul 24, 2013 3:01 pm UTC
Forum: General
Topic: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x-d?
Replies: 908
Views: 172371

Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

NOT TRUE! if S'(x-d,0,0) = S(x,0,0) does not mathematically extrapolate to x' = x-d. Steve, it's simple algebra. S'(x',0,0) = S(x,0,0) x' = x - d S'(x-d,0,0) = S(x,0,0) Someone needs to make this distinction between x the coordinate and (x,0,0) the point. Thanks for dropping the vt requirement. Now...
by steve waterman
Wed Jul 24, 2013 2:33 pm UTC
Forum: General
Topic: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x-d?
Replies: 908
Views: 172371

Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

The labels x, y, and z aren't special. They do not inherently mean horizontal, vertical, and into plane. We simply usually define them that way. When we have more than one coordinate system, we use different labels for the second coordinate system, sometimes x', y', and z', sometimes u, v, w, somet...
by steve waterman
Wed Jul 24, 2013 1:44 pm UTC
Forum: General
Topic: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x-d?
Replies: 908
Views: 172371

Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

I equate point S'(x',0,0) = P = point S(x-d,0,0) in the manifold . Is that what you believe too? I'll let others deal with the nature of coincident coordinate systems, but real quick - this is backwards, isn't it? (Demonstrating the dangers of those primes.) Shouldn't it be S'(x-d,0,0) = S(x,0,0)? ...
by steve waterman
Wed Jul 24, 2013 1:04 pm UTC
Forum: General
Topic: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x-d?
Replies: 908
Views: 172371

Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

I equate point S'(x',0,0) = P = point S(x-d,0,0) in the manifold . Is that what you believe too? I'll let others deal with the nature of coincident coordinate systems, but real quick - this is backwards, isn't it? (Demonstrating the dangers of those primes.) Shouldn't it be S'(x-d,0,0) = S(x,0,0)? ...
by steve waterman
Wed Jul 24, 2013 12:26 pm UTC
Forum: General
Topic: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x-d?
Replies: 908
Views: 172371

Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

If S(x,y,z) and S'(x',y',z') are coincident, with x = x', y = y', z=z' for all points, then, making the usual assumptions (same unit of measurement, both are Cartesian, etc), S and S' are two names for the same coordinate system. Nope. S has only (x,y,z) coordinates and S' has only (x',y',z') coord...
by steve waterman
Wed Jul 24, 2013 11:36 am UTC
Forum: General
Topic: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x-d?
Replies: 908
Views: 172371

Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Have some more reading to do, as I just briefly read through the recent posts. Meanwhile, perhaps it is best to go one question at at time, for a bit. When we are given S(x,y,z) coincident S'(x',y',z') with x = x', y = y', z = z' and d = 0, that mathematically means the first coordinate in S equals ...
by steve waterman
Tue Jul 23, 2013 10:21 pm UTC
Forum: General
Topic: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x-d?
Replies: 908
Views: 172371

Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Everyone else believes x' = x - d equates the relationship between coordinates in different systems for a single point How does that sound for wording regarding what everyone else believes? This is a very logical place to start. That's true, but it's not really a belief. There's no meaning inherent ...
by steve waterman
Tue Jul 23, 2013 9:14 pm UTC
Forum: General
Topic: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x-d?
Replies: 908
Views: 172371

Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

everyone else believes x' = x - d equates the relationship of points in the manifold between the two mappings.[/quote] This is not a relationship between points. It is a relationship between coordinates in different systems for a single point. Yes, thanks. That's sounds much better, I am okay with t...
by steve waterman
Tue Jul 23, 2013 7:51 pm UTC
Forum: General
Topic: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x-d?
Replies: 908
Views: 172371

Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Steve, can you state cogently and strictly the statement that everyone else believes is true. Pardon please, it is likely some sloppy wording that follows...please check first, as perhaps I have used one of your terms incorrectly, so, I am throwing this out there for mutual discussion.... let vt = ...
by steve waterman
Tue Jul 23, 2013 12:20 am UTC
Forum: General
Topic: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x-d?
Replies: 908
Views: 172371

Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

I honestly don't understand what Steve is contending any more. Steve, can you state cogently and strictly the statement that everyone else believes is true, what you believe is true, and each logical step used to disprove what everyone else thinks is true? Because from what I can see it looks like ...
by steve waterman
Sat Jul 20, 2013 5:09 pm UTC
Forum: General
Topic: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x-d?
Replies: 908
Views: 172371

Re: Galilean:x' with respect to S'?

wiki - The notation below describes the relationship under the Galilean transformation between the coordinates (x,y,z,t) and (x′,y′,z′,t′) of a single arbitrary event, as measured in two coordinate systems S and S', in uniform relative motion (velocity v) in their common x and x’ directions, with th...
by steve waterman
Sat Jul 20, 2013 4:37 pm UTC
Forum: General
Topic: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x-d?
Replies: 908
Views: 172371

Re: Galilean:x' with respect to S'? AND SPECIAL BONUS x' = x

Steve, There is a distinction that needs to be made here. Time has been used in two senses in this discussion. First, we have considered time as one of the dimensions over which our coordinates run when we are trying to identify points in the manifold of interest (that is, spacetime). This is perfe...

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