Time in Special Relativity

Who here can prove the light sphere in the moving frame assuming the light sphere in the stationary frame?

This means for all (x,y,z) on the stationary light sphere, all corresponding (x',y',z') are a constant distance r' from the origin of the moving frame.

 

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I'm using simple coordinates, components of the vectors. It's equivalent to using vectors based at the origin. It's not as general, but it's perfectly valid if used in a limited context, as I have been. Unlike you, Jack, I know my limitations.

And like I said, both Alpha and James (and rpenner, and I might be forgetting others) have posted rigorous proofs, which you were completely unable to comprehend. All you are able to do is keep repeating your vacant mantra "No one has proven anything..."

 

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you really don't like that time coordinate, do you Jack.

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No wonder you don't get it

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I see, why don't you plug your t'=0 into this logic of yours.

Let me know what you find.

 

Yea, I can talk about coords on the light sphere.

I will train you.

http://www.fourmilab.ch/etexts/einstein/specrel/www/

Einstein used an arbitrary point (x,y,z) on the light sphere to "prove" there was a moving light sphere.

He committed the logical fallacy,

a dicto simpliciter ad dictum secundum quid

I assume you can prove this moving light sphere?

I will wait.

 

You never did bother looking at those tables, did you.

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:roflmao:
But you have no clue about time coordinates!
Remember the burn mark thread?
There's an absolutely hilarious dialog in there, [post=2482189]starting about here[/post], where you keep insisting that you "circumvented time" by not including a clock in your scenario... then when I pointed out that time still happened, you berated me for saying that clocks make time!

And you never did manage to figure out the spacetime diagrams in that thread, either, did you?

I think we're about through, Jack. You really are a small, sad little man. I really do hope that you find fulfilment some day.

 

No, by specifying x,y, and z, one parameterizes all points on a sphere which is expanding at a certain speed.

When he is talking about a point on a sphere, he means any damn point just met by the expanding wavefront. So where the hell is this logical fallacy of ignoring the details that you speak of?

Any spherical expanding wavefront is dead simple when written in the language of algebraic geometry.

Example:

\(\sqrt{\left( x - x_0 \right)^2 + \left( y - y_0 \right)^2 + \left( z - z_0 \right)^2} = V \left( t - t_0 \right)\)
Which implies
\(V^2 \left( t - t_0 \right)^2 = \left( x - x_0 \right)^2 + \left( y - y_0 \right)^2 + \left( z - z_0 \right)^2\)
or
\(V^2 \left( t - t_0 \right)^2 - \left( x - x_0 \right)^2 - \left( y - y_0 \right)^2 - \left( z - z_0 \right)^2 = 0\)

and when V = c, and using the assertion that (t_0 = 0 and so forth) you get:

\(c^2 t^2 - x^2 - y^2 - z^2 = 0\)

So you again make empty claims and fail to even address what Einstein conveyed to working physicists in 1905 when he wrote:

This is dead-simple geometry, which you have not addressed. You failed to point out any error, but simply assert that it exists. You failed to do any math. Your kind, even though in the minority, is less than a dime a dozen because your assertions, which come fast and furious, are baseless.

You posted the equivalent of claiming that any work that has \(x = f(t)\) commits a fallacy because it's talking about a single time, when it is universally understood to those who have done the prerequisites that t varies over all times in the instant universe of discourse.

 

Yeah, blatant trolling.

Ban request: Jack_

 

Fine then, I will send in Mr helper.

You will notice you are selecting points of the stationary sphere that obey the logic that ct is a constant for all selected points you choose.

However, the LT mapped points do not obey this simple principle required of a sphere.

Hence, your proof is a logical fallacy called:
a dicto simpliciter ad dictum secundum quid

You must prove the light sphere in the moving frame has a constant radius just like the one in the stationary frame to prove logical consistency.

I can easily break your proof by using (r,0,0,r/c) and (-r,0,0,r/c). These two points prove you are not proving the light sphere in the moving frame. Remember, it must have a constant radius.

 

You may do as you do.

At this point, all of my arguments against relativity are secure. And, I just keep them coming.

I wonder how you fit with this factual logic.

Now, RPenner is the only one advanced enough to operate on Einstein's original proof of logical consistency. I am surprised you and others have not joined in.

As usual, I will win this debate as well.

 

you offer nothing troll.

 

Yes. And how do I know? Because I read it, worked through it, understand it and have passed exams written by other people who learnt it, worked through it and researched it. For god sake actually read up on this stuff before making claims about it. And I see you still haven't mastered the quote button. Is quoting just the bit you're replying to too much to ask?

Your quote does nothing to retort what I said. There's a difference between coordinates and a coordinate induced basis. The former are the location parameters, the latter vector components. You not only couldn't retort what I said, you demonstrated you didn't even understand it.

I'll provide plenty of textbook references if you'd like, they'll all back me up. You trot out your one and only person to quote because you haven't read anything by anyone else and you couldn't even give a relevant quote.

Wrong. Open ANY book on linear algebra, vector calculus or differential geometry. Lorentz transformations, rotations, boosts, symplectic transformations, linear maps on vectors, they ALL can be regarded as act as elements of End(V), the space of linear maps from V to itself, where V is \(\pi^{-1}(p)\) for p in Minkowski space-time.

If I give you a vector you can transform it using a matrix. Even you should know that. That is all a LT is, a transformation OF A VECTOR.

That's a list of space-time coordinates, not a vector in the tangent space. The difference is subtle but important and its one I outlined in my previous post, the difference between the two \(\mathbb{R}^{n}\) in \(\mathcal{U} \times V \sim \mathbb{R}^{n} \times \mathbb{R}^{n}\). Proof you didn't understand what I said, despite your unwillingess to admit it.

This isn't something I'm guessing or something I half remember or something no one really looks out, its the subject matter of countless books, taught to every mathematics undergraduate, the thing some people devote decades of their lives to examining. There's no confusion other than in your head.

Get the book I told you about before, by Geroch. It'll back up everything I've said. Or the book by Wald, it'll back up everything I've said. Or the book by Joyce. It'll back up everything I said. Those three are world renowned professors specialising in differential geometry.

You simply do not know anything about this stuff, all you can do is the simplest of algebra. You have no actual understanding of the underlying principles or results and you're afraid to admit you don't understand. You seem to have bitten off more than you can chew with these threads but now you've spent so much time attesting to your greatmess that you're unable to man up and say "I was wrong".

You don't bother because you're afraid to listen to anyone who might break your delusions of grandeur. You're just repeating your unjustified assertions now. How many months you been peddling this stuff now? You're still not honest enough to submit your work to a journal.

The inconsistency is in your head. Everyone else has got it, you're the one left behind here. You're unable to grasp non-Euclidean geometry or even what vectors are and you're unable to admit it.

How many times are you doing to do this Jack? How many times are you going to demand people retort you and then ignore any and all replies. When I post a lengthy explanation you ignore it or mass quote it and then ignore it. I've posted dozens of responses to you, at least 10 of which have been lengthy, detailed and included numerous equations and sometimes diagrams. NONE have been retorted by you, you just quote and ignore, quote and ignore.

Its obvious you don't want a discussion, you're certainly incapable of an honest one, so you're just becoming more and more of a troll.

Now you're trying to make excuses. It's not that you're wrong, its just that you're not been trying. Sure....

Tell you what, from now on whenever you post this lie again I'll report the post. The light sphre thread in Pseudo is full of posts of mine where I explain your mistakes, where I demonstrate your misunderstandings, where I cover vectors, geodesics, light cones, frames, bundles, Lie groups and Lie algebras, all using equations and diagrams. You just mass quoted and ignored, quoted and ignored, quoted and ignored. You failed to provide anything close to an honest informed discussion, because you're neither. That thread was locked because you couldn't do anything than repeat the one and only talking point you have, which had already been explained to you. The thread is there for all to read and anyone can read for themselves my posts explaining your mistakes and they can see how you failed to retort them, ignored them, lie about them, avoided replying to direct questions, repeatedly, and generally be dishonest and ignorant. If you want to discuss the light spheres again then go to that thread, copy the posts of mine where I talk about G-bundles, tangent bundles, vector spaces and those where I provide diagrams and then start a new thread discussing what I've said. If you don't undestand something, ask for clarification. If you disagree with something, explain clearly why. If you make it clear you'll put some effort in then I'll be happy to talk more in depth but if all you plan to do is quote and ignore, quote and ignore tough.

I suggest you start with this post, seeing as you ignored what I said several times, even that post is a repost in order to try to get you to respond. You want mathematics, there it is.

The 'true issue' with SR is that so many people don't like it being counter intuitive. Like you. They make an argument from ignorance because they are naive.

Actually he's just using common notation which makes use of the fact you can upgrade vector components to coordinates by solving the trivial geodesic equation. Like I said, read Nakahara or Geroch or Joyce. They'll all agree with me.

Hell, would you like me to scan in the relevant page from one of them, where it says they map vectors to vectors?

Learn how to do basic algebra, so you can understand everything better. The light sphere maps to a light sphere. Rpenners just proven it. I provided the same proof in previous threads and I also did it using tensors.

]Hypocrisy, thy name is Jack_.

Seconded. At tge very least a suspension for wasting people's time, lying, not providing any response to direct questions, demanding people respond and then ignoring when they do and then claiming later that no one has responded. He's a stuck record, playing the same 2 or 3 lines over and over.

 

Wrong.

It's not a constant sphere -- it's an expanding spherical flash of light which is a sphere in every time later than the flash for every observer.

Pick a time in \(t_A\) the \((x,y,z,t)\) frame -- then there a whole sphere of x, y and z that satisfy \(\sqrt{\left( x - x_0 \right)^2 + \left( y - y_0 \right)^2 + \left( z - z_0 \right)^2} = c(t_A - t_0)\).

Now from this instantaneous sphere you can pick any point, \((x_B, y_B, z_B, t_A)\) which because it was picked from the sphere, still obeys: \(\sqrt{\left( x_B - x_0 \right)^2 + \left( y_B - y_0 \right)^2 + \left( z_B - z_0 \right)^2} = c(t_A - t_0)\).

Now this event -- a point in 4-space -- is labelled by another observer as \((\xi_B, \eta_B, \zeta_B, \tau_A)\) which is a part of a whole sphere of points which satisfy \(\sqrt{\left( \xi_B - \xi_0 \right)^2 + \left( \eta_B - \eta_0 \right)^2 + \left( \zeta_B - \zeta_0 \right)^2} = c(\tau_A - \tau_0)\).

What exact value of tau you get may indeed vary on the relative velocity of the observers and which point on the sphere you point, but the simultanous slice of the spherically expanding light in still spherical when sliced by another observer who doesn't have a physical reason to prefer the first observer's definition of simultaneous to his very own.

This is dead simple geometry in Einstein's antique language. It is even simpler in the post 1908 observation that Lorentz tranforms maps 4-D spherical light cones to 4-D spherical light cones.

That is the geometrical content of \(c^2 (\Delta t)^2 - (\Delta x)^2 - (\Delta y)^2 - (\Delta z)^2 = c^2 (\Delta \tau)^2 - (\Delta \xi)^2 - (\Delta \eta)^2 - (\Delta \zeta)^2\). Making specious claims in Latin doesn't serve you cause when you don't support any point in math, physics or logic.

 

Wrong.

Einstein claimed consistency based on mapping the stationary light sphere to the moving light sphere.

He claimed by using one point on the stationary light sphere that is on the light sphere of the stationary frame and through LT satisifies ξ² + η² + ς² = c² τ²*.

The problem is that c² τ² must be constant for all (x,y,z,t) selected from the stationary light sphere to prove consistency.

Any fool knows a light sphere has an origin at the center with a constant radius. Do you understand this?

Do you produce this from the stationary frame using LT?

If so, let's see this constant radius which is a necessary condition for a sphere.

If you do not have a center point and constant radius, then a high school student knows you do not have a sphere.

 

Jacks has ignored my post where I respond to him. He's ignored what Rpenner has demonstrated and is just falling back on his one and only talking point, claiming its not a sphere when now Rpenner and I have proven a light sphere maps to a light sphere many different times and with varying explanations. Jack has failed to heed any of them,

If Reiku could get banned for wasting people's time with the same repetitive nonsense then surely the same applied to Jack?

 

Jack_ has been banned for 3 days for repeating behavior that earned a warning.
I guess I'll start a new thread.

 

I'm amazed he's actually trying to argue again the Lorentz image of a light sphere being a light sphere. I see why he's doing it, he thinks radial lines (which are all the same length) should map to radial lines, all of the same length, which they don't, as I went through with him here. The fact he thinks he's talking about something we haven't considered or don't already know shows he not only doesn't know the mainstream material but he doesn't remember or understand (or both) posts he's already read and quoted (though invariably not responded to directly). Never the less the resultant position of all photons forms a sphere about a particular point, which is not the Lorentz image of the original sphere centre (a point he really fails to grasp is not a contradiction).

Jack, the definition of an N dimensional sphere embedded in \(\mathbb{R}^{N+1}\) such that its radius is R and its centred on the origin is \(\sum_{n=1}^{N} x_{n}^{2} = R^{2}\). I went through this with you here and here and here and here and here. There's more but you get the picture. In that thread I also explain tangent spaces and their relevance to the discussion, but you didn't engage in a discussion on them nor retort what I said. Now you're in this thread demanding I provide what I've already provided. That post demonstrates I explained the nature of Lorentz transformations weeks ago and that in that time you've made no effort to check what I've said, to see if I'm right. You quoted it and said "I'm okay with this" but now in this thread you are saying the opposite, that I'm wrong in what my description of the nature of Lorentz transformations are. Why didn't you say it before? Why did you quote my post and say you're 'okay with it' yet now you're claiming I am wrong. What changed? Why am I wrong now but was right then? Why didn't you say "I'm not okay with this"? Surely if you understood my post you'd not say "I'm okay with it" if your views are and have always been that Lorentz transformations act on coordinates, not vectors.

If I were giving you the benefit of the doubt I'd just think you were not paying attention but you and I both know its because you didn't (and don't) understand my posts. What compels you to continue to tell lies, you know you haven't looked at or understood these things and you know I (and others) have. Are you desperate for attention, such that you view lying to get people riled as better than you being honest but not the centre of attention?

/edit

By the way, why not use your 3 day holiday to write up your work in a document for a journal? Type it up as a post here, so that you can include LaTeX tags and then I can quickly convert it to proper LaTeX pdf formats for a reputable journal like Physics Review D. You're obviously not going to convince anyone here you're right, so rather than waste your breath on it, submit to a journal. I am offering my help here, you've really got no excuse other than admitting you know you're wrong and thus won't submit to a journal. You've been here months and gotten nowhere, move on.

 

Time in Special Theory of Relativity

Hi
Time is run of clocks in a timeless space,
see publication:
Amrit S. Sorli, Davide Fiscaletti, Dusan Klinar, Time is a measuring System derived from Light Speed, Physics Essays, Vol 23. Num 2. (2010)

yours Zweistein