Is there length contraction?

Let's see, if SR claims light is always measured c, how can the light sphere be anything but a sphere from any frame?

Let me see the math.

 

Log in or Sign up to hide all adverts.

I did not see this.

If there was no length contraction then both observers could not both observe the coordination of mirrors, flashes and reflections.

Please show me the math.

Without length contraction, one observer would simply see the light at some other time than another.

Your requirement of length contraction is directly related to light emission points in SR and the confession that each frame's light emission point is the absolute start of the path of light in the absolute Newtonian sense.

Hence, length contraction is a derivation of the absolute Newtonian absolute light path for all frames.

 

Log in or Sign up to hide all adverts.

Don't be such an ass. In your mewling and malicious manner, which has already been cited as a breach of the peace, you quoted the whole of the math on the very thread I linked to. You just didn't address the high-school level application of algebra. So I am not responsible for your failure to converse intelligently. You deserve to have all your privileges revoked.

 

Log in or Sign up to hide all adverts.

http://www.sciforums.com/showthread.php?t=99729&page=8

Its getting pretty boring having to point you to things you've already seen because you demand in a different thread to be 'shown the math' again. If you can't retort it in that thread please stop lying in other threads by claiming you haven't been shown the math or no one has responded.

You've been doing it for weeks now and I'm sure even the mods are getting sick of it.

 

OK, it looks like a consensus that I am wrong.

I said,

Your requirement of length contraction is directly related to light emission points in SR and the confession that each frame's light emission point is the absolute start of the path of light in the absolute Newtonian sense.


This means I think length contraction is based on SR confessing different light emission points after any time t in either frame

I guess I am just plain wrong.

So, can you all please teach me without using multiple light emission points the art of length contraction?

Since I said it results from multiple light emission points and I am wrong, there must be an explanation I simple cannot understand.


Thanks.

 

OK, I am learning.

d = z(1 - v/c) = a'/γ
d' = a' = γ d = γ z(1 - v/c)

What is v/c? I said it is the difference in light emission points and of course we know I am wrong. You said I am wrong. So what is it?

Also, I am not seeing the reciprocol relationship with the length contraction in your calculations.
Is it only one way? If not and you are correct, why is it missing?


So, I am most interested in the term, v/c.

Thanks for your help.

ps. If length contraction is reciprocol and you left this off, then your post is only partially true.

 

The endpoints of d and d' are the worldlines of A and AM, which are moving according to observer Z and not moving according to observer A. Thus Z measures d and A measures d' for the constant distance between simultaneous events on worldlines A and AM.
v is the velocity of A as measured by Z and -v is the velocity of Z as measured by A, provided they agree on convention of directions. c is the speed of light, and thus v/c is a dimensionless number between 0 and 1 for the accompanying description to make sense.
The only event where light is emitted is given as the event when A and Z coincide with each other.
Reciprocal relationships exist in the kinematics, i.e. the Lorentz transform and the laws of physics, not necessarily in every setup. But it's trivial to find them:
Write the statement you want to see the reciprocal relationship for:
"d and d' show length contraction d < d' because d is measured as the distance between constant-separated worldlines A and AM for an observer which is in relative motion and d' is measured by an observer whic is not"
Then swap observers mutatis mutandis and by inventing a symbol (e) we have:
"e' and e show length contraction e' < e because e' is measured as the distance between constant-separated worldlines Z and ZM for an observer which is in relative motion and e is measured by an observer which is not"
Indeed, we have a measurement of the distance between Z and ZM in the unprimed coordinate system. It is called z. But in phyti's setup, he also gives the simplest way to extract z' from the primed coordinate system. From A's perspective, the event 1 happens when it meets with Z and the event 4 should happen when A meets ZM.
We have already calculated the time (t' in A's viewpoint) between 1 and 4 as:
a'/c + a'/v = γ(z/v - vz/c²) = γz(1 - v²/c²)/v = γz/(γ²v) = z/(γv).
Which is exactly the time it takes for a length of z' = z/γ takes to travel past an observer at speed |v|. Thus e' = z' < e = z and A measures the moving length between Z and ZM as length-contracted, which is as nicely reciprocal as Z's measuring the moving length between A and AM as length-contracted as you might want.

What's so hard to understand about the obvious fact that v/c is a number between 0 and 1?
v is a velocity with units of length over time, c is also a velocity. Phyti said v = 0.5c, so v/c = 0.5, v²/c² = 0.25, 1 - v²/c² = 0.75 and γ = 1/sqrt(1 - v²/c²) = 1/sqrt(0.75)

How is my post only "partially true" when it doesn't mention any untruths and answers all of phyti's questions? I think you should retract and rephrase that statement, because I am not going to fill every post ever with every single truth I know, mind-boggling trivial or wholly irrelevant as they may be. I failed to mention detailed box scores of Pete Rose's professional games, but that hardly had bearing on phyti's question. Likewise, phyti already correctly calculated the time (t') for events 1 and 4 as seen by A, so anyone who wanted to could extract e' as (0.5)(17.3) which is less than e as seen by Z as 10 from phyti's original post.

 

Leaving aside the logistical difficulties of the nets, we can swoop our 1m hoops over each others 2m boards. (I'm changing our poles to boards to avoid innuendo!)

Specifically, you can sweep your hoop down around me and my board so that at a particular instant, my board is bound fore and aft by your hoop, and I can do the same.


The reason this is possible is in that italicised phrase... a particular instant is not well-defined across space. The events that happen at any particular instant are relative, just like a particular location (eg "here") is relative.

 

You have to understand Jack's logic. If you say something he doesn't understand then you're wrong. If you say something which is at odds with what he's said then you're wrong. If you in any way demonstrate he's wrong then you're wrong.

So by the logic you're very wrong. In Jack's Bizarro backwards world of "Everyone is wrong but Jack!".

 

First, you did not address the fact you cannot support length contraction without miultiple light emission points.

More specifically, given

x' = ( x - vt )γ.

Since we are dealing with light to support length contraction,

t = x/c

x' = ( x - vx/c )γ.

As we can see, vx/c is the context switch to the moving frame to calculate x'.

vx/c is the change to the moving frame's light emission point just like I said.

You call this v/c a dimensionless value as if it has no meaning. But, is tis the method to switch to the other frame. You forgeot to thin in terms of -x(v/c)

You have two choices to refute my argument. You may exclude light which then invalidates length contraction.

Or, you may claim v/c is not involved with the different light emission points as I demonstrated it does above.

So, you can refute my argument two ways, no way and no how.

Finally, if you give lecture to the OP, then it is expected you would give the entire truth which you confess you did not.

Your argument would lead one to believe length contraction is absolue as that is all your math proves.

I am satisifed with my conclusions.

 

You may join into Rpenner's failed logic.

I have posted a reply.

It seems both of you still do not understand the multiple light emission points of SR and how that leads to all of its conclusions.

 

Phyti only had one light emission -- a flash of light that happened when A and Z coincided (event 1), and phyti's example has length contraction both of the distance between A and AM as well as that between Z and ZM. So multiple light emissions are not necessary. Indeed, one would expect that one could do it with NO light emission at all.

It is not light that forces length contraction to be real. It is Lorentzian geometry combined with the definition of length as to be the size of the space-like separation of two events which are simultaneous.

So I shall now exclude light.

P and Q are two world lines of objects at rest to the first observer.
Thus \(x_P(t) = x_{0,P}\\t_P(t) = t\\x_Q(t) = x_{0,Q}\\t_Q(t) = t\\D(t) = x_P(t) - x_Q(t) = x_{0,P} - x_{0,Q} = D(0)\). Clearly D(t) is constant.
For a moving observer, we have the Poincare transform (inhomogenous Lorentz transform):
\(x' = x_T + \frac{x - vt}{\sqrt{1 - \frac{v^2}{c^2}}} \\ t' = t_T + \frac{t - vx/c^2}{\sqrt{1 - \frac{v^2}{c^2}}}\)
Applying this we have:
\(x_P'(t) = x_T + \frac{x_{0,P} - vt}{\sqrt{1 - \frac{v^2}{c^2}}} \\t_P'(t) = t_T + \frac{t - v x_{0,P}/c^2}{\sqrt{1 - \frac{v^2}{c^2}}} \\t = ( t_P'(t) - t_T )(\sqrt{1 - \frac{v^2}{c^2}}) + v x_{0,P}/c^2 \\x_P'(t_P') = x_T + \frac{x_{0,P}(1 - v^2/c^2) - v ( t_P' - t_T )(\sqrt{1 - \frac{v^2}{c^2}}) }{\sqrt{1 - \frac{v^2}{c^2}}} = x_T + x_{0,P}\sqrt{1 - v^2/c^2} - v ( t_P' - t_T ) \)
Similarly \(x_Q'(t_Q') = x_T + x_{0,Q}\sqrt(1 - v^2/c^2) - v ( t_Q' - t_T )\) so \(D'(t') = x_P'(t') - x_Q'(t') = (x_{0,P} - x_{0,Q})\sqrt{1 - v^2/c^2} = D(0) \sqrt{1 - v^2/c^2}\) which is clearly constant and length-contracted. (Also, all the inhomogenous parts drop out, which means that the same result is gotten from the Lorentz transform.)

Your satisfaction is that of someone who is content in ignorance. Your logic is no such thing, but an attempt to bully by assuming authority. Your manners are lacking. Your rights are void.

 

Ignoring Jack for a bit, what if D(t) was not constant. To make things simple, let's put our oberver between P and Q and set the origin of time to the time where P and Q coincide.
\(x_P(t) = u t \\ t_P = t \\ x_Q(t) = -u t \\ t_Q = t \\ D(t) = x_P(t) - x_Q(t) = 2u t\)
So for the other observer,
\(x_P'(t) = x_T + \frac{(u-v)t}{\sqrt{1 - \frac{v^2}{c^2}}}\\t_P'(t) = t_T + \frac{(1 - \frac{uv}{c^2})t}{\sqrt{1 - \frac{v^2}{c^2}}}\\t = (t_P' - t_T)\frac{\sqrt{1 - \frac{v^2}{c^2}}}{1 - \frac{uv}{c^2}} \\ x_P'(x_T') = x_T + \frac{u-v}{\sqrt{1 - \frac{v^2}{c^2}}}(t_P' - t_T)\frac{\sqrt{1 - \frac{v^2}{c^2}}}{1 - \frac{uv}{c^2}} = x_T + (t_P' - t_T)\frac{u-v}{1 - \frac{uv}{c^2}}\)
Similarly \(x_Q'(t_Q') = x_T + (t_Q' - t_T)\frac{-u-v}{1 + \frac{uv}{c^2}}\).
So \(D'(t') = t_P'(t') - x_Q'(t') = (t' - t_T)\left ( \frac{u-v}{1 - \frac{uv}{c^2}} +\frac{u+v}{1 + \frac{uv}{c^2}} \right) = 2 u (t' - t_T) \frac{c^4-c^2 v^2}{c^4-u^2 v^2}\) as you might expect from the Einstein velocity addition law.

It's not enough to get x'(t) -- you need x'(t') if you are going to put yourself into the other observer's shoes.

 

Is it possible for the mods to either tell Jack to STFU or to keep his "OMG I hate relativity!" posts in specific threads he starts. He's repeating the same things in this thread as he did in others and he's having to be told the same things as he's already been told. By posting in other thread he thinks he can pretend we haven't already told him where he's incorrect again and again, because no one has replied to him in the new thread. Rpenner and I have already been through this with him.

 

That was not my issue.

I said specifically, you cannot prove length contraction without multiple light emission points. I said that.

Thus, you claim the light path is absolute for each frame and that light path is "free from contradictions".

How do you support this absolute Newtonian logic for the light path?

 

All my proofs lie dormant and secure from both of you.

Why is that?

Both of you, go refute the twins contradiction.

This will indicate you are telling the truth.

 

Until you submit your work to a journal and accept the review of people you can't ignore or excuse you're basically admitting you know you're a fraud.

 

You are a screen dot splasher.

You cannot keep up with me and you just keep saying this.

Otherwise, use math and refute me.

 

Not really, since journals don't consider non-mainstream stuff. You should use different reasoning.