# New article shows a fatal math error in SR

Discussion in 'Pseudoscience' started by chinglu, Aug 9, 2013.

1. ### rpennerFully WiredValued Senior Member

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Equivalently, we may look at the sign of the cross product of light striking two ends of the detector.

So we have a detector which runs from $(-\xi_0, \eta_0)$ to $(-\xi_0, \eta_0 + \Delta)$ in system k where the detector is stationary.

Thus we have events O, A and B where the light flash occurs and is received at the two points respectively. These same events have representations in the system K (with coordinates t, x and y).

$\begin{array}{c|ccc} & O & A & B \\ \hline \\ \tau & 0 & \frac{1}{c} \sqrt{\xi_0^2 + \eta_0^2} & \frac{1}{c} \sqrt{\xi_0^2 + \eta_0^2 + 2 \Delta \eta_0 + \Delta^2} \\ \xi & 0 & -\xi_0 & -\xi_0 \\ \eta & 0 & \eta_0 & \eta_0 + \Delta \\ \hline \\ t & 0 & \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} \left( \frac{1}{c} \sqrt{\xi_0^2 + \eta_0^2} - \frac{v}{c^2} \xi_0 \right) & \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} \left( \frac{1}{c} \sqrt{\xi_0^2 + \eta_0^2 + 2 \Delta \eta_0 + \Delta^2} - \frac{v}{c^2} \xi_0 \right) \\ x & 0 & \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} \left( -\xi_0 + \frac{v}{c} \sqrt{\xi_0^2 + \eta_0^2} \right) & \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} \left( -\xi_0 + \frac{v}{c} \sqrt{\xi_0^2 + \eta_0^2 + 2 \Delta \eta_0 + \Delta^2} \right) \\ y & 0 & \eta_0 & \eta_0 + \Delta \end{array}$

So the cross product in system k is $\xi_A \eta_B - \xi_B \eta_A = - \Delta \xi_0 < 0$
And the cross product in system K is $x_A y_B - x_B y_A = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} \left( - \Delta \xi_0 + \frac{v}{c} \left( ( \eta_0 + \Delta) \sqrt{\xi_0^2 + \eta_0^2} - \eta_0 \sqrt{\xi_0^2 + (\eta_0 + \Delta)^2} \right) \right) < 0$
This does not undergo a sign change at any speed $0 < v < c$ including $v_0$.

Thus because of the finite propagation speed of light, the expanding beam of light sweeps across the object in the same way, hitting the same face, a face which effectively has been rotated.

This interaction between ray-tracing beams of propagating light and the Lorentz transformation is known as Terrell rotation, not to be confused with Thomas precision which is another relationship between rotation and Lorentz transforms.

http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=2049244
http://prola.aps.org/abstract/PR/v116/i4/p1041_1
http://math.ucr.edu/home/baez/physics/Relativity/SR/penrose.html

So not only is Andrew Banks completely wrong about Einstein's approach in 1905, but the effect he ignores was demonstrated as a general geometric effect in 1959. Any legitimate scientific venue for publication of matters related to the math of special relativity would have realized this along with many other flaws of this paper.

3. ### TachBannedBanned

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No, it doesn't , wacko. The "article" is written by just another wacko and it is wrong.

5. ### TachBannedBanned

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Bur "Asian...." is not a legitimate journal, it is just another Chinese scam that takes 100\$ and publishes any crap in return.

7. ### chingluValued Senior Member

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"in system k where the detector is stationary.'

We already agree in k, the light strikes the mirror and reflects.

What we are talking about is the system K. It does not reflect there.

So, yet again you have been refuted.

8. ### chingluValued Senior Member

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So, can you prove this claim crank?

9. ### TachBannedBanned

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Ignoring chinglu for a while, how did you get that the expression is smaller than 0? It isn't obvious .

10. ### TachBannedBanned

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rpenner already did. As predicted, you are wacko enough never to admit. Go away.

11. ### chingluValued Senior Member

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"Thus because of the finite propagation speed of light, the expanding beam of light sweeps across the object in the same way, hitting the same face, a face which effectively has been rotated."

How did you get the mirror to rotate when it is fixed?

Did God do it or does some unknown flat earth technology do it?

You need to prove this assertion.

12. ### TachBannedBanned

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It is a relativistic effect called Terrell-Penrose rotation. Go away.

13. ### chingluValued Senior Member

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Crackpot, rpenner is now claiming the mirror is rotated.

you are behind he times.

14. ### chingluValued Senior Member

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That is fine.

Let me see the math that proves the mirror rotates in the unprimed frame while it remains fixed in the primed frame.

I think all would like to see your proof.

15. ### TachBannedBanned

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Crank. Incurable.

16. ### chingluValued Senior Member

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Do you have a proof from your flat earth world yes or no?

otherwise, you must submit to the conclusions of the article of this thread.

if you do not, then you are a crank and crackpot.

17. ### TachBannedBanned

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I agree, you are a crank and a crackpot. Your only consolation is that you are incurable, as well.

18. ### Fednis48Registered Senior Member

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Two people have separately pointed out that the mirror in the unprimed frame hits the light in front of it, not the light behind it. These have been your responses. They have no meaning. I can parse them as English, but they have no semantics - just piles of physics words strung together. From the first response, at least, it sounds like you think you can express this concept with math, so please do so.

19. ### brucepValued Senior Member

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4,098
This thread, and the trolling, reminds me of why physforum is dead and populated by intellectual zombies. Clearly the science threads are no longer being moderated in a meaningful way. These science boards are so boogered up with nonsense it's a trolls paradise.

20. ### UndefinedBannedBanned

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Hi Aqueous Id.

Here is my polite exchange with billvon regarding his rash 'maths' example to chinglu...

Can you please tell me what I said to billvon therein that prompted you to post the following remark?

No-one has indicated any objections to what I said to billvon therein, except you. Your comment seems a non-sequitur and unjustified by the substance of my friendly urging to caution there to billvon. Can you please clarify what reason you found in it for posting your comment? Thanks.

21. ### billvonValued Senior Member

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I know. That's why you don't understand.

And my example contained math that cannot be refuted! 2+2=4. Do you deny that? The math stands.

22. ### CptBorkValued Senior Member

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Chinglu, do you understand the difference between an effective rotation and a real rotation?

23. ### rpennerFully WiredValued Senior Member

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It's ridiculous when you start making mistakes in the sentence before you attempt to "correct" me. Einstein was proposing no experiment. Einstein was addressing educated people who fully well could work out the implications of basic geometric and electromagnetic assumptions.
That is absolutely what it looks like Andrew Banks is claiming. While Einstein makes it clear that the system called K uses Latin labels x, y, z, and t for coordinates, while the system called k uses Greek labels $\xi, \; \eta, \; \zeta, \; \textrm{and} \; \tau.$. Also in sections 1 and 2 Einstein establishes that he is using primed coordinates for different values in the same coordinate system. Thus when he eventually writes x' = x - v t, this only makes sense with x, x', t and v being defined in the same coordinate system -- the only system he has fleshed out at that point, the stationary system K.

It would have been better if Andrew Banks had quoted Einstein or at least properly cited the 1905 paper. Also, I would like to point out that I linked to this document first at the bottom of my initial post and I did quote Einstein from the same source you advocate now.

That is largely undisputed, with only the minor quibble that scare quotes should be placed around stationary as the whole point of the 1905 paper is to establish that the coordinate system k is physically indistinguishable from "stationary" in light of the assumptions made in the paper. But the four paragraphs at the top of section 3 of Einstein's 1905 paper establish that system K uses lowercase Latin labels (x,y,z,t) while system k uses lowercase Greek labels ($\xi, \eta, \zeta, \tau$). At no point does Einstein establish a "primed coordinate system" as that is a convention used by later authors who set up their coordinates in different ways.

Section three then continues like this:

You misquote Einstein, in the important way that he did not write "t" but "$\tau$". This is as basic an error as mistaking "丁" for "十". Further the use of x' is an example of metonymy where what is meant is "the point stationary in system k, but uniquely identified uniquely such that at time t=0 the point has coordinates (x', y, z) in system K and at any time t it has coordinates in system K given parametrically as (x' + v t, y, z)." The problem is one of English comprehension because you have to read more than one paragraph to understand what Einstein is saying, so your tiny quote (actually a misquote) does not convey that which was meant.

Einstein didn't say mirror, he said "a point at rest in the system k" which he endows with the property of reflecting light. Lots of things reflect light other than mirrors. The context around your tiny quote demonstrates your interpretation of Einstein's words to be in error, as he develops a functional relationship between coordinates in system K (t and x') with $\tau$ a coordinate in system k.

Reasonable and competent people have disagreed with your interpretation for 108 years.

That is my conclusion based on the Lorentz transform and the finite propagation speed of light. For the same reason when you are driving in a rainstorm all the rain seems to come at the front windshield, as you are literally driving into the rain. The same phenomenon is seen in astronomy where the motion of the Earth about the sun changes the apparent angular position of the stars in the sky. This is known as stellar aberration and is a predicted consequence of the finite propagation speed of light even in Newtonian mechanics. That Andrew Banks ignores it demonstrates his lack of competence and the lack of competence of the purportedly scientific journal.

That is not the case.

That's not a refutation -- that's a repetition of an assertion, but it ignored the argument, geometry and calculation of [post=3096606]my second post[/post].

I didn't say rotated, I said "effectively .. rotated" because of the finite speed of light the motion of the mirror affects how light arrives at the mirror. Stellar aberration is the same effect. http://en.wikipedia.org/wiki/Aberration_of_light

Thus the argument, geometry and math which you ignore.
It's still there in [post=3096606]my second post[/post].

Good question!