Special Relativity invalid - a triviality

RJBeery, being a natural philosopher, naturally tend to be deluded by illusions as he only uses his eyes and then philosophizes with his feet about length and take them as revelation from the Virgin Mother.

The fact that two dumb 1-meter rod 100 meters apart sees each other the size of thumbnails does not change the lengths of the rod - this is why there is such a thing called absolute length and not "relativity" length.

The proof of the eating is in the pudding (Damm it! Hope what looks like a pudding is not a rock!). All the eminent professors in your ivy league universities very dutifully resolved the twin paradox by using real time-dilated clocks and added a smaller time accumulation when the clock runs slower, not because the clock "looks like running slower". So Special Relativity is nothing to be "relativity" about when it comes to facts - clocks and their rates are as real as when a clock pendulum fly off and hit your head and you bleed.

Wikipedia is fringe-pedia and the authors H & K are only apparent humanoid and their clocks cannot be trusted as there are no "Rolex" label!

So I win? No! You win. See my other posts.

Chan Rasjid.
OK, call it morbid curiosity, but how can you accept absolute length but not proper time? Foreshortening of length and dilation of time both occur due to perspective changes. And you didn't answer my question about explaining time dilation without SR. I'm giving you a chance to explain your position; if you make another post with no substance then I jump on the dog pile with everyone else...
 
@ Chan Rasjid,

The problem of both clocks being slower than each other can only occur if one presumes an absolute universal reference frame, if I am not mistaken.

Special relativity whether valid or not, does not allow the use of a universal reference frame.

To argue that SRT is invalid using a universal reference frame as your premise is futile because it's use is not applicable to SRT.


Alternatively consider:


How can both clocks be assessed as running slower than each other if they are not compared simultaneously using a universal reference frame as the premise for the comparision?


and if I have missed the point I am sure someone will step in and correct me...:)
 
@ Chan Rasjid,

The problem of both clocks being slower than each other can only occur if one presumes an absolute universal reference frame, if I am not mistaken.

Special relativity whether valid or not, does not allow the use of a universal reference frame.

To argue that SRT is invalid using a universal reference frame as your premise is futile because it's use is not applicable to SRT.
A universal reference frame is permissible in SR. Any arbitrary frame will do and we can declare it "special" by fiat. Then one of the clocks A or B will be faster than the other, OR they will both be clocking at the same rate. The apparent contradiction only occurs when we compare A's observations of B with B's observations of A.
 
Yes, I am fully aware, this is why I called it crackpot.

I know. That was for any other reader who didn't know what ViXra was.

There is a concerted effort to suppress any criticism of special relativity. Any decent person reading my original post can see that there is nothing in the content that is in any way trolling or spamming - it is just decent criticism of Special Relativity. As to whether it is already old news is irrelevant - it is clearly decent. But pushing it to "pseudoscience" from "physics and maths" obviously discourages and frustrates those who want to debate decently about the validity of Special Relativity. After a while, even with replies to the thread, it sinks down and never to be seen again! So who with real questioning would want to posts when they know their effort just get into "pseudoscience" and no sane person goes there! So what you find in "science and maths" are only glorification of Einstein's theory, no disputes.

I know the argument - "Go start your own forum".

Chan Rasjid.

And you're still a jackass.


Instead of accepting responsibility for what was pointed out, you blame the "institution" in full fledged blindness.
"Suppression" and "glorification" are not the issues here. This is your common (and old news) theme that you play in order to give the illusion of being the persecuted genius.
 
I know. That was for any other reader who didn't know what ViXra was.



And you're still a jackass.


Instead of accepting responsibility for what was pointed out, you blame the "institution" in full fledged blindness.
"Suppression" and "glorification" are not the issues here. This is your common (and old news) theme that you play in order to give the illusion of being the persecuted genius.
Well what's sad is that I gave him a sincere opportunity to explain his position but he chose not to because the thread didn't remain in Physics and Math. It makes me think the attention he was seeking was more important than the message he had.
 
Well what's sad is that I gave him a sincere opportunity to explain his position but he chose not to because the thread didn't remain in Physics and Math. It makes me think the attention he was seeking was more important than the message he had.
Yes.

See, it's like Mazulu. I want to be Mazulu's friend. Ok, stretch... but you know what I mean. Yeah, he's crazy- but that's ok. So I'm mostly "nice" (Albeit brutally honest) with Mazulu.
Yet, total one eighty here. Why?
Because Mazulu's just misguided. By many things. But he's not the bad guy. Chan Rasjid is totally dishonest. He's a charlatan.
There's an old saying, "Give 'em an inch..."
 
...Anyway, I'm giving you the benefit of the doubt here, please explain HK time dilation without SR!
... I'm giving you a chance to explain your position; if you make another post with no substance then I jump on the dog pile with everyone else...


Well what's sad is that I gave him a sincere opportunity to explain his position but he chose not to because the thread didn't remain in Physics and Math. It makes me think the attention he was seeking was more important than the message he had.
I clasp my Rolex watch within my palms and vigorously shake it and discover time dilation. It does not mean current physics will have an explanation for it; Special Relativity is not the explanation by default!

A universal reference frame is permissible in SR. Any arbitrary frame will do and we can declare it "special" by fiat. Then one of the clocks A or B will be faster than the other, OR they will both be clocking at the same rate. The apparent contradiction only occurs when we compare A's observations of B with B's observations of A.

On the issue I brought up about the invalidity of Special Relativity and about time dilation, there is no need to bring in other concepts if, without them, things could be clarified. There is no need to bring in universal reference frames or whether there is, or is not, absolute motion and an absolute reference frame.

When I hold two clocks in my hands and slowly bring them together, this is actually a symmetric twin paradox. As I do not know time dilation, but rely only on symmetry, I predict that the twins A and B would end up the same age. If twin A knows time dilation, then he predicts that, as B is moving, it will end up younger. Lorentz time dilation is conditional only on inertial frames with relative uniform motions; and inertial frames are all equivalent - not equivalent with certain qualifications restriction. So reciprocity applies and B too, if he relies on time dilation, will predict that A will end up younger.

About "The apparent contradiction only occurs when we compare A's observations of B with B's observations of A": Time dilation of the Lorentz transformation has nothing to do with "observations of clocks". You, as well as many others, would like to introduce the concepts of "observing clocks" at infinite distances as being fundamental in physics. It is about how real clock actually behaves. Special Relativity is invalid simply because it is Lorentz transformation and it is not a transformation that accords with the real world.

I don't expect that my explanation will ever satisfy you just as those before rejected Herbert Dingle. The arguments here will not settle anything. The only usefulness is they are for others to read and ponder. Debates, in general, does not settle anything - only claims of things being settled could be made. Newtonian mechanics is not correct or "true"; but only correct because everyone says so. So a correct theory is simply just what is universally accepted. A cheat may be called a saint as long as he is not found out. Is Special Relativity universally accepted? Some may say it will not be only because it is counter-intuitive and most are not qualified to understand it (including RJBeery).

Chan Rasjid.
 
There is a concerted effort to suppress any criticism of special relativity.
Your criticism hasn't been suppressed. It's been cataloged and pointed out as fundamentally misguided. The evidence shows that "on board that care about science, there is a concerted effort to correct miseducation on the subject of special relativity."
Any decent person reading my original post can see that there is nothing in the content that is in any way trolling or spamming - it is just decent criticism of Special Relativity.
No, it isn't. It's a bitter polemic filled with unsustainable attacks on nearly all physicists over the past 100 years. Just look at all this troll-like content:
... a religious dogma ... not about a debate in physics ... blatantly confounded logic ... plain absurdity ... their propaganda and obfuscation; ... a fraud propagated on the world by the mass media ... propagating it as an indisputable dogma ... the obfuscation on the invalidity ... convoluted and incomprehensible
These are harsh charges which you don't begin to demonstrate. At the core of your argument is that you claim that the predictions are a "plain absurdity" but you are actually only talking about a conflict with a set of contradictory assumptions. We know the assumptions are contradictory because we can put both theories in the same axiomatic framework and your argument amounts to asserting both that $$K=0\; \textrm{and} \; K=c^{\tiny -2}$$. Thus thus self-contradiction lies with you, not special relativity.

And if you didn't want it called spam, maybe you shouldn't have cut and pasted it into more than one forum: http://www.mrelativity.net/VBForum/showthread.php?422-Special-Relativity-invalid-a-triviality

As to whether it is already old news is irrelevant - it is clearly decent. But pushing it to "pseudoscience" from "physics and maths" obviously discourages and frustrates those who want to debate decently about the validity of Special Relativity.
Maybe next time you should debate physics with the weapons of physics: empirical observations, testable models, math and logic. What you brought was a load of fetid dingo kidneys and a smear campaign. You also completely ignored post #11 the only post to tease apart your initial post claim-by-claim.
After a while, even with replies to the thread, it sinks down and never to be seen again!
This claim is not demonstrated. This forum keeps threads the same amount of time regardless of which forum they are classified under and they don't disappear off the Internet.
So who with real questioning would want to posts when they know their effort just get into "pseudoscience" and no sane person goes there!
You have insulted yourself and your readers with this line.
So what you find in "science and maths" are only glorification of Einstein's theory, no disputes.
There are no disputes at issue, which is the point of post #11.
I know the argument - "Go start your own forum".
It is better than rolling in broken glass.

Chan Rasjid was online about 4 hours ago, but hasn't yet responded to post #11, which began as follows:
Chan Rasjid -- there are a great number of ways to do physics wrong. In this thread, you have not managed to invent any interesting new ways of being wrong. In largest part, this is due to your personal ignorance of the subject you are discussing and overreliance on the purported authority of so-called experts who in this case have not mastered the subject.
 
A universal reference frame is permissible in SR. Any arbitrary frame will do and we can declare it "special" by fiat. Then one of the clocks A or B will be faster than the other, OR they will both be clocking at the same rate. The apparent contradiction only occurs when we compare A's observations of B with B's observations of A.
Possibly you missed the important qualifier in my post when referring to universal reference frames.
The key word was "absolute".
I do understand your point though however the only way that two clocks can be deemed to behave in the manner described in the OP is to presume an Absolute Universal Reference Frame [ frame of reference ] as far as I can deduce...
 
You need to watch it, you may end up as crazy as Dingle.
Chan, I can read your reply even though it does not show up in this thread for some reason (perhaps it must be approved or something?). Anyway I've asked for YOU to explain time dilation without SR, but the only thing you've done is claim that Lorentz transforms are bunk because they reciprocate. Claiming that you have a problem accepting a theory is COMPLETELY DIFFERENT from claiming that you have an alternative explanation.

Shaking your Rolex very fast will make it move slower in your hand. This is well defined and understood in Relativity. How do you explain it without Relativity?
 
You need to watch it, you may end up as crazy as Dingle.
Oh wow, my response to Chan is eerily similar to Einstein's response to Dingle:
Einstein said:
In spite of serious efforts I have not succeeded in quite understanding H. Dingle's essay, not even as concerns its aim. Is the idea of the special theory of relativity to be expanded in the sense that new group-characteristics, which are not implied by the Lorentz-invariance, are to be postulated? Are these postulates empirically founded or only by way of a trial "posited"? Upon what does the confidence in the existence of such group-characteristics rest?
HAH!
 
Chan, I can read your reply even though it does not show up in this thread for some reason (perhaps it must be approved or something?). Anyway I've asked for YOU to explain time dilation without SR, but the only thing you've done is claim that Lorentz transforms are bunk because they reciprocate. Claiming that you have a problem accepting a theory is COMPLETELY DIFFERENT from claiming that you have an alternative explanation.

Shaking your Rolex very fast will make it move slower in your hand. This is well defined and understood in Relativity. How do you explain it without Relativity?
My answer was : "I clasp my Rolex watch within my palms and vigorously shake it and discover time dilation. It does not mean current physics will have an explanation for it; Special Relativity is not the explanation by default!".

To me my answer is as clear and sufficient as what could be given; but if it does not satisfy you, what can I do - there is currently no technique for "consciousness transplant" so that you could understand as I do. Maybe we could settle it by poll by electing members who have posted here to say if I have answered you. If you just keep using "WOWs and HAAAs"(at least, not vulgar) and we each keep claiming to be right, then the argument will go to 100 posts of "WOWs and HAAAs"; and you would call upon Albert Einstein and I calling upon Mahatma Gandhi (who is one of the greatest among man and who also unequivocally repudiated Newton's Third Law by evidence of his person!). I would exasperate you further by applying Special Relativity - I am righter than you because my reference is the only one that dispenses with judgment - "I righter and you righter" but "you still wronger".

Thought I have answered you about your request that I explain the Hafele-Keating time dilation without Special Relativity, I do so again in a slightly different manner. Let's say the clocks of the HK experiment truly shows time dilation and, according to you, Special Relativity clearly account for the data. To you, it has significance - a further feather on the hat of Special Relativity. But to me, who is of the view that Special Relativity is invalid, the explanation using Special Relativity is irrelevant. What I am trying to emphasize is that whether I could, or could not, explain time dilation without Special Relativity is irrelevant. There should still be many physical phenomena that have been observed for which science do not yet have any satisfactory explanation - I include time dilation if it is confirmed.

If, even after this reply, you are still not satisfied, then I don't know how further exchanges between us could be fruitful. As I wrote earlier, our exchanges settle's nothing; they are only for others to read, ponder and then to decide for themselves whether my argument, or the counter-arguments, have any merit.

Best Regards,
Chan Rasjid.
 
But to me, who is of the view that Special Relativity is invalid, the explanation using Special Relativity is irrelevant.

...especially given the FACT that the explanation for HK experiment is GR, not, as claimed in your crass ignorance, SR.
 
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...especialyy given the FACT that the explanation for HK experiment is GR, not, as claimed in your crass ignorance, SR.
I read the Arab's have a popular saying:

He who knows not he knows not, he is ignorant; avoid him.
He who knows he knows not, he is simple; guide him.
He who knows he knows, he is wise; follow him.
He who knows not he knows, he is asleep; wake him.

I am not too sure which category you would fall into; being an accredited valued member, my bet is very likely it is either the third or the fourth category. If it were the fourth, then I am diffident I am qualified to wake you to your dormant deep and wide knowledge - let others do it.

As for myself, I have been thumbing round and round each of the four categories; finally I have to accept that things sometimes, like relativity, is difficult and counter-intuitive; I just have to slot myself into the fifth category out of the four.

Best Regards,
Chan Rasjid.
 
Chan Rasjid was online about 4 hours ago, but hasn't yet responded to post #11
Looks like his latest post was held in moderator, and not available to be read at the time I posted. Boy is my face red -- oh wait! He still hasn't replied to post #11?
I clasp my Rolex watch within my palms and vigorously shake it and discover time dilation. It does not mean current physics will have an explanation for it; Special Relativity is not the explanation by default!
You don't understand special relativity so you are incapable of parsing the logical foundations of special relativity or the experimental evidence for special relativity. There is no logic, math or science in your posts, just the subcromulent bloviations of an ignoramus.
When I hold two clocks in my hands and slowly bring them together, this is actually a symmetric twin paradox. As I do not know time dilation, but rely only on symmetry, I predict that the twins A and B would end up the same age. If twin A knows time dilation, then he predicts that, as B is moving, it will end up younger. Lorentz time dilation is conditional only on inertial frames with relative uniform motions; and inertial frames are all equivalent - not equivalent with certain qualifications restriction. So reciprocity applies and B too, if he relies on time dilation, will predict that A will end up younger.
You nakedly assert this without calculation and so violate the principle that one needs to find the predictions of a theory before one can fairly criticize the predictions of the theory.

Case I. Viewpoint of the midpoint-man. Inertial coordinates $$(t, \vec{x})$$, proper times $$\tau_A \; \textrm{and} \; \tau_B$$
Clock A moves from event $$\xi$$ to event $$\chi$$ where it meets clock B which moved at the same speed v, from event $$\zeta$$ to event $$\chi$$. For the mid-point man, events $$\xi$$ and $$\zeta$$ are simultaneous such that $$t_{\xi} = t_{\zeta} < t_{\chi}$$. So we know the distances $$v \left( t_{\chi} - t_{\xi} \right) = v \left( t_{\chi} - t_{\zeta} \right) = \left| \vec{x}_{\chi} - \vec{x}_{\xi} \right| = \left| \vec{x}_{\chi} - \vec{x}_{\zeta} \right|$$ or coloquially, $$v \Delta t_A = v \Delta t_B = \left| \Delta \vec{x}_A \right| = \left| \Delta \vec{x}_B \right| $$. From this we calculate $$\tau_A = \sqrt{ \left( \Delta t_A \right)^2 - \frac{1}{c^2} \left( \vec{x}_A \right)^2 } = \sqrt{ 1 - \frac{v^2}{c^2} } \Delta t_A = \sqrt{ 1 - \frac{v^2}{c^2} } \Delta t_B = \sqrt{ \left( \Delta t_B \right)^2 - \frac{1}{c^2} \left( \vec{x}_B \right)^2 } = \tau_B$$.

So $$\tau_A = \tau_B$$.

Case II. Viewpoint of A. Inertial coordinates $$(t', \vec{x}')$$, proper times $$\tau'_A \; \textrm{and} \; \tau'_B$$

We need to apply a Lorentz transform $${\huge \Lambda }_{\frac{\Delta \vec{x}_A}{\Delta t_A}}$$ to cancel out A's motion.
Thus:
$$t'_{\xi} = \frac{1}{\sqrt{1 - \frac{v^2}{c^2} }} \left( t_{\xi} - \frac{\Delta \vec{x}_A}{c^2 \Delta t_A} \cdot \vec{x}_{\xi} \right)
\vec{x}'_{\xi} = \vec{x}'_{\xi} + \left( \frac{ \frac{1}{\sqrt{1 - \frac{v^2}{c^2} }} - 1 }{ v^2 } \frac{\Delta \vec{x}_A}{\Delta t_A} \cdot \vec{x}_{\xi} - \frac{1}{\sqrt{1 - \frac{v^2}{c^2} }} t_{\xi} \right) \frac{\Delta \vec{x}_A}{\Delta t_A}
t'_{\zeta} = \frac{1}{\sqrt{1 - \frac{v^2}{c^2} }} \left( t_{\zeta} - \frac{\Delta \vec{x}_A}{c^2 \Delta t_A} \cdot \vec{x}_{\zeta} \right)
\vec{x}'_{\zeta} = \vec{x}'_{\zeta} + \left( \frac{ \frac{1}{\sqrt{1 - \frac{v^2}{c^2} }} - 1 }{ v^2 } \frac{\Delta \vec{x}_A}{\Delta t_A} \cdot \vec{x}_{\zeta} - \frac{1}{\sqrt{1 - \frac{v^2}{c^2} }} t_{\zeta} \right) \frac{\Delta \vec{x}_A}{\Delta t_A}
t'_{\chi} = \frac{1}{\sqrt{1 - \frac{v^2}{c^2} }} \left( t_{\chi} - \frac{\Delta \vec{x}_A}{c^2 \Delta t_A} \cdot \vec{x}_{\chi} \right)
\vec{x}'_{\chi} = \vec{x}'_{\chi} + \left( \frac{ \frac{1}{\sqrt{1 - \frac{v^2}{c^2} }} - 1 }{ v^2 } \frac{\Delta \vec{x}_A}{\Delta t_A} \cdot \vec{x}_{\chi} - \frac{1}{\sqrt{1 - \frac{v^2}{c^2} }} t_{\chi} \right) \frac{\Delta \vec{x}_A}{\Delta t_A}$$

Then
$$\Delta t'_A = t'_{\chi} - t'_{\xi} = \frac{1}{\sqrt{1 - \frac{v^2}{c^2} }} \left( t_{\chi} - t_{xi} - \frac{\Delta \vec{x}_A}{c^2 \Delta t_A} \cdot \left( \vec{x}_{\chi} - \vec{x}_{xi} \right) \right) = \frac{1}{\sqrt{1 - \frac{v^2}{c^2} }} \left( \Delta t_A - \frac{\Delta \vec{x}_A \cdot \Delta \vec{x}_A}{c^2 \Delta t_A} \right) = \frac{ 1 - \frac{v^2}{c^2} } {\sqrt{1 - \frac{v^2}{c^2} }} \Delta t_A = \tau_A
\Delta \vec{x}'_A = \vec{x}'_{\chi} - \vec{x}'_{\xi} = \left( \vec{x}_{\chi} - \vec{x}_{\xi} \right) + \left( \frac{ \frac{1}{\sqrt{1 - \frac{v^2}{c^2} }} - 1 }{ v^2 } \frac{\Delta \vec{x}_A}{\Delta t_A} \cdot \left( \vec{x}_{\chi} - \vec{x}_{\xi} \right) - \frac{t_{\chi} - t_{\xi}}{\sqrt{1 - \frac{v^2}{c^2} }} \right) \frac{\Delta \vec{x}_A}{\Delta t_A} = \Delta \vec{x}_A + \left( \frac{ \frac{1}{\sqrt{1 - \frac{v^2}{c^2} }} - 1 }{ v^2 } \frac{\Delta \vec{x}_A}{\Delta t_A} \cdot \Delta \vec{x}_{A} - \frac{\Delta t_A}{\sqrt{1 - \frac{v^2}{c^2} }} \right) \frac{\Delta \vec{x}_A}{\Delta t_A} = \Delta \vec{x}_A + \left( \left( \frac{1}{\sqrt{1 - \frac{v^2}{c^2} }} - 1 \right) \Delta t_A - \frac{\Delta t_A}{\sqrt{1 - \frac{v^2}{c^2} }} \right) \frac{\Delta \vec{x}_A}{\Delta t_A} = \Delta \vec{x}_A - \Delta \vec{x}_A = 0
\Delta t'_B = t'_{\chi} - t'_{\zeta} = \frac{1}{\sqrt{1 - \frac{v^2}{c^2} }} \left( \Delta t_B - \frac{\Delta \vec{x}_A \cdot \Delta \vec{x}_B}{c^2 \Delta t_A} \right)
\Delta \vec{x}'_B = \vec{x}'_{\chi} - \vec{x}'_{\zeta} = \Delta \vec{x}_B + \left( \frac{ \frac{1}{\sqrt{1 - \frac{v^2}{c^2} }} - 1 }{ v^2 } \frac{\Delta \vec{x}_A}{\Delta t_A} \cdot \Delta \vec{x}_{B} - \frac{\Delta t_B}{\sqrt{1 - \frac{v^2}{c^2} }} \right) \frac{\Delta \vec{x}_A}{\Delta t_A}
\tau'_A = \sqrt{ \left( \Delta t'_A \right)^2 - \frac{1}{c^2} \left( \vec{x}'_A \right)^2 } = \sqrt{ \tau_A^2 } = \tau_A
\tau'_B = \sqrt{ \left( \Delta t'_B \right)^2 - \frac{1}{c^2} \left( \vec{x}'_B \right)^2 }
= \sqrt{ \left( \frac{1}{\sqrt{1 - \frac{v^2}{c^2} }} \left( \Delta t_B - \frac{\Delta \vec{x}_A \cdot \Delta \vec{x}_B}{c^2 \Delta t_A} \right) \right)^2 - \frac{1}{c^2} \left( \Delta \vec{x}_B + \left( \frac{ \frac{1}{\sqrt{1 - \frac{v^2}{c^2} }} - 1 }{ v^2 } \frac{\Delta \vec{x}_A}{\Delta t_A} \cdot \Delta \vec{x}_{B} - \frac{\Delta t_B}{\sqrt{1 - \frac{v^2}{c^2} }} \right) \frac{\Delta \vec{x}_A}{\Delta t_A} \right)^2 }
= \sqrt{ \frac{ \left( \Delta t_B \right) ^2 - 2 \Delta t_B \frac{\Delta \vec{x}_A \cdot \Delta \vec{x}_B}{c^2 \Delta t_A} + \left( \frac{\Delta \vec{x}_A \cdot \Delta \vec{x}_B}{c^2 \Delta t_A} \right) ^2}{ 1 - \frac{v^2}{c^2} } - \frac{ \left( \Delta \vec{x}_B \right)^2 }{c^2} - 2 \frac{ \frac{ \frac{1}{\sqrt{1 - \frac{v^2}{c^2} }} - 1 }{ v^2 } \frac{\Delta \vec{x}_A}{\Delta t_A} \cdot \Delta \vec{x}_{B} - \frac{\Delta t_B}{\sqrt{1 - \frac{v^2}{c^2} }} }{c^2} \frac{\Delta \vec{x}_A \cdot \Delta \vec{x}_B}{\Delta t_A} - \left( \frac{ \frac{1}{1 - \frac{v^2}{c^2}} + \frac{-2}{\sqrt{1 - \frac{v^2}{c^2} }} + 1 }{ v^4 } \frac{ \left( \Delta \vec{x}_A \cdot \Delta \vec{x}_{B} \right)^2 }{ \left( \Delta t_A \right)^2 } + 2 \frac{ \frac{1}{\sqrt{1 - \frac{v^2}{c^2} }} - 1 }{ v^2 } \frac{\Delta \vec{x}_A \cdot \Delta \vec{x}_{B} }{\Delta t_A } \frac{\Delta t_B}{\sqrt{1 - \frac{v^2}{c^2}} } - \frac{ \left( \Delta t_B \right)^2 }{1 - \frac{v^2}{c^2} } \right) \frac{v^2}{c^2} }
= \sqrt{ \frac{ c^2 \left( \Delta t_A \right)^2 - 2 \Delta \vec{x}_A \cdot \Delta \vec{x}_B + \frac{ \left( \Delta \vec{x}_A \cdot \Delta \vec{x}_B \right)^2 }{c^2 \left( \Delta t_A \right)^2 } }{ c^2 - v^2 } - \frac{ v^2 \left( \Delta t_A \right)^2 }{c^2} + \frac{ 1 - \frac{1}{1 - \frac{v^2}{c^2}} }{ c^2 v^2 } \frac{\left( \Delta \vec{x}_A \cdot \Delta \vec{x}_{B} \right)^2 }{\left(\Delta t_A \right)^2} + 2 \frac{\sqrt{1 - \frac{v^2}{c^2}} \Delta \vec{x}_A \cdot \Delta \vec{x}_B}{c^2 - v^2} + 2 \frac{ 1 - \sqrt{1 - \frac{v^2}{c^2} } }{ c^2 - v^2} \left( \Delta \vec{x}_A \cdot \Delta \vec{x}_{B} \right) - \frac{ v^2 \left( \Delta t_A \right)^2 }{c^2 - v^2} }
= \sqrt{ \frac{ (c^2 - v^2) \left( \Delta t_A \right)^2 }{ c^2 - v^2 } - \frac{ v^2 \left( \Delta t_A \right)^2 }{c^2} + \left( \frac{1}{c^4 - c^2 v^2} + \frac{ \frac{c^2 - v^2}{c^2 - v^2} - \frac{c^2}{c^2 - v^2} }{ c^2 v^2 } \right) \frac{\left( \Delta \vec{x}_A \cdot \Delta \vec{x}_{B} \right)^2 }{\left(\Delta t_A \right)^2} } = \sqrt{ 1 - \frac{v^2}{c^2} } \Delta t_A = \tau_A
$$.

So $$\tau_A = \tau_B = \tau'_A = \tau'_B$$ contradicting your position, Chan Rasjid.


Case III. Viewpoint of B. Inertial coordinates $$(t'', \vec{x}'')$$, proper times $$\tau''_A \; \textrm{and} \; \tau''_B$$
Care to try your hand at actually doing special relativity?
 
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My answer was : "I clasp my Rolex watch within my palms and vigorously shake it and discover time dilation. It does not mean current physics will have an explanation for it; Special Relativity is not the explanation by default!".

To me my answer is as clear and sufficient as what could be given; but if it does not satisfy you, what can I do - there is currently no technique for "consciousness transplant" so that you could understand as I do. Maybe we could settle it by poll by electing members who have posted here to say if I have answered you. If you just keep using "WOWs and HAAAs"(at least, not vulgar) and we each keep claiming to be right, then the argument will go to 100 posts of "WOWs and HAAAs"; and you would call upon Albert Einstein and I calling upon Mahatma Gandhi (who is one of the greatest among man and who also unequivocally repudiated Newton's Third Law by evidence of his person!). I would exasperate you further by applying Special Relativity - I am righter than you because my reference is the only one that dispenses with judgment - "I righter and you righter" but "you still wronger".

Thought I have answered you about your request that I explain the Hafele-Keating time dilation without Special Relativity, I do so again in a slightly different manner. Let's say the clocks of the HK experiment truly shows time dilation and, according to you, Special Relativity clearly account for the data. To you, it has significance - a further feather on the hat of Special Relativity. But to me, who is of the view that Special Relativity is invalid, the explanation using Special Relativity is irrelevant. What I am trying to emphasize is that whether I could, or could not, explain time dilation without Special Relativity is irrelevant. There should still be many physical phenomena that have been observed for which science do not yet have any satisfactory explanation - I include time dilation if it is confirmed.
From the bold, you are admitting that you do not have an alternative theory and you cannot explain time dilation in HK or any other experiment. You simply don't like the idea of SR so you declare it invalid. That is your prerogative and it is clearly the same goofy position as Dingle's, but a position is not a theory and in this case isn't even science.
 
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