Mathematical Obscurities in Special Relativity

Maybe Janra will have some luck figuring this out:

In 1905, "On the Electro...", Einstein used the fact that the moving
observer sees the light going from A to B as tB - tA = rAB/c-v and
tA'- tB =rAB/c+v, instead of the tB-tA = rAB/c and tA'-tB = rAB/c
for the stationary observer, to make the claim that simultaneity
is relative for observers in different frames.

This relativity of simultaneity then became the popular way of
resolving the contradiction of both observers observing
time dilation of each other when symmetry is imposed.

I have a couple of problems with this. First, how come Einstein
used c+v and c-v for the speed of light as observed by the
moving observer? Didn't he go into lengths in 1920 about why
the Galilean relativity is wrong- for the very fact that
it uses c+v and c-v? Doesn't the relativity of simultaneity
contradict his second postulate?

Second, if time dilation existed, shouldn't the moving observer
observe the speed of light as c so that his timing of AB would
be the same as that observed by the stationary observer, making
events in the stationary frame simultaneous with the moving frame?

What is Einstein saying here?

It appears to me that either moving observers observe the
speed of light as c+v and c-v, so that the events are not simultaneous with the stationary frame, or that they observe time dilation so that the events are simultaneous. To claim both seems
to be a contradiction.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by 1234567890</i>
<br />how come Einstein used c+v and c-v for the speed of light as observed by the moving observer?<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">The "moving" observer sees the speed of light as c. However, the "fixed" observer sees the speed of light as c +/- v in the moving observer's frame because it is c in his own frame.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">if time dilation existed, shouldn't the moving observer
observe the speed of light as c so that his timing of AB would
be the same as that observed by the stationary observer, making
events in the stationary frame simultaneous with the moving frame?<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">The moving observer does observe the speed of light as c. That is why events in the stationary and moving frames can never be "simultaneous" except at the origin.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">It appears to me that either moving observers observe the speed of light as c+v and c-v, so that the events are not simultaneous with the stationary frame, or that they observe time dilation so that the events are simultaneous. To claim both seems
to be a contradiction.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">The concept of "simultaneous" is gone from SR unless observers and the event are co-located in space and time. Distant simultaneity for different frames <i>does not exist</i> in SR. -|Tom|-

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by tvanflandern</i>
<br />

<i>Originally posted by 1234567890</i>
<br />how come Einstein used c+v and c-v for the speed of light as observed by the moving observer?<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

[TVF]The "moving" observer sees the speed of light as c. However, the "fixed" observer sees the speed of light as c +/- v in the moving observer's frame because it is c in his own frame.

[123]I don't see how this changes the argument I posed since
velocity is relative- the relativity of
simultaneity was still developed under the assumption that c+v
and c-v is observed of a frame in motion relative to a reference frame, which is what Einstein said was wrong
with Galilean relativity.

It is the c+v and c-v in the denominator that makes the clocks nonsynchronous for the moving observer. If time dilation
had existed to make the speed of light to be observed
as c for all observers observing light in and from any
frame, the moving clock would be synchronous with the stationary
clock so that both observers would observe the events as simultaneous, contradicting the starting assumption that
simultaneity is relative.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by 1234567890</i>
<br />If time dilation had existed to make the speed of light to be observed as c for all observers observing light in and from any frame, the moving clock would be synchronous with the stationary clock so that both observers would observe the events as simultaneous, contradicting the starting assumption that simultaneity is relative.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">If our frame sees light moving at c and an observer in another frame moving at v, then <i>we</i> judge that the other observer is moving at a speed of c +/- v relative to the light wave. The other observer will see the same lightwave, measure speed c for it, notice us moving at speed -v, and determines that we are moving at c -/+ v relative to the light wave.

So our judgments about other frames are different from our judgments about our own frame. But observers in those other frames make the same kinds of judgments about our frame differing from their frame.

It gets worse. If I stand here and peer into another frame, and let my gaze focus on a single clock moving rapidly by in that other frame, I will see it ticking slower than my own clock. But if I focus instead on the nearest spot in the other frame and watch a series of clocks synchronized in that other frame go by, the readings on a series of clocks will increase <i>faster</i> than time on my own clock. This is because points in the other frame approaching us are <i>already in the future</i> for that other frame! Yet everything will seem normal and truly synchronized to an observer inside that frame, who instead sees our frame's past and future.

Nothing whatever can be synchronized between two frames in SR because of this "seeing into the past and future" aspect of peering into another frame. So while we may see a shortened rivet approaching a longer hole, we may be seeing the front end of the rivet as it was in the past, and the rear end as it will be in the future, making it <i>appear</i> shorter to us now when it might actually be longer than the rivet hole if it were brought into our frame.

If you can't give up your intuitive notion of simultaneity, you cannot grok SR. -|Tom|-

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by tvanflandern</i>
<br /><blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by 1234567890</i>
<br />If time dilation had existed to make the speed of light to be observed as c for all observers observing light in and from any frame, the moving clock would be synchronous with the stationary clock so that both observers would observe the events as simultaneous, contradicting the starting assumption that simultaneity is relative.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">If our frame sees light moving at c and an observer in another frame moving at v, then <i>we</i> judge that the other observer is moving at a speed of c +/- v relative to the light wave. The other observer will see the same lightwave, measure speed c for it, notice us moving at speed -v, and determines that we are moving at c -/+ v relative to the light wave.

So our judgments about other frames are different from our judgments about our own frame. But observers in those other frames make the same kinds of judgments about our frame differing from their frame.

It gets worse. If I stand here and peer into another frame, and let my gaze focus on a single clock moving rapidly by in that other frame, I will see it ticking slower than my own clock. But if I focus instead on the nearest spot in the other frame and watch a series of clocks synchronized in that other frame go by, the readings on a series of clocks will increase <i>faster</i> than time on my own clock. This is because points in the other frame approaching us are <i>already in the future</i> for that other frame! Yet everything will seem normal and truly synchronized to an observer inside that frame, who instead sees our frame's past and future.

Nothing whatever can be synchronized between two frames in SR because of this "seeing into the past and future" aspect of peering into another frame. So while we may see a shortened rivet approaching a longer hole, we may be seeing the front end of the rivet as it was in the past, and the rear end as it will be in the future, making it <i>appear</i> shorter to us now when it might actually be longer than the rivet hole if it were brought into our frame.

If you can't give up your intuitive notion of simultaneity, you cannot grok SR. -|Tom|-

<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

What I was objecting to is that SR uses Galilean relativity but rejects it at the same time. Relativity of simultaneity is redundant with time dilation- both imply a constancy of c. To use both simultaneously results in a contradiction.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by 1234567890</i>
<br />You are trying to tell me that I have to abandon my notion of simultaneity to understand SR while I'm talking about a possible contradiction (or some sort of redundancy) with relativity of simultaneity with time dilation.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">These two things are intimately related. All contradictions claimed for SR by thousands before you over the last 98 years have been based on a failure to understand SR's lack of remore simultaneity. Your examples have shown the same failure.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">If there is a contradiction then your patronizing remarks about us not understanding SR, et al, start to sound ridiculous.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">And if there is not a contradiction, then your arrogant "I'm smarter than all the physicists of the past 98 years, and they must be nuts not to see the obvious" attitude is truly offensive.

In the present situation, you are arguing with the rare physicist willing to grant you that SR is a falsified theory. So we are more or less on the same side. I'd hate to see how you argue with dyed-in-the-wool relativists.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">Where is there ever a need for time dilation if observers can deduce the speed of light as c, whether from a moving frame or a rest frame?<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">No such deduction is ever possible. The constancy of c is a postulate that must be assumed and enforced on clocks by using Einstein synchronization. That automatically makes the speed of light c no matter what nature says it is because it requires that the signal time in both directions must be the same. There is no way to test or check this postulate using lightspeed signals or anything slower. In SR, it must simply be so.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">Einstein used vector addition for light to argue for relativity of simultaneity, the very thing he said was wrong with Galilean relativity in 1920.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">You have failed to notice a crucial distinction made by Einstein, relativists, and me in previous messages. SR says the speed of light must be c within any inertial frame, but must be c +/- v when peering into any other inertial frame. The same remarks apply to observers in those other frames. That way, all inertial frames are equivalent.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">Of course if we had just taken into account of relative velocity when transforming events from a rest frame, the speed of light would have been constant c in Galilean relativity but then time dilation and length contraction become redundant.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">Not so when you apply the Lorentz transformations with the time slippage term and force them to work both ways between two frames. That is impossible unless time and length can be adjusted to conform to these seemingly conflicting requirements. -|Tom|-