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From: Peter Webb on 6 Mar 2010 07:26

"Bruce Richmond" <bsr3997(a)my-deja.com> wrote in message
news:26e68f86-9827-4534-9390-31137fb9853e(a)q15g2000yqj.googlegroups.com...
On Mar 5, 1:04 am, "Peter Webb" <webbfam...(a)DIESPAMDIEoptusnet.com.au>
wrote:
> > You are reading more into that than what I wrote. I am not choosing
> > LET over SR. They use the same math
> > ==================================================
>
> Well, e = mc^2 is maths. It appears in SR, but not LET.
>
> So I guess you were wrong, and they don't use the same maths.

It can be derived using LET. SR wasn't the first place it showed up,
so it doesn't own it any more than LET does.

Others here say they use the same math, so I guess you are wrong :)~

_________________________________
You said that SR uses the same maths.

1. e=mc^2 is maths
2. It appears in SR
3. It does not appear in LET
4. Therefore the maths in LET is not the same as the maths in SR

Which part of this do you disagree with?

More generally, you are missing the difference between LET and SR. LET
compared to SR is a bit like Kepler's laws of planetary motion compared to
Newton's laws of gravity. Mathematically, inverse square laws imply
elliptical orbits (and Kepler's equal area formula), and Kepler's laws
require inverse square forces for gravity. You could say that Kepler is
mathematically identical to Newton for calculating planetary motion, because
you could derive the inverse square law purely from Kepler. Just as you can
derive time dilation purely from LET.

What Newton did, in a sense, is create a model of the solar system which
obeys the same physical laws as Kepler, but did so using a completely
different starting point and framework. Newton and Kepler predict exactly
the same kinds of orbits, but Kepler's laws of planetary movement are not
the same as Newton's law of gravity, even though mathematically they produce
exactly the same orbits.

A very similar relationship exists between SR and LET. SR in a sense
"explains" LET, just as Newton "explained" Kepler.

Kepler's laws were statements about what is observed, Newton explains why
these observations occurred. LET was statements about what was observed, SR
explains why these observations occur.

When Newton's law of gravity came out, it did not invalidate Kepler, and nor
did it even make any new predictions concerning elliptical orbits. It did
explain however why Kepler's laws were in a sense correct. Physicists did
not say immediately after Newton that Kepler was wrong, or his equations
were wrong (and indeed they produce mathematically identical elliptical
orbits). Newton just told a whole lot more of the story a lot more clearly,
and Newton's laws were immediately taken as more fundamental and useful than
Kepler.

When SR came out, it did not invalidate LET, and nor did it even make any
new predictions concerning time dilation. It did explain however why LET's
equations were in a sense correct. Physicists did not say immediately after
SR that LET was wrong, or its equations are wrong (and indeed they produce
mathematically identical time dilation). SR just told a whole lot more of
the story a lot more clearly, and SR was immediately taken as more
fundamental and useful than LET.

Had Kepler known calculus, he could have worked out that the acceleration of
a planet is proportional to the inverse square of the distance, and
eventually got Newton's law of gravity, which is implicit in elliptical
orbits. He didn't. More to the point, he had no explanation of why his laws
held; they were empirical and not theoretical in that they described the
results of experiments, but provided no theoretical framework.

Similarly, if Lorentz and the others had considered the relationships
between energy and momentum in the right way, they would have got e=mc^2.
They didn't. More to the point, Lorentz had no explanation of why the
various transforms worked, they were empirical and not theoretical in that
described the results of experiments, but provided no theoretical framework.

You can use LET to calculate time dilation, just as you can use Kepler to
calculate orbits. But that doesn't mean that Kepler's theories are the same
as Newton's, or that LET is the same as SR.

HTH


From: Peter Webb on 6 Mar 2010 07:35
> I think the issue is as I described in "plain English" to Ste.
>
> Let's take 3 clocks, one (A) which gets left behind, one (B) that
> sallies out at speed v for a distance L and returns, and one (C) that
> sallies out at speed v for a distance 2L and returns. At speed v, the
> clocks sent forth are running slow by, say, 2%. I'm really not going
> to worry about the accelerations at all because, as all have said, the
> acceleration profiles are all the same. Clock B will arrive back at
> home having run slow by 2% for the time of its trip and it is now 2
> hours behind clock A, say. Once B arrives home and comes to rest
> alongside A, its rate is no longer slower than A's by 2%, and so while
> it sits there and waits for C to come home it will *continue* to be 2
> hours behind A. Finally, C comes home, having run slower than A by 2%
> for twice as long as B did, and so it will be 4 hours behind A. Since
> B is only 2 hours behind A, clock B and clock C are no longer
> synchronized.
>
> What am I missing?

What confuses me is that, if the clocks run slow by 2% for all the
time that they are moving, how does one reconcile this with the fact
that, if one uses the frame of one of the moving clocks, say clock B,
then it seems to be to be your argument that there is no slowdown at
all for B, and it is the other clocks, A and C, that slow down (i.e.
*disregarding* both acceleration and propagation delays).

________________________________
A, B and C are not equivalent. A stays in one inertial reference frame, B
and C do not. You would be well advised to read a standard explanation of
the twin's paradox. http://en.wikipedia.org/wiki/Twin_paradox is OK, and if
you look at the first few paragraphs of "Resolution of the paradox in
Special Relativity" on that page it discusses exactly that point, and
explains its significance.
http://www.phys.unsw.edu.au/einsteinlight/jw/module4_twin_paradox.htm is
similar.


From: Peter Webb on 6 Mar 2010 07:47
> This should make perfect sense to you. If a clock is running 2%
> slower, then it is running 2% slower regardless of distance. But if,
> as a result of running 2% slower, it falls behind 6 minutes after
> running a certain amount of time, then it will fall behind 12 minutes
> after running for twice as long.

Agreed.

The question now is, if we agree that both clocks suffer time dilation
in this way, then when they return to the start point, how do they
each reconcile the fact that (after accounting for the effects of
acceleration) it ought to be the other clock which is slow, when in
fact one clock (the one that went furthest from the start point) will
be slower than the other? And a third clock, left at the start point,
will be running ahead of both?

_________________________
They know that the operations were not symmetric. Only one clock remained in
the same inertial reference frame throughout. The other two clocks spent
different amounts of time in at least 3 different inertial reference frames.
Everybody can see this is true, and so nobody expects that the clocks will
remain synchronised.

If you really want to understand the twin paradox, read
http://en.wikipedia.org/wiki/Twin_paradox and feel free to ask any questions
you may have. When you read and understand this, then you will understand
what is going on. The question with 3 clocks is not materially different to
that for two clocks, and it would be trivial to change their diagrams to
also include the third clock.

This web page obviously took far more time to put together than you can
expect that I or anybody else will provide in newsgroup message, and you are
not going to understand the twin paradox until you sit down and go through
an explanation similar to this. I note it involves no maths beyond the
equations of SR itself (simple algebra).

So, why don't you?





From: Peter Webb on 6 Mar 2010 07:56
>
> Ste: This is exactly what I was telling you earlier, that people will
> be less inclined to teach things on your terms, using your language
> and indulging your lack of skills, and will advise you that it is more
> efficient in the long run to teach after you've acquired some relevant
> skills and vocabulary. You didn't seem to think this was the case, and
> here you have others telling you the same thing. Reconsider?

As I say Paul, the words "total acceleration" I think should have
given people some clue as to the meaning - and indeed the more
intelligent amongst us here did recognise the meaning, and suggested
an alternative word. That said, in this case I'm happy to use an
alternative formulation like "impulse", because I can see that it will
add further precision to my meanings in future.

____________________________
http://physics.about.com/od/glossary/g/Impulse.htm


It's quite different from the disputes that arose over words like
"physical" and "material", where each side seems to battle childishly
over whose idiosyncratic understanding of the word will prevail, when
the time could be better used getting on with the substantive argument.

________________________________
"Physical" and "material" are words that you introduced that have no real
meaning in physics. Impulse, on the other hand, has a very specific meaning
in this context; it is integral of Force over time (=Momentum, cf Force over
distance which is Energy). Use words like that correctly and you might start
understanding SR, because instead of discussing the interpretation of
English words you are actually discussing physics.


From: Peter Webb on 6 Mar 2010 08:18

"Ste" <ste_rose0(a)hotmail.com> wrote in message
news:e75f3463-ac9f-4b6c-ac9f-52b8622956a0(a)z4g2000yqa.googlegroups.com...
On 5 Mar, 14:46, mpalenik <markpale...(a)gmail.com> wrote:
> On Mar 5, 3:55 am, Ste <ste_ro...(a)hotmail.com> wrote:
>
> > So what you're saying (and I had recognised this problem before you
> > said it) is that it is the "original" position of emission that
> > matters?
>
> > And the "original" position changes depending on the frame (i.e. in
> > the source frame, the source does not move, whereas in the receiver
> > frame, the sources are constantly moving from their "original"
> > positions)?
>
> Right. The sources send out one pulse at one particular point in
> time. The only thing that matters is where they were located when
> they sent out that pulse. That location is the "source" of the pulse.

Ok. But one observation I would make first is that, I presume, from
the source inertial frame, both the rising and falling edges of the
wave have the same origin. However, in the receiver inertial frame,
the rising edge does not have the same origin as the falling edge - so
there is a lack of symmetry between what is being described in these
inertial frames.

_____________________________________
No, they can still be symmetric, and the choice of origin is arbitrary. The
rising and falling edges of the photon's E field (which I assume you are
talking about) is a complete red herring in the context of this thread; this
is what gives rise to the Relativistic Doppler Effect, but you seem to be
discussing time dilation generally, and this is not tied to using light -
you would get the same answers using neutrinos for signalling, and as far as
we know they don't "wave" at all.


Secondly, we talk of the sources being in a "particular place" when
the pulse is emitted, and yet by your own argument they are not in a
"particular place" at all - in one frame, the sources are in the same
place at all times, and in the other frame, the sources are never in
the same place for more than an instant. So is it really meaningful to
talk of the "place of origin" of the source as a well-defined, single
point in space and time?

____________________________________
Well yes, it is, but in a somewhat more abstract sense than in Newton.
Individuals in their own co-ordinate systems in 3D space will measure these
differently, but they are the same point in spacetime viewed from different
angles.

Much earlier on, somebody replied to a question about the ladder/barn
paradox by pointing out that an 80 foot high ladder can fit under a 10 foot
high door by rotating it. As you live in a world where speeds near c are
uncommon, its as if every ladder you have ever seen is standing upright and
you had no idea they could be tilted.

You are now asking a question which use of this analogy will help answer. If
your question "is it really meaningful to talk about a single well defined
origin for an event" was translated as "is it really meaningful to talk
about the *height* of a ladder", the answer is no, because by tilting it you
can have whatever height you want. OTOH, if it is translated as "is it
really meaningful to talk about the *length* of a ladder", the answer is yes
because this is invariant; an 80 foot ladder lying flat on the ground is
still 80 feet long, even if it has almost zero height.

HTH. Really, I do hope this helps; if you take the time to frame half decent
questions civilly I will take the time to give you half decent answers,
civilly.


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