Re: Basics series proposed

From: Androcles (dummy_at_dummy.net)
Date: 10/26/04 

Date: Tue, 26 Oct 2004 19:45:57 GMT

"Paul Draper" <pdraper@yahoo.com> wrote in message
news:74768d2d.0410260626.18bf4412@posting.google.com...
: "Androcles" <dummy@dummy.net> wrote in message
news:<eX9fd.45116$i02.18816@fe1.news.blueyonder.co.uk>...
: > "Paul Draper" <pdraper@yahoo.com> wrote in message
: > news:74768d2d.0410250722.4ba80e9@posting.google.com...
: > : "Androcles" <dummy@dummy.net> wrote in message
: > news:<jDSed.148683$BI5.112628@fe2.news.blueyonder.co.uk>...
: > :
: > : [snip, purely for Google-imposed length restrictions]
: > :
: > : > : > : > Assumption:
: > : > : > : > The meaning of simple mathematical terms is understood
: > between
: > : > us
: > : > and
: > : > : > : > used generally. Examples: the X-axis is orthogonal
the
: > : > Y-axis.
: > : > 'v'
: > : > : > : > represents
: > : > : > : > velocity. 'c' represents the speed of light and the
: > positive
: > velocity
: > : > : > : > of light.
: > : > : > :
: > : > : > : Let's also assume the synchronization procedure as
proposed
: > by
: > AE
: > : > : > : (though others could be chosen).
: > : > : >
: > : > : > Not agreed.
: > : > : > If you want to specify a procedure then follow your own
ground
: > rules
: > : > : > which I have accepted. "We'll go things one little step at
a
: > time."
: > : > :
: > : > : Well, we have to agree on SOME synchronization procedure,
: > because
: > it's
: > : > : essential to AE's presentation. I was simply arguing that we
: > adopt
: > his
: > : > : because there's nothing wrong with it, and it serves the
: > purpose.
: > : >
: > : > Whoa. This is a sidetrack, but a clock consists of an
oscillator
: > and a
: > : > counter. The counter can be remote from the oscillator. I can
: > : > synchonize two counters to the same reading. I am discussing
: > : > Einstein's method,
: > : > not adopting it.
: > : >
: > : >
: > : > : The
: > : > : key thing the synch procedure provides is the equation that
: > comes
: > from
: > : > : the bounce of light from A to B back to A: (1/2)[t'(A) +
t(A)] =
: > t(B),
: > : > : regardless of the frame the synch procedure is done in
(provided
: > that
: > : > : it's done on clocks in that frame). That equation is used
later
: > in
: > the
: > : > : derivation, so if it's not accepted, we should start over.
: > : >
: > : > It is one of the bases of discussion. That is not the same as
: > : > acceptance.
: > : > "In agreement with experience we further assume the quantity
: > : > 2AB/(t'A-tA) = c to be a universal constant- the velocity of
light
: > in
: > : > empty space." - Einstein.
: > : > Note that the '2' here is later used in the form '½' in the
: > equation
: > : > ½(tau0 +tau2) = tau1, but this ONLY applies when A and B are
: > : > relatively at rest.
: > :
: > : Agreed. The synchronization procedure that Einstein proposes
only
: > : works if A and B are at rest with respect to each other.
Moreover,
: > : this only works if the clocks are at rest with respect to the
frame
: > in
: > : which the synchronization is done. This is a key point. Einstein
: > : assumes nothing more than this.
:
: I'm going to refer to the preceding paragraph below.
:
: >
: > :
: > : > If there is any motion between A and B, then the distance AB
: > differs
: > : > from BA. 2AB does not apply.
: > : > I do not agree on the legitimacy of '½'.
: > : > I do not accept (0.33 + 0.67) / 2 = 0.33, and never will, even
if
: > you
: > : > include the coordinates A and B and a function tau(), so that
: > : > ½[ tau(A,t0) + tau(A,t2)] = tau(B,t1)
: > : > unless, of course, v = 0.
: > : > I might consider:
: > : > tau (½) * [ tau(A,t0) + tau(A,t2)] = tau(B,t1)
: > : > but that is not Einstein's math.
: > :
: > : Since the above extract is irrelevant to the paper, I'm not
: > responding
: > : to it.
: >
: >
: > "I anticipate you will be either be subjective (most are), or
ignore
: > it."--Androcles, 15/10/04.
: >
: > You are under no obligation to respond. I'm quite happy
: > to prove my point before the Google readership without
: > your defense.
: >
: > Einstein assumes that 2AB = AB +BA from which (AB +BA)/2 = AB.
: > He then assumes the time for the light to traverse AB is (tB-tA)
from
: > which c = AB/(tB-tA).
: > This latter I do not dispute, it is the definition of speed.
: >
: > Next he assumes the time for the light to traverse BA, (t'A-tB),
: > is equal to (tB-tA).
: > "This is a key point", to echo your phrase. I do not assume it.
: > If A approaches B, (t'A-tB) is less than (tB-tA).
: > If A recedes from B, (t'A-tB) is greater than (tB-tA).
: > Hence I do not accept, in general, that 2AB/(t'A-tA) = c.
: > I will accept that to be true if and only if v, the relative
velocity
: > between A and B, is zero.
: > In general, BA/(t'A-tB) + AB/(tB-tA) = (AB +BA)/(t'A-tA)
: > but AB + BA is not equal to 2AB.
: > However, that doesn't equal c, it equals beta.c were beta
: > can be determined algebraically.
: > That he asks his readership to accept such an absurd assumption
: > couched in the persuasive manner "in agreement with experience"
: > demonstrates his willingness to deceive the gullible.
: > Einstein was a huckster.
: >
: > Now I put this question to you, bluntly, and upon your
: > oath as an honourable gentlemen to be truthful, reply as
requested.
: > Do you accept Einstein's equation,
: > 2AB/(t'A-tA) = c ,
: > to be valid in general?
: >
: > Please respond with yes or no.
:
: No, not in general as you've defined it. See my above comments on
the
: conditions that must be met for this statement to be true. Add one
: more requirement, and I will change my answer to yes.
:
: > If yes, we can continue as I nail the *** to the cross.
: > If no, you can say
: > "Oh... Really?...Oh. I see I was confused. OK, I get it now.",
: > or we can still continue as I nail the *** to the cross.
: >
: >
: > Failure to respond at all will terminate the dialogue of which you
: > said
: > "I like this process. It looks to be productive." - Paul Draper,
: > news:74768d2d.0410221055.72835b50@posting.google.com
: >
: > If you feel demoralized, I can only advise you this way.
: > "If you can't take the heat, stay out of the kitchen" - Harry
Truman
: >
: > Androcles.
:
: I have to admit, I'm a little disappointed that you haven't
responded
: to my comments below. However, let's get over this little point
here,
: and then we can resume.

I can't think why you should be expressing the emotion of
disappointment.
I'm within the ground rules you established and I agreed to.

Quote:
"But I want this to be a fruitful exchange between the two of us, so
let's agree on some ground rules. We'll go things one little step at
a time. When we get to a point of conflict, we'll identify what the
error is on either side, and the party in error MUST acknowledge the
error and remove the erroneous statement from further discussion.
Unquote.

Einstein's equation 2AB/(t'A-tA) = c is not valid for any relative
motion between A and B to which you have agreed.
There need be no explanation, or "Add one more requirement, and I will
change my answer to yes." There is no other requirement. A is the
origin,
B is the mirror.
We are not permitted to conclude ½(tau0+ tau2) = tau1,
the ½ is invalid and the remainder of Einstein's paper is invalid.
That is really the end, no matter what else either may say, but since
you
seem to think there is more, I'll continue.
You have not yet said "Oh... Really?...Oh. I see I was confused. OK,
I get it now.", but clearly you are confused even if you don't get it
yet.

I'll snip some of what has been asked and answered.
On to the next sticking point.

: > : > : > Yes. a symbol that is primed belongs to k and corresponds
to
: > the
: > : > : > same symbol in K without the prime.
: > : > :
: > : > : No, this is not what Einstein says.
: > : >
: > : > He says a lot of things that are nonsense. Our job is to sift
the
: > : > wheat from the chaff.
: > :
: > : I would strongly advise against this strategy, and I don't agree
: > with
: > : it.

I'm not seeking your advice on my strategy, whether you agree with it
or not. We are discussing a paper written by Einstein, and you are
confused by it. I am not.
The symbols representing events in the K-frame are (x,y,z,t) and the
symbols representing events in the k-frame are (xi, eta, zeta,tau).
You are not permitted to write "stare at" equations. If x' = x-vt,
then x' is fixed in the k- frame as much as the symbols 0,1,2,3...
are.
x' is where the mirror is. Period.
The event of reflection is at (xi = x', eta, zeta, tau) in k.

"Oh... Really?...Oh. I see I was confused."
Yes or no?
**

: > We need to take everything as Einstein proposes them, follow
: > them
: > : to their logical conclusions, unless we see an error in
something
: > that
: > : he has said.

I agree. The first error is 2AB/(t'A-tA)= c unless v = 0,
that being "one more requirement, and I will change my answer to yes."
"Unless we see an error" is now in effect, because we agree we DO see
 an error.

: > : We should not reinterpret and say, "Einstein should not
: > : have said what he said here. What he meant to say was..." That
: > : introduces the biases and assumptions of the reader, and has the
: > : potential for introducing false inconsistencies.

I agree, so why are you doing it?
I don't write "stare at" equations, you do.

: > :
: > : >
: > : > He's very careful about this. The
: > : > : event coordinates in the k frame are xi, eta, zeta, tau.
: > : > Yes.
: > :
: > : Agreed then.
: > :
: > : >
: > : >
: > : > : The
: > : > : coordinates in the K frame are x, y, z, and t.
: > : > Right on.
: > : >
: > :
: > : Agreed then.
: > :
: > : >
: > : >
: > : > : He's making no claims
: > : > : whatsoever that x' represents the event coordinates in
EITHER
: > the k
: > : > : frame or the K frame.
: > : >
: > : > I can't agree. He defines x' = x -vt.
: > : > You've just said the coordinates of the K frame are x,y,z,t.
: > : > Therefore x' is moving relatively to x if v is non-zero,
: > : > and it is moving at v, which is what the k-frame is doing
: > : > relatively to the K-frame, and therefore is fixed in the
k-frame.
: > :
: > : Yes, but just because it is fixed in the k frame does not mean
that
: > it
: > : is also equal to the value of xi in the k frame.

That's your problem, not my problem.
One small step at a time. x' is a fixed distance from the origin of k.
Yes or no?
**

: > : For example,

We do not need examples.

[example snipped.]

We should not reinterpret and say, "Einstein should not
have said what he said here. What he meant to say was...

Don't even try to teach me, I can read for myself.
You'll by now have found that I agree with much of what you say
in principle, and the disagreements are solely in Einstein's
deliberately
confusing rhetoric and misleading claptrap.

: > : > Sorry to have to say this, but your argument is a simple
denial
: > : > and will not be entertained.
: > :
: > : I take a softer view. I would presume that if my interpretation
of a
: > : paper yielded an internal inconsistency within the paper, then I
: > : should re-read the paper and re-examine my interpretation.

Correct. I totally agree. There is internal inconsistency and you
should
re-read the paper to find it, and re-examine your interpretation. You
also
have the good fortune of me to help you.

: > : >
: > : >
: > : > : To do so would be leaping to conclusions.

Yes, I agree.
So you should not leap to the conclusion that he was right.

In
: > : > : fact, what he's trying to do is to determine what the
functional
: > forms
: > : > : of xi(x,y,z,t), eta(x,y,z,t), zeta(x,y,z,t), and
tau(x,y,z,t)
: > are,
: > : > : without making any prejudicial assumptions at all.
: > : >
: > : > In fact, he is not succeeding.
: > : > In fact, he fails miserably.
: > : > In fact, I will not accept rhetoric that claims 'fact' as a
: > : > persuasion of what Einstein is trying to do.
: > : > The facts speak for themselves.
: > :
: > : But I thought that's what we had agreed to do! We'd take it a
step
: > at
: > : a time, focus on points where there is a disagreement, and then
: > allow
: > : each to persuade the other! Now you're not interested in
conceding
: > any
: > : persuasion? Nor are you interested in persuading me that I am in
: > : error?

Persuasion, no. I expect to have a logical debate in which each will
arrive at the correct conclusion through rigorous proof. In fact,
(and when I commence a sentence with "in fact", it IS a fact) I'm
not interested in whether you are right or wrong, or of persuading you
that you are. My objective is to prove Einstein was wrong. Since
he is dead he cannot answer for himself and you are representing him,
otherwise I'd be lambasting him directly. It is a waste of time
talking to
the dingbats that contribute spite, malice, vitriol and blind faith to
this
newsgroup, nobody can overcome a religious faith with mere logic.
I've agreed with many of your points. You cannot persuade me I'm
wrong, you have to prove I'm wrong.

: > : >
: > : > :
: > : > : So what's this x' thing? It's not an event coordinate in
either
: > : > frame.
: > : >
: > : > The ray reflects at (x', eta, zeta, tau1) in the k-frame.
: > :
: > : That's not quite what he said. He said the following:
: > : "From the origin of system k let a ray be emitted at the time
(tau0)
: > : along the X-axis to x', and at the time (tau1) be reflected
thence
: > to
: > : the origin of the co-ordinates, arriving there at the time
(tau2);"
: > : He is clearly mixing terms between the two frames (for example,
: > : referring to the X-axis rather than the Xi-axis), but I don't
see
: > : anywhere where he assigns k-frame coordinates (x', eta, zeta,
tau1),
: > : as a collection, to this event.

Ok, point conceeded.
This summarizes "x', and at the time (tau1) be reflected"
The event of reflection, measured in k, is (xi = x', eta, zeta, tau =
tau1).
That needs no staring at. Is it better?
yes/no.
**

: > :
: > : > That reflection is an event.
: > : > I will not accept simple denial of this as a mathematical
proof.
: > : > The variables are xi, eta,zeta, tau in k.
: > : > x' is a coordinate, not a variable.
: > : > You are incorrect.
: > :
: > : This interpretation would of course lead to an immediate
internal
: > : inconsistency in the paper with his later statement that xi =
: > : beta*(x-v*t).

Too bad if it does. I say there is internal inconsistency although
I wasn't necessarily pointing at that one.

: > :Rather than adopting an interpretation that makes the
: > : paper worthless, I'm considering an interpretation that is not
: > : obviously ruled out, and which admits internal inconsistency. Is
: > there
: > : a reason why you won't do this?

Yes. The paper is worthless trash. No ½ measures.
Throw it to the dogs, then we can get back to real physics.
Understanding this curve is plenty of reason to scrap it,
 http://www.androc1es.pwp.blueyonder.co.uk/actual_data.htm
and that will form the basis of astronomy for the next century.
Also study this
 http://www.androc1es.pwp.blueyonder.co.uk/SekerinTime.htm
which rips into GR as well.
I told you I do not have a theory, I have a discovery.
The planets in close orbit to delta-Cepheus and beta-Perseus
are further than any planet discovered by anyone else, and
I am there discoverer.
Hmm.. on second thoughts you can salvage this line:
"But the ray moves relatively to the initial point of k, when measured
 in the stationary system, with the velocity c-v ..."

That happens to be internally inconsistent with

"It follows, further, that the velocity of light c cannot be altered
by composition with a velocity less than that of light.
For this case we obtain V = (c+w)/(1+w/c) = c."

: > : >
: > : >
: > : > : It is simply a change in variable,
: > : >
: > : > It is not a variable, it is a coordinate.
: > : > You are incorrect.
: > : >
: > : > : like what you would use in calculus
: > : >
: > : > grammar?
: > : >
: > : >
: > : > : to make solving an integral easier, even if the new variable
has
: > no
: > : > : physical meaning in the problem. Why is he doing it?
: > : >
: > : > So that he can make a vital prime vanish and pull the wool
over
: > : > your eyes, agree with Lorentz and make a name for himself.
: > : > You can fool all the people some of the time,
: > : > All of the people some of the time,
: > : > But you cannot fool all of the people all of the time.
: > : > Einstein was a huckster. Many criminals are extremely
intelligent,
: > : > and Einstein was a criminal.
: > : > Well, you did ask.
: > : > It has no relevance to the discussion, though, and neither
: > : > does your attempt at explaining dummy variables.
: > :
: > : Well, I usually try to give articles the benefit of the doubt
until
: > I
: > : run into an obvious error, without resorting to libelous claims
: > about
: > : the author.

Truth isn't libel. I'd welcome a law suit.
Einstein was a criminal huckster; his only defense is stupidity,
and I'll settle for that. He damaged the reputation of men far
greater than himself for his own glory. Giants like Galileo and
Newton, Kepler, upon whose shoulders I stand, seeing further
 than any man before me.

: > : Note that the paper appeared in a peer-reviewed journal,
: > : which meant that it had to pass the inspection of careful
readers.

Not careful enough readers.

: > : Note too that this paper appeared the same year as Einstein's
useful
: > : but not spectacular PhD thesis, so it's not likely that readerss
: > were
: > : swayed by his reputation -- he had none. The readers were
apparently
: > : able to accept the change-in-variable interpretation as
reasonable
: > and
: > : consistent. This seems to be your sticking point.

Piltdown man, jawbone of an ape and human skull was a hoax of
Einstein's era too (1912). That took 40 years to expose.
Backing Darwin as the "missing link", it can hardly be surprising.
Not that I object to Darwin's theory, but it took a hit when the
hoax was discovered and creationism is still very much alive in
the USA.
That got past peer review, too. So much for peer review.

: > :
: > : >
: > : > : It will make a
: > : > : later step easier. All that is true of x' is the following:
A
: > point
: > : > : that is stationary in the frame k will not have a constant
value
: > of
: > x
: > : > : in the frame K,

Correct, but we know that. x' = x-vt.

 but x' (as defined in the K frame, not the k
: > frame)
: > : > : WILL have a constant value.

Correct, but we know that. x' is where the reflection takes place.

: > :That is, while the x value of that
: > point
: > : > : will have time dependence that we would have to worry about
in a
: > later
: > : > : derivative, the x' value of that point will not.

Correct, but we know that. Einstein says "it is clear", and it is.

: > : > :
: > : > : Einstein is NOT saying that x' is the value of the
coordinate in
: > the
: > k
: > : > : frame.
: > : > Yes he is. That is the name of the point where the ray
reflects.
: > : > You are incorrect.
: > :
: > : Yes, and that point is seen in both the K and k frames.
Therefore it
: > : has an x value and a xi value,

Yes. The x value is x'+vt, and the xi value is x'.

: > and as it turns out, a value of x'
: > that
: > : we can calculate from x by its definition.

Right. So what is the point? Or are you just thinking on paper?

: > :
: > : >
: > : > : That would be presuming that xi will end up to be x'. No
such
: > : > : presumption is made, nor in fact will that be the conclusion
in
: > the
: > : > : end. Nor should we presume it. It's not obvious.
: > : >
: > : > I do not presume it, and it is obvious. The ray reflects at
x'.
: > : > Einstein says so.
: > : > "From the origin of system k let a ray be emitted at the time
tau0
: > : > along the X-axis to x', and at the time tau1 be reflected
thence
: > to
: > : > the origin of the co-ordinates"
: > : > You should not presume x' to be anything else, and I will not
: > accept
: > : > any other definition.
: > : > You are incorrect.
: > :
: > : I'm sorry I'm so dense. It is not obvious to me at all. Where
does
: > he
: > : say that xi for that event is x'?

He doesn't. You did that, in your confused "stare at" equation.
Einstein the huckster is careful to avoid such a statement,
it would be an obvious internal inconsistency to say
xi = (x-vt)/sqrt(1-v^2/c^2)
and
xi = x'
and
x' = x-vt.
That would then be
xi = x'/sqrt(1-v^2/c^2)
and it is obvious v = 0.

The peers reviewing that would pick up on it right away.
Einstein did as we all do, he scribbled his ideas on the back
of an envelope. The paper itself was carefully polished, rewritten,
and the one essential prime was omitted. Why use a prime anyway?
Obvious, isn't it? It is small enough to hide and deliberate
misdirection when you put it in a lengthy equation.
½[tau(0,0,0,t)+tau(0',0,0,t+x'/(c-v)+x'/(c+v))] =
tau(x',0,0,t+x'/(c-v))
We don't normally prime a number, so it slipped past 100 years
of peer review.

Back to 2AB/(t'A-tA) = c, and put A and B in.

½[tau(A,t)+tau(A',t+x'/(c-v)+x'/(c+v))] = tau(B,t+x'/(c-v))
Not so easy to hide A', is it?

Einstein was a huckster.
"Oh... Really?...Oh. I see I was confused. OK, I get it now." ?
**

: > :
: > : >
: > : > :
: > : > : What I *suspect* he is doing
: > : >
: > [snip for length and staying on topic...]
: > : >
: > : > I'm here to prosecute Einstein for fraud, before all Google
: > readers to
: > : > see.
: > : > You've chosen to be his defence attorney. Let the record show
that
: > so
: > : > far you've denied x' is a place where an event occurs and are
now
: > : > showing uncertainty of Einstein's intentions, my learned
friend.
: > I'm
: > : > not prosecuting you, please understand, but your client.
: > :
: > : I've denied that x' is the value of the xi coordinate in the k
: > frame,
: > : that's all. I've not denied that the event has certain value of
x',
: > : only that it is not the same as xi. You seem extremely focused
on
: > this
: > : one sentence.

Then you are stuck with
xi = x'/sqrt(1 - v^2/c^2),
which you cannot derive, and
"(x',y,z,t) = (x',y,z,t1) [yes, this line takes some staring at]"
because x' belongs to the k-frame and it should be
(xi,eta,zeta,tau) = (x',eta,zeta,tau1) which needs no staring at.

Einstein was a huckster.
"Oh... Really?...Oh. I see I was confused. OK, I get it now." ?
**

I'll break here.
Androcles.

: > : >
: > : >
: > : > : (we'll found out in a bit) is that he is
: > : > : using the change in variable to do the derivation in two
steps.
: > He's
: > : > : going to find out the form of, for example, tau(x',y,z,t)
and
: > then
: > : > : undo the variable change to find out the form of
tau(x,y,z,t).
: > The
: > use
: > : > : of x' is just a mathematical trick to make the derivation
: > easier,
: > even
: > : > : though it does it in two steps.
: > : > :
: > : > : So let's let Einstein use this change of variable from x to
x'
: > in
: > the
: > : > : K frame and see where he goes with it. Let's not assume
anything
: > or
: > : > : read meanings in that aren't there yet.
: > : > :
: > : > : Agreed?
: > : >
: > : > No, not agreed.
: > : > x' moves at velocity v relative to the K-frame, because x' =
x-vt.
: > : > Chose any x in K, and x' is displaced from x by a distance vt.
: > : > That includes x = 0.
: > :
: > : That is certainly true. x' does move to the right at velocity v
: > : relative to the K frame. That does not automatically make it the
xi
: > : coordinate for the k frame, which also moves to the right with
: > : velocity v. As I indicated above, it is POSSIBLE (we've yet to
see)
: > : that xi could be xi = c*x', where c is a number or a function
: > : independent of x, yet to be determined.
: > :
: > : (In fact, to presume that xi MUST be the same as x' is
tantamount to
: > : insisting that space and time respect Galilean transforms rather
: > than
: > : any other possible transform. It's no wonder that insisting on a
: > : Galilean transform yields an inconsistency with a Lorentz
: > transform.)
: > :
: > : >
: > : > The judge wants to adjourn for lunch, and so do I. Take time
out
: > : > to regroup, your argument needs some polish. :-)
: > : >
: > :
: > : Well, that's a pity because there is much useful discussion on
the
: > : SAME topic below that I would have liked to see you respond to.
: > :
: > : PD
: > :
: > : >
: > : >
: > : >
: > : > : **
: > : > :
: > : > : > Diagramically, we have
: > : > : > O'-------------xi-----x'
: > : > : > O---------------------x
: > : > : > where ' is to be the origin of k, aka (0,0,0,tau) and
: > : > : > o is the origin of K, (0,0,0,t).
: > : > : > We have to establish the relationship between xi and x,
tau
: > and t,
: > : > : > eta and y, zeta and z.
: > : > : > I think you will stipulate to eta = y, zeta = z.
: > : > : > I have drawn xi < x' to represent length contraction of
the
: > moving
: > k
: > : > : > frame.
: > : > : > Recall that Einstein claims
: > : > : > xi = (x-vt) * gamm = x' * beta, where beta =
1/sqrt(1-v^2/c^2)
: > : > : > Note that I have carefully primed O', the origin of the
: > moving
: > frame
: > : > : > to distinguish it from O, the origin of the stationary
frame.
: > : > : > I shall prove that xi = x' = x, v = 0.
: > : > :
: > : > : Moving too far ahead. Let's back up (see above) and take it
a
: > step
: > at
: > : > : a time.
: > : > :
: > : > : >
: > : > : > : >
: > : > : > : > and
: > : > : > : > ½[tau(0,0,0,t)+tau(0,0,0,t+x'/(c-v)+x'/(c+v))] =
: > : > : > : > tau(x',0,0,t+x'/(c-v)) {2}
: > : > : > : > **
: > : > : > :
: > : > : > : Correct. This statement follows the synchronization
: > procedure
: > : > that
: > : > AE
: > : > : > : proposed, asserting that in the frame k, the time tau to
go
: > from
: > the
: > : > : > : origin of the K frame (call it O') to x' must be the
same as
: > the
: > time
: > : > : > : tau to go from x' back to O'. Agreed on the meaning?
: > : > : > : **
: > : > : > No. the origin of the K-frame is O, not O'
: > : > :
: > : > : You may be right. I may have mistyped. But you know what?
Let's
: > not
: > : > : use O and O' anyway. They're not in the paper, and we don't
need
: > them.
: > : > : Let's drop them from further discussion. OK?
: > : > : **
: > : > :
: > : > : >
: > : > : >
: > : > : > : >
: > : > : > : > Fact 3:
: > : > : > : > The basis of {2} is
: > : > : > : > t0 = t
: > : > : > : > t1 = t0+x'/(c-v)
: > : > : > : > t2 = t1 + x'/|(c+v)
: > : > : > : > **
: > : > : > :
: > : > : > : Sorta. That's PART of the basis. The other part of the
basis
: > is
: > that
: > : > : > : (1/2)[tau0 + tau2] = tau1, as I mentioned above. The
: > : > substitutions
: > : > for
: > : > : > : t0, t1, and t2, are just as you say.
: > : > : >
: > : > : > Of course. I simply wanted to abbreviate.
: > : > :
: > : > : OK, note that this stems directly from the synchronization
: > procedure
: > : > : that I asked that we presume. See above.
: > : > :
: > : > : >
: > : > : >
: > : > : > : >
: > : > : > : > Fact 4:
: > : > : > : > The spatial coordinates that correspond to the times
are
: > (0,0,0),
: > : > : > : > (0,0,0)
: > : > : > : > and (x',0,0); This yields events (0,0,0,t0),
(0,0,0,t2)
: > and
: > : > : > : > (x',0,0,t1) and
: > : > : > : > these events are the argument to the function tau().
: > : > : > : > **
: > : > : > :
: > : > : > : OK, here is where I'm not clear what you mean by spatial
: > : > : > coordinates.
: > : > : >
: > : > : > (x,y,z) are spatial coordinates. (t) represents time.
: > : > : > "If we place x'=x-vt, it is clear that a point at rest in
the
: > system k
: > : > : > must
: > : > : > have a system of values x', y, z, independent of time."-
: > Einstein.
: > : > :
: > : > : Note that he is NOT saying that these are the values of the
: > : > : coordinates in k. I read this to mean:
: > : > : Take a point that is rest in k. Then while x (a coordinate
of
: > that
: > : > : point as measured in K) has a value that is dependent on
time,
: > instead
: > : > : x' (a change of variable of the position of that point as
: > measured
: > in
: > : > : K) has a value that is independent of time. Thus, x', y, z
are
: > : > : suitable coordinates of that point, as measured in K, that
are
: > : > : independent of time.
: > : > :
: > : > : Agreed?
: > : > : **
: > : > :
: > : > : > In system k, this would be better expressed as (x', eta,
zeta)
: > to
: > : > : > avoid
: > : > : > confusion.
: > : > :
: > : > : Disagree. This is leaping to a conclusion that we can't
make.
: > We're
: > : > : trying to find the functional dependence of xi on x, y, z,
t.
: > We're
: > : > : NOT to presume that we already know that xi = x' = x - vt.
That
: > would
: > : > : be premature. Agree to hold off on this presumption?
: > : > : **
: > : > :
: > : > : > Recall that k is the 'greek' frame, Kappa is the 'roman'
: > : > : > frame :-)
: > : > : > Before you dispute this, read on, because I anticipate
this
: > may be
: > : > : > a sticking point that I have tried to clarify below, where
you
: > have a
: > : > : > line that needs staring at.
: > : > : > **
: > : > : >
: > : > : > Incidentally, (t) is not a vector. There is no going back
to
: > when
: > you
: > : > : > were.
: > : > :
: > : > : I don't think we have to imply anything about the nature of
the
: > : > : assembly of coordinates as a vector yet. We are simply
defining
: > four
: > : > : values to associate with an event: x, y, z, and t as
measured in
: > the
: > K
: > : > : frame, and xi, eta, zeta, tau as measured in the k frame.
Take
: > them
: > to
: > : > : be independent scalar values, if you like. And all we are
saying
: > is
: > : > : that xi can be written as a function of x, y, z, and t, and
so
: > on.
: > No
: > : > : assumption about the conglomerates [x,y,z,t] or
: > [xi,eta,zeta,tau]
: > need
: > : > : to be taken at this point.
: > : > :
: > : > : > That's just another way of saying time has no additive
: > inverse.
: > : > : > Exploring "If it did" belongs to the realm of sci-fi, the
: > grandfather
: > : > : > paradox looms ugly, and while bed-time reading fun it has
no
: > place
: > in
: > : > : > physics, which is the topic of our discussion. With that,
I
: > dismiss
: > : > : > Minkowski as irrelevant.
: > : > : > **
: > : > :
: > : > : Again, leaping too far ahead. Let's take it a step at a
time.
: > : > :
: > : > : >
: > : > : >
: > : > : > : Are you saying these are the coordinates (x,y,z) as
measured
: > in
: > : > the
: > : > K
: > : > : > : frame?
: > : > : >
: > : > : > The coordinates (x',y,z) belong to the k-frame, and y =
eta, z
: > =
: > zeta.
: > : > : > Coordinates cannot be measured, they simply ARE. We can
only
: > compare
: > : > : > (i,e. make measurement) between frames.
: > : > : > **
: > : > :
: > : > : Disagree. See the above. Presuming too much, too fast. x' is
: > simply
: > a
: > : > : change of variable in the K frame, not asserting part of the
: > answer
: > : > : for the k frame.
: > : > :
: > : > : >
: > : > : >
: > : > : > : If that's what you're saying, then I disagree. Einstein
was
: > : > : > : postulating tau to be a function not of x, y, z, and t,
but
: > of
: > : > x',
: > : > y,
: > : > : > : z, and t.
: > : > : >
: > : > : > x' does not belong to the K frame. We've only two frames,
and
: > : > : > x' = x-vt.
: > : > : > x' is moving, being constantly displaced from x by a
distance
: > vt.
: > : > : > x' belongs to the k-frame.
: > : > : > Perhaps your thinking is represented by this diagram:
: > : > : >
: > : > : > O'---------------xi---
: > : > : > O----------------x'---x
: > : > : > or this;
: > : > : > -----O'---------------xi
: > : > : > O----------------x---x'
: > : > : >
: > : > : > I will not consider a third frame.
: > : > : > We have point of contention, so maybe we should break here
to
: > clear it
: > : > : > up.
: > : > : > However, I'll try to right now by answering your next
point.
: > : > :
: > : > : I'm not thinking of a third frame. x' is not a coordinate in
: > either
: > : > : frame, nor does it have to be a coordinate in any frame. It
is a
: > : > : change of variable used as a mathematical device, without
much
: > : > : physical content except that its value for a point
stationary in
: > the
: > k
: > : > : frame is constant, independent of time.
: > : > :
: > : > : >
: > : > : >
: > : > : > : I quote from the paper: "We first define (tau) as a
function
: > of
: > : > x',
: > : > y,
: > : > : > : z, and t."
: > : > : > : Thus, for example, the ray proceeds from
: > : > : > : (x',y,z,t) = (0,0,0,t)
: > : > : > : to
: > : > : > : (x',y,z,t) = (x',y,z,t1) [yes, this line takes some
: > staring
: > at]
: > : > : > : and back to
: > : > : > : (x',y,z,t) = (0,0,0,t2)
: > : > : > :
: > : > : > : Are we in agreement?
: > : > : > : **
: > : > : > You are using x' as a variable.
: > : > :
: > : > : Exactly. This is precisely what Einstein has in mind.
: > : > : Agreed?
: > : > : **
: > : > :
: > : > : > It is supposed to be a coordinate
: > : > : > and therefore fixed relative to the origin.
: > : > :
: > : > : Disagree. It's not a coordinate per se. The thing that is
fixed
: > with
: > : > : respect to the origin of the k frame is the light source and
the
: > : > : mirror that is used for synchronization. The value of x' of
the
: > light
: > : > : source and the value of x' of the mirror, as seen in the K
: > frame,
: > are
: > : > : constant values, independent of time. But that doesn't mean
that
: > x'
: > IS
: > : > : the coordinate of anything in either the K or k frames.
: > : > :
: > : > : Let's just allow the change in variable without assigning
any
: > : > : coordinate interpretation for the time being. OK?
: > : > : **
: > : > :
: > : > : >That is why it is
: > : > : > difficult
: > : > : > to comprehend the line that needs staring at. You'll need
to
: > use
: > : > : > a different symbol, perhaps 'm' for mirror, and then
you'll
: > have
: > : > : > (x',y,z,t) = (0,0,0,t0)
: > : > : > (x',y,z,t) = (m,y,z,t1)
: > : > : > (x',y,z,t) = (0,0,0,t2)
: > : > :
: > : > : This is right, as seen in the K frame.
: > : > :
: > : > : >
: > : > : > This is then identical to
: > : > : >
: > : > : > (x,y,z,t) = (0,0,0,t0)
: > : > : > (x,y,z,t) = (m,y,z,t1)
: > : > : > (x,y,z,t) = (0,0,0,t2)
: > : > :
: > : > : This is not right, as seen in the K frame. In the K frame,
the
: > light
: > : > : source and the mirror are moving to the right all the time.
Thus
: > the
: > : > : light source generally has the values, for example:
: > : > : (x,y,z,t) = (0+vt, y, z, t)
: > : > : If we say that at time t0, the light source is at x=0 and
the
: > mirror
: > : > : is at x=m, the three events then have the values
: > : > : (x,y,z,t) = (0+v*t0, 0, 0, t0) Light emitted from source
: > : > : (x,y,z,t) = (m+v*t1, 0, 0, t1) Light bouces from mirror --
: > note
: > : > : mirror has slid to right
: > : > : (x,y,z,t) = (0+v*t2, 0, 0, t2) Light returns to source --
: > note
: > : > : source has slid to right
: > : > :
: > : > : Since these coordinates depend on time, which will possibly
: > cause
: > : > : trouble later when doing some calculus, let's do a variable
: > change
: > : > : from x to x'=x-vt, which yields for the three events, as
seen
: > the K
: > : > : frame but in changed variables
: > : > : (x',y,z,t) = (0,0,0,t0)
: > : > : (x',y,z,t) = (m,0,0,t1)
: > : > : (x',y,z,t) = (0,0,0,t2)
: > : > :
: > : > : > which yields the same result, x' = x and x' = x-vt, hence
v =
: > 0.
: > : > : > You could then argue that we should use m', but there is
to be
: > : > : > but one mirror. Decide if it moves.
: > : > :
: > : > : No, incorrect conclusion, but again it's leaping too far
ahead.
: > Take
: > : > : little steps.
: > : > :
: > : > : >
: > : > : > : >
: > : > : > : > Fact 5:
: > : > : > : > The arguments to the function tau() belong to the
: > "stationary"
: > K-frame
: > : > : > : > which is the domain of the function. The codomain (or
: > image as
: > : > it
: > : > is
: > : > : > : > often
: > : > : > : > referred to in the USA) is the "moving" k-frame.
: > : > : > : > **
: > : > : > :
: > : > : > : Sorta. The arguments are not the coordinates (x,y,z,t)
of
: > the K
: > frame,
: > : > : > : but a related set of coordinates (x', y, z, t).
: > : > : > : Agreed?
: > : > : > : **
: > : > : > No. There is no third frame. Now I'll stop.
: > : > : > Androcles.
: > : > :
: > : > : A change in variables does not force the x' variable to
: > represent a
: > : > : coordinate in any frame. I'm not presuming a third frame,
only a
: > : > : change in variables.
: > : > :
: > : > : >
: > : > : >
: > : > : > :
: > : > : > : >
: > : > : > : > Fact 6: ( a quotation)
: > : > : > : > "From the origin of system k let a ray be emitted at
the
: > time
: > tau0
: > : > : > : > along the X-axis to x', and at the time tau1 be
reflected
: > : > thence
: > : > to
: > : > : > : > the origin of the co-ordinates, arriving there at the
: > time
: > tau2;"
: > : > : > : > **
: > : > : > :
: > : > : > : Agreed, indicating the synchronization procedure to be
: > followed
: > : > in
: > : > any
: > : > : > : frame.
: > : > : > :
: > : > : > : >
: > : > : > : > Fact 7:
: > : > : > : > The light has returned to the origin of K. If k is
indeed
: > moving
: > : > : > : > relative to K, the tip of the ray has gone past the
origin
: > of
: > : > k,
: > : > now
: > : > : > : > displaced from the origin K by a distance v(t2-t0).
: > : > : > : > **
: > : > : > :
: > : > : > : No. This is NOT what Einstein said. It returns to the
origin
: > of
: > : > k,
: > : > not
: > : > : > : the origin of K. This follows mathematically from the
fact
: > that
: > : > tau
: > : > is
: > : > : > : a function of x', y, z, and t, not of x, y, z, and t.
But
: > let's
: > see
: > : > : > : why he does it this way.
: > : > : > :
: > : > : > : Read again the synchronization procedure. Einstein
proposes
: > a
: > : > point
: > : > A
: > : > : > : and B in a frame, but let's make it concrete. Let's
suppose
: > at A
: > : > is
: > : > a
: > : > : > : light source (a camera flash) and a photodiode, and at B
is
: > a
: > mirror.
: > : > : > : There is a clock at both locations. It's important that
the
: > equipment
: > : > : > : at both ends be stationary in the frame where the
: > synchronization
: > : > : > : procedure is done -- that's how he defined it. Thus the
: > procedure is
: > : > : > : to fire the flash, bounce the light off the mirror, and
: > receive
: > it
: > : > : > : back at the location of the source. If the time elapsed
in
: > both
: > : > : > : directions is the same, then the clocks in that frame
are
: > : > : > : synchronized. This is the basis of the second line of
your
: > Fact
: > 2.
: > : > : > : Because this is done to synchronize the clocks in k,
this
: > equipment
: > : > : > : must be at rest in the frame k, meaning of course that
they
: > are
: > : > : > : traveling to the right with speed v in frame K. Thus, if
the
: > : > flash
: > : > is
: > : > : > : at the origin of k when it is fired, the return pulse is
: > again
: > : > : > : received at the origin of k. This corresponds to x' = 0,
but
: > not
: > x=0,
: > : > : > : in the frame K.
: > : > : > :
: > : > : > : Acknowledge the error?
: > : > : > : **
: > : > : > :

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