Re: Basics series proposed

From: Androcles (dummy_at_dummy.net)
Date: 10/24/04 

Date: Sun, 24 Oct 2004 18:37:03 GMT

"Paul Draper" <pdraper@yahoo.com> wrote in message
news:74768d2d.0410240505.78a94f20@posting.google.com...
: "Androcles" <dummy@dummy.net> wrote in message
news:<Afged.137751$BI5.33142@fe2.news.blueyonder.co.uk>...
: > "Paul Draper" <pdraper@yahoo.com> wrote in message
: > news:74768d2d.0410221055.72835b50@posting.google.com...
: > : "Androcles" <dummy@dummy.net> wrote in message
: > news:<lzRdd.130845$BI5.57887@fe2.news.blueyonder.co.uk>...
: > : > "Paul Draper" <pdraper@yahoo.com> wrote in message
: > : > news:74768d2d.0410210447.10946e15@posting.google.com...
: > : > : "Androcles" <dummy@dummy.net> wrote in message
: > news:<SQBdd.89041$ay5.7962@fe1.news.blueyonder.co.uk>...
: > : > : >
: > : > : > BTW, the spatial coordinates when the light leaves the
origin
: > : > : > of k are (0,0,0) and when it returns, they are (0,0,0) in
his
: > 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))
: > : > : > so v = 0, sqrt(1-v^2/c^2) = 1.
: > : > : >
: > : > : > Now you can say
: > : > : > "Oh... Really?...Oh. I see I was confused. OK, I get it
now."
: > : > : > I have this strange feeling you will not.
: > : > : >
: > : > : > 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, in your case, I will get over my disenchantment.
: > : > :
: > : > : 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.
: > : >
: > : > I'll agree to your terms.
: > : > My terms:
: > : > Either one of us could inadvertantly make a typographical
error
: > : > or simple arithmetic error, and should correct it if noticed.
: > : > I'd require: the error to be acknowledged and corrected; the
: > : > discussion continued until I have convince you or you have
: > : > convinced me. Failing to respond in a reasonable time
: > : > is a Pyrrhic victory and unsatisfactory. The penalty for
failing
: > : > to respond is to be hounded by me at any time I choose.
: > :
: > : Note my other response to this, indicating an anticipated gap in
the
: > : very near future, where I won't be accessing the newsgroup.
There
: > may
: > : have to be some flexibility in "reasonable time", but the abuse
: > should
: > : be self-evident.
: > :
: > : >
: > : > Note:
: > : > The hidden penalty for agreeing with me is to be hounded by
: > : > the puppy Dinky van de Torquemada the spermless. :-)
: > : > Since you are somewhat emotional, being prone to depression
: > : > (showing it by confessing a sensation of demoralization), you
: > : > may wish to reconsider your challenge.
: > : > You'll then have to choose whether to be dishonourable
: > : > and retire or agree and retire, but I'd prefer you were brave
: > enough
: > : > to continue. I had hoped to see sal convinced, but he resorted
: > : > to the tactic of the relativist and ignored or simply denied
the
: > vital
: > : > points I made. For excuse he pleads pressure of work, which
: > : > is lame. The entire correspondence could be easily picked up
: > : > at a later date. As I write now, he has not responded for a
: > : > couple of days (because he's stuck).
: > : >
: > : > :
: > : > : We can proceed any of three ways:
: > : > : 1. We start with the assumptions and implications of your
: > theory.
: > : >
: > : > Not possible. I don't have a theory. Everything I offer is the
: > : > result of some previously accepted concept. I do claim to have
a
: > : > discovery, though, and I think I deserve recognition of that.
: > : >
: > : >
: > : > : 2. We start with the assumptions and implications of special
: > : > : relativity.
: > : >
: > : > Hmm... well, there are a lot of those, so that is bound to be
: > : > part of the discussion.
: > : >
: > : > : 3. We start with what you think is specifically factually
wrong
: > with
: > : > : SR, internally inconsistent, or inconsistent with other
accepted
: > : > : theoretical models.
: > : > :
: > : > : Your choice.
: > : >
: > : > (3.) predominantly, from a mathematical standpoint. This will
: > : > inevitiably lead through (2) to astrophysics (1), my
discovery.
: > : >
: > : >
: > : > 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.
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.

:
: >
: > :
: > : > The alternative is to give a predefined list of definitions,
but
: > in
: > : > this case we
: > : > would have to predefine
: > : > V = c+v
: > : > and
: > : > V = (c+v)/ ( 1 + v/c)
: > : > which are contradictory; they will will be part of the
discussion,
: > and
: > : > therefore cannot be predefined.
: > : >
: > : > Here goes.
: > : >
: > : > Fact 1:
: > : > Einstein derived the so-called Lorentz equations in his paper
: > : > "On the Electrodynamics of Moving Bodies", (translated from
: > : > the German here, but the equations transcend language
: > difficulties).
: > : > **
: > : > ( Indicate agreement after each double asterisk following a
fact,
: > or
: > : > explain the sticking point.)
: > : >
: > : > Non-obligatory advice:
: > : > See http://www.fourmilab.ch/etexts/einstein/specrel/www/
: > :
: > : Thanks, that will keep it handy.
: > :
: > : >
: > : >
: > : > Fact 2:
: > : > The equations he uses are
: > : > x' = x-vt {1}
: > : > **
: > :
: > : Agreed. This is a variable he uses. Let's stop here for clarity.
: > This
: > : is merely to establish that a point that is stationary in the
frame
: > k
: > : will have coordinates in the frame K that are functions of x',
y, z
: > : and NOT t. Correct?
: > : **
: > 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.

He's very careful about this. The
: event coordinates in the k frame are xi, eta, zeta, tau.
Yes.

: The
: coordinates in the K frame are x, y, z, and t.
Right on.

: 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.
It certainly does represent an event coordinate, the ray reflects
at x' at time tau1.
 Sorry to have to say this, but your argument is a simple denial
and will not be entertained.

: To do so would be leaping to conclusions. 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.

:
: 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 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.

: 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.

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

: 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.

:
: What I *suspect* he is doing

He's doing exactly what he says he is doing.
If you have any suspicions, direct them at the criminal mind of the
man.
He will not be the first.
The most recent accusations of forgery made against Ptolemy came from
Newton in [12]. He begins this book by stating clearly his views:-

This is the story of a scientific crime. ... I mean a crime committed
by a scientist against fellow scientists and scholars, a betrayal of
the ethics and integrity of his profession that has forever deprived
mankind of fundamental information about an important area of
astronomy and history.

"Towards the end Newton, having claimed to prove every observation
claimed by Ptolemy in the Almagest was fabricated, writes [12]:-

[Ptolemy] developed certain astronomical theories and discovered that
they were not consistent with observation. Instead of abandoning the
theories, he deliberately fabricated observations from the theories so
that he could claim that the observations prove the validity of his
theories. In every scientific or scholarly setting known, this
practice is called fraud, and it is a crime against science and
scholarship. "
http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Ptolemy.html

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.

: (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.

The judge wants to adjourn for lunch, and so do I. Take time out
to regroup, your argument needs some polish. :-)

Androcles.

: **
:
: > 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?
: > : **
: > :
: > : >
: > : > That seems to be a good place to pause.
: > : > If you still indicate agreement at this point, I'll continue.
: > : > If not, we'll discuss your disagreement.
: > : > Androcles.
: > :
: > : I like this process. It looks to be productive.
: > :
: > : PD

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