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<DIV style="FONT-SIZE: 12pt; FONT-FAMILY: 'Calibri'; COLOR: #000000">
<DIV>Chip:</DIV>
<DIV> </DIV>
<DIV>I don’t think we’re quite saying the same thing, but I reckon it’s nothing
a few beers couldn’t sort out. Somehow I find that actually talking face to face
with people is much better for seeing the common ground than emails. When you
don’t talk face to face, it’s all too easy to spend all your time talking about
the things you differ on, and making a big deal about it.</DIV>
<DIV> </DIV>
<P class=MsoNormal><SPAN style="COLOR: "><EM>From the local reference frame,
time slows, distance gets shorter, and the speed of light remains the
same.</EM></SPAN></P>
<P class=MsoNormal><SPAN style="COLOR: "></SPAN> </P>
<P class=MsoNormal><SPAN style="COLOR: "><FONT face=Calibri>Yep. You go slower,
everything goes slower. So we say time slows down. And the guy who measures slow
light with a slow clock and a slowed-down brain will say the speed of light
remains the same. </FONT></SPAN></P>
<P class=MsoNormal><SPAN style="COLOR: "><FONT
face=Calibri></FONT></SPAN> </P>
<P class=MsoNormal><SPAN style="COLOR: "><EM><FONT face=Calibri>From an
observer’s reference frame, time slows, distance gets shorter, and since light
has less distance to travel in more time, light gets
slower.<o:p></o:p></FONT></EM></SPAN></P>
<DIV> </DIV>
<DIV>IMHO that’s not quite right. Light slows, along with all other
electromagnetic phenomena, including the piezo-electric vibrations in your
watch, and the electrochemical signals in your brain. The second is bigger
<EM>because</EM> the light slows down. Then the metre is the distance travelled
by light in 1/299792458th of a second. The light goes slower so the second is
bigger, but they cancel each other out leaving the metre unchanged. </DIV>
<DIV> </DIV>
<DIV>Regards</DIV>
<DIV>JohnD </DIV>
<DIV> </DIV>
<DIV style="FONT-SIZE: 12pt; FONT-FAMILY: 'Calibri'; COLOR: #000000"></DIV>
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<DIV><FONT size=3 face=Calibri></FONT> </DIV>
<DIV style="BACKGROUND: #f5f5f5">
<DIV style="font-color: black"><B>From:</B> <A title=chipakins@gmail.com
href="mailto:chipakins@gmail.com">Chip Akins</A> </DIV>
<DIV><B>Sent:</B> Friday, February 27, 2015 12:31 PM</DIV>
<DIV><B>To:</B> <A title=general@lists.natureoflightandparticles.org
href="mailto:general@lists.natureoflightandparticles.org">'Nature of Light and
Particles - General Discussion'</A> </DIV>
<DIV><B>Subject:</B> Re: [General] Black holes</DIV></DIV></DIV>
<DIV> </DIV></DIV>
<DIV
style='FONT-SIZE: small; TEXT-DECORATION: none; FONT-FAMILY: "Calibri"; FONT-WEIGHT: normal; COLOR: #000000; FONT-STYLE: normal; DISPLAY: inline'>
<DIV class=WordSection1>
<P class=MsoNormal><SPAN style="COLOR: black">Hi John W and John
D<o:p></o:p></SPAN></P>
<P class=MsoNormal><SPAN style="COLOR: black"><o:p><FONT
face=Calibri></FONT></o:p></SPAN> </P>
<P class=MsoNormal><SPAN style="COLOR: black">I think you are both saying the
same thing regarding the actual physics, but differing in your language, and in
your definitions.<o:p></o:p></SPAN></P>
<P class=MsoNormal><SPAN style="COLOR: black"><o:p><FONT
face=Calibri></FONT></o:p></SPAN> </P>
<P class=MsoNormal><SPAN style="COLOR: black">Regarding a gravitational frame
where the gravity has increased…<o:p></o:p></SPAN></P>
<P class=MsoNormal><SPAN style="COLOR: black"><o:p><FONT
face=Calibri></FONT></o:p></SPAN> </P>
<P class=MsoNormal><SPAN style="COLOR: black">From the local reference frame,
time slows, distance gets shorter, and the speed of light remains the
same.<o:p></o:p></SPAN></P>
<P class=MsoNormal><SPAN style="COLOR: black"><o:p><FONT
face=Calibri></FONT></o:p></SPAN> </P>
<P class=MsoNormal><SPAN style="COLOR: black">From an observer’s reference
frame, time slows, distance gets shorter, and since light has less distance to
travel in more time, light gets slower.<o:p></o:p></SPAN></P>
<P class=MsoNormal><SPAN style="COLOR: black"><o:p><FONT
face=Calibri></FONT></o:p></SPAN> </P>
<P class=MsoNormal><SPAN style="COLOR: black">Chip<o:p></o:p></SPAN></P>
<P class=MsoNormal><SPAN style="COLOR: black"><o:p></o:p></SPAN> </P>
<DIV>
<DIV
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<P class=MsoNormal><B><SPAN
style='FONT-SIZE: 11pt; FONT-FAMILY: "Calibri",sans-serif'>From:</SPAN></B><SPAN
style='FONT-SIZE: 11pt; FONT-FAMILY: "Calibri",sans-serif'> General
[mailto:general-bounces+chipakins=gmail.com@lists.natureoflightandparticles.org]
<B>On Behalf Of </B>John Williamson<BR><B>Sent:</B> Friday, February 27, 2015
2:56 AM<BR><B>To:</B> Nature of Light and Particles - General
Discussion<BR><B>Subject:</B> Re: [General] Black
holes<o:p></o:p></SPAN></P></DIV></DIV>
<P class=MsoNormal><o:p></o:p> </P>
<DIV>
<P class=MsoNormal><SPAN
style='FONT-SIZE: 10pt; FONT-FAMILY: "Tahoma",sans-serif; COLOR: black'>Hello
everyone,<BR><BR>In relativity BOTH space and time change. Look at the
equations! One man's time transforms to anothers space and vice versa. Now
(special) relativity may not be the complete theory of everything (and I do not
think it is) ... but, whatever it is, it is simply not so that space is constant
in it where time varies. You want relativity ... you have space changing to time
and time to space (with the speed of light being the point (for tachyonic
matter) where time crosses completely into space and vice-versa. At least that
is what the maths tells you - but that is mere maths of course.<BR><BR>In fact
the problem (of the hypnotic box and the two glasses of wine (good idea by the
way!) is even worse that you think it is. The diagram shows two boxes of
the same length , but with different velocities. This is not what particles do.
The (energy) frequency goes up, the size goes down. The upper box has not been
transformed - but the effect for what you have drawn is anyway is the wrong way
- it should be smaller ... making the frequency discrepancy even bigger if you
allow the velocity variation. The clocks would only agree if you made the top
box bigger. This is the point. It is far more complicated that just velocity and
frequency. What it means is that the clock thing is not fixed by ONLY changing
the speed of light- as in the two boxes picture.<BR><BR>The problem is anyway
that this isn' t really the problem. Even if we were to agree on whether the
speed of light is constant or not or whether time is motion the real problem
will remain: what is light and what are particles and how do we make up a theory
to describe them and understand them? If I throw out time in the differential
equations I use to describe the dynamics of nature (in the Maxwell or
Schroedinger equations for example) .. the d/dt part - what, practically, do I
replace it with? In fact, is not most people simple concept of dynamics that
which changes in time. Have a go- just try thinking of dynamics without any
notion of time .... Take out time and what does it gain you. One is left with
nothing more to say. With, as the dutch would say, a mouthful of teeth.
<BR><BR>I'm not sure precisely what you mean by "motion" here. Lets call it m
anyway and try to write a theory for d/dm. While something like this is possible
- one can formulate quantum mechanics in either the set of space and time or
energy and momentum d/dt d/dx d/dy and d/dz OR d/DE d/dpx d/dpy d/dpz -- those p
thingys are momentum - not "motion". We need to define just what it is we are
talking about. Otherwise (at Wittgenstein, Godels mentor would have said) its
not worth talking about.<BR><BR>Also E and t and p and x have the little quantum
problem of not being simultaneosly measureable. Now there lies the real
underlying problem... and that is what I should be looking at not arguing about
the speed of light!<BR><BR>I am not saying myself that motion is not fundamental
- it is! <BR><BR>What I am saying (and have been saying all along) is
precisely that it is fundamental. Things that do not have (at least internal)
motion do not exist. It is a John-Martin module that what you see is the less
fundamental stuff... that which is left over after whatever is strong has
satisfied itself. This is why you do not see magnetic monopoles. What I am
saying is that, to a good first approximation, one can take this motion to be
constant. If you do. That is exactly what a non-variable speed of light
means. Light is motion. The motion is constant. <BR><BR>Where that gets you is,
at least somewhere. Let m = c - some universal constant (the speed of light
say). Now one could write (allowing time to exist for a moment just for the sake
of argument) dc/dt = 0 and dc/ds = 0. At this point we are at the simple point I
have been talking about all along. If you like we have set dm = 0. We have a
speed of light, constant in any frame in which it is measured locally. As is
measured experimentally.<BR><BR>Extend this (therefore!) to be true in each and
every Lorentz frame with local measure of space s and measure of time t. One has
a theory which has some measures in common now with relativity. To make it
exactly match relativity one need only put in a proper, invariant, measure of
length -agreed upon by all observers of each others frames. This is
ct^2-x^2-y^2-z^2. There you go. Bob is your uncle.<BR><BR>Comments below ... (in
Red)<o:p></o:p></SPAN></P>
<DIV>
<DIV class=MsoNormal style="TEXT-ALIGN: center" align=center><SPAN
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<HR align=center SIZE=2 width="100%">
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<DIV id=divRpF267316>
<P class=MsoNormal style="MARGIN-BOTTOM: 12pt"><B><SPAN
style='FONT-SIZE: 10pt; FONT-FAMILY: "Tahoma",sans-serif; COLOR: black'>From:</SPAN></B><SPAN
style='FONT-SIZE: 10pt; FONT-FAMILY: "Tahoma",sans-serif; COLOR: black'> General
[general-bounces+john.williamson=glasgow.ac.uk@lists.natureoflightandparticles.org]
on behalf of John Williamson [John.Williamson@glasgow.ac.uk]<BR><B>Sent:</B>
Friday, February 27, 2015 7:34 AM<BR><B>To:</B> Nature of Light and Particles -
General Discussion<BR><B>Subject:</B> Re: [General] Black holes</SPAN><SPAN
style="COLOR: black"><o:p></o:p></SPAN></P></DIV>
<DIV>
<DIV>
<P class=MsoNormal><SPAN
style='FONT-SIZE: 10pt; FONT-FAMILY: "Tahoma",sans-serif; COLOR: black'><o:p></o:p></SPAN> </P>
<DIV>
<DIV class=MsoNormal style="TEXT-ALIGN: center" align=center><SPAN
style="COLOR: black">
<HR align=center SIZE=2 width="100%">
</SPAN></DIV>
<DIV id=divRpF727745>
<P class=MsoNormal style="MARGIN-BOTTOM: 12pt"><B><SPAN
style='FONT-SIZE: 10pt; FONT-FAMILY: "Tahoma",sans-serif; COLOR: black'>From:</SPAN></B><SPAN
style='FONT-SIZE: 10pt; FONT-FAMILY: "Tahoma",sans-serif; COLOR: black'> General
[general-bounces+john.williamson=glasgow.ac.uk@lists.natureoflightandparticles.org]
on behalf of John Duffield [johnduffield@btconnect.com]<BR><B>Sent:</B>
Thursday, February 26, 2015 7:57 PM<BR><B>To:</B> Nature of Light and Particles
- General Discussion<BR><B>Subject:</B> Re: [General] Black holes</SPAN><SPAN
style="COLOR: black"><o:p></o:p></SPAN></P></DIV>
<DIV>
<DIV>
<DIV>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: black'>John:</SPAN><SPAN
style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: black'>I think this speed of
light thing is crucial because one thing leads onto another. Ideally I would
like a weekend with you to hammer this out, because it is so very important. But
here we are, with email. And this is a big one. You are blue. Bear with
me:</SPAN><SPAN style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: blue'>I would like us to agree
to make the simple postulate that time is what clocks measure.</SPAN><SPAN
style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: black'>This is where it goes
wrong, right at the very beginning. This is what </SPAN><SPAN
style="COLOR: black"><A
href="http://www.amazon.co.uk/World-without-Time-Forgotten-Einstein/dp/0465092942"
target=_blank>A World Without Time</A></SPAN><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: black'> is all about. Take a
look inside a clock. Can you see time flowing through it like it’s some kind of
chronological gas meter? No. You see springs and rockers and cogs, moving.
And/or a vibrating crystal. And/or a pendulum*. And so on. It’s always something
moving, usually in some regular cyclical fashion. Hence the inner mechanism of a
clock is called a movement. What clocks do, is “clock up” some kind of regular
cyclical motion and show you some cumulative result that you call the
time**. Clocks don’t measure time, they measure <I>motion</I>. When some
guy in some SciFi movie has a gizmo that stops time, what it actually stops is
<I>motion</I>. </SPAN><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: red'>Really they equally
display length : how far the little wheely things have gone round. If they
displayed motion the motion would just be a constant. Clocks are designed
precisely to maintain a constant motion. Then the length the hands have moved is
proportional to the time that has passed (presuming motion = distance/time)
Anyway clocks do not matter.. what matters are elemetary particles. These go
round an sound (constituting a kind of clock) and have a certain size
(constituting a kind of ruler. These are the ruler-clocks (the rocks) that
Martin mentioned.</SPAN><SPAN style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: blue'>You are kind of assuming
that there is an absolute clock reference - and that is not what relativity is
about.</SPAN><SPAN style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: black'>I’m not. I’m pointing to
the empirical evidence, and to what Einstein said. </SPAN><SPAN
style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style="COLOR: black"><o:p></o:p></SPAN> </P>
<P class=MsoNormal style="MARGIN-BOTTOM: 12pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: red'>Good enough -- an absolute
ruler then</SPAN><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: black'><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: blue'>You are ascribing changes
in the velocity to (quite proper) changes in the clock. One can do this but it
has consequences and can lead to confusion in thinking - as we observe here.
</SPAN><SPAN style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: red'>Nope - motion constant -
clock and ruler variable.</SPAN><SPAN
style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: black'>There is no confusion.
But there is a consequence, and it is this: <I>when the clock goes slower, it’s
because that motion goes slower</I>. There is no time flowing through the clock.
There is <EM><SPAN style='FONT-FAMILY: "Calibri",sans-serif'>motion</SPAN></EM>
occurring in the clock. Even when it’s an optical clock. </SPAN><SPAN
style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: blue'>I think we need to look
at proper changes in ruler as well.</SPAN><SPAN
style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: black'>We define the second
using the motion of light. When the light goes slower the second is bigger. When
we then use the slower light and the bigger second to define the metre, they
cancel each other out. </SPAN><SPAN
style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: red'>Within the narrow context
here we have an equation relating space, time and velocity. We can choose to
keep any one fixed , and allow the variation the other two to match experiment
-for this set of 3. This would be ok if it did not have consequences elsewhere -
in such things as the definition of Energy and momentum for example - whose
definition in a wave-function is with respect to time and space. We could fix
this by developing a (pre) canonical quantisation with respect to velocity - and
people (Im thinking about Kanatchikow) have tried this. We have to look at
the whole of physics - all at once - and get something
self-consistent.</SPAN><SPAN style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: blue'>Indeed -experimentally
-clocks slow down as you enter a gravitational potential </SPAN><SPAN
style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: black'>That they do. And there
is no time flowing through any of them. Whether it’s a mechanical clock or a
quartz wristwatch or an atomic clock, they all go slower when you’re lower.
Because the motion inside them goes slower. Everything goes slower, and we say
time goes slower. But that’s just a figure of speech. There is no actual thing
called time going anywhere. </SPAN><SPAN
style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: blue'>Equivalently, light
reduces its frequency (in step) as one goes up, to overcome the work done
against gravity. </SPAN><SPAN style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: black'>Cross my heart and hope
to die: this is a fallacy. Your clock goes faster when you go up, so you measure
the frequency to be reduced, even though it hasn’t changed a jot. In similar
vein if you move fast through space away from the light source, you measure the
frequency to be reduced, even though it hasn’t changed a jot. Conservation of
energy applies.</SPAN><SPAN style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: red'>That is the point. Light
energy must go down, otherwise light energy in a box would not make it heavier
(see Martin paper).</SPAN><SPAN style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: blue'>Conversely if one climbs
a hill one has to do work. </SPAN><SPAN
style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: black'>True. You do work on a
brick if you throw it up in the air. The kinetic energy you give it is converted
into potential energy, the brick reaches its maximum height, and then it falls
back down. This doesn’t happen to a photon, because a photon is all kinetic
energy. It doesn’t slow down. And nor does the descending photon speed
up. </SPAN><SPAN style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: blue'>The work done goes into
winding all the little oscillators inside your body up </SPAN><SPAN
style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: black'>Agreed. </SPAN><SPAN
style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: blue'>if I use an absolute
standard clock at some level of gravitational potential as "the" absolute clock,
then clocks lower go slower </SPAN><SPAN
style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: black'>Agreed. But let’s make
them light clocks. They go slower because the light goes slower.
</SPAN><SPAN style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: blue'>However this is not what
the initial postulate relating to the speed of light says or means. It says that
the speed of light, experimentally in vacuo, is a constant.</SPAN><SPAN
style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: black'>When you measure a
change, it’s either because the thing you measured changed, or because
<I>you</I> changed, along with your measuring devices. When you <I>don’t</I>
measure a change, it might be because nothing changed. But it might be because
the thing you measured changed and <I>you changed too</I>.</SPAN><SPAN
style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: red'>That is the point. Your
measure of space AND your measure of time have changed. ... gota
go</SPAN><SPAN style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: blue'>Now if time is what
clocks measure, then what is space.</SPAN><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: black'> </SPAN><SPAN
style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: black'>Space is empirical. Hold
your hands up a foot apart. See that gap between them? That’s a space. That’s
what space is. Now waggle your hands. That’s motion. That’s empirical too. I can
show you space and motion. Now you try showing me time. </SPAN><SPAN
style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: blue'>Let’s make a further
postulate - that rulers are what measure space. </SPAN><SPAN
style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: black'>We use the motion of
light through space in light clocks to measure time, and then we use radar, the
motion of light through space, along with those light clocks, to measure space.
Motion is king. <I>And electrons are made of it</I>. And rulers are made of
electrons. And other things too, but you get the gist. </SPAN><SPAN
style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: blue'>That means taking a
standard ruler, dividing it by a standard time IN THAT FRAME gives a standard
velocity. It is indeed a tautology that the speed of light is then a constant -
in vacuo.</SPAN><SPAN style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: black'>It’s a tautology because
we use the motion of light to define the second and the metre, and then use them
to measure the motion of light. </SPAN><SPAN
style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: blue'>I believe that that is
the current status of all of experiment. Am I wrong? </SPAN><SPAN
style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: black'>No. You aren’t wrong.
But the clockwork man using his clockwork clock to measure the speed of
clockwork will say the same. </SPAN><SPAN
style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: blue'>Now. What a velocity (or
speed) is- its distance divided by time. Time is not motion, space is not
motion. Motion is motion.</SPAN><SPAN
style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: black'>Motion is motion, but
without motion there is no time. Imagine I sit you at a desk with a big red
button. I tell you that if you press the button, all motion in the universe will
cease. Then I tell you that if you press it a second time, motion resumes. Do
you press the button?</SPAN><SPAN style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: blue'>Motion is space divided
by time. OK? </SPAN><SPAN style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: black'>No. Motion is empirical.
So is space. Time isn’t. </SPAN><SPAN
style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: blue'>Can we agree that speed =
ds/dt and velocity is dv/dt? A little bit of space divided by a little bit of
time. Do that, with light, in vacuo, anywhere, any time, you get the same
number. Experimentally. Lets call it c. The speed of light.</SPAN><SPAN
style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: black'>You get the same number
because the second is the </SPAN><SPAN lang=EN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: black'>duration of <SPAN
class=nowrap1>9192631770</SPAN> periods of the radiation corresponding to the
transition between the two hyperfine levels of the ground state of the caesium
133 atom. And because the metre is the length of the path travelled by light in
vacuum during a time interval of 1/299792458th of a second. If the light goes
slower, the second is bigger, they cancel each other out, and you <EM><SPAN
style='FONT-FAMILY: "Calibri",sans-serif'>still</SPAN></EM> say the speed of
light is 299792458 m/s. </SPAN><SPAN
style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: blue'>Something is, indeed,
changing. Something is, indeed, missing. But just what that change or missing
thing is depends on how we choose to split up our thinking. What we choose to be
primary, and what do we choose to be derived. Do we take space as primary?
</SPAN><SPAN style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: black'>Yes. </SPAN><SPAN
style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: blue'>Do we take the constancy
of the speed of light as primary? </SPAN><SPAN
style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: black'>No. Einstein didn’t. Nor
does Shapiro, nor Magueijo and Moffat, nor Wright, nor Koks, nor me.
</SPAN><SPAN style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: blue'>Is something else
primary? </SPAN><SPAN style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: black'>Motion. We live in a
world of space and motion. Clocks clock up motion. The little hand moves. The
big hand moves. And we say they tell the time. But they just <EM><SPAN
style='FONT-FAMILY: "Calibri",sans-serif'>moved</SPAN></EM>. </SPAN><SPAN
style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: blue'>However, there is one
thing I know about that is missing - that most other people do not know that is
missing. Luckily some clever people have discovered it independently over the
years. One of them was Martin, Another, (quite) a bit before was Louis de
Broglie. It is the Harmony of phases. </SPAN><SPAN
style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: black'>I’m guessing that <A
href="http://www.bougainvilleaclinic.com/Dr-Andrew-Worsley.php"
target=_blank>Andrew Worsley</A> discovered it too. </SPAN><SPAN
style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: blue'>Also I love and respect
and idolise Einstein as much as the next man. As someone who has read some of
his stuff, in German, and found mistakes and mis-directed steps in his work, I
cannot take him as an absolute authority. </SPAN><SPAN
style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: black'>The evidence and
experiment is the authority. And the evidence says this: when you open up a
clock, you don’t see time flowing through it. </SPAN><SPAN
style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: blue'>The quote from Einstein
is correct - but both he (and you) can choose whether you see it as a change in
velocity or a change in speed</SPAN><SPAN
style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: black'>I’ve read the original
German. It’s a change in speed. That’s why he referred to the SR postulate. If
you try to insist on the vector-quantity, you leave Einstein saying light curves
because it curves. </SPAN><SPAN
style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: blue'>In Martin and my 1997
model the photon curves (changing velocity) but the speed remains that of the
speed of light everywhere (c), for example.</SPAN><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: black'><BR></SPAN><SPAN
style="COLOR: black"><BR></SPAN><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: black'>You can make a car go
round in circles by deflating the tyres on the left a little. But a much better
way is to turn the steering wheel. Your second email:</SPAN><SPAN
style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: blue'>In the narrow context of
space, time and light-speed (defined as = space/time at the rest-massless limit)
there are two valid viewpoints (consistent with experiment) and six invalid
viewpoints. Viz:</SPAN><SPAN style="COLOR: blue"><BR><BR></SPAN><B><SPAN
style='FONT-FAMILY: "Courier New"; COLOR: blue'> space
time speed
valid<BR></SPAN></B><SPAN style='FONT-FAMILY: "Courier New"; COLOR: blue'>1
fixed fixed fixed
no<BR>2 fixed fixed varies
yes<BR>3 fixed varies varies
no<BR>4 fixed varies fixed
no<BR>5 varies fixed fixed
no<BR>6 varies fixed varies
no<BR>7 varies varies varies no<BR>8
varies varies fixed
yes</SPAN><SPAN style="COLOR: blue"><BR></SPAN><SPAN
style="COLOR: black"><BR></SPAN><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: blue'>Now you can have case 2
or case 8 but not both </SPAN><SPAN style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: black'>Case3 is valid. When the
light goes slower the second is bigger but the metre stays the same. So space is
fixed, time varies, and speed varies. Only I didn’t mention radial length
contraction. </SPAN><SPAN style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: blue'>The lab on earth is not
good as it is effectively (according to the postulate of equivalence)
accelerating at g. </SPAN><SPAN style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: black'>I root for relativity,
but I will tell you this: the principle of equivalence only applies to an
infinitesimal region. It doesn’t apply to the room you’re in. In truth, it was
merely an enabling principle, a way forward. Accelerating through homogeneous
space, it’s not the same as standing still in inhomogeneous space. In the former
situation, light appears to curve, but actually, it doesn’t. In the latter
situation, it does. Your third email:</SPAN><SPAN
style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: blue'>For any
particle-as-a-clock both (energy) frequency goes up and (clock ) frequency goes
down. </SPAN><SPAN style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: black'>Imagine an electron in
front of you. It has an energy and a frequency. When you drop it, gravity
converts internal kinetic energy into external kinetic energy. Then when you
catch it, you dissipate that kinetic energy, and the electron now has a mass
deficit. Its mass is lower. And all it really is, is an E=hf photon going round
and round. Its energy is lower. So its frequency is lower too. </SPAN><SPAN
style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: blue'>The main point of the
harmony of phases is that the phase of both of these oscillations, is in harmony
for all space and all time and in any Lorentz frame. </SPAN><SPAN
style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: black'>You must read Friedwardt
Winterberg’s paper. When you drop an electron into a black hole, its downward
speed relates to the difference in the “coordinate” speed of light at two
elevations, which you can gauge with optical clocks. When the electron has
fallen to a place where the coordinate speed of light is halved, I don’t think
things are harmonious any more. </SPAN><SPAN
style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: blue'>it does indeed make no
sense to say the speed of light varies.</SPAN><SPAN
style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: black'>But the experiment says
it does. If it didn’t vary, optical clocks wouldn’t go slower when they’re
lower. </SPAN><SPAN style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: blue'>What this means
mathematically is that the speed of light is fundamentally, in fact, infinite.
</SPAN><SPAN style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: black'>But experiment says it
isn’t. You and I shine a laser at the moon, and it’s circa two seconds before we
see the reflection. The speed of light is not infinite. It is
<I>indefinite.</I> </SPAN><SPAN
style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: blue'>If we could just throw a
switch and double the speed of light we would then not notice.</SPAN><SPAN
style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: black'>True. Because <EM><SPAN
style='FONT-FAMILY: "Calibri",sans-serif'>we are made of light</SPAN></EM>. The
speed of everything would be doubled. </SPAN><SPAN
style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: blue'>This is why it can, and
should, become common knowledge that photon events always take place at a single
space-time point ( the concept you were having trouble with before).</SPAN><SPAN
style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: black'>If the speed of light
was infinite, everything would happen at once. There would be no time. Just as
there would be no time if the speed of light was zero. </SPAN><SPAN
style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: blue'>I have talked (and
written) about this before for photons (the first time was in 2008 at Cybcon)-
but have not yet managed to get it peer-reviewed published or even found any
individual with whom the idea had any significant traction - outside of Martin
of course. </SPAN><SPAN style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: black'>Sorry to be an awkward
sod. But I feel driven to get across this inhomogeneous space so that the road
is clear for curved space. </SPAN><SPAN
style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: blue'>I think it is the single
most important thing we should be communicating to everyone in the year of
light. IMHO.</SPAN><SPAN style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: black'>I wish we agreed on
everything. But there again, if we did, whatever would we talk about?
</SPAN><SPAN style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: blue'>I think i need to find a
new job or just give this one up though as the present one is giving me 50 hour
weeks of teaching...</SPAN><SPAN style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: black'>Maybe somebody is trying
to keep you busy. </SPAN><SPAN style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: black'>Regards</SPAN><SPAN
style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: black'>John D</SPAN><SPAN
style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style="COLOR: black"> <o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: black'>* the pendulum
clock is the odd man out, in that the clock rate depends on the first derivative
of gravitational potential rather than gravitational potential. The “force of
gravity”. </SPAN><SPAN style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: black'>** Just keep gazing at
the image below. Have a glass of wine or two. Keep looking at it. There’s some
weird psychological barrier to all this, wherein people insist that clocks go
slower when they’re lower because time goes slower, when the time is just the
number of reflections, or oscillations, or turns of a
cog. </SPAN><SPAN
style="COLOR: black"><o:p></o:p></SPAN></P>
<P class=MsoNormal style="MARGIN-BOTTOM: 10pt; LINE-HEIGHT: 13pt"><SPAN
style='FONT-FAMILY: "Calibri",sans-serif; COLOR: black'><IMG id=_x0000_i1027
border=0 alt=parallel src="cid:94C34B4E60AC47F1AD47CD3E94952D6D@HPlaptop"
width=133 height=196></SPAN><SPAN
style="COLOR: black"><o:p></o:p></SPAN></P></DIV></DIV></DIV></DIV></DIV></DIV></DIV></DIV></DIV>
<P>
<HR>
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