<div dir="ltr"><div class="gmail_default" style="font-family:arial,helvetica,sans-serif"><span style="font-family:arial,sans-serif">On Wed, Jul 19, 2017 at 9:05 AM, Stuart LaForge </span><span dir="ltr" style="font-family:arial,sans-serif"><<a href="mailto:avant@sollegro.com" target="_blank">avant@sollegro.com</a>></span><span style="font-family:arial,sans-serif"> wrote:</span><br></div><div class="gmail_extra"><div class="gmail_quote"><br></div><div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex"><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex"><font size="4"><span class="gmail-">
><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">></div>There are only 3 possibilities:<br></span><span class="gmail-">><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">></div>1) Nothing exists outside the cosmological horizon.</span></font></blockquote><span class="gmail-">
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</span><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">> </div>Gakk. "Nothing" is a loaded term in modern cosmology. Define it please? </blockquote><div><br></div><font size="4">Infinite unbounded homogeneity<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">.</div></font></div><div class="gmail_quote"><font face="arial, helvetica, sans-serif" size="4"><br></font><div><br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex"><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex"><span class="gmail-"><font size="4">
><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">> </div>2) A Finite amount of stuff exists outside the cosmological horizon.</font></span></blockquote><span class="gmail-">
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</span><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">> </div>Again is flat space-time or quantum vacuum "stuff" in your opinion? </blockquote><div><br></div><div><div class="gmail_default"><font size="4"><font face="arial, helvetica, sans-serif">Yes and there are 2 possibilities, you can only stuff a finite number of </font>Planck volume cubes (a Planck length cubed) into the universe or there is room for a infinite number of such cubes. It's got to be one or the other but I don't see how I can ever know which possibility is true.</font></div><div class="gmail_default" style="font-family:arial,helvetica,sans-serif"><br></div></div><div class="gmail_default" style="font-family:arial,helvetica,sans-serif"><br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex"><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex"><span class="gmail-"><font size="4">
><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">> </div>3) A infinite amount of stuff exists outside the cosmological horizon.</font></span></blockquote><span class="gmail-">
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</span><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">> </div>An infinite amount of flat spacetime could exist outside the cosmological<br>
horizon but that would be incredulously unlikely. I mean come on: a finite<br>
island of matter embedded in infinite space-time and we happen to be in<br>
the exact center of it?</blockquote><div><br></div><div><font size="4"><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">If </div>spacetime<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> is infinite it has no center, if </div>spacetime<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> is finite and flat and bounded then it does. </div></font></div><div><br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex">
<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">> </div>Instead, I think it much more likely that a countably infinite amount of<br>
matter and an uncountably infinite amount of space-time exist outside of<br>
the cosmological horizon.</blockquote><div><br></div><div><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"><font size="4">That would be my hunch too but I think it's useful to sometimes put theory asides and remind ourselves what our largest telescopes actually observe; they observe a boundary and they observe that we are the same distance from that boundary regardless of what direction the telescope is pointed. </font></div></div><div><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"><font size="4"> </font></div></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex"><span class="gmail-">
</span><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">> </div>Much of reality, finite or not, lies outside your lightcone.</blockquote><div><br></div><div><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"><font size="4">There might be a infinite number of stars that are more distant from me than 13.8 billion light years, or there might be none at all, given the fact that the universe is not only expanding it is accelerating there is no way I can ever know. </font></div> </div><div> <br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex"><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex"><font size="4"><span class="gmail-">
><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">></div>The human mind is not infinitely powerful so in dealing with the<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div></span><span class="gmail-">staggering complexity of the world <div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">a</div>pproximations are needed. The idea that<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div></span><span class="gmail-">the planets moved in perfect circles around the sun worked pretty well but<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div></span><span class="gmail-">Kepler showed that a more complex <div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">m</div>athematical curve, the ellipse, worked<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div></span><span class="gmail-">better. And then Einstein showed that even a ellipse wasn't quite right,<br></span><span class="gmail-">but to understand how and why Einstein said the planets move high school<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div></span><span class="gmail-">geometry is not enough, you need 4 dimensional Tensor calculus and<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div></span><span class="gmail-">hyperbolic spacetime. And even Einstein wasn't quite right because he<br></span><span class="gmail-">didn't take quantum mechanics into account. So when a child asks you how<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div></span><span class="gmail-">planets move it's best to just say "in a circle".</span></font></blockquote></blockquote><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex"><font size="4"> </font></blockquote><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex"><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">> </div>But if the Lorentz transformation is correct that implies that for every<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>elliptical orbit there exists at least one inertial reference frame in<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>which the orbit *is* circular.</blockquote><div><br></div><div><font size="4">Lorentz transform<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">s only apply for things </div>at constant velocity relative to each other<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">, but p</div><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">lanets in orbit around the sun are undergoing constant acceleration and thus are not in a </div>inertial reference frame<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">.</div> <div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">When things accelerate Special Relativity isn't good enough, you've got to go to General Relativity. </div></font><br></div><div> <br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex"><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex"><font size="4"><span class="gmail-"><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">>> </div>without a brain made of atoms that obey the laws of physics "you"<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div></span><span class="gmail-">can't have probability amplitudes<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>, in fact you can't even have you.</span></font></blockquote><span class="gmail-">
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</span><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">> </div>But if the laws of physics are only useful fictions<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>created by the mind</blockquote><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex">
with no physical reality than how do the physically real atoms of my brain<br>
know them well enough to obey them?<br></blockquote><div> </div><font size="4">The laws of physics are<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>certainly <div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">not</div><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>useful fictions, but something human beings <div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">have </div>call<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">ed</div><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> "</div>probability amplitudes<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">" for the last few decades might be. Or maybe not.</div></font></div><div class="gmail_quote"><font face="arial, helvetica, sans-serif" size="4"><br></font></div><div class="gmail_quote"><font face="arial, helvetica, sans-serif" size="4"><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> John K Clark</div><br></font><div> </div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex"><div class="gmail-HOEnZb"><div class="gmail-h5"><br></div></div></blockquote></div></div></div>