<div dir="ltr"><div class="gmail_default" style="font-family:arial,helvetica,sans-serif"><span style="font-family:arial,sans-serif">On Mon, Jan 15, 2018 at 1:08 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"><span class="gmail-m_-7994127284698324755m_7590379065420493182gmail-m_-2754253135307595008gmail-im" style="font-size:12.8px"><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">> </div>A causal cell is a finite volume of space-time enclosed by an event<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>horizon wherein all observers should agree on the temporal ordering of<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div></span><span style="font-size:12.8px">events </span></blockquote><div> </div><font size="4">If you and I are moving with respect to each other we won't agree on the temporal ordering of events if the events happen at different positions in space.</font></div><div class="gmail_quote"><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"><span style="font-size:12.8px"><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">> </div>for which they were mutually present. </span></blockquote><div> </div>
<div><font size="4">I'm not sure what you mean by that, two different observers can't occupy the same position in space.<span style="font-family:arial,helvetica,sans-serif"></span></font><br></div><div class="gmail_quote"><br></div></div><blockquote 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" class="gmail_quote"><div class="gmail_extra"><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">>><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div><font size="4">Is it<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>[a causal cell]<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>the volume of the universe that could have had a effect on us<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">, </div>or the volume of we can see now, or the volume we can still effect? Those are 3 different volumes and if its the last 2 its shrinking with the<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>passage of time.</font></blockquote></div></div></blockquote><div class="gmail_extra"><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><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>T<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"></div>echnically it is none of those volumes. In our specific case, it is the<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>Hubble volume.</blockquote><div><br></div><font size="4">If your "causal cell" is the Hubble volume then it is case #2 that I mentioned above, it is the volume of the universe we can see now. If they mean the same thing I think it would be wise to use the more standard term rather than one you made up, it would help avoid confusion.</font></div><div class="gmail_quote"><br><div class="gmail-m_-7994127284698324755m_7590379065420493182gmail-m_-2754253135307595008gmail-yj6qo gmail-m_-7994127284698324755m_7590379065420493182gmail-m_-2754253135307595008gmail-ajU"><blockquote 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" class="gmail_quote"><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">> </div> It is a volume of space-time enclosed in a spherical shell<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>whose surface area A multiplied by the average density D of the space<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>enclosed is equal to a constant I call L.</blockquote><div><br></div><font size="4">If L=A*D then L can not be a constant because, due to the expansion and acceleration of the universe, the area A of the Hubble volume is shrinking, and so is the density of the Hubble volume.</font>
<div> </div><blockquote class="gmail_quote" style="font-size:small;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>Yes, causal cells are not invariant. What is invariant is the product of<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>the density and event horizon surface area of a casual cell.</blockquote><div style="font-size:small"><br></div><div>
<div class="gmail_default" style="font-family:arial,helvetica,sans-serif"><font size="4"><span style="font-family:arial,sans-serif">I don't see how that could be if both are shrinking.</span><span style="font-family:arial,sans-serif"> </span></font></div><div class="gmail_default" style="font-size:small;font-family:arial,helvetica,sans-serif"><span style="font-family:arial,sans-serif"> </span><br></div></div><blockquote class="gmail_quote" style="font-size:small;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>However you<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>do hit upon a spot that is giving me a bit of trouble in my math. My math<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>predicts that the our causal should be shrinking,</blockquote><div><br></div><div><font size="4">That's not a bug that's a feature, if causal cell means Hubble volume then the math should say its shrinking because it is shrinking. </font> </div>
<div style="font-size:small"><br></div></div></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"><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">> </div>consider the case when there are two black holes<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>that collide. In all such cases, at least temporarily, there are *two*<br>
such singularities. Now since you can draw a straight line connecting the<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>two singularities, the singularities are colinear and the time axis in the<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>"intersingular" spacetime is precisely that line.<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>But which direction does time flow along that axis?</blockquote><div><br></div><div><font size="4">I think if you're going to talk about reversing the arrow of time you can't just stick with General Relativity, you're going to have to get into Quantum Mechanics because CPT Symmetry says a observer couldn't tell if time reversed direction,...well..., that is to say an observer couldn't tell if positive and negative electrical charge was also reversed and things were viewed in a mirror. </font></div><div><font size="4"><br></font></div><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"><font size="4">John K Clark</font></div>
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