<div dir="ltr">On Fri, Jan 19, 2018 at 10:21 PM, Stuart LaForge <<a href="mailto:avant@sollegro.com">avant@sollegro.com</a>> wrote:<br><br><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">> Ok, let me a rephrase that again: 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 inertial observers should agree on the temporal ordering of time-like or light-like separated events, thus sharing an arrow of time. In other words, if there was any possible way A could have caused B, then we would all agree that A happened before B.</blockquote><br>If I say A caused me to do B nobody within my Hubble volume would disagree and say my doing B caused A to happen, although somebody outside my Hubble volume might.<br><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">>> 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.</blockquote><br>>Firstly, "now" is a word fraught with peril in General Relativity. Whose now? My now? Your now?</blockquote><br>If we’re talking about my Hubble volume then the answer to your question is my now, if you’re standing a foot from me your Hubble volume will be slightly different than mine, very very very slightly. <br><br><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">>> 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.</blockquote><br>> I know that equation looks ridiculously simple but it is derived from the Schwartzschild metric and as counter intuitive as it sounds, a white-hole's density should *increase* as it loses matter and energy and its event horizon shrinks. </blockquote></div><div><br>Then we can’t be living in a white hole because there is no experimental evidence the density of the universe is increasing and plenty of evidence it is decreasing.</div><div><br></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"><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><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">>>> Yes, causal cells are not invariant. What is invariant is the product of the density and event horizon surface area of a casual cell.</blockquote></div></blockquote></blockquote><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></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><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">>> I don't see how that could be if both are shrinking.</blockquote></div></blockquote><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><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">> That's just it. It is not possible for both of them to be shrinking. The Friedmann Equations are wrong because they are based on the Robertson-Walker metric. </blockquote></div><div><br>Forget the mathematics, in physics as in all science empirical evidence always outranks theory, if what a theory predicts and the facts about the universe are inconsistent the universe doesn’t care because facts remain facts. Experiment outranks theory and the facts say both the density and the area of our Hubble volume are decreasing, so the product of the two can’t be constant.<br><br><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">> The R-W metric takes it as an assumption the universe is isotropic and homogeneous. While observations clearly indicate it is neither.</blockquote><br>Obviously on a small scale that is true, but if you look at boxes a few hundred million light years on a side it is pretty homogeneous, and without simplifying assumptions none of the fundamental laws of physics would have ever been discovered because things are just too complicated. <br><br><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">> the so-called-universe cannot possibly be homogeneous because there is an actual bona-fide event horizon 14 billion light years away from us.</blockquote><br>You’re using the same word for both the surface area of a Black Hole and of a Hubble volume, and I think that’s a bad idea. If I’m anywhere inside a Black Hole I will come into contact with things at the event horizon when we both reach the singularity, but I will never come into contact with things on the surface of my Hubble volume. <br><br></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><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">>> 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.</blockquote></div></blockquote><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><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">>If I want to bring electrical charges into it, I have to switch from Schwarzschild metric to Reissner–Nordström metric. Maybe later, after I have the fundamentals down.</blockquote></div><div><br>If you want to preserve CPT symmetry I think you’ll need to switch to the Kerr–Newman metric because although Reissner–Nordström understands electrical charge it ignores spin, and a key element of spin is parity. And parity is the P in CPT. <br><br> John K Clark</div></div>