<div dir="ltr"><div class="gmail_default" style="font-family:arial,helvetica,sans-serif"><span style="font-family:arial,sans-serif">On Sat, Feb 17, 2018 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"><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><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"><span class="gmail-m_-3687586070656582247gmail-m_-1234253790195329950gmail-m_8988400975959697630gmail-m_5313854845224051650gmail-m_1746095381141922665gmail-">
><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">></div> You need a reference point to set to zero, it could be anything but<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div> average velocity would be convenient , its the reference frame that shows<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div> zero dipole moment in the Cosmic Microwave Background.</span></blockquote><span class="gmail-m_-3687586070656582247gmail-m_-1234253790195329950gmail-m_8988400975959697630gmail-m_5313854845224051650gmail-m_1746095381141922665gmail-">
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</span><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">> </div><i>The average velocity of everything you can see being set to zero is less<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>convenient and less sensible than setting your own velocity to zero. </i></blockquote><div><br></div><div><div class="gmail_default" style="font-family:arial,helvetica,sans-serif">Copernicus would have disagreed with you and so would Kepler who found it vastly more convenient to set the sun's motion as zero rather than that of the Earth when he calculated the motion of Mars. </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"><span class="gmail-m_-3687586070656582247gmail-m_-1234253790195329950gmail-m_8988400975959697630gmail-m_5313854845224051650gmail-m_1746095381141922665gmail-">
</span><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">><i> </i></div><i>Let me get this straight. You concede the existence of stuff you can't see<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>gravitationally attracting you</i></blockquote><div><br></div><div><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">Not </div>gravitationally attracting <div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">me but </div>gravitationally attracting<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> something that I can see. If I see a galaxy 12 billion light years away move in an odd way I might conclude that something more distant than 13.8 billion light years, which is the limit of what I can see, is pulling on it </div> gravitationally<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">. Or if I observe a large blemish in CMB (which we have not) I might even conclude that our universe had collided with another universe I can not see. </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"><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">><i> </i></div><i>but you don't concede the existence of an<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>event horizon at the Hubble radius when that event horizon is precisely<br>
the reason you can't see the stuff that is attracting you?<br></i></blockquote><div><br></div><div><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"></div>Things at the Hubble radius<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>aren't at a event horizon they are at a causal horizon (sometimes called a absolute horizon), the two things are related but not identical, one is a subset of the other. All event horizons are<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>are causal horizons but not all causal horizons are event horizons. I may or may not be inside a event horizon<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">,</div> if I am then I'm heading toward a singularity and there is no way to avoid it, but I'm <div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">most </div>certainly inside a causal horizon because everything is<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">,</div> but I'm not necessarily heading toward a singularity. I can't send information outside <div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">what you call a </div>causal horizon<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>but I might be able to see things beyond it or at least deduce information about it; this asymmetry is do to the accelerating expansion of the universe, things are moving away from me faster now than they were long ago.<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> But if I'm inside a event horizon I'm completely cut off from anything outside it.</div></div><div><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"><br></div></div><div><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">However the two types of horizons are similar enough that l</div><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">ike a Black Hole's event horizon the causal horizon of the universe also has a temperature and also gives off radiation, it's called </div>Gibbons–Hawking<font face="arial, helvetica, sans-serif"> </font><div class="gmail_default" style="display:inline"><font face="arial, helvetica, sans-serif">radiation, but unlike a Black Hole's Hawking radiation the universe's </font></div><font face="arial, helvetica, sans-serif"></font>Gibbons–Hawking<font face="arial, helvetica, sans-serif"> </font><div class="gmail_default" style="display:inline"><font face="arial, helvetica, sans-serif">radiation does not change with time.</font></div></div><div><br></div></div><div class="gmail_quote">The universe is doubling in size every 12.2 billion years, so after 850<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>billion years the CMB will have a wavelength of 22 billion light years and be too weak to be important<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">,</div> but the background temperature will never be zero because the Gibbons–Hawking effect<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>will start to dominate <div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">then</div>. The universe will never get any colder than 7*10^-31 K<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>thanks to the<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>Gibbons–Hawking effect<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"></div>, that's very cold but its not absolute zero.<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><i>You *can't* set the universe's average velocity to zero. You don't know<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>how big it is.</i></blockquote><div><br></div><div><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">I know how big the observable </div><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">universe is and I can set that to zero, it is the only reference frame that doesn't show a dipole pattern in the CMB.</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"><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">><i> </i></div><i>a dimensionless constant, I shall call<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>S.<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>S:= H^2*Tp^2 = H^2*h*G/c^5 or approximately 1.4*10^-122 where H is the<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>Hubble parameter and Tp is the Planck time, h is the reduced Planck's<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>constant, G is the gravitational constant, and c is the speed of light.</i><br></blockquote><div><br></div>I checked your math and you're right, the units check out and it is indeed dimensionless<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"> </div>I get a number closer to <b>1.9*10^-129</b>, but the accepted value of the the Hubble's constant H<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>has changed lot in just the last few years and we may have been using different values, and you're taking the square of it. In meter-kilogram-seconds units<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>I figured the<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>Hubble's constant H is <div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">1.</div>62*10^-18 s^-1 (although I wouldn't bet much money on the accuracy of the last of those 3 digits, or even on the last two)<br>so<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">:</div><br><br><div><span style="color:rgb(80,80,80);font-family:arial,helvetica,clean,sans-serif;font-size:14.079px;line-height:19.1052px"> H^2 is </span><span style="color:rgb(80,80,80);font-family:arial,helvetica,clean,sans-serif;font-size:14.079px;line-height:19.1052px"><b>2.6*10^-36 s^-2</b><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"><b>. </b></div></span><br></div><div><div class="gmail_quote"><div class="gmail_default" style="font-family:arial,helvetica,sans-serif"><span style="color:rgb(80,80,80);font-family:arial,helvetica,clean,sans-serif;font-size:14.079px;line-height:19.1052px">The Plank constant h is </span><b style="color:rgb(80,80,80);font-family:arial,helvetica,clean,sans-serif;font-size:14.079px;line-height:19.1052px">2.6*10^-36 </b><b style="color:rgb(80,80,80);font-family:arial,helvetica,clean,sans-serif;font-size:14.079px;line-height:19.1052px"> (m^2) (kg/s)</b></div><div class="gmail_default"><font color="#505050" face="arial, helvetica, clean, sans-serif"><span style="font-size:14.079px;line-height:19.1052px">The gravitational constant G is </span></font><b style="font-family:arial,helvetica,clean,sans-serif;color:rgb(80,80,80);font-size:14.079px;line-height:19.1052px">6.8*10^-11 m^3/kg*s^2</b></div><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">The speed of light c is </div>3*10^9<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> m/s so c^5 is <b>2.43 *10^47 m^5/s^5</b></div></div><div class="gmail_quote"><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"><b><br></b></div></div><div class="gmail_quote"><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">So </div>H^2*h*G/c^5<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> = </div><span style="color:rgb(80,80,80);font-family:arial,helvetica,clean,sans-serif;font-size:14.079px;line-height:19.1052px"><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">[</div>2.6*10^-36<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">[</div></span><span style="color:rgb(80,80,80);font-family:arial,helvetica,clean,sans-serif;font-size:14.079px;line-height:19.1052px">2.6*10^-36<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">[</div></span><span style="font-family:arial,helvetica,clean,sans-serif;color:rgb(80,80,80);font-size:14.079px;line-height:19.1052px">6.8*10^-11<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">]/</div></span><span style="color:rgb(80,80,80);font-family:arial,helvetica,clean,sans-serif;font-size:14.079px;line-height:19.1052px"> <div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">[</div></span><span style="font-family:arial,helvetica,sans-serif">2.43 *10^47<div class="gmail_default" style="display:inline"> ]</div></span>=<span style="font-family:arial,helvetica,sans-serif"><div class="gmail_default" style="display:inline"><b><i> </i>1.89*10^-129</b></div></span></div></div><div class="gmail_quote"><span style="font-family:arial,helvetica,sans-serif"><div class="gmail_default" style="display:inline"><b><br></b></div></span></div>In<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> addition to the uncertainty in the Hubble constant the </div><span style="font-family:arial,helvetica,sans-serif">Gravitational constant is known to only 6 significant digits<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> and the </div></span><span style="font-family:arial,helvetica,sans-serif">Planck constant is only known to only 9 significant digits.<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div></span><span style="font-family:arial,helvetica,sans-serif">And we're talking about 122 digits<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">, or maybe 129.</div></span><div><br></div>Also the<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>Hubble<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>constant<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>has the name it does for historical reasons but we now know the<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>Hubble<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>"constant" is not a constant, it<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>is a time dependent<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>variable, a function<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>of the<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>CMB red-shift. <div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">Therefore</div> your value S can't be a constant either, but as far as we know the density of Dark Energy is constant, so it doesn't work.<div><div class="gmail_default" style="display:inline"><font color="#242729" face="arial, helvetica, sans-serif"><span style="font-size:15px;line-height:19.5px"><br></span></font></div></div>And most important of all<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">,</div> did you have a physical reason for coming up with <div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">(</div><i>H^2<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">)</div>*h*G/c^5 <div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div></i>or did you just pick it because if gave you a number you liked?</div><div class="gmail_quote"><div><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"><br></div></div><div><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">John K Clark</div></div><div><br></div></div><div class="gmail_quote"><br></div></div></div>