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On Sun, Jan 21, 2018 at 7:30 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"> > the fact that there is such a thing as CMB rest frame that our galaxy can be moving with respect to violates the Cosmological Principle and invalidates it.</blockquote><br>There is no violation, the Cosmological Principle says that on large enough scales the universe is uniform, and if you look at a cube about 200 million light years on a side it is, and the laws of physics are the same in any reference frame. Movement can only be defined in reference to something else and the CMB rest frame is just the frame that is moving with the average velocity of all the matter in the universe. If movement is allowed to exist in the universe then obviously not everything in it is going to be moving at the exact same velocity, so the fact that the Earth is moving at a velocity slightly different from the average is not at all surprising. <br><br>It should also be remembered that in all the colorful pictures of the CMB the contrast has been cranked way way up, in actuality the difference between the hot spots and the cold spots is only about one part in a hundred thousand.</div><div class="gmail_quote"><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">> Couple that with the fact that the cosmic microwave background is spatially the largest dipole we have ever measured,</blockquote><div> </div>
I'm not sure what you mean by that but it would be astounding if we didn't see a dipole in the CMB because if there were none that would mean if you plotted the velocity of everything in the universe the Earth would be in the exact center of that movement plot, and I would consider that a pretty wild coincidence.
<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">> No, I will not forget the mathematics. In and of itself, math is the only thing in the world guaranteed to be true and for all of time and in every place no less.</blockquote><div> </div>
Mathematics alone can’t explain everything because although physics uses mathematics physics is not mathematics. It’s easy to come up with a physical theory that is mathematically consistent but its far far harder to come up with one that also fits the facts. Mathematics is the language of physics but like any language it can say things that are untrue. I can't prove it but I have a hunch physics is more fundamental than mathematics.
<p class="gmail-p1">> That's why prime numbers matter and the laws of physics use math instead of say French for example.</p>
Physics and mathematics can sometimes give conflicting answers. I know that Euclid proved mathematically that there are a infinite number of primes but if that was really true then whatever prime number you mention it will always be possible to find a larger one, but Seth Lloyd proved physically that is not the case:</div><div class="gmail_quote"><br></div><div class="gmail_quote"><a href="http://fab.cba.mit.edu/classes/862.16/notes/computation/Lloyd-2002.pdf">http://fab.cba.mit.edu/classes/862.16/notes/computation/Lloyd-2002.pdf</a> </div><div class="gmail_quote"><br></div><div class="gmail_quote">Lloyd showed that since the Big Bang the entire universe was only capable of performing 10^120 operations on 10^90 bits. So there must be a largest prime number in the sense that it is impossible even for the universe itself to find a larger one.<br><br>And physics can come up with things that mathematics can't handle. Consider the Busy Beaver sequence: 1, 6, 21, 107,.. . What's the next term? Nobody knows for sure, all we know is that it's at least 47,176,870 . <br><br>The Busy Beaver involves a physical object that could actually be built, a Turing Machine. Starting with a blank tape and a Turing Machine that can be in N states (that is to say have N rules) then BB(N) is the largest FINITE number of operations the machine will undergo before it halts; that is to say sometimes the machine will continue forever but ignore them, of those machines that eventually stop BB(N) is the maximum number of operations performed before halting. The Busy Beaver function starts out modestly enough: </div><div class="gmail_quote"><br></div><div class="gmail_quote">BB(1)=1<br><br>BB(2)=6<br><br>BB(3)=21<br><br>BB(4)=107 </div><div class="gmail_quote"><br></div><div class="gmail_quote">But then things go nuts. BB(5) is at least 47,176,870 , that is to say one 5 state Turing Machine has been found that halts after 47,176,870 operations, but another 5 state Turing Machine is still going strong well past that point, if it eventually stops then that larger number of operations is BB(5) if not then it’s 47,176,870 ; but if so we'll never be able to prove it’s 47,176,870 because we'll never be able to prove that other 5 state machine will never stop. Turing showed that in general you can’t determine if one of his machines will eventually stop, all you can do is observe it and wait to see if it stops, and you might be waiting forever. So some (perhaps all) BB numbers greater than 4 are not computable. It’s a little like having a perfect watch that will never stop, you can’t make money betting somebody that it will never stop because there is no point where enough evidence is in to allow you to claim you won and get the money. </div><div class="gmail_quote"><br></div><div class="gmail_quote">As for BB(6) its at least 7.4* 10^36,534 and probably much larger. BB(7) is greater than or equal to 10^10^10^10^7. Its been proven that BB(7,918) isn't just huge the number is not computable, even a Jupiter Brain will never know what BB(7,918) is, even the universe itself does not have sufficient resources to produce it so I'm not sure it make sense to say it exists. It's unknown what the smallest non-computable BB number is, all we know is its larger than BB(4) and less than or equal to BB(7,918). </div><div class="gmail_quote"><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">> And any assertion of what *might* be out there is an extrapolation of one<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>sort or another. What the Robertson-Walker metric does is extrapolate an<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>*observation* i.e. it looks flat, isotropic and homogeneous in here so it<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>must be flat, isotropic, and homogeneous *out there*.</blockquote><div> </div>
They are just using induction and induction is even more important than deduction in science and in life. And besides, what is the alternative, there are a infinite number of ways things could be "out there" so how do you even start to think about it? The obvious way is to assume things out there are pretty much like things in hear and then see where that leads.</div><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">
> That's no different than going back to the casino because you won the last time you were there.</blockquote><div> </div>
Induction is a very useful rule of thumb, but it doesn't always work. Induction just says that in our universe things usually continue. If things always continued then induction would always work and things wouldn't be very interesting, all the atoms in the universe would be arranged in a unchanging perfect crystal lattice that is infinite in all directions. A world where things never continue and induction never worked would also be dull, it would be nothing but white noise. Our universe with all its complexity and richness is between these two extremes, here induction is a great rule of thumb because it USUALLY works.</div><div class="gmail_quote"><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, so let me get this straight: on the smallest scales space-time is flat<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>enough that you can do calculus on Lorentzian manifolds. But then as your<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>scale gets bigger, on the scale of stars and galaxies, it is curved. But<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>then, as your scale gets bigger, to scale of dark matter filaments and<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>voids, space-time becomes flat again .</blockquote>
<p class="gmail-p1">Yep, that's about it, that's what observation shows. </p>
<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">> out to infinity?</blockquote><div> </div>
Unknown. At the largest scales the universe is pretty flat but it could have a tiny<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>curvature<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>that is too small for us to measure.</div><div class="gmail_quote"><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">> You yourself quoted Einstein to me once: "Every thing should be made as simple as possible, but no simpler." The Robert-Walker metric is too simple.</blockquote><div> </div>
Everybody knows the universe isn't perfectly homogeneous and isotropic , but you can get some pretty good approximations by assuming that it is on the scale of a few hundred million light years, and doing so greatly simplifies the equations of General relativity although they're still horrendously complex. </div><div class="gmail_quote"><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">> if you are in a spaceship being uniformly accelerated, then as you draw closer to the speed of a light, a big flat event horizon will appear behind you and start following you around. And the closer you get to the speed of light, the closer the event horizon will get to your ship. If this event horizon contacts your ship, then Bell's Spaceship paradox ensues and your spaceship breaks apart.</blockquote><div> </div>
Bell's Spaceship Paradox is not really a paradox. If I tacked a delicate string inside the cockpit of my accelerating spaceship from the front wall to the back wall the string would NOT break because the atoms and electromagnetic fields inside the string would shrink by Lorentz contraction at the same rate as the atoms in the cockpit 's side walls. However if I tied a string from the front of my spaceship to the back of another spaceship 10 feet ahead of mine and we both accelerated at the same rate the string would break because the atoms in the string would shrink just as they did before but now there is nothing else between the two spaceships to counterbalance that effect, there is only empty space .<br><br> John K Clark </div></div></div>