[ExI] Dark Energy and Causal Cells
John Clark
johnkclark at gmail.com
Wed Jan 31 16:39:41 UTC 2018
>
> On Sun, Jan 21, 2018 at 7:30 PM, Stuart LaForge <avant at sollegro.com>
wrote:
> 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.
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.
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.
> Couple that with the fact that the cosmic microwave background is
> spatially the largest dipole we have ever measured,
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.
>
> > 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.
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.
> That's why prime numbers matter and the laws of physics use math instead
of say French for example.
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:
http://fab.cba.mit.edu/classes/862.16/notes/computation/Lloyd-2002.pdf
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.
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 .
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:
BB(1)=1
BB(2)=6
BB(3)=21
BB(4)=107
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.
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).
> And any assertion of what *might* be out there is an extrapolation of one
>
> sort or another. What the Robertson-Walker metric does is extrapolate an
>
> *observation* i.e. it looks flat, isotropic and homogeneous in here so it
>
> must be flat, isotropic, and homogeneous *out there*.
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.
> That's no different than going back to the casino because you won the
> last time you were there.
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.
> Ok, so let me get this straight: on the smallest scales space-time is flat
>
> enough that you can do calculus on Lorentzian manifolds. But then as your
>
> scale gets bigger, on the scale of stars and galaxies, it is curved. But
>
> then, as your scale gets bigger, to scale of dark matter filaments and
>
> voids, space-time becomes flat again .
Yep, that's about it, that's what observation shows.
> > out to infinity?
Unknown. At the largest scales the universe is pretty flat but it could
have a tiny
curvature
that is too small for us to measure.
> 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.
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.
> 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.
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 .
John K Clark
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