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BIG BANG OR BIG BOUNCEAfrican Institute for Mathematical Sciences, 23 Sept 2016Sean Gyrb
VS
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A HOT BEGINNING
We believe the Universe is expanding now.
It appears that it always has been.
Thus, there was a moment in the past where everything we can see was focused in an infinitely hot region of zero volume.
This was the Big Bang.
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BUT…
IS THIS THE WHOLE STORY?
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HUBBLE
Measured that galaxies are moving away from each other.
Can interpret this as expansion of Universe.
How?
Go back to Mach!
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MACH
Recall: Inertial Frames (a = 0) given by (nearly) fixed stars.
Therefore, Inertial Frames are not absolute/fixed.
Given by motion of galaxies.
What if galaxies are moving?
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NEWTON
Inertial Frames = straight lines (zero acceleration)
Therefore, parallel lines never diverge.
And no acceleration between Inertial Frames!
They are static, eternal and God given.
d
d
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EINSTEIN
Mach: inertial frames are given by matter (e.g., galaxies)
They are not eternal, or God given, or static!
Einstein: if matter diverges, so should inertial frames.
But (inertial frames = straight lines), can only diverge if space-time is curved.
t
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EINSTEIN
In a curved spacetime:
Therefore
Curved inertial structure (new term) comes from matter.
Therefore: diverging galaxies = expanding space
a
i =d2xi
dt2+X
jk
�ijk(x)v
jv
k
d2~x
dt2= 0 6= ~a = 0
The math…
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GRAVITY
Einstein realised that the new term could also explain gravity.
Equivalence Principle: Free fall = inertial motion
The new term can relate free falling observers to observers in space.
Einstein equations: relate matter to �ijk(x)
(Aside)
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LEMAÎTRE
Using Einstein’s theory and Hubble’s data, he (and others) found that, at some point in the past (~13.8 billion years), space must have had zero volume!
This is the Big Bang!
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MINUTE PHYSICS: ON BIG BANG
https://www.youtube.com/watch?v=q3MWRvLndzs
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QUANTUM MECHANICS
CAN QUANTUM MECHANICS SAVE THE DAY?
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SINGLE SLIT
Take laser pointer and shine light through a small slit.
A distinct interference pattern will appear on a distant screen.
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SINGLE SLIT: LIGHT
The pattern has a large center peak surrounded by dark regions.
The m’th dark region from the center can easily be found to be at a distance ‘y’:
y =m�D
a
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SINGLE SLIT: ELECTRONS
Now replace light with an electron.
de Broglie:
Note, the uncertainty in x is approximately:
Similarly, the uncertainty is px is:
Putting this together, we get:
� =h
p
�x ⇡ a
�px
⇡ y
Dp
�x�p
x
⇡ h
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UNCERTAINTY IN THE UNIVERSE
Now apply this “Uncertainty Principle” to the Big Bang.
At the Big Bang, the volume of the Universe is exactly zero.
But then ∆V = 0 and ∆pV →∞ if ∆V ∆pV ≈ h.
Thus, if we limit uncertainty in p, then we retain uncertainty in V.
Therefore, the volume can never be exactly zero
Therefore, there can be no Big Bang!
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A BIG BOUNCE
So far, it has been difficult to show that quantum mechanics implies that our Universe could avoid the Big Bang.
We found a way.
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OUR MODEL
We used an approximation: the Universe is homogenous and isotropic.
We treated time differently than anyone has ever done before:
Time must be measured by a clock, and that clock must have some uncertainty. (Recall Mach)
We found that this uncertainty leads to a Bounce, and not a Bang!
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THE KEYS
One must be Machian about time.
One must take into account the uncertainty in the measurement of time.