Upload
arif-heller
View
228
Download
0
Embed Size (px)
Citation preview
8/11/2019 debunking the kalam.pdf
1/79
Is the Universe
Eternal?
Vic Stenger
8/11/2019 debunking the kalam.pdf
2/79
time
now-!
infinite
time
Theologian:
8/11/2019 debunking the kalam.pdf
3/79
time
now-!
infinite
time
Theologian: Therefore eternaluniverse is impossible
8/11/2019 debunking the kalam.pdf
4/79
time
now-!
infinite
time
timenow-10100
finitetime
years
Theologian:
Mathematician:
Therefore eternaluniverse is impossible
8/11/2019 debunking the kalam.pdf
5/79
time
now-!
infinite
time
timenow-10100
finitetime
years
Theologian:
Mathematician:
Therefore eternaluniverse is impossible
Eternal universeis possible
8/11/2019 debunking the kalam.pdf
6/79
The Kalam Cosmological Argument_
William Lane Craig
8/11/2019 debunking the kalam.pdf
7/79
The Kalam Cosmological Argument
1. Everything that begins has a cause
_
William Lane Craig
8/11/2019 debunking the kalam.pdf
8/79
The Kalam Cosmological Argument
1. Everything that begins has a cause
2. The universe had abeginning
_
William Lane Craig
8/11/2019 debunking the kalam.pdf
9/79
The Kalam Cosmological Argument
1. Everything that begins has a cause
2. The universe had abeginning
3. Therefore the universe had a cause
_
William Lane Craig
8/11/2019 debunking the kalam.pdf
10/79
The Kalam Cosmological Argument
1. Everything that begins has a cause
2. The universe had abeginning
3. Therefore the universe had a cause
_
William Lane Craig
That cause must be a personal God
8/11/2019 debunking the kalam.pdf
11/79
The Kalam Cosmological Argument
1. Everything that begins has a cause
2. The universe had abeginning
3. Therefore the universe had a cause
_
William Lane Craig
That cause must be a personal God
Not in quantum mechanics
8/11/2019 debunking the kalam.pdf
12/79
time
space
Did the universe begin with a singularity?
Hawking and
Penrose 1970General Relativity
8/11/2019 debunking the kalam.pdf
13/79
time
space
Did the universe begin with a singularity?
Hawking and
Penrose 1970General Relativity
Singularity
8/11/2019 debunking the kalam.pdf
14/79
time
space
Did the universe begin with a singularity?
Hawking and
Penrose 1970General Relativity
Singularity
Beginning of time?
8/11/2019 debunking the kalam.pdf
15/79
time
space
Quantum Mechanics: No Singularity
Hawking 1988
8/11/2019 debunking the kalam.pdf
16/79
8/11/2019 debunking the kalam.pdf
17/79
Borde, Guth, Vilenkin Theorem (2003)
8/11/2019 debunking the kalam.pdf
18/79
Borde, Guth, Vilenkin Theorem (2003)
Inflation must have hadabeginning
8/11/2019 debunking the kalam.pdf
19/79
Borde, Guth, Vilenkin Theorem (2003)
Inflation must have hadabeginning
time
space
8/11/2019 debunking the kalam.pdf
20/79
Borde, Guth, Vilenkin Theorem (2003)
Inflation must have hadabeginning
Craig: Therefore universecannotbe eternal
time
space
8/11/2019 debunking the kalam.pdf
21/79
Borde, Guth, Vilenkin Theorem (2003)
Inflation must have hadabeginning
Craig: Therefore universecannotbe eternal
time
space
Aguirre and Gratton,Carroll and Chen:
8/11/2019 debunking the kalam.pdf
22/79
Borde, Guth, Vilenkin Theorem (2003)
Inflation must have hadabeginning
Craig: Therefore universecannotbe eternal
time
space
Aguirre and Gratton,Carroll and Chen:
8/11/2019 debunking the kalam.pdf
23/79
Borde, Guth, Vilenkin Theorem (2003)
Inflation must have hadabeginning
Craig: Therefore universecannotbe eternal
time
space
Aguirre and Gratton,Carroll and Chen:
Universe can be eternal
8/11/2019 debunking the kalam.pdf
24/79
A Natural Scenario for
the Origin of Our Universe
8/11/2019 debunking the kalam.pdf
25/79
A Natural Scenario for
the Origin of Our Universe
Reference:
Atkatz, David. "Quantum cosmology for pedestrians,"
American Journal of Physics62 (1994): 619-27.
8/11/2019 debunking the kalam.pdf
26/79
Cosmological Friedmann equations from General Relativity
8/11/2019 debunking the kalam.pdf
27/79
Cosmological Friedmann equations from General Relativity
d2a
dt2 = !
4"G
3
#+ 3p
( )a +
$
3
a
da
dt!"# $%&
2
=
8'G(
3a
2
) k+ *3 a2
cosmological constant
k = -1, 0, 1
8/11/2019 debunking the kalam.pdf
28/79
Cosmological Friedmann equations from General Relativity
Let k= 1,!= p = 0
Empty universe
d2a
dt2 = !
4"G
3
#+ 3p
( )a +
$
3
a
da
dt!"# $%&
2
=
8'G(
3a
2
) k+ *3 a2
cosmological constant
k = -1, 0, 1
8/11/2019 debunking the kalam.pdf
29/79
Cosmological Friedmann equations from General Relativity
Let k= 1,!= p = 0
Empty universe
d2a
dt2 = !
4"G
3
#+ 3p
( )a +
$
3
a
da
dt
!"#
$%&
2
= 2a
2
ao
2'1
da
dt
!"#
$%&
2
=
8'G(
3a
2
) k+ *3 a2
ao
=
!
3
cosmological constant
k = -1, 0, 1
8/11/2019 debunking the kalam.pdf
30/79
Cosmological Friedmann equations from General Relativity
Let k= 1,!= p = 0
Empty universe
d2a
dt2 = !
4"G
3
#+ 3p
( )a +
$
3
a
da
dt
!"#
$%&
2
= 2a
2
ao
2'1
da
dt
!"#
$%&
2
=
8'G(
3a
2
) k+ *3 a2
d2a
dt2 =
a
ao
ao
=
!
3
cosmological constant
k = -1, 0, 1
8/11/2019 debunking the kalam.pdf
31/79
Cosmological Friedmann equations from General Relativity
Let k= 1,!= p = 0
Empty universe
d2a
dt2 = !
4"G
3
#+ 3p
( )a +
$
3
a
da
dt
!"#
$%&
2
= 2a
2
ao
2'1
da
dt
!"#
$%&
2
=
8'G(
3a
2
) k+ *3 a2
d2a
dt2 =
a
ao
ao
=
!
3
a(t) = aocosh
t
ao
!
"#$
%&Solution:
cosmological constant
k = -1, 0, 1
8/11/2019 debunking the kalam.pdf
32/79
The Inflationary Biverse
8/11/2019 debunking the kalam.pdf
33/79
The Inflationary Biverse
H =1
ao
=
1
a
da
dt
a(t) = ao cosht
ao
!
"#$
%&
=
ao
2
exp(Ht) + exp('Ht)()
*+
8/11/2019 debunking the kalam.pdf
34/79
The Inflationary Biverse time
space
time
H =1
ao
=
1
a
da
dt
a(t) = ao cosht
ao
!
"#$
%&
=
ao
2
exp(Ht) + exp('Ht)()
*+
8/11/2019 debunking the kalam.pdf
35/79
The Inflationary Biverse time
space
time
H =1
ao
=
1
a
da
dt
a(t) = ao cosht
ao
!
"#$
%&
=
ao
2
exp(Ht) + exp('Ht)()
*+
Ouruniverse
8/11/2019 debunking the kalam.pdf
36/79
The Inflationary Biverse time
space
time
H =1
ao
=
1
a
da
dt
a(t) = ao cosht
ao
!
"#$
%&
=
ao
2
exp(Ht) + exp('Ht)()
*+
Ouruniverse
Mirroruniverse
8/11/2019 debunking the kalam.pdf
37/79
The Inflationary Biverse time
space
time
H =1
ao
=
1
a
da
dt
a(t) = ao cosht
ao
!
"#$
%&
=
ao
2
exp(Ht) + exp('Ht)(
)
*
+
Ouruniverse
Mirroruniverse
Arrow of time opposite to ours
8/11/2019 debunking the kalam.pdf
38/79
EV
Quantum tunneling
8/11/2019 debunking the kalam.pdf
39/79
EV
Quantum tunneling
imaginary momentum p2
< 0
K=E-V< 0
8/11/2019 debunking the kalam.pdf
40/79
Quantizing the Friedmann Equations
8/11/2019 debunking the kalam.pdf
41/79
Quantizing the Friedmann Equations
Assume a Lagrangian
L =3!4G
"da
dt
#$%
&'(
2
a + a 1"a
2
ao
2
#
$%
&
'(
)
*
++
,
-
.
.
8/11/2019 debunking the kalam.pdf
42/79
Quantizing the Friedmann Equations
Assume a Lagrangian
L =3!4G
"da
dt
#$%
&'(
2
a + a 1"a
2
ao
2
#
$%
&
'(
)
*
++
,
-
.
.
Define canonical momentum
p = !L
!da
dt
"#$
%&'
=(3)2G
ada
dt
8/11/2019 debunking the kalam.pdf
43/79
Quantizing the Friedmann Equations
Assume a Lagrangian
L =3!4G
"da
dt
#$%
&'(
2
a + a 1"a
2
ao
2
#
$%
&
'(
)
*++
,
-..
Define canonical momentum
p = !L
!da
dt
"#$
%&'
=(3)2G
ada
dt
Hamiltonian
H = pda
dt !L
=!3"4G
a 1+da
dt
#$%
&'(
2
!a
2
ao
2
)
*
++
,
-
.
.
8/11/2019 debunking the kalam.pdf
44/79
p2+
3!
2G
"#$
%&'
2
a2
1(a
2
ao
2
"
#$
%
&' = 0
8/11/2019 debunking the kalam.pdf
45/79
p2+
3!
2G
"#$
%&'
2
a2
1(a
2
ao
2
"
#$
%
&' = 0
p = !i
"
"a
8/11/2019 debunking the kalam.pdf
46/79
d2
da2!
3"
2G
#$%
&'(
2
a2
1!a
2
ao
2
#
$%
&
'(
)
*++
,
-../ = 0
Wheeler-DeWittequation
p2+
3!
2G
"#$
%&'
2
a2
1(a
2
ao
2
"
#$
%
&' = 0
p = !i
"
"a
8/11/2019 debunking the kalam.pdf
47/79
d2
da2!
3"
2G
#$%
&'(
2
a2
1!a
2
ao
2
#
$%
&
'(
)
*++
,
-../ = 0
Wheeler-DeWittequation
Wave function of the universe
p2+
3!
2G
"#$
%&'
2
a2
1(a
2
ao
2
"
#$
%
&' = 0
p = !i
"
"a
8/11/2019 debunking the kalam.pdf
48/79
Potential energy
8/11/2019 debunking the kalam.pdf
49/79
Potential energy
/3!
2G
"#$
%&'
2
Potential energy
8/11/2019 debunking the kalam.pdf
50/79
Potential energy
/3!
2G
"#$
%&'
2
Physical
region
Potential energy
8/11/2019 debunking the kalam.pdf
51/79
Potential energy
/3!
2G
"#$
%&'
2
Unphysical
region
Physical
region
Potential energy
8/11/2019 debunking the kalam.pdf
52/79
Potential energy
/3!
2G
"#$
%&'
2
Unphysical
region
Physical
region
a(!) = aocos
!
ao
"
#$
%
&'t = i! imaginary
8/11/2019 debunking the kalam.pdf
53/79
8/11/2019 debunking the kalam.pdf
54/79
Imaginary time
a(t) = aocosh t
ao
!"#
$%&' a > a
o
8/11/2019 debunking the kalam.pdf
55/79
Imaginary time
a(t) = aocosh t
ao
!"#
$%&' a > a
o
For a < ao let ! = it
Then a(!) = aocos
!
ao
"
#$%
&'
8/11/2019 debunking the kalam.pdf
56/79
Imaginary time
a(t) = aocosh t
ao
!"#
$%&' a > a
o
For a < ao let ! = it
Then a(!) = aocos
!
ao
"
#$%
&'
Euclidean space-time (unphysical)
s2=x
2+y
2+z
2! ct( )
2
" = ict
=x2+y
2+z
2+ "
2
8/11/2019 debunking the kalam.pdf
57/79
Imaginary time
a(t) = aocosh t
ao
!"#
$%&' a > a
o
For a < ao let ! = it
Then a(!) = aocos
!
ao
"
#$%
&'
Euclidean space-time (unphysical)
s2=x
2+y
2+z
2! ct( )
2
" = ict
=x2+y
2+z
2+ "
2
i m
a g i n a r y t i m
e
space
South Pole
!
= 0
s
a
!
8/11/2019 debunking the kalam.pdf
58/79
Imaginary time
a(t) = aocosh t
ao
!"#
$%&' a > a
o
For a < ao let ! = it
Then a(!) = aocos
!
ao
"
#$%
&'
Euclidean space-time (unphysical)
s2=x
2+y
2+z
2! ct( )
2
" = ict
=x2+y
2+z
2+ "
2
No
boundary
i m
a g i n a r y t i m
e
space
South Pole
!
= 0
s
a
!
8/11/2019 debunking the kalam.pdf
59/79
Tunneling solution of Vilenkin:
8/11/2019 debunking the kalam.pdf
60/79
!V(a > ao ) =K(a)"1/ 2 exp "i #2G ao
2a
2
ao
2"1$
%&'
()
3/ 2*
+,,
-
.//
K(a) =3!
2G
"
#$
%
&'a
a2
ao2(1
"
#$
%
&'
1/ 2
gOnly outgoing waves
!V(0 < a < a
o) =K(a)
"1/ 2
1
2exp "
#2G
ao
2 1"a
2
ao
2
$
%
&'
(
)
3/ 2*
+
,
,
-
.
/
/
+iexp #2G
ao
2 1"a
2
ao
2
$
%&
'
()
3/ 2*
+
,,
-
.
//
0
1
222
3
222
4
5
222
6
222
8/11/2019 debunking the kalam.pdf
61/79
our time
space
unphysical
region
Hartle-Hawking:
8/11/2019 debunking the kalam.pdf
62/79
!HH
(a > ao) =K(a)"1/ 2 cos #
2ao
2 a
2
ao
2"1$
%& '
()
3/ 2*
+,,
-
.//
K(a) =3!
2G"#$
%&'
2
aa2
ao
2(1"
#$ %
&'
1/ 2
gEqual amounts of incoming and outgoing
waves
!HH
(0 < a < ao) =K(a)"1/ 2 exp
#2ao
2 a2
ao
2"1$
%&
'()
3/ 2*
+
,,
-
.
//
Hartle Hawking wave function of the universe
8/11/2019 debunking the kalam.pdf
63/79
Hartle-Hawking wave function of the universe
Hartle Hawking wave function of the universe
8/11/2019 debunking the kalam.pdf
64/79
Hartle-Hawking wave function of the universe
physical region
Hartle-Hawking wave function of the universe
8/11/2019 debunking the kalam.pdf
65/79
Hartle-Hawking wave function of the universe
unphysical region
(nothing)
physical region
our time
8/11/2019 debunking the kalam.pdf
66/79
prior time
space
unphysical
region
8/11/2019 debunking the kalam.pdf
67/79
P! exp "2 dx2mV(x)"E1/ 2
a
b
#
$
%&
'
()
2m = 1 E = 0 a = 0 b = ao
8/11/2019 debunking the kalam.pdf
68/79
P! exp "2 dx2mV(x)"E1/ 2
a
b
#$
%&
'
()
2m = 1 E = 0 a = 0 b = ao
Tunneling
probability
8/11/2019 debunking the kalam.pdf
69/79
P! exp "2 dx2mV(x)"E1/ 2
a
b
#$
%&
'
()
2m = 1 E = 0 a = 0 b = ao
P! exp "3
8G2#
$%&
'()
#! G"2 * P= exp "3
8
$
%&
'
() = 0.687
Tunneling
probability
8/11/2019 debunking the kalam.pdf
70/79
P! exp "2 dx2mV(x)"E1/ 2
a
b
#$
%&
'
()
2m = 1 E = 0 a = 0 b = ao
P! exp "3
8G2#
$%&
'()
#! G"2 * P= exp "3
8
$
%&
'
() = 0.687
something (physical universe) 2x as likely asnothing (unphysical universe)
Tunneling
probability
Is the Universe Eternal?
8/11/2019 debunking the kalam.pdf
71/79
Is the Universe Eternal?
8/11/2019 debunking the kalam.pdf
72/79
Eternal universe not mathematicallyforbidden
Is the Universe Eternal?
8/11/2019 debunking the kalam.pdf
73/79
Eternal universe not mathematicallyforbidden
Cant proveuniverse had a beginning fromany theorems based on general relativity
Is the Universe Eternal?
8/11/2019 debunking the kalam.pdf
74/79
Eternal universe not mathematicallyforbidden
Cant proveuniverse had a beginning fromany theorems based on general relativity
The biverse is a possible natural scenario
Is the Universe Eternal?
8/11/2019 debunking the kalam.pdf
75/79
Eternal universe not mathematicallyforbidden
Cant proveuniverse had a beginning fromany theorems based on general relativity
The biverse is a possible natural scenario
Does creationmake any sense withdifferent arrows of time?
Is the Universe Eternal?
8/11/2019 debunking the kalam.pdf
76/79
Eternal universe not mathematicallyforbidden
Cant proveuniverse had a beginning fromany theorems based on general relativity
The biverse is a possible natural scenario
Does creationmake any sense withdifferent arrows of time?
Two universes beganat t= 0
8/11/2019 debunking the kalam.pdf
77/79
8/11/2019 debunking the kalam.pdf
78/79
Is the UniverseEternal?
8/11/2019 debunking the kalam.pdf
79/79
Is the UniverseEternal?
Paradox: Universe has a
beginning and is eternal