debunking the kalam.pdf

8/11/2019 debunking the kalam.pdf

1/79

Is the Universe

Eternal?

Vic Stenger


2/79

time

now-!

infinite

time

Theologian:


3/79

time

now-!

infinite

time

Theologian: Therefore eternaluniverse is impossible


4/79

time

now-!

infinite

time

timenow-10100

finitetime

years

Theologian:

Mathematician:

Therefore eternaluniverse is impossible


5/79

time

now-!

infinite

time

timenow-10100

finitetime

years

Theologian:

Mathematician:

Therefore eternaluniverse is impossible

Eternal universeis possible


6/79

The Kalam Cosmological Argument_

William Lane Craig


7/79

The Kalam Cosmological Argument

1. Everything that begins has a cause

_

William Lane Craig


8/79



2. The universe had abeginning

_

William Lane Craig


9/79




3. Therefore the universe had a cause

_

William Lane Craig


10/79





_

William Lane Craig

That cause must be a personal God


11/79





_

William Lane Craig

That cause must be a personal God

Not in quantum mechanics


12/79

time

space

Did the universe begin with a singularity?

Hawking and

Penrose 1970General Relativity


13/79

time

space


Hawking and


Singularity


14/79

time

space


Hawking and


Singularity

Beginning of time?


15/79

time

space

Quantum Mechanics: No Singularity

Hawking 1988


16/79


17/79

Borde, Guth, Vilenkin Theorem (2003)


18/79


Inflation must have hadabeginning


19/79



time

space


20/79



Craig: Therefore universecannotbe eternal

time

space


21/79




time

space

Aguirre and Gratton,Carroll and Chen:


22/79




time

space



23/79




time

space


Universe can be eternal


24/79

A Natural Scenario for

the Origin of Our Universe


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.


26/79

Cosmological Friedmann equations from General Relativity


27/79


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


28/79


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


k = -1, 0, 1


29/79


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


k = -1, 0, 1


30/79


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


k = -1, 0, 1


31/79


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:


k = -1, 0, 1


32/79

The Inflationary Biverse


33/79

The Inflationary Biverse

H =1

ao

=

1

a

da

dt

a(t) = ao cosht

ao

!

"#$

%&

=

ao

2

exp(Ht) + exp('Ht)()

*+


34/79

The Inflationary Biverse time

space

time

H =1

ao

=

1

a

da

dt

a(t) = ao cosht

ao

!

"#$

%&

=

ao

2


*+


35/79


space

time

H =1

ao

=

1

a

da

dt

a(t) = ao cosht

ao

!

"#$

%&

=

ao

2


*+

Ouruniverse


36/79


space

time

H =1

ao

=

1

a

da

dt

a(t) = ao cosht

ao

!

"#$

%&

=

ao

2


*+

Ouruniverse

Mirroruniverse


37/79


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


38/79

EV

Quantum tunneling


39/79

EV

Quantum tunneling

imaginary momentum p2

< 0

K=E-V< 0


40/79

Quantizing the Friedmann Equations


41/79


Assume a Lagrangian

L =3!4G

"da

dt

#$%

&'(

2

a + a 1"a

2

ao

2

#

$%

&

'(

)

*

++

,

-

.

.


42/79


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


43/79


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

)

*

++

,

-

.

.


44/79

p2+

3!

2G

"#$

%&'

2

a2

1(a

2

ao

2

"

#$

%

&' = 0


45/79

p2+

3!

2G

"#$

%&'

2

a2

1(a

2

ao

2

"

#$

%

&' = 0

p = !i

"

"a


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


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


48/79

Potential energy


49/79

Potential energy

/3!

2G

"#$

%&'

2

Potential energy


50/79

Potential energy

/3!

2G

"#$

%&'

2

Physical

region

Potential energy


51/79

Potential energy

/3!

2G

"#$

%&'

2

Unphysical

region

Physical

region

Potential energy


52/79

Potential energy

/3!

2G

"#$

%&'

2

Unphysical

region

Physical

region

a(!) = aocos

!

ao

"

#$

%

&'t = i! imaginary


53/79


54/79

Imaginary time

a(t) = aocosh t

ao

!"#

$%&' a > a

o


55/79

Imaginary time

a(t) = aocosh t

ao

!"#

$%&' a > a

o

For a < ao let ! = it

Then a(!) = aocos

!

ao

"

#$%

&'


56/79

Imaginary time

a(t) = aocosh t

ao

!"#

$%&' a > a

o


Then a(!) = aocos

!

ao

"

#$%

&'

Euclidean space-time (unphysical)

s2=x

2+y

2+z

2! ct( )

2

" = ict

=x2+y

2+z

2+ "

2


57/79

Imaginary time

a(t) = aocosh t

ao

!"#

$%&' a > a

o


Then a(!) = aocos

!

ao

"

#$%

&'


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

!


58/79

Imaginary time

a(t) = aocosh t

ao

!"#

$%&' a > a

o


Then a(!) = aocos

!

ao

"

#$%

&'


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

!


59/79

Tunneling solution of Vilenkin:


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


61/79

our time

space

unphysical

region

Hartle-Hawking:


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


63/79

Hartle-Hawking wave function of the universe

Hartle Hawking wave function of the universe


64/79


physical region



65/79


unphysical region

(nothing)

physical region

our time


66/79

prior time

space

unphysical

region


67/79

P! exp "2 dx2mV(x)"E1/ 2

a

b

#

$

%&

'

()

2m = 1 E = 0 a = 0 b = ao


68/79


a

b

#$

%&

'

()

2m = 1 E = 0 a = 0 b = ao

Tunneling

probability


69/79


a

b

#$

%&

'

()

2m = 1 E = 0 a = 0 b = ao

P! exp "3

8G2#

$%&

'()

#! G"2 * P= exp "3

8

$

%&

'

() = 0.687

Tunneling

probability


70/79


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?


71/79



72/79

Eternal universe not mathematicallyforbidden



73/79


Cant proveuniverse had a beginning fromany theorems based on general relativity



74/79



The biverse is a possible natural scenario



75/79




Does creationmake any sense withdifferent arrows of time?



76/79




Does creationmake any sense withdifferent arrows of time?

Two universes beganat t= 0


77/79


78/79

Is the UniverseEternal?


79/79

Is the UniverseEternal?

Paradox: Universe has a

beginning and is eternal

debunking the kalam.pdf

Documents

Transcript of debunking the kalam.pdf