Origin of probabilities and their application to the multiverse Andreas Albrecht UC Davis Phy 262 lectures Adapted from a U. Penn Seminar April, 2014 1 A. Albrecht Prob. Lectures for Phy 262
Dec 25, 2015
Origin of probabilities and their application to the multiverse
Andreas AlbrechtUC Davis
Phy 262 lecturesAdapted from a U. Penn Seminar
April, 2014
1A. Albrecht Prob. Lectures for Phy 262
A. Albrecht Prob. Lectures for Phy 262 2
My history with this topic
AA: All randomness/
probabilities are quantum (coin flip, card choice
etc)
A. Albrecht Prob. Lectures for Phy 262 3
My history with this topicAll
randomness/probabilities are
quantum (coin flip, card choice etc)
A. Albrecht Prob. Lectures for Phy 262 4
My history with this topic
Page: Quantum probabilities cannot
address key multiverse questions.
(OK, just use classical
ones)
All randomness/proba
bilities are quantum (coin flip,
card choice etc)
A. Albrecht Prob. Lectures for Phy 262 5
My history with this topic
Page: Quantum probabilities
cannot address key multiverse
questions. (OK, just use
classical ones)
All randomness/proba
bilities are quantum (coin flip,
card choice etc)
AA: All randomness/
probabilities are quantum (coin flip, card choice
etc)
A. Albrecht Prob. Lectures for Phy 262 6
My history with this topic
Page: Quantum probabilities
cannot address key multiverse
questions. (OK, just use
classical ones)
AA: All randomness/
probabilities are quantum (coin flip, card choice
etc)
All randomness/proba
bilities are quantum (coin flip,
card choice etc)
Hartle, Srednicki, Aguirre, Tegmark, …
A. Albrecht Prob. Lectures for Phy 262 7
My history with this topic
Page: Quantum probabilities
cannot address key multiverse
questions. (OK, just use
classical ones)
AA: All randomness/
probabilities are quantum (coin flip, card choice
etc)
All randomness/proba
bilities are quantum (coin flip,
card choice etc)
AA: A deeper problem than the measure problems for
the multiverse
A. Albrecht Prob. Lectures for Phy 262 8
My history with this topic
Page: Quantum probabilities
cannot address key multiverse
questions. (OK, just use
classical ones)
AA: All randomness/
probabilities are quantum (coin flip, card choice
etc)
All randomness/proba
bilities are quantum (coin flip,
card choice etc)
AA: A deeper problem than the measure problems for
the multiverseA potential issue even for finite models
A. Albrecht Prob. Lectures for Phy 262 9
My history with this topic
Page: Quantum probabilities
cannot address key multiverse
questions. (OK, just use
classical ones)
AA: All randomness/
probabilities are quantum (coin flip, card choice
etc)
All randomness/proba
bilities are quantum (coin flip,
card choice etc)
AA: A deeper problem than the
measure problems for the
multiverseAA: Write paper
explaining this with Phillips
A. Albrecht Prob. Lectures for Phy 262 10
My history with this topic
Page: Quantum probabilities
cannot address key multiverse
questions. (OK, just use
classical ones)
AA: All randomness/
probabilities are quantum (coin flip, card choice
etc)
All randomness/proba
bilities are quantum (coin flip,
card choice etc)
AA: A deeper problem than the
measure problems for the
multiverseAA: Write paper
explaining this with Phillips
AA: This is fundamentally about giving permission to dismiss certain probability
questions (the non quantum ones) as “ill posed”.
A. Albrecht Prob. Lectures for Phy 262 11
My history with this topic
Page: Quantum probabilities
cannot address key multiverse
questions. (OK, just use
classical ones)
AA: All randomness/
probabilities are quantum (coin flip, card choice
etc)
All randomness/proba
bilities are quantum (coin flip,
card choice etc)
AA: A deeper problem than the
measure problems for the
multiverseAA: Write paper
explaining this with Phillips
AA: This is fundamentally about giving permission to dismiss certain probability
questions (the non quantum ones) as “ill
posed”.
Perhaps this type of discipline can help
resolve the measure problems of the
multiverse/eternal inflation
A. Albrecht Prob. Lectures for Phy 262 12
My history with this topic
Page: Quantum probabilities
cannot address key multiverse
questions. (OK, just use
classical ones)
AA: All randomness/
probabilities are quantum (coin flip, card choice
etc)
All randomness/proba
bilities are quantum (coin flip,
card choice etc)
AA: A deeper problem than the
measure problems for the
multiverseAA: Write paper
explaining this with Phillips
AA: This is fundamentally about giving permission to dismiss certain probability
questions (the non quantum ones) as “ill
posed”.
Perhaps this type of discipline can help
resolve the measure problems of the
multiverse/eternal inflation
X ?
A. Albrecht Prob. Lectures for Phy 262 13
My history with this topic
Page: Quantum probabilities
cannot address key multiverse
questions. (OK, just use
classical ones)
AA: All randomness/
probabilities are quantum (coin flip, card choice
etc)
All randomness/proba
bilities are quantum (coin flip,
card choice etc)
AA: A deeper problem than the
measure problems for the
multiverseAA: Write paper
explaining this with Phillips
AA: This is fundamentally about giving permission to dismiss certain probability
questions (the non quantum ones) as “ill
posed”.
Apparently this type of discipline can help
resolve the measure problems of the
multiverse/eternal inflation
X ?
A. Albrecht Prob. Lectures for Phy 262 14
Outline
1) Quantum vs non-quantum probabilities (toy model/multiverse)
2) Everyday probabilities
3) Be careful about counting!
4) Implications for multiverse/eternal inflation
A. Albrecht Prob. Lectures for Phy 262 15
Outline
1) Quantum vs non-quantum probabilities (toy model/multiverse)
2) Everyday probabilities
3) Be careful about counting!
4) Implications for multiverse/eternal inflation
NB: Very different subject from “make probabilities
precise” in “Stanford sense”.
A. Albrecht Prob. Lectures for Phy 262 16
Outline
1) Quantum vs non-quantum probabilities (toy model/multiverse)
2) Everyday probabilities
3) Be careful about counting!
4) Implications for multiverse/eternal inflation
A. Albrecht Prob. Lectures for Phy 262 17
Planck Data--- Cosmic Inflation theory
-200 -100 0 100 2000
0.5
1
1.5
2
2.5x 10
4
/MP
V/M
GU
T4
Slow rolling of inflaton
A. Albrecht Prob. Lectures for Phy 262 18
Observable physics
generated here
-200 -100 0 100 2000
0.5
1
1.5
2
2.5x 10
4
/MP
V/M
GU
T4
Slow rolling of inflaton
A. Albrecht Prob. Lectures for Phy 262 19
Observable physics
generated here Extrapolating
back
-200 -100 0 100 2000
0.5
1
1.5
2
2.5x 10
4
/MP
V/M
GU
T4
Slow rolling of inflaton
Q
A. Albrecht Prob. Lectures for Phy 262 20
“Self-reproducing regime” (dominated by quantum
fluctuations): Eternal inflation/Multiverse
Observable physics
generated here Extrapolating
back
Steinhardt 1982, Linde 1982, Vilenkin 1983, and (then) many others
A. Albrecht Prob. Lectures for Phy 262 21
Classically Rolling
A
Self-reproduction regime
Classically Rolling
C
Classically Rolling
B
Classically Rolling
D
The multiverse of eternal inflation with multiple classical rolling directions
Where are we? (Young universe, old universe, curvature, physical properties A, B, C, D, etc)
A. Albrecht Prob. Lectures for Phy 262 22
Classically Rolling
A
Self-reproduction regime
Classically Rolling
C
Classically Rolling
B
Classically Rolling
D
The multiverse of eternal inflation with multiple classical rolling directions
Where are we? (Young universe, old universe, curvature, physical properties A, B, C, D, etc)
“Where are we?” Expect the theory to give you a probability distribution in this space… hopefully with some sharp predictions
A. Albrecht Prob. Lectures for Phy 262 23
Classically Rolling
A
Self-reproduction regime
Classically Rolling
C
Classically Rolling
B
Classically Rolling
D
The multiverse of eternal inflation with multiple classical rolling directions
Where are we? (Young universe, old universe, curvature, physical properties A, B, C, D, etc)
“Where are we?” Expect the theory to give you a probability distribution in this space… hopefully with some sharp predictions
String theory landscape even more complicated (e.g. many
types of eternal inflation)
A. Albrecht Prob. Lectures for Phy 262 24
Quantum vs Non-Quantum probabilities
Non-Quantum probabilities in a toy model:
U A B : 1 , 2A A
A : 1 , 2B B
B
: 11 , 12 , 21 , 22UA B
ij i j
Page, 2009; These slides follow AA & Phillips 2012/14
A. Albrecht Prob. Lectures for Phy 262 25
Quantum vs Non-Quantum probabilities
ˆ 1 1 2 2A AA B
iP i i i i i i 1
ˆ 1 1 2 2B BB A
iP i i i i i i 1
Non-Quantum probabilities in a toy model:
U A B : 1 , 2A A
A : 1 , 2B B
B
: 11 , 12 , 21 , 22UA B
ij i j
Possible Measurements Projection operators:
Measure A only:
Measure B only:
Measure entire U: ijP ij ij
A. Albrecht Prob. Lectures for Phy 262 26
Quantum vs Non-Quantum probabilities
ˆ 1 1 2 2A AA B
iP i i i i i i 1
ˆ 1 1 2 2B BB A
iP i i i i i i 1
Non-Quantum probabilities in a toy model:
U A B : 1 , 2A A
A : 1 , 2B B
B
: 11 , 12 , 21 , 22UA B
ij i j
Possible Measurements Projection operators:
Measure A only:
Measure B only:
Measure entire U:
BUT: It is impossible to construct a projection operator for the case where you do not know whether it is A or B that is being measured.
ijP ij ij
A. Albrecht Prob. Lectures for Phy 262 27
Quantum vs Non-Quantum probabilities
ˆ 1 1 2 2A AA B
iP i i i i i i 1
ˆ 1 1 2 2B BB A
iP i i i i i i 1
Non-Quantum probabilities in a toy model:
U A B : 1 , 2A A
A : 1 , 2B B
B
: 11 , 12 , 21 , 22UA B
ij i j
Possible Measurements Projection operators:
Measure A only:
Measure B only:
Measure entire U:
BUT: It is impossible to construct a projection operator for the case where you do not know whether it is A or B that is being measured.
Could Write
ˆ ˆ ˆA Bi A i B iP p P p P
ijP ij ij
A. Albrecht Prob. Lectures for Phy 262 28
Quantum vs Non-Quantum probabilities
ˆ 1 1 2 2A AA B
iP i i i i i i 1
ˆ 1 1 2 2B BB A
iP i i i i i i 1
Non-Quantum probabilities in a toy model:
U A B : 1 , 2A A
A : 1 , 2B B
B
: 11 , 12 , 21 , 22UA B
ij i j
Possible Measurements Projection operators:
Measure A only:
Measure B only:
Measure entire U:
BUT: It is impossible to construct a projection operator for the case where you do not know whether it is A or B that is being measured.
Could Write
ˆ ˆ ˆA Bi A i B iP p P p P
ijP ij ij
Classical Probabilities to measure
A, B
A. Albrecht Prob. Lectures for Phy 262 29
Quantum vs Non-Quantum probabilities
ˆ 1 1 2 2A AA B
iP i i i i i i 1
ˆ 1 1 2 2B BB A
iP i i i i i i 1
Non-Quantum probabilities in a toy model:
U A B : 1 , 2A A
A : 1 , 2B B
B
: 11 , 12 , 21 , 22UA B
ij i j
Possible Measurements Projection operators:
Measure A only:
Measure B only:
Measure entire U:
BUT: It is impossible to construct a projection operator for the case where you do not know whether it is A or B that is being measured.
Could Write
ˆ ˆ ˆA Bi A i B iP p P p P
ijP ij ij
ˆ ˆ ˆi j ij jPP P
Classical Probabilities to measure
A, B
Does not represent a
quantum measurement
A. Albrecht Prob. Lectures for Phy 262 30
Quantum vs Non-Quantum probabilities
ˆ 1 1 2 2A AA B
iP i i i i i i 1
ˆ 1 1 2 2B BB A
iP i i i i i i 1
Non-Quantum probabilities in a toy model:
U A B : 1 , 2A A
A : 1 , 2B B
B
: 11 , 12 , 21 , 22UA B
ij i j
Possible Measurements Projection operators:
Measure A only:
Measure B only:
Measure entire U:
BUT: It is impossible to construct a projection operator for the case where you do not know whether it is A or B that is being measured.
Could Write
ˆ ˆ ˆA Bi A i B iP p P p P
ijP ij ij
ˆ ˆ ˆi j ij jPP P
Classical Probabilities to measure
A, B
Does not represent a
quantum measurement
Page: The multiverse requires
this (are you in pocket universe A
or B?)
A. Albrecht Prob. Lectures for Phy 262 31
Quantum vs Non-Quantum probabilities
ˆ 1 1 2 2A AA B
iP i i i i i i 1
ˆ 1 1 2 2B BB A
iP i i i i i i 1
Non-Quantum probabilities in a toy model:
U A B : 1 , 2A A
A : 1 , 2B B
B
: 11 , 12 , 21 , 22UA B
ij i j
Possible Measurements Projection operators:
Measure A only:
Measure B only:
Measure entire U:
BUT: It is impossible to construct a projection operator for the case where you do not know whether it is A or B that is being measured.
Could Write
ˆ ˆ ˆA Bi A i B iP p P p P
ijP ij ij
ˆ ˆ ˆi j ij jPP P
Classical Probabilities to measure
A, B
Does not represent a
quantum measurement
Page: The multiverse requires
this (are you in pocket universe A
or B?)
A. Albrecht Prob. Lectures for Phy 262 32
• All everyday probabilities are quantum probabilities
AA & D. Phillips 2012
A. Albrecht Prob. Lectures for Phy 262 33
• All everyday probabilities are quantum probabilities
AA & D. Phillips 2012
Our *only* experiences with successful practical
applications of probabilities are with quantum
probabilities
A. Albrecht Prob. Lectures for Phy 262 34
• All everyday probabilities are quantum probabilities
• One should not use ideas from everyday probabilities to justify probabilities that have been proven to have no quantum origin
AA & D. Phillips 2012
A. Albrecht Prob. Lectures for Phy 262 35
• All everyday probabilities are quantum probabilities
• One should not use ideas from everyday probabilities to justify probabilities that have been proven to have no quantum origin
AA & D. Phillips 2012
A problem for many
multiverse theories
A. Albrecht Prob. Lectures for Phy 262 36
• All everyday probabilities are quantum probabilities
• One should not use ideas from everyday probabilities to justify probabilities that have been proven to have no quantum origin
AA & D. Phillips 2012
A problem for many
multiverse theories (as practiced)
A. Albrecht Prob. Lectures for Phy 262 37
Quantum vs Non-Quantum probabilities
ˆ 1 1 2 2A AA B
iP i i i i i i 1
ˆ 1 1 2 2B BB A
iP i i i i i i 1
Non-Quantum probabilities in a toy model:
U A B : 1 , 2A A
A : 1 , 2B B
B
: 11 , 12 , 21 , 22UA B
ij i j
Possible Measurements Projection operators:
Measure A only:
Measure B only:
Measure entire U:
BUT: It is impossible to construct a projection operator for the case where you do not know whether it is A or B that is being measured.
Could Write
ˆ ˆ ˆA Bi A i B iP p P p P
ijP ij ij
ˆ ˆ ˆi j ij jPP P
Classical Probabilities to measure
A, B
Does not represent a
quantum measurement
Page: The multiverse requires
this (are you in pocket universe A
or B?)
A. Albrecht Prob. Lectures for Phy 262 38
Quantum vs Non-Quantum probabilities
ˆ 1 1 2 2A AA B
iP i i i i i i 1
ˆ 1 1 2 2B BB A
iP i i i i i i 1
Non-Quantum probabilities in a toy model:
U A B : 1 , 2A A
A : 1 , 2B B
B
: 11 , 12 , 21 , 22UA B
ij i j
Possible Measurements Projection operators:
Measure A only:
Measure B only:
Measure entire U:
BUT: It is impossible to construct a projection operator for the case where you do not know whether it is A or B that is being measured.
Could Write
ˆ ˆ ˆA Bi A i B iP p P p P
ijP ij ij
ˆ ˆ ˆi j ij jPP P
Classical Probabilities to measure
A, B
Does not represent a
quantum measurement
Page: The multiverse requires
this (are you in pocket universe A
or B?)
Where do these come from anyway?
A. Albrecht Prob. Lectures for Phy 262 39
Outline
1) Quantum vs non-quantum probabilities (toy model/multiverse)
2) Everyday probabilities
3) Be careful about counting!
4) Implications for multiverse/eternal inflation
A. Albrecht Prob. Lectures for Phy 262 40
Outline
1) Quantum vs non-quantum probabilities (toy model/multiverse)
2) Everyday probabilities
3) Be careful about counting!
4) Implications for multiverse/eternal inflation
A. Albrecht Prob. Lectures for Phy 262 41
Quantum effects in a billiard gas
l
b
r
A. Albrecht Prob. Lectures for Phy 262 42
Quantum effects in a billiard gas
lQuantum Uncertainties
b
r
A. Albrecht Prob. Lectures for Phy 262 43
b
Quantum effects in a billiard gas
l
r
pb x t
m
A. Albrecht Prob. Lectures for Phy 262 44
Quantum effects in a billiard gas
l2
2
p lb x t a
m a mv
2
2exp
2
x
a
b
r
A. Albrecht Prob. Lectures for Phy 262 45
Quantum effects in a billiard gas
l
min 3/2
22
2 / 22 dB
p lb x t a
m a mv
ll
mv
b
r
2
2exp
2
x
a
A. Albrecht Prob. Lectures for Phy 262 46
Quantum effects in a billiard gas
l
min 3/2
22
2 / 22 dB
p lb x t a
m a mv
ll
mv
b
r
2
2exp
2
x
a
Minimizing conservative estimates for my purposes (also motivated by decoherence in some cases)
A. Albrecht Prob. Lectures for Phy 262 47
1b
Quantum effects in a billiard gas
l
b
r
Subsequent collisions amplify the initial uncertainty (treat later collisions classically additional conservatism)
A. Albrecht Prob. Lectures for Phy 262 48
1b
Quantum effects in a billiard gas
l 1 2 /
n
nb b l r
After n collisions:
b
r
A. Albrecht Prob. Lectures for Phy 262 49
Quantum effects in a billiard gas
Qn is the number of collisions so thatQnb r
log
2log 1
Q
br
nlr
(full quantum uncertainty as to which is the next collision)
A. Albrecht Prob. Lectures for Phy 262 50
AirWater BilliardsBumper Car
r l m v dB b Qn
for a number of physical systemsQn(all units MKS)
A. Albrecht Prob. Lectures for Phy 262 51
AirWater BilliardsBumper Car
r l m v dB b Qn
for a number of physical systemsQn(all units MKS)
1 2 150 0.5 361.4 10 183.4 10 25
A. Albrecht Prob. Lectures for Phy 262 52
AirWater BilliardsBumper Car
r l m v dB b Qn
for a number of physical systemsQn(all units MKS)
0.029 1 0.16 1 346.6 10 175.1 10 8
1 2 150 0.5 361.4 10 183.4 10 25
A. Albrecht Prob. Lectures for Phy 262 53
AirWater BilliardsBumper Car
r l m v dB b Qn
for a number of physical systemsQn(all units MKS)
103.0 10 105.4 10 263 10 460 127.6 10 101.3 10 0.6
0.029 1 0.16 1 346.6 10 175.1 10 8
1 2 150 0.5 361.4 10 183.4 10 25
A. Albrecht Prob. Lectures for Phy 262 54
AirWater BilliardsBumper Car
r l m101.6 10 73.4 10 264.7 10
v dB b Qn360
for a number of physical systemsQn(all units MKS)
126.2 10 92.9 10 0.3103.0 10 105.4 10 263 10 460 127.6 10 101.3 10 0.6
0.029 1 0.16 1 346.6 10 175.1 10 8
1 2 150 0.5 361.4 10 183.4 10 25
A. Albrecht Prob. Lectures for Phy 262 55
AirWater BilliardsBumper Car
r l m101.6 10 73.4 10 264.7 10
v dB b Qn360
for a number of physical systemsQn(all units MKS)
126.2 10 92.9 10 0.3103.0 10 105.4 10 263 10 460 127.6 10 101.3 10 0.6
0.029 1 0.16 1 346.6 10 175.1 10 8
1 2 150 0.5 361.4 10 183.4 10 25
Quantum at every collision
A. Albrecht Prob. Lectures for Phy 262 56
AirWater BilliardsBumper Car
r l m101.6 10 73.4 10 264.7 10
v dB b Qn360
for a number of physical systemsQn(all units MKS)
126.2 10 92.9 10 0.3103.0 10 105.4 10 263 10 460 127.6 10 101.3 10 0.6
0.029 1 0.16 1 346.6 10 175.1 10 8
1 2 150 0.5 361.4 10 183.4 10 25
Quantum at every collision
( breakdown of formula,
but conclusion robust)
A. Albrecht Prob. Lectures for Phy 262 57
AirWater BilliardsBumper Car
r l m101.6 10 73.4 10 264.7 10
v dB b Qn360
for a number of physical systemsQn(all units MKS)
126.2 10 92.9 10 0.3103.0 10 105.4 10 263 10 460 127.6 10 101.3 10 0.6
0.029 1 0.16 1 346.6 10 175.1 10 8
1 2 150 0.5 361.4 10 183.4 10 25
Quantum at every collisionEvery
Brownian Motion is a
“Schrödinger Cat”
A. Albrecht Prob. Lectures for Phy 262 58
AirWater BilliardsBumper Car
r l m101.6 10 73.4 10 264.7 10
v dB b Qn360
for a number of physical systemsQn(all units MKS)
126.2 10 92.9 10 0.3103.0 10 105.4 10 263 10 460 127.6 10 101.3 10 0.6
0.029 1 0.16 1 346.6 10 175.1 10 8
1 2 150 0.5 361.4 10 183.4 10 25
Quantum at every collisionEvery
Brownian Motion is a
“Schrödinger Cat”
Albrecht @ ICTP, Trieste 7/23/13 58
(independent of “interpretation”)
10,000,000,000,00
A. Albrecht Prob. Lectures for Phy 262 59
AirWater BilliardsBumper Car
r l m101.6 10 73.4 10 264.7 10
v dB b Qn360
for a number of physical systemsQn(all units MKS)
126.2 10 92.9 10 0.3103.0 10 105.4 10 263 10 460 127.6 10 101.3 10 0.6
0.029 1 0.16 1 346.6 10 175.1 10 8
1 2 150 0.5 361.4 10 183.4 10 25
Quantum at every collisionEvery
Brownian Motion is a
“Schrödinger Cat”
This result is at the root of our claim that
all everyday probabilities are
quantum
An important role for Brownian motion: Uncertainty in neuron transmission times
Brownian motion of polypeptides determines exactly how many of them are blocking ion channels in neurons at any given time. This is believed to be the dominant source of neuron transmission time uncertainties 1nt ms
Image from http://www.nature.com/nrn/journal/v13/n4/full/nrn3209.html
A. Albrecht Prob. Lectures for Phy 262 61
Analysis of coin flip
hv
fv
Coin diameter d
hf n
h f
vt t
v v
2t ft t
4 fvfd
0.5tN f t
Using:1nt ms 5 /h fv v m s
0.01d m
A. Albrecht Prob. Lectures for Phy 262 62
Analysis of coin flip
hv
fv
Coin diameter d
hf n
h f
vt t
v v
2t ft t
4 fvfd
0.5tN f t
Using:1nt ms 5 /h fv v m s
0.01d m
50-50 coin flip probabilities are
a derivable quantum result
A. Albrecht Prob. Lectures for Phy 262 63
Analysis of coin flip
hv
fv
Coin diameter d
hf n
h f
vt t
v v
2t ft t
4 fvfd
0.5tN f t
Using:1nt ms 5 /h fv v m s
0.01d m
50-50 coin flip probabilities are
a derivable quantum result
Without reference to “principle of
indifference” etc. etc.
A. Albrecht Prob. Lectures for Phy 262 64
Analysis of coin flip
hv
fv
Coin diameter d
hf n
h f
vt t
v v
2t ft t
4 fvfd
0.5tN f t
Using:1nt ms 5 /h fv v m s
0.01d m
NB: Coin flip is “at the margin” of deterministic vs random: Increasing d or deceasing vh can reduce δN substantially
A. Albrecht Prob. Lectures for Phy 262 65
Analysis of coin flip
hv
fv
Coin diameter d
hf n
h f
vt t
v v
2t ft t
4 fvfd
0.5tN f t
Using:1nt ms 5 /h fv v m s
0.01d m
NB: Coin flip is “at the margin” of deterministic vs random: Increasing d or deceasing vh can reduce δN substantially
Still, this is a good illustration of how quantum uncertainties can filter up into the macroscopic world, for
systems that *are* random.
A. Albrecht Prob. Lectures for Phy 262 66
Analysis of coin flip
hv
fv
Coin diameter d
hf n
h f
vt t
v v
2t ft t
4 fvfd
0.5tN f t
Using:1nt ms 5 /h fv v m s
0.01d m
NB: Coin flip is “at the margin” of deterministic vs random: Increasing d or deceasing vh can reduce δN substantially
Still, this is a good illustration of how quantum uncertainties can filter up into the macroscopic world, for
systems that *are* random.
A. Albrecht Prob. Lectures for Phy 262 67
Physical vs probabilities vs “probabilities of belief”
Bayes:
|
|P Data Theory
P Theory Data P TheoryP Data
Physical probability: To do with physical properties of detector etc
A. Albrecht Prob. Lectures for Phy 262 68
Physical vs probabilities vs “probabilities of belief”
Bayes:
|
|P Data Theory
P Theory Data P TheoryP Data
Probabilities of belief:• Which data you trust most• Which theory you like best
A. Albrecht Prob. Lectures for Phy 262 69
Physical vs probabilities vs “probabilities of belief”
Bayes:
This talk is about physical probability only
|
|P Data Theory
P Theory Data P TheoryP Data
A. Albrecht Prob. Lectures for Phy 262 70
Physical vs probabilities vs “probabilities of belief”
Bayes:
NB: The goal of science is to get sufficiently good data that probabilities of belief are inconsequential
|
|P Data Theory
P Theory Data P TheoryP Data
A. Albrecht Prob. Lectures for Phy 262 71
Physical vs probabilities vs “probabilities of belief”
Bayes:
NB: The goal of science is to get sufficiently good data that probabilities of belief are inconsequential
|
|P Data Theory
P Theory Data P TheoryP Data
A. Albrecht Prob. Lectures for Phy 262 72
Physical vs probabilities vs “probabilities of belief”
Adding new data (theory priors can include earlier data sets):
5
5 5 45
||
P D TP T D P T
P D
4
4 4 34
||
P D TP T D P T
P D
A. Albrecht Prob. Lectures for Phy 262 73
Physical vs probabilities vs “probabilities of belief”
Adding new data (theory priors can include earlier data sets):
5
5 5 45
||
P D TP T D P T
P D
4
4 4 34
||
P D TP T D P T
P D
…………
1
1 1 01
||
P D TP T D P T
P D
A. Albrecht Prob. Lectures for Phy 262 74
Physical vs probabilities vs “probabilities of belief”
Adding new data (theory priors can include earlier data sets):
5
5 5 45
||
P D TP T D P T
P D
4
4 4 34
||
P D TP T D P T
P D
…………
1
1 1 01
||
P D TP T D P T
P D
This initial “model uncertainty” prior is the only P(T) that is a pure probability of belief.
A. Albrecht Prob. Lectures for Phy 262 75
Physical vs probabilities vs “probabilities of belief”
Adding new data (theory priors can include earlier data sets):
5
5 5 45
||
P D TP T D P T
P D
4
4 4 34
||
P D TP T D P T
P D
…………
1
1 1 01
||
P D TP T D P T
P D
This initial “model uncertainty” prior is the only P(T) that is a pure probability of belief.
This talk is only about wherever it appears
|P D T
A. Albrecht Prob. Lectures for Phy 262 76
Physical vs probabilities vs “probabilities of belief”
Adding new data (theory priors can include earlier data sets):
5
5 5 45
||
P D TP T D P T
P D
4
4 4 34
||
P D TP T D P T
P D
…………
1
1 1 01
||
P D TP T D P T
P D
This initial “model uncertainty” prior is the only P(T) that is a pure probability of belief.
This talk is only about wherever it appears
|P D T
NB: The goal of science is to get sufficiently good data that probabilities of belief are inconsequential
A. Albrecht Prob. Lectures for Phy 262 77
Physical vs probabilities vs “probabilities of belief”
Adding new data (theory priors can include earlier data sets):
5
5 5 45
||
P D TP T D P T
P D
4
4 4 34
||
P D TP T D P T
P D
…………
1
1 1 01
||
P D TP T D P T
P D
This initial “model uncertainty” prior is the only P(T) that is a pure probability of belief.
This talk is only about wherever it appears
|P D T
NB: The goal of science is to get sufficiently good data that probabilities of belief are inconsequential
This is the only part of the formula where physical
randomness appears
A. Albrecht Prob. Lectures for Phy 262 78
Physical vs probabilities vs “probabilities of belief”
Adding new data (theory priors can include earlier data sets):
5
5 5 45
||
P D TP T D P T
P D
4
4 4 34
||
P D TP T D P T
P D
…………
1
1 1 01
||
P D TP T D P T
P D
This initial “model uncertainty” prior is the only P(T) that is a pure probability of belief.
This talk is only about wherever it appears
|P D T
NB: The goal of science is to get sufficiently good data that probabilities of belief are inconsequential
This is the only part of the formula where physical
randomness appears
A. Albrecht Prob. Lectures for Phy 262 79
• Proof by exhaustion not realistic
All everyday probabilities are quantum probabilities
A. Albrecht Prob. Lectures for Phy 262 80
• Proof by exhaustion not realistic• One counterexample (practical utility of non-quantum
probabilities) will undermine our entire argument.
All everyday probabilities are quantum probabilities
A. Albrecht Prob. Lectures for Phy 262 81
• Proof by exhaustion not realistic• One counterexample (practical utility of non-quantum
probabilities) will undermine our entire argument• Can still invent classical probabilities just to do multiverse
cosmology
All everyday probabilities are quantum probabilities
A. Albrecht Prob. Lectures for Phy 262 82
• Proof by exhaustion not realistic• One counterexample (practical utility of non-quantum
probabilities) will undermine our entire argument• Can still invent classical probabilities just to do multiverse
cosmology• Not a problem for many finite theories (AA, Banks &
Fischler)
All everyday probabilities are quantum probabilities
A. Albrecht Prob. Lectures for Phy 262 83
• Proof by exhaustion not realistic• One counterexample (practical utility of non-quantum
probabilities) will undermine our entire argument• Can still invent classical probabilities just to do multiverse
cosmology• Not a problem for many finite theories (AA, Banks &
Fischler)• Which theories really do require classical probabilities
not yet resolved rigorously.
All everyday probabilities are quantum probabilities
A. Albrecht Prob. Lectures for Phy 262 84
• Proof by exhaustion not realistic• One counterexample (practical utility of non-quantum
probabilities) will undermine our entire argument• Can still invent classical probabilities just to do multiverse
cosmology• Not a problem for many finite theories (AA, Banks &
Fischler)• Which theories really do require classical probabilities
not yet resolved rigorously (symmetry?... simplicity? See below)
All everyday probabilities are quantum probabilities
A. Albrecht Prob. Lectures for Phy 262 85
• Proof by exhaustion not realistic• One counterexample (practical utility of non-quantum
probabilities) will undermine our entire argument• Can still invent classical probabilities just to do multiverse
cosmology• Not a problem for many finite theories (AA, Banks &
Fischler)• Which theories really do require classical probabilities
not yet resolved rigorously (symmetry?... simplicity? See below)
All everyday probabilities are quantum probabilities
Some further thoughts:
A. Albrecht Prob. Lectures for Phy 262 86
-60 -50 -40 -30 -20 -10 0 10-70
-60
-50
-40
-30
-20
-10
0
10
log(a/a0)
log(
RH/R
H0)
Here
Cosmic structureCo
smic
leng
th s
cale
Scale factor (measures expansion, time)
Today
Observable Structure
comoving
SBBHR
Cosmic structure originates “superhorizon” in Standard Big Bag
(why would they be quantum?)
A note on “probability censorship”
A. Albrecht Prob. Lectures for Phy 262 87
-60 -50 -40 -30 -20 -10 0 10-70
-60
-50
-40
-30
-20
-10
0
10
log(a/a0)
log(
RH/R
H0)
Here
Cosmic structureCo
smic
leng
th s
cale
Scale factor (measures expansion, time)
Today
Observable Structure
comoving
SBBHR
Cosmic structure originates “superhorizon” in Standard Big Bag
(why would they be quantum?)InfHR
Cosmic structure originates in quantum
ground state in inflationary cosmology
A note on “probability censorship”
A. Albrecht Prob. Lectures for Phy 262 88
• Proof by exhaustion not realistic• One counterexample (practical utility of non-quantum
probabilities) will undermine our entire argument• Can still invent classical probabilities just to do multiverse
cosmology• Not a problem for many finite theories (AA, Banks &
Fischler)• Which theories really do require classical probabilities
not yet resolved rigorously (symmetry?... simplicity? See below)
All everyday probabilities are quantum probabilities
Compare with identical particle statistics
A. Albrecht Prob. Lectures for Phy 262 89
3.141592653589793238462643383279502884197169399375105820974944592307816406286 208998628034825342117067982148086513282306647093844609550582231725359408128481 117450284102701938521105559644622948954930381964428810975665933446128475648233 786783165271201909145648566923460348610454326648213393607260249141273724587006 606315588174881520920962829254091715364367892590360011330530548820466521384146 951941511609433057270365759591953092186117381932611793105118548074462379962749 567351885752724891227938183011949129833673362440656643086021394946395224737190 702179860943702770539217176293176752384674818467669405132000568127145263560827 785771342757789609173637178721468440901224953430146549585371050792279689258923 542019956112129021960864034418159813629774771309960518707211349999998372978049 951059731732816096318595024459455346908302642522308253344685035261931188171010 003137838752886587533208381420617177669147303598253490428755468731159562863882 353787593751957781857780532171226806613001927876611195909216420198938095257201 065485863278865936153381827968230301952035301852968995773622599413891249721775 283479131515574857242454150695950829533116861727855889075098381754637464939319 255060400927701671139009848824012858361603563707660104710181942955596198946767 837449448255379774726847104047534646208046684259069491293313677028989152104752 162056966024058038150193511253382430035587640247496473263914199272604269922796 782354781636009341721641219924586315030286182974555706749838505494588586926995 690927210797509302955321165344987202755960236480665499119881834797753566369807 426542527862551818417574672890977772793800081647060016145249192173217214772350 141441973568548161361157352552133475741849468438523323907394143334547762416862 518983569485562099219222184272550254256887671790494601653466804988627232791786 085784383827967976681454100953883786360950680064225125205117392984896084128488 626945604241965285022210661186306744278622039194945047123713786960956364371917 287467764657573962413890865832645995813390478027590099465764078951269468398352 595709825822620522489407726719478268482601476990902640136394437455305068203496
Further discussion
Bet on the millionth digit of π (or Chaitin’s Ω)
(Carroll)
A. Albrecht Prob. Lectures for Phy 262 90
3.141592653589793238462643383279502884197169399375105820974944592307816406286 208998628034825342117067982148086513282306647093844609550582231725359408128481 117450284102701938521105559644622948954930381964428810975665933446128475648233 786783165271201909145648566923460348610454326648213393607260249141273724587006 606315588174881520920962829254091715364367892590360011330530548820466521384146 951941511609433057270365759591953092186117381932611793105118548074462379962749 567351885752724891227938183011949129833673362440656643086021394946395224737190 702179860943702770539217176293176752384674818467669405132000568127145263560827 785771342757789609173637178721468440901224953430146549585371050792279689258923 542019956112129021960864034418159813629774771309960518707211349999998372978049 951059731732816096318595024459455346908302642522308253344685035261931188171010 003137838752886587533208381420617177669147303598253490428755468731159562863882 353787593751957781857780532171226806613001927876611195909216420198938095257201 065485863278865936153381827968230301952035301852968995773622599413891249721775 283479131515574857242454150695950829533116861727855889075098381754637464939319 255060400927701671139009848824012858361603563707660104710181942955596198946767 837449448255379774726847104047534646208046684259069491293313677028989152104752 162056966024058038150193511253382430035587640247496473263914199272604269922796 782354781636009341721641219924586315030286182974555706749838505494588586926995 690927210797509302955321165344987202755960236480665499119881834797753566369807 426542527862551818417574672890977772793800081647060016145249192173217214772350 141441973568548161361157352552133475741849468438523323907394143334547762416862 518983569485562099219222184272550254256887671790494601653466804988627232791786 085784383827967976681454100953883786360950680064225125205117392984896084128488 626945604241965285022210661186306744278622039194945047123713786960956364371917 287467764657573962413890865832645995813390478027590099465764078951269468398352 595709825822620522489407726719478268482601476990902640136394437455305068203496
Further discussion
Bet on the millionth digit of π (or Chaitin’s Ω)• The *only* thing random is the choice of digit to bet on
A. Albrecht Prob. Lectures for Phy 262 91
3.141592653589793238462643383279502884197169399375105820974944592307816406286 208998628034825342117067982148086513282306647093844609550582231725359408128481 117450284102701938521105559644622948954930381964428810975665933446128475648233 786783165271201909145648566923460348610454326648213393607260249141273724587006 606315588174881520920962829254091715364367892590360011330530548820466521384146 951941511609433057270365759591953092186117381932611793105118548074462379962749 567351885752724891227938183011949129833673362440656643086021394946395224737190 702179860943702770539217176293176752384674818467669405132000568127145263560827 785771342757789609173637178721468440901224953430146549585371050792279689258923 542019956112129021960864034418159813629774771309960518707211349999998372978049 951059731732816096318595024459455346908302642522308253344685035261931188171010 003137838752886587533208381420617177669147303598253490428755468731159562863882 353787593751957781857780532171226806613001927876611195909216420198938095257201 065485863278865936153381827968230301952035301852968995773622599413891249721775 283479131515574857242454150695950829533116861727855889075098381754637464939319 255060400927701671139009848824012858361603563707660104710181942955596198946767 837449448255379774726847104047534646208046684259069491293313677028989152104752 162056966024058038150193511253382430035587640247496473263914199272604269922796 782354781636009341721641219924586315030286182974555706749838505494588586926995 690927210797509302955321165344987202755960236480665499119881834797753566369807 426542527862551818417574672890977772793800081647060016145249192173217214772350 141441973568548161361157352552133475741849468438523323907394143334547762416862 518983569485562099219222184272550254256887671790494601653466804988627232791786 085784383827967976681454100953883786360950680064225125205117392984896084128488 626945604241965285022210661186306744278622039194945047123713786960956364371917 287467764657573962413890865832645995813390478027590099465764078951269468398352 595709825822620522489407726719478268482601476990902640136394437455305068203496
Further discussion
Bet on the millionth digit of π (or Chaitin’s Ω)• The *only* thing random is the choice of digit to bet on• Fairness is about lack of correlation between digit choice
and digit value
A. Albrecht Prob. Lectures for Phy 262 92
3.141592653589793238462643383279502884197169399375105820974944592307816406286 208998628034825342117067982148086513282306647093844609550582231725359408128481 117450284102701938521105559644622948954930381964428810975665933446128475648233 786783165271201909145648566923460348610454326648213393607260249141273724587006 606315588174881520920962829254091715364367892590360011330530548820466521384146 951941511609433057270365759591953092186117381932611793105118548074462379962749 567351885752724891227938183011949129833673362440656643086021394946395224737190 702179860943702770539217176293176752384674818467669405132000568127145263560827 785771342757789609173637178721468440901224953430146549585371050792279689258923 542019956112129021960864034418159813629774771309960518707211349999998372978049 951059731732816096318595024459455346908302642522308253344685035261931188171010 003137838752886587533208381420617177669147303598253490428755468731159562863882 353787593751957781857780532171226806613001927876611195909216420198938095257201 065485863278865936153381827968230301952035301852968995773622599413891249721775 283479131515574857242454150695950829533116861727855889075098381754637464939319 255060400927701671139009848824012858361603563707660104710181942955596198946767 837449448255379774726847104047534646208046684259069491293313677028989152104752 162056966024058038150193511253382430035587640247496473263914199272604269922796 782354781636009341721641219924586315030286182974555706749838505494588586926995 690927210797509302955321165344987202755960236480665499119881834797753566369807 426542527862551818417574672890977772793800081647060016145249192173217214772350 141441973568548161361157352552133475741849468438523323907394143334547762416862 518983569485562099219222184272550254256887671790494601653466804988627232791786 085784383827967976681454100953883786360950680064225125205117392984896084128488 626945604241965285022210661186306744278622039194945047123713786960956364371917 287467764657573962413890865832645995813390478027590099465764078951269468398352 595709825822620522489407726719478268482601476990902640136394437455305068203496
Further discussion
Bet on the millionth digit of π (or Chaitin’s Ω)• The *only* thing random is the choice of digit to bet on• Fairness is about lack of correlation between digit choice
and digit value• Choice of digit comes from Brain (neurons with quantum uncertainties) Random number generator seed time stamp
(when you press ENTER) brain Etc
A. Albrecht Prob. Lectures for Phy 262 93
3.141592653589793238462643383279502884197169399375105820974944592307816406286 208998628034825342117067982148086513282306647093844609550582231725359408128481 117450284102701938521105559644622948954930381964428810975665933446128475648233 786783165271201909145648566923460348610454326648213393607260249141273724587006 606315588174881520920962829254091715364367892590360011330530548820466521384146 951941511609433057270365759591953092186117381932611793105118548074462379962749 567351885752724891227938183011949129833673362440656643086021394946395224737190 702179860943702770539217176293176752384674818467669405132000568127145263560827 785771342757789609173637178721468440901224953430146549585371050792279689258923 542019956112129021960864034418159813629774771309960518707211349999998372978049 951059731732816096318595024459455346908302642522308253344685035261931188171010 003137838752886587533208381420617177669147303598253490428755468731159562863882 353787593751957781857780532171226806613001927876611195909216420198938095257201 065485863278865936153381827968230301952035301852968995773622599413891249721775 283479131515574857242454150695950829533116861727855889075098381754637464939319 255060400927701671139009848824012858361603563707660104710181942955596198946767 837449448255379774726847104047534646208046684259069491293313677028989152104752 162056966024058038150193511253382430035587640247496473263914199272604269922796 782354781636009341721641219924586315030286182974555706749838505494588586926995 690927210797509302955321165344987202755960236480665499119881834797753566369807 426542527862551818417574672890977772793800081647060016145249192173217214772350 141441973568548161361157352552133475741849468438523323907394143334547762416862 518983569485562099219222184272550254256887671790494601653466804988627232791786 085784383827967976681454100953883786360950680064225125205117392984896084128488 626945604241965285022210661186306744278622039194945047123713786960956364371917 287467764657573962413890865832645995813390478027590099465764078951269468398352 595709825822620522489407726719478268482601476990902640136394437455305068203496
Further discussion
Bet on the millionth digit of π (or Chaitin’s Ω)• The *only* thing random is the choice of digit to bet on• Fairness is about lack of correlation between digit choice
and digit value• Choice of digit comes from Brain (neurons with quantum uncertainties) Random number generator seed time stamp
(when you press ENTER) brain Etc
• The only randomness in a bet on a digit of π is quantum!
A. Albrecht Prob. Lectures for Phy 262 94
10001000111101010
10001000101001010
10001000101101010
11011000101001010
10001010111101010
Classical Computer: The “computational degrees of freedom” of a classical computer are very classical: Engineered to be well isolated from the quantum fluctuations that are everywhere • Computations are deterministic• “Random” is artificial• Model a classical billiard gas on
a computer: All “random” fluctuations
are determined by (or “readings of”) the initial state.
Further discussion
A. Albrecht Prob. Lectures for Phy 262 95
10001000111101010
10001000101001010
10001000101101010
11011000101001010
10001010111101010
Classical Computer: The “computational degrees of freedom” of a classical computer are very classical: Engineered to be well isolated from the quantum fluctuations that are everywhere • Computations are deterministic• “Random” is artificial• Model a classical billiard gas on
a computer: All “random” fluctuations
are determined by (or “readings of”) the initial state.
Further discussion
Std. thinking about classical
probabilities
A. Albrecht Prob. Lectures for Phy 262 96
10001000111101010
10001000101001010
10001000101101010
11011000101001010
10001010111101010
Classical Computer: The “computational degrees of freedom” of a classical computer are very classical: Engineered to be well isolated from the quantum fluctuations that are everywhere • Computations are deterministic• “Random” is artificial• Model a classical billiard gas on
a computer: All “random” fluctuations
are determined by (or “readings of”) the initial state.
Further discussion
Std. thinking about classical
probabilitiesSee digits of
discussion
A. Albrecht Prob. Lectures for Phy 262 97
10001000111101010
10001000101001010
10001000101101010
11011000101001010
10001010111101010
Classical Computer: The “computational degrees of freedom” of a classical computer are very classical: Engineered to be well isolated from the quantum fluctuations that are everywhere • Computations are deterministic• “Random” is artificial• Model a classical billiard gas on
a computer: All “random” fluctuations
are determined by (or “readings of”) the initial state.
Further discussion
Std. thinking about classical
probabilitiesSee digits of
discussion
My claim: • The real world does not have
these sorts of solid classical ties to initial conditions.
• If it did, that would be a counterexample to my claim
• Quantum prob. enters randomness on a real computer via IC’s
A. Albrecht Prob. Lectures for Phy 262 98
Our ideas about probability are like our ideas about color:• Quantum physics gives the correct foundation to
our understanding• Our “classical” intuition predates our knowledge
of QM by a long long time, and works just fine for most things
• Fundamental quantum understanding needed to fix classical misunderstandings in certain cases.
Further discussion
A. Albrecht Prob. Lectures for Phy 262 99
Our ideas about probability are like our ideas about color:• Quantum physics gives the correct foundation to
our understanding• Our “classical” intuition predates our knowledge
of QM by a long long time, and works just fine for most things
• Fundamental quantum understanding needed to fix classical misunderstandings in certain cases.
Further discussion
A. Albrecht Prob. Lectures for Phy 262 100
Our ideas about probability are like our ideas about color:• Quantum physics gives the correct foundation to
our understanding• Our “classical” intuition predates our knowledge
of QM by a long long time, and works just fine for most things
• Fundamental quantum understanding needed to fix classical misunderstandings in certain cases.
Further discussion
A. Albrecht Prob. Lectures for Phy 262 101
Outline
1) Quantum vs non-quantum probabilities (toy model/multiverse)
2) Everyday probabilities
3) Be careful about counting!
4) Implications for multiverse/eternal inflation
A. Albrecht Prob. Lectures for Phy 262 102
Outline
1) Quantum vs non-quantum probabilities (toy model/multiverse)
2) Everyday probabilities
3) Be careful about counting!
4) Implications for multiverse/eternal inflation
A. Albrecht Prob. Lectures for Phy 262 103
Central message:
• “Randomness is (quantum) physics”• Counting may or MAY NOT have a role in
inferring or representing physical randomness
Heads
A. Albrecht Prob. Lectures for Phy 262 104
Central message:
• “Randomness is (quantum) physics”• Counting may or MAY NOT have a role in
inferring or representing physical randomness• Example: Flip a coin and choose a ball:
Heads
Tails
Results
A. Albrecht Prob. Lectures for Phy 262 105
Central message:
• “Randomness is (quantum) physics”• Counting may or MAY NOT have a role in
inferring or representing physical randomness• Example: Flip a coin and choose a ball:
Heads
TailsCounts of red & green
balls here can be related in very
concrete terms to the probability of heads
vs tails
A. Albrecht Prob. Lectures for Phy 262 106
Central message:
• “Randomness is (quantum) physics”• Counting may or MAY NOT have a role in
inferring or representing physical randomness• Example: Flip a coin and choose a ball:
Heads
TailsCounts of red & green
balls here can be related in very
concrete terms to the probability of heads
vs tails
107
Now ask: What is the probability that a ball drawn from the “Results” bowl is red?
HeadsA. Albrecht Prob. Lectures for Phy 262
Results
108
Now ask: What is the probability that a ball drawn from the “Results” bowl is red?• Different physical “completions” of this question are
possible which give different answers. (≈ measures)
Heads
Tails
A. Albrecht Prob. Lectures for Phy 262
Results
Results Results
109
Now ask: What is the probability that a ball drawn from the “Results” bowl is red?• Different physical “completions” of this question are
possible which give different answers. (≈ measures)• Counting is NOT enough.
Heads
Tails
A. Albrecht Prob. Lectures for Phy 262
Results
Results Results
110
Now ask: What is the probability that a ball drawn from the “Results” bowl is red?• Different physical “completions” of this question are
possible which give different answers. (≈ measures)• Counting is NOT enough.
Heads
Tails
A. Albrecht Prob. Lectures for Phy 262
Results
Results ResultsIn a multiverse with many copies
of you, there simply is *no* physical completion for the
question “which observer am I?”. Future data may address this, but not in time to make predictions.
111
Now ask: What is the probability that a ball drawn from the “Results” bowl is red?• Different physical “completions” of this question are
possible which give different answers. (≈ measures)• Counting is NOT enough.
Heads
Tails
A. Albrecht Prob. Lectures for Phy 262
Results
Results ResultsIn a multiverse with many copies
of you, there simply is *no* physical completion for the
question “which observer am I?”. Future data may address this, but not in time to make predictions.
112
Now ask: What is the probability that a ball drawn from the “Results” bowl is red?• Different physical “completions” of this question are
possible which give different answers. (≈ measures)• Counting is NOT enough.
Heads
Tails
A. Albrecht Prob. Lectures for Phy 262
Results
Results ResultsIn a multiverse with many copies
of you, there simply is *no* physical completion for the
question “which observer am I?”. Future data may address this, but not in time to make predictions.
This is where things go wrong in the
standard treatment of the multiverse
113
Now ask: What is the probability that a ball drawn from the “Results” bowl is red?• Different physical “completions” of this question are
possible which give different answers. (≈ measures)• Counting is NOT enough.
Heads
Tails
A. Albrecht Prob. Lectures for Phy 262
Results
Results ResultsIn a multiverse with many copies
of you, there simply is *no* physical completion for the
question “which observer am I?”. Future data may address this, but not in time to make predictions.
This is where things go wrong in the
standard treatment of the multiverse
In many cases counting observers has no predictive
value
114
Now ask: What is the probability that a ball drawn from the “Results” bowl is red?• Different physical “completions” of this question are
possible which give different answers. (≈ measures)• Counting is NOT enough.
Heads
Tails
A. Albrecht Prob. Lectures for Phy 262
Results
Results ResultsIn a multiverse with many copies
of you, there simply is *no* physical completion for the
question “which observer am I?”. Future data may address this, but not in time to make predictions.
This is where things go wrong in the
standard treatment of the multiverse
In many cases counting observers has no predictive
value
No point in counting for these
cases
A. Albrecht Prob. Lectures for Phy 262 115
Outline
1) Quantum vs non-quantum probabilities (toy model/multiverse)
2) Everyday probabilities
3) Be careful about counting!
4) Implications for multiverse/eternal inflation
A. Albrecht Prob. Lectures for Phy 262 116
Outline
1) Quantum vs non-quantum probabilities (toy model/multiverse)
2) Everyday probabilities
3) Be careful about counting!
4) Implications for multiverse/eternal inflation
A. Albrecht Prob. Lectures for Phy 262 117
Outline
1) Quantum vs non-quantum probabilities (toy model/multiverse)
2) Everyday probabilities
3) Be careful about counting!
4) Implications for multiverse/eternal inflation
A. Albrecht Prob. Lectures for Phy 262 118
Pocket A with quantum amplitude so
118
118
118
1) No “volume factors”2) Boltzmann Brain problem reduced3) No “youngness/end of time” problem
Implications for eternal inflation
Pocket B with quantum amplitude so
A. Albrecht Prob. Lectures for Phy 262 119
Pocket A with Ap
Pocket B with Bp
119
119
119
1) No “volume factors”2) Boltzmann Brain problem reduced3) No “youngness/end of time” problem
Implications for eternal inflation
(from quantum branching ratio)
A. Albrecht Prob. Lectures for Phy 262 120
Pocket A with Ap
Pocket B with Bp
120
120
120
1) No “volume factors”2) Boltzmann Brain problem reduced3) No “youngness/end of time” problem
Implications for eternal inflationOne semiclassical universe having many more possible observers in it than another (often counted
by volume), does *not* give that universe greater statistical weight. Quantum branching ratio into one
vs the other ( ) does count/A Bp p
A. Albrecht Prob. Lectures for Phy 262 121
Pocket A with Ap
Pocket B with Bp
121
121
121
1) No “volume factors”2) Boltzmann Brain problem reduced3) No “youngness/end of time” problem
Implications for eternal inflation
A. Albrecht Prob. Lectures for Phy 262 122
Pocket A with Ap Pocket B with Bp
1) No “volume factors”2) Boltzmann Brain problem reduced3) No “youngness/end of time” problem
Implications for eternal inflation
A. Albrecht Prob. Lectures for Phy 262 123
Pocket A with Ap Pocket B with Bp
1) No “volume factors”2) Boltzmann Brain problem reduced3) No “youngness/end of time” problem
Implications for eternal inflation
This model has no “Boltzmann Brain” problem as long as
Is not too small/A Bp p
A. Albrecht Prob. Lectures for Phy 262 124
Pocket A with Ap Pocket B with Bp
1) No “volume factors”2) Boltzmann Brain problem reduced3) No “youngness/end of time” problem
Implications for eternal inflation
This model has no “Boltzmann Brain” problem as long as
Is not too small/A Bp p
Boltzmann brains are observers which look good vs current data but which
quickly go bad
A. Albrecht Prob. Lectures for Phy 262 125
Pocket A with Ap Pocket B with Bp
1) No “volume factors”2) Boltzmann Brain problem reduced3) No “youngness/end of time” problem
Implications for eternal inflation
A. Albrecht Prob. Lectures for Phy 262 126
Pocket A with Ap Pocket B with Bp
1) No “volume factors”2) Boltzmann Brain problem reduced3) No “youngness/end of time” problem
Implications for eternal inflation
Are there additional amplitudes hidden in this picture?
If so, they may provide a more detailed (and well defined) measure
1) No “volume factors”2) Boltzmann Brain problem reduced3) No “youngness/end of time” problem
Implications for eternal inflation
A. Albrecht Prob. Lectures for Phy 262 127
More pocket universes produced later vs earlier (due to more inflation)
1) No “volume factors”2) Boltzmann Brain problem reduced3) No “youngness/end of time” problem
Implications for eternal inflation
A. Albrecht Prob. Lectures for Phy 262 128
More pocket universes produced later vs earlier (due to more inflation) & experience any time cutoff
Time cutoff regulator
1) No “volume factors”2) Boltzmann Brain problem reduced3) No “youngness/end of time” problem
Implications for eternal inflation
A. Albrecht Prob. Lectures for Phy 262 129
More pocket universes produced later vs earlier (due to more inflation) & experience any time cutoff
Time cutoff regulator
1) No “volume factors”2) Boltzmann Brain problem reduced3) No “youngness/end of time” problem
Implications for eternal inflation
A. Albrecht Prob. Lectures for Phy 262 130
More pocket universes produced later vs earlier (due to more inflation) & experience any time cutoff
Time cutoff regulator See also Guth & Vanchurin
1) No “volume factors”2) Boltzmann Brain problem reduced3) No “youngness/end of time” problem
Implications for eternal inflation
A. Albrecht Prob. Lectures for Phy 262 131
More pocket universes produced later vs earlier (due to more inflation) & experience any time cutoff
Time cutoff regulator
Wavefunction cannot give probabilities for which pocket you are in.
Time cutoff only there as (wrong) attempt to determine which pocket
The youngness/end of time problem is asking a question the theory cannot answer
A. Albrecht Prob. Lectures for Phy 262 132
1) No “volume factors”2) Boltzmann Brain problem reduced3) No “youngness/end of time” problem
Implications for eternal inflation
2|A Ap
Quantum Branching
A
B2|B Bp
Eternal inflation
A. Albrecht Prob. Lectures for Phy 262 133
1) No “volume factors”2) Boltzmann Brain problem reduced3) No “youngness/end of time” problem
Implications for eternal inflation
2|A Ap
Quantum Branching
A
B2|B Bp
ABB
A
B
BB
A
ABA`
Eternal inflation
Answer given by these
No need to worry about counting infinite A’s and B’s (if sufficient symmetry)
A. Albrecht Prob. Lectures for Phy 262 134
1) All practically applicable probabilities are of physical (quantum) origin.
2) Counting of objects may or MAY NOT be a way of accessing legitimate quantum probabilities
3) Standard discussions of probabilities in cosmology often make errors re 2)
4) 1) and care about 2) allow us to introduce better discipline into cosmological discussions (just say “no”). Implications so far:
a) No (counting based) volume factorsb) Reduced Boltzmann Brain problemc) No youngness/end of time problemd) Measure problems apparently resolved
Conclusions
A. Albrecht Prob. Lectures for Phy 262 135
1) All practically applicable probabilities are of physics (quantum) origin.
2) Counting of objects may or MAY NOT be a way of accessing legitimate quantum probabilities
3) Standard discussions of probabilities in cosmology often make errors re 2)
4) 1) and care about 2) allow us to introduce better discipline into cosmological discussions (just say “no”). Implications so far:
a) No (counting based) volume factorsb) Reduced Boltzmann Brain problemc) No youngness/end of time problem
Conclusions I still have other concerns about eternal inflation that
makes me prefer finite theories, but this “probability
discipline” may resolve what I used to think was the most
troubling issue
A. Albrecht Prob. Lectures for Phy 262 136
1) All practically applicable probabilities are of physics (quantum) origin.
2) Counting of objects may or MAY NOT be a way of accessing legitimate quantum probabilities
3) Standard discussions of probabilities in cosmology often make errors re 2)
4) 1) and care about 2) allow us to introduce better discipline into cosmological discussions (just say “no”). Implications so far:
a) No (counting based) volume factorsb) Reduced Boltzmann Brain problemc) No youngness/end of time problemd) Measure problems apparently resolved
Conclusions I still have other concerns about eternal inflation that
makes me prefer finite theories, but this “probability
discipline” may resolve what I used to think was the most
troubling issue
Landscape OK too
A. Albrecht Prob. Lectures for Phy 262 137
1) All practically applicable probabilities are of physics (quantum) origin.
2) Counting of objects may or MAY NOT be a way of accessing legitimate quantum probabilities
3) Standard discussions of probabilities in cosmology often make errors re 2)
4) 1) and care about 2) allow us to introduce better discipline into cosmological discussions (just say “no”). Implications so far:
a) No (counting based) volume factorsb) Reduced Boltzmann Brain problemc) No youngness/end of time problemd) Measure problems apparently resolved
Conclusions I still have other concerns about eternal inflation that
makes me prefer finite theories, but this “probability
discipline” may resolve what I used to think was the most
troubling issue
Landscape OK too
In a systematic treatment the
classical probabilities will reappear as
“priors”. Same math but very different
role.
A. Albrecht Prob. Lectures for Phy 262 138
1) All practically applicable probabilities are of physics (quantum) origin.
2) Counting of objects may or MAY NOT be a way of accessing legitimate quantum probabilities
3) Standard discussions of probabilities in cosmology often make errors re 2)
4) 1) and care about 2) allow us to introduce better discipline into cosmological discussions (just say “no”). Implications so far:
a) No (counting based) volume factorsb) Reduced Boltzmann Brain problemc) No youngness/end of time problemd) Measure problems appaently resolved
Conclusions
Perhaps related to work by Nomura and
Garriga & Vilenkin and collaborators
I still have other concerns about eternal inflation that
makes me prefer finite theories, but this “probability
discipline” may resolve what I used to think was the most
troubling issue
Landscape OK too
In a systematic treatment the
classical probabilities will reappear as
“priors”. Same math but very different
role.
A. Albrecht Prob. Lectures for Phy 262 139
1) All practically applicable probabilities are of physics (quantum) origin.
2) Counting of objects may or MAY NOT be a way of accessing legitimate quantum probabilities
3) Standard discussions of probabilities in cosmology often make errors re 2)
4) 1) and care about 2) allow us to introduce better discipline into cosmological discussions (just say “no”). Implications so far:
a) No (counting based) volume factorsb) Reduced Boltzmann Brain problemc) No youngness/end of time problemd) Measure problems apparently resolved
Conclusions
Perhaps related to work by Nomura and
Garriga & Vilenkin and collaborators
I still have other concerns about eternal inflation that
makes me prefer finite theories, but this “probability
discipline” may resolve what I used to think was the most
troubling issue
Landscape OK too
Clashes with my work on the “clock ambiguity”
In a systematic treatment the
classical probabilities will reappear as
“priors”. Same math but very different
role.
A. Albrecht Prob. Lectures for Phy 262 140
1) All practically applicable probabilities are of physics (quantum) origin.
2) Counting of objects may or MAY NOT be a way of accessing legitimate quantum probabilities
3) Standard discussions of probabilities in cosmology often make errors re 2)
4) 1) and care about 2) allow us to introduce better discipline into cosmological discussions (just say “no”). Implications so far:
a) No (counting based) volume factorsb) Reduced Boltzmann Brain problemc) No youngness/end of time problemd) Measure problems apparently resolved
Conclusions
A. Albrecht Prob. Lectures for Phy 262 141
1) All practically applicable probabilities are of physics (quantum) origin.
2) Counting of objects may or MAY NOT be a way of accessing legitimate quantum probabilities
3) Standard discussions of probabilities in cosmology often make errors re 2)
4) 1) and care about 2) allow us to introduce better discipline into cosmological discussions (just say “no”). Implications so far:
a) No (counting based) volume factorsb) Reduced Boltzmann Brain problemc) No youngness/end of time problemd) Measure problems apparently resolved
Conclusions
A. Albrecht Prob. Lectures for Phy 262 142
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