Time of Philosophers, Time of Physicists, Time of ...fabien.besnard.pagesperso-orange.fr/articles/slidestime.pdf · Frontiers of Fundamental Physics: 11th Symposium – 8 / 14 An

Time of phil./phys./math. Frontiers of Fundamental Physics: 11th Symposium – 1 / 14

Time of Philosophers, Time of Physicists, Time of Mathematicians

Fabien BesnardEPF

7 July 2010

Table of contents

• Philosophies of time

• The Andromeda Paradox• Consequences of theAndromeda Paradox• Other simultaneityrelations ? (1)

• Other simultaneityrelations ? (2)

• Accelerated observersand PE• Accelerated observersand OS• Presentism andpossibilism in GeneralRelativity

• Closed time-like curves

• Quantum heads-or-tails• The positivistic and realistpostulates

• Conclusion


Philosophies of timeThe Andromeda ParadoxConsequences of the Andromeda ParadoxOther simultaneity relations ? (1)Other simultaneity relations ? (2)Accelerated observers and PEAccelerated observers and OSPresentism and possibilism in General RelativityClosed time-like curvesQuantum heads-or-tailsThe positivistic and realist postulatesConclusion

Philosophies of time







• Conclusion


1. Presentism: only the present exists








• Conclusion



(a) Time passes,

(b) The future is open,

(c) One may travel in space, not in time,

(d) Ontological parsimony.








• Conclusion



(a) Time passes,




2. Possibilism (growing universe): the present and the past exist








• Conclusion



(a) Time passes,




2. Possibilism (growing universe): the present and the past exist

(a) Reality grows,

(b) The future is open.

3. Eternalism (block-universe): the past, the present, and the futureexist

The Andromeda Paradox







• Conclusion


O

A B

M

On Earth, A and B meet at O, relative speed = 4 km/h.Event M : Andromedians launch a float of spaceships to invade Earth.

Consequences of the Andromeda Paradox







• Conclusion


Presentism implies that reality depends on simultaneity.SR implies that simultaneity depends on the observer.








• Conclusion


Presentism implies that reality depends on simultaneity.SR implies that simultaneity depends on the observer.Thus one cannot hold the following together:

1. there exists an objective, observer-independent reality,

2. a philosophy of time must be compatible with SR,

3. presentism/possibilism.








• Conclusion






MRBO ⇔ “M is real for B when B is at O”








• Conclusion







1. NRAM 6⇒ MRBN

2. MRAO 6⇒ MRBOO

A B

M M N

A B








• Conclusion







1. NRAM 6⇒ MRBN

2. MRAO 6⇒ MRBOO

A B

M M N

A B

• Presentism turns away from common sense.

• The reality of O depends on O’s movement: weird !

Other simultaneity relations ? (1)







• Conclusion


Poincare-Einstein convention (PE):H

M

t1

t2

t1 t2 /2+( )








• Conclusion


Poincare-Einstein convention (PE):H

M

t1

t2

t1 t2 /2+( )

Theorem [Malament, 1977] Let H = be (the world-line of) an inertialobserver. PE relation wrt H is the only one which is:

1. a non-trivial equivalence relation,

2. invariant under causal automorphisms which stabilize H.








• Conclusion


Invariance under causal automorphisms is too strong → allow only thosewhich preserve a spatial and a temporal orientation.Theorem [Sarkar & Stachel, 1999]

1. PE is the only relation which satisfies the above requirements andonly depends on the direction of H.

2. The relations defined by the past (resp. future) light cones are theonly ones which satisfy the above requirements and only depend onthe position of H.








• Conclusion


Invariance under causal automorphisms is too strong → allow only thosewhich preserve a spatial and a temporal orientation.Theorem [Sarkar & Stachel, 1999]

1. PE is the only relation which satisfies the above requirements andonly depends on the direction of H.

2. The relations defined by the past (resp. future) light cones are theonly ones which satisfy the above requirements and only depend onthe position of H.

→ 2 possible definitions of the present: PE and OS (observedsimultaneity).→ 2 possible versions of (relativized) presentism/possibilism.A clear-cut definition of reality for OS presentism: “what is real is what Isee”.

Accelerated observers and PE







• Conclusion


An observer which is inertial, then accelerated, then inertial.

O

A

M

O'

P








• Conclusion



O

A

M

O'

P

M is present for A both at O and at O′.








• Conclusion



O

A

M

O'

P

M is present for A both at O and at O′.P is in the past for A at some moment, but later it’s in the future !








• Conclusion



O

A

M

O'

P

M is present for A both at O and at O′.P is in the past for A at some moment, but later it’s in the future !

→ PE version of the present is only local.

Accelerated observers and OS







• Conclusion


In SR, past cones do not intersect.








• Conclusion


In SR, past cones do not intersect.A uniformely accelerated observer:

O

A

M

O'

Some events are never in the present of A !








• Conclusion


In SR, past cones do not intersect.A uniformely accelerated observer:

O

A

M

O'

Some events are never in the present of A !

→ OS version of the present is also local (but in a more natural way).

Presentism and possibilism in General Relativity







• Conclusion


Two new features:

• the metric is not a background structure anymore + it hasnon-vanishing curvature

• the global topology might be non-trivial.








• Conclusion


Two new features:



PE becomes purely conventional.








• Conclusion


Two new features:



PE becomes purely conventional.OS still has a physical meaning, but:

the past light cones generally intersect.

Closed time-like curves







• Conclusion


So far, GR =⇒

1. only OS convention is consistent,

2. an event can be both past and present: OS possi-bilism still works, but not presentism,

3. reality is local for every observer (absolute eventhorizons).

Closed time-like curves







• Conclusion


So far, GR =⇒

1. only OS convention is consistent,

2. an event can be both past and present: OS possi-bilism still works, but not presentism,

3. reality is local for every observer (absolute eventhorizons).

But if CTC’s exist, even OS possibilism becomes inconsistent !

Quantum heads-or-tails







• Conclusion


S = spin-1/2 particle prepared in pure state |+, z〉Sequence of measures along (Oz), (Ox), (Oz) etc. . . at time interval∆τ > 0.

Quantum heads-or-tails







• Conclusion


S = spin-1/2 particle prepared in pure state |+, z〉Sequence of measures along (Oz), (Ox), (Oz) etc. . . at time interval∆τ > 0.

+

?

P

A B

OO'

• A fixed, P varies in the past of A on O.

• B can be anywhere in the elsewhere of future of A.

The positivistic and realist postulates







• Conclusion


Postulate P what cannot be determined for an observer, even in principle,is not real for this observer.








• Conclusion



• at the root of presentism/possibilism !








• Conclusion




• Postulate P + QM rule out PE presentism/possibilism andeternalism.








• Conclusion





• OS presentism/possibilism survive.








• Conclusion






Eternalism can survive QM only by a dismissal of Postulate P.

Postulate R Reality is independent from the observer/observations.








• Conclusion








• at the root of eternalism,








• Conclusion









• Postulate R + QM ⇒ MWI.








• Conclusion









• Postulate R + QM ⇒ MWI.

Works as long as there is a mathematical structure encompassing all partialobservations (Minkowski spacetime, GR spacetime, Everett multiverse)

Conclusion







• Conclusion


On the one hand: open future (pure randomness, free will ?), passage oftime, . . .

• Only my past cone exists,

• Only some portion of spacetime ever exists,

• Only my branch of the multiverse exists.

Conclusion







• Conclusion






Presentism/possibilism + physics =⇒ “radical positivism”. Realitybecomes narrower.

Conclusion







• Conclusion







On the other hand: none of the above words has an objective meaning.What exists: all of spacetime, all branches of the multiverse,. . .

Conclusion







• Conclusion







On the other hand: none of the above words has an objective meaning.What exists: all of spacetime, all branches of the multiverse,. . .These are timeless mathematical objects.

Eternalism + physics =⇒ mathematical ontology. Reality becomes bigger.

Documents

Time of Philosophers, Time of Physicists, Time of ...fabien.besnard.pagesperso-orange.fr/articles/slidestime.pdf · Frontiers of Fundamental Physics: 11th Symposium – 8 / 14 An