Transcript ptt-file - Parmenides Foundation

Physikalisches Institut
Albert-Ludwigs-Universität Freiburg
Relational events, an extended present and the
conflict between relativity and the collapse
Thomas Filk
Department for Theoretical Physics, Univ. of Freiburg
Parmenides Center for the Study of Thinking, Munich
Pullach, May 1st 2010
Overview
•
•
•
•
•
•
Two simple questions
The meaning of “is”
E+F scheme
Relational events
A “temporal extension” operator
The non-locality problem from a relational
perspective
• Where is the present?
Overview
•
•
•
•
•
•
Two simple questions
The meaning of “is”
E+F scheme
Relational events
A “temporal extension” operator
The non-locality problem from a relational
perspective
• Where is the present?
Two Simple Questions
Which is which?
Where is something?
Two Simple Questions
Which is which?
E={a,b,c,d,e,f}
Where is something?
Two Simple Questions
Which is which?
E={a,b,c,d,e,f}
Where is something?
Without any additional
structure both questions
are ill defined.
In mathematics the “identifiability” of elements in a set is part
of the axiomatic formulation of set theory.
In physics we associate mathematical structures to physical
entities and the identification is far from trivial.
Possible solutions
Which is which?
Where is something?
E={a,b,c,d,e,f}
1. We define “properties” for the elements
2. We define relations among the elements
Possible solutions
Which is which?
Where is something?
E={a,b,c,d,e,f}
1. We define “properties” for the elements
2. We define relations among the elements
Relations
Which is which?
E={a,b,c,d,e,f}
Where is something?
For some graphs these
questions have no answer at all.
For some graphs these questions have
partial answers.
And for some graphs the
intrinsic identifiability is unique.
Relations
Which is which?
E={a,b,c,d,e,f}
c
d
b
e
a
f
Where is something?
a – degree one, next to degree three
b – degree three, next to degree one
c – degree three, next to degree two
d – degree two
e – degree four
f – degree one, next to degree four
For graphs without symmetry a unique identification is
possible by intrinsically referring to the structure.
Relations
Which is which?
E={a,b,c,d,e,f}
c
d
b
e
a
f
Where is something?
a – distance 2 from c and e
b – distance 1 from c, 3 from e
c – the red element
d – distance 1 from c and e
e – the green element
f – distance 1 from e, 3 from c
In some cases certain elements have to be “marked” arbitrarily
in order to break the symmetry, making a unique identification
possible.
The problem of identification
The problem of “identification” (the “which is
which?”-question) of the elements of space-time
(events) is relevant for a relational formulation of
General Relativity.
Intrinsic properties are:
- the curvature (components) at a point
- the distance to other points with characteristic
curvatures
- correlations of such distances.
Overview
•
•
•
•
•
•
Two simple questions
The meaning of “is”
E+F scheme
Relational events
A “temporal extension” operator
The non-locality problem from a relational
perspective
• Where is the present?
The problem of localization
The problem of “localization” (the “where is something?”question) assumes that the identification is given.
Let “p” be a red dot ( ) and “R” be a
(relational) structure where the
concept of “location” is to be defined.
c
d
b
e
a
f
What could be the meaning of the following questions?
-Where is “p” in “R”?
-What is the position/location of “p” in “R”?
The problem of localization
-Where is “p”in “R”?
-What is the position/location of “p” in “R”?
The usual way to answer this question is to say:
“p is at c”.
c
d
b
e
a
f
“position” is defined as a mapping
from the set of objects into the set of
“possible positions”.
Position: {p}  {a,b,c,d,e,f}
Position(p) = c
The problem of localization
c
d
b
e
a
f
However, intrinsically the “position”
of an element of the underlying
structure is defined by the relations
of this element to the other elements.
Position: {c}  {(c,d),(c,e),(c,b)}
The problem of localization
c
d
b
e
a
f
However, intrinsically the “position”
of an element of the underlying
structure is defined by the relations
of this element to the other elements.
Position: {c}  {(c,d),(c,e),(c,b)}
Notice that the underlying structure itself is defined as a set with a
relational structure.
I define “location” of an object with respect to such an underlying
structure. Other approaches try to get rid of the underlying structure
altogether and define “location” as a relation among the objects
alone. In my approach the underlying structure is part of reality.
The problem of localization
p
c
d
b
e
a
f
Why not consider “position” as a relation
between an object (“p”) and the underlying
structure?
Position: R(p)  {p}×{a,b,c,d,e,f}
“position” of a single object is a subset of E (R(p)={c,d,f}) and
can be represented as a mapping from the underlying structure E
into the set {0,1}.
Descartes: “Location” denotes ... the position of a body among
other bodies. In order to determine the location of a body, we
have to consider these other bodies, which we assume to be at
rest.
The problem of localization
p
c
Instead of the classical
d
b
- “ p” is at “c” or “d” or “f”
e
a
f
or the quantum mechanical
- “p” is at “c” AND “d” AND “f”
we can say:
- “p” has relations to “c” and “d” and “f”.
The problem of localization
p
c
Instead of the classical
d
b
- “ p” is at “c” or “d” or “f”
e
a
f
or the quantum mechanical
- “p” is at “c” AND “d” AND “f”
we can say:
- “p” has relations to “c” and “d” and “f”.
More general, the “position” of a single object becomes a field:
Position p ~ R(p)R ~ ψp(x) (xR)
and the “position” of two objects is represented as two fields.
Feynman‘s sum over histories
• Standard interpretation of the double slit experiment:
A particle propagates along path 1 AND path 2
path 1
path 2
• Relational interpretation:
Relation 1 (between a particle and a spatial point)
propagates along path 1
AND relation 2 propagates along path 2
Advantages of a relational concept of position
A relational object can “be” at two places at the same time
Advantages of a relational concept of position
In a relational picture, two objects which seem to be
“miles apart” can actually be nearest neighbors
What is distance?
1?
1033 ?
The “relational distance” may not be the same as the
“observed distance”.
Flow of energy or information may require different
types of relations as “quantum correlations”.
T.F. (2006) Int. J. Theor. Physics 45, p.1166
What is distance?
The same network may allow for different “distance
structures” (metrical structures)
For a society of people we can define “distance”
according to:
• physical distance
• friendship distance
• communication distance (two people making a phone
call are “close” to each other with respect to this distance,
even though they are far away physically), etc.
There is a dynamic in a society related to each of these
distance concepts, and these dynamics are partially
coupled.
“Microrelational” Quantum Theory
In a minimalistic version, this type of “microrelational”
quantum theory just replaces the concept of
“probability amplitude” by “relation”, with the
additional postulate that “the absolute value of the
relation is equal to the probability of measuring an
object at a certain location”.
T.F. (2006) in Quantum Theory: Reconsideration of Foundations - 3,
T.F. (2006) Int. Journ. Theor. Phys. 45, p.1166
An “everyday” example
A relevant document (e.g., a boarding
pass) may be stored (virtually) in the
main server (the unit entity).
Every computer or printer has
immediate access to the document
(the relation to the network).
As soon as the document is
transferred to one of the computers,
e.g. for print-out (the
“measurement”),
the access from the other computers
is blocked (the collapse).
An “everyday” example
The document exists as a virtual
entity. It is not “spread” over the
network but remains a unity.
The document becomes “reality”
upon entering the e-code and
making a printout.
One never observes “half of a
boarding card” at one printer and
the other half at a different printer.
One never gets two boarding cards
with the same e-code.
Overview
•
•
•
•
•
•
Two simple questions
The meaning of “is”
E+F scheme
Relational events
A “temporal extension” operator
The non-locality problem from a relational
perspective
• Where is the present?
E + F and relational quantum theory
F-scheme
E-scheme
(refers to facts)
(refers to the “statu nascendi” of
facts = events)
-boolean predication
-paratactic predication
-causal closure
-autogeneity
-sequential time
-extended present
-dichotomy of observer and
observed
-non-separability of observer and
observed
T.F. and A.v. Müller (2009) Mind and Matter 7, p.59
T.F. and A.v. Müller (2010), submitted
E + F and relational quantum theory
E-scheme
Relational interpretation
-paratactic predication
-propositions as relations
-autogeneity
-“collapse” as an autogenetic
selection of relations
-Extended present
-Relational network of events
(see next section)
-Non-separability of
observer and observed
- “relational quantum theory”
in the sense of Carlo Rovelli
Overview
•
•
•
•
•
•
Two simple questions
The meaning of “is”
E+F scheme
Relational events
A “temporal extension” operator
The non-locality problem from a relational
perspective
• Where is the present?
Relational network of events
Events to not happen at a
certain point of space-time,
but the network of events is
the canvas of space-time.
Relational network of events
However, the grid of events has a
causal structure.
This implies that there are three
possible types of relations:
• in-coming causal
• out-going causal, and
• non-causal.
If the (causal) Green’s functions of
quantum field theory are a
phenomenological expression for
these relations, this distinction may
be due to the different roles of the
real and imaginary parts.
Particles in an accelerated system
A static test particle in the field of a
charged particle “sees” an electric field.
E
Particles in an accelerated system
A static test particle in the field of a
charged particle “sees” an electric field.
If the probe moves with constant
velocity it “sees” an electric and a
magnetic field.
E,B
v
Particles in an accelerated system
A static test particle in the field of a
charged particle “sees” an electric field.
If the probe moves with constant
velocity it “sees” an electric and a
magnetic field.
If the probe accelerates in the field of
the charge it “sees” a time-dependend
electric and magnetic field – i.e.
radiation.
E(t),B(t)
a
Particles in an accelerated system
A static test particle in the field of a
charged particle “sees” an electric field.
If the probe moves with constant
velocity it “sees” an electric and a
magnetic field.
If the probe accelerates in the field of
the charge it “sees” a time-dependend
electric and magnetic field – i.e.
radiation.
E(t),B(t)
a
If the probe carries a detector, it measures photons. Where
do the photons come from?
Feynman graphs as “summation over relations”
In a Feynman diagram the
relations of events x and y are
expressed by causal
propagators. The integration
over all “internal” locations
of the events (emission of
exchange particle; absorption
of exchange particle)
expresses the summation over
all relations.
x1
x2
x
x3
y
x4
A( x1 , x2 , x3 , x4 )  N  dx  dy S ( x1 , x) S ( x2 , y ) S ( x3 , x) S ( x4 , y )G ( x, y )
Relational network of events
If the location of an event is defined by its relations
to other events, then an event does not happen at a
sharp instant.
„time“
Relational network of events
For two events, even if they are related to the same process, the
propositions “a before b” and “b before a” are not exclusive.
For quantum processes, event a can have an influence on event b
AND event b has an influence onto a.
Sequentiality of events – even along the same world line – may
be lost.
„time“
Overview
•
•
•
•
•
•
Two simple questions
The meaning of “is”
E+F scheme
Relational events
A “temporal extension” operator
The non-locality problem from a relational
perspective
• Where is the present?
There is no time operator
The uncertainty relations between energy and time cannot be
derived from a time operator but follow from the properties of
Fourier transforms of waves.
[H,T]=iħ

exp(-iεT)|E~|E–ε
(but H should be bounded from below)
There is no time operator
The uncertainty relations between energy and time cannot be
derived from a time operator but follow from the properties of
Fourier transforms of waves.
[H,T]=iħ

exp(-iεT)|E~|E–ε
(but H should be bounded from below)
But:
Measurements of T do not refer to objects (particles) but to events.
In contrast to position measurements which (in principle) can be
performed everywhere, temporal measurements can only be
performed in “the present”.
Measurements of T can only be planned for the future.
Temporal extension of events
If events have temporal relations to other events, we can define a
measure for this temporal extension.
„time“
If it is not possible to define a time operator, may be one can
define a “temporal extension” operator which measures for each
event its temporal extension. It should be complementary to the
energy operator measuring the energy transfer in this event.
A “temporal extension operator”
A “temporal extension operator” measures ΔTi (without
measuring T). It should have a positive spectrum (by definition).
i
Δt
“time”
The operator is applied to an event i. A “dual” operator Hi may not
refer to “energy” in general, but to the “energy transfer” involved
in this event (or even to the “information transfer”) involved in this
event.
Overview
•
•
•
•
•
•
Two simple questions
The meaning of “is”
E+F scheme
Relational events
A “temporal extension” operator
The non-locality problem from a relational
perspective
• Where is the present?
The conflict between relativity and the collapse
How fast is the collapse?
A measurement – interaction between two systems – can lead to a
reduction (collapse) of the quantum state.
It is generally assumed that this reduction happens
“instantaneously”.
If the quantum state as the property of “non-locality”, this
instantaneous reduction seems to be in conflict with relativity.
The conflict between relativity and the collapse
How fast is the collapse?
A measurement – interaction between two systems – can lead to a
reduction (collapse) of the quantum state.
It is generally assumed that this reduction happens
“instantaneously”.
If the quantum state as the property of “non-locality”, this
instantaneous reduction seems to be in conflict with relativity.
The problem of non-local reduction is not restricted to “entangled
states”. The quantum state of a single particle can be non-local (a
photon in a Mach-Zehnder interferometer).
It is reminiscent of the conflict between relativity and the rigid body.
The conflict between relativity and the collapse
There is no conflict, if
- one assumes that the quantum state has no ontological
counterpart (e.g., is related to my knowledge about a system),
The conflict between relativity and the collapse
There is no conflict, if
- one assumes that the quantum state has no ontological
counterpart (e.g., is related to my knowledge about a system),
- one has a “relative frequency” interpretation of quantum theory
The conflict between relativity and the collapse
There is no conflict, if
- one assumes that the quantum state has no ontological
counterpart (e.g., is related to my knowledge about a system),
- one has a “relative frequency” interpretation of quantum theory
- one restricts “relativistic locality” to the transfer of energy or
information
The conflict between relativity and the collapse
There is no conflict, if
- one assumes that the quantum state has no ontological
counterpart (e.g., is related to my knowledge about a system),
- one has a “relative frequency” interpretation of quantum theory
- one restricts “relativistic locality” to the transfer of energy or
information
- one assumes a “hyper-deterministic” world in which the future
decisions about experiments are included in the initial conditions.
The conflict between relativity and the collapse
There is no conflict, if
- one assumes that the quantum state has no ontological
counterpart (e.g., is related to my knowledge about a system),
- one has a “relative frequency” interpretation of quantum theory
- one restricts “relativistic locality” to the transfer of energy or
information
- one assumes a “hyper-deterministic” world in which the future
decisions about experiments are included in the initial conditions.
There is a conflict in the many-worlds interpretation, even though
there is no collapse. The “splitting” of the wave function happens
simultaneously at separate points.
The conflict between relativity and the collapse
If we assume an ontological collapse, there seems to be a
distinguished spatial hypersurface indicating an observer
independent notion of simultaneity.
This would be a prerequisite for the concept of a
universal “present”.
The conflict between relativity and the collapse
In a relational picture one can keep “locality” without violating
the predictions of quantum theory and without giving up an
ontology for quantum states.
The “spatial” relations determine the distance, however, the
quantum relations determine the reduction.
For an EPR-state, the spatial relations may already exist for the
charge and the mass of the particle, but not yet for the spin. The
spin is still related to its partner particle.
Overview
•
•
•
•
•
•
Two simple questions
The meaning of “is”
E+F scheme
Relational events
A “temporal extension” operator
The non-locality problem from a relational
perspective
• Where is the present?
Where “is” the present?
Napoleon: “Where is God in your model?”
Laplace: “There was no need for that particular hypothesis”.
We should distinguish between “the present of an
event” and “the present” (in the sense of “now”).
Most of the statements about the non-sequentiality of
time-space or the extension of the present can be
formulated within the framework of the first meaning.
The second is up to pure speculations.
Where “is” the present?
Conscious systems (IGUSs?) are the probes for time and a
present. But: no probe - no present?
Where “is” the present?
Conscious systems (IGUSs?) are the probes for time and a
present. But: no probe - no present?
There is no hint in Newton‘s laws indicating a distinguished
“present”. Maybe there are hints in quantum theory.
Where “is” the present?
Conscious systems (IGUSs?) are the probes for time and a
present. But: no probe - no present?
There is no hint in Newton‘s laws indicating a distinguished
“present”. Maybe there are hints in quantum theory.
The “present” marks the transition from possibilities
(potentialities) to facts, and facts are traces in the canvas of the
space-time network of events indicating that certain events have
happened.
Where “is” the present?
Conscious systems (IGUSs?) are the probes for time and a
present. But: no probe - no present?
There is no hint in Newton‘s laws indicating a distinguished
“present”. Maybe there are hints in quantum theory.
The “present” marks the transition from possibilities
(potentialities) to facts, and facts are traces in the canvas of the
space-time network of events indicating that certain events have
happened.
The most direct hint to a present may be the collapse – i.e. the
non-deterministic change of relations with respect to a single
event.
The present as “relating events to history”
Lets imagine a set of
events without any
further structure.
The present may mark
the layer of events which
become related to a
history.
The present as “relating events to history”
Lets imagine a set of
events without any
further structure.
The present may mark
the layer of events which
become related to a
history.
The present as “relating events to history”
Lets imagine a set of
events without any
further structure.
The present may mark
the layer of events which
become related to a
history.
The present as “relating events to history”
Lets imagine a set of
events without any
further structure.
The present may mark
the layer of events which
become related to a
history.
The present as “relating events to history”
Lets imagine a set of
events without any
further structure.
The present may mark
the layer of events which
become related to a
history.
The present as “relating events to history”
Lets imagine a set of
events without any
further structure.
The present may mark
the layer of events which
become related to a
history.
The present as “relating events to history”
Lets imagine a set of
events without any
further structure.
The present may mark
the layer of events which
become related to a
history.
The present as “relating events to history”
Lets imagine a set of
events without any
further structure.
The present may mark
the layer of events which
become related to a
history.
The present as “relating events to history”
Lets imagine a set of
events without any
further structure.
The present may mark
the layer of events which
become related to a
history.
The present as “relating events to history”
Lets imagine a set of
events without any
further structure.
The present may mark
the layer of events which
become related to a
history.
The present as “relating events to history”
Lets imagine a set of
events without any
further structure.
The present may mark
the layer of events which
become related to a
history.
The present as “relating events to history”
Lets imagine a set of
events without any
further structure.
The present may mark
the layer of events which
become related to a
history.
The present as “relating events to history”
Lets imagine a set of
events without any
further structure.
The present may mark
the layer of events which
become related to a
history.
The present as “relating events to history”
Lets imagine a set of
events without any
further structure.
The present may mark
the layer of events which
become related to a
history.
The present as “relating events to history”
Lets imagine a set of
events without any
further structure.
The present may mark
the layer of events which
become related to a
history.
The present as “relating events to history”
Lets imagine a set of
events without any
further structure.
The present may mark
the layer of events which
become related to a
history.
The “dual” interpretation
Lets imagine a network
of events, in which every
event is related to almost
every other event.
At his stage almost any
“history” is possible.
The present as the “interface” of reduction
The “present” now
marks the layer of events
where the collapse leads
from possibilities to
facts.
The present as the “interface” of reduction
The “present” now
marks the layer of events
where the collapse leads
from possibilities to
facts.
The present as the “interface” of reduction
The “present” now
marks the layer of events
where the collapse leads
from possibilities to
facts.
The present as the “interface” of reduction
The “present” now
marks the layer of events
where the collapse leads
from possibilities to
facts.
The present as the “interface” of reduction
The “present” now
marks the layer of events
where the collapse leads
from possibilities to
facts.
The present as the “interface” of reduction
The “present” now
marks the layer of events
where the collapse leads
from possibilities to
facts.
The present as the “interface” of reduction
The “present” now
marks the layer of events
where the collapse leads
from possibilities to
facts.
The present as the “interface” of reduction
The “present” now
marks the layer of events
where the collapse leads
from possibilities to
facts.
The present as the “interface” of reduction
The “present” now
marks the layer of events
where the collapse leads
from possibilities to
facts.
The present as the “interface” of reduction
The “present” now
marks the layer of events
where the collapse leads
from possibilities to
facts.
Conclusion
-The solution to the paradoxical aspects of quantum
theory may require new concepts of space, time, location,
distance, ...
-It may also require to reintroduce a concept of the
present into our physical models
-Two candidates:
-relational space + time as an expression of a change
of relations
-relational space-time (+an extra dimension of time in
which “the present” propagates)