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The End of Time
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The end of Time
(defining time and space)
Hajnal Andréka and István Németi
A model where
Time and space are
concepts
concepts
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We have experimenters communicating with each other.
Observing the the laws of this communication, they
create the concepts of time and space in order to act in
this world more effectively.
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No clocks
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No meter rods
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Experimenters and signals in a concrete spacetime
Signals
s
e’
e
Connects(e,s,e’)
Experimenters
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Goal to find out
Experimenters know only this
s
Signals
s
e’
e
e
Connects(e,s,e’)
e'
Experimenters
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Getting familiar
Experimenters know only this
s
sz
e’
a’
e
s
e'
z
a
e
a
Rich , structured model
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a’
Bare, puritan model
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What is SPACE?
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Motionless 1
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Motionless 2
e
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e’
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Desargues’s theorem
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By now experimenters have meter rods.
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What is TIME?
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Event = congruence class of sending and receiving signals “at the same time”
e sends s
≡
e’ sends z
≡
z
s
e receives s’ ≡ …
s’
e’
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e
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Order of events
Equi-duration of time-lapses
Addition
Multiplication.
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Multiplication
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By now experimenters have clocks.
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Using these concepts, our experimenters can observe finitely
many regularities between the events (they can state them to
be physical laws) such that on the base of this they can know
that their space-time is a 4-dimensional space over a field F .
Formally, this amounts to a finite set Sigma in the language
of the bare models such that the models of Sigma are
exactly “our bare models” with an arbitrary field F in place
of the field of reals.
If they add the finite schema of axioms for a real-closed field,
they can derive everything that is true in their world.
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The End of Time
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Infinity of things to say yet:
Direction of time
Schwarzschild black hole
Operational semantics for SpecRel
Interpretation between theories
Comparing theories
Ontology of concepts
.
.
.
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THE END
OF TIME
as a basic notion
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Thank you for your attention!
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