Download Heisenberg`s uncertainty principle in financial markets

Workshop Philosophy of Physics and Finance
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Heisenberg’s uncertainty principle in financial markets
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Table of Contents
Heuristic phenomena and basic question
The connecting pattern: „the quantum of action and the catalyst“
Theory transfer: from quantum mechanics to financial markets
Formal transfer: from physical to economic cause-effect quantities
Conclusions
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Heuristic phenomena and basic question
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Heuristic phenomena and basic question
The fish market effect
Sell all fish by the end of the day
 Supply and trading volume is fixed during the
day
 Range of prices attained for fish is large and
the prices obtained are completely uncertain
Fix the price for fish for the day
 The amount of fish sold is completely
uncertain
 Unsold fish goes off
Fresh fish implies uncertain prices
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Heuristic phenomena and basic question
The central bank‘s dilemma
Fix the money supply
 The interest rate at which the economy
absorbs the given central banks money
supply is uncertain
Fix the interest rate
 The amount of central bank money
absorbed by the economy is uncertain
The central bank cannot set both, the price of money and the money
supply. Stirring both introduces uncertainty for both quantities.
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Heuristic phenomena and basic question
The antagonism of momentum and value
Value investors
 If all market participants would buy and
sell stocks according to value principles
the price would not be able to gain
momentum above or beneath fair value
Momentum investors
 If all market participants would buy and
sell stocks according to momentum
principles than the price would be
completely detached from its
fundamental value during that period
Market reality reflects the thinking and action of market participants
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Heuristic phenomena and basic question
The duality of regulation and speculation
 If regulation is completely clear and
unambiguous, …
...then it is also possible to safely circumvent
the regulation, which is often accompanied by
speculation and may generate more
regulation (e.g. clear rules for AAA ratings,
innovative solutions to deal with rules
 speculative leverage of AAA-CDOs )
The specification of rules can have unintended side effects, which can be
demonstrated both conceptually and experimentally with an experiment in
an artificial market laboratory.
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Heuristic phenomena and basic question
The complementarily of position and
monumentum
Heisenberg’s
uncertainty
principle
 In quantum mechanics, the Heisenberg uncertainty principle
states that certain pairs of physical properties, like position and
momentum, cannot both be known to arbitrary precision; that is,
the more precisely one property is known, the less precisely the
other can be known
Are Heisenberg’s uncertainty principle and
Basic question




the fish market effect,
the central bank’s dilemma,
the antagonism of momentum and value,
the duality of regulation and speculation
not essentially the same?
Can the mathematical formalism of quantum mechanics be used to
explain economic phenomena?
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The connecting pattern:
„the quantum of action and the catalyst“
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The connecting pattern
The common, shared elements
Quantum of action
«The catalyst»
Fish market effect
One fish
as unit of (trans)action
Price
as catalyst for trans(action)
Central bank’s
dilemma
One unit of tradable goods
as unit of (trans)action
Currency
as catalyst for trans(action)
Momentum-value
One whole theme cycle
as unit of action
Securities, tradable etc.
Participation
as catalyst for trans(action)
Regulation
as units of trans(action)
Quantum physics
Planck’s quantum of action h
(the cause to action)
Currency*
as catalyst for trans(action)
Will be discussed later
* It is not the «rule», as the rule is part of the boundary conditions for trade
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The connecting pattern
The three catalyst properties as
defined in this concept
1
In an environment ENV an action A can take place, also in
absence of the catalyst C
2
The presence of the catalyst C accelerates action A in the
environment ENV
3
The catalyst C remains unchanged while generating action A
The «catalyst» is a concept from biochemistry,
which can also be viewed as a general logical concept.
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The connecting pattern
Examples for typical catalyst in the
economy
Environment
Catalyst
Approach &
Action
Solution
Barter economy
Money
Trade
Stock exchange
Research coverage of a stock
Price realization of hidden value
of the stock
Auction
Price increase
Reduction of demand
Financial market
Participation cycle in the theme
Theme cycle of market prices
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The connecting pattern
The catalyst in quantum physics: a
closer look at the photon (1/2)
Consider the source of light and an observer in two different situations:
 Observer is, relative to source of light, at rest (observer 1)
 Observer has a relative velocity, v>0, towards the source of light (observer 2)
observer 1
observer 2
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source of light
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The connecting pattern
The catalyst in quantum physics: a
closer look at the photon (2/2)
Given:
 Env = electromagnetic field of the photons of the light source
 A = h, Planck’s quantum of action
 C = space where relative motion takes place between the observer and the source of
light
Catalyst
properties
1
In the absence of C (i.e. no relative motion of the observer and the source of light)
Planck’s quantum of action A=h is produced by the electromagnetic field with
the frequency  (energy of the photon equals h* )
2
By the Doppler-effect: if the relative space C is introduced (i.e. there is a relative motion
of the observer and the source of light) then the observer is measuring a higher
frequency (’>  ) of the action A=h (with higher energy h* ’ of the photon)
3
The catalyst C (i.e. the relative space which the observer passes through) remains
unchanged during this process
The space, which the observer passes through relative to the source of
light, meets the three catalyst properties.
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The connecting pattern
Summary
 The concept of the catalyst originated in biochemistry
 Its essential mode of operation can be expressed in three properties,
which allows us to generalize the catalyst concept to a broader range of applications
 In several economic situations catalyst properties can be identified
 In quantum physics the catalyst properties have been verified for the relative space in
the electro-magnetic field of the photon
Is the theory transfer from quantum mechanics to economics possible?
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Theory transfer:
from quantum mechanics to financial markets
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Theory transfer
Transferring the photon concept to the
economy (1/4)
Manytz conditions for “theory transfer”:
“Theory transfer in a strict sense presupposes – and assumes –
isomorphism between the empirical phenomena to be described and
explained (i.e., a 1:1 relationship between the elements, properties, and
relationships of interdependence in the two fields).” Mayntz 1992*
*Mayntz, Renate. 1992, “The influence of Natural Science Theories on Contemporary Social Science”. [ed.] M. Dierkes and B. Biervert,
European Social Science in Transition. Boulder: Westview Press, 1002, pp.27-79.
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Heuristic phenomena and basis question
The use of Mayntz isomorphism
Quantum mechanics
TQM (Theory)
HQM (Hypothesis)
List of items
-
List of items
-
Incomplete
Mayntz transfer
Transfer item per item
Transfer item per item
Financial markets
List of items
-
TFM (Theory)
List of items
-
HFM (Hypothesis)
EQM (Empiricism)
EFM (Empiricism)
TQM (Theory)
TFM (Theory)
After the theory transfer, the new theory for financial markets can be
completely understood within financial markets
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Theory transfer
Transferring the photon concept to the
economy (2/4)
The auctioneer’s photon:
 Photon = sell offer during an auction
 Catalyst = price increase mechanism used by the auctioneer
 Quantum of action = renewal of the sell offer at the increased price while still meeting a demand
1:1
Isomorphism:
-
Emission of a photon   putting a sell offer into the auction
-
Absorption of a photon   transaction, allocation to the buyer
-
Heisenberg uncertainty:
Momentum=fixed   quantity to sell=fixed
Position=uncertain   price=uncertain
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Theory transfer
Transferring the photon concept to the
economy (3/4)
The central bank’s photon:
 Photon = unit of money in circulation (currency)
 Catalyst = unit of money
 Quantum of action = exchange unit of goods against unit of money
1:1
Isomorphism:
-
Emission of a photon   putting a unit of money into circulation
-
Absorption of a photon   re-collection of money unit by central bank
-
Heisenberg uncertainty:
Momentum=fixed   transaction volume per unit of currency (e.g. by regulation)
Position=uncertain   number of hand changeovers until re-collection=uncertain
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Theory transfer
Transferring the photon concept to the
economy (4/4)
The market-cycle photon:
 Photon = production of a market cycle per participation cycle
 Catalyst = market participation cycle
 Quantum of action = run through a complete market cycle
1:1
Isomorphism:
-
Emission of a photon   issuing equity into public equity market
(public participation)
-
Absorption of a photon   buy back of public equity
-
Heisenberg uncertainty:
Momentum=fixed   one market cycle
per (public) participation cycle=fixed
Position=uncertain   phase in the participation cycle=uncertain
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Formal transfer:
from physical to economic cause-effect quantities
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Formal transfer
Definition of quantum of action and of
space
Step 1
Definition of quantum of action
 Set the (economic) quantum of action A equal to h.
Step 2
Definition of space
 Space emerges through repeated recycling (self-access) of the
catalyst C:
C
C
C
C
C
x-axis of space dimension
 Momentum = action per unit of space.
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Formal transfer
Definition of time and of velocity v<c
Step 3
Definition of time
 Time emerges tautologically through the pulse of the recycling of
catalyst C “speed of light” is absolute and constant c=1.
C
C
C
C
C
t=time measured through pulse of catalyst’s self access
 Energy = action per unit of time.
Step 4
Definition of velocity v<c
 Due to the Doppler-effect:
 Different catalysts (for the same action) generate different
inertial frames which move with constant relative velocity.
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Formal transfer
Definition of mass
Step 5
Definition of mass
 We assign to the inertial frames a total energy Etot and a total
momentum Mtot.
 If not all potential of action in the environment Env is transformed
to photons by catalysts, i.e. not all of the energy is “radiated”, then
objects emerge which can be considered as emitters of photons and
have a rest mass > 0 .
 In order to properly define rest mass and position of rest mass,
additional information of the environment Env is required, in
particular the concept of inertia has to be deduced from this
additional information.
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Formal transfer
Definition of force
Step 6
Definition of force
 If two objects, with rest mass>0, cannot only emit photons but
also absorb photons (of the other object) then an exchange of
particles emerges. Through this exchange a force between objects
can be defined.
 Here, the environment Env determines how the distance between
the objects varies during the exchange (distances between objects =
average length of paths between emission and absorption of
photons).
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Formal transfer
The definition of the wave function
Step 7
The definition of the wave function
 All the properties and observables, such as momentum, energy,
mass, position, etc, of quantum mechanical systems can be
expressed with a so called wave function of the system,
e.g. if p=momentum and E=energy of a photon then the wave
function of a photon is expressed as follows:
 (x,t)   0 exp(i (
p
E
x  t ))
h
h
 Lemma: if a (cause-action-)system follows step 1 to step 6 then it
can be expressed with a formally identical wave function as one
uses for quantum mechanical systems.
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Formal transfer
Transfer of the Heisenberg uncertainty
principle
Step 8
Transfer of the Heisenberg uncertainty principle
 Every system whose properties can be expressed by a wave
function (which is formally identical to a wave function for a quantum
mechanical system) must obey the Heisenberg uncertainty principle:
h
p x 
2
The uncertainty of the momentum p, times the uncertainty of the
position x, is greater or equal to half the quantum of action, h.
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Conclusions
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Conclusions
 We have shown how the Heisenberg uncertainty principle can have more general
applications in the economy and in financial markets.
– As one major result we could formally prove that price and supply in economic
markets are complementary, i.e. that the Heisenberg uncertainty principle applies
to price and supply in economic systems in general.
 Since the mathematics of the wave function of quantum mechanical systems have a
much broader range of applications, this method of theory transfer opens up a large
field of new possible scientific research in economics and capital markets theory.
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