Why field theories are deterministic, but QM isn't?
dud...@gmail.com
believed to be better approximation of physics than quantum mechanics
- for example because it allows for extremely accurate predictions of
Lamb shift.
http://en.wikipedia.org/wiki/Quantum_electrodynamics
One of formulations of field theories is due to Lagrangian density -
physics finds the field which minimizes integral of this density over
four dimensional space - so called action.
Now using Euler-Lagrange equations, we can find necessity condition
for such minimization, which is in form of time evolution - we get
'evolving 3D' picture.
These equations are completely deterministic - we don't have a problem
with for example probabilities, wavefunction collapses ...
So why its predecessor which we commonly use - quantum mechanics is
completely undeterministic - we can usually talk only about
probabilities????
For me it clearly shows that QM is forgetting about something - kind
of 'subquantum noise' ... which determines quantum choices.
We cannot fully measure QM ... so it's probably even worse with this
'subquantum information'.
We can say only about probabilities of quantum choices - but in fact
they should be deterministic - they are stored somewhere there!
What we can talk about is that events have been causally connected in
the past - we call it entanglement: if two photons have been created
together we cannot know what spin they have, but we know that it's the
same one.
So from our point of view - the future will decide which of entangled
events will be chosen ... but in fact it's written in some subquantum
information, but we cannot even think about measuring it.
Bohm's interpretation uses 'pilot-wave' which goes into future to
choose how to elongate trajectory.
But maybe it would be better to use CPT conservation as in QED and try
to interpret QM fully fourdimensionally.
Now everything is clear:
- probability is proportional to the square of amplitude, because it
has to agree in both past and future halfplanes,
- knowing only the past we can predict only probabilities,
- entanglements means that events are causally connected in the past.
One of them will be chosen in the future (as in Wheeler's
experiment).
Here is expanded this topic:
http://www.advancedphysics.org/forum/showthread.php?t=11844
What do You think about it?
Knecht
>
> These equations are completely deterministic - we don't have a problem
> with for example probabilities, wavefunction collapses ...
>
> So why its predecessor which we commonly use - quantum mechanics is
> completely undeterministic - we can usually talk only about
> probabilities????
>
> For me it clearly shows that QM is forgetting about something - kind
> of 'subquantum noise' ... which determines quantum choices.
> We cannot fully measure QM ... so it's probably even worse with this
> 'subquantum information'.
I highly recommend reading the chapter entitled "Chaos and the
Quantum" in Ian Stewart's Does God Play Dice? for a new and very
refreshing view of how one might construct a local, realistic, causal
and fully deterministic underpinning for QM, which can also be in
agreement with all empirical results. Somewhat presaged by t' Hooft.
Knecht
maxwell
> Quantum electrodynamics (relativistic quantum field theory) is
> believed to be better approximation of physics than quantum mechanics
> - for example because it allows for extremely accurate predictions of
> Lamb shift.http://en.wikipedia.org/wiki/Quantum_electrodynamics
Don't get hung up on numerical accuracy. The Ptolemaic scheme gave
much better predictive accuracy of planetary motion than the
Copernican scheme (mainly because epicycles are one way of
representing ellipses).
------Moderator's Note------------------------
I've deleted the irrelvant full quote of the previous posting. Please
cite only text relevant for your argument! HvH
Gerard Westendorp
[..]
> So why its predecessor which we commonly use - quantum mechanics is
> completely undeterministic - we can usually talk only about
> probabilities????
The indeterminism only shows up in connection with observation.
The dynamic equations of quantum (field) theory do not have any
probability element in them.
For example, the Schrodinger equation is a deterministic wave equation.
Only when we set up an experiment to measure either position or
momentum, do we get a probability.
Gerard
Knecht
T.N. Palmer's refreshingly unique and very promising approach to
determinism at the subquantum level, the role of gravitation in this
domain, and the potential importance of nonlinear dynamical systems
theory to the evolution of physics can be studied by acessing his
paper: http://arxiv.org/ftp/arxiv/papers/0812/0812.1148.pdf .
Something genuinely new. Probably not the final answer, but a very
worthy beginning.
Knecht
maxwell
> ...
> For example, the Schrodinger equation is a deterministic wave equation.
> Only when we set up an experiment to measure either position or
> momentum, do we get a probability.
>
Schrodinger's Equation does NOT correspond to laboratory clock time
when measurements are involved? It may also be viewed as the phase-
space sampling parameter (only one sample at a time) of the
mathematical set of possibilities described by the wave function; in
this light, determinism has nothing to do with QM.
dud...@gmail.com
I've get gives transactional interpretation of QM by John G. Cramer.
You can find very good links here:
http://en.wikipedia.org/wiki/Transactional_interpretation
This interpretation is being taught on the University of Washington.
Prof. Cramer wanted to observe 'retrocausability' by something like
Wheeler's experiment:
http://www.newscientist.com/article/mg19125710.900-whats-done-is-done-or-is-it.html
On the forum I've linked before can be found explanation why it
couldn't work.
Jarek
Nicolaas Vroom
<dud...@gmail.com> schreef in bericht
news:49d69ff7-7e2f-45c0...@p11g2000yqe.googlegroups.com...
>
> These equations are completely deterministic - we don't have a problem
> with for example probabilities, wavefunction collapses ...
>
> So why its predecessor which we commonly use - quantum mechanics is
> completely undeterministic - we can usually talk only about
> probabilities????
>
I have a much simpler question:
If you study the behaviour carefull you can observe that each of the planets
influences each other. For example the movement of Mercury is influenced
by the Earth.
This behaviour is described by Newton's Law and by introducing the concepts
of Force and Mass.
You could call this behaviour deterministic.
On the other hand there are also people who call all physical changes
determistic.
But what is the added value of such a concept ?.
To call changes deterministic only makes sense if you clearly make a
distinction
between deterministic versus undeterministic.
Along this same line: What is the purpose to call any field deterministic ?
What is the purpose to call an electric field determistic ?
Does the electric field of a wire describe the behaviour of the
individual electrons involved ? The answer is No.
Does the magnetic field of a magnet describe how internally within the
magnet the different magnetic areas are aligned in almost the same
direction in order to create this field ? The answer is No.
In the quantum mechanical area you clearly have to specify
what you are studying.
You could study the behaviour of two electrons which are
entangled.
In that case at one place two electrons are created which each
are detected an equal distance d apart from the source at A and B
In that case you first have to demonstrate that there is a certain event,
and that each time when there is that event two electrons
are created.
Next you can measure the spin of each electron in a
certain direction.
Of course it will be interesting if you measure +x for at A
that then other one at B is -x. If fact the correlation is -1.
Does it make sense to call such a behaviour determinstic ?
Or the mathematics involved ?
(Assuming that when you repeat the experiment you have equal
chance to get +x or -x at A ?)
It makes much more sense to study if this correlation is exactly
-1 or approximate.
Nicolaas Vroom
http://users.pandora.be/nicvroom/
Igor Khavkine
> Quantum electrodynamics (relativistic quantum field theory) is
> believed to be better approximation of physics than quantum mechanics
> - for example because it allows for extremely accurate predictions of
>
> One of formulations of field theories is due to Lagrangian density -
> physics finds the field which minimizes integral of this density over
> four dimensional space - so called action.
> Now using Euler-Lagrange equations, we can find necessity condition
> for such minimization, which is in form of time evolution - we get
> 'evolving 3D' picture.
Right, but only for the classical version of the theory, which the
classical theory of coupled Maxwell and Grassmann-valued Dirac fields.
That is not QED, only its classical counterpart.
> These equations are completely deterministic - we don't have a problem
> with for example probabilities, wavefunction collapses ...
>
> So why its predecessor which we commonly use - quantum mechanics is
> completely undeterministic - we can usually talk only about
> probabilities????
What I think hasn't been clearly stated in this thread yet is that all
of the features of QM that you refer to are also part of QED. The
classical field theory obtained from an action principle, as you
described, is quantized and the result is QED. Instead of particle
positions, the dynamical variables are field values. Beyond that, the
quantum mechanical formalism is the same.
QED and QFT in general is no more and no less deterministic than QM of
particles.
Igor
Knecht
posting had various non-ASCII characters garbled. :( -- jt]]
On Apr 1, 10:54M-BM- am, Igor Khavkine <igor...@gmail.com> wrote:
>
> QED and QFT in general is no more and no less deterministic than QM of
> particles.
See http://www.newscientist.com/article/mg20127011.600-can-fractals-make-sense-of-the-quantum-world.html?full=true
for an extremely interesting and provocative discussion of T.N.
Palmer's remarkable new ideas regarding a possible deterministic
underpinning for Quantum Mechanics. Physics is clearly not "finished".
Knecht
Arnold Neumaier
in the newsgroup.]
Gerard Westendorp schrieb:
How can QM be stochastic while the Schroedinger equation is not?
The Schroedinger equation is a deterministic wave equation.
But when we set up an experiment to measure either position or
momentum, we get uncertain, stochastic outcomes.
So - is quantum mechanics deterministic or stochastic?
One has to be careful in the interpretation of the foundations...
Fortunately, the same apparent paradox already occurs in classical
physics; hence the paradox cannot have anything to do with the
peculiarities of quantum mechanics.
Indeed, a Focker-Planck equation is a deterministic partial
differential equation. But when measuring a process modelled by it
- such as the position of a grain of pollen in Brownian motion -,
we get only probabilistic results. Now Focker-Planck equations are
essentially equivalent to classical stochstic differential equations.
So - do they describe a deterministic or a stochastic process?
The point resolving the issue is that, both in stochstic differential
equations and in quantum mechanics, probabilities satisfy deterministic
equations, while the quantities observed to deduce the probabilities
do not.
Thus, in both cases, probabilities are deterministic ''observables''
while the position of a grain of pollen in classical mechanics, or
position and momentum in quantum mechanics, ar not.
Arnld Neumaier
Nicolaas Vroom
news:49D9C163...@univie.ac.at...
> [I had sent this before, but apparently it never appeared
> in the newsgroup.]
>
>
> Gerard Westendorp schrieb:
>> dud...@gmail.com wrote:
>>
>>> So why its predecessor which we commonly use - quantum mechanics is
>>> completely undeterministic - we can usually talk only about
>>> probabilities????
>>
>> The indeterminism only shows up in connection with observation.
>> The dynamic equations of quantum (field) theory do not have any
>> probability element in them.
>>
>> For example, the Schrodinger equation is a deterministic wave equation.
>> Only when we set up an experiment to measure either position or momentum,
>> do we get a probability.
>
>
> How can QM be stochastic while the Schroedinger equation is not?
>
>
> The Schroedinger equation is a deterministic wave equation.
> But when we set up an experiment to measure either position or
> momentum, we get uncertain, stochastic outcomes.
>
> So - is quantum mechanics deterministic or stochastic?
The question to answer is: What type of physical experiments
are described by the Schroedinger equations ?
Maybe the answer can be found here:
http://en.wikipedia.org/wiki/Theoretical_and_experimental_justification_for_the_Schr%C3%B6dinger_equation
Specific: Are the Schroedinger equations a description
of the outcome of two slit experiment with single photons ?
With single electrons ?
The answer could be: For a single event: No
On average (1000 events): Yes
If that is the case (i.e. all what we quantify in laws at this scale
are probabilities) does it make sense to have a discussion
if QM is either deterministic or not ?
Anyway if you have a discussion about determismic you must first
have a good definition of what means deterministic.
As part of this definition you must also answer the question if all
physical changes are determistic. If the answer is Yes the whole
concept has no meaning.
Nicolaas Vroom
maxwell
The probability implications are implicit in the definition of the
wave function as a weighted set of complete functions. The whole
combination evolves (like the crime wave stats for NYC from 2005 to
2006) but reality is always one instance (of the stats) so 'doing a
measurement' is participating directly in reality & not relying on
statistics. People are only robbed by muggers (not compilers of
statistics).
Now, if you want to ask why does the world appear to behave
probabilistically, that's a whole different question.
Arnold Neumaier
> "Arnold Neumaier" <Arnold....@univie.ac.at> schreef in bericht
> news:49D9C163...@univie.ac.at...
>> [I had sent this before, but apparently it never appeared
>> in the newsgroup.]
>>
>> Gerard Westendorp schrieb:
>>> dud...@gmail.com wrote:
>>>
>>>> So why its predecessor which we commonly use - quantum mechanics is
>>>> completely undeterministic - we can usually talk only about
>>>> probabilities????
>>> The indeterminism only shows up in connection with observation.
>>> The dynamic equations of quantum (field) theory do not have any
>>> probability element in them.
>>>
>>> do we get a probability.
>>
>> How can QM be stochastic while the Schroedinger equation is not?
>>
>>
>> The Schroedinger equation is a deterministic wave equation.
>> But when we set up an experiment to measure either position or
>> momentum, we get uncertain, stochastic outcomes.
>>
>> So - is quantum mechanics deterministic or stochastic?
>
> The question to answer is: What type of physical experiments
> are described by the Schroedinger equations ?
No experiment is described by the Schroedinger equation.
Experiments are always described by additional context in which
(sometimes) the Schroedinger equation appears as a basic tool.
> Maybe the answer can be found here:
> http://en.wikipedia.org/wiki/Theoretical_and_experimental_justification_for_the_Schr%C3%B6dinger_equation
>
> Specific: Are the Schroedinger equations a description
> of the outcome of two slit experiment with single photons ?
> With single electrons ?
>
> The answer could be: For a single event: No
> On average (1000 events): Yes
>
> If that is the case (i.e. all what we quantify in laws at this scale
> are probabilities) does it make sense to have a discussion
> if QM is either deterministic or not ?
This answer (if taken at face value) qualifies quantum mechanics as
a stochastic theory, since, as any good stochastic theory, it
correctly predicts averages.
> Anyway if you have a discussion about determismic you must first
> have a good definition of what means deterministic.
The definition of causal determinism given in
http://en.wikipedia.org/wiki/Deterministic#Varieties_of_determinism
seems quite adequate.
> As part of this definition you must also answer the question if all
> physical changes are determistic. If the answer is Yes the whole
> concept has no meaning.
If the concept had no meaning, it would not be meaningful to answer
the question with Yes.
Arnold Neumaier
dud...@gmail.com
indeterminism of QM is a result of zero-point oscillations: "QUANTUM
FIELD THEORY OVERCOMES EINSTEIN'S OBJECTIONS AGAINST QUANTUM
MECHANICS" I. A. Boloshin, M. E. Gertsenshtein, and M. P. Suvorov
http://www.springerlink.com/content/n27p29417130h25h/fulltext.pdf
Doesn't it means that physics is deterministic and in quantum
mechanics we get probabilities because it's not complete theory - it
assumes that we just don't have (cannot have) full knowledge?
So maybe if we have entangled photons means: because they were created
in the same episode - they are causally connected in the past. In fact
they are in some state, but we have only information to say that they
have the same spin.
Jarek
Gerard Westendorp
[..]
>>> So - is quantum mechanics deterministic or stochastic?
>> The question to answer is: What type of physical experiments
>> are described by the Schroedinger equations ?
>
> No experiment is described by the Schroedinger equation.
>
> Experiments are always described by additional context in which
> (sometimes) the Schroedinger equation appears as a basic tool.
I am not sure if the energy levels of the Hydrogen atom count as an
"experiment". The Schroedinger equation predicts these correctly.
When the electron of a Hydrogen atom stays in an orbital it seems to
behave in a deterministic way, described by the Schroedinger equation.
it can stay indefinitely in the lowest orbital, and for quite a long
time in higher ones. Until suddenly, it goes into a lower orbital,
emitting a photon. The time at which it decides to do that seems to be
completely random.
On the other hand, instead of jumping orbitals, the electron could team
up with an electron of a neighboring Hydrogen atom, and form the
covalent bond of an H2 molecule. Once the covalent bond is established,
the electrons again go into "deterministic mode", and stay part of an H2
molecule for years on end, without ever doing anything manifestly random.
Gerard
Hendrik van Hees
> I am not sure if the energy levels of the Hydrogen atom count as an
> "experiment". The Schroedinger equation predicts these correctly.
Sure, the Hydrogen spectrum is one of the first applications of atomic
physics which has been solved by early (real) quantum theory, even
before Schrödinger's wave equation appeared on the scene. Pauli did the
beautiful calculation, using the SO(4) symmetry (and the Runge-Lenz
vector) within the just invented "matrix mechanics".
>
> When the electron of a Hydrogen atom stays in an orbital it seems to
> behave in a deterministic way, described by the Schroedinger equation.
> it can stay indefinitely in the lowest orbital, and for quite a long
> time in higher ones. Until suddenly, it goes into a lower orbital,
> emitting a photon. The time at which it decides to do that seems to be
> completely random.
Quantum theory is not deterministic but causal. The complete
determination of a state (represented by a ray in Hilbert space) at one
time causes the determination of a state at any other time (if the
Hamiltonian of the system is known).
However, even in the case the state of the system is completely known,
only some observables have a determined value, and this may change in
time. These are those observables for which the prepared state is
represented by an eigenstate of the operator associated with this
observable. The outcome of measurements of all other observables are
unpredictable, and the state provides only statistical (probabilistic)
information about such measurements. That's Born's probabilistic
interpretation.
>
> On the other hand, instead of jumping orbitals, the electron could
> team up with an electron of a neighboring Hydrogen atom, and form the
> covalent bond of an H2 molecule. Once the covalent bond is
> established, the electrons again go into "deterministic mode", and
> stay part of an H2 molecule for years on end, without ever doing
> anything manifestly random.
There are no jumps in quantum mechanics, and there is no "deterministic
mode", i.e., there's no state, in which the atom can be prepared, such
that all possible observables take simultaneously sharp values.
--
Hendrik van Hees Institut für Theoretische Physik
Phone: +49 641 99-33342 Justus-Liebig-Universität Gießen
Fax: +49 641 99-33309 D-35392 Gießen
http://theory.gsi.de/~vanhees/faq/
Robert L. Oldershaw
> When the electron of a Hydrogen atom stays in an orbital it seems to
> behave in a deterministic way, described by the Schroedinger equation.
> it can stay indefinitely in the lowest orbital, and for quite a long
> time in higher ones. Until suddenly, it goes into a lower orbital,
> emitting a photon. The time at which it decides to do that seems to be
> completely random.
>
> On the other hand, instead of jumping orbitals, the electron could team
> up with an electron of a neighboring Hydrogen atom, and form the
> covalent bond of an H2 molecule. Once the covalent bond is established,
> the electrons again go into "deterministic mode", and stay part of an H2
> molecule for years on end, without ever doing anything manifestly random.
Sort of reminds one of the behavior of nonlinear dynamical systems
which can be "locked" into a periodic attractor for an arbitrary
amount of time until a slight "shove" sends it off into a different
orbit, or off to infinity, or into chaotic dynamics. Maybe Tim Palmer
is onto something quite useful with his nonlinear subquantum dynamics.
Robert L. Oldershaw
Gerard Westendorp
[..]
>> On the other hand, instead of jumping orbitals, the electron could
>> team up with an electron of a neighboring Hydrogen atom, and form the
>> covalent bond of an H2 molecule. Once the covalent bond is
>> established, the electrons again go into "deterministic mode", and
>> stay part of an H2 molecule for years on end, without ever doing
>> anything manifestly random.
>
> There are no jumps in quantum mechanics, and there is no "deterministic
> mode", i.e., there's no state, in which the atom can be prepared, such
> that all possible observables take simultaneously sharp values.
With "deterministic mode" I meant that the the system remains in a known
state, like an atom in ground state. This as opposed to an excited atom,
which can decay to its ground state, emitting a photon. We cannot
predict when the excited atom will do that.
You say there are no jumps in quantum mechanics, but how do you describe
these spontaneous decay events?
Gerard
Hendrik van Hees
> You say there are no jumps in quantum mechanics, but how do you
> describe these spontaneous decay events?
Given an initial condition for the state of the decaying particle, this
state develops continuously in time via the unitary time evolution of
quantum mechanics. The state describes of course only probabilistic
information about the particle, and the time when an unstable particle
decays after this unstable particle has been prepared to be "here", is
not determined by this preparation. So quantum theory provides only
a "mean lifetime" of the particle and doesn't predict when the
individual particle decays.
dud...@gmail.com
because of Bell's inequalities, which are claimed to contradict
existence of some additional, hidden variables.
But if we will think as in field field theories: in CPT conserving
fourdimensional way, this problematic fact - that the probability is
proportional to the square of amplitude - occurs just naturally.
There is simple model to understand what living in 4D world means:
consider a space of all trajectories going forward in time in 4D with
Boltzmann distribution - probability of a path is proportional to
minus exponent of integral of potential over this path.
In this model paths/particles don't interact with each other, are
infinitely 'thin' and don't rotate its phases (as in QM to create
interference) ...
... but in such extremely simplified model we already get QM like
statistical behavior - like that the stationary probability
distribution is the square of the ground state of the Hamiltionian...
http://arxiv.org/abs/0710.3861 (second section)
In this model we can clearly see that the square of amplitude comes
from 4D nature of spacetime - we have time evolutions using
Hamiltonian from both past and future (conjugated) and they have to
agree in this moment.
Let's use this model to understand the square in EPR experiments,
which lead to Bell's inequalities understood as contradiction of
hidden variables models.
So assume we have two entangled particles and measured one of them.
If we would try to measure the second one in the same direction - we
should get full correlation, but in other cases we get this mysterious
square which is believed to lead to probabilistic paradoxes.
This square comes from 4D nature of our world - to get given
measurement, both past and future paths has to meet in one point,
giving us the measurement.
We know the probability of the past one (from the other measurement),
we know that the future one gives the same value and with our
knowledge the best its approximation is the same as for the past one -
and so we get the square.
Jarek
Igor Khavkine
> Quantum mechanics and so physics is believed to be non deterministic
> because of Bell's inequalities, which are claimed to contradict
> existence of some additional, hidden variables.
> But if we will think as in field field theories: in CPT conserving
> fourdimensional way, this problematic fact - that the probability is
> proportional to the square of amplitude - occurs just naturally.
I'm sorry, but could you be slightly more vague? As is, there are
still specific aspects of your statements that can be criticized.
Your original question asked why QED is deterministic while QM (of
particles) is not. The only possible answer is to point out that your
question is based on a false premise: that QED is somehow more
deterministic than QM. It is not. QED is no more nor less
deterministic than QM. I've yet to see you acknowledge this fact in
your more recent posts.
At this point you seem to be advocating some kind of classical field
theory to replace QM, while being vague enough that it's completely
unclear what kind of field you have in mind. Never mind that this
direction has nothing to do with your original question. Even in this
case, I'd like to make a preemptive remark. Any attempt to replace
replace the Schroedinger wave function by a classical field will fail
as soon as you move from single particle wave functions to multiple
particles wave functions, the latter no longer being defined on a
space-time at all.
Finally, if 3+1-dimensionality is somehow crucial in your alternative
model of QM, it is very unfortunate. Because you are then leaving 1+1-
and 2+1-dimensional quantum mechanics in limbo, even though they are
highly successful in describing, for example, the behavior of
electrons in thin wires and in thin layers of materials.
Igor
slawom...@gmail.com
> particles) is not. The only possible answer is to point out that your
> question is based on a false premise: that QED is somehow more
> deterministic than QM. It is not. QED is no more nor less
> deterministic than QM. I've yet to see you acknowledge this fact in
> your more recent posts.
Where is indterminism in field theories, like QED, standard model,
general relativity?
Look at Lagrangian density formulation - we have to find a field which
optimizes fourdimensional integral of this differential operator.
While choosing some time direction, we can write it as evolution
equations using Euler-Lagrange equations - knowing the field on given
hyperplane, we can expand it to the whole spacetime in only one way.
Look at the paper I've linked in the paper I've liked ('Quantum field
theory....') - it claims that the answer to my question - the thing we
are forgetting in QM is stored in zero-point oscillations.
What is indeterminism?
We have some time direction and assume that there is fixed
'wavefunction of universe in this moment' and say that there are some
'real random generators' (?) which will help in determining what we
call future - do You agree with this definition?
But this time direction changes while changing the frame of reference
(make a boost) ... so doesn't indeterminism means that we have also
spatial indeterminism?
> Finally, if 3+1-dimensionality is somehow crucial in your alternative
> model of QM, it is very unfortunate. Because you are then leaving 1+1-
> and 2+1-dimensional quantum mechanics in limbo, even though they are
> highly successful in describing, for example, the behavior of
> electrons in thin wires and in thin layers of materials.
I apologies for not specifying - You are talking about simplified
models and I'm asking about the physics of our world (whole).
... about understanding this '+1' - that this time direction cannot be
threated as a completely separate dimension, what we know well from
SRT.
QM is one of the last places in physics in which we stubbornly want to
treat this parameter only as a evolution parameter.
In field theories there are minimized 'tensions' from all 4D
directions - also from the past and the future ...
Jarek
ps. there is a mistake in my previous post - of course Bolzman
distribution among paths means that probability of a path is
proportional to exponent of minus integral of potential over this path.
Igor Khavkine
> > Your original question asked why QED is deterministic while QM (of
> > particles) is not. The only possible answer is to point out that your
> > question is based on a false premise: that QED is somehow more
> > deterministic than QM. It is not. QED is no more nor less
> > deterministic than QM. I've yet to see you acknowledge this fact in
> > your more recent posts.
>
> Where is indterminism in field theories, like QED, standard model,
> general relativity?
> Look at Lagrangian density formulation - we have to find a field which
> optimizes fourdimensional integral of this differential operator.
> While choosing some time direction, we can write it as evolution
> equations using Euler-Lagrange equations - knowing the field on given
> hyperplane, we can expand it to the whole spacetime in only one way.
As I pointed out in my first reply in this thread, what you just
described are *classical* field theories. Classical general relativity
and electrodynamics are prime examples of those. On the other hand,
QED is explicitly not classical. As the Q in its name means that it is
a *quantization* of electrodynamics. Also, from standard usage, the
standard model is generally only considered in its quantized version.
Once a field theory is quantized, it gets all the features of quantum
mechanics: Hilbert space, state superposition, operators, expectation
values, interference, uncertainty, etc. All the features that one
might consider indeterministic in QM are there in *Q*FT.
> Look at the paper I've linked in the paper I've liked ('Quantum field
> theory....') - it claims that the answer to my question - the thing we
> are forgetting in QM is stored in zero-point oscillations.
Unless you can show that you can make a clear distinction between
quantum and classical field theory (and which category QED belongs
to), I doubt that your paper would be very illuminating.
Igor
dud...@gmail.com
First of all, look at mathematical formulation of these *quantum*
field theories.
Instead of wave function there is operator - a functional (Psi)
changing a function into a (complex) number.
And using E-L equations, we get deterministic evolution equations for
this operator/functional.
It's like QM, but with only Schrodinger's equation - there is no
indeterministic wavefunction collapse.
Secondly - we've used that physics is local in time, but this
direction isn't in fact emphasized, so physics should be local
fourdimensionally, that means
delta^2 Psi[phi]/(delta phi(x) delta phi(y)) vanishes for x
different than y.
That means Psi[phi] is integral over spacetime of some function of
values, derivatives of phi in given point - in each point we have some
function: so finally quantum field theory is a (higher order)
classical field theory on the same space.
A third way I can think of showing it, is that quantum field theories
can be written in Feynman path integrals formulations, which is also
clearly deterministic.
In the paper You can find more ways to see it.
------
Generally I have to admit that I have a reluctance to this
quantization approach. It's made specially for perturbative
understanding - space of non interacting, not localized particles ...
and there is artificially introduced some mystical phi^4 like term to
make them interact ...
For me quantization is only a mathematical trick and I'm not surprised
that it's full of infinities...
I want to believe that in fact we live in some quite simple
fourdimensional, CPT conserving classical field - people
underestimates its power.
The problem is that operating on such fields is in fact extremely
difficult mathematically, but it should have all properties meet in
QM, quantum field theory.
The foundation is to understand what particle is - kind of localized
in three (spatial) dimension and long in the last one (time) stable
solution of this field - for me their stability, that charges are
integer multiplicities, have corresponding antiparticle, repels/
attract (if the same/anti) ... clearly say that they are topological
singularities and charge is in fact topological charge.
Now these 'spaghettis' interact with each other by kind of connections
- excitations of the field - we get Feynman's diagrams.
They rotate their internal phase - we get interference.
Their trajectories are chosen to optimize some 4D action.
Jarek
Igor Khavkine
> > As I pointed out in my first reply in this thread, what you just
> > described are *classical* field theories. (...)
>
> First of all, look at mathematical formulation of these *quantum*
> field theories.
> Instead of wave function there is operator - a functional (Psi)
> changing a function into a (complex) number.
> And using E-L equations, we get deterministic evolution equations for
> this operator/functional.
> It's like QM, but with only Schrodinger's equation - there is no
> indeterministic wavefunction collapse.
To be honest, I don't quite understand what exactly you mean here, but
the last phrase is definitely wrong. There are different ways to
characterize wave function collapse. But, however your characterize
it, it's there in QFT as much as it is in QM. Case in point: there are
experiments in quantum optics which measure the electromagnetic field/
perform photon counting and these measurements are indeterministic in
exactly the same way as the measurements of the position of a quantum
simple harmonic oscillator.
A note about the Euler-Lagrange equations. They are present in both QM
and QFT. They are the Heisenberg equations of motion for operators in
the Heisenberg picture. If you switch to the Schroedinger picture, you
get a *different* equation which evolves the state as a function of
time (usually called the Schroedinger equation), again both in QM and
in QFT.
> Secondly - we've used that physics is local in time, but this
> direction isn't in fact emphasized, so physics should be local
> fourdimensionally, that means
> delta^2 Psi[phi]/(delta phi(x) delta phi(y)) vanishes for x
> different than y.
> That means Psi[phi] is integral over spacetime of some function of
> values, derivatives of phi in given point - in each point we have some
> function: so finally quantum field theory is a (higher order)
> classical field theory on the same space.
OK, I simply have no idea what you mean by this functional Psi[phi]
and what it can possibly have to do with either classical or quantum
field theory.
> A third way I can think of showing it, is that quantum field theories
> can be written in Feynman path integrals formulations, which is also
> clearly deterministic.
OK, stop right there. A path integral formulation is essentially
equivalent to the Hilbert space + operators formulation of QM. Both
are possible for QM and for QFT. And both exhibit the same kind of
indeterminism you are trying to avoid.
[...snip rest not addressing the main question...]
Igor
dud...@gmail.com
(after introducing creation/annihilation operators).
But in this picture we can also see determinism - without interactions
(phi^4 like terms) we have Fock space of non interacting particles - I
think You can agree that there is no place for indeterminism here.
Now let's introduce interaction. In QM "'photons interact with
matter" by some mystical, discrete (not continuous) episode:
wavefunction collapse.
In QED it's continuous evolution - for example by phi^4 term -
photons of interaction are continuously created and then annihilated -
there is no place for indeterminism...
Please look at the mathematical formulation before perturbation - to
what corresponds the field (to Psi), at Euler-Lagrange equations -
there is clear deterministic evolution.
Where do You find indeterminism (like wavefunction collapse) in QED
formulation?
Jarek
Moderator's note
----------------
Todate, there's no consistent deterministic interpretation of quantum
theory, independent from its realization as relativistic quantum-field
theory or non-relativistic single-particle approximations.
Gerard Westendorp
> Gerard Westendorp wrote:
>
>> You say there are no jumps in quantum mechanics, but how do you
>> describe these spontaneous decay events?
>
> Given an initial condition for the state of the decaying particle, this
> state develops continuously in time via the unitary time evolution of
> quantum mechanics. The state describes of course only probabilistic
> information about the particle, and the time when an unstable particle
> decays after this unstable particle has been prepared to be "here", is
> not determined by this preparation. So quantum theory provides only
> a "mean lifetime" of the particle and doesn't predict when the
> individual particle decays.
Agreed.
The mental picture I have is that quantum states time evolve
deterministically, but that in certain "experiments", you force nature
to make a choice. This choice is then governed by probability.
In many cases, the setup of the experiment has a kind of obvious
relation to which observable that you are making nature choose from. For
example, in the double slit experiment, you force nature to choose
position. In EPR experiments, you force nature to choose spin direction
(up or down).
However, in some cases the "experiment" may not be a conscious effort by
an experimenter, and it may not be obvious what observable we are
considering. In the case of spontaneous decay, there need not be a
conscious effort by an experimenter, (the particles decay anyway) but
the observed quantity is obviously decay time.
A question that bothers me is:
Are there more "hidden experiments" in nature? Do wave functions only
collapse in controlled laboratory setups, or are they collapsing all the
time around us?
Gerard
Arnold Neumaier
> Arnold Neumaier wrote:
>
>>>> So - is quantum mechanics deterministic or stochastic?
>>> The question to answer is: What type of physical experiments
>>> are described by the Schroedinger equations ?
>> No experiment is described by the Schroedinger equation.
>>
>> Experiments are always described by additional context in which
>> (sometimes) the Schroedinger equation appears as a basic tool.
>
> I am not sure if the energy levels of the Hydrogen atom count as an
> "experiment". The Schroedinger equation predicts these correctly.
The energy levels of the Hydrogen atom count as results that can be
computed from the Schroedinger equation and can be compared with
experiment. But the experiment consists in observing spectral lines
(the additional context mentioned), and these are differences of
computed energy levels.
In practically all comparisons of theory and experiment, the situation
is similar: Some quantities computed with the help of the Schroedinger
equation can be compared with some quantities measured or computed from
measurements. Thus your wanted ''description by the Schroedinger
equation'' is only quite indirect.
Of course, the energy levels of hydrogen are deterministic.
But this does not make quantum mechanics deterministic. As the term is
usually understood, determinism refers to the predictability of all
observables of a system at all times given the observation at a fixed
time and a dynamical law.
The indeterminism of quantum mechanics for hydrogen is seen in the
impossibility of predicting at all times the position of the electron
surrounding the nucleus given its position at a fixed time.
Instead, one can only predict the probability of being in a
certain orbital or jumping to a different orbital, and the prediction
of the position within an orbital is even more fuzzy.
Note that (in spite of the claim by Hendrik van Hees in this thread
that ''there are no jumps in quantum mechanics'', quantum jumps are
observable. See, e.g., the frequently cited paper
Th. Sauter, W. Neuhauser, R. Blatt, and P. E. Toschek,
Observation of Quantum Jumps,
Phys. Rev. Lett. 57, 1696 - 1698 (1986).
> When the electron of a Hydrogen atom stays in an orbital it seems to
> behave in a deterministic way, described by the Schroedinger equation.
> it can stay indefinitely in the lowest orbital, and for quite a long
> time in higher ones. Until suddenly, it goes into a lower orbital,
> emitting a photon. The time at which it decides to do that seems to be
> completely random.
... which proves the indeterministic nature of the quantum
mechanical description. (But this does not exclude the existence of a
deeper underlying deterministic description.)
> On the other hand, instead of jumping orbitals, the electron could team
> up with an electron of a neighboring Hydrogen atom, and form the
> covalent bond of an H2 molecule. Once the covalent bond is established,
> the electrons again go into "deterministic mode", and stay part of an H2
> molecule for years on end, without ever doing anything manifestly random.
Its detailed motion is still random. Being in the ground state is a
deterministic feature of the state, but the electron's position in
the ground state is not. The ground state only predicts probabilities
for being somewhere, no certainties.
Essentially the same holds for all quantum systems.
For a more in depth discussion of the deterministic and stochastic
features of quantum mechanics see the Chapter on ''Models, statistics,
and measurements'' in
Arnold Neumaier and Dennis Westra,
Classical and Quantum Mechanics via Lie algebras,
Cambridge University Press, to appear (2009?).
http://www.mat.univie.ac.at/~neum/papers/physpapers.html#QML
arXiv:0810.1019
Arnold Neumaier
Igor Khavkine
> Please look at the mathematical formulation before perturbation - to
> what corresponds the field (to Psi), at Euler-Lagrange equations -
> there is clear deterministic evolution.
I don't know why you bring up perturbation theory, because it is
completely unrelated to the current discussion.
The mathematical formulation (whether perturbative or not) for both QM
and QFT is the same. Both have operators for observables, both have
states as vectors in a Hilbert space, both predict statistical
variation for almost any observable: <(O-<O>)^2> is not zero for most
combinations of state and operator O. Hence the indeterminacy in both
cases: repeated measurements do not yield the same values for the
observable O, only the statistical properties of the repeated
measurements are predictable. If you want to call this wave function
collpse, fine. It's there in both cases.
> Where do You find indeterminism (like wavefunction collapse) in QED
> formulation?
I already offered the example of photon counting experiments in
quantum optics. Unfortunately, you don't seem to have noticed.
I'm sorry I have to repeat this, but you are holding an inconsistent
position. Your evidence for determinism in QFT are mathematical
structures that are present in QM of particles as well, hence defeating
your own argument. If one is indeterministic, then both are, no way
around it.
Igor
Arnold Neumaier
> I've found a paper which tries to answer this question: it says that
> indeterminism of QM is a result of zero-point oscillations: "QUANTUM
> FIELD THEORY OVERCOMES EINSTEIN'S OBJECTIONS AGAINST QUANTUM
> MECHANICS" I. A. Boloshin, M. E. Gertsenshtein, and M. P. Suvorov
> http://www.springerlink.com/content/n27p29417130h25h/fulltext.pdf
>
> Doesn't it means that physics is deterministic and in quantum
> mechanics we get probabilities because it's not complete theory - it
> assumes that we just don't have (cannot have) full knowledge?
In the standard interpretation, quantum field theory is also
probabilistic. Indeed, quantum mechanics is essentially the
nonrelativistic limit of QFT; nothing changes with respect
to probablility.
Arnold Neumaier
dud...@gmail.com
of determinism denotes that we cannot fully measure physics(?).
I completely agree with it (but maybe it's a matter of better
understanding and tools).
I'm talking about objective determinism - that there is some kind of
'wavefunction of the universe', which 'evolves' in deterministic way
and what we measure is a result of it.
And probably it has many 'degrees of freedom' we will never be able to
measure - so we sometimes call it indeterminism.
QM is deterministic until we make a measurement - a wavefunction
collapse.
In QED such collapse is made continuously - is divided into single
photon exchanges - which could be seen as continuous process of
creation and later annihilation (it's perturbative picture!).
Ok - different question: what do You think about Wheeler's experiment?
Photon goes through 2 slits and then we choose detector which can or
cannot distinguish between these 2 slits.
Doesn't it means that the photon already knew how to behave? What
detector we will chose? That 'the future is already there'? ... from
our perspective it's equivalent with that the future is already
determined ...
Jarek
Arnold Neumaier
> A question that bothers me is:
> Are there more "hidden experiments" in nature? Do wave functions only
> collapse in controlled laboratory setups, or are they collapsing all the
> time around us?
They always decohere, due to interactions with the uncontrolled
environment. Collapse is restricted to the case where the context
selects a discrete variable to be measured and the transition time
between the relevant states is extremely short.
Arnold Neumaier
Igor Khavkine
> Igor, I think we are talking about different things: for You the lack
> of determinism denotes that we cannot fully measure physics(?).
> I completely agree with it (but maybe it's a matter of better
> understanding and tools).
I don't think that's what I'm talking about. I'm talking about one
thing and one thing only: you are putting forward a claim that is
logically inconsistent, and hence false. And you do that one more time
below.
> I'm talking about objective determinism - that there is some kind of
> 'wavefunction of the universe', which 'evolves' in deterministic way
> and what we measure is a result of it.
> And probably it has many 'degrees of freedom' we will never be able to
> measure - so we sometimes call it indeterminism.
I've said this before and I'll have to repeat it. You are not making
yourself clear. In fact, going by the above definition, it is not
clear whether quantum theory falls into either the deterministic or
indeterministic categories. However, that's beside the point, because
the fault in your position shows up below.
> QM is deterministic until we make a measurement - a wavefunction
> collapse.
> In QED such collapse is made continuously -
False ...
> is divided into single
> photon exchanges - which could be seen as continuous process of
> creation and later annihilation (it's perturbative picture!).
... and perturbation theory still has nothing to do with it.
Both QM and QFT (which includes QED) use the exact same mathematical
framework, including the description of measurements (the only real
distinction is between the difference in the number of dimensions of
the phase space of particle mechanics and field theory). If you want
to introduce wave function collapse into the description of
measurements, fine. But then you have to introduce it into both QM
*and* QFT. No way around it.
It doesn't matter how you define indeterminism (as long as it's
reasonably close to its standard meaning). Either both QM and QFT are
or both are not.
> Ok - different question: what do You think about Wheeler's experiment?
Don't know enough about it and don't care to look it up at the moment.
Igor