Time arrow and causality
Peter
A colleague of mine guesses that the time arrow is caused by the
asymmetry of causality (cause and effect are not interchangeable),
while the relationship to the invariance against time reversal of
equations is not so tight. What do you think?
Thank you and best wishes,
Peter
Uncle Al
>
> Dear all,
>
> A colleague of mine guesses that the time arrow is caused by the
> asymmetry of causality (cause and effect are not interchangeable),
> while the relationship to the invariance against time reversal of
> equations is not so tight. What do you think?
When did cause and effect become strictly ordered in a relativistic
universe? Quantum eraser and quantum double eraser experiments have
the effect (twice single or once double slit refraction) occuring
before the cause (look or don't look behind the slits). The arrow of
time is defined by angular momentum - Feynman's sprinkler. No appeals
to the large number theorem are necessary.
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz4.htm
Juan R. González-Álvarez
The equations of mechanics, the Maxwell equations, the Hilbert-Einstein
equations, the Schr?dinger, Klein-Gordon, and Dirac equations of quantum
wave mechanics, and the formal Schr?dinger equation of quantum field
theory are all causal but time-symmetric.
The time arrow has its root on the asymmetry on the flow of
correlations.
--
http://www.canonicalscience.org/
BLOG:
http://www.canonicalscience.org/en/publicationzone/
canonicalsciencetoday/canonicalsciencetoday.html
Igor Khavkine
> Dear all,
>
> A colleague of mine guesses that the time arrow is caused by the
> asymmetry of causality (cause and effect are not interchangeable),
> while the relationship to the invariance against time reversal of
> equations is not so tight. What do you think?
As far as we know, all the time asymmetry that we have seen is due to
initial conditions.
BTW, you might be interested in a book on this very question (the
arrow of time) that is coming out early next year (2010):
Sean Carroll, _From Eternity to Here_ (Dutton, 2010)
http://www.amazon.com/dp/0525951334/
Hope this helps.
Igor
Bob_for_short
***...What do you think?
Take an electron at rest. Scatter something off it. According to QED,
an infinite number of soft photons will be emitted.
Is this process reversible? Is it possible to get that infinite number
of photons ready to scatter a la back?
The problem of reversibility is a problem of many-particle interacting
systems - systems with infinitely many coupled degrees of freedom.
Reversibility can be approximately achieved in case of relatively
little influence of always present additional degrees of freedom
(friction, fluctuations, etc.) for a certain period of time.
Vladimir Kalitvianski.
-----------------------------------------
http://vladimirkalitvianski.wordpress.com
Robert L. Oldershaw
>
> As far as we know, all the time asymmetry that we have seen is due to
> initial conditions.
>
But is this not hiding the "explanation" for the arrow of time in the
unobservable past?
If the cause/effect asymmetry is the correct explanation for the arrow
of time, then it operates on all spatial scales of nature and on all
time scales. We still like observable unified explanations in physics,
right?
Juan R. González-Álvarez
> Peter wrote:
(...)
> The arrow of time is
> defined by angular momentum - Feynman's sprinkler.
It is not. And of course Feynman did not support this point of view
Juan R.
> On Nov 12, 11:49 pm, Peter <end...@dekasges.de> wrote:
>> Dear all,
>>
>> A colleague of mine guesses that the time arrow is caused by the
>> asymmetry of causality (cause and effect are not interchangeable),
>> while the relationship to the invariance against time reversal of
>> equations is not so tight. What do you think?
>
> As far as we know, all the time asymmetry that we have seen is due to
> initial conditions.
No. When we solve the equations of mechanics using initial conditions,
the entropy is constant and the overall evolution reversible.
When we solve the equations of thermodynamics we *also* use initial
conditions, but the overall evolution can be either reversible or
irreversible in function of the production of entropy.
> BTW, you might be interested in a book on this very question (the
> arrow of time) that is coming out early next year (2010):
>
> Sean Carroll, _From Eternity to Here_ (Dutton, 2010)
> http://www.amazon.com/dp/0525951334/
It will be interesting to read what he has to say now. Some of the
ideas he tried in the past are summarized by Motl
http://motls.blogspot.com/2008/12/
richard-feynman-mr-x-and-arrow-of-time.html
Igor Khavkine
wrote:
I have a feeling you are trying to make a statement with a rhetorical
question. Unfortunately, for the life of me, I can't figure out what
it is. I've pointed out scientific consensus, which has been tested
and prodded since the time of Boltzmann. If you have a comment or
objection, please state it plainly.
Igor
Peter
> Peter wrote:
>
> > Dear all,
>
> > A colleague of mine guesses that the time arrow is caused by the
> > asymmetry of causality (cause and effect are not interchangeable),
> > while the relationship to the invariance against time reversal of
> > equations is not so tight. What do you think?
> When did cause and effect become strictly ordered in a relativistic
> universe? �
IMHO, always, when it makes sense; events with space-like distance
have no cause-effect relationship => no ordering
> Quantum eraser and quantum double eraser experiments have
> the effect (twice single or once double slit refraction) occuring
> before the cause (look or don't look behind the slits). �The arrow of
> time is defined by angular momentum - Feynman's sprinkler. �No appeals
> to the large number theorem are necessary.
>
> --
> Uncle Al
See Juans reply - I think that none experiment should be interpreted
this way
Thank you for responding,
Peter
Robert L. Oldershaw
> Dear all,
>
> A colleague of mine guesses that the time arrow is caused by the
> asymmetry of causality (cause and effect are not interchangeable),
> while the relationship to the invariance against time reversal of
> equations is not so tight. What do you think?
>
I think your colleague is exactly right: for any real system observed
without limitation, its evolution can only proceed one way - cause to
effect and past to future - deterministically.
The time reversal invariance of equations is a mathematical
idealization that is not a physical property of real systems, although
systems in integrable periodic states [temporarily semi-isolated from
the larger environment] might fool one into thinking that this
invariance is realizable in nature.
That's my thinking on the issue. Of course I could be wrong.
RLO
www.amherst.edu/~rloldershaw
Lester Welch
A good discussion about whether a biological system ("observer") can
detect time "flowing backward" is given in
arXiv:0802.0438 and arXiv:0911.2610
Igor Khavkine
> > As far as we know, all the time asymmetry that we have seen is due to
> > initial conditions.
>
> No. When we solve the equations of mechanics using initial conditions,
> the entropy is constant and the overall evolution reversible.
>
> When we solve the equations of thermodynamics we *also* use initial
> conditions, but the overall evolution can be either reversible or
> irreversible in function of the production of entropy.
*yawn*
The the time-reversal asymmetry of thermodynamic equations is a
consequence of the time-reversal asymmetry of initial-final conditions
of the underlying mechanical system.
If you agree, your objection is only semantic. If you don't, then you
are implying new physics, which is precisely why I prefixed my
statement with "as far as we know". If there is new physics in this
picture, it's not yet been found and identified.
Igor
Peter
> On Nov 12, 11:49 pm, Peter <end...@dekasges.de> wrote:
>
> > Dear all,
>
> > A colleague of mine guesses that the time arrow is caused by the
> > asymmetry of causality (cause and effect are not interchangeable),
> > while the relationship to the invariance against time reversal of
> > equations is not so tight. What do you think?
>
> As far as we know, all the time asymmetry that we have seen is due to
> initial conditions.
See my reply to Juan's posting
>
> BTW, you might be interested in a book on this very question (the
> arrow of time) that is coming out early next year (2010):
>
> Sean Carroll, _From Eternity to Here_ (Dutton, 2010)
> http://www.amazon.com/dp/0525951334/
>
> Hope this helps.
>
> Igor
Thank you for this hint,
Peter
Peter
wrote:
...
> If the cause/effect asymmetry is the correct explanation for the arrow
> of time, then it operates on all spatial scales of nature and on all
> time scales.
Yes, of course
> We still like observable unified explanations in physics, right?
Me, yes, see my unification of CM and CEM :-)
Peter
<email.addr...@not.supplied> wrote:
> Peter wrote on Thu, 12 Nov 2009 22:49:12 +0000:
>
> > Dear all,
>
> > A colleague of mine guesses that the time arrow is caused by the
> > asymmetry of causality (cause and effect are not interchangeable), while
> > the relationship to the invariance against time reversal of equations is
> > not so tight. What do you think?
>
> > Thank you and best wishes,
> > Peter
>
> The equations of mechanics, the Maxwell equations, the Hilbert-Einstein
> equations, the Schr?dinger, Klein-Gordon, and Dirac equations of quantum
> wave mechanics, and the formal Schr?dinger equation of quantum field
> theory are all causal but time-symmetric.
>
> The time arrow has its root on the asymmetry on the flow of
> correlations.
>
>
> BLOG:http://www.canonicalscience.org/en/publicationzone/
> canonicalsciencetoday/canonicalsciencetoday.html
I admit that my original statement/guess was not precise enough,
sorry!
Causality: Cause => effect, is an implication, and an implication is
not reversible (it would be an equivalence, therefore, no change)
Time is understood to be created by changes of the universe; if the
motions of the planets around the sun would be reversed, time would
not be reversed; if you hit initially a pendulum watch into the
opposite direction than the last time of winding up, time is not
reversed either
Peter
wrote:
As I have understood Newton (Principia, Chap. Definitions), the mass
is the cause of the gravity field; the latter is the cause of the
gravity force; the latter is the cause of the fect, that two bodies
move towards each another, if they are not hindered to do so by other
forces or by constraints. This has nothing to do with reversibility.
Newton's force law describes a rather general relationship, when
compared with the initial conditions. The latter are the cause for
that the specific observed motion hapens (say, the orbit of the
Earth). This is not reversible: the Earth's orbit is not the cause of
the initial conditions.
Juan R.
(...)
> Time is understood to be created by changes of the universe;
I prefer to say: "changes happen in time".
> if the
> motions of the planets around the sun would be reversed, time would not
> be reversed; if you hit initially a pendulum watch into the opposite
> direction than the last time of winding up, time is not reversed either
Maybe you are confused by the term "time reversal". The aplication of the
time-reversal operation T to equations of mechanics inverts the evolution
but time continues to flow from past to future in either cases.
--
Lester Welch
Let me offer something slightly speculative... :-)
Suppose that time can and does flow both forward and backward and that
when time flows backward it is a perfect reversal of the forward flow,
i.e., memories are erased instead of created; hot bodies absorb
radiation instead of emitting it, entropy decreases instead of
increasing, etc.
First question - would we know it, if time were flowing backwards? I
submit "no" because a forward flow of time requires a memory
increase.
Time could be a random walk - back and forth - along the temporal axis
- akin to the drunkard's walk - and thus the mean distance from the
origin always increases - we age, etc.. If we're at t=45 we remember
only t=1,2,...44. If time - randomly -goes to t=44 then we only
remember t=1,...43, however if time flows forward to t=46 then we
remember t=1,...45.
I also submit that, in principle, there is no experimental way to test
such a speculation and thus it is not science - but could offer a
explanation of the "arrow of time."
Gerry Quinn
says...
> Peter wrote:
> >
> > Dear all,
> >
> > A colleague of mine guesses that the time arrow is caused by the
> > asymmetry of causality (cause and effect are not interchangeable),
> > while the relationship to the invariance against time reversal of
> > equations is not so tight. What do you think?
>
> When did cause and effect become strictly ordered in a relativistic
> universe? Quantum eraser and quantum double eraser experiments have
> the effect (twice single or once double slit refraction) occuring
> before the cause (look or don't look behind the slits).
And therefore it's best not to refer to cause and effect in such cases.
It's not sensible to speak of an 'effect' caused by quantum erasure; no
detection event exists if the detection event is erased.
And such an experiment also involves a single reversible quantum event.
Causality - and thus the arrow of time - depends on irreversibility.
As a contrasting example, you can't in practice erase the 'memories'
associated with a ball rolling down the stairs.
You can do all the erasure experiments you want with the single quantum
event controlling the poison bottle in a Schrodinger cat experiment -
but still when you open the box one of two outcomes will be seen, and
each will demonstrably contain a history of cause and effect relating
to physiological processes associated with either a live or a dead cat.
> The arrow of
> time is defined by angular momentum - Feynman's sprinkler. No appeals
> to the large number theorem are necessary.
That doesn't make sense. The sprinkler system dissipates large amounts
of free energy; thus it naturally enters the domain of causality.
- Gerry Quinn
Robert L. Oldershaw
<juanREM...@canonicalscience.com> wrote:
>
> Maybe you are confused by the term "time reversal". The aplication of the
> time-reversal operation T to equations of mechanics inverts the evolution
> but time continues to flow from past to future in either cases.
>
Even this definition of reversibility is technically unacceptable if
it is applied to the real world.
There is no ideal time reversal symmetry in nature, only temporary
approximations within very limited and highly controlled
circumstances. Initial conditions cannot be known to infinite
accuracy, and there are both quantum and classical sources of
uncertainty that make this supposedly exact symmetry only a qualified
quasi-symmetry, at best.
I would welcome hearing about realizable, testable experiments with
actual physical systems that refute the my argument presented above.
Juan R. González-Álvarez
As explained in virtually any treatise on non-equilibrium statistical
mechanics, there exists not that "scientific consensus"!
Regarding Boltzmann, he did not show that irreversiblity is due to
original conditions. In 1872 he claimed that he had obtained the second
law *from* mechanics. His derivation was totally flawed, as showed by
Kelvin in 1874 and by others. Boltzmann replied with a paper in 1877 with
assumptions contradicting what he said in 1872.
More objections were raised in 1893 by Poincaré and latter by Zermelo.
Boltzman answers in 1896 were similarly flawed and inconsistent. The
history of the subject is fascinating:
Much confusion resulted from the fact that for many years Boltzmann was
inconsistent in his statements about the matter, sometimes using the
probability argument and sometimes saying that it was not necessary to
invoke probability theory. When pressed, Boltzmann invoked the
probability argument to justify his argument but sometimes insisted that
he had arrived at his function H on the basis of pure mechanics.
Boltzmann seems never to have properly understood [...] The answer is
that in his derivation of the expression for H he had made some hidden
assumptions about the characteristics of typical collision between
atoms. [...] His H theorem had therefore not done what he had originally
intented it to do: lead to the second law by a purely dynamical
argument. That does not mean that it was a waste of time.
Indeed the H theorem and the underlying kinetic theory have been tested
but it has been also showed that any attempt to derive it from mechanics
plus initial conditions is "mathematical funambulism" :-D
Currently his kinetic theory is rigorously derived from *extensions*
of mechanics worked by the different known Schools.
Check literature cited.
Juan R.
> On Nov 17, 5:41 am, "Juan R." Gonz?lez-?lvarez
> <juanREM...@canonicalscience.com> wrote:
>>
>> Maybe you are confused by the term "time reversal". The aplication of
>> the time-reversal operation T to equations of mechanics inverts the
>> evolution but time continues to flow from past to future in either
>> cases.
>>
>>
> Even this definition of reversibility is technically unacceptable if it
> is applied to the real world.
I already explained this to you before. I will do again now but not more.
Any scientific law, theory, or model is an approximation to the real
world:
- The Maxwell laws given in most tratises in electrodynamics ignore
gravitation (for curved spacetime generalizations check a textbook on GR
as Wald).
- The GR equation (R^ab - 1/2 g^ab R) = kappa T^ab is an approximation
that ignores quantum effects. Semiclassical gravity is based in adding
some quantum corrections to the above GR equation.
- Newtonian F = ma, with F the Newton force is another approximation
that ignores relativistic effects.
Of course, I have not cited all the approximations involved in above laws,
just some few as illustration. For instance the Newtonian and Maxwell
expressions are also missing quantum effects.
Reversible equations are another approximation to more general laws.
Take the fundamental equation of motion
d(rho)/dt = L rho + D rho
It is not know what is the more general expression for D and each School
gives different expressions for this term.
Zubarev School (NESOM or NSOM) gives
D rho == epsilon (rho - rho_A)
Prigogine School (Austin Brussels School) gives a series expansion in
powers of creation and destruction correlation operators. The expression
is very complex and I will not write here.
Chang Eu gives not explicit expression (except for weak regimes where the
form is known and in agreement with any experiment done) but gives three
conditions for D. The first guarantees conservation laws of mass,
momentum... the second assures the existence of a microscopic H theorem
and the asymptotic stability of equilibrium states. The third condition is
an requirement of invariance under canonical transformations that
facilitates the use of analytical dynamics in applications.
Etc.
In all cases reversibility is obtained in the limit when D rho = 0 or very
small in comparison with the term L rho.
d(rho)/dt = L rho
This equation is reversible and it reduces to the Schrodinger one when one
does the additional approximation rho --> |Psi><Psi|
Reversible equations are perfectly valid within their limits of
applicability. Many branches of physics are build over reversible
equations. Just as many of physics are build ignoring gravitation or
thermal effects or relativity and that does not do them "technically
unacceptable".
> There is no ideal time reversal symmetry in nature, only temporary
> approximations within very limited and highly controlled circumstances.
Again, laws, theories, and models would not be confused with reality.
> Initial conditions cannot be known to infinite accuracy, and there are
> both quantum and classical sources of uncertainty that make this
> supposedly exact symmetry only a qualified quasi-symmetry, at best.
>
> I would welcome hearing about realizable, testable experiments with
> actual physical systems that refute the my argument presented above.
If one is studying an electron involved in some dissipative processes in a
dense fluid one can use the equation that Eu has developed and applied in
hundred of publications Phys. Rev. E, J. Chem. Phys., J. Phys. Chem. B.,
Acc. Chem. Res., Phys. Rev. lett., etc.
In fact, his equations let us to obtain expression cannot be obtained by
old methods based in reversible equations or even from Mori response
theory or Kubo theory. See for instance the expression Theta_{j a}^v in
http://www.canonicalscience.org/en/researchzone/time.html
If one is studying an electron in a diluted gas phase Hydrogen atom, then
the D term is so tiny that experiments cannot measure it and we work with
the equation
d(rho)/dt = L rho
or adding a pure state approximation
d|Psi>/dt = H |Psi>
The same chain of approximations happen in macroscopic thermodynamics.
The variation of entropy using DeDonder notation is
dS = d_iS + d_eS
And the thermodynamics of irreversible processes says us what is the form
for d_iS in terms of the flows of matter, energy...
The well-known bilinear product of thermodynamic forces F and flows J
d_iS = F_b J_b
When d_iS is zero or so tiny that cannot be measured (for instance when
the thermal gradient is very small or the heat conductivity is) then
dS = d_eS
and all the equations of thermodynamics are *reversible* in this case.
The neglect of d_iS is perfectly justified by experience in certain cases.
Moreover, the term is technically demanding and not suitable for a first
course (already the thermodynamics of equilibrium is too difficult for
most students) and those are the reasons which introductory treatises on
thermodynamics never give students an expression for this term.
Difficulty is also the reason which students learn the reversible equation
d|Psi>/dt = H |Psi>
but not the irreversible equation
d(rho)/dt = L rho + D rho
which in much more complex.
However, there is situations (specially in research) where it is very
important to consider terms as d_iS or D and then you may open textbooks
or papers in thermodynamics of irreversible processes and monographs,
reviews, and papers in non-equilibrium and irreversibility; learn all that
stuff and apply it in the lab.
One of the arts of becoming a competent scientist relies on knowing when
and how to apply approximations.
Robert L. Oldershaw
<juanREM...@canonicalscience.com> wrote:
>
> One of the arts of becoming a competent scientist relies on knowing when
> and how to apply approximations.
>
Yes, and one of the lessons of becoming a competent natural
philosopher is that all descriptions of physical systems and physical
phenomena, whether they are verbal, graphic or mathematical, are but
limited approximations to the actual systems and phenomena.
This is an important lesson which has been sporadically forgotten in
recent decades and has produced some remarkable examples of
intellectual arrogance in theoretical physics.
Daryl McCullough
>There is no ideal time reversal symmetry in nature, only temporary
>approximations within very limited and highly controlled
>circumstances. Initial conditions cannot be known to infinite
>accuracy, and there are both quantum and classical sources of
>uncertainty that make this supposedly exact symmetry only a qualified
>quasi-symmetry, at best.
I think that we need to clarify exactly what we mean by
time-reversal symmetry. It could possibly mean two different
things.
The simplest explanation is in terms is in terms of classical
deterministic dynamics of particles (no fields). In that case,
the state of a system is a function of the positions and velocities
of all the particles: S= f(q_i, v_i) where q_i is the ith position
coordinate, and v_i is the ith velocity coordinate. The
time-reversed state S* is by definition the state in
which all the velocities are flipped: S* = f(q_i,-v_i).
To say that the *dynamics* has time-reversal symmetry
is to say that if state S evolves to state S' in time t,
then S'* will evolve to S* in time t. Some weak decays
have been found to violate time-reversal symmetry, so
this is just an approximate symmetry.
To say that the *state* has time-reversal symmetry is
to say that the time-reversed S* is equal to the original
state, S. A completely static universe (and some
steady-state universes) would have time-reversal symmetry,
but ours doesn't seem to.
When you say "initial conditions cannot be known to
infinite accuracy", I'm not sure for what notion of
time-reversal symmetry that is relevant. It is certainly
true that we only know the initial state, S, to a finite
accuracy, so the time-reversed state, S*, is also
known only to a finite accuracy. So presumably that
means that tests of time-reversal symmetry in the
dynamics are only approximate. But there is a difference
between (1) The symmetry is only approximate, and
(2) Our knowledge is only approximate. The symmetry
could be exact, even if we only have approximate
ways of testing it.
--
Daryl McCullough
Ithaca, NY
p.ki...@ic.ac.uk
> As far as we know, all the time asymmetry that we have seen is due to
> initial conditions.
If I time reverse a system with specified initial contitions,
it becomes a system with specified final conditions.
Assuming the dynamics is reversible,
surely both systems can be mapped onto each other?
--
---------------------------------+---------------------------------
Dr. Paul Kinsler
Blackett Laboratory (Photonics) (ph) +44-20-759-47734 (fax) 47714
Imperial College London, Dr.Paul...@physics.org
SW7 2AZ, United Kingdom. http://www.qols.ph.ic.ac.uk/~kinsle/