Visita a Julian Barbour em Oxford
Autor: Daniel Wagner | Publicado: 2012-07-02T09:37:00-07:00

A alguns meses atrás tive o privilégio de visitar pessoalmente Julian Barbour, autor de The End of Time, e físico teórico que já trabalhou com grandes nomes da ciência contemporânea (Carlo Rovelli, Lee Smolin, por exemplo), sendo ele próprio considerado por muitos um nome muito influente na física. Suas idéias são bastante radicais, e ele está construindo uma teoria que dispensa os conceitos de tempo (como pano de fundo externo) e espaço absoluto (só distâncias relativas são importantes) e trata transformações não observáveis (translação, rotação do universo inteiro) como não físicos.

&nbsp;Os resultados me parecem muito interessantes, particularmente pela filosofia positivista que me atraía bastante já na adolescência. A idéia de partir de novas concepções da natureza do movimento para chegar a &nbsp;pistas da gravitação quântica me inspira a fazer o mesmo, e aprofundar as idéias de Barbour, Mach e outros.




Tive o prazer de discutiR um pouco sobre algumas idéias minhas. Acima uma foto em College Farm, onde ele conduz suas pesquisas com alguns colaboradores. Escrevi um pequeno essay sobre alguns pensamentos meus e lhe entreguei. Também estou estudando teoria das categorias para tentar finalmente expressar matematicamente minha filosofia. Espero conseguir fazer isso antes do deadline do concurso do FQXi desse ano. Aí vai o essay que escrevi para Barbour:



A FEW THOUGHTS ABOUT SPACE, TIME AND THEIR INHABITANTS




A good deal of philosophical debate on space
and time has dealt with the question of how is the best way of conceiving
motion. The relational and absolute philosophies are the most famous
methodologies that have addressed this (I don't know of any other very
different). &nbsp;I will show more explicitly
how the relational conception of motion can be seen as an intellectual
apparatus built upon questioning the meaning of statements about the physical
world. This would make it easier to then introduce some novel thoughts at the
end. Some typical debate about the relational vs absolute nature of motion goes
like this (lets stick to space and forget the relational conception of time for
a moment): 



1) Let’s try to find what’s the meaning
of the following statement: 



(1.a)=&nbsp; ''Physical object 1 has velocity x with
physical object 2 as referential''



Let us postulate that



(1.b):&nbsp;&nbsp; (1.a) &nbsp;is a true sentence if and only if and only if
physical object 1 is observed to have velocity x with respect to
physical object 2.



&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;Once you define what empirical experience
corresponds to ''observing&nbsp; physical
object 1 to have velocity x with respect to physical object 2'' , (1.a) becomes
meaningful and empirically verifiable. Assuming we can observe things, measure
their relative distances, and calculate the time rate of change of those
distances, that is fairly easy. 



2)

(2.a)= '' Physical
object 2 has velocity x'' 



(2.b):&nbsp;&nbsp; (2.a) is a true sentence if and only if
physical object 2 is observed to have velocity x.



&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; It
turns out that once you have defined movement and velocity to make sense out of
(1.a) in the usual way, (2.a) is never true or false because movement is
defined to relate a physical object to another physical object . There is, by
definition, no truth or falsehood in statements like (2.a), they are literally
meaningless. &nbsp;



3)

(3.a)= ''Physical
object 3 has acceleration x''



(3.b): (3.a) &nbsp;is a true sentence if and only if physical
object 3 is observed to have acceleration x.



&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; There
is a 1-1 correspondence of the acceleration magnitude of a system in relation
to the distant stars with inertial forces experienced in it. Assuming the
distant stars have nothing to do with the behaviour of local physical systems, (3.a)
seems meaningful even without a referential. To make it compatible with (1.a)
and (1.b) define invisible absolute space to be the physical object to be the referential
to which all movement should be referred. Since the definition of movement
taken on (1) requires observation, there should be a way to “see” absolute
space in an indirect way. Now (2.a) can also make sense if movement refers to
absolute space, but empirical experience says it does not (galilean/lorentzian
invariance). Remark: this procedure of defining absolute space is natural
because the earth was taken to be the ultimate referential for centuries, so
statement like that of (2.a) were very frequently said without major concerns.
Once the earth was found to be moving, absolute space came to save the day. That
could be a historical mistake, however. 



Relational solution: Deny the invisible absolute space since it
cannot be observed directly (positivist reasoning). And since the referential
used to measure the so called absolute acceleration was that of the distant
stars, create a physical theory that generates inertial forces from the
relative motion between the physical object and the distant stars (or more
precisely, the bulk of matter of the universe). This is a piece of Mach's idea.


From these ideas, one can construct
a whole new physics that takes this relational solution. Then there should be a
mechanism for the generation of inertia from the bulk of matter of the
universe. Also, all that matters are shapes, since they are all directly
observable information that remains. The relational solution concerning time
goes in a similar fashion. 



4) 

(4.a)=&nbsp; ''n seconds have passed''



(4.b): (4.a) is a true
sentence if and only if n seconds are observed to have passed



&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Now,
once again, we need to define what empirical experience corresponds to
''observing n seconds have passed''. Assuming we can map successive shapes of
the universe to the real numbers (parameterize curves in shape space), we must
find such a parameter that can be measured from observable data in shape space
and which can make motions seem correlated by some specific law, so that ''n
seconds have passed'' can have any useful meaning. Let's call this the
clock parameterization. We can then state that ''n seconds have passed'' means
''the clock parameterization is observed to indicate n''. 

&nbsp;The relational conception of motion becomes
extremely compelling once we take as criteria of meaning of statement about
motion and time the observation of the behaviour of physical objects. For
example, take a look again at the construction of meaning of the statements
above:



(1.a) &nbsp;is a true sentence if and only if and
     only if physical object 1 is observed to have velocity x with
     respect to physical object 2.




(4.a) is a true sentence if and
     only if n seconds are observed to have passed




&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; We
can see that once we take observation as a fundamental ingredient of the
meaning of statements about the physical world, the relational approach seems
to express all its power and purpose. The constraint of meaning upon
observation reduces our physics from configuration space to shape space, and so
on. So from this it is already clear how different definitions and philosophies
of movement may have a big impact in physics, since the mathematical structure
of the relational and absolute pictures are very different.

Now comes an interesting point. By
the above construction it seems clear that the relational approach is an
intellectual apparatus built upon questioning the meaning of statements about
the physical world. Upon the requirement of meaning upon observation, the
relational approach becomes compelling. And the ‘’physical objects’’ are the
observed entities, the primitive notion from which physics is built upon. But
would happen if we ask ourselves what is the meaning of ‘’observing a physical
object in such and such state’’? Or what is a physical object? Is this
questioning too far? This is not something usually asked in the Machian picture
of the world, maybe because it would seem very hard to do physics ‘’beginning
from nothing’’.&nbsp; There may be lots of
ways to answer the question ‘’what is the meaning of observing a physical
object in such and such state’’, I certainly did not explore this question as
much as it deserves, but what is interesting for me is that it seems that we
can use the concepts of time and space again (denied as redundant for the
relational picture) for a definite resolution for that question, and then upon
that conception of a physical object, apply the relational approach one more time.
Stated verbally it looks obviously vague. But if possible, the mathematical
structure of physics resulting from this procedure would be, at least,
interesting, for the point of view of quantum gravity. Let me try to be
clearer:

Following a relational picture,
statements such as ‘’does time run in an empty universe’’ are completely
meaningless since time is defined only upon the behaviour of physical objects. Time
is a derived concept upon that of physical object. But the notion of a physical
object does not exist by itself: just as we perceive time by motion we also
perceive physical objects by motion. One objection could be stated: our mind
seems to take us to the ‘’snapshot intuition’’. Suppose you take a snapshot of
a mechanical system, then you can start to make physics from the physical
objects that are observable upon that. But how
do you identify what is a physical, material object using that snapshot?
&nbsp;Looking at where are the black dots in
the white paper looks like cheating. &nbsp;There may be different ways to answer this
question (I haven’t found any, though). But is there a way to define what is a physical
object inside dynamics itself, just like we defined time inside dynamics
itself?

The notion of a physical object
without a time in which to evolve may seem an extrapolation just as time
without objects is an extrapolation. All these concepts are tied together. Our
mind can easily make pictures of ‘’still images’’, but finding out what’s
the information contained in these still image seems a hard task. Since
there is a ‘’constraint’’ in the meaning of space and time upon that of observation
of physical objects could there be a ‘’constraint’’ on the meaning of a
physical object upon that of space and time too?&nbsp; Also, taking a look again at the (positivist)
meaning of statements:



(1.a) &nbsp;is a true sentence if and only if and
     only if physical object 1 is observed to have velocity x with
     respect to physical object 2.




(4.a) is a true sentence if and
     only if n seconds are observed to have passed




Notice that the concept of physical
object does not exist in the above sentences, but only “observation of physical
objects”. It may be that we don’t need to define exactly what we mean by a
physical object, but what we mean by
the observation of physical objects in such and such state. This
suddenly starts to resemble quantum mechanics. Could there be any link? 

I have struggled, yet without
success, to describe those ideas in a mathematical, rigorous way. One of my
ideas was to use model theory. Model theory is about interpreting a language,
where by language I mean a set of symbols and string of symbols and deductive
system built upon them. There may be statements from the set of all statements
built upon those symbols whose truth or falsehood cannot be determined by the
deductive system itself, but only through an interpretation of the meaning of
some of the symbols. It is usually used to study the fundamentals of
mathematics. For example, suppose A, B and C are mathematical statements of
some sort about the real numbers. Then from 



(A-&gt;B)&nbsp;&nbsp; is true

(B-&gt;C)&nbsp;&nbsp; is true



It follows that (A-&gt;C) is true.

But there are statements such as 



3&gt;2



That are true or false only upon an
interpretation of the symbol ‘’&gt;’’. The study of the interpretations of a
language is model theory. 

Could that be of any help for the
construction of the physics described above?

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Where
all this could take us? Maybe the idea may simply reveal not to be fruitful.
But at least it seems certain that there may be different ways of conceiving
motion than those of the absolute or relational tradition, and that a
systematic study of these possibilities is relevant for physics. Also it seems
that new ways of conceiving motion are fundamentally a work of find the ways
one can meaningfully describe the universe.



By Daniel Wagner Fonteles Alves