Mieli dalyviai! Visa mano kūryba ir kartu visi šie puslapiai yra visuomenės turtas, kuriuo visi kviečiami laisvai naudotis, dalintis, visaip perkurti. - Andrius
Pokalbis su Thomas Gajdosik: Thinking entropy on the quantum level. Entanglement etnropy. What is observed thermodynamical entropy. Statistical property.
Entropija - informacija yra ko reikėtų atstatyti būklę, perkeisti koordinates. Entropija + informacija = konservacija ?
Ar tyrimas yra entropijos raiška? Pavyzdžiui, metu kamuolį ant kalno viršūnės ir žiūriu, kaip jisai nuriedės, tada vėl numetu ir taip toliau. Kokia tikimybė, kad tai vyktų atbulai, atvirkščia laiko kryptimi? Tyrime laikas teka viena kryptimi, atvirkščiai tiesiog neįmanoma.
Viskas turi tą pačią temperatūrą - tai žemiausia entropija. Bet jeigu sumažiname mąstą tada temperatūros sąvoka pasikeičia.
Vietinė savybė: energijos visuma nesikeičia, tik raiška keičiasi.
Visuminė savybė: entropija didėja, energija sistemoje išsilygina.
Visuminius ir vietinius reiškinius jungia koordinačių sistema.
Teisingumas: Esame visi paskiri, nepriklausomi, kovojame už save, nevieningi. Malonė: esame visi vieningi, vienas kitą palaikome.
Virsmo taškas: kaip maži dalykai daro didelę įtaka - žemos entropijos esmė - valdymo teorijos esmė.
Entropy and local structure
I've been reading through parts of "The Road to Reality" by John Penrose. (Here is a free download).
It's 1,000+ pages. I wish I had gotten to read it in grad school. It's a very explanatory survey of the mathematical ideas behind all of physics. I'm jumping around, reading the end, the beginning, and chapters in the middle. He provides a lot of intuition so that on a first read I don't have to worry about understanding all of the details. So it's very inspiring to feel that I have a chance to grapple with the big picture and learn about different mathematical structures and why it might be worthwhile to study them.
I've come anew to this subject because of my interest in entropy. I've been trying to summarize my philosophy, especially the different ways of looking at things from God's point of view. The concept of entropy distinguishes the bad kid's point of view (that we live in "justice", a closed system that is zero-sum and can only get worse) and the good kid's point of view (that we live in "grace", an open system that is fed by an external source of love). There is a key ambiguity between these two points of view: Is our system open or closed?
Taking up Penrose's book, I've gotten interested in physics more generally, trying to get an inkling of quantum field theory. Overall, it's interesting that the idea of entropy seems to be quite central to the big picture. I have very much to learn and relearn.
Penrose's book has quite a lot to say intuitively about entropy. For example, he notes that, counterintuitively, as regards gravitational force, entropy is lower when matter is spread out in space, and entropy is higher as matter comes together in a small area. He is also critical of the kind of open/closed system distinction that I made as regards an external energy source. He notes that the earth reflects the same amount of energy as it receives from the sun. The key point is that the energy coming in from the sun is qualitatively different. It is fewer photons of higher energy. The reflected photons are greater in number and lower in energy. The entropy is lower when there are fewer photons.
The main idea that comes to me is that there should be a very conceptual accord between the global, external geometry of the universe (an ever expanding "big bang") and the local, internal geometry of the universe (an ever refining grid as per an ever shrinking Plank's constant). Conceptually, they should be inverses of each other. This would address many issues:
So these are some of the kinds of ways that physics could be thought of as describing the unfolding of "the edge" of the universe, which happens both locally and globally.
I was surprised to hear that there might not have been much thinking along such lines because it seems to suggest itself.
Entropy and coincidence
I have a bucket of ash in my room which I accidentally knocked over. So that created a mess.
That helped me realize what it means that from the point of view of the law of physics, it would be possible for all of the interactions to be reversed so that the ash climbed back into the bucket. It means that there is heat energy - kinetic energy of particles - such that if the momentum was all reversed, then those particles would all coincidentally work together and impart their energy to push all of those specks of ash and knock the bucket vertical with all the ash inside, and knock my foot, too. Such a coincidence is possible but it would be amazing.
It seems the main point is that when we have an interaction, the outputs can exceed the inputs. In which case it would require an enormous amount of coincidence to reverse it. So entropy is the measure of that coincidence.
And coincidence is a concept that brings together time and space, although I have yet to understand it. Coincidence has to do with the relationship between subsystems and systems. In physical modeling it's crucial that we be able to talk about subsystems. But how do those subsystems come back together?