The Power of 10...macrocosmic integration with the subatomic realm

[petrushka.googol]

Some years back I had seen a presentation titled "Power of 10" where slides detailing the realm of the very small (gluons etc) to the very large (galactic clusters etc.) were listed.

 

I was wondering whether it is possible in theory for a subsystem to have an opposing set of laws to the macro environment.

For example, could we have a subsystem where entropy increases as a subset of a larger system where the entropy increases?

 

My answer is no for the concept of local cannot be dissociated from the whole and to enable seamless integration and conformity practical reasoning avers that the subset cannot exist independent of the whole.

 

For example, we might be tempted to opine that there could be "Atlantis" style micro-universes in the known Universe that supposedly defy the laws of the parent.

 

Considering the argument above, it seems unlikely.

 

Your thoughts...

[imatfaal]

You might want to read about the Fluctuation Theorem - this shows mathematically the probability for a limited small system to act in a way that the second law of thermodynamics would not allow a macrosystem to act. It is not really what you are looking for - but it is a area in which small systems can be seen to be acting in the reverse that you would expect a large system.

[petrushka.googol]

You might want to read about the Fluctuation Theorem - this shows mathematically the probability for a limited small system to act in a way that the second law of thermodynamics would not allow a macrosystem to act. It is not really what you are looking for - but it is a area in which small systems can be seen to be acting in the reverse that you would expect a large system.

 

May I also add...

 

This means that as the time or system size increases (since is extensive), the probability of observing an entropy production opposite to that dictated by the second law of thermodynamics decreases exponentially. (reference - http://en.wikipedia.org/wiki/Fluctuation_theorem).

 

I am looking for stability of systems and sub-systems over an appreciably large finite time (not spontaneous) and this seems to be in agreement with my argument.

[Bignose]

My answer is no for the concept of local cannot be dissociated from the whole

This is basically the opposite of what an awful lot of differential equations say.

 

For example, when I write the Navier Stokes equations... the velocity and pressure at a single point in a fluid is a function only of the gradients at that point (i.e. the differentials). Those gradients are measured over an infintesimal span of space.

 

And you cannot tell me that differential equations have not be supremely successful at making very accurate predictions and describing phenomena very well.

 

All that said, the differential equations are the result of turning integral equations -- obstensively representing the 'whole' -- into the differential equations via forms like the Divergence Theorem, Stokes' Theorem, the Reynolds Transport Theorem, etc. And so very often the most important factor in solving those differential equations correctly are the boundary conditions.

 

I think the local descriptions have been very good, but it does leave open the question about larger scales.

[petrushka.googol]

I think the local descriptions have been very good, but it does leave open the question about larger scales.

 

Actually instead of integration all sub-spaces into the whole you could look at it as the differentiation of the Universal "super-space" into the smallest possible sub-space.

 

That the laws of the Universe observe the second law of thermodynamics is an attested fact, if we progressively scale down to a scale that is practical (not infinitely small i.e. much larger than the Planck length by a very large scale) then the postulate that I have stated holds good.

 

At an infinitesimal level may be there may be some degree of incongruity, but this could not be treated ideally as am independently existing self-sustaining subsystem.

 

For example, if you consider a human being exchanging energy with the environment, we all know that this is a self-sustaining subsystem that integrates with the whole, and which obeys the second law of thermodynamics. (which is why we need energy input i.e. food, also this is why we age. due to cellular entropy etc).

 

If we peek into the detail (e.g. at the cellular level) then we may be prompted to conclude otherwise.

 

This is much like Newton's Laws fail at relativistic velocities.

 

But they are adequate for all commonly occurring scenarios and hold good.

 

This is my viewpoint on the subject.