Does the universe have "Garden of Eden" configurations?

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Does the universe have "Garden of Eden" configurations?

Postby D-503 » Wed Jul 30, 2014 11:15 am UTC

In cellular automatons Garden of Eden patterns are states that cannot be reached from any other possible state. For more info see: https://en.wikipedia.org/wiki/Garden_of ... _automaton)
This has made me curious about whether there are valid physical states in the universe that cannot occur in the future. One possible set of states are those that contain masses that have not radiated any gravity. However, I don't know if they are provably Garden of Eden configurations, perhaps there are ways to manipulate gravitational fields that could be used make masses appear as though they have not radiated any gravity.

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Re: Does the universe have "Garden of Eden" configurations?

Postby doogly » Wed Jul 30, 2014 1:17 pm UTC

Having radiated gravity isn't something that is distinguishable.

There's nothing physically special about any particular place or time, but there are things you are highly unlikely to see again. Radiation dominated universe, for example. In the distant future, it will likely become the case that people on earth cannot see the light from any other galaxy. Those are all large scale stuff though. There isn't really a small, contained phenomenon like a cellular phenomenon that can get cut off and is unique.
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Re: Does the universe have "Garden of Eden" configurations?

Postby Hypnosifl » Wed Jul 30, 2014 2:20 pm UTC

Garden of Eden states aren't possible with reversible cellular automata, the Garden of Eden (cellular automaton) article notes:
In a cellular automaton, two finite patterns are twins if one can be substituted for the other wherever it appears, without changing future states. A cellular automaton is injective if every pair of distinct configurations of the automaton remain different after a step of the automaton, and locally injective if it has no twins. It is surjective if and only if every configuration has a predecessor; that is, if and only if it has no Garden of Eden configuration. An automaton that is both injective and surjective is called a reversible cellular automaton.

All the known fundamental laws of physics are "reversible" in the sense that a given state has a unique past state if you rewind it back by some time T (at least if we are talking about the deterministic evolution of the wavefunction in QM, ignoring the question of whether 'measurement' in QM introduces any genuine randomness, but in any case adding a random element to a cellular automaton with reversible rules wouldn't create Garden of Eden states). Some laws exhibit T-symmetry, meaning that a reversed movie of a system would appear to obey exactly the same dynamical laws as the forward version, while others exhibit CPT-symmetry, where after reversing the movie you'd also have to switch the labels for positive and negative charges (rename electrons as positrons and vice versa for example), and also perform a mirror flip on all three spatial axes, in order for the new movie to be guaranteed to obey the same laws of physics as the original before you reversed it and made these other changes. But as long as either symmetry is respected, the laws of physics will be reversible so I would think that, by analogy with reversible cellular automata, there couldn't be Garden of Eden states.

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Re: Does the universe have "Garden of Eden" configurations?

Postby eSOANEM » Wed Jul 30, 2014 4:59 pm UTC

Classically, anything at 0K would be a garden of Eden because the third law prohibits reaching it from any other state in a finite number of operations (and therefore time).
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Re: Does the universe have "Garden of Eden" configurations?

Postby Hypnosifl » Wed Jul 30, 2014 5:27 pm UTC

eSOANEM wrote:Classically, anything at 0K would be a garden of Eden because the third law prohibits reaching it from any other state in a finite number of operations (and therefore time).

That'd be true as long as it remains completely isolated from interaction with other systems, but if it's not isolated it should be able to change temperature; and by time-reversibility, a non-isolated subsystem of a larger system should be able to evolve into a 0 K state. But this part of the Garden of Eden (cellular automaton) wiki article suggests that not even a finite region of a larger cellular automaton grid can evolve into the specified pattern, regardless of the finite region's surroundings:
A Garden of Eden is a configuration of the whole lattice (usually a one- or two-dimensional infinite square lattice). Each Garden of Eden configuration contains at least one finite pattern (an assignment of states to a finite subset of the cells) that has no predecessor regardless of how the surrounding cells are filled. Such a pattern is called an orphan. Alternatively, an orphan is a finite pattern such that each configuration containing that pattern is a Garden of Eden.

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Re: Does the universe have "Garden of Eden" configurations?

Postby doogly » Wed Jul 30, 2014 5:36 pm UTC

This sort of thing is why cellular automata are not very good guides for thinking about physics, and you may want to poke something like
http://www.scottaaronson.com/blog/?p=1896
instead.
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Re: Does the universe have "Garden of Eden" configurations?

Postby eSOANEM » Wed Jul 30, 2014 10:57 pm UTC

Hypnosifl wrote:
eSOANEM wrote:Classically, anything at 0K would be a garden of Eden because the third law prohibits reaching it from any other state in a finite number of operations (and therefore time).

That'd be true as long as it remains completely isolated from interaction with other systems, but if it's not isolated it should be able to change temperature; and by time-reversibility, a non-isolated subsystem of a larger system should be able to evolve into a 0 K state. But this part of the Garden of Eden (cellular automaton) wiki article suggests that not even a finite region of a larger cellular automaton grid can evolve into the specified pattern, regardless of the finite region's surroundings:
A Garden of Eden is a configuration of the whole lattice (usually a one- or two-dimensional infinite square lattice). Each Garden of Eden configuration contains at least one finite pattern (an assignment of states to a finite subset of the cells) that has no predecessor regardless of how the surrounding cells are filled. Such a pattern is called an orphan. Alternatively, an orphan is a finite pattern such that each configuration containing that pattern is a Garden of Eden.


Thermo isn't time reversible though.

Of course, if we move out of the realm of classical thermodynamics then the third law stops being valid and 0K can be achieved.
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Re: Does the universe have "Garden of Eden" configurations?

Postby Tub » Thu Jul 31, 2014 10:27 am UTC

As far as I understand, both Wormholes and Alcubierre drives are constructs that are theoretically compatible with relativity, but have no way to be constructed. I'd imagine there are other highly instable configurations that aren't reachable because they decay before construction can be finished.

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Re: Does the universe have "Garden of Eden" configurations?

Postby doogly » Thu Jul 31, 2014 1:34 pm UTC

The "no way to be constructed" is that they require negative energy, which means that even if they are compatible with GR, they are probably not compatible with QFT.

It's possible that they are actually possible... but I would bet against it.
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Re: Does the universe have "Garden of Eden" configurations?

Postby Hypnosifl » Thu Jul 31, 2014 4:13 pm UTC

eSOANEM wrote:Thermo isn't time reversible though.

Some processes in isolated systems are irreversible, but I think a non-isolated system can be put into any macrostate that's part of its state space if you allow it to be acted on by arbitrary external systems (you can certainly decrease the entropy of a non-isolated system, life couldn't exist without this possibility). Are you suggesting there is anything in classical thermo that prevents a 0 K system (which in classical statistical mechanics would just mean all the particles are in a stable configuration with zero kinetic energy, at a local minimum of potential) from having its temperature raised if placed in contact with a hotter system (whose particles have nonzero kinetic energy and can collide with the resting particles of the first system)? Doesn't the second law actually demand that heat flow from the warmer to the colder in such a case?

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Re: Does the universe have "Garden of Eden" configurations?

Postby eSOANEM » Thu Jul 31, 2014 6:35 pm UTC

The earliest form of the third law of thermodynamics (they're all equivalent and easy to prove from each other) was simply that no process can lower a system to 0K.

From my thermo notes this year, the argument (starting from Planck's formulation that the entropy goes to a constant value at 0K and the fact that adiabats cannot cross) is that Planck's formulation implies that any transformation at 0K is adiabatic (dU=TdS so, as T=0, dU=0) and so, at 0K, isotherms are no longer distinct from adiabats.

It then argues that any cooling process can be decomposed into adiabatic and isothermal steps. Obviously to lower the temperature to 0K we'll need to cool adiabatically to the 0K isotherm. However as we said earlier, isotherms aren't distinct from adiabats at 0K and so, in order to do this we'd need two adiabats to cross. As stated earlier, adiabats cannot cross.

This gives us a contradiction from the fact that we assumed we could cool adiabatically to 0K.

As any cooling process can be broken into adiabatic cooling and isothermal steps, we therefore cannot achieve 0K.


I think this argument should work time-reversed (since it's essentially an argument based on the geometry of the T-S diagram) so yes, a 0K system can't be heated up to a finite temperature in a finite time.

Of course, in practice, this doesn't matter because there are no 0K systems in the universe.
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Re: Does the universe have "Garden of Eden" configurations?

Postby Hypnosifl » Thu Jul 31, 2014 8:50 pm UTC

eSOANEM wrote:The earliest form of the third law of thermodynamics (they're all equivalent and easy to prove from each other) was simply that no process can lower a system to 0K.

I'll take your word for it that this is impossible in deterministic classical thermodynamics. I was thinking in terms of classical statistical mechanics--I assume it can't still be true there since in classical statistical mechanics particles are essentially treated like tiny billiard balls, since it's quite possible to have billiard balls A,B,C starting with nonzero kinetic energy in the lab frame, then experiencing collisions with balls X,Y,Z that cause A,B,C to come to rest.

Even in classical statistical mechanics it seems like at least some form of the Third Law should hold for at least some systems, though. Specifically, it seems like it should still be true that the entropy of a system with a unique minimum-potential state (like the "perfect crystal" mentioned in the formulation of the third law on the wiki page) should be zero when the particles are in this state at 0 K, since none of the particles can trade kinetic for potential to move from the minimum of their potential wells, and thus their phase space at that energy can consist of only a single unique microstate which implies 0 entropy. But I see p. 28 of this book mentions that the third law can't hold in general in classical statistical mechanics since there are plenty of classical systems with degenerate ground states, meaning that even at minimum energy there would be more than one available microstate so the entropy wouldn't be zero. I had always imagined classical statistical mechanics would reproduce all the results of classical thermodynamics with probability 1 in the limit as the number of particles went to infinity, but I guess that wouldn't be the case here.

If we want to be more realistic and talk about quantum statistical mechanics, then in that case the uncertainty principle prevents 0 K states from existing at all, so not only can't you lower a system to 0 K, but you can't even have it as an allowable initial condition, unlike with "Garden of Eden" states that don't break any rules if you use them as initial conditions.

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Re: Does the universe have "Garden of Eden" configurations?

Postby eSOANEM » Thu Jul 31, 2014 10:56 pm UTC

Stat phys (and the 3rd law as formulated by planck) just says that, in general, entropy isn't a function of the state variables. The constant it tends to depends on the degeneracy of the ground state in stat phys but is a tricky concept in classical thermo because it pretty much only cares about derivatives of entropy (or derivatives wrt entropy). The relevant thing is that at 0K, all the derivatives of entropy (wrt state variables) go to 0.

As for the reproducing the results, it kind of does. As the number of particles goes to infinity, the energy of any one particle needs to be infinite for the overall state to have non-zero temperature (because it's proportional to the average energy). Each "step" in heating up the 0K material corresponds to knocking a single particle into motion. It's clear then that, in the limit, the number of "steps" to heat the material goes to infinity as well.

Of course, in real life, we only have a finite number of atoms in any piece of material so, because we're not in a world of bulk materials obeying classical thermo, a 0K material wouldn't really be a garden of eden.

I should also have been clearer in my first post, when I'd said classically, I'd meant in classical thermo specifically and not stat-phys (despite that being a classical theory).
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Re: Does the universe have "Garden of Eden" configurations?

Postby Frenetic Pony » Fri Aug 01, 2014 10:59 pm UTC

doogly wrote:The "no way to be constructed" is that they require negative energy, which means that even if they are compatible with GR, they are probably not compatible with QFT.

It's possible that they are actually possible... but I would bet against it.


Ok now I know a theoretical paper came out recently that shows that negative mass at the very least isn't, currently, theoretically impossible in the right state. http://arxiv.org/abs/1407.1457

Of course it doesn't prove anything by measurement. And even if one did eventually I'd still say time travel is probably impossible, and even if negative mass, and negative energy required as such for a wormhole, exists then we'd be missing something about time.

Regardless, this is an interesting question regarding time and physics. The measurement of time is a big interest of mine. Overall one could definitely say, assuming thermodynamics is conserved, that the entire state of the universe as a whole is unique at any one moment. I'd almost want to say that individual parts... however you would measure that (relativity being what it is) could "repeat" themselves, but I doubt even that.

On the smallest scale of course "time" repeats itself all the uhh, time. An o2 floating around, taken by itself, should be able to look identical to some other o2 particle in some other place and time. But beyond a certain scale, when T asymmetry operations are interacting, then irreversibility should as well.

EG take the "planet earth" as it exists right *Now* (freezes frame for a... planck units of time probably don't exist and I'm not convinced the planck length really does either as anything meaningful in a "fundamental" manner, but call it a planck unit of time). Now this moment of time relies on every possible input interacting with it. Every stray photon, every last minute tug of gravity, every stray neutrino even, or it would come out, even to the slightest degree, differently. Now one could dig into chaos theory and feedback and feedforward loops, and say that something nigh indistinguishable could happen given known physics.

But the exact state of that "moment" in time relies on the exact energy available in the universe at that time and the exact interaction of everything in our current cosmological horizon. So even if, a hundred million years from now, a planet with our exact composition, around a star indistinguishable from ours, existed with humans with the exact same DNA and etc. etc. etc. It would still be impossible for the exact moment we froze to ever be recreated, because the stars and constellations would be different, distant galaxies would be further from it than they are now, the exact state of the universe itself would be (theoretically, keeping conservation of energy and etc.) be different, thus disallowing the exact repetition of that moment, the energy input of the moment would necessarily be different.

So all moments of time (if there is such a thing as "moment") are theoretically utterly unique and unrepeatable (assumptions holding). I suppose that could be a similarity to your "garden of eden" configuration.

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Re: Does the universe have "Garden of Eden" configurations?

Postby doogly » Mon Aug 11, 2014 4:54 am UTC

Ah, but these negative masses are only asymptotic, and they still obey the dominant energy condition. This energy condition is even known to have violations. The trick is that for wormholes or time machines you need something truly heinous, you need a violation of the averaged null energy condition. Local or asymptotic bits of negative mass simply aren't foul enough.
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Re: Does the universe have "Garden of Eden" configurations?

Postby Hypnosifl » Mon Aug 11, 2014 5:00 pm UTC

Frenetic Pony wrote:But the exact state of that "moment" in time relies on the exact energy available in the universe at that time and the exact interaction of everything in our current cosmological horizon. So even if, a hundred million years from now, a planet with our exact composition, around a star indistinguishable from ours, existed with humans with the exact same DNA and etc. etc. etc. It would still be impossible for the exact moment we froze to ever be recreated

Not impossible, just very very very unlikely--all the particles could quantum tunnel back into a prior state, for example. And if you can treat the whole of the universe (or perhaps just the observable universe) as an isolated system in thermodynamics terms, I think the [url=http://en.wikipedia.org/wiki/Poincaré_recurrence_theorem]Poincare recurrence theorem[/url] would imply that if the number of possible states is finite the universe will eventually return to previous states (and if the number of possible states is infinite it should pass through states arbitrarily close to any given previous state).
Frenetic Pony wrote:So all moments of time (if there is such a thing as "moment") are theoretically utterly unique and unrepeatable (assumptions holding). I suppose that could be a similarity to your "garden of eden" configuration.

Technically a "Garden of Eden configuration" should really be a state S such that, even if you had arbitrary power to choose the precise state S' at some earlier time, there's no way it could naturally evolve to state S according to the dynamical rules. So, even if it were true that each moment was guaranteed to be unique with probability 1 in our universe's history, each moment still wouldn't be a Garden of Eden configuration since there would be an earlier state that evolved into it (and if the universe were deterministic and you could even hypothetically create a new universe with the same earlier state, then you would get the same later state).

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Re: Does the universe have "Garden of Eden" configurations?

Postby Frenetic Pony » Sat Aug 16, 2014 3:58 am UTC

Hypnosifl wrote:
Frenetic Pony wrote:But the exact state of that "moment" in time relies on the exact energy available in the universe at that time and the exact interaction of everything in our current cosmological horizon. So even if, a hundred million years from now, a planet with our exact composition, around a star indistinguishable from ours, existed with humans with the exact same DNA and etc. etc. etc. It would still be impossible for the exact moment we froze to ever be recreated

Not impossible, just very very very unlikely--all the particles could quantum tunnel back into a prior state, for example. And if you can treat the whole of the universe (or perhaps just the observable universe) as an isolated system in thermodynamics terms, I think the [url=http://en.wikipedia.org/wiki/Poincaré_recurrence_theorem]Poincare recurrence theorem[/url] would imply that if the number of possible states is finite the universe will eventually return to previous states (and if the number of possible states is infinite it should pass through states arbitrarily close to any given previous state).


Ok ok, I said assumptions holding, maybe quantum tunneling can break thermodynamics, and maybe the universe is some kind of loop where we end up in a "big crunch". It COULD happen.

Frenetic Pony wrote:So all moments of time (if there is such a thing as "moment") are theoretically utterly unique and unrepeatable (assumptions holding). I suppose that could be a similarity to your "garden of eden" configuration.

Technically a "Garden of Eden configuration" should really be a state S such that, even if you had arbitrary power to choose the precise state S' at some earlier time, there's no way it could naturally evolve to state S according to the dynamical rules. So, even if it were true that each moment was guaranteed to be unique with probability 1 in our universe's history, each moment still wouldn't be a Garden of Eden configuration since there would be an earlier state that evolved into it (and if the universe were deterministic and you could even hypothetically create a new universe with the same earlier state, then you would get the same later state).[/quote]

Thanks for the more clear definition of a Garden of Eden state.

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Re: Does the universe have "Garden of Eden" configurations?

Postby drachefly » Fri Aug 22, 2014 6:40 pm UTC

Frenetic Pony wrote:Ok ok, I said assumptions holding, maybe quantum tunneling can break thermodynamics


It doesn't.

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Re: Does the universe have "Garden of Eden" configurations?

Postby Frenetic Pony » Sat Aug 23, 2014 11:32 pm UTC

drachefly wrote:
Frenetic Pony wrote:Ok ok, I said assumptions holding, maybe quantum tunneling can break thermodynamics


It doesn't.


Hypothetically, maybe it can. The "laws" of physics we have are just what we imagine the universe working as, not necessarily how the universe does work.

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Re: Does the universe have "Garden of Eden" configurations?

Postby doogly » Sun Aug 24, 2014 3:47 am UTC

Quantum tunneling doesn't. Some magic new hypothetical physics might, but it probably doesn't, and quantum tunneling certainly doesn't.
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Re: Does the universe have "Garden of Eden" configurations?

Postby lgw » Sun Aug 24, 2014 9:57 pm UTC

In physics, a "Garden of Eden" is simply the consequence of any conservation law. Neat, right?

If mass is conserved, then the same laws of physics work for various total masses in the system, but a total mass of 3 cannot by any means evolve into a total mass of 2 or 4 or pi. If momentum is conserved, then the total momentum of the system cannot change over time, and cannot be reached from a system state with any other total momentum.

Consider a classical system (deterministic in both directions in time). In "phase space", where you describe every possible state of the system by a point, deterministic laws will describe the evolution of the system (in both directions in time) as a path through that point. If we had a universe of 10 particles, and it was sufficient to describe the universe at some point in time (a thing you can do in classical mechanics) by knowing the position and momentum of every particle in 3 spatial dimensions, then the phase space needs 60 dimensions: 3 each for position and momentum times 10 particles. The entire past and future of this system is described then by a path through this phase space passing through the initial conditions. Further, every possible set of initial conditions is on such a path, and these paths fill all of phase space without ever crossing (colorfully called a foliation of phase space - cue joke about ivy-covered universities and/or professors) .

Each path through phase space is it's own "Garden of Eden configuration", and if you extend that idea into modern non-deterministic physics you may get surfaces instead of paths, but you still have disjoint regions: phase space (the set of all possible configurations) is fractured along the fault lines of conservation principles.

I think that's amazing.
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Re: Does the universe have "Garden of Eden" configurations?

Postby doogly » Mon Aug 25, 2014 5:08 am UTC

That is a looser notion of "Garden of Eden" than what is actually meant by the term.
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Re: Does the universe have "Garden of Eden" configurations?

Postby lgw » Mon Aug 25, 2014 8:15 pm UTC

doogly wrote:That is a looser notion of "Garden of Eden" than what is actually meant by the term.


OK, fair enough, but I was thinking "the laws of physics are time-reversible, so: no" had been talked to death for the narrow sense.

There are a variety of complex configurations in various cellular automata that you can't build up from simpler pieces, but will evolve in some interesting way, producing a long chain of states that you can only get to by starting off somewhere in the chain. Some of them even loop (or loop if you ignore bits thrown off never to interact with the core again). That's exactly what a conservation law looks like, though it's a bit of a challenge to describe what's being conserved.

The neat thing IMO about (first order) cellular automata is that they're set directly in phase space. The rules of evolution of the world are directly the rules of evolution of the phase space, often presented in a way that's easy to visualize - unlike the 60-dimensional space I mention for a simple system above, a 60-cell automata can be illustrated with ASCII art, and it's fun to watch it evolve. While I agree with your comment above that "cellular automata are not very good guides for thinking about physics", I personally find them a great tool to help understand what the heck "phase space" is - they're a metaphor for phase space, not real space.
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Re: Does the universe have "Garden of Eden" configurations?

Postby gmalivuk » Mon Aug 25, 2014 9:59 pm UTC

Frenetic Pony wrote:
drachefly wrote:
Frenetic Pony wrote:Ok ok, I said assumptions holding, maybe quantum tunneling can break thermodynamics

It doesn't.

Hypothetically, maybe it can.
doogly wrote:Quantum tunneling doesn't. Some magic new hypothetical physics might, but it probably doesn't, and quantum tunneling certainly doesn't.
It's kind of like, forces that push positive masses away from each other can exist, but gravity certainly isn't such a force.
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Re: Does the universe have "Garden of Eden" configurations?

Postby Frenetic Pony » Thu Aug 28, 2014 12:09 am UTC

Ok, bad example. Quantum tunneling was a reference to some question as to the actual "speed" of quantum tunneling, and yes some probably systemic error suggesting it occurred instantaneously and broke special relativity. But that doesn't mean we "know" it works fine, even if it probably does.

EG current dark energy models can call for a universal constant, which is "weird" but seems to work. I've never seen anything wrong with breaking thermodynamics as a theoretical concept to cconsider, just like Bell's seems to show (or at least place constraints on) how "real" and deterministic physics is. Nice and convenient as a totally "real" physical world might be, (God does not play dice) doesn't mean it's so. Just because it'd be nice and convenient for entropy to not be broken, doesn't mean that something that does break it has to be "magical".


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