# What would entropy look like in an infinite number of universes?

There was a question recently about gatekeepers controlling the flow of goods between universes. The gatekeepers became a religious order. The premise got me thinking, and I have come to a conundrum over one of the lateral associations.

String theory allows for, even proposes, an infinite number of universes. Infinity, of course, means the system is not closed. The universes may be closed individually, but collectively there would not be a closed system. String theory also allows for the hypothetical interaction and interplay, including collisions, between universes.

So, in a world where goods and energy COULD be transported between universes, through a system of gates, then it couldn't be said definitively that the individual universe was a closed system. Energy could still come in from outside - from another universe. If energy could be transferred between an infinite number of universes, then energy itself would be infinite.

What would entropy look like under such a system? What would happen to a universe that had an excess amount of energy brought in, and what would happen to the universe that lost the energy? The Laws of Thermodynamics apply only to a closed system.

Here is a reference that addresses the issue. Confronting the Multiverse: What 'Infinite Universes' Would Mean

'Is such a multiverse merely speculation? Certainly it is not as widely accepted by scientists as quantum physics or the Standard Model of particle physics. But it is motivated by real science, and it does follow from the equations of cosmology that optimally explain the origin and structure of our universe. In fact, in some of Linde's mathematical models, cosmic inflation must be expanding eternally and chaotically.'

Mission Beyond The Stars: Book #1 of "Saga Of The Lost Worlds" by Neely and Dobbs

https://www.kobo.com/ca/en/ebook/mission-beyond-the-stars-book-1-of-saga-of-the-lost-worlds-by-neely-and-dobbs

A saga that addresses what happens if one universe starts appropriating energy from another universe, upsetting the multiverse balance and the entropy within a universe.

To reduce the scope of the question somewhat, I will eliminate the concept of cosmological inflation. Universes are not continuously appearing. Big Bangs do not occur randomly out of nothingness. What we have is what we've got. It's just that there is an infinite number of them. Sort of a static infinity. Since the answers so far apparently assume this already, it does not change any answer.

To further clarify the question, I should clarify my terms. Entropy has been used as a fudge factor variable, whose definition tends to change from situation to situation, the primary purpose of witch is to provide a reason for why something can not be done, in the absence of any other factual reason.

I am talking about the SI definition of entropy, (carnot?) with the units joule/kelvin. If the temperature is zero, division by zero presents a real problem. If energy (joules) keeps increasing, then so to does the maximum entropy level. If there is finite energy, then it would seem the limit of entropy is the maximum energy. Apparently, very bad things happen when this limit is reached. If entropy can never be destroyed (lowered), then at this limit this energy could not be used to generate more heat. Ostensibly, this is because there is no more energy potential difference - no more potential for energy to go from a higher level to a lower level. All available energy is equally distributed. Heat is produced when energy flows from higher potential to lower. Presumably, the temperature would therefore be close to, but not exactly, zero. More energy, obviously, raises the entropy limit. But also, obviously, only if it is available to produce heat through a potential difference. A warmer universe that can provide available heat for transfer would lower entropy. Heat and energy are not the same thing.

So a gate between universes at a different energy level would presumably produce an energy potential difference at the gate. If one universe were warmer than the other, heat could be transferred.

So, if energy were drawn from another universe, would its entropy drop? Recall that mass IS energy, and moving mass from one universe to another is moving energy. Would it end up cooling faster?

Would trade through these gates be one colossally huge application of a negative balance of trade? Could they make it up from another universe?

Could you set up a universe-to-universe Carnot engine, for example?

• Comments are not for extended discussion; this conversation has been moved to chat. – Monica Cellio Nov 12 '17 at 3:52

As long as the division between the universes remains in place over most of its domain, the system can still be considered closed. Openings in the system are possible, but they exist at such a low probability level that their presence does not come into play in the overwhelming majority of individually located moments in time within the space time domain of the universe.

To create an opening in the otherwise closed system, the universe must birth a star which can have satellites and then that star has to give birth to a planet of appropriate composition and hurl it out into orbit and just the right trajectory and energy level that it settles into a stable orbit within the Goldilocks zone where life can exist. That planet, in turn has to give birth to life and nurture it across eons of time till it evolves to a level of intelligence which can create inter-universal gates. Even then, the creation of a gateway is uncertain, but if just the right thoughts converge with just the right resources and motivations, a gateway will be born.

...and that gateway will be used for the purposes chosen by the life form, not in service of the universe, but in service of that life form's limited view of existence. Energy and materials will pass between domains and each instance of such transfer will be a violation of many of the parent universe's physical laws. But in short order, the life form will extinguish itself upon the fires of its own excesses. And once it is gone, the universe will be closed again.

And even while the life form lives and its gateways are open, the vast majority of the universe, which is out of range of its contamination due to that convenient light-speed limitation, remain closed.

The only long term effect of the occasional openings between universes is that the equations which future intelligent lifeforms use to predict the exact size and energy content of the universe, will be slightly off. ...which might be enough to keep those races from discovering how to build gateways; further assuring the ongoing closed nature of the universe.

• This is speculation on how a 'gate' would form between universes. It presupposes that these gates are designed by consciousness. THAT is another issue entirely. There are credible physicists who are positing that the entire universe, and perhaps all universes, are conscious. That is, life as we define it is not necessary for consciousness. Is the Universe Conscious? Some of the world's most renowned scientists are questioning whether the cosmos has an inner life similar to our own. – Justin Thyme Nov 8 '17 at 15:58
• Britain tried bleeding other countries dry, through a 'limited' opening (primitive sea transport) but this 'opening' rapidly expanded. The 'prey' became the 'predator'. Japan is almost entirely dependent on resources from other countries. I am sure this is not a limitation that human ingenuity can not overcome. – Justin Thyme Nov 8 '17 at 16:02
• You also contradict yourself. The constant c does not have to be universal across all universes. There could easily be universes where c is infinite. The rules of physics, and the physical constants as we know them, are (like you said) not the same across all universes. They may not even be consistent WITHIN a universe. Any limitations caused by the value of c in our universe do not have to apply in other universes. – Justin Thyme Nov 8 '17 at 16:06
• Sorry @JustinThyme, I took your mention of "Gate Keepers" to mean that the gates were finite creations of whatever race those keepers are a part of. As for conscious universes, I love the idea! Notice that in my answer, I treated the universe as a direct actor with both motive (to create gates) and method (birth planets with intelligent life). I see life as part of each universe's evolutionary path, a method for giving matter a mind (which is privately my answer to heat death but that is another issue entirely). – Henry Taylor Nov 8 '17 at 16:07
• On predator/prey, I'm missing the relevance, but if we keep this up in comments, the forum cops will soon move us to chat which is someplace that I never go. Constant c might not be true everywhere but why would a life form which isn't limited by light speed attempt to move sideways through universes. They already have infinity to play in. Good luck in your project. Hope something that I have offered here has helped. – Henry Taylor Nov 8 '17 at 16:19

If all the universes are linked then although there is an infinite amount of energy there are also an infinite amount of universe sized drains on that energy. The rate of entropic decay remains the same, all the universes will eventually die. But can we keep one universe alive?

Consider that universe A is a parasite, linking on to a universe with lower entropy, stealing a load of energy then closing it’s gate before locating a new universe with lower entropy. Staying connected to a high entropy universe is a bad idea: you’ll end up losing energy to it eventually.

The first issue is that the time needed to locate the next victim universe tends towards infinity. Whenever universe A claims a victim the number of universes with higher energy that A decreases, so the ratio of higher energy to lower energy universes also decreases, tending towards 0. If we assume the chance of finding a suitable victim universe is related to the inverse of this ratio we can see that for every victim a longer and longer search time is required.

The second issue is that potential victims will continue to run down over time. Their total useful energy decreases at the same rate regardless of whether they’re connected to a gate or not.

The third issue is that there will be an infinite number of parasitic universes, exacerbating the above issue by rapidly running down any useful universes, potentially connecting to multiple at a time. They will then have to prey on each other, forming a sort of Ponzi scheme with one seemingly everlasting universe at the top preying on an infinite stack of lower entropy universes.

Where this falls down is point 1. As soon as any universe uses more energy in the time it takes to find its next victim than it gets from said victim the entire pyramid collapses, and eventually all the universes can do is slowly but surely run down.

Basically: N universes of finite resources/N universes of consumption = finite time you can consume for.

Based on a comment by Andrey, let’s do a thought experiment. Imagine a model universe that is an infinite line of glass pipes filled with water. For the purposes of our model we can assume gravity always points uniformly in one direction parallel to the pipes, and the pipes are both frictionless and indestructible. At the base of all the pipes we also have a ‘void’ that sucks the water away and destroys it. We fill each pipe with a finite amount of water and start time for our model universe.

Now, each pipe represents a ‘normal universe’, and the amount of water is the total amount of usable energy. Your gates allow you to transfer arbitrary amounts of water from one pipe to any other pipe, but the water level in all pipes will continue to drop until your supply of water has, eventually, run out.

The two ways out of this are adding additional universes (and therefore more water) or having a number of universes with infinite water. You could start moving all the water into one universe from all the others, but that means those universes will run out faster, and unless you can instantly and infallibly find other pipes with more water in them through the infinity of all pipes you will eventually lose more water in the time it takes to find a full pipe than you’ll get from the full pipe.

• Actually infinite resources over infinites consumers can give any result you want -- zero time, a finite time, or infinite time. That's why when you ask a computer to divide infinity by infinity the result is Not a Number. – AlexP Nov 8 '17 at 14:25
• This depends on the truth of the equation that infinity divided by infinity equals 1. Suppose infinity divided by infinity is infinity? – Justin Thyme Nov 8 '17 at 15:34
• I upvoted this because it is a credible attempt, with a plausible answer. However, the answer IS biased towards preserving entropy, without a justification for this bias except, well, the preservation of the status quo. – Justin Thyme Nov 8 '17 at 15:38
• This is a very good description of what happened on earth, as the big powers colonized the rest of the earth. Eventually, they ran out of places to colonize as they depleted resources. However, now we are talking about colonizing the nearby planets and asteroids. When we run out of them, we will colonize nearby star systems, And so on and so forth. Would we colonize universes and bleed them dry? Undoubtedly. – Justin Thyme Nov 8 '17 at 15:43
• What is infinity minus 1? Is it still infinity, or is it one less than infinity? If so, then infinity is actually finite. THAT is the conundrum that this addresses. Entropy demands that infinity minus 1 is something less than infinity. – Justin Thyme Nov 8 '17 at 15:46

I regret that this answer, given our comment conversation, might be a hair disappointing in that I haven't put in all the horrid equations. However, the basic calculus will stand up.

Simplifying this discussion almost to the point of making angels weep....

Entropy describes the tendency of the universe to "settle down" to an energy state after which no work can be done. From the point of view of electricity, you need a difference in voltage to make something happen. For example, your hair dryer needs (in the U.S.) 110 volts AC. It has two prongs. It doesn't matter1 if one prong is 0 and the other 110, or one prong is 10,000 and the other 10,110. So long as the difference is 110 volts, the hair dryer operates.

The problem is when both prongs are, for instance, 10,000 volts AC. Your hair dryer stops working. There's no "potential" with which it can operate.

That's entropy. Everything settles to a "common value" after which there's no potential for more work. (Can you hear the angels weep? I can....)

Now, a little Calculus...

Entropy can be thought of as the limit of all potential energy as time approaches infinity.

$\lim_{t→∞} E \frac{de}{dt} = 0$

That differential (de/dt where e and E are energy and t is time) is the problem. Time is always in the denominator. No matter how much E you have, no matter how great the de you have, you will always have a finite energy in each individual universe and divide by infinity. (If you want interesting reading, go to math.SE.com and read questions and answers about infinite finite systems.)

Because this simple oversimplification (the angels are starting to break mirrors in preparation for slitting their wrists), it doesn't matter how many universes you have. Since each individual universe must obey the same rule, no matter how much energy is transferred between any of them, and no matter how many universes there are...

An infinite number of parallel universes will eventually succumb to entropy. If one universe discovered how to rape all the others of their energy, because entropy is defined as time approaches infinity, entropy will always win. It'll just take a little longer.

Here's the easiest way to look at the problem. This is what is meant by an infinitely finite system. Remember, E is always a finite number, the final thermal bias of any universe.

$\sum_{i=1}^\infty \frac{E}\infty = 0$

(And the dead bodies of angels have just started to fall from heaven. It doesn't change the intrinsic veracity of the result... but I do feel bad about the angels.)

One last thing from our comments above. There is no magic bullet here. Even if each universe settled to a different thermal bias, allowing for a potential to exist between universes, entropy would still win. The universe draining all the others would last a little longer (as I said above), but in the end, everything stops. The only way to change this is the impossible: a power source independent of all universes that outlasts time itself. Perpetual energy. (And the last angel just hit the ground.)

It's difficult to imagine what the end result of entropy is: no planet moves because all mass has settled into gravimetric balance. No light, no background radiation, no emissive sources at all. No kinetic energy such as asteroids colliding. Not even a quantum burp. It is, IMHO, the most lonely and depressing thing I can imagine.

But it's why I can say, from the perspective of the mathematics we understand today, that each universe is a closed system, and therefore the "parent system" of all parallel universes is also closed, despite the infinite number (remember that math.SE link). You can rob Peter only so long before there's nothing left to pay Paul because everything's draining toward zero at the same time, if not the same rate.

1 There are other consequences to having a 10,000 volt DC bias, but I'm blatantly ignoring them for the sake of brevity.
See also Heat Death of the Universe which, not surprisingly, reads a lot like what I just said, and Entropy.
EDIT :-) That's a lotsa comments.

• No, it doesn't look like nor become a massive black hole. The math suggests you reach a state of gavitic equilibrium where everything stops moving: not a condition where all mass has fallen into one black hole. Gravity doesn't effect everything at an infinite distance. There are things even the largest black hole cannot draw into itself (according to the theoretical math).

• You are correct that limits as time approaches infinity always approach, but never reach, their value. However, I'm an engineer, and I know there comes a point where you're "so close it no longer matters." There really isn't a way to avoid entropy without that perpetual motion machine (not even by logic).

• Size and expansion do not matter, at least insofar as the math as we know it expresses it. A large universe does not push against a parallel universe (as we understand the mathematics, remember, we have no proof of any of this so we're now moving into "primarily opinion-based" territory). Note, however, that you cannot define entropy by "entirely expanded" or "entirely collapsed." Entropy is "entirely static." What the state of the universe is at that point is irrelevant, but as I said before, the math suggests gravitic equilibrium. There will be mass spread out in the universe... doing a whole lot of nothing.

• An expanding universe would actually fall to its lower energy state faster than one that wasn't because there's fewer interactions to re-energize things. Also, remember what I said above, it doesn't matter what bias you end up with in any universe. If one rapes them all, you just prolong the inevitable. There's no way to cheat entropy.

• Aaaaaand finally... Maxwell may not have considered gravity, but modern physicists have. Gravitic equilibrium. If your universe has the energy to waste to move a black hole, it doesn't need the black hole. In a very, very small nutshell (the one angel who hid in a closet is about to jump off a cliff): it takes energy to do something. You will always have less when you're done than when you started (no perpetual motion machines...). So, the energy required to move a black hole will exceed the energy you can get from a black hole (thereby speeding up your demise). This point is actually why people's belief in mega-strutures like Dysonspheres is ridiculous. The energy needed to create and maintain them exceeds what you can get from the star they surround. But many will consider than an outrageous opinion, and we don't want those around here! :-)

• This is one of the best illustrations (descriptions) of entropy I have seen in a long time. Kudos! and an upvote. It does address the question, not from being opinion-based, but knowledge-based. Not meaning to be facetious in any way, it is worthy. Now, here is the counter, since I don't like angels weeping. Entropy has two sides - not just energy, but work. That is the ultimate objective of harnessing energy. It's not about the energy itself. A universe at entropic equilibrium would still exist, just nothing would happen. A digression - would that just look like a massive black hole? – Justin Thyme Nov 9 '17 at 15:24
• The problem with time approaching infinity, is that it never actually gets there. Therefore, the limit approaches 0, but never quite gets there. I can not help thinking about the tan function - it wraps around infinity and comes out the other side. Consider if there really IS a fundamental unit of time - a true Planck unit of time. When you get to that last 'infinity' unit, there is always one more. – Justin Thyme Nov 9 '17 at 15:31
• But there is an inherent conflict of assumptions - that entropy is the same value (temperature) for every universe (To eliminate potentials), vs every universe has the same total energy (to eliminate potentials). Suppose one universe has enough energy and size to produce an entropic temperature of x, and another universe an entropic temperature of y. There is a potential between the universes that can be exploited. This would mean that ALL universes would have to reach the same entropic temperature. – Justin Thyme Nov 9 '17 at 15:46
• But if they were all different sizes, each would have a different energy LEVEL (bigger universe, greater heat capacity, more energy to maintain a target heat level). Now to save a few angels - is an expanding universe conducive to the concept of zero entropy? Would an expanding universe upset the equilibrium between two universes? Would a disequilibrium between universes expanding at different rates eventually produce an entropic potential? At T=infinity, would the universes have to be totally expanded, or totally collapsed? – Justin Thyme Nov 9 '17 at 15:53
• Anecdotally, we had a classic safety lecture about your 10,000 volt bias. A certain wanabe electrician was working on a circuit that he thought was 110Vac. That's what he measured across the terminals. Then, he connected the neutral (or what he thought was neutral) to ground. Typical procedure, usually, but some bright efficiency expert, when wiring the circuit, decided to not use a transformer, and just connected between a 1,000 volts and a 1,110 volts line. Crispy critters. Never assume. – Justin Thyme Nov 10 '17 at 2:58