1. Okay, so we know roughly that there are around 10^89 protons within the universe.

Now lets say that at the point of T=0 any possible outcome was possible but that the initial inflation/BB then set the universe into a pre-determinable course (that is if you could hyperthetically do away with the uncertainty principle)

My question is. mathematically what would you say that the number of possibilites are at T=0. What are the number of possible outcomes. Think about outcomes such as a universe where my front door is green instead of the colour white, which it is. Or another possibility maybe that i have one less atom in my body than i do. Or that a football field has one blade of grass less than it does, or even one of the blades of grass has one atom less than it does.....I hope you know what im getting at here.

The possibilities are definately NOT infinate, as there our universe IS finite. So my question is, at a guess, how many possible possibilities in difference are there ?

2.

3. I suppose we need to first think about the qualities of a "state" of this universe, before you can estimate the possible number of such states.

For starters let's say we disregard particle interaction and all particles are of identical mass and internal properties (energy associated with spin, vibration, ...). A state would then be described by the positions and velocities of all particles within a given space (size of the universe), kind of in the sense of Boltzmann's kinetic theory. If you allow for certain laws of physics, such as conservation and discreteness of energy, we would also have some constraints. For example we would know that the initial energy can be distributed in only so many ways.

Now we try to further qualify our universe. First of all, how do we define the size? If it were infinite, we'd easily arrive at the answer you intially rejected: We would have an infinite number of possibilities. Actually, we have to be careful of "infinite" number of states even in the case of a finite size. Properties that are associated with energy (like velocity) might be discrete and limited, so there is only a limited number of values. But how about space? Is space discrete? Well, if it is, then we need to know the spacing, i.e. the spatial equivalent of a quantum (maybe this is an already settled property and I am just ignorant of the answer). If space is continuous, such that a particle can assume any arbitrary position, the number of possibilities might again be infinite, unless we have some constraints provided by laws of physics. The latter, however, would require that these laws of physics clearly determine a state given the initial conditions, which rules out "chaos".

Having established all the above we then need to look at interaction, e.g. in how many ways can particles combine to atoms, molecules,... how close can they come to each other (limiting space)... and so on

it's hard to grasp the value of 10^89 as a number of particles, but that number is nothing compared to the number of universal states... call it infinite for all I care.

4. Even in a finite set you can have an infinte number of degrees of freedom - so the number of possibilites would be infinite (cue penrose notation etc)

5. Originally Posted by river_rat
Even in a finite set you can have an infinte number of degrees of freedom - so the number of possibilites would be infinite (cue penrose notation etc)
Agreed. If we assume that at T=0 anything could have happened, then anything could have happened.

Of course, if you follow the theories that the universe has blown up before, the question becomes "is this time 'round consistent with the last?"

6. Even in a finite set you can have an infinte number of degrees of freedom - so the number of possibilites would be infinite
Really? That's surprising. Say my universe consists of a finite number of entities and each entity has a finite number of properties, and each property itself can assume a finite number of values (discrete space), and each of those values is itself a finite number,... can the number of possible combinations (i.e. the state of my universe) be infinite?

In other worths, when you say in a finite set you "can" have an infinite number of DOF... what are the conditions for this situation and what exactly is a "finite set"?

7. No. Adding up a static or even dynamic set of finite values will not give you an infinite value. You can never approach infinity in a finite set...such is the nature of infinity.

Thou shalt not question infinity!

8. Except that you're not adding, you're exponentiating.

9. Well, yeah...

Stupid semantics...

Actually, to further my reasoning, if you assume that there are a finite number of combinations, then the end result will always be finite. Until you throw in infinity, the equation remains finite.

Now you could state that an equation grows towards infinity, but that doesn't imply infinity.

10. Ok, so far so good. Now where does "infinity" enter Leohopkins' universe?

Saying "anything can happen at T=0" makes the whole problem seem trivial, nothing left to discuss. So let's say we do have a clearly defined initial condition at T just after 0. Let's also say we have certain laws of physics from that point on. Is the number of possible outcomes at T=1 infinite?

11. Originally Posted by M
Ok, so far so good. Now where does "infinity" enter Leohopkins' universe?

Saying "anything can happen at T=0" makes the whole problem seem trivial, nothing left to discuss. So let's say we do have a clearly defined initial condition at T just after 0. Let's also say we have certain laws of physics from that point on. Is the number of possible outcomes at T=1 infinite?
Dear lord...thank god it's friday...

Okay the only way there could be an infinite number of possible outcomes at T=0 is if the number of possible outcomes remains infinite.

If at T=0 the number of outcomes becomes fixed, then it's finite.

That said, the only way the outcomes could become infinite at T=1 is if they were infinite at T=0. If they were finite at T=0, they'd have to remain finite.

Of course, the likelihood that there are a finite number of outcomes greater than 1 but not infinite, is probably very slim. It is more likely that the outcome is finite, and fixed to one possible outcome alone.

If you assume that at T=0 an infinite number of combinations could occur, that entails that the laws that govern the details after T=0 are created at T=1.

If you assume that at T=0 there is a finite set of combinations because the laws exist already at T=0, then there will be a predictable number of variations, if any. More than likely, if there is a law governing the details at T=0, then T=1 will show only one possible outcome.

Lastly, if you assume that at T=0 there is a finite set of combinations, but the laws that exist at T=0 allow for variant combinations, then at T=1 there will be a finite set of combinations greater than 1 (but, of course, not infinite).

12. Originally Posted by M
Really? That's surprising. Say my universe consists of a finite number of entities and each entity has a finite number of properties, and each property itself can assume a finite number of values (discrete space), and each of those values is itself a finite number,... can the number of possible combinations (i.e. the state of my universe) be infinite?

In other worths, when you say in a finite set you "can" have an infinite number of DOF... what are the conditions for this situation and what exactly is a "finite set"?
Ok i must confess to being lose with the usage of the term degrees of freedom as what i was referring to here is not in the strict sense a count of the number of DOF of the system in question.

What i was doing was counting the number of possible points in the "parameter space". So if any one parameter allows an infinite number of possible entries then the total number of possible initial values would be infinite etc.

13. The degrees of freedom would be much much greater than the numbers of elementary particles, but surely in order to get an infinte number of possibilities then you would also have to make sure that the numbers of sub-atomic particles within any given universe was anything from zero to infinate. Which maybe the case if multiverse theory is true then if the multiverse is contructed in a "serial manner" i.e: a universe is a blackhole inside another black hole, which is inside another black hole. Ad infinitum. Then I suppouse the number could be infinate. However, if the universes are constucted in a parrallel fashion (of which I do not understand) then IMO the numbers of particles within THIS universe would be the same as any other, and you would have the same amount of degrees of freedom within any of the parrallel universes, however the amount of universes, in this instance would most definately be finante, even if the number were in the region of 10^1234513451234561234561234561346 or something stupendous like that.

14. I don't see why that must be true - suppose i give you 2 particles and ask you how many ways can you place those two particles in the universe? Well supposing that space is a continuum then there would be an infinite number of ways of doing that, as there are an infinite number of places to choose from for the second particle after you have placed the first particle.

15. Originally Posted by river_rat
I don't see why that must be true - suppose i give you 2 particles and ask you how many ways can you place those two particles in the universe? Well supposing that space is a continuum then there would be an infinite number of ways of doing that, as there are an infinite number of places to choose from for the second particle after you have placed the first particle.
Good point...but I think you've just drawn up an argument for the existence of rules governing element creation.

16. Well supposing that space is a continuum...
That was exactly my point/question. If space is a continuum, the answer becomes trivial, as there is an infinite number of possible positions between any two non-identical points in space.

We have come a long way from believing that matter and energy are continuous, over simple atomic models, to quantum physics. Could space turn out to be discrete as well?

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