Are possibilities endless?

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How many possible sculptures are there, infinite or not?

How many possible inventions are there, infinite or not?

How many possible situations are there, infinite or not?


If possibilities are not infinite, then what particular laws of physics or constants of nature would be the most responsible for defining some such "ultimate" limits?
 

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  • #2
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"inventions" and "situations" are not well defined... you need to come up with a precise definition of those terms if you want to think about this kind of question.

As far as sculptures... yes there are an infinite amount of them. Just think of a sculpture as a closed three dimentional volume and it's obvious there are infinitely many such shapes.
 
  • #3
collinsmark
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Classically the number is infinite. But if we take quantum physics into account, the number may be finite.

The number of possible quantum configurations within a given volume is proportional to the surface area of the horizon bounding the volume in question. And since the observable universe is within a horizon of sorts (the edge of the observable universe, from the perspective of a given observer, can be considered a type of horizon, a finite distance away) the number of configurations of the observable universe is finite.

Therefore it follows that the number of possible configurations of any sculpture, being within the observable universe, is also a finite number. Although that number is vast, for sure.

[Edit: Don't necessarily take this as canon though, it's still an area of active research (Ha! see what I did there: an area of active research. Ha! Okay, I'll be quiet now).]

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If possibilities are not infinite, then what particular laws of physics or constants of nature would be the most responsible for defining some such "ultimate" limits?
Quantum entropy is where you would want to look for such things. Studying the entropy of a black hole might be a good place to start.
 
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  • #5
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Classically the number is infinite. But if we take quantum physics into account, the number may be finite.

The number of possible quantum configurations within a given volume is proportional to the surface area of the horizon bounding the volume in question.
I don't understand why this would be the case. Take a penny placed inside a circle. The penny is the "quanta" and the circle the horizon.

We can start with the penny at the center and begin to create new "sculptures" by moving it incrementally toward the circumference. The first move is halfway to the circumference. For the second move you take the remaining distance, halve it, and move that distance toward the circumference. And so on, according to Xeno. So long as each move is 1/2 the remaining distance, you can never exhaust all the possible "sculptures".

What in quantum physics prevents this from being the case?
 
  • #6
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I'd say possibilities are finite, both classically and quantum mechanically, whether defined or undefined.

Take a blank ordinary photograph with some finite resolution and finite brightness/color range. The number of possible images this photograph can hold is finite, and yet it contains every single thing anyone ever saw and will ever see, ever imagine or dream of. It contains all the movies ever made and all the movies never made. It contains a picture of every planet and sun, a picture of every invention and every situation, real or imaginary, and as seen from every distance and every angle. There is a picture of me riding a horse on the moon, and picture of you playing poker with Newton and Einstein.

The number of combinations within a finite ordinary photograph contains everything and anything, known and unknown, real and imaginary, actual or conceptual, every possible future and all of the past. But however the number of those combinations is large, the possibilities are not really endless.
 
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  • #7
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I'd say possibilities are finite, both classically and quantum mechanically, whether defined or undefined.

Take a blank ordinary photograph with some finite resolution and finite brightness/color range. The number of possible images this photograph can hold is finite, and yet it contains every single thing anyone ever saw and will ever see, ever imagine or dream of. It contains all the movies ever made and all the movies never made. It contains a picture of every planet and sun, a picture of every invention and every situations, real or imaginary, and as seen from every distance and every angle. There is a picture of me riding a horse on the moon, and picture of you playing poker with Newton and Einstein. The number of combinations within this blank photograph contains everything and anything, known and unknown, real and imaginary, actual or conceptual. But however the number of those combinations is large, the possibilities are not really endless.
You're assuming that mapping some physical situation to a digitial photograph is invertible - it isn't. When you take a digital image which is a bitmap as you describe, you're looking at a compressed set of information, and that compression throws away information.
 
  • #8
collinsmark
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I don't understand why this would be the case. Take a penny placed inside a circle. The penny is the "quanta" and the circle the horizon.

We can start with the penny at the center and begin to create new "sculptures" by moving it incrementally toward the circumference. The first move is halfway to the circumference. For the second move you take the remaining distance, halve it, and move that distance toward the circumference. And so on, according to Xeno. So long as each move is 1/2 the remaining distance, you can never exhaust all the possible "sculptures".

What in quantum physics prevents this from being the case?
Great question. I'll try to give it a feeble shot at an answer.

Let me simplify it further by substituting an electron for the penny. And let's say the electron is confined to a hollow sphere (or a box would be fine too. My point is that it's confined within something anyway).

And by the way, it's important that the electron be confined. What I'm about to say doesn't work if you have a truly "free" electron. Which is why I brought up the horizon (of sorts) comprising the boundary of the observable universe.

We also must assume that the electron's energy is finite -- less than some arbitrary value, although that value can be arbitrarily large. It just cannot be infinite. And we have to apply this finite energy rule not just before we observe the particle, but also after. If we allow the electron's energy the possibility of being infinite then what I'm about to say doesn't work either.

With that we can describe the electron's position as the superposition of a finite number of quantum eigenstates. This is the electron's wavefunction.

The fact that we're limiting the electron's energy to be below some arbitrary amount is important here. That means that the electron's wavefunction before or even after measurement must be comprised of the superposition of a finite number of energy eigenstates. That also has an impact on the momentum of the electron; by limiting hte electron's energy, it's momentum can't be infinite either. So the uncertainty in the electron's momentum is finite (not infinite).

If the uncertainty in the electron's momentum is finite, what does that say about the uncertainty in the electron's position, given Heisenburg's uncertainty principle? It means the uncertainty in position must be greater than [STRIKE]zero[/STRIKE] some minimum value. And with that, Xeno's paradox-like exercises fall apart at small distances.

Anyway, the point here is that if you (a) confine an electron to some volume of space, and (b) only allow the electron's energy to be below some specific value (before and after observation -- your equipment used to measure the electron's position for example, cannot have access to infinite amounts of energy), you limit the number of eigenstates that the electron can take on when it is observed. With those restrictions, even when measuring the electron's position, it's wavefunction will still contain some position uncertainty, even immediately after measurement.
 
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  • #9
ZombieFeynman
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Great question. I'll try to give it a feeble shot at an answer.

Let me simplify it further by substituting an electron for the penny. And let's say the electron is confined to a hollow sphere (or a box would be fine too. My point is that it's confined within something anyway).

And by the way, it's important that the electron be confined. What I'm about to say doesn't work if you have a truly "free" electron. Which is why I brought up the horizon (of sorts) comprising the boundary of the observable universe.

We also must assume that the electron's energy is finite -- less than some arbitrary value, although that value can be arbitrarily large. It just cannot be infinite. And we have to apply this finite energy rule not just before we observe the particle, but also after. If we allow the electron's energy the possibility of being infinite then what I'm about to say doesn't work either.

With that we can describe the electron's position as the superposition of a finite number of quantum states. This is the electron's wavefunction.

The fact that we're limiting the electron's energy to be below some arbitrary amount is important here. That means that the electron's wavefunction before or even after measurement must be comprised of the superposition of a finite number of energy eigenstates. That also has an impact on the momentum of the electron; by limiting hte electron's energy, it's momentum can't be infinite either. So the uncertainty in the electron's momentum is finite (not infinite).

If the uncertainty in the electron's momentum is finite, what does that say about the uncertainty in the electron's position, given Heisenburg's uncertainty principle? It means the uncertainty in position must be greater than zero. And with that, Xeno's paradox-like exercises fall apart at small distances.

Anyway, the point here is that if you (a) confine an electron to some volume of space, and (b) only allow the electron's energy to be below some specific value (before and after observation -- your equipment used to measure the electron's position for example, cannot have access to infinite amounts of energy), you limit the number of eigenstates that the electron can take on when it is observed. With those restrictions, even when measuring the electron's position, it's wavefunction will still contain some position uncertainty, even immediately after measurement.
I don't agree with you at all. The difference between a Very Large Number like 10^10^23 and infinity is for the purposes of a physicist negligble. This is precisely the reason why if we have a chunk of copper, we can treat its energy spectrum as a continuum, even though in principle there are finitely many with a finite spacing.
 
  • #10
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You're assuming that mapping some physical situation to a digitial photograph is invertible - it isn't. When you take a digital image which is a bitmap as you describe, you're looking at a compressed set of information, and that compression throws away information.
Zoom is arbitrary. Every distance is included to the smallest details. It's not limited to just actual photographs, but includes abstract representations like diagrams, written symbols and equations. It contains descriptions of photons, unicorns and black holes, the things that can not really be seen. Whether material thing or abstract concept, as long as it is different from "nothing" it can have visual representation, and the number of combinations in even an ordinary photograph already contains them all.
 
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  • #11
collinsmark
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I don't agree with you at all. The difference between a Very Large Number like 10^10^23 and infinity is for the purposes of a physicist negligble. This is precisely the reason why if we have a chunk of copper, we can treat its energy spectrum as a continuum, even though in principle there are finitely many with a finite spacing.
I agree completely that the number is vast. And taking the limits of integration to infinity is a wonderful trick that is particularly useful in solid state physics and any physics that deals with bulk matter/materials.

But I don't think the OP was asking if the number is merely vast. We can all agree that the number of possible sculptures is vast. No, I interpreted the OP as specifically distinguishing vast from infinite.
 
  • #12
ZombieFeynman
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I agree completely that the number is vast. And taking the limits of integration to infinity is a wonderful trick that is particularly useful in solid state physics and any physics that deals with bulk matter/materials.

But I don't think the OP was asking if the number is merely vast. We can all agree that the number of possible sculptures is vast. No, I interpreted the OP as specifically distinguishing vast from infinite.
I suppose that I am trying to hammer home (perhaps more to the OP than to you) that for a physicist the distinction is arbitrary.

EDIT: I should add that I am a humble squalid state physicist and so my viewpoint here may be biased,
 
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  • #13
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But I don't think the OP was asking if the number is merely vast. We can all agree that the number of possible sculptures is vast. No, I interpreted the OP as specifically distinguishing vast from infinite.
Yes, it's either infinite or not. Vast is finite, only a matter of scale. The puzzle is how can a photograph containing only a finite number of possible images hold every image of everything to any arbitrarily, including infinitely, small detail?

You want to cut the distance in half, I move camera there and snap a photo. You keep cutting distance in half to infinity, and every time I follow and make a new photograph (or draw new diagram). And every photograph (or diagram, or equation) was already one of possible images from the very beginning. How can this possibly be, that infinite is included within finite constraints? It looks like infinity can not actually exist, and if we keep zooming in, perhaps the things will simply start repeating after a while.
 
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  • #14
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If the uncertainty in the electron's momentum is finite, what does that say about the uncertainty in the electron's position, given Heisenburg's uncertainty principle? It means the uncertainty in position must be greater than [STRIKE]zero[/STRIKE] some minimum value. And with that, Xeno's paradox-like exercises fall apart at small distances.
So, are you saying it falls apart because we can't measure for certain if the electron has moved 1/2 the remaining distance?
 
  • #15
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If the uncertainty in the electron's momentum is finite, what does that say about the uncertainty in the electron's position, given Heisenburg's uncertainty principle? It means the uncertainty in position must be greater than [STRIKE]zero[/STRIKE] some minimum value. And with that, Xeno's paradox-like exercises fall apart at small distances.
What do you mean by "fall apart"? The paradox is solved, maybe doesn't apply any more?


Anyway, the point here is that if you (a) confine an electron to some volume of space, and (b) only allow the electron's energy to be below some specific value (before and after observation -- your equipment used to measure the electron's position for example, cannot have access to infinite amounts of energy), you limit the number of eigenstates that the electron can take on when it is observed. With those restrictions, even when measuring the electron's position, it's wavefunction will still contain some position uncertainty, even immediately after measurement.
But position uncertainty doesn't imply infinite possible positions. You said the uncertainty is not infinite, so how else could that possibly be other than by the number of possible locations being finite itself?
 
  • #16
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Zoom is arbitrary. Every distance is included to the smallest details. It's not limited to just actual photographs, but includes abstract representations like diagrams, written symbols and equations. It contains descriptions of photons, unicorns and black holes, the things that can not really be seen. Whether material thing or abstract concept, as long as it is different from "nothing" it can have visual representation, and the number of combinations in even an ordinary photograph already contains them all.
You're pretty much talking nonsense.
 
  • #17
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You're pretty much talking nonsense.
What sentence doesn't make sense to you and why? Try to give us an example of something, anything, that can not be visually represented and described within the limits of an ordinary photograph.
 
  • #18
.Scott
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I suppose that I am trying to hammer home (perhaps more to the OP than to you) that for a physicist the distinction is arbitrary.

EDIT: I should add that I am a humble squalid state physicist and so my viewpoint here may be biased,
Even for a state physicist, it is an interesting distinction. Lets say that instead of a sculpture, it's a clock. And instead of the limited area of a box, it is the limited area of the entire universe. Since the clock can only have a limited number of states, what does that say about time?
 
  • #19
ZombieFeynman
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What sentence doesn't make sense to you and why? Try to give us an example of something, anything, that can not be visually represented and described within the limits of an ordinary photograph.
I agree that you're pretty much talking nonsense. Any time we look at something, we use some kind of wave (light, neutrons, electrons, etc). Eventually we will reach the resolution limitations of that wave and not be able to make out anything beyond a certain small scale.
 
  • #20
ZombieFeynman
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Even for a state physicist, it is an interesting distinction. Lets say that instead of a sculpture, it's a clock. And instead of the limited area of a box, it is the limited area of the entire universe. Since the clock can only have a limited number of states, what does that say about time?
Except for me it's not an interesting distinction and I think people on this forum spend entirely too much time muddling around with these things. So much time is spent talking about the twin paradox, quantum zeno paradox, Bell's theorem and other things that make it into the Pop Sci books but which the majority of physicists don't really care much about. Now it's not up to me what people discuss on the Internet. Do what you'd like, think about what you'd like, write about and talk about what you please. But I do wish that the discussions on this forum accurately represented what the interests and specializations of most practicing physicists are. I think that many young people especially get caught with their head in the clouds when they could be actually working their way into one of the relatively well-funded areas of physics. Perhaps the two are NOT mutually exclusive, and perhaps I'm just a crabby graduate student. You shouldn't pay much attention to angry graduate students any way.
 
  • #21
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Any time we look at something, we use some kind of wave (light, neutrons, electrons, etc). Eventually we will reach the resolution limitations of that wave and not be able to make out anything beyond a certain small scale.
If you want to make a sculpture on the scale of neutrons, there is every diagram of it and full description in every language already existing within the number of combinations an ordinary photograph could look like.

How about some new invention involving some yet undiscovered particles? All those descriptions and diagrams already exist and are accounted for as possible images in the number of combinations an ordinary photograph can take. Can you see that is true?
 
  • #22
ZombieFeynman
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If you want to make a sculpture on the scale of neutrons, there is every diagram of it and full description in every language already existing within the number of combinations an ordinary photograph could look like.

How about some new invention involving some yet undiscovered particles? All those descriptions and diagrams already exist and are accounted for as possible images in the number of combinations an ordinary photograph can take. Can you see that is true?
And just how would you make such a sculpture out of neutrons? I don't understand what you're talking about in the rest of your post...
 
  • #23
Evo
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This thread has become endlessly pointless and is closed.
 
  • #24
collinsmark
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So, are you saying it falls apart because we can't measure for certain if the electron has moved 1/2 the remaining distance?
That was just my feeble attempt at describing the limitations of Xeno in a quantum world.

More to the point, it seems that there may be a finite amount of information that can fit into a given volume as .Scott pointed out with the Berenstein bound.
https://en.wikipedia.org/wiki/Bekenstein_bound

And that might be of particular importance if that volume is bounded by a horizon.
http://en.wikipedia.org/wiki/Holographic_principle

[Oops. Sorry Evo. Didn't see you post.]
 
  • #25
Evo
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My bad, I got sidetracked by the dog and forgot to close it.
 

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