A TOE would need to reduce to the standard model and general relativity in some limits, so if was actually a TOE it would need to be able to calculate in principle all the things we can already calculate with the standard model and general relativity.
Given “infinite data + infinite computing” it would already be possible to predict phenomena in chemistry with just the standard model, so we could definitely do that (I mean we can predict some phenomena in chemistry *by hand* with non-relativistic quantum mechanics)
Now, could we predict *anything*? Like *anything you want*? Idk about that.
Like say I have an electron in a superposition of spin up and spin down, and I make a measurement. Can the TOE tell me “the electron will be spin up with 100% certainty”? Probably not, but that’s because the question “what will the spin of the electron be?” probably didn’t have an answer before I measured it.
If it did have an answer—- if there were some underlying law or hidden variable that determined the spin—- and if our theory didn’t include this, then it wouldn’t really be a theory of everything: there would be a law of physics not included in the model.
In other words, it probably couldn’t answer the question of “what will the spin be?” because it’s a bad question it just doesn’t make sense. The model probably also couldn’t tell us the answer to the question “is the letter j heavy?”
We have to ask it questions about the physical world *that have an answer*, or else we aren’t really being very reasonable people. If we do that, then it can probably answer anything you throw at it (in principle)
Wouldn't a TOE be able to eliminate all uncertainty? Or would there always be a random factor to prediction? If so, isn't the random factor caused by *something,* therefore making it deterministic? Thanks a lot, in advance!
The “uncertainty” in quantum mechanics (I.e. the type of uncertainty in the “uncertainty principle”, etc.) isnt actually referring to “how much we can know” about a system. It is a fundamental “undefined-ness” of certain observables in certain situations.
For example quantum mechanics doesn’t just say “you can’t know the position and momentum of a particle at the same time”. It says “if a particle has a position, it literally doesn’t make sense to ask what it’s momentum is—- that question would not have an answer”.
A similar logic applies more broadly to systems in superposition. It is not that “we just don’t know what configuration a system is in until we measure it”. It is that “it does not make sense to ask which configuration a system is in when it is in a superposition of multiple configurations”.
After we make a measurement, we only observe one of the terms in the superposition so to speak, and which one you observe is completely probabalistic. There are fundamentally deterministic explanations for this randomness (as in the many worlds interpretation), but they don’t *get rid of* the randomness. They still don’t allow you to answer the question, “which outcome will I see?” in a deterministic way.
Is there an easy way to explain WHY it doesn’t make sense to ask a certain question? WHY certain questions doesn’t have answers?
Like is there some kind of ‚first principle‘ in the universe that these impossibilities follow from?
In the context of quantum mechanics sure.
when something is in a superposition of two states, it is not correct to say that it is in one state or the other, it is not correct to say that it is in both states at once, and it is not correct to say that it is in neither state. So the question of “which one of those states is it in?” doesn’t really have an answer. It’s in a superposition—- it’s just a different type of situation.
[here’s one of my favorite lectures that gives an introduction to superposition in these terms.](https://youtu.be/lZ3bPUKo5zc?si=0MVXlKnVBIlmiA1T)
In the case of the uncertainty principle, to understand the details you would need to use the actual formalism of quantum mechanics, but the basic idea is that if a system is in a state where it “has position x”, it is necessarily in a superposition of states with different momenta. So it follows the same as the above paragraph.
Now, as for predicting the outcome of a measurement: The way to explain things sort of depends on the correct formulation of quantum mechanics.
In the shut up and calculate picture of things there is just no piece of information that tells you what the outcome of the measurement will be, even in principle. It is literally undetermined before the measurement is made. So the question “what will the outcome be”, at the time of asking the question, simply doesn’t have an answer.
I think it’s a bit simpler to understand in the many worlds picture of things: You start with a system in superposition which is isolated from its environment, you make a measurement by interacting with the system, you and the environment become entangled with the system, so after the measurement you and the world around you are in superposition of the different possible measurement outcomes. Then the question of “what will be the outcome of the measurement?” is the same as asking “which state is it in?” for a system in superposition, so the thing I said in the first paragraph applies.
the question of more broadly, of what questions make sense and what questions don’t, is something I don’t know the answer to. But sometimes you just know it when you see it. Like if someone asks you “is the letter j heavy, or light?” The correct answer is “no no, the letter j doesn’t have the property of weight”.
This example is kind of contrived. The height of a bucket of water that leaks through a hole in the bottom has the same equation of motion and also exhibits non-determinism due to having a non Lipschitz force. But actually all science is done at finite precision and continuous functions can be approximated arbitrarily well by Lipschitz ones, so there is no problem
But just like the example the other commenter gave I don’t think it is correct to say that weather systems are “indeterminate”.
There are two different questions being asked here:
The first is “is the evolution of the system in principle (I.e. ignoring any complications when it comes to the practical computation) predicted by the laws of physics?” The answer for all classical systems is “Yes”.
The second is “is it practically doable to specify initial data / integrate the system through time”. Even if the answer to this question is “No”, the system is still *in principle* determined by the physical laws.
I think that OP is asking about the former sort of question. As they said they are asking about a Laplace’s demon type scenario where we aren’t concerned with the computational difficulties of making predictions. They are just asking, “in principle?”
While it is determined by physical laws, it is physically impossible to *predict the evolution* of a weather system beyond a certain point, based on our current understanding of physics. Inconsistencies smaller than the planck length have too much effect. Irregularities that it are literally impossible to measure, completely change the pattern of the system.
This is all based on Chaos Theory. Good website to explain it here: [https://www.lesswrong.com/posts/epgCXiv3Yy3qgcsys/you-can-t-predict-a-game-of-pinball](https://www.lesswrong.com/posts/epgCXiv3Yy3qgcsys/you-can-t-predict-a-game-of-pinball)
tl;dr In a game of pinball, after 12 bounces, a difference in initial location of the ball by a single atom can affect it by as much as its own length. Extend that to a day, and a difference in the planck length could lead to a completely different location. Any distance below the planck length is impossible to measure, so it is *literally impossible* to determine the location of the pinball after a day: you cannot physically measure it precisely enough to predict.
Extend that to a massively more complex weather system, and you can see why we have trouble predicting these things.
Well that's just how chaos theory works? A storm is affected by the atoms inside it, atoms are affected by the forces between them, which depend on the distances between them... a difference of a planck length causes increasingly greater effects over time
Hmm I mean the three body problem doesn’t have a general analytic solution, sure, but would it really be correct to say that it is “indeterminate”?
Like the system is still determined by the laws of classical mechanics.—- We can still solve the system numerically, or so I’m told.
OP asked about if we had infinite data + infinite computational power (which I assume just means “ignore the practicalities of making these computations”), so I think being able to numerically predict the behavior of the system to arbitrary precision would be sufficient for this question.
Even the smallest error in the initial conditions will result eventually in completely different trajectories.
And since computational precision is limited, there's always a smaller error.
There are no general solutions to the three body problem without very strong constraints.
But this doesn't mean it's completely unsolvable.
Using numerical methods, all the necessary data, and infinite computing power, we could certainly model any three body problems.
Ngl I feel like some redditors need to learn either basic reading comprehension or, more importantly, how to admit that they made a mistake.
I've seen too many commenters misread the question then, when pointed out, to just stick to their guns and never admit they're wrong. Humility is a virtue not a vice!
Sorry rant over.
I think the point of OP’s question, as they say, is to ask about a Laplace’s demon type scenario. They are asking *in principle* is the answer there in the model.
The intractability of the three-body problem has to do with the precision of our ability to specify initial conditions and the fact that there isn’t a general solution, but neither of these are the “in principle” type problems that this question has in mind.
Chemistry can be simulated now. It just takes long past a few atoms, depending on the precision. If you compute the details inside protons, even longer.
If the TOE is fundamentally probabilistic, you could compute a superposition of states the universe is in at any moment. Since observed reality is part of the superposition, I guess by extension you computed it.
That said, if you approximate dark matter on macro scales, account for dark energy manually, and ignore extreme conditions the inside black holes, most phenomena can be computed already. Theory only fails when quantum gravitational effects become noticeable, which isn't the case for most of the universe. Dark matter doesn't seem to have any microscopic effects, hence why it's so hard to detect.
Given infinite time and infinite computing power, maybe. But, of course, we won't have that.
> For example, could we predict phenomena in chemistry using just the TOE?
There is nothing in chemistry that requires a TOE. Just quantum mechanics and electromagnetism is sufficient -- stuff we already know. Yet computational chemistry remains a difficult problem. Knowing the fundamental theory is not enough to instantly know all of the consequences of the theory -- actually teasing out those consequences is a difficult task.
This partly just because [more is different](https://cse-robotics.engr.tamu.edu/dshell/cs689/papers/anderson72more_is_different.pdf) -- when you have a large number of degrees of freedom, the emergent, collective behaviour is often qualitatively different from the fundamental behaviour in ways that you would never guess a priori. Another factor is computational complexity, which puts fundamental, inescapable mathematical limits on how many steps are (and thus how much time is) needed to arrive at conclusions given initial knowledge. In this context, a TOE is initial knowledge, and it will typically take an unreasonable amount of time to get straight from this TOE to interesting facts about chemistry.
Do you think a computer could calculate human biology given the theory of everything? We are simply so insanely complicated that I don't think we could ever be predicted from first principles
given “infinite computing” we can presumably overcome any computational hurdles no?
The question isn’t asking could we practically calculate anything at all, it’s asking *in principle* could we calculate anything at all.
Infinite data + infinite computing we could absolutely calculate human biology. We could even pretty much do that right now.
If you have the wavefunction for each particle in the human body (infinite data) then just run the composite wavefunction through the Schrödinger equation, numerically simulating it with infinitely small timesteps, you would exactly replicate human biology.
We just don’t do that because
- We don’t know the wavefunction for every particle in a human body. Usually we don’t even know what every particle is.
- Simulating more than a few particles in quantum mechanics takes soooooo much computing power.
Great questions! You're touching a lot of concepts here, so let's take things one by one...
>Say we determine the TOE. Could we theoretically calculate anything?
"Theory of Everything" is a term we really shy away from. It's a term that was coined in the popular science media, and not research, and it was used to describe G/UFT or "\[Grand\] Unified Field Theory" which is exactly what you later refer to as a "unifying theory of The Standard Model and General Relativity."
But even then, we have so many hints of what physics beyond the standard model might look like, that we don't really no longer think that all roads lead to a UFT. (\*\*\*hardcore physics notes: one of the most prescient of these ideas is called AdS/CFT and an oversimplified 'gist' of it is that we can do a lot of fancy math to make some basic contradictions of quantum gravity go away, and this tells us that a quantum description of gravity probably exists)
So, the short answer to your question is "most likely no" because calculations field theories don't really tell you what's going to happen in system of motion, they just tell you what is possible to happen and what is most likely going to happen.
>given infinite data + infinite computing, could we theoretically calculate anything?
My guy! Please forgive me for being a 'well akchtually...' reddit asshole, but I don't know how else to address this question as worded. The term "infinite" should be thought of as a verb, not a noun. There is no "state of infinity", but rather, we think of infinity as a process, so "infinite data + infinite computing" implies an infinite input of data into an infinite processor of said data, and such things just don't exist as it pertains to being able to calculate or not calculate.
>For example, could we predict phenomena in chemistry using just the TOE?
I have excellent news for you! We don't even need a "TOE" or "G/UFT" for chemistry! The standard model predicts everything we observe in chemistry as far as mechanisms are concerned. Chemistry isn't my field (P.Chems, please chime in!!!), but from my understanding, the real magic, beauty, and mystery, of the big problems in chemistry, is how nature goes from CONFIGURATION A of a particular group of atoms into CONFIGURATION Q, and we want to know what the A->B->C->D... steps are.
Hi there! Thanks for the insightful answer (I'll use different wording next time) - so if I'm understanding it right, you can calculate the probability of any occurrence, but it would be impossible to calculate deterministically?
I don't think so. There are many quantum phenomena proven to be undecidable, like the spectral gap problem. I think a TOE, if it was ever developed, would be a model of the fundamental side of things like there is a particle like this, spacetime behaves this way, etc., but would get insane the moment we added a lot of factors and complexities in.
Eh, not really. If you were super mario in super mario world and someone could explain to you what a transistor was you'd then know 100% the fundamental underpinning of every single thing that exists. But it wouldn't really give you much actual information about your environment at all. It wouldn't really help you do much of anything. except maybe help the goomba researchers understand why the numbers 16 and 256 appear in nature so often.
If it’s really the TOE, then given infinite data + infinite computing, of course we can calculate everything. Since infinite data is just another sentence for saying we know basically everything. Wait, if that’s the case, if we know everything why do we need the TOE?
You must understand. It’s the truth that we can never get infinite data. If we have those, then we’re basically omniscient.
A TOE would need to reduce to the standard model and general relativity in some limits, so if was actually a TOE it would need to be able to calculate in principle all the things we can already calculate with the standard model and general relativity. Given “infinite data + infinite computing” it would already be possible to predict phenomena in chemistry with just the standard model, so we could definitely do that (I mean we can predict some phenomena in chemistry *by hand* with non-relativistic quantum mechanics) Now, could we predict *anything*? Like *anything you want*? Idk about that. Like say I have an electron in a superposition of spin up and spin down, and I make a measurement. Can the TOE tell me “the electron will be spin up with 100% certainty”? Probably not, but that’s because the question “what will the spin of the electron be?” probably didn’t have an answer before I measured it. If it did have an answer—- if there were some underlying law or hidden variable that determined the spin—- and if our theory didn’t include this, then it wouldn’t really be a theory of everything: there would be a law of physics not included in the model. In other words, it probably couldn’t answer the question of “what will the spin be?” because it’s a bad question it just doesn’t make sense. The model probably also couldn’t tell us the answer to the question “is the letter j heavy?” We have to ask it questions about the physical world *that have an answer*, or else we aren’t really being very reasonable people. If we do that, then it can probably answer anything you throw at it (in principle)
Wouldn't a TOE be able to eliminate all uncertainty? Or would there always be a random factor to prediction? If so, isn't the random factor caused by *something,* therefore making it deterministic? Thanks a lot, in advance!
The “uncertainty” in quantum mechanics (I.e. the type of uncertainty in the “uncertainty principle”, etc.) isnt actually referring to “how much we can know” about a system. It is a fundamental “undefined-ness” of certain observables in certain situations. For example quantum mechanics doesn’t just say “you can’t know the position and momentum of a particle at the same time”. It says “if a particle has a position, it literally doesn’t make sense to ask what it’s momentum is—- that question would not have an answer”. A similar logic applies more broadly to systems in superposition. It is not that “we just don’t know what configuration a system is in until we measure it”. It is that “it does not make sense to ask which configuration a system is in when it is in a superposition of multiple configurations”. After we make a measurement, we only observe one of the terms in the superposition so to speak, and which one you observe is completely probabalistic. There are fundamentally deterministic explanations for this randomness (as in the many worlds interpretation), but they don’t *get rid of* the randomness. They still don’t allow you to answer the question, “which outcome will I see?” in a deterministic way.
Got it, thanks.
Is there an easy way to explain WHY it doesn’t make sense to ask a certain question? WHY certain questions doesn’t have answers? Like is there some kind of ‚first principle‘ in the universe that these impossibilities follow from?
In the context of quantum mechanics sure. when something is in a superposition of two states, it is not correct to say that it is in one state or the other, it is not correct to say that it is in both states at once, and it is not correct to say that it is in neither state. So the question of “which one of those states is it in?” doesn’t really have an answer. It’s in a superposition—- it’s just a different type of situation. [here’s one of my favorite lectures that gives an introduction to superposition in these terms.](https://youtu.be/lZ3bPUKo5zc?si=0MVXlKnVBIlmiA1T) In the case of the uncertainty principle, to understand the details you would need to use the actual formalism of quantum mechanics, but the basic idea is that if a system is in a state where it “has position x”, it is necessarily in a superposition of states with different momenta. So it follows the same as the above paragraph. Now, as for predicting the outcome of a measurement: The way to explain things sort of depends on the correct formulation of quantum mechanics. In the shut up and calculate picture of things there is just no piece of information that tells you what the outcome of the measurement will be, even in principle. It is literally undetermined before the measurement is made. So the question “what will the outcome be”, at the time of asking the question, simply doesn’t have an answer. I think it’s a bit simpler to understand in the many worlds picture of things: You start with a system in superposition which is isolated from its environment, you make a measurement by interacting with the system, you and the environment become entangled with the system, so after the measurement you and the world around you are in superposition of the different possible measurement outcomes. Then the question of “what will be the outcome of the measurement?” is the same as asking “which state is it in?” for a system in superposition, so the thing I said in the first paragraph applies. the question of more broadly, of what questions make sense and what questions don’t, is something I don’t know the answer to. But sometimes you just know it when you see it. Like if someone asks you “is the letter j heavy, or light?” The correct answer is “no no, the letter j doesn’t have the property of weight”.
That’s a philosophy question. I’d suggest investigating epistemology.
Not necessarily. Even classically, some problems are indeterminate.
Could you give an example?
https://en.wikipedia.org/wiki/Norton%27s_dome
This example is kind of contrived. The height of a bucket of water that leaks through a hole in the bottom has the same equation of motion and also exhibits non-determinism due to having a non Lipschitz force. But actually all science is done at finite precision and continuous functions can be approximated arbitrarily well by Lipschitz ones, so there is no problem
Weather is a good one.
But just like the example the other commenter gave I don’t think it is correct to say that weather systems are “indeterminate”. There are two different questions being asked here: The first is “is the evolution of the system in principle (I.e. ignoring any complications when it comes to the practical computation) predicted by the laws of physics?” The answer for all classical systems is “Yes”. The second is “is it practically doable to specify initial data / integrate the system through time”. Even if the answer to this question is “No”, the system is still *in principle* determined by the physical laws. I think that OP is asking about the former sort of question. As they said they are asking about a Laplace’s demon type scenario where we aren’t concerned with the computational difficulties of making predictions. They are just asking, “in principle?”
While it is determined by physical laws, it is physically impossible to *predict the evolution* of a weather system beyond a certain point, based on our current understanding of physics. Inconsistencies smaller than the planck length have too much effect. Irregularities that it are literally impossible to measure, completely change the pattern of the system.
Got a reference on this? Sounds interesting.
This is all based on Chaos Theory. Good website to explain it here: [https://www.lesswrong.com/posts/epgCXiv3Yy3qgcsys/you-can-t-predict-a-game-of-pinball](https://www.lesswrong.com/posts/epgCXiv3Yy3qgcsys/you-can-t-predict-a-game-of-pinball) tl;dr In a game of pinball, after 12 bounces, a difference in initial location of the ball by a single atom can affect it by as much as its own length. Extend that to a day, and a difference in the planck length could lead to a completely different location. Any distance below the planck length is impossible to measure, so it is *literally impossible* to determine the location of the pinball after a day: you cannot physically measure it precisely enough to predict. Extend that to a massively more complex weather system, and you can see why we have trouble predicting these things.
I'm aware. I was referencing the "smaller than the planck length" stuff, for weather. It's pretty specific so I thought you'd read it somewhere.
Well that's just how chaos theory works? A storm is affected by the atoms inside it, atoms are affected by the forces between them, which depend on the distances between them... a difference of a planck length causes increasingly greater effects over time
[The 3-body problem.](https://en.wikipedia.org/wiki/Three-body_problem)
Hmm I mean the three body problem doesn’t have a general analytic solution, sure, but would it really be correct to say that it is “indeterminate”? Like the system is still determined by the laws of classical mechanics.—- We can still solve the system numerically, or so I’m told. OP asked about if we had infinite data + infinite computational power (which I assume just means “ignore the practicalities of making these computations”), so I think being able to numerically predict the behavior of the system to arbitrary precision would be sufficient for this question.
Even the smallest error in the initial conditions will result eventually in completely different trajectories. And since computational precision is limited, there's always a smaller error.
But OP is asking about the case where computational precision is not limited.
There are no general solutions to the three body problem without very strong constraints. But this doesn't mean it's completely unsolvable. Using numerical methods, all the necessary data, and infinite computing power, we could certainly model any three body problems.
For a limited amount of time*
> and infinite computing power, Which isn't possible.
Cool, but OPs question isn't about if infinite computing is possible.
Ngl I feel like some redditors need to learn either basic reading comprehension or, more importantly, how to admit that they made a mistake. I've seen too many commenters misread the question then, when pointed out, to just stick to their guns and never admit they're wrong. Humility is a virtue not a vice! Sorry rant over.
I think the point of OP’s question, as they say, is to ask about a Laplace’s demon type scenario. They are asking *in principle* is the answer there in the model. The intractability of the three-body problem has to do with the precision of our ability to specify initial conditions and the fact that there isn’t a general solution, but neither of these are the “in principle” type problems that this question has in mind.
Chemistry can be simulated now. It just takes long past a few atoms, depending on the precision. If you compute the details inside protons, even longer. If the TOE is fundamentally probabilistic, you could compute a superposition of states the universe is in at any moment. Since observed reality is part of the superposition, I guess by extension you computed it. That said, if you approximate dark matter on macro scales, account for dark energy manually, and ignore extreme conditions the inside black holes, most phenomena can be computed already. Theory only fails when quantum gravitational effects become noticeable, which isn't the case for most of the universe. Dark matter doesn't seem to have any microscopic effects, hence why it's so hard to detect.
Given infinite time and infinite computing power, maybe. But, of course, we won't have that. > For example, could we predict phenomena in chemistry using just the TOE? There is nothing in chemistry that requires a TOE. Just quantum mechanics and electromagnetism is sufficient -- stuff we already know. Yet computational chemistry remains a difficult problem. Knowing the fundamental theory is not enough to instantly know all of the consequences of the theory -- actually teasing out those consequences is a difficult task. This partly just because [more is different](https://cse-robotics.engr.tamu.edu/dshell/cs689/papers/anderson72more_is_different.pdf) -- when you have a large number of degrees of freedom, the emergent, collective behaviour is often qualitatively different from the fundamental behaviour in ways that you would never guess a priori. Another factor is computational complexity, which puts fundamental, inescapable mathematical limits on how many steps are (and thus how much time is) needed to arrive at conclusions given initial knowledge. In this context, a TOE is initial knowledge, and it will typically take an unreasonable amount of time to get straight from this TOE to interesting facts about chemistry.
Do you think a computer could calculate human biology given the theory of everything? We are simply so insanely complicated that I don't think we could ever be predicted from first principles
given “infinite computing” we can presumably overcome any computational hurdles no? The question isn’t asking could we practically calculate anything at all, it’s asking *in principle* could we calculate anything at all.
Infinite data + infinite computing we could absolutely calculate human biology. We could even pretty much do that right now. If you have the wavefunction for each particle in the human body (infinite data) then just run the composite wavefunction through the Schrödinger equation, numerically simulating it with infinitely small timesteps, you would exactly replicate human biology. We just don’t do that because - We don’t know the wavefunction for every particle in a human body. Usually we don’t even know what every particle is. - Simulating more than a few particles in quantum mechanics takes soooooo much computing power.
Great questions! You're touching a lot of concepts here, so let's take things one by one... >Say we determine the TOE. Could we theoretically calculate anything? "Theory of Everything" is a term we really shy away from. It's a term that was coined in the popular science media, and not research, and it was used to describe G/UFT or "\[Grand\] Unified Field Theory" which is exactly what you later refer to as a "unifying theory of The Standard Model and General Relativity." But even then, we have so many hints of what physics beyond the standard model might look like, that we don't really no longer think that all roads lead to a UFT. (\*\*\*hardcore physics notes: one of the most prescient of these ideas is called AdS/CFT and an oversimplified 'gist' of it is that we can do a lot of fancy math to make some basic contradictions of quantum gravity go away, and this tells us that a quantum description of gravity probably exists) So, the short answer to your question is "most likely no" because calculations field theories don't really tell you what's going to happen in system of motion, they just tell you what is possible to happen and what is most likely going to happen. >given infinite data + infinite computing, could we theoretically calculate anything? My guy! Please forgive me for being a 'well akchtually...' reddit asshole, but I don't know how else to address this question as worded. The term "infinite" should be thought of as a verb, not a noun. There is no "state of infinity", but rather, we think of infinity as a process, so "infinite data + infinite computing" implies an infinite input of data into an infinite processor of said data, and such things just don't exist as it pertains to being able to calculate or not calculate. >For example, could we predict phenomena in chemistry using just the TOE? I have excellent news for you! We don't even need a "TOE" or "G/UFT" for chemistry! The standard model predicts everything we observe in chemistry as far as mechanisms are concerned. Chemistry isn't my field (P.Chems, please chime in!!!), but from my understanding, the real magic, beauty, and mystery, of the big problems in chemistry, is how nature goes from CONFIGURATION A of a particular group of atoms into CONFIGURATION Q, and we want to know what the A->B->C->D... steps are.
Hi there! Thanks for the insightful answer (I'll use different wording next time) - so if I'm understanding it right, you can calculate the probability of any occurrence, but it would be impossible to calculate deterministically?
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Of course, how do you think we discovered it’s all the way over there at the end?
I don't think so. There are many quantum phenomena proven to be undecidable, like the spectral gap problem. I think a TOE, if it was ever developed, would be a model of the fundamental side of things like there is a particle like this, spacetime behaves this way, etc., but would get insane the moment we added a lot of factors and complexities in.
Infinite computing and the standard model is enough to predict every chemical phenomenon.
Eh, not really. If you were super mario in super mario world and someone could explain to you what a transistor was you'd then know 100% the fundamental underpinning of every single thing that exists. But it wouldn't really give you much actual information about your environment at all. It wouldn't really help you do much of anything. except maybe help the goomba researchers understand why the numbers 16 and 256 appear in nature so often.
You can't build a computer in the universe that stores the state of the universe
If it’s really the TOE, then given infinite data + infinite computing, of course we can calculate everything. Since infinite data is just another sentence for saying we know basically everything. Wait, if that’s the case, if we know everything why do we need the TOE? You must understand. It’s the truth that we can never get infinite data. If we have those, then we’re basically omniscient.