A realist takes on quantum mechanics(nature.com)
nature.com
A realist takes on quantum mechanics
https://www.nature.com/articles/d41586-019-01101-0
45 comments
Your equations are for Galilean space, in which your objection is correct; there is no way of distinguishing time from space, making the distinction arbitrary. This was not noticed for a long time. It was hard to tell until we had Einsteinian relativity to compare to. (Galilean space is actually broken in a lot of ways.)
In relativity, those are not the correct equations; the correct equations observe the Minkowski [1] invariant -t^2 + x^2 + y^2 + z^2 staying invariant under all Lorentz transformations, and it's that negative sign before the t^2 that separates time in relativity. Time and space can be mixed in relativity, but they do still retain a distinctiveness; even when they get turned entirely "on their side" as inside a blackhole, time and space are still distinct, just very very twisted relative to the rest of the universe.
[1]: https://en.wikipedia.org/wiki/Minkowski_space#Four-dimension...
In relativity, those are not the correct equations; the correct equations observe the Minkowski [1] invariant -t^2 + x^2 + y^2 + z^2 staying invariant under all Lorentz transformations, and it's that negative sign before the t^2 that separates time in relativity. Time and space can be mixed in relativity, but they do still retain a distinctiveness; even when they get turned entirely "on their side" as inside a blackhole, time and space are still distinct, just very very twisted relative to the rest of the universe.
[1]: https://en.wikipedia.org/wiki/Minkowski_space#Four-dimension...
Another interesting thing to note: because of the negative sign, Minkowski space obeys an inverse triangle law: a straight line is the longest route between two points (in terms of the relativistic interval) rather than the shortest. That is the reason for "time dilation". Clocks don't actually measure "time", they measure the relativistic interval, which just happens to be what we call "time" in our own reference frame.
This insight makes it easier to understand the "twin paradox". If a clock takes any non-inertial trajectory between two events, its path through Minkowski space is shorter than it would be on an inertial (straight-line) trajectory, so the reading on the clock is lower than a clock that travelled on an inertial trajectory (straight line) between the same two events.
This insight makes it easier to understand the "twin paradox". If a clock takes any non-inertial trajectory between two events, its path through Minkowski space is shorter than it would be on an inertial (straight-line) trajectory, so the reading on the clock is lower than a clock that travelled on an inertial trajectory (straight line) between the same two events.
I' repeat the quote:
> Smolin concludes with the implications of all this for our understanding of space and time. He suggests that time is irreversible and fundamental, in the sense that the processes by which future events are produced from present ones are truly basic: they do not need to be explained in terms of more basic ideas. Space, however, is different. He argues that it emerges from something deeper.
Let's call the "truly basic" coordinate magic and the coordinates the "emerges from something deeper" nonmagic.
In Galilean space you can't mix the special and temporal coordinates. The transformation, so they mix the special coordinates when there is a rotation, the time is the same time for everyone.
In the Minkowski space there is 1 time-like component and 3 space-like components, and they are different, because it is not an Euclidean space where the metric is defined by a positive-definite matrix (that is usually take as the identity to make the calculation simpler).
In spite the 1 time-like component and 3 space-like components are somewhat different, they can't be very different because they get mixed with the boost, i.e.
Let's suppose that in your reference frame (ct, x, y, z) time is magic and space is not magic (or the other way around). What happens in a reference frame that is moving at a different speed and the coordinates are (ct', x', y', z')?
Is the new time ct' magic? But ct' is a linear combination of the original magic ct and the nonmagical x. In the original notation, is ct' something "truly basic" or it "emerges from something deeper" or it is a combination? How can it be "truly basic" if the result you get for ct' when you change your reference frame includes "somethin deeper"?
Repeat the analysis for x', y' or z' depending on the direction of the boost.
> Smolin concludes with the implications of all this for our understanding of space and time. He suggests that time is irreversible and fundamental, in the sense that the processes by which future events are produced from present ones are truly basic: they do not need to be explained in terms of more basic ideas. Space, however, is different. He argues that it emerges from something deeper.
Let's call the "truly basic" coordinate magic and the coordinates the "emerges from something deeper" nonmagic.
In Galilean space you can't mix the special and temporal coordinates. The transformation, so they mix the special coordinates when there is a rotation, the time is the same time for everyone.
ct' = ct
x' = x + v/c ct
In the Minkowski space there is 1 time-like component and 3 space-like components, and they are different, because it is not an Euclidean space where the metric is defined by a positive-definite matrix (that is usually take as the identity to make the calculation simpler).
In spite the 1 time-like component and 3 space-like components are somewhat different, they can't be very different because they get mixed with the boost, i.e.
ct' = something(ct) + something (x)
x' = something(ct) + something (x)
Let's suppose that in your reference frame (ct, x, y, z) time is magic and space is not magic (or the other way around). What happens in a reference frame that is moving at a different speed and the coordinates are (ct', x', y', z')?
Is the new time ct' magic? But ct' is a linear combination of the original magic ct and the nonmagical x. In the original notation, is ct' something "truly basic" or it "emerges from something deeper" or it is a combination? How can it be "truly basic" if the result you get for ct' when you change your reference frame includes "somethin deeper"?
Repeat the analysis for x', y' or z' depending on the direction of the boost.
> Your equations are for Galilean space
At first I misread that as "Gallifreyan space", which almost makes sense.
At first I misread that as "Gallifreyan space", which almost makes sense.
The thing with the time dimension is causation. Things that happened at t=0 influence t=1. The x, y, z dimensions have no such property. Stuff that happens on x=0 have no effect on x=1.
Probability and entropy arise as a result of the causative nature of time, thus creating an arrow: "The arrow of time." There is no "The arrow of space."
Probability in mathematics has certain axioms and the equations that arise from these axioms somehow apply very well to the real world. Like theories in physics probability is in itself a theory about the way the world works. It is also the axiomatic basis which we use to verify other theories. We assume probability is true. All other science arises as a result.
Thus with probability being the axiomatic foundation of our sciences there is, as a result, no science behind itself. To use probability to verify theories of physics like gravity is one thing, but then what do we use it to verify the theory of probability itself? Nothing. We just assume it's true.
That being said, I have not read the books described in the article but is understandable why at some point there is no rigor. It's because rigor at this point doesn't exist. When it comes to time, probability and entropy we are at the foundational assumption of all science. The only tools at this point are philosophical conjecture and random speculation.
There is a difference with time and the other dimensions. We can see it with our eyes when we watch the world unfold and entropy rise... we literally have no clue why it's like this, this is one of the fundamental limits of our understanding.
Probability and entropy arise as a result of the causative nature of time, thus creating an arrow: "The arrow of time." There is no "The arrow of space."
Probability in mathematics has certain axioms and the equations that arise from these axioms somehow apply very well to the real world. Like theories in physics probability is in itself a theory about the way the world works. It is also the axiomatic basis which we use to verify other theories. We assume probability is true. All other science arises as a result.
Thus with probability being the axiomatic foundation of our sciences there is, as a result, no science behind itself. To use probability to verify theories of physics like gravity is one thing, but then what do we use it to verify the theory of probability itself? Nothing. We just assume it's true.
That being said, I have not read the books described in the article but is understandable why at some point there is no rigor. It's because rigor at this point doesn't exist. When it comes to time, probability and entropy we are at the foundational assumption of all science. The only tools at this point are philosophical conjecture and random speculation.
There is a difference with time and the other dimensions. We can see it with our eyes when we watch the world unfold and entropy rise... we literally have no clue why it's like this, this is one of the fundamental limits of our understanding.
One key difference is that time has a direction from past to future, while space doesn't.
That is true, but it's not related to this problem. One important point is that you can't replace the "something" in the equation with whatever you like, for example something2 must be always smaller than something1 (if you add a few c here and there to have the correct units).
If you select an event (i.e. a particular point of space, in a particular time) there is a cone of future events and a cone of past events and a region with the remainder events. The transformations don't change the future and past cones, but they mix space and time, so they must be mixable.
If you select an event (i.e. a particular point of space, in a particular time) there is a cone of future events and a cone of past events and a region with the remainder events. The transformations don't change the future and past cones, but they mix space and time, so they must be mixable.
At a cosmic level, space doesn't either. We're all affected by the big bang and can't go back.
At small scales there are time-reversible (or symmetric) systems called time crystals.
(I am not a physicist, so feel free to refute me.)
At small scales there are time-reversible (or symmetric) systems called time crystals.
(I am not a physicist, so feel free to refute me.)
You can set up the imaginary plane and do transformations like that across it, but imaginary numbers and reals still have demonstrably different natures.
I'm afraid, you infer too much from a mathematical formalism that is only good for calculations.
No. I infer this from the experimental results that say that[1] there is no preferred inertial reference frame, the speed of light is the same constant in all of them, and to change from a the coordinate system from a inercial reference frame to another inertial reference frame that is moving with a constant velocity you must use the Lorentz transformations that mix the spatial and temporal coordinates, and this transformation and other similar results in Special Relativity are verified experimentally [1].
[1] In a small scale and where gravity is small enough to ignore General Relativity. But General Relativity doesn't solve the mixing problem, it make it worst.
[1] In a small scale and where gravity is small enough to ignore General Relativity. But General Relativity doesn't solve the mixing problem, it make it worst.
I feel like when people say ‘realist’ in this context, they mean someone who believes that ordinary intuitions about the way the world works are how the world must work at all levels. And there is no reason to believe that our minds were evolved to understand reality at anything but the macro level.
I’ve long thought that the study of physics at the extremes is as much a study of the human mind and what we’re capable of comprehending as it is a probe of fundamental reality. Which is to say that experiments are essentially a chain of processes by which we translate information from whatever we’re studying into a form capable of being understood by our mind — often translating it into something visual so our visual cortex can process it and store it.
But I wonder how much is out there that is simply impossible to transform in such a way.
I’ve long thought that the study of physics at the extremes is as much a study of the human mind and what we’re capable of comprehending as it is a probe of fundamental reality. Which is to say that experiments are essentially a chain of processes by which we translate information from whatever we’re studying into a form capable of being understood by our mind — often translating it into something visual so our visual cortex can process it and store it.
But I wonder how much is out there that is simply impossible to transform in such a way.
Realist in this context refers to the belief that quantum mechanics is an approximation of a deeper deterministic theory in which "god doesn't play dice".
The underlying theory should reproduce all predictions of quantum mechanics in the relevant limit, so it has nothing to do with human understanding at macro level.
Wanting to believe the laws of nature at the lowest level are deterministic is more like a religious belief than anything else at the moment because as of now, there's no experiment which shows that.
By the way, people who use quantum mechanics for practical ends tend to not care whether the dice is really real or "emulated" to give the exact same probability distribution, because to them, this is rather a philosophical question with no practical implications.
The underlying theory should reproduce all predictions of quantum mechanics in the relevant limit, so it has nothing to do with human understanding at macro level.
Wanting to believe the laws of nature at the lowest level are deterministic is more like a religious belief than anything else at the moment because as of now, there's no experiment which shows that.
By the way, people who use quantum mechanics for practical ends tend to not care whether the dice is really real or "emulated" to give the exact same probability distribution, because to them, this is rather a philosophical question with no practical implications.
> I feel like when people say ‘realist’ in this context, they mean someone who believes that ordinary intuitions about the way the world works are how the world must work at all levels.
From the article:
> Like Einstein, Smolin is a philosophical ‘realist’ — someone who thinks that the real world exists independently of our minds and can be described by deterministic laws.
So no, they don’t.
Also, realism is consistent with quantum experiment — non-realism is merely an interpretation that’s had more developers work on it, not somehow a proven component of reality. (Commonly called Copenhagen interpretation; MWI and Bohmian are other interpretations; arguably loop quantum gravity too.)
I agree with Smolin: non-realism is an extraneous assumption meant to preserve locality, but reality is empirically non-local.
Ironically, it’s actually the non-realists who are guilty of what you say — they can’t let go of their Euclidean intuitions, and so come up with nonsense like denying realism. Their entire model is fundamentally predicated on things looking like a smooth Euclidean space at all scales below some threshold — that is, that reality all the way down looks like what we see when we look around.
Non-realists insist on a Euclidean world despite contrary experimental evidence.
If you view energy as distributed across the topology of your space, which often is radically non-Euclidean, you immediately have realism back — the world just is nothing like what’s in front of your eyes. (Enter loop quantum gravity.)
From the article:
> Like Einstein, Smolin is a philosophical ‘realist’ — someone who thinks that the real world exists independently of our minds and can be described by deterministic laws.
So no, they don’t.
Also, realism is consistent with quantum experiment — non-realism is merely an interpretation that’s had more developers work on it, not somehow a proven component of reality. (Commonly called Copenhagen interpretation; MWI and Bohmian are other interpretations; arguably loop quantum gravity too.)
I agree with Smolin: non-realism is an extraneous assumption meant to preserve locality, but reality is empirically non-local.
Ironically, it’s actually the non-realists who are guilty of what you say — they can’t let go of their Euclidean intuitions, and so come up with nonsense like denying realism. Their entire model is fundamentally predicated on things looking like a smooth Euclidean space at all scales below some threshold — that is, that reality all the way down looks like what we see when we look around.
Non-realists insist on a Euclidean world despite contrary experimental evidence.
If you view energy as distributed across the topology of your space, which often is radically non-Euclidean, you immediately have realism back — the world just is nothing like what’s in front of your eyes. (Enter loop quantum gravity.)
> non-realism is an extraneous assumption
Realism is as much an assumption as non-realism. It doesn't feel that way, because realism fits the common sense of some evolved monkeys. Common sense sometimes is correct, sometimes is not. It doesn't really mean anything when we deal with these matters.
In fact, I would argue that Occam's Razor advises us to prefer non-realism. With non-realism, we are restricted to something we know to exist, by virtue of our human experience: our first-person perception of things. The independent reality, or third-person perspective, is undoubtedly a useful model, but we have no empirical data to suggest it is real. In fact, I would argue that quantum mechanic does raise some serious issues w.r.t. the this model.
Btw, this debate is almost as old as human culture. It was already present in Aristotle (materalism) vs. Plato (idealism). You can also find many traces of it in Eastern thought, e.g. the idea of Maya, or the question of: how can you really know if you are dreaming right now?
> not somehow a proven component of reality
There are no proven components of reality. Proof is something possible in the domain of mathematics, if one accepts certain axioms. Science is not in the business of proving things, it is an empirical endeavor. It gives us theories that resist falsification (until seen) + eternal doubt. Once you abandon doubt, you abandon science.
Realism is as much an assumption as non-realism. It doesn't feel that way, because realism fits the common sense of some evolved monkeys. Common sense sometimes is correct, sometimes is not. It doesn't really mean anything when we deal with these matters.
In fact, I would argue that Occam's Razor advises us to prefer non-realism. With non-realism, we are restricted to something we know to exist, by virtue of our human experience: our first-person perception of things. The independent reality, or third-person perspective, is undoubtedly a useful model, but we have no empirical data to suggest it is real. In fact, I would argue that quantum mechanic does raise some serious issues w.r.t. the this model.
Btw, this debate is almost as old as human culture. It was already present in Aristotle (materalism) vs. Plato (idealism). You can also find many traces of it in Eastern thought, e.g. the idea of Maya, or the question of: how can you really know if you are dreaming right now?
> not somehow a proven component of reality
There are no proven components of reality. Proof is something possible in the domain of mathematics, if one accepts certain axioms. Science is not in the business of proving things, it is an empirical endeavor. It gives us theories that resist falsification (until seen) + eternal doubt. Once you abandon doubt, you abandon science.
> Btw, this debate is almost as old as human culture. It was already present in Aristotle (materalism) vs. Plato (idealism).
Materialism vs. idealism is not the same disagreement as realism vs. non-realism. Both materialism and idealism preserve counterfactual definiteness (CFD). The quantum interpretations that give up CFD are a fundamentally new paradigm, and a ridiculous one IMO.
For instance, the mathematical universe hypothesis is a new form of idealism, but it preserves CFD and so is realist.
Materialism vs. idealism is not the same disagreement as realism vs. non-realism. Both materialism and idealism preserve counterfactual definiteness (CFD). The quantum interpretations that give up CFD are a fundamentally new paradigm, and a ridiculous one IMO.
For instance, the mathematical universe hypothesis is a new form of idealism, but it preserves CFD and so is realist.
Thanks you for your reply. I will think more deeply about what you say, but unfortunately I have to work :) A quick reaction follows.
> Materialism vs. idealism is not the same disagreement as realism vs. non-realism.
True, but they are deeply related. Non-realism is only weird if you assume materialism. I'm not sure idealism is sufficiently well-defined that one can say that it preserves (or not) your definition of CFD.
> The quantum interpretations that give up CFD are a fundamentally new paradigm, and a ridiculous one IMO.
How do you interpret delayed-choice quantum eraser experiments? This is not a rhetorical question btw, I am 100% open to reading your take.
> For instance, the mathematical universe hypothesis is a new form of idealism, but it preserves CFD and so is realist.
Only with Tegmarks's later-added assumption that only objects describable by decidable computations are real.
> Materialism vs. idealism is not the same disagreement as realism vs. non-realism.
True, but they are deeply related. Non-realism is only weird if you assume materialism. I'm not sure idealism is sufficiently well-defined that one can say that it preserves (or not) your definition of CFD.
> The quantum interpretations that give up CFD are a fundamentally new paradigm, and a ridiculous one IMO.
How do you interpret delayed-choice quantum eraser experiments? This is not a rhetorical question btw, I am 100% open to reading your take.
> For instance, the mathematical universe hypothesis is a new form of idealism, but it preserves CFD and so is realist.
Only with Tegmarks's later-added assumption that only objects describable by decidable computations are real.
> How do you interpret delayed-choice quantum eraser experiments?
A Bohmian interpretation will suffice to explain how realism tackles it: https://en.wikipedia.org/wiki/Wheeler%27s_delayed-choice_exp...
A Bohmian interpretation will suffice to explain how realism tackles it: https://en.wikipedia.org/wiki/Wheeler%27s_delayed-choice_exp...
> In fact, I would argue that Occam's Razor advises us to prefer non-realism.
Can you list these arguments, please? IMHO, Occam's Razor is at side of realism: our Universe has no bounds in space, in time, and in scale. So, we can predict future of any particle if we will have enough information about it, but we cannot do that with 100% confidence, because Universe is endlessly deep. We can only collect information about particles at our "layer" of Universe only (or "dimension" in terms of String theory). The deeper we will go, the more uncertainty we will have, because particles will be influenced by "layer(s)" ("dimensions") below our.
Can you list these arguments, please? IMHO, Occam's Razor is at side of realism: our Universe has no bounds in space, in time, and in scale. So, we can predict future of any particle if we will have enough information about it, but we cannot do that with 100% confidence, because Universe is endlessly deep. We can only collect information about particles at our "layer" of Universe only (or "dimension" in terms of String theory). The deeper we will go, the more uncertainty we will have, because particles will be influenced by "layer(s)" ("dimensions") below our.
> Can you list these arguments, please?
I can give you mine... Realism argues that we (as minds, let's say) exist within a reality that keeps existing when we are not looking, i.e. that is independent of our own existence. These are two types of entities, mind-body beings such as you and me + the external, persistent material world. If there's just entities like you and me (whatever we are) sharing a collective dream, that is one less type of entity. Occam's Razor advises against the unnecessary propagation of entities in explanatory endeavors.
This of course does not falsify realism, but it demands that it is there only if to explain something that could not be explained otherwise.
> our Universe has no bounds in space, in time, and in scale
Perhaps I don't understand what you mean. I would say that our universe (forgetting MWI stuff) is bounded in time (Big Bang was 13.7 billion years ago), in space (expanding but finite) and in scale (there is such a thing as the fundamental building blocks of matter, maybe they have internal structure, but they seem to be below the level where the concept of "structure" even makes sense -- they are phenomena more than "things").
> So, we can predict future of any particle if we will have enough information about it,
Not really. https://en.wikipedia.org/wiki/Quantum_indeterminacy
> but we cannot do that with 100% confidence, because Universe is endlessly deep.
You are alluding to chaos theory, but quantum indeterminacy is more fundamental than that. Also, nobody knows if the Universe is "endlessly deep", and current empirical evidence points to "it's not".
I can give you mine... Realism argues that we (as minds, let's say) exist within a reality that keeps existing when we are not looking, i.e. that is independent of our own existence. These are two types of entities, mind-body beings such as you and me + the external, persistent material world. If there's just entities like you and me (whatever we are) sharing a collective dream, that is one less type of entity. Occam's Razor advises against the unnecessary propagation of entities in explanatory endeavors.
This of course does not falsify realism, but it demands that it is there only if to explain something that could not be explained otherwise.
> our Universe has no bounds in space, in time, and in scale
Perhaps I don't understand what you mean. I would say that our universe (forgetting MWI stuff) is bounded in time (Big Bang was 13.7 billion years ago), in space (expanding but finite) and in scale (there is such a thing as the fundamental building blocks of matter, maybe they have internal structure, but they seem to be below the level where the concept of "structure" even makes sense -- they are phenomena more than "things").
> So, we can predict future of any particle if we will have enough information about it,
Not really. https://en.wikipedia.org/wiki/Quantum_indeterminacy
> but we cannot do that with 100% confidence, because Universe is endlessly deep.
You are alluding to chaos theory, but quantum indeterminacy is more fundamental than that. Also, nobody knows if the Universe is "endlessly deep", and current empirical evidence points to "it's not".
The very notion of “you and me” is an appeal to realism: without an external world, there is only me — “you” become a figment of my imagination.
Realism explains why my paper a) arrives while I’m asleep and b) sometimes surprises me with the content or by not arriving.
I’ve yet to see a non-realist explanation of my paper that doesn’t seem deeply more convoluted than “someone like me, but not me dropped it off independent of my awareness”.
I’m not saying you can’t make a model out of that, but you quickly arrive at the equivalent of epicycles to explain even basic things like my newspaper arriving (or not).
Also, “quantum indeterminacy” is an assumption, not a proven fact supported by evidence. That’s the exact thing under discussion now: it’s justification as an interpretative assumption.
Realism explains why my paper a) arrives while I’m asleep and b) sometimes surprises me with the content or by not arriving.
I’ve yet to see a non-realist explanation of my paper that doesn’t seem deeply more convoluted than “someone like me, but not me dropped it off independent of my awareness”.
I’m not saying you can’t make a model out of that, but you quickly arrive at the equivalent of epicycles to explain even basic things like my newspaper arriving (or not).
Also, “quantum indeterminacy” is an assumption, not a proven fact supported by evidence. That’s the exact thing under discussion now: it’s justification as an interpretative assumption.
There’s also an “outside the box” problem: in a non-local universe, it may be impossible for you to compute the trajectory of something without perturbing it, eg, because you slightly jiggle all of the electrons everywhere.
So the co-trajectory of your computation and the particle only ever agree by so much: attempts to increase the accuracy of the calculation kick the particle around, rendering it inaccurate.
There’s deep senses in which uncertainty emerges from being part of the system you’re measuring, in any paradigm.
So the co-trajectory of your computation and the particle only ever agree by so much: attempts to increase the accuracy of the calculation kick the particle around, rendering it inaccurate.
There’s deep senses in which uncertainty emerges from being part of the system you’re measuring, in any paradigm.
> With non-realism, we are restricted to something we know to exist, by virtue of our human experience: our first-person perception of things.
Take that to it's logical extreme and you end up with solipsism. Why suppose anything else exists other than your own first person perceptions in this moment? If you allow for other first person perceptions which you don't experience yourself, then why not a world of space and time for those experiences to exist inside of with bodies and everything else that constitutes or supports our first person perceptions?
Take that to it's logical extreme and you end up with solipsism. Why suppose anything else exists other than your own first person perceptions in this moment? If you allow for other first person perceptions which you don't experience yourself, then why not a world of space and time for those experiences to exist inside of with bodies and everything else that constitutes or supports our first person perceptions?
Alternatively, the non-realists prefer to view the Uncertainty Principle as deeply true instead of seeing Special Relativity as deeply false.
Yes — so much so, they added it as an extra assumption to their model.
The original justification is that we have things like Bell’s experiment that say reality is non-local or non-deterministic, because they exclude local determinism.
But since then, we’ve found increasing evidence that it’s non-local, and so the choice made for the Copenhagen interpretation, to preserve locality at the cost of determinism, becomes unjustified.
It’s now included as an extra assumption out of tradition, and because no one wants to seriously rewrite things. However, as Smolin contends, that may be a dead-end intellectually and an impediment to unifying QM with relativity.
A non-local, but real QM interpretation has a more straightforward paradigm to merge with relativistic gravity: it aligns their models philosophically.
The original justification is that we have things like Bell’s experiment that say reality is non-local or non-deterministic, because they exclude local determinism.
But since then, we’ve found increasing evidence that it’s non-local, and so the choice made for the Copenhagen interpretation, to preserve locality at the cost of determinism, becomes unjustified.
It’s now included as an extra assumption out of tradition, and because no one wants to seriously rewrite things. However, as Smolin contends, that may be a dead-end intellectually and an impediment to unifying QM with relativity.
A non-local, but real QM interpretation has a more straightforward paradigm to merge with relativistic gravity: it aligns their models philosophically.
I'm reading the book. By 'realist', Smolin means that science shouldn't be satisfied with wave function collapse, which he nicely illustrates with Schrödinger's thought experiment of a cat in box. He's not at all disputing that observations of quantum behavior are surprising and counter-intuitive, but he rejects interpretations that require us to distinguish "measurements from other processes in nature".
> But I wonder how much is out there that is simply impossible to transform in such a way.
Given transformations are mathematical, the only way "phenomena that are impossible to transform" is not the empty set is if there are non-mathematical phenomena.
So my bet is that the set is empty.
Given transformations are mathematical, the only way "phenomena that are impossible to transform" is not the empty set is if there are non-mathematical phenomena.
So my bet is that the set is empty.
In this thread, a bunch of people who don’t know about Gödel’s Incompleteness Theorem and the halting problem. Math can’t do everything, guys.
The halting problem is not a problem, one doesn't gain anything by solving it and there's no requirement to solve it.
Thanks, I'm very familiar with them both. They're irrelevant unless you can prove some natural phenomenon can solve the Halting problem. I'd love to see that.
You can't make that bet. Mathematics is just a language; if there were phenomena that couldn't be explained by mathematics, they could not be explained at all. And we probably couldn't communicate about them in any consistent manner or conceive of them in a useful way. That doesn't mean these things can't exist, only that we could never be rationally justified in saying that they do.
Thus it is possible that the true nature of reality is forever beyond the reach of human understanding. Of course, that's almost irrelevant to anyone who's trying to advance human understanding rather than, say, command complete mastery over the universe.
Thus it is possible that the true nature of reality is forever beyond the reach of human understanding. Of course, that's almost irrelevant to anyone who's trying to advance human understanding rather than, say, command complete mastery over the universe.
> You can't make that bet. Mathematics is just a language
I surely can make that bet! Calling it "just a language" is seriously understating the implications of language. A language is a structured organization of symbols forming a grammar.
So basically, mathematics is a description of structure. Everything has structure except a true random number generator.
Given the regularity of existence, the unreasonable effectiveness of mathematics, and the fact that a form of mathematical monism adequately explains all of these facts in the most parsimonious fashion, either we are in an exceedingly unlikely zone of stability of a random process (13 billion years running!), or I'm making a pretty safe bet.
I surely can make that bet! Calling it "just a language" is seriously understating the implications of language. A language is a structured organization of symbols forming a grammar.
So basically, mathematics is a description of structure. Everything has structure except a true random number generator.
Given the regularity of existence, the unreasonable effectiveness of mathematics, and the fact that a form of mathematical monism adequately explains all of these facts in the most parsimonious fashion, either we are in an exceedingly unlikely zone of stability of a random process (13 billion years running!), or I'm making a pretty safe bet.
A true random number generator definitely has structure. That's the structure in the definition of randomness.
And I would not take it as a given that the effectiveness of mathematics is in any way unreasonable.
And I would not take it as a given that the effectiveness of mathematics is in any way unreasonable.
> A true random number generator definitely has structure. That's the structure in the definition of randomness.
True randomness has no structure because that's what makes it inherently unpredictable. Don't confuse pseudo-randomness with randomness.
The fact that the output may conform to a distribution over many samples does not necessarily entail it has structure. Whether true randomness actually exists is an open question. The things we model as random variables could easily be pseudo-random variables whose internals we are simply ignorant of, like how quantum uncertainty is eliminated in Bohmian mechanics.
> And I would not take it as a given that the effectiveness of mathematics is in any way unreasonable.
https://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness...
True randomness has no structure because that's what makes it inherently unpredictable. Don't confuse pseudo-randomness with randomness.
The fact that the output may conform to a distribution over many samples does not necessarily entail it has structure. Whether true randomness actually exists is an open question. The things we model as random variables could easily be pseudo-random variables whose internals we are simply ignorant of, like how quantum uncertainty is eliminated in Bohmian mechanics.
> And I would not take it as a given that the effectiveness of mathematics is in any way unreasonable.
https://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness...
True randomness has the structure of randomness. You can measure and identify it. A random number generator will generate numbers at random. That's structure. If you want to think about something without structure, think about what happens inside models that assume a contradiction.
>https://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness....
Oh, argument by meme. I would believe you if maybe you had an XKCD of it.
>https://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness....
Oh, argument by meme. I would believe you if maybe you had an XKCD of it.
> True randomness has the structure of randomness
Stating it as a tautology doesn't make your sentence coherent. Randomness having structure would entail that it's compressible, but randomness is incompressible by definition.
> Oh, argument by meme
I have no idea what you're talking about. I pointed you to the book written by an eminent physicist explaining precisely why mathematics is unreasonably effective if mathematics were not somehow intrinsic to existence.
This addresses not only your assertion that mathematics is not unreasonably effective, but it also supports my point that mathematics is in some way intrinsic.
Stating it as a tautology doesn't make your sentence coherent. Randomness having structure would entail that it's compressible, but randomness is incompressible by definition.
> Oh, argument by meme
I have no idea what you're talking about. I pointed you to the book written by an eminent physicist explaining precisely why mathematics is unreasonably effective if mathematics were not somehow intrinsic to existence.
This addresses not only your assertion that mathematics is not unreasonably effective, but it also supports my point that mathematics is in some way intrinsic.
A random signal is incomprehensible. The fact that the signal is random is not. The medium is not. And you can't have a signal without a medium, so there is always structure.
Mathematicians study randomness, and what they study about it is the structure that it has.
>I have no idea what you're talking about. I pointed you to the book written by an eminent physicist [...]
You pointed me to a wikipedia article which contains right inside it reasonable people who disagree with that point of view. So read what you link.
Mathematicians study randomness, and what they study about it is the structure that it has.
>I have no idea what you're talking about. I pointed you to the book written by an eminent physicist [...]
You pointed me to a wikipedia article which contains right inside it reasonable people who disagree with that point of view. So read what you link.
> A random signal is incomprehensible. The fact that the signal is random is not.
I said incompressible not incomprehensible.
> Mathematicians study randomness, and what they study about it is the structure that it has.
They study the structure of its distribution. That's not the kind of structure that's relevant to the question we're debating here, which is the structure of the process generating the output. True randomness would need infinite structure to describe its infinitely unpredictable output corresponding exactly to its output.
Such a hypothesis should never be preferred over other hypotheses with more concise structure. Therefore, I continue to assert that I would take that bet, and further, that it's a very safe bet.
> You pointed me to a wikipedia article which contains right inside it reasonable people who disagree with that point of view. So read what you link.
Reasonable people whose arguments are unconvincing. You should read some more philosophy of mathematics. There's a reason why Platonism and other forms of mathematical realism are still predominant.
I said incompressible not incomprehensible.
> Mathematicians study randomness, and what they study about it is the structure that it has.
They study the structure of its distribution. That's not the kind of structure that's relevant to the question we're debating here, which is the structure of the process generating the output. True randomness would need infinite structure to describe its infinitely unpredictable output corresponding exactly to its output.
Such a hypothesis should never be preferred over other hypotheses with more concise structure. Therefore, I continue to assert that I would take that bet, and further, that it's a very safe bet.
> You pointed me to a wikipedia article which contains right inside it reasonable people who disagree with that point of view. So read what you link.
Reasonable people whose arguments are unconvincing. You should read some more philosophy of mathematics. There's a reason why Platonism and other forms of mathematical realism are still predominant.
> True randomness has no structure because that's what makes it inherently unpredictable.
That is its structure. "No structure" is a perfectly valid value for "degree of structure". Not seeing that is the same as not seeing that 0 is a perfectly valid number.
Both "no structure" and 0 play their fundamental role as the identity elements in their respective algebraic structures.
That is its structure. "No structure" is a perfectly valid value for "degree of structure". Not seeing that is the same as not seeing that 0 is a perfectly valid number.
Both "no structure" and 0 play their fundamental role as the identity elements in their respective algebraic structures.
> You can't make that bet. Mathematics is just a language
Not just any language. It is an ever-changing, ever-growing language, which always expands along with our understanding of the universe. There is no a priori limit to either the language, or our understanding.
Together, they comprise the infinite sequence of learning, converging towards its limit. Since we live in time, we can only access the approximations, so it will always be true (in this plane of existence) that we cannot know everything, even while our knowledge continues to increase.
Not just any language. It is an ever-changing, ever-growing language, which always expands along with our understanding of the universe. There is no a priori limit to either the language, or our understanding.
Together, they comprise the infinite sequence of learning, converging towards its limit. Since we live in time, we can only access the approximations, so it will always be true (in this plane of existence) that we cannot know everything, even while our knowledge continues to increase.
> Mathematics is just a language
Perhaps, for some definitions of the word 'language,' but by and large this is a gross misconception propagated by (theoretical) physicists and other heavy users of more or less abstract mathematics. (In contrast with those who use mathematics to perform computations, such as engineers; unfortunately, this has also been happening within mathematics itself in regards to the relationship between its different branches.)
Perhaps, for some definitions of the word 'language,' but by and large this is a gross misconception propagated by (theoretical) physicists and other heavy users of more or less abstract mathematics. (In contrast with those who use mathematics to perform computations, such as engineers; unfortunately, this has also been happening within mathematics itself in regards to the relationship between its different branches.)
Mathematics being a language does not preclude it from being a computational or physical process, so I don't know what you're objecting to. Nothing I would assert, anyway.
From the article:
> The book is, however, upbeat and, finally, optimistic. Unapologetically drawing on historical tradition and even modern philosophy, Smolin proposes a new set of principles that applies to both quantum mechanics and space-time. He then explores how these principles might be realized as part of a fundamental theory of nature, although he stops short of supplying details of the implementation.
That's nice. Too bad QM doesn't care about tradition, philosophy, or your feelings.
> Smolin concludes with the implications of all this for our understanding of space and time. He suggests that time is irreversible and fundamental, in the sense that the processes by which future events are produced from present ones are truly basic: they do not need to be explained in terms of more basic ideas. Space, however, is different. He argues that it emerges from something deeper.
Smolin routinely bullshits, and does not back up much with rigorous theory. He attempts to make a name for himself in a publish-or-perish field by getting his ridiculously unsupported and contrarian ideas traction in the press.
In short, he's all talk, with no substance to back it up.
> The book is, however, upbeat and, finally, optimistic. Unapologetically drawing on historical tradition and even modern philosophy, Smolin proposes a new set of principles that applies to both quantum mechanics and space-time. He then explores how these principles might be realized as part of a fundamental theory of nature, although he stops short of supplying details of the implementation.
That's nice. Too bad QM doesn't care about tradition, philosophy, or your feelings.
> Smolin concludes with the implications of all this for our understanding of space and time. He suggests that time is irreversible and fundamental, in the sense that the processes by which future events are produced from present ones are truly basic: they do not need to be explained in terms of more basic ideas. Space, however, is different. He argues that it emerges from something deeper.
Smolin routinely bullshits, and does not back up much with rigorous theory. He attempts to make a name for himself in a publish-or-perish field by getting his ridiculously unsupported and contrarian ideas traction in the press.
In short, he's all talk, with no substance to back it up.
Having read Three Roads to Quantum Gravity, I think there's a lot of substance there. It's a book made to even include high schoolers, so you have to give it some benefit of the doubt.
As per the philosophy question, neither classical mechanics, relativity, or even death cares about what we think. What matters here is how we perceive and understand a concept.
As per the philosophy question, neither classical mechanics, relativity, or even death cares about what we think. What matters here is how we perceive and understand a concept.
In Special Relativity space and time can be mixed (almost interchangeable), like the x, y and z usual coordinates.
If your coordinates and x and t, in a moving system the coordinates x' and t' are
The coordinates in the other system are just linar combinations of your coordinates. So how can be time and space have a different nature?