Emergent space-time from what?

[nomadreid]

TL;DR Summary

When one conjectures about emergent spacetime, one usually refers to either the holographic theory (which only reduces the dimensions), or networks of entanglement, or networks of tensors, or strings, or some combination. But it seems that, for all these, there is an underlying basis of quantum states, but quantum states are defined in terms of spacetime. Isn't this circular?

Googling "emergent spacetime" I get lots of articles which offer various conjectures about what that may be; an overview for example is given in http://guava.physics.uiuc.edu/~nigel/courses/569/Essays_Spring2018/Files/gupta.pdf. However, although I understand that emergent spacetime is not yet a solid theory, don't all these conjectures ultimately rest upon information coded in quantum states? But the variables of quantum states include those of space and time, no? I am not qualified to go deeply into all of these theories to unravel the seeming circularity of defining spacetime in terms of spacetime, but perhaps someone could give me a rough outline as to why this is not circular?

While I am at it (might as well get hung for a sheep as for a lamb): using the holographic theory, one ends up with information encoded on the boundary. Can one say that this is generating spacetime, or just reducing the dimensions used in our description of spacetime?

 

[Demystifier]

Why do you think that quantum states are defined in terms of spacetime? The Schrodinger equation
$$H|\psi(t)\rangle=i\hbar\partial_t|\psi(t)\rangle$$
requires time $t$, but, in general, a definition of $H$ does not require space.

 

[nomadreid]

Why do you think that quantum states are defined in terms of spacetime? The Schrodinger equation
$$H|\psi(t)\rangle=i\hbar\partial_t|\psi(t)\rangle$$
requires time $t$, but, in general, a definition of $H$ does not require space.

Ah, interesting point for the time-independent form. I was thinking of things like the time-dependent Schrödinger equation and the Born rule, which are formulated in terms of ψ(r,t).

Even if we only use time, an emergence of spacetime defined in terms of time reduces to an emergence of space, no?

 

[Demystifier]

Even if we only use time, an emergence of spacetime defined in terms of time reduces to an emergence of space, no?

Yes. But note that spacetime is not merely space+time. It is space and time treated on an equal footing, as in relativity theory. So to have an emergent spacetime, you need emergent space + emergent relativity.

 

[nomadreid]

Thanks, Demystifier. Food for thought...

 

[WhatIsGravity]

Emergent relativity?

 

[ohwilleke]

In loop quantum gravity type theories (e.g. causal dynamical triangles), the links between points in space-time are fundamental, and the apparent dimensionality, continuity and locality of space-time are emergent approximations of a network of points and connections.

 

[Fra]

I am not qualified to go deeply into all of these theories to unravel the seeming circularity of defining spacetime in terms of spacetime, but perhaps someone could give me a rough outline as to why this is not circular?

As these are open questions, all research programs has different levels of ambition as far as explanatory depth goes. At best I think one can try to classify the different approaches in categories. Usually emergence implies a starting point yes. Like you "expain" Y in terms of X + some emergence process that has some natural logic. Often statistical or entropic in nature, where emergence may refer to the low energy limit.

But if starting point X, is something even more weird or raising more question than Y in the first place, the explanatory value is questionable.

With string theory the logic is the postulate the existence of something even more complex and unovservable structures, and then explain from there. But without providing a good arguments for the a priori existence of X, except they think it might work. This belongs to one category of attempts. There may not be much circularity here, but there are other problems.

Surely, at least in its standard formulation, QM is in defined presumiing existence of classical observers, and thus classical clocks etc. Ie. QM applies to small subsystems withing the classical world. So in that case it raises circular questions to envision emergence of spacetime from a pure quantum theory. the idea may be possible, but then I do not think it can be emergence from a quantum theory as we know it. It would be a new theory that replaces quantum theory, that would also reduce to "classical quantum theory" in the limit of classical observers, observing a small subsystem

I think the solution out of the circularity is to view it as evolutionary. We do not usually say life is circular, we think of it as evolutionary with small improvements on each cycle.

/Fredrik

 

[nomadreid]

Thanks, Fredrik. That confirms my idea that quantum theory in its present form cannot supply the basis from which spacetime evolved; I am afraid that string theory is a bit beyond me (the popular expositions are not very clear: they either say that spacetime comes from the one-dimensional strings and the p-dimensional branes, which are composed of energy, but since energy is defined in terms of spacetime... or other expositions say that the basis is information, without giving a clear definition of information except maybe as the flip side of entropy or probability, but those refer to events, and events are defined in terms of spacetime, which brings us back to the original problem). So something different, as yet undetermined... I will just have to wait for a Physics Leaky to find the spacetime Mitochondrial Eve...

 

[Fra]

or other expositions say that the basis is information, without giving a clear definition of information except maybe as the flip side of entropy or probability, but those refer to events, and events are defined in terms of spacetime, which brings us back to the original problem).

Genereally distinguishable observable events need no a priori order nor form a continuum. This event set can indexed by the available complexions of the implicit observer (whatever that is).

The agreement of order and dimensionaöity of common 4d spacetime as in formation of equivalence classes that satisfy SR ans GR symmetries in the relevant limit is to be explained.

The headache is how to explain/justify/accept and tame such a wild starting point?
and of course to make it work... ;)

Equivalences are a kind of holographic correspondence but the question and a key point of disagreement is howto understand the nature of the equivalence? Should we understand it as a mathematical constraint(the more common and most conservative view) or as a result of evolution (ie generalisation of equilibration)

/Fredrik

 

[nomadreid]

distinguishable observable events need no a priori order

Interesting. Could you give me a concrete example which either does not involve time, either explicitly or implicitly?

 

[Fra]

Interesting. Could you give me a concrete example which either does not involve time, either explicitly or implicitly?

Beeing very concrete is not that easy in this case, until the problem is solved.

As as we are discussing possible new foundations here, I am not takling about human scientists as observers.
Obviously any human endavour would involve time, which is also the problem.

I am entertaining the idea of an abstraction of an observers, that can generealized beyond the typically imaginable, into something that can serve the purpose of beeing a mathematical block for reconstructing a measurement theory that does not come with the troublesome baggage of classical contex. The foundations of quantum mechanics as it stands, rests on traditional probability theory. And its this connection that makes the quantum formalism dependent on the classical context; as that it where the statistics that define the probability distributions are encoded and processed.

I think one of the most irreducible notions of an observers with minimum complexity is that of distinguishability. A set of discrete observable events does not an a priori metric. Its just a collection of "indexes", without a priori order or distance relation or no notion of neighbourhoods etc, that the observer can separate.

The metric, a priori transition probabilities, and further structures are higher order evolved properties to be explained, one the complexity of the observer grows. In the extrem limit here; we will of course recover a "classical observer" will all the regular notions of time and space. The problem is how to bridge the gap here. Quantum mechanics is a measurement theory formulated from the luxury context of a classical observer. What would the corresponding "optimal inference theory" look like, when formulated from the minimal context of a Planck scale observer? Here I think it is obvious that an preconception of time and space is fallacious.

/Fredrik

 

[nomadreid]

I never assume a human observer; I am, like Hume, a Philosophical Idealist on weekends but in Physics I act as a Philosophical Materialist. That is, allow me to formulate this in very rough analogy to model-theoretic concepts, and based on that, pose two questions. The first question is whether this analogy holds water, or if it doesn't, is it possible to plug up the holes?

The relevant concepts (for better definitions, see any introductory text to Model Theory):
(1) A theory, a collection of well-formed formulas,
(2) A model (aka interpretation) of the theory: a structure composed of (a) a class (universe) of individuals, classes of relations, functions, special classes, (b) an interpretation function between the symbols of the theory and corresponding parts of the elements of those classes, and (c) a lattice of truth values with an assignment of a nonzero value from the lattice to each ordered pair (formula, interpretation of that formula).

A theory can have many models; a frame is a structure of models ("worlds") with an accessibility relationship from one model to the other. (Let us say that two models are adjacent to one another if there is an accessibility relationship between them.)

Applying this to physical concepts, again roughly:

A quantum state of an individual in the universe (of the model) is the collection of sentences in the theory which have nonzero truth values (i.e., are not identical to the minimum of the lattice); a classical state is one in which all sentences are true (i.e., whose truth value is the maximum of the lattice).

Any union of states constitutes information, whereby the distinction between quantum and classical information carries over, which further carries over to the consideration if two individuals are only distinct (different quantum states) or also discernible (i.e., there is a sentence which is true for one and false for the other: measurable.)

An event is a change of classical information from one world to an adjacent world.

An individual present in two adjacent worlds that changes its state in an event, then that individual is an observer, and the change is an observation.

The nature of the accessibility relation determines whether we are referring to spacetime or not. Therefore it is conceivable that there may be some accessibility relation that is more basic than the ones of spacetime.

I just don't know where one would start. That is the second question.

 

[Fra]

The nature of the accessibility relation determines whether we are referring to spacetime or not. Therefore it is conceivable that there may be some accessibility relation that is more basic than the ones of spacetime.

I just don't know where one would start. That is the second question.

Are you saying that for example that if the relations between all the possible descriptions(worldviews/worlds if you prefer) from all the possible observers form an equivalence class that has the properties of SR and GR, then we presume spacetime, otherwise not? Is this a fair summary?

If that is what you mean, then I think that yes there are more basic relations. However, my current understanding insists that these basic relatios does not a priori form an equivalence class, that was my main point. The argument for this, is that existence or rather emergence of equivalences classes is exactly what is to be shown, not assumed.

This will of course lead to "inconsistencies", but these inconsistencies are not necessarily bad if they can be shown to lead to a natural flow forward. Inconsistencies may be responsible for the flow of time.

Where to start is indeed a big problem though. My personal plan is to start at the end of minimum complexity and count on that the possibilities there are finite enough to be able to work out. As complexity grows, larger equivalence classes should form. But at any stage, there will be some "noise" in the system that are due to the inconsistencies, but the vision is that the inconsistencies will be small enough to be handled like we handle noise even in classical mechanics.

/Fredrik

 

[nomadreid]

Are you saying that for example that if the relations between all the possible descriptions(worldviews/worlds if you prefer) from all the possible observers form an equivalence class that has the properties of SR and GR, then we presume spacetime, otherwise not?

No, not exactly. The variables in the sentences I mentioned which serve as the base for the information need not a priori spacetime variables. At the moment they are: Energy, mass, momentum, fields, etc. are all based on spacetime variables, but it is thinkable that there could be other variables, and that spacetime is an emergent property which satisfies our present physical theories. When I said that I didn't know where to start, I meant that I could not imagine what other variables these alternative variables might be, but perhaps that is because I am too tied to the intuition given by the present physics.

these basic relatios does not a priori form an equivalence class

I am not sure where the equivalence classes you are negating come in; equivalence classes will come into any theory which purports to make laws: that is, physical laws are fixed points, the domain of the relation for which a fixed point is defined is thus an equivalence class under a corresponding relation.

This will of course lead to "inconsistencies", but these inconsistencies are not necessarily bad if they can be shown to lead to a natural flow forward. Inconsistencies may be responsible for the flow of time.

That sounds vaguely Hegelian or an argument for paraconsistent logics. . The contradictions I presume you are referring to variations on the quip, “'Time,' he said, 'is what keeps everything from happening at once.'" (attributed to many, many people, but apparently first appearing in 1919 in an otherwise forgettable short story). That is, such sentences as those you are referring to are not contradictions in the strict sense (false in all models) but merely false in a model without time, and true in models with time.

My personal plan is to start at the end of minimum complexity and count on that the possibilities there are finite enough to be able to work out.

Why finite? Axioms of infinity can be viewed as means to be able to have a model with new abilities, including finite ones. For example, the existence of Ramsey cardinals allows the existence of infinitesimals which then can be used to make sense out of differential equations which describe various finite phenomena.

start at the end of minimum complexity

That would be the empty set, no? As ZFC shows, you can do a lot starting from the empty set. Throw in the Axiom of an inaccessible cardinal, and you get most of mathematics... which is then most of physics.

As complexity grows, larger equivalence classes should form.

This sounds like the von Neumann hierarchy. All hail the Power Set!

 

[Fra]

I am not sure where the equivalence classes you are negating come in; equivalence classes will come into any theory which purports to make laws: that is, physical laws are fixed points, the domain of the relation for which a fixed point is defined is thus an equivalence class under a corresponding relation.

Yes exactly. They come in as "observer equivalence".

You can understand this observer equivalence in two ways, and my suggestion here is that the conservative or most common understanding among physicists, that observer equivalence is a hard consistency constraint on any physical law - is limiting us from understanding HOW laws are formed, how laws are actually supported in nature.

That sounds vaguely Hegelian or an argument for paraconsistent logics.

. The contradictions I presume you are referring to variations on the quip, “'Time,' he said, 'is what keeps everything from happening at once.'" (attributed to many, many people, but apparently first appearing in 1919 in an otherwise forgettable short story). That is, such sentences as those you are referring to are not contradictions in the strict sense (false in all models) but merely false in a model without time, and true in models with time.

I was referring to that an idea that cosmological or evolutionary time, is driven by a kind of "inconsistencies", that challenge and cause mutations or the prior logical system. Without such inconsistencies we just have parametertime, or consistent histories, that are timeless, and no cosmologial arrow of time.

The idea here is that the logical system of an observer, is constantly challenged by the environment. I think if you are to compare it to logical systems, then the axioms are a bit like the genes. Logical systems that arent fit, have genes replaced.

At some point we have a system of happily coexisting rather than competing logical systems that constitutes the particle zoo and their relations the laws of physics. But to understad that, we need to understand the process prior to reaching this state.

Why finite?

This is just a regulatory trick when constructing the theory to avoid getting lost in landscapes. I have been thinking for a while on "where to start" as well, and this is the only way I can find. Ie. we need to generalize and constrain at the same time to make progress. To understand continuum models, one must not loose track of their origin. Infinite uncountable sets are not to be thrown around lightly. Sometimes I believe this is what we have done in contemporary physics, and look what we get. Renormalization done backwards in ad hoc ways.

/Fredrik

 

[nomadreid]

a kind of "inconsistencies", that challenge and cause mutations or the prior logical system.

An alternative to positing inconsistencies is to posit that the systems grow until there is a situation described by an undecidable statement, and then time then adds something equivalent to a new axiom, deciding the conundrum (or, if you like the Many-Worlds Interpretation, all situations equivalent to the addition of a deciding new axiom are created)

To understand continuum models, one must not loose track of their origin. Infinite uncountable sets are not to be thrown around lightly.

If one is wary of uncountability, one can simply take advantage of the Skolem paradox, so that one has one's cake (most mathematics that is traditionally based on uncountability) and eat it too (the fact that most mathematics can be done while assuming that the universe is countable; e.g., Gödel's constructible universe L. In fact you have to make quite a stretch to find anything in physics that actually requires any assumption as strong as the existence of a Ramsey cardinal. (I would be happy to be contradicted on this, though.)

 

[Fra]

An alternative to positing inconsistencies is to posit that the systems grow until there is a situation described by an undecidable statement, and then time then adds something equivalent to a new axiom

This would be a different thing, as it would just mean adding more axioms, without having to revise. This will not work in my idea of things.

I am suggesting that axioms may get kicked out, or as i like to think of it informally, they dissipate away beacuse axioms effectively represent how the observers expectation of the environment responds to new information.

Good axioms make the observer more "fit", bad axioms make the observer consistently take bad actions. Usually axioms are free choices, but in this picture things are more subtle. There are axioms which are beneficial, and those that are not.

I don't think axiom sets are the best abstraction here though, the framework to actually communicate and describe this is also an open question for me at least. You need bits and pieces from many parts of foundations.

/Fredrik

 

[nomadreid]

I am suggesting that axioms may get kicked out, or as i like to think of it informally, they dissipate away beacuse axioms effectively represent how the observers expectation of the environment responds to new information.

Good axioms make the observer more "fit", bad axioms make the observer consistently take bad actions. Usually axioms are free choices, but in this picture things are more subtle. There are axioms which are beneficial, and those that are not.

That sounds like AGM: https://plato.stanford.edu/entries/logic-belief-revision/

 

[Fra]

That sounds like AGM: https://plato.stanford.edu/entries/logic-belief-revision/

Yes belief revision is indeed what I am suggesting.

Ie. the "statistical basis" of quantum mechanics that rests on regular probabilit theory can not handle the most general foundational questions, in the observer - observer abstractions. Not even regular bayesian view is sufficient. A new reconstruction of measures of degrees of belief is needed, both for representation of degrees of belief, and the rules for revision. This is at the heart of the trouble of physics.

/Fredrik

 

[windy miller]

In loop quantum gravity type theories (e.g. causal dynamical triangles), the links between points in space-time are fundamental, and the apparent dimensionality, continuity and locality of space-time are emergent approximations of a network of points and connections.

Im not sure I am following this. So are you saying that these theories are saying that certain properties of space-time are not fundamental like locality but other properties are fundamental such as the way they link together? Have I understood that right. How universal is this notion of emergent space time across quantum gravity theories?

 

[Fra]

Im not sure I am following this. So are you saying that these theories are saying that certain properties of space-time are not fundamental like locality but other properties are fundamental such as the way they link together? Have I understood that right. How universal is this notion of emergent space time across quantum gravity theories?

As I understand the essence of Carlo Rovellis relational logic, with both its beauty and flaw, it is roughly this:

A priori, there is no background or observer independent space. All there is are the view of various observers.
Space is rather defined/built only in terms of relations between observers. In particular as physical interactions or communications between observers.

This is so far IMO excellent.

But the IMO flawed step of this logic is when Rovelli in one of this books then throws in this

"But communication is a physical interaction and therefore is quantum mechanical. In particular, it is intrinsically probabilistic."
-- Rovelli, Relational Quantum Mechanics, https://arxiv.org/abs/quant-ph/9609002v2

The problem here, where i lost interest in Rovellis reasoning, is that he simplys "uses the existing QM formalism, uncritically". For me this is not working. But up until that point, what he said is well spoken.

The fallacy is that usage of QM and "probability" implicitly contains already a "background", where the P-foundations are attached. Therefore his argument is not consistent.

/Fredrik

 

[*now*]

"But communication is a physical interaction and therefore is quantum mechanical. In particular, it is intrinsically probabilistic."
-- Rovelli, Relational Quantum Mechanics, https://arxiv.org/abs/quant-ph/9609002v2

The problem here, where i lost interest in Rovellis reasoning, is that he simplys "uses the existing QM formalism, uncritically". For me this is not working. But up until that point, what he said is well spoken.

The fallacy is that usage of QM and "probability" implicitly contains already a "background", where the P-foundations are attached. Therefore his argument is not consistent.

Is there some chance there is more to it than just that description? For instance, could this issue be a question of categories with respect to correspondence with something like functional range or such? For a couple of examples, as well as that description the source linked provides an italicised description, and there is also a description of physics generally.

 

[Fra]

Is there some chance there is more to it than just that description? For instance, could this issue be a question of categories with respect to correspondence with something like functional range or such? For a couple of examples, as well as that description the source linked provides an italicised description, and there is also a description of physics generally.

Not sure what you refer to? As for Rovellis ideas and LQG there are plenty of papers and books.

You can judge a theory in two two ways, either by its de facto success, or by it constructing principles. As most theories on quantum gravity really does not have much hard results that speaks for itself, IMO we need to jugde its constructing principles.

I started to read rovellis book years ago:
https://www.physicsforums.com/threa...able-in-classical-and-quantum-gravity.220841/

and came to a conclusion that while his initial reasoing appears brilliant and is worth reading even if you do not follow hime to the end! His weak spot is that he is far to conservative to have a chance to address all things.

Best is to judge for yourself, starting with his books, he references himself in previously submitted papers on relational QM. Maybe you like it better than I do.

/Fredrik

 

[*now*]

Yes, from the link I think my questions about differing views of qm seems to have been considered to some extent in that thread. Perhaps as well, different types of probability theory or differing background independence definitions might be involved. There seems to be various areas for possible alternatives which could potentially challenge judgements. And, yes I think I do like it.

 

[JRB]

Im convinced ST emerged and is sustained by an infinite higher dimension. QM as it stands is a rough mathematical model of all or part of that infinite dimension but the point has been lost due to the perspective of the physicists involved who believed they were dealing with the small scale basement of ST. Therefore all the mathematics that produced infinities was seen as a terrible mistake and were cut out with renormalisation. CQF puts them back in but then Malacenda turned those infinite degrees of freedom back into a mere spatial dimension, which throws up intriguing ideas but is problematic due to the extra dimension. However if his 4th dimension was actually an aspect or sub-dimension of an infinite dimension it could make more sense. The 2D surface of the Holographic principle infinitely far away would actually be a surface in an infinite higher dimension that is projecting ST. Boundaries between a finite dimensional and an infinite dimensional space are deeply abstract and boggle the mind. We are not equipped for this because our brain and our measuring apparatus are made from and exist in this lower dimension and so we can't directly perceive any higher dimensional phenomena. We only ever see its projection, which we call particles and quantum fields etc. However set theory has demonstrated that we can still think about this formally so there is no reason why we can have a formal physical model of an infinite higher dimension projecting a lower dimensional ST.

 

[WhatIsGravity]

Interesting argument, it will take some thinking upon. But unless we exist in a simulation, or God is real; ‘infinity’, you keep using that word... I do not think that word means what you think it means.

 

[JRB]

Im not sure because I don't know what you think I think it means! :) I am working off the rigorous definition of infinity from set theory, which demonstrates there isn't just one infinity but an infinite hierarchy of infinitely greater infinities, ending in a proper class (an absolute). This of course is counter intuitive but its what the proofs demonstrate. I don't believe in God or we live in a simulation I think that if set theory universe reflects reality in any way then its infinitely more complex and mind boggling than a simulation. But if we could work through the maths for just one infinite higher dimension generating space-time that in itself would be profound. I believe the biggest stumbling block for the last 90 odd years is perspective. We have been trying to stuff an infinite higher dimension into a finite dimension ie reconcile QM with Relativity and wondering why despite so many brilliant minds its still not working.

 

[nomadreid]

an infinite hierarchy of infinitely greater infinities, ending in a proper class (an absolute)

um, there is no maximum to this hierarchy. So it doesn't really "end" in a class, although an infinite hierarchy can be contained in a class. I hope you are not thinking about Cantor's Absolute.

 

[Demystifier]

Im convinced ST emerged and is sustained by an infinite higher dimension. ...

I stopped reading after "Im convinced".

 

[JRB]

I understand Demystifier and others this is my first post on a physics forum and I thought later I shouldn't have said that! :)

 

[JRB]

Yes thanks for that nomadreid its contained and yes I am thinking of Cantor's Absolute, apparently he called it the infinity of infinities. Its paradoxical to talk about bounded infinities even if mathematically they can be tamed but I am thinking from the perspective of the absolute. Does it make any sense to say the infinite hierarchy exists within it, yet the absolute is something beyond, more or different to the hierarchy and so in some sense it does end there, as there is nothing more or beyond the absolute?

 

[nomadreid]

Its paradoxical to talk about bounded infinities

The "paradox" disappears quickly, for example, when you consider that an infinite set is just a set which can be put into one-to-one correspondence with a proper subset. If you are interpreting the word "infinite" as "unattainable" (not to use the word "inaccessible", which is the name of one type of infinite set), then you just need to remember that it is only unattainable using a certain collection of axioms, but is perfectly attainable when you add an appropriate axiom. Also, you may be getting "finite" mixed up with "bounded", which is not the same. A finite set is bounded, but a bounded set need not be finite: bounded will mean that there is something which it is less than, and interpreting "less than" as set membership, since an infinite set can be a member of another set, it is easy to see that an infinite set can be bounded.

yes I am thinking of Cantor's Absolute

That is a problem, since Cantor's Absolute turned out to be rather non-mathematical. There is of course always a kind of absolute from the point of view of a particular theory-model pair, to wit, the universe of that model, but this "relative absolute" was not what Cantor had in mind. For example, the fact that there is no such thing as a greatest ordinal, or Löwenheim-Skolem's upward theorem, and other technicalities made Cantor's idea untenable in mathematics. Of course, the other side of his idea, associating this concept with a divinity, is also outside the realm of mathematics.

Does it make any sense to say

The rest of your questions assume the existence of this Absolute, so since this Absolute is not a tenable notion in mathematics, the answer to those questions is that those assertions do not make mathematical sense. Whether they make some kind of metaphysical sense is not something I would touch upon here.