# Emergent space-time from what?

• I
Gold Member

## 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?

## Main Question or Discussion Point

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?

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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.

Gold Member
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.

Gold Member
Thanks, Demystifier. Food for thought....

Emergent relativity?

ohwilleke
Gold Member
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

Gold Member
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....