Could MWI create universes with fundamentally different physical laws?

[PeterDonis]

If this isn't true and a landscape requires multiple Hilbert spaces to be defined

As I understand it, it does; the landscape is equivalent to multiple different vacua in QFT (each individual "universe" in the landscape is equivalent to a different vacuum state), which require multiple Hilbert spaces to be defined.

 

[akvadrako]

As I understand it, it does; the landscape is equivalent to multiple different vacua in QFT (each individual "universe" in the landscape is equivalent to a different vacuum state), which require multiple Hilbert spaces to be defined.

I understand that too, but that those are the outputs of the theory. To be defined at all requires some space to live on.

 

[PeterDonis]

To be defined at all requires some space to live on.

That would be the "space" of all possible vacua, i.e., the landscape. Not a single Hilbert space.

 

[Suekdccia]

Since the MWI is based on a specific set of laws of physics, it can't predict different ones.

The terminology of "parallel universes" and "multiverse" applied to the MWI is very confusing, given that those terms are also used in reference to very different (speculative) theories such as string theory, in which "different universes with different laws of physics" does make sense. But it doesn't in the MWI as used in standard QM.

In that case how could Wheeler refer to MWI when he proposed that there were parallel universes with different fundamental laws? String Theory was hardly developed at that time, so what did Wheeler want to say with this?

That is my point: If "standard" MWI could not produce other universes with fundamentally different laws then what is happening here?

 

[charters]

I think you are just reading into the word "law" too much. In a vacua with 4 spatial dimensions you have an inverse cube "law" instead of an inverse square "law" for massless, unconfined gauge interactions. So that's something we call a law that changes across vacua. But the uncertainty principle or speed of light are laws that must hold in all vacua.

Whether MWI can have very early branching into different vacua does not require string theory per se - its conceivable to make this anthropic argument in any form of quantum cosmology/gravity where the universe starts off in a high energy false vacua. String theory just does a somewhat better job at defining the stable and metastable points in the vacuum decay chain.

 

[PeterDonis]

In that case how could Wheeler refer to MWI when he proposed that there were parallel universes with different fundamental laws?

I have no idea. And unfortunately Wheeler is no longer around to clarify the matter.

If "standard" MWI could not produce other universes with fundamentally different laws then what is happening here?

I couldn't say. They were talking about speculations, and advanced speculations at that. I would not spend too much time worrying about it if the speculations don't make sense to you. They weren't trying to do pedagogy. They were speculating.

 

[PeterDonis]

String Theory was hardly developed at that time

Neither was the MWI. As I said, they were speculating.

 

[DarMM]

I mean an instance of a string theory landscape. As in you can describe a landscape as existing on some Hilbert space. If this isn't true and a landscape requires multiple Hilbert spaces to be defined, then this is my misunderstanding

Generally separate vacua live in different Hilbert spaces in QFT and string theory. Placing the landscape in an eternally inflating background permits tunneling into other vacua across a bubble. Of course what vacuum a given bubble has depends on the state of its neighbour at the point of nucleation. In MWI thus when a bubble $A$ nucleates into a bubble $B$ then $B$ will have all vacua since $A$ will have explored all of its states under MWI. Under Copenhagen $B$ will nucleate only into one vacua. However even under Copenhagen as space expands the whole landscape is explored as each vacua will eventually be present in some bubble.

It can be hard to know "properly" the quantum structure of things in String Theory because often the calculations are semi-classical and we don't know the underlying structure of the theory.

To give an example of two Hilbert spaces in a QFT, the $\phi^4$ Hamiltonian:
$$H = \int{\left[\frac{\pi^2}{2} + \frac{\left(\nabla\phi\right)^2}{2} + \frac{m^2 \phi}{2}+ \left(\phi^2 - \nu^2\right)^{2}\right]}$$
can be defined on two separate Hilbert spaces $\mathcal{H}_{\nu}$ and $\mathcal{H}_{-\nu}$ corresponding to the vacuum expectation value of the field, i.e. $\langle\phi\rangle = \pm\nu$. The Hilbert space of one vacuum is utterly disconnected from the other and states cannot unitarily evolve from a state in one Hilbert space to a state in the other. So in a MWI account of this theory the multiverse would not contain both vev values.

You can form a Hilbert space as their direct sum $\mathcal{H} = \mathcal{H}_{\nu} \oplus\mathcal{H}_{-\nu}$. However a state like:
$$\Psi = \Psi_\nu + \Psi_{-\nu}$$
with $\Psi_\nu \in \mathcal{H}_{\nu}$ and $\Psi_{-\nu} \in \mathcal{H}_{-\nu}$, will not represent quantum superposition but simply classical ignorance as to the vacuum. Unitary evolution decomposes on this space (is not ergodic), this what I meant earlier by unitary evolution not giving a transition between vacua. It's a sign that the Hilbert spaces are disconnected and vector sums across them don't correspond to quantum superposition.

So in a QFT the Hamiltonian does not completely fix the quantum theory, there is a choice of Hilbert space. Non-Relativistic QM has only one Hilbert space by the Stone-VonNeumann theorem.

This is also what is going on in QED. Technically states with different charges are actually separate Hilbert spaces.

 

[Michael Price]

In that case how could Wheeler refer to MWI when he proposed that there were parallel universes with different fundamental laws? String Theory was hardly developed at that time, so what did Wheeler want to say with this?

That is my point: If "standard" MWI could not produce other universes with fundamentally different laws then what is happening here?

I only introduced string theory as a modern speculative example. Wheeler was enough of a physicist to know that the setting of physical constants in our laws might one day be revealed to be set by more fundamental laws. In which case MWI would have kicked in and produced universes which have different values for their physical constants.

As has been repeatedly emphasised, he was (and we are) speculating, in time honoured scientific tradition.

 

[akvadrako]

Thanks; this seems like a clear explanation; let me see if I understand what you are saying...

In MWI thus when a bubble A nucleates into a bubble B then B will have all vacua since A will have explored all of its states under MWI. Under Copenhagen B will nucleate only into one vacua. However even under Copenhagen as space expands the whole landscape is explored as each vacua will eventually be present in some bubble.

So in my own words:

• in Copenhagen the universe now exists in one vacua state which eventually transitions into a new one, chosen randomly from the landscape. So the landscape is explored serially; the multiverse only exists over time. Transitions between vacua / Hilbert spaces occur via unitary evolution + collapse.
• in MWI all the vacua now exist - each branch has some vacua. Eventually all those branches will merge and nucleate into a new bubble and all those vacua will again be created in new branches. There are no transitions between Hilbert spaces; the Hilbert space is always the sum of all vacua' Hilbert spaces: no simpler common space is possible.

Unitary evolution decomposes on this space (is not ergodic), this what I meant earlier by unitary evolution not giving a transition between vacua. It's a sign that the Hilbert spaces are disconnected and vector sums across them don't correspond to quantum superposition.

So in a QFT the Hamiltonian does not completely fix the quantum theory, there is a choice of Hilbert space. Non-Relativistic QM has only one Hilbert space by the Stone-VonNeumann theorem.

I see how this can apply to effective field theories, where physicists can basically invent any Hilbert space to work in, even if it doesn't exist in the landscape, and how those won't transition into each other. I guess I understood string theory wrong; I thought all the low-energy vacua were supposed to be dynamically emergent from a simpler background. I do think there is still some hope for that since we don't know if the non-perturbative string theory is a field theory or something like matrix theory; which seems more like NRQM and maybe also only has one Hilbert space.

 

[Suekdccia]

I think you are just reading into the word "law" too much. In a vacua with 4 spatial dimensions you have an inverse cube "law" instead of an inverse square "law" for massless, unconfined gauge interactions. So that's something we call a law that changes across vacua. But the uncertainty principle or speed of light are laws that must hold in all vacua.

Whether MWI can have very early branching into different vacua does not require string theory per se - its conceivable to make this anthropic argument in any form of quantum cosmology/gravity where the universe starts off in a high energy false vacua. String theory just does a somewhat better job at defining the stable and metastable points in the vacuum decay chain.

I am not sure that "speed of light must hold in every vacua" since there are models in string theory where this constant would vary (https://www.dummies.com/education/science/physics/string-theory-and-variable-speed-of-light/)

 

[DarMM]

in Copenhagen the universe now exists in one vacua state which eventually transitions into a new one, chosen randomly from the landscape. So the landscape is explored serially; the multiverse only exists over time

It's explored serially indeed but across space. Let's use a very simple model. Say the universe is originally a region $A$, then it expands to be two causally disconnected region $A\cup B$. $B$ will then have a different string vacuum than $A$ did, but it does depend on the quantum state of matter in $A$ before $B$ nucleated off. Eventually as the universe becomes larger and larger you'll have enough disconnected regions to obtain every vacuum at least once. So you have all vacua living side by side across space in Copenhagen.

However Copenhagen only has one "layout" for the bubble grid, i.e. each bubble $A_i$ has one vacuum $\Omega_i$. Which $\Omega_i$ it has depends the state its neighbour had before it broke off.

In MWI on the other hand there's basically an extra "layer" of bubbles $A_{ij}$ since each bubble will nucleate off several bubbles in different vacua. One for each MWI branch in the bubble.

You could imagine Copenhagen would be a plane of different vacua where as Many Worlds would be a volume.

I see how this can apply to effective field theories

It applies to field theories that are not cutoff as well, i.e. not effective.
Actually usually if you have a cutoff there will be only one Hilbert space like in NRQM.

I do think there is still some hope for that since we don't know if the non-perturbative string theory is a field theory or something like matrix theory; which seems more like NRQM and maybe also only has one Hilbert space

My reading would confirm the same. I think most ideas for non-perturbative string theory have it more like NRQM in this regard. I'll try and find out more.

 

[Michael Price]

In MWI on the other hand there's basically an extra "layer" of bubbles $A_{ij}$ since each bubble will nucleate off several bubbles in different vacua. One for each MWI branch in the bubble.

You could imagine Copenhagen would be a plane of different vacua where as Many Worlds would be a volume.

Which fits with the intuition I expressed earlier, that the MWI universe is a richer place than Copenhagen's.

 

[DarMM]

Which fits with the intuition I expressed earlier, that the MWI universe is a richer place than Copenhagen's.

Not in the space of vacua explored, in both cases all of the vacua are explored, but there are more copies of each vacua at given time in MWI.

 

[Michael Price]

Not in the space of vacua explored, in both cases all of the vacua are explored, but there are more copies of each vacua at given time in MWI.

That's a "no" that sounds like a "yes". What does "explored" mean? Realised?

 

[DarMM]

That's a "no" that sounds like a "yes". What does "explored" mean? Realised?

It's not a no or a yes, it's just an explanation of their differences.

Explored means realized. In Copenhagen all vacua are realized but there aren't as many copies of a given vacua at a specfic time.

 

[Michael Price]

It's not a no or a yes, it's just an explanation of their differences.

Explored means realized. In Copenhagen all vacua are realized but there aren't as many copies of a given vacua at a specfic time.

Some of these "vacua" may be infinitely complex, in which case they (presumably) are not subject to being copied.

 

[DarMM]

Some of these "vacua" may be infinitely complex, in which case they (presumably) are not subject to being copied.

Most calculations show that eventually a vacuum is reached via tunneling as the universe gets larger and more bubbles nucleate off. I'm not sure what you mean by copied. In both MWI and Copenhagen a given vacuum will eventually be obtained.

 

[Michael Price]

Most calculations show that eventually a vacuum is reached via tunneling as the universe gets larger and more bubbles nucleate off. I'm not sure what you mean by copied. In both MWI and Copenhagen a given vacuum will eventually be obtained.

I meant as in a copy existing, not in as being copied by information transfer.

 

[DarMM]

Well in both Copenhagen and MWI the universe will each a point where each vacuum will physically exist in some bubble. MWI will simply have more copies at a given time.

 

[Michael Price]

Well in both Copenhagen and MWI the universe will each a point where each vacuum will physically exist in some bubble. MWI will simply have more copies at a given time.

but a copy will evolve stochastically in Copenhagen, deterministically in MWI, so equivalence of two copies at a later time is broken in Copenhagen..

 

[DarMM]

but a copy will evolve stochastically in Copenhagen, deterministically in MWI, so equivalence of two copies at a later time is broken in Copenhagen..

MWI and Copehagen will differ in how the space of states which are excitations of a given vacuum are explored. MWI will span more of each vacuum's state space.

However in relation to the thread title MWI does not have access to more physical laws than Copenhagen, each will obtain all sets of laws.