No Boundry Proposal: Hartle & Hawking's Theory Explained

[Jarwulf]

Does Hartle and Hawking's no boundary theory mean that the time we're familiar with doesn't exist and that the universe is basically a bubble with our past and future selves existing simultaneously with us?

 

[Chalnoth]

Does Hartle and Hawking's no boundary theory mean that the time we're familiar with doesn't exist and that the universe is basically a bubble with our past and future selves existing simultaneously with us?

Well, no. What you're talking about here is just a consequence of basic relativity.

In essence, in both special and general relativity, there is no such thing as a global "now". If one observer sees two events separated by some distance as being simultaneous, then another observer will, in general, not interpret those events as occurring at the same time. This means that there is no fundamental way of saying that different events separated by some distance happened at the same time: whether or not they did happen at the same time depends upon the observer.

So, one way you could think of this is that the entire universe is a 4-dimensional configuration, and we experience 3-dimensional slices of this configuration in sequence, one after the other. Which 3-dimensional slices we experience depends upon how we move through it.

 

[Naty1]

Seems like the no boundary proposal has nothing to do with your description unless I am missing something. The no boundary proposal has to do with geometries at singularities in which right after the big bang, Riemann geometrry which closes off the singularity transitions to Lorentzian...(in other words, in really highly curved space, this is a clever mathematical approach to avoid a "point" singularity...and eliminate infinities.)

but there IS a superposition of spacetimes and maybe that's what you are addressing. But what little I underastand about it is that these exist at the singularity and its immediate vicinity' a classical Lorentzian geometry dominates away fromthe singularity...

You can read some commentary and criticisms/objections by Roger Penrose, The Road to Reality beginning at page 770...but the mathematical references and descriptions are PHD level...

 

[Jarwulf]

Well, no. What you're talking about here is just a consequence of basic relativity.

In essence, in both special and general relativity, there is no such thing as a global "now". If one observer sees two events separated by some distance as being simultaneous, then another observer will, in general, not interpret those events as occurring at the same time. This means that there is no fundamental way of saying that different events separated by some distance happened at the same time: whether or not they did happen at the same time depends upon the observer.

So, one way you could think of this is that the entire universe is a 4-dimensional configuration, and we experience 3-dimensional slices of this configuration in sequence, one after the other. Which 3-dimensional slices we experience depends upon how we move through it.

This is what confuses me, does relativity require that the reality of the universe literally be one where the entire past present and future is frozen in a block, or one where there is a 4d space is sprinkled with predetermined paths where each object moves with all its past and future selves or is this simply a convenient way of representing things?

 

[Chalnoth]

This is what confuses me, does relativity require that the reality of the universe literally be one where the entire past present and future is frozen in a block, or one where there is a 4d space is sprinkled with predetermined paths where each object moves with all its past and future selves or is this simply a convenient way of representing things?

Well, you're sort of mixing two somewhat different things here. In General Relativity, there are no separate paths, there is just one universe. In GR, if you perfectly knew the state of the universe at one time, you could in principle calculate the state of the universe forever before or after that time.

In quantum mechanics, this doesn't really change a whole lot, except that specifying the entire state of the universe requires specifying the entire wavefunction of the universe at a given time (as opposed to just the positions, masses, and velocities of every particle in the universe in GR). This wavefunction includes an infinite number of classical worlds.

One thing to note here is that as I stated earlier, there is no global now, so the statement "at a given time" should be taken to mean that you define a three-dimensional slice through the universe, and call that your "reference time", computing everything based upon it. Typically we choose such slices to accord with the way we experience time.

 

[Jarwulf]

Well, you're sort of mixing two somewhat different things here. In General Relativity, there are no separate paths, there is just one universe. In GR, if you perfectly knew the state of the universe at one time, you could in principle calculate the state of the universe forever before or after that time.

In quantum mechanics, this doesn't really change a whole lot, except that specifying the entire state of the universe requires specifying the entire wavefunction of the universe at a given time (as opposed to just the positions, masses, and velocities of every particle in the universe in GR). This wavefunction includes an infinite number of classical worlds.

One thing to note here is that as I stated earlier, there is no global now, so the statement "at a given time" should be taken to mean that you define a three-dimensional slice through the universe, and call that your "reference time", computing everything based upon it. Typically we choose such slices to accord with the way we experience time.

I wasn't actually referring to QM just whether a block universe either with objects frozen as 4d structures in a 4d block or divided into all its past and future counterparts moving along a 'timeline' through a 4d 'block' was a necessary reality of relativity or just a way to represent things and time need not actually be the same thing as a spatial dimension.

 

[TimBowe]

The No boundary condition...

A quantum hypothesis for the origin of the universe, as an alternative to either infinite existence or creation out of a singularity. It proposes that time and space were initially merged as a single entity, to form a closed finite surface with no boundary. This would be associated with multiple histories, to describe all possible universes which could arise, and it is among those based on imaginary time that the higher probabilities of matching our universe are found. Such a universe would have many attractive features.

 

[Chalnoth]

I wasn't actually referring to QM just whether a block universe either with objects frozen as 4d structures in a 4d block or divided into all its past and future counterparts moving along a 'timeline' through a 4d 'block' was a necessary reality of relativity or just a way to represent things and time need not actually be the same thing as a spatial dimension.

It's basically a requirement of the fact that there is no global "now".

 

[Jarwulf]

It's basically a requirement of the fact that there is no global "now".

But wouldn't that mean there was a global now in a sense since an hypothetical external viewer could see all the past and future selves of all objects existing simultaneously?

 

[Chalnoth]

But wouldn't that mean there was a global now in a sense since an hypothetical external viewer could see all the past and future selves of all objects existing simultaneously?

No, because time is a direction within the space-time. There is no "super time" that exists outside.

 

[Dmitry67]

I am confused by the diagram in the lower-right corner.
Why do we use imaginary time only for the beginning of the Universe?
What happens if we do the same for the whole history?

So, Hawking says that the BB singularity is not a real one and we can get rid of it using some mathematical transformation?

 

[Chalnoth]

So, Hawking says that the BB singularity is not a real one and we can get rid of it using some mathematical transformation?

Well, it is definitely a proposal of different physics, not just a mathematical transformation of current physics. It's just proposing that it is conceivable you might have a beginning without an actual singularity.

 

[Dmitry67]

I understand, but how it is different from say Kruskal–Szekeres coordinates? They also create some 'imaginary' time and get rid of the singularity on the horizon?
(Crying to Hawking with a voice of Homer Simpson: boooring! :) )

 

[Chalnoth]

I understand, but how it is different from say Kruskal–Szekeres coordinates? They also create some 'imaginary' time and get rid of the singularity on the horizon?
(Crying to Hawking with a voice of Homer Simpson: boooring! :) )

Well, the difference is that the "singularity" at the horizon of a black hole is a coordinate artifact, not a real singularity (the curvature doesn't do anything strange at the horizon of a black hole). The singularity in the finite past for any universe obeying General Relativity is coordinate-independent (which is one big reason why I think GR must break down on small scales).

 

[Dmitry67]

I am also confused by the word "imaginary"

First of all, our normal time is sort of "imaginary" because our space is pseudo-euclidean.
Is Hawking "imaginary" time because it is "differently scaled" (but collinear) to the "real" one?

Or it is imaginary because the ratio to real time is "i"? In that case "imaginary" "imaginary" time is real time :) so there is 4D *euclidean* space, but there is a *illusionary* property called "time", which emerges at macroscopic level and is perceived by the observers, and for some reason, the direction of that "time" is *i (imaginary) to the real one?

 

[Chalnoth]

I am also confused by the word "imaginary"

Edit: I looked into this a tiny bit more, and apparently at the heart of the no boundary proposal is the proposal that time is a complex number, with the line we call time being the real part of the number. Apparently, if time is a complex number, then there is no big bang singularity any longer.

 

[TimBowe]

The No boundary condition...

The most potent and elegant reformulation and extension of the quantum cosmology approach of Wheeler and de Witt concerning the wave function of the quantum spacetime was proposed in 1983 by S.W. Hawking and J.B. Hartle and goes by the name of the No-Boundary Proposal for the wave function. This utilizes the so-called Euclidean approach to quantum gravity, according to which spacetime is replaced by a Riemannian manifold and the signature of the spacetime metric becomes (+, +, +, +,). This may be thought of as going over to imaginary time and it is in this regime that the Universe is supposed to have started from.

 

[Dmitry67]

ok, so in fact it is real time (,+), which is "imaginary" to our imaginary (,-) time.

 

[TimBowe]

The No boundary condition...

The description of black-hole thermodynamics by such path integrals was one of Hawking's original motivations to introduce this proposal, cf. Hawking (1979). The 'no-boundary condition' states that the wave function Ψ is for a compact three-dimensional space Σ given by the sum over all compact Euclidean four-geometries of all topologies that have Σ as their only boundary. This means that there does not exist a second, 'initial', boundary on which one would have to specify boundary data.

 

[marcus]

Stephen Hawking has had some great insights and made important contributions. He deserves our respect.

It encourages disrespect to keep bringing up an unfortunate failed idea of his, from 25 years ago.

The way to show decent respect for Hawking is to avoid mentioning the No Boundary folly and let it be quietly forgotten. For the most part, this is how professional cosmologists behave.

Other great physicists have also had follies. We honor them by remembering their successful ideas and valuable contributions, while overlooking the not-so-valuable.

 

[TimBowe]

The no-boundary condition lies within conventional physics and is consistent with all the known data, it may be dated but it is an ingenious concept.

 

[TimBowe]

Time can behave like another direction in space under extreme conditions.

According to the ideas initiated by J. Hartle and S. Hawking, "the universe, at those extreme densities where its quantum attributes become overwhelming, behaves like a four dimensional ball".

 

[Dmitry67]

Interesting, found in unrelated thread:

Now, I'm sure you are familiar with the formal similarities between the classical diffusion equation and the non-relativistic Schroedinger equation. In fact, mathematically, the *only* difference between the two equations is the fact that the diffusion constant in the Schroedinger equation is complex-valued, whereas in the classical diffusion equation, it is real-valued; and this difference corresponds to wave solutions for the Schroedinger equation, and diffusive solutions for the classical diffusion equation. Moreover, it is well-known that a Wick rotation, t => i*t, of the Schroedinger equation converts it into a diffusion equation (in imaginary-time), while the same Wick rotation converts the classical diffusion equation into a Schroedinger equation (in imaginary-time)

So if our imaginary-valued time is a psycological illusion (as time always points to the direction where entropy increases) and the physical time is real-valued, then all physical, all laws must be reworked, so we will see totally different equations.

So No boundary proposal = sort of Wick rotation?

 

[Dmitry67]

Oops. It is explicitly stated in wiki:

http://en.wikipedia.org/wiki/Wick_rotation

When Stephen Hawking wrote about "imaginary time" in his famous book A Brief History of Time, he was referring to Wick rotation.

 

[Haelfix]

The "No boundary proposal" is really a proposal for a set of initial conditions done in canonical gravity, whereas the wick rotation is just a technical tool utilized to solve the equations (and is the norm in quantum field theory).

It is amongst the few known analytic solutions (along with Vilenkins tunneling solution) for the Wheeler-DeWitt equation and is textbook material by now. The associated analytic continuation issues are still heavily studied and researched.