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Jarwulf
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Does Hartle and Hawking's no boundry 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.Jarwulf said:Does Hartle and Hawking's no boundry 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 said: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.
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.Jarwulf said: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 said: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.
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.
It's basically a requirement of the fact that there is no global "now".Jarwulf said: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.
Chalnoth said:It's basically a requirement of the fact that there is no global "now".
No, because time is a direction within the space-time. There is no "super time" that exists outside.Jarwulf said: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?
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 said:So, Hawking says that the BB singularity is not a real one and we can get rid of it using some mathematical transformation?
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 said: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! :) )
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.Dmitry67 said:I am also confused by the word "imaginary"
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.
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.
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".
Maaneli said: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)
When Stephen Hawking wrote about "imaginary time" in his famous book A Brief History of Time, he was referring to Wick rotation.
The No Boundry Proposal, also known as the Hartle-Hawking state, is a theory proposed by physicists James Hartle and Stephen Hawking in 1983. It suggests that the universe has no boundaries in space or time, and that time did not exist before the Big Bang. This theory attempts to resolve the issue of the singularity in the Big Bang model.
The No Boundry Proposal differs from other theories, such as the Steady State theory and the Inflationary theory, in that it does not have a beginning or an end. It also does not rely on the concept of time, as it suggests that time did not exist before the Big Bang.
One of the main pieces of evidence that supports the No Boundry Proposal is the Cosmic Microwave Background (CMB) radiation. This radiation is considered the "echo" of the Big Bang, and it is consistent with the predictions of the Hartle-Hawking state. Additionally, the theory has been used to make successful predictions about the universe, such as its overall structure and the amount of dark matter present.
Yes, there have been some criticisms of the No Boundry Proposal. One criticism is that the theory does not explain the initial conditions of the universe, such as why the universe began in a low entropy state. Additionally, some physicists argue that the theory is not testable and therefore cannot be considered a scientific theory.
The No Boundry Proposal has significant implications for our understanding of the universe. It suggests that the universe has no beginning or end, which challenges traditional views of the universe's origin. It also raises questions about the concept of time and how it relates to the universe. Furthermore, if the theory is proven to be true, it could potentially lead to a more complete understanding of the laws of physics and the nature of reality.