Loop Quantum Gravity (LQG)

Discussion in 'Physics & Math' started by Fork, Aug 15, 2013.

  1. river

    Yet you not read anything about T.T. Brown and/or by Paul LaVioette

    It will give you a different perspective

    Then evaluate

    As mentioned in my post #19 gravity is geometric in GR
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  3. brucep Valued Senior Member

    Based on what?. How would you know if charge is something we have to account for in the metric?

    Sounds like Thomas Valone needs to do his homework. For the Kerr metric solution the angular momentum sums to invariant mass of the system. For the Kerr-Newman metric solution the system charge sums to the invariant system mass the same way the system angular momentum does. If the system is rotating the mass of the system includes the system angular momentum. If the system is rotating with charge >0 then the angular momentum and the charge sum to the invariant system mass. GR isn't a theory of electromagnetism so why do you, or the author of that book, come to the conclusion that GR fails to describe electromagnetic phenomena when it was never meant to do anything of the sort. Yet the electromagnetic phenomena that it does describe [IE the natural path of radiation through the gravitational field and issues associated with system charge] it does so well.
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  5. brucep Valued Senior Member

    Whether I read those things, or not, it isn't going to fix the nonsense you've been posting.
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  7. MarkM125 Registered Senior Member

    Considering this thread is about LQG, I'll type a quick post about the subject.

    What is LQG?

    Loop Quantum Gravity is an attempt to quantize General Relativity by introducing gauge fields (like any QFT) onto a curved background. In doing so, two basic symmetries are demanded of the theory - gauge invariance, and invariance under the diffeomorphism group.

    Most readers are probably familiar with the first, if not, here's the basic idea: A local gauge transformation is a transformation performed on a Lagrangian dependent on the point in spacetime (i.e. it's local). For example, a transformation of the form \( A_\mu \rightarrow A_\mu + \epsilon B_\mu \) (Where \(A_\mu\) is the vector potential. You can verify this by simply plugging this in to the equations giving the E and B fields in terms of the vector potential. ) is a global gauge transformation - it will leave the classical Maxwell Equations invariant, but it doesn't depend on the coordinates. Instead, a local GT will have such a position dependence. The result is then this: the gauge transformations of a particular form (i.e. Multiplication by a unitary matrix) will form a Lie Group, which in tern has several generators. The generators then can be associated with vectors fields, which are then quantized into particles. These particles are then your gauge bosons, such as photons, W bosons, Z bosons, and gluons. For example: the group \( U(1) \) is a symmetry group of QED, and gives rise to the photon and its interactions.

    Diffeomorphism invariance is a property of general relativity. It's the ultimate form of relativity - as long as we perform some continuous deformation of the background spacetime, we still have a consistent theory. Thus, any theory with the spirit of GR should, as is felt by proponents of cannonical approaches to quantum gravity, contain this symmetry. Essentially, DI demands that we construct a theory that has no dependence on the background spacetime. We can associate this mathematical idea with general covariance - choose any frame you wish, and physics is the same.

    Now, one of the critical equations in the field of quantum gravity is the Wheeler-DeWitt equation, taking the form

    \( H \mid \psi \rangle = 0 \)

    Where \( \psi \) is the "wavefunction of the universe", or simply, the quantum representation of one possible state of spacetime. In analogy to quantum mechanics, we should find the solutions to this equation, use them to construct a general Hilbert (or Fock? Not sure) space, and then express the quantum state of spacetime, and hence the gravitational field.

    Following a mathematical reformulation of GR in terms of Ashtekar variables, it was determined that solutions could take the form of "spin netowrks" (see John Baez's page for a ton of info) that evolve in time as "spin foams". Then the dynamics of the gravitational field can be expressed as a superposition of these spin foams. Spin foams can be thought of as the repeated action of a scalar constraint \(\mid \psi (t_{1})\rangle \sim e^{-iH\delta t} \mid \psi (t_{0})\rangle \).

    That's the basic structure. Here are the consequences:

    1. Firstly, the graviton propagator reduces to the inverse square law over long distances.

    2. The symmetries of GR are retained.

    3. The usual action remains, consisting of the Ricci Scalar with additional quantum corrections.

    4. The use of "Wilson Loops" in the theory preserves gauge invariance and results in a minimum area of \( 10^{-66} \) meters squared. The square root is roughly the Planck length.

    If you're interested into delving into the theory, there are various lecture notes on the subject. I'd recommend the one by Pietro Dona and Simmone Spezial.
    Last edited: Aug 17, 2013
  8. Farsight

    Quality post, Mark.

    I'm sorry, Fork, but a "self-excited circuit" doesn't say anything. See this pdf for "Beyond the Black Hole". The eye and the U is in there. I'm not a fan of Wheeler myself.

    Ask Mark about LQG. Ask him what the spin foam is made of.
  9. Fork Banned Banned



  10. Fork Banned Banned

    Non-locality implies that events within a certain space and time are connected to events in another space at the same time or another time (think retrocausality, it flows backward as well as forward). As a path integral, reality as a whole contains information about each and every event taking place at one time and one space and this information propagates outward at the speed of light. So reality "recognizes" itself.
  11. Fork Banned Banned

    Reality is One.
  12. Fork Banned Banned

    Multiple realities can be created by a freely generative cosmic background otherwise known as nothingness/ anythingness.

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