jby
What does it mean by background independent and background dependent?
Isn't Minkowski spacetime the background for relativity?selfAdjoint said:In a background dependent theory you start with a given space, such as Minkowski spacetime or a Calabi-Yau manifold, and develop your theory with respect to that. In a background independent theory you have no specific spacetime to build your theory in, the spacetime is to be part of the physics and will emerge from your theory when you get it built. This is what Einstein did in general relativity.
Actually, Minkowski spacetime was developed after Einstein published his relativity papers. You can find more information on it here : http://www.geocities.com/ResearchTriangle/System/8956/Bondi/a1.htmIsn't Minkowski spacetime the background for relativity?
That is the background for special relativity. General relativity has no background.jby said:Isn't Minkowski spacetime the background for relativity?
indeed this has motivated theorists attempting to quantize gravity to try background independent approaches----in accord with the theory of gravity (GR) they want to find a quantum version of.Stingray said:That is the background for special relativity. General relativity has no background.
Mike2 said:What is this silliness of quantizing space-time? Quantization is acheived through the eigenvalues of a differential equation of continuous variables. So there must be some background of continuous variables.
I read it. As far as I can tell, Lee Smolin did not go into any detail as to the discrete nature of space and time. How are the discrete portions of the crystal of spacetime connected to the other point/portions?sol2 said:After reading Three Roads to Quantum Grvaity by Lee Smolin, this question ( discreteness and continuity), becomes really interesting in terms of the background.
I believe it was Witten who proved that an expanding universe can only develop from a singularity, from a point. That being the case, if a universe must proceed from a singularity, then all information of any previous parent universe is completely lost. And we will never even in theory be able to prove that there was a parent universe. So why would we bother to entertain such notions?sol2 said:Now you have two choices. Marcus helps to elucidate this question, as it is one of deep copncern. I have been trying to concretize this in conceptualization...
Again the logic here of Venn diagrams is troublesome, in that we have to answer this question. Tis also points ius to the question of the universe and its formation.
Self Adjoint in Mkaku today, speaks to this in energy conservation, and for me, this lays the foundation of the Eykroptic universe, versus the Big Bang.
A very important question. Here's part of my answer:jby said:What does it mean by background independent and background dependent?
Lets give an example to produce some insight thinking?jby said:What does it mean by background independent and background dependent?
Why not say that the micro-gravity of the observer influences the micro-gravity of the quantum particle?Olias said:Now on the Quantum scale there is a loop-hole, the Backgound becomes scale dependant, this is to say that the laws(background) change as one reduces the horizon one looks at. The very act of observation changes the outcome of effects in reduced horizon/domains.
Example, the trajectory of the space-ship is governed by Laws you cannot change in GR, looking at the moon will not alter its Gravitational Orbit.
Now if one looks at a Quantum Particle, the particle moves along by given amount of energy, the energy that one uses to look at a Quantum Particle defines where it exists, and will alter its path/trajectory during observation.
So if one does not look at a Quantum Particle it remains within a confined existence that is independant of the Background, as you move in close to a reduced Quantum domain you produce the dynamics by which the Particle and its path are governed, you are in fact making the Particle dependant on your ability of observing!..Gravity on this Micro Scale is over-ruled by an Observer.
Geometry is determined by the metric, right? So Quantum Gravity is trying to quantize the metric, right? I'm still not sure if that allows propagation of waves. Does a metric exist for all of the underlying spacetime? If not, then how can it be determined how long it will take to travel a section of space that has no asigned measure of distance (the metric)? Or are you saying that the metric is piecewise linear? Also, isn't the rest of QED and QCD done with respect to a continuous metric? If you manage to quantize the metric or even spacetime itself, then what happens to the validity of QED and QCD?marcus said:Quantizing gravity means to quantize geometry.
It does not necessarily mean to quantize spacetime in the sense of dividing spacetime up into a powder!!!
gravity is geometry
geometry is determined by things like areas and angles and volumes
one can quantize the geometry without needing to pulverize spacetime
Yes, of course, numerical models used by computers necessarily use discretizations of continous things. That's not my objection. It simply seems obvious that there can be no propagation through no medium at all in reality. Computer models assign rules for propagation between discrete points. But that is an artificial tool for computational purposes. But reality would not have the benifit of an outside computer to assign such a rule between discrete points. If it did, it would fill the gaps and amount to a continuum.marcus said:a lattice of points is just a mathematical model and waves can travel thru it-----lattice field theory does this----one just needs a rule
for how the wave at one point affects the wave at nearby points
lattice field theory is a major part of physics. I am not talking quantum Gravity now, but QFT. Lattice field theory uses a lattice of discrete points (a disconnected set)
your posts often reiterate the notion that waves cannot travel thru a disconnected mathematical model of space.
this is a mistaken idea and goes against the experience of
generations of physicists who have used lattice theories
(which often work for calculation when continuum theories fail)
I don't know that keeping an "open mind" should extent to suspending logic to the point of accepting a contradiction that a signal could travel through no medium at all.marcus said:Suppose a discrete spacetime theory turns out to be right!!!
Would you want to be objecting to it because it modeled space with a
discrete set of points?
To me it seems advisable to let theory-builders use whatever mathematical model of
space works for them, whether it is connected or not, or a set of discrete points or a continuum or whatever. We should try to keep an open mind.
Without a continous manifold, do we at least have a topology? Or are you saying that there are unions and intersections of reality that are somehow not part of reality?marcus said:--------------------
I guess the third point would be that you seem to like theories to have an underlying continuum, an underlying manifold.
the Dynamical Triangulations approach of the Ambjorn Jurkiewicz Loll paper uses an underlying continuum
and so does LQG
If you could name the procedure which uses this lattice for a regulator, maybe I could look it up. Thanks. But even then, don't they remove the regulator at the end of the procedure to acheive real results?selfAdjoint said:Your dismissal of lattice based physics as just for computer purposes misses its essential point. The lattice serves as a permanent regulator of the quantum field theory, so they can use it to obtain nonperturbative results that are just not available to them in continuum field theory.
on page 3 of the AJL paper, five lines from the bottomselfAdjoint said:...In the AJL approach, AFAICS, there is no manifold scaffolding, and the simplex structure...
Just found this paper, it has some amazing consequences, I have not read the paper until now, which is after my post, let me give a closing summary quote:pelastration said:Why not say that the micro-gravity of the observer influences the micro-gravity of the quantum particle?
Gravity rules over both (observer/particle), and rules over all other "forces".
Gravity is the only dynamic parameter of interconnectivity that stay when all other forces are dropped.
Einstein said that gravity is not even a force but an aspect of the constant changing geometry of space.
Olias, I am impressed by Uwe Fischer's article, which you spotted.Olias said:Just found this paper... let me give a closing summary quote:
"The primary statement to be drawn from the present article is that phonons, i.e.,low-energy linear-dispersion quasiparticles, moving in a spatially and temporally inhomogeneous Bose-Einstein-condensed superfluid gas, are kinematically equivalent to photons, the quanta of the electromagnetic field, moving on geodesics in a curved space-time. We have explored the classical as well as the quantum aspects of this
statement.
On the classical side, the analogy helps to provide us with a simple general
means to study quasiparticle propagation in an inhomogeneous medium in motion.
An example of such an application is the gravitational lensing effect exerted by a superfluid vortex. 13 On the quantum field theoretical side, we can access within the analogy phenomena which are extremely difficult if not impossible to access with light. One of the fundamentals of quantum field theory, the fact that the particle content of a quantum field depends on the observer, can thus be experimentally verified for the first time..."
http://uk.arxiv.org/PS_cache/cond-mat/pdf/0406/0406086.pdf
Thanks Marcus, I have most, if not all of Fischer's/co-authored papers, it is something I have been interested for many years, and I have recently been waiting for a number of papers which are throwing up experimental Idea's which can be placed onto 'table-top' practical scientific experiments, some as the author states will have very interesting consequences for our future understanding.marcus said:Olias, I am impressed by Uwe Fischer's article, which you spotted.
I think it could be an important article, because it points to a new experimental track. Let me first take time to look at Uwe Fischer's other work to get some perspective on him, then I will know more what I think.
Quasiparticle universes in Bose-Einstein condensates
http://arxiv.org/cond-mat/0406086 [Broken]
the man who wrote this paper was more excited than usual, I think one can sense this in the wording, and this might be a good sign
you Olias have in the past spotted potentially important papers that I would have missed, I seem to recall, here could be another instance of this
I have looked up Fischer's papers in arxiv and there are about 20 on what appears to be more or less the same thing: vortices in superfluid helium.
It may be that he is permanently excited about the experimental prospects this offers. And maybe he is right