What does it mean by background independent and background dependent?
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.
Isn't Minkowski spacetime the background for relativity?
On one hand, a background dependent theory only works in a specific space, but you can generalise to any space, right? On the other hand, background independent does not have a specific space, so it is a generalisation of background dependent, right?
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.htm
That is the background for special relativity. General relativity has no background.
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.
on the other hand other people say that it is misguided to try to achieve background independence in a quantum theory of gravity----they urge those who are trying to stop because it will never lead to good physics, or whatever---there are various versions of this message.
A good instance of this is Lubos Motl's recent post in sci.physics.strings.
It presented as a reply to John Baez Week's Finds #206
I will get a link for Lubos' post, and try to find the relevant quotes about background independence.
Here is Lubos' post:
I hope you fellows don't mind as I am trying concretize the differences between background and background independance and have yet to bring in Smolins discriptions of this as well.
But in looking I came across JB's discription for consideration.
As our theories become more radical, it gets increasingly tricky to
decide what are the background structures in these theories - but I
think it's always a worthwhile exercise, since it sharpens our thinking
about what these theories really mean. I've spend a lot of time worrying
about these issues in the context of spin foam models, because these are
the theories I like best. Here spacetime is a quantum superposition
of all possible 2-dimensional cell complexes with faces labelled by
group representations and edges labelled by intertwining operators.
What if anything are the background structures here? We don't have
anything remotely like a spacetime diffeomorphism group anymore! But
we can still ask questions about what affects what, and what is or
is not state-independent.
I seem to be the only other around on this thread at the moment
and I certainly dont mind. I think you are broadening the discussion
because what is normally meant by
background independence is
independence of a background metric
but as you suggest, and as JB has mused philosophically about,
after getting rid of any preconceived background metric
one can look around and see if there is any other junk that it would
be practical to get rid of.
e.g. maybe one can dispense with the differentiable manifold itself!
I think there is a kind tradeoff or balancing act in scientific theory
A in order to get any results you need to assume some structure to start with
B it is more elegant not to have to assume a great complicated load of
contraptions at the start----it is more elegant if one can begin with a very spare collection of mathematical contrivances and build up one's understanding from there
and of course assuming a lot of prior structure restricts applicability
eg. we know spacetime is not minkowski
minkowski spacetime does not expand, but our U does
and minkowski is perfectly flat and in the real world light bends
so any theory constructed on minkowski space is automatically wrong
in the sense that it does not fit the real world but can be at best only an approximation on a rigid geometrical background.
also any theory constructed on a rigid curved geometry is wrong in the same sense, just like a theory based on a rigid flat minkowski geometry.
what people usually mean when they talk about background independence is getting rid of the prior assumption of some definite rigid geometry
just doing that much would be great! and is very hard to do.
but you and JB remind us that there is a seemingly endless list of things to get rid of. once one erases the rigid geometry one still has other theoretical structure to test and perhaps dispense with.
I appreciate your response Marcus.
I'll add what is recorded in Smolin's Three Roads To Quantum Gravity Glossary as well here to help enlighten this issue some more. Your comments fit well with what is shown here of Smolin.
Background-A scientific model or theory often only describes part of the universe. Some features of the rest of the universe may be included as necessary to define the properties of that part of the universe studied. These features are called the background. For example, in Newtonian physics space and time are part of the background because they are taken to be absolute.
Background dependent- A theory such a Newtonian physics that makes use of the background
Background independent- A theory that does not make use of a division of the universe into a part that is modelled and the rest, which is taken to be part of the background. General relativity is said to be background independent becuase the geometry of space and time is not fixed, but evolves in time just as any other field, such as the electromagnetic field.
Should we then classify the difference between LQG and Stringtheory here?
Marcus:I think there is a kind tradeoff or balancing act in scientific theory
where A in order to get any results you need to assume some structure to start with B it is more elegant not to have to assume a great complicated load of contraptions at the start----it is more elegant if one can begin with a very spare collection of mathematical contrivances and build up one's understanding from there
If Gr is married to QM, and and Gr is not background dependent, then we have to assume the dynamics here of "movement," can be seen in relation too, is being defined with the photon?
Here's my problem. I know the universe can be very dynamical and revealing, using the photon's travel. Influenced, by these strong gravitational field's.
We know there are vast difference's, in the way these field's represent "discretization," within those galaxy systems. So if we looked at the young's experiment, and what is revealled in the backdrop, how would we not know that the spectrum has revealled some issues about it's travel. Does this make sense?
Applicable Lightcones here help in these discriptions, yet I have complicated it haven't I:)
Add superstringtheory to this picture or loop. What can one do better then the other in describing this situation?
After reading Three Roads to Quantum Grvaity by Lee Smolin, this question ( discreteness and continuity), becomes really interesting in terms of the background.
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.
The dynamical nature of this one scenario, recognizes the dynamical nature that this universe is going through, and does not define some beginning.
Taken aside The Continuum Hypothesis has been a issue along this line I tried to understand and the issue was rebuked here by logical explanation in the following linked responses. Is this part of our troubles in acceptance of the Eykroptic scenario?
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?
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?
Mike, could I mention that while real singularities are the total anti physics disasters that you describe, complex singularities (poles) have useful structure. This is because a real line interval is broken by the singularity, but the disc shaped complex neighborhood is merely punctured. You can draw a circle around a pole, and you can integrate around that circle, and all sorts of wonders ensue from that.
A very important question. Here's part of my answer:
If gravity is determined by the metric of spacetime, then what can it mean to quantize gravity accept that you quantize spacetime? But how can you quantize spacetime without resulting in a discontinuity of spacetime. Can you quantize spacetime without disconnecting it? But if spacetime itself is disconnected, then it is not possible to propagate a signal through it. What happens at one point cannot travel to the next point since there is no medium to travel through. Doesn't the logic of causality require that spacetime be continuous for a signal at one point to cause a reponse in another point? Or can the metric be quantized apart for spacetime itself?
Lets give an example to produce some insight thinking?
In General Relativity the Background is the Horizon one exists within, if you look out across space, as far as the Eye can see the laws are equivilent no matter where one travels to Gravity will govern your experience for local events. If you are in a freefalling rocket-ship the Laws that govern the rocket-ship govern everything that extends as far as the Eye can see,they are by defination equivilent and absolutely constant.
Closing ones eyes has no effect of altering the Laws of Gravity, for instance in a stationary Rocket-ship you are floating inside the ship due to Gravitational effects, if one starts the engine of ship the floor will rise up and catch you, its the same gravitational effects that are BACKGROUND to every Planet-Star-Galaxy as pertained by the Horizon that extends to the edge of the known Universe.
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.
Bell labs used this Quantum trickery to produce a Quantum Corral wherby they re-arranged atoms into a configuration of a 'circle', they over-ruled the laws of Gravity, this created standing waves on a surface material, all localized to within a precise area, this is a non-dependant extension to the Quantum Realms.
In the Quantum realm closing one's Eyes has a definate outcome on localized effects, one can shut out Gravity just by the 'blink-of-an-Eye' so to speak,
In GR the opening and closing of ones Eyes has no effects on the local Physical Laws, you are Background Dependant, the Laws Govern You .
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.
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?
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.
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.
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?
As far as the original papers, would you be kind enough to supply the short list of what you are talking about. The ones I've looked at start off with a discrete model and it is not obvious what is being discretized, spacetime, then metric. Nor do they state whether it is piecewise linear or disconnected sections or what. They simply state the existence of a "lattice" without any further ado. I don't remember where exactly they are anymore. Though "Three roads to QG" was one of them.
The Ashtekar school starts with a manifold and a connection (that is still technically prior to a metric, but the Ashtekar "new variables" can be used - still at the classical level - to generate the metric, and in fact reproduce Einstein's GR.
When the go to quantize these variables they restrinct themselves to a three dimensional spacelike slice of the manifold and build their nets of simplices in that. The edges of the simplices carry spinor representations, and where the simplices join each other there are intertwining functions; spins in mapped to spins out, so that's how communications across the net are accomplished. Once the quantization is accomplished, the three dimensional manifold is no longer needed.
In the AJL approach, AFAICS, there is no manifold scaffolding, and the simplex structure, which they have succeeded in making "Minkowski causal", yields a four dimansional local structure in statistical simulations. Here again the simplices are in contact with each other, so there is no bar to transmission.
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.
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?
on page 3 of the AJL paper, five lines from the bottom
the spacelike manifold of the foliation is topologically S3
I basically agree but it depends some on what one means by
there certainly is a manifold, at each proper time,
and the spaceline tetrahedra triangulate it
and they force this to be the case
so that each leaf of the foliation turns out to be topologically a 3-sphere
so in their monte carlo computer program which comes first
the triangulation chicken or the 3-sphere egg?
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