What were they dependent on?
If you have a set of fundamental laws that describe the evolution of the universe and you need of some initial conditions, then these take somehow the same status than the laws, because they become undemostrable principles that can be only proved by experimental tests. However, other approaches might be possible. For example, the solutions to the equations could be unique in the sense that they do not need of any initial conditions, as was expected by de-Witt after the formulation of the canonical quantization of general relativity some decades ago. Moreover, for example, one may assume that there are no initial or boundary conditions (as in Hartle and Hawking's no-boundary proposal), or that all possible boundary conditions may hold.
Have a look at this recent paper
The Issue of the Beginning
http://arxiv.org/abs/physics/0605078 (it's free, just click where it says "PDF")
Large parts of this article are in plain words without math---you can skip the technical parts in the middle if you wish and just read the introduction and the conclusions. The author has worldclass stature as an authority on quantum geometry and cosmology. Stephen Hawking gets more press coverage than this guy, but does not necessarily have anything more useful to say.
I think having this to refer to will help us be clear about what we mean by initial conditions.
I prefer an initial condition of 0,0,0,0 - which assumes no canvas upon which to paint spacetime [i.e., is background independent],
In the LQG framework (loop quantum cosmology) the existing universe is assumed as a given homogeneous and isotropic space-time, and the equations that follow from this reduction to minisuperspace allow to trace backwards the evolution of the universe beyond the classical singularity. It seams to me that for such a procedure no initial conditions are needed. The problem is formulated in terms that initial conditions do not have any meaning.
Personally I think that the question about initial conditions is a necessary one for every model that claims to be fundamental. If the model does avoid this question then it seams to me that something is wrong, at least, the model cannot be fundamental. In general, I have the impression that foundational questions about quantum cosmology that were treated in detain in the framework of geometrodynamics (de-Witt, Hawking, Vilenkin, etc.) are being forgotten or neglected within the framework of the new quantum gravity theories.
several recent papers are engaged in weakening this assumption. I don't remember if Ashtekar mentioned this. Just curious, did you happen to have a look at "The Issue of the Beginning"?
I think this misses the main point. There is no way avoid the question of a model's basic conditions---prime fundamental assumptions---call it what you will. These conditions just don't have to be anchored to a particular moment in time. Every physical model has basic underlying assumptions. There can be a moment in time when they they suddenly take effect (a 'beginning' located in time) or they can have always been in effect.
Newton's and Laplace's model universe did not have a beginning---the time stretches from minus infinity to plus infinity---Newton's idea of a creator is outside temporal creation. Anyway, so I'm told (I didn't read Principia :-) )
There is no rule that says cosmological models must have a beginning located at some particular instant of time. Ashtekar's point is that the pendulum is swinging back.
There is now no scientific reason to believe that time started some 14 billion years ago. Because one has EQUALLY GOOD MODELS some saying that time continues back and some which break down and cannot go back any further.
LQC fits the data as well as classic GR. It has classic GR as limit within a few hundred planck times.
So one cannot, for the present, say that there was a bounce, or that there was not a bounce. Future observations will be able to distinguish and will check to see if the LQC bounce model predicts more precisely than the classical one, or does not. Right now we cannot say and just have to be patient.
I think you are mistaken if you think that, to be fundamental, a model must address conditions at some particular instant of time that you think is 14 billion years ago. LQC has a bounce and continues on back past that time. Of course one can always ask "What were conditions like at the bounce?" and that would play somewhat the same role as asking what were the initial conditions.
I expect in this case we will just have to let Nature decide for us what is required for a model to be fundamental.
I hope I have understood your points, and that this helps.
Yes, this is exacly the point. I do see reasons that make eternal models unphysical.
First, eternal models seam not to be according to the second law of thermodynamics. But this might be a minor issue. If time streches back to an infinite past, and the causal sequence of events does not follow infinitely fast, how can present time have been reached? Consider for example an body located at infinite distance. It may start approaching us, but an infinite distance will never become shorter and even after infinite time the body will not reach us. To my eyes this situation with an infinite distance is a similar problem than an infinite time. Infinite time and infinite distance make no sense in physics.
Of couse this is my personal view and I agree with you that infinite models, spatial and temporal, are usually postulated without taking care about this issues. The flat infinite classical Friedmann model is the best example of this. However, I believe that this is only a model and I don't think the questions I addressed above are irrelevant. In my oppinion our cosmological models are just too simple. It is usually extrapolated from physics (general relativity of quantum gravity) to cosmology without taking care about the special conditions, initial conditions and boundary conditions, that must hold for a truly fundamental cosmological model.
From this point of view initial conditions are a fundamental issue in any fundamental cosmology. I believe that any fundamental cosmology must describe a universe that emerges from an atemporal state. Of course it may turn out that postulating initial conditions as an add-on to the laws is not necessary if the equations of motion provide a unique solution.
I agree. I would be happy to see some experimental confirmation of any of the quantum gravity theories that currently postulate quantum cosmological models.
Anyway, I undestand your points (by the way, thanks for the detailed reply) and I agree that they are standard. Take into account that I am defending a very personal view on this issue.
I understand your view better, thanks for the clarification.
No reason to debate personal perspectives. Good to have various viewpoints.
A couple of comments:
1. on an infinite timeline there is no point at infinity. all points are a finite distance away. the issue of something "at infinity" whose effects cannot reach us, and suchlike issues, don't seem to me to arise at all
2. you might be interested, since you mention the SECOND LAW and its relevance to cosmology, that Penrose has been developing and promoting an infinite-time cosmology which satisfies the second law. I heard him lecture on this at Berkeley this year. he also lectured about it at Perimeter and it is in the video archive so you can see his slides and hear him expound.
it is kind of entertaining. He DERIVES his cosmology from thermodynamic considerations, from the second law in particular, and he critiques other cosmologies.
his cosmology is not bounded as one goes back in time, so in that aspect it is similar to several other recent cosmologies (like those discussed by Smolin and by Ashtekar) but unlike them, the onset of expansion does not, for Penrose, require a prior gravitational collapse
(well BHs and their evaporation do play a minor role so I suppose in that limited sense, but the fresh expansion does not stem directly from a BH collapse)
If you haven't seen Penrose lecture, I can almost guarantee you'll find it interesting and like no other cosmology youve ever seen.
just type Penrose in the PIRSA search engine.
But you can always find a point in time farther away than any other. Consider that you "travel" with finite "speed" along the real line. In the same way that you will never reach infinity from any definite real value, how can you assume that any definite real value can be reached starting from (past) infinity (or having an infinite amount of time before it)?
I will search for this Penrose lecture, thanks.
Glad you are interested, hellfire!
here is PIRSA (perimeter inst. recorded seminar archive)
if you click "advanced search" you get
then if you type Penrose you get a menu of two of his talks, one of which is
Title: Before the Big Bang: an Outrageous Solution to a Profound Cosmological Puzzle
for me, when I click "Windows Media" it starts streaming and playing the video.
I think you can access it more directly just by typing in the number 06090005 in the first PIRSA screen you get.
I recommend the lecture, I don't know what I think about his new cosmology idea. Penrose is brilliant. I'm neutral about this specific idea of his.
He is very concerned about thermodynamics and the first half of the lecture is a tutorial on the way he sees the PROBLEMS of cosmology, it is not about his own solution. That comes in the second half of the talk. In some ways the tutorial on cosmology and the second law may be the more valuable part.
Please let me know what you think of it!
How could something atemporal (in the sense of a non-changing state) ever become temporal. How could the universe emerge from a non-existent state?
How could motion arise from motionlesness? etc.
These are all deep philosophical issues, which have been questioned extensively throughout history.
My intuition would say quite the opposite, an emerging from nothing can not ever be a start of any physical state, let alone the universe.
So this would lead to a model which would not have a begin (since a begin of the universe would mean a begin in or from nothing, which is not a begin, sinc e nothing does not contain a begin of any something, nothing is just nothing.... etc.)
Which however is not like saying that there can be a physical model of the universe which models the universe in total. In that sense my intuition coincides with yours. Physics can only model the physical world in a finite way, which is incomplete.
It is beyond our possibility to make a model of the universe at large.
I'm very skeptic about claims as if we are near a 'theory of everything' (the 'holy grail' of physics). We'll never have a complete and total understanding of the physical world.
Most of this miscomprehending (on the issue of the beginning, on the finiteness/infiniteness of the world) are based on a lack of understanding of the infinite. Most of the problems arise because the infinite is tried to be grasped without contradiction. But the infinite is a concept which can not be grapsed without contradiction and is in fact full of contradictions.
Imagine a line extending in both ways to infinity, and place two points on the line, wherever you like. Now it is clear that the two points are nowhere near infinity, but always distantiated a finite distance from each other.
There is also this famous 'Kalam cosmological' argument, which tries to argue against the infinity of time, and shows a 'proof' that time must have had a beginning. It claims that if time were infinite, an infinite amount of time would already have been elapsed, which is impossible. It therefore concludes that time must have had a beginning.
But as we can see, this reasoning already smuggled into it's premises that time had to have a start (which is the thing to be proven), since how else could one claim to have started counting time in the first place? The contradiction (and in fact an absurd one) arises because the infinite time is imagined to have such a starting point. But precisely because the infinite timeline does not have such a point, we could never begin to count in the first place.
The error in all these cases is that one tries to handle the infinite without contradiction, which only leads to further and worse contradictions.
It is just because infinity is a contradiction, that it is an eternal process, unfolding endlessly in time.
Welcome to the "beyond the standard model" thread.
If you hadn't started posting here, I'd have never thought you understood anything about the standard model, much less things beyond it.
I've been having difficulties understanding how it can be that SU(2) is a double cover of SO(3) when 2 is smaller than 3. Do you have any thoughts on the subject? Also, do you think it's better to represent Clifford algebras with quaternionic matrices or matrices with complex numbers? The mathematicians seem to favor the quaternionic representations, but I understand complex numbers a lot better so I'm willing to work with matrices that don't have all their [tex]2N\times N[/tex] real degrees of freedom.
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