what is the big bang and how do i understand it?

He was using a sphere as an analogy for demonstrating the fact that time is just a coordinate.The actual shape of spacetime isn't actually anything like a sphere.

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Because it represents the UNIverse, of which there is only one. The other globe is the same universe, just earlier in time.

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This is actually the crux of the problem.
The other sphere wouldn't be our universe at an earlier time.
All time would end at our south pole.
What you would have is two universes which both become undefined near a singular point.

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Then we would be in one of many uni(multi)verses. How does the neck concept save the problem? Just because of the overlap of multiple spheres touching at one point?

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Because it prevents singularities and also prevents the spheres being two seperate universes.This message has been edited by Son Goku, 08-18-2005 06:32 PM

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The part where Einstein G is based on Newton g is based on empirical data fitting?

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Einstein's G is a bilinear form and Newton's small g is an acceleration, how are they related?

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Cute, but relation to reality is? This is one of the aspects I have most trouble with: enchantment with the mathematics and the clever things you can make the systems do. The object is to determine what is really happening and how to model that reality.

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To be honest it isn't really that sinister, one day Kaluza just went "Hey, I wonder what happens if I add one more space dimension to Einstein's Field equation".
He did and it turned out that it gave out General Relativity and Maxwell's electromagnetism and afterwards people thought that this might mean Gravity and Electromagnetism are both geometric phenomena and in fact the one phenomena.
There has never been any evidence of the 4th spatial dimension and so there is no evidence for what Kaluza said thus far.
People will explore the maths to see if there is more to the equations than what is initially apparent, it's just human curiosity.

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okay I was using g to differentiate G_Einstein from G_Newton rather than g = (G_Newton)(M_Earth)

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Still Newton's big G is a constant and Einstein's is a bilinear form.
They can't really be compared.

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The question is whether the math is being conciously used to model what we know about the universe, or are people making up "pretty" math equations and "elegant" solutions and getting away from the reason for the model in the first place.

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But it is speculation and not science. Until there is evidence to validate predicted results.

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There will always be a point in time when a mathematical construct has not been validated.
Until then they are all just speculation/a hypothesis, it'd be very difficult to come up with a model that never exists in the speculative stage.Kulaza's model unifies Gravity and Electromagnetism at the cost of an extra dimension.
There has been no evidence of this extra dimension so Kaluza's idea is still an unproven hypothesis, but back in the 1920's it was reasonable for him to get excited about it and present it to others.
We can't restrict our models to what can be proven in the forseeable future.

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Math can be made to do all kinds of things: that doesn't mean that the models are real.

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Pure Mathematics can be made to do almost anything, however mathematical physics is far more restrictive and playing around with the maths inside a tested construct allows you to sweat out details that may not have been immediately apparent.

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Funny, that is not the impression I get from the wikipedia article that says:
General relativity - Wikipedia

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Okay the G you are discussing is Newton's G and only Newton's G, even though it makes an apparence in the Einstein Field Equation. When Einstein originally formulated the Field Equation he got
G(u,v) = k T(u,v).
Unfortunatly he had no way of figuring out what that constant 'k' would be in our unit system.
However by examining the the Field Equation in the weak field and slow velocity limit he was able to determine the value of k, which is 8(Pi)G/c⁴.
So although the Field Equation contains G it is still Newton's G.
There is no Einstein G in this sense.

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My problem is when more time is spent playing with the model than on what the model is supposed to represent, to the point of forgetting the original purpose.

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And if you never get out of the hypothesis stage then you never get to the predictions, falsification tests, refinements and observations that validate the concept as a theory.

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It's not that I want to rule out the happy moments, I just don't think they should be viewed as the {rule\goal}.

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That makes perfect sense, I do understand that sometimes people play with the maths without any regard to the physical world.
However very few of us actually play around with the stuff in that sense.
There is maybe one or two papers like that a year in my area.
Most of what is done in Relativity is numerical analysis of what sort of orbits, e.t.c. it predicts in different kinds of solar systems and Gravitational Wave research.
It is still important to have these kind of papers though, they give us a potential glimpse of what lies ahead.

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In quantum gravity we seem to run out of reality and all we seem to be left with is the mathmatics.

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I particularly find that in Loop Quantum Gravity.

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Observations at the high-energy limit are very difficult: either technologically infeasible or potentially devastating to the universe And I'm not kidding

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For anybody wondering, the core of the Sun would be a boring lazy place compared with the high energy limit.

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The theoretical approach would be to derive the whole formula, coefficients and all, from first principals: there should be no need in this case to find out what {k} or {G} or {the cosmic fudge factor} value is, it should be derived. We see this in the other {forces}.

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It seems to me that we have stopped half-way through one, and then embarked on the other approach, so that what we have is a muddle tripping over itself.

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First "constants" like G or Epsilon zero, only appear in equations because of our measuring system.
Basically they exist because the abstract reasoning cannot conclude specifics about the measurement system to be used.
Take for example Newton's Equation:
F = G (m1*m2)/r²
The real relation is:
F = (m1*m2)/r²G makes an appearance simply because the equation can't assume we have a perfectly matched measurement system.
In the above case our force unit is miniscule compared with the units encompassed by the left hand side and so needs an adjusting factor.Also Einstein didn't use any empirical methods in the derivation of the Field Equation, he got the constant 'k' by reducing the Field Equation to the Newtonian Limit and comparing it with the Newtonian Field equation.
From this he found that the only value of 'k' that allows for a reduction to Newtonian theory was the one quoted above.

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Based on this fact, it is unreasonable (imho) to then say we must have {dark stuffs} when they are just mathematical inventions to make the observations fit the calculations. Rather one should be looking for {currently unknown} mechanisms.

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The Field Equations in its completely extended form is: The lambda sign is the cosmological constant.
Normally this is assumed to zero.Now, Dark energy is postulated because the Field Equation goes from lambda equals zero, into regions where lambda does not equal zero on the Universal scale.
Dark Energy is simply a catch-all phrase for whatever gives rise to non-zero values of lambda.
The Dark stuff isn't postulated to make observation fit theory, instead General Relativity already allows the observations, but we have no theory of what is causing lambda to be greater than zero.

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In other words, adding a fudging factory to the universe so the observations (fudged) match the theory.

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No, lambda exists as a natural component of the Einstein Field Equation.
Simply in most space times of local interest the conditions are such that it is zero.
On a global scale they are such that it is not zero, with the simplest assumption being that there is "dark matter" that only comes into play when the volume being considered is cosmological.

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We don't need any special unit dependency because the empirical solution includes it automatically.

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Oh yes you do. Unless you from a society whose standard units correspond exactly with the Planck units.

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The problem is when a theory no longer matches {new} observations, you can either change the theory or change the observations by adding stuffs that aren't necessarily there and for which there is no other evidence.

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General Relativity still does match the observations, the only problem is explaining the discrepancy between the local "lambda equals zero" behaviour and the "lambda does not equal zero" global behaviour.

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The theories of Einstein are not much different. Except for being a notch up on explaining time problems and a whole lot more cumbersome with the maths .

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They're a huge notch up on explaining invariance under accelerative transformations and in gravitational conditions.This message has been edited by Son Goku, 09-14-2005 03:23 PM

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can also be modelled in other ways (such as the universal constant)

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Do you mean omega or something else?

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Why assume this? Perhaps GR will be like Newtonian Physics: close enough in controlled conditions to use for workable solution, or perhaps it will be replaced entirely if the new theory is much easier to use.

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It's unlikely that the new theory will be easier to use if its limiting case is a non-linear theory.
The new theory won't change the gross nature of General Relativity because "Quantum Gravity" (or whatever its eventual name is) only applies in areas where General Relativity breaks down.
Which is inside black holes and at the Big Bang, which are places predicted by GR in the first place.
So Quantum Gravity won't really be a replacement of General Relativity, rather it will (probably) explain how spacetime emerges from something more fundamental, which won't change GR, it being the theory of spacetime itself.

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Try any other field with a theory that only explains (what is it 4% total?) of the known behaviour, but which then claims to be the best theory ....

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Occams razor tells me that when {the adjustment to the data} gets to be more than {the data} to make the theory work, that the theory is wrong.

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To me this is one of the great unknowns, and this shouldn't be glazed over by any pretending that dark stuffs is really the answer.

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That isn't the real motivation behind dark matter.
General Relativity has so far perfectly predicted all gravitational systems we have ever observed.
So it is an excellent theory of local gravity.When it comes to cosmological scales General Relativity still explains the properties of accelerative expansion.
The only difference is that a special case of lambda = 0 is sufficient for local/closed systems, but the dynamics of the cosmos requires the field equation in all generality.The question is what couples to lambda, what is lambda's origin.
It can be Dark Matter, it could be anything, General Relativity doesn't care because it's still right.We haven't observed any situation in which General Relativity breaks down, from 6 micrometers up to billions of light years and that is the reason it has not been replaced.

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You could also say that GR only applies in areas where Newtonian physics breaks down and that GR doesn't change the gross nature of Newtonian Physics.

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GR doesn't change the gross nature of Newtonian Physics, but there is a difference between the relationship between Newtonian Physics and GR and GR and "Quantum Gravity".
Newtonian Physics is very much a variable->0 type limit, where as GR isn't a limit in that sense of Quantum Gravity.

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I prefer to think that a whole new way of looking at Quantum Gravity could replace GR rather than cling to the "standard" - and I have to wonder if this kind of clinging doesn't obscure some of those new ways.

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What I mean is that it won't replace it in a computational sense.
It will supersede it on explanatory power, but unless you've got time to kill you're going to use GR for the calculations of the majority of gravitational systems.

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um, isn't this begging the conclusion?

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No, I can see why you're reading that way though.
I don't mean "right" in the absolute sense, simply that General Relativity doesn't care about lambda's origin.
It still matches observational evidence perfectly, it is a current goal in observational and theoretical cosmology to fully account for all the quantum or classical effects which couple or contribute to lambda.
Basically we don't have lambda's source but General Relativity is still right.
Dark energy is a possible source of lambda and the Casimir experiments make it a safer bet than most of the current alternatives.

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I have some real problems with this insistence that GR covers {all\every} situation, when the result of the theory is that we only know about 4% of everything: knowing {all\everything} about only 4% of a system is a far way from knowing the system with any kind of confidence.

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What do you think General Relativity is a theory of and what do you think it tries to explain?
General Relativity is not a theory of matter, it is a theory of how spatio-temporal geometry couples to matter.
In a local system it requires only the Einstein Tensor and Stress-Energy Tensor of the source.
At the cosmological distance it requires the Einstein Tensor plus a scalar multiple of the metric, this multiple being lambda.Although only a certain percent of the matter can be directly accounted for, this percentage is the dominant form of Stress-Energy in the universe.
It is the source of the Gravitational field.
The remaining percentage only interact to give lambda.
Whatever the remaining percent is, it results in a scalar field permeating the cosmos, however that scalar field isn't a source of gravity.
Rather it changes the geometries matter is permitted to mould, rather than fixing the geometry itself.General Relativity isn't leaving out this remaining percent, it has it there by default, but it doesn't discuss the nature of the remaining percent because it isn't a theory of matter, it's a theory of what geometries the material content of the universe spits out.

cavediver has covered most points, so I'll only be adding a bit.

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Now this sounds like chucking out the dark stuffs and adjusting the formula to make the calculations match the observations. How is this different?

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It isn't an adjustment because it was in the theory from its creation.

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Why assume that {something unobserved} is responsible for this lambda rather than {some relationship} that is not yet {theorized\observed}?

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Something, some relationship, it doesn't make a difference.
A physical process couples to lambda, be it a relationship or a thing.
Dark energy was a guess and the Casimir experiments make it the most likely candidate so far.

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... it isn't a theory of matter, it's a theory of what geometries the material content of the universe spits out.

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and you get upset when I think that this branch of physics is getting more concerned with working out the mathematics of the theory than with explaining the physical universe?

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I don't understand what is wrong with this.
Given a configuration of matter, General Relativity will give you the geometry it produces and this geometry is gravity.
What exactly do you mean by "more concerned with working out the mathematics than explaining the physical universe"?
The maths has to be solved to explain the universe.
To give you an example I've seen first hand, it took a parrellel network of super-computers several days to solve Einstein's equation for two binary neutron stars.
The information on this arangement of mass was fed in and using Einstein's Field equation read outs of the resultant gravity was obtained.
Information from the "PSR J0737-3039" system and several others since match the outputs of these calculations so exactly you'd need a microscope to see the margin of experimental error.

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I'm looking for a theory that predicts observed gravitational behavior with a minimum of assumptions or theoretical complications, especially related to the amount of the universe that we know about.

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That would be General Relativity.

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Adding unobserved matter or energy..... just to make the equations "balance" seems to beg the question on how much we really know.

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The unobserved matter isn't added to General Relativity to fix or make it match observational evidence.
General Relativity matches observational evidence. The question is: "Why do I need all of General Relativity for cosmological distances?"

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Adding unobserved.......dimensions

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Nobody has ever added extra dimensions to account for unexplained observations.

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To me that means starting with the observed behavior and then generating the formulas to match that behavior instead of starting with formulas and then adjusting the universe to match the calculated results.

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That would leave a horrible mess of scalar equations which would be unusable.

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It seems to me that we are lost in a "snapshot" perspective of the universe, that all the calculations are done as if only any one instant were involved in the computations. Whether you use Newtonian or Einsteinian formulas for the calculations.

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Considering that Einstein's theory is a theory of spacetime that would be a difficult view to keep in General Relativity.

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Seems to me you are making a logical fallacy here (appeal to authority) to dismiss the new kid on the block

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He's referencing papers, not appealing to authority.For all you hear about the Pioneer Anomaly, from a physical point of view it's kind of uninteresting.(8.74 1.33) 10’10 m/s2 is a miniscule acceleration.Given the mass of the Pioneer craft, the Force is equivilant to the weight of a 100 blood cells in the Earth's gravity.
Not exactly something of overwhelming magnitude, or something that requires new physics.
The tinest of surface evaporations account for it.
In fact the main report on it said it was probably due to an "unknown systematic".