Summations Only

Just being real, virtual particles and the mechanism in Quantum Gravitational theories where by the universe "pops" into existence are completely unrelated processes.
The universe popping into existence is more closely related to a phenomena called quantum tunneling.Basically most quantum theories have a classical version. For instance the quantum hydrogen atoms has a classical version where the electron is simply a ball orbiting the nucleus through electric attraction.
Of course the quantum and classical versions of a given theory can have very different physics. The quantum hydrogen atom is stable, where as the classical hydrogen atom implodes very quickly releasing a burst of gamma radiation.A general feature of quantum theories is that they allow particles to jump across barriers present in their classical versions. For instance in a classical model of the nucleus, the edge of the nucleus is like a hard wall preventing the nucleons from escaping. Nucleons can either live inside or outside the nucleus. However the typical energy possessed by a nucleon makes it impossible for it to go from the inside to the outside.
The quantum model of the nucleus however allows nucleons to "jump" across the barrier. This is quantum tunneling, but I should explain it better.The real problem with moving through the barrier in classical mechanics is the energy required to do it. You and I have no problem walking around the inside and outside of a building, but moving through the wall separating the two is not possible for us with typical walking energies.
Here is the main point: Classical Mechanics requires objects to have consistent histories. You can't get from one side of the wall to the other without moving through the wall.Quantum Mechanics has no such restriction, it provides a particle with some non-negligible probability to just suddenly be on the other side of the wall, without any requirement of historical consistency of having actually moved from A to B via the points in between.So if you take a classical theory, it's quantum version allows objects to be in one state A and then suddenly be in another state B, without actually "going from" A to B.Now, if you think of classical gravity, that is General Relativity, we could take the two following states:A = No universe.
B = Small expanding hot universe.Now, classically of course you can't go from A to B. Classical intuition, which we all possess, prevents such a transition, how could something come from nothing?This is perfectly correct, but quantum theories of gravity bypass it by basically just dropping the transition between states. You just occupy state A and then state B with no "history" in between.This is quantum tunneling.

I just wanted to say that the reality of virtual particles is a bit of a thorny issue, but for scientific as opposed to philosophical reasons.To cut an extremely long story short, a quantum field is a physical system which, like any other, can be in a variety of different states. The most interesting of these states are what are commonly known as particles, which are essentially (i.e. ignoring quantum mechanical issues) small bundles of mass and energy.However a quantum field can also be in a state that cannot be understood as a collection of particles. These states are extremely difficult to deal with, however they are quite common. If you collide an electron and a positron (both states of the electron field) with each other, then the electron field and the electromagnetic field it interacts with, enter into one of these non-particle states. However after a while the fields settle down into a particle like state, a state of two photons. So:
[Electron + Positron] => [Extremely complex field state] => [Two photons].(I'm ignoring quantum mechanics here, since the final particle states are usually a superposition of [Two photons] and [Electron + Positron] at the same time.)This equations which deal with this time evolution are far too complicated for us to actually solve. However they become much simpler if you make the initial state and the final state to be infinitely far apart in time, an idealisation known as scattering theory.The main point is that it turns out that all the complicated details and physics of the intermediate field states, the ones that cannot be interpreted as particles, can be completely ignored and replaced with the physics of the transmission of energy conservation violating virtual particles.These virtual particles are not real, in the sense that the theory does not predict they actually exist. Rather they are a more convenient way of encoding the dynamics of the intermediate non-particle states. This trick only works in the idealisation of infinite time separation between the initial and final states. Otherwise you would have to deal with the non-particle states directly.In case the idealisation of infinite period of separation seems unrealistic, a typical time period for particle physics is a Yoctosecond, so on these time scales the milli/centiseconds it takes for particle physics experiments are quite close to the infinite time limit.Most calculations in Quantum Field Theory are scattering theory ones. Although I should point out that over the last two decades we've found that even in the infinite time approximation ignoring the non-particle states completely can lead to errors, as not all non-particle states can be approximated using fictitious virtual particles even in the infinite time limit.Examples would be certain states related to quantum tunneling, as discussed above, these states being known as Instantons.

The strength of gravity has no meaning in modern physics. In old Newtonian physics you could imagine gravity having different strengths by adjusting Newton's constant G. However in General Relativity, G has no meaning, it's just constant that appears because humans happen to measure mass and distance in different units. This is completely false. See for instance the paper:
Weakless UniverseThis is a universe without the Weak Force, that's an entire force removed, not even just a few parameters tuned. Yet it has stars that burn as long as ours do, which make heavy elements and in which planets can be formed.

Why guess that? It's been read by several others and passed the peer review process in Physical Review D. It's a pretty silly thing to guess without reading the paper. Could you explain this point? In the paper above the Strong Force is adjusted to be capable of providing essential heating mechanisms which in our universe occur through the Weak Force.

Gravity is not a force. Discussing its strength has absolutely no meaning in Modern Physics.Frank Wilczek has said: In modern physics gravity has no strength. A given amount of mass simply generates a given amount of spacetime curvature, that amount is completely fixed, with no tuning possible (In fact tuning would be meaningless, but that's a long story). The real question is why do you have to build up such a huge volume of matter before you have enough mass to generate a good bit of gravity.
This question really comes down to why are nucleons so light. Since nucleons are light you need a lot of atoms to build up any mass.However both nucleons are light due to the same physics, the physics of quarks and gluons, that is quantum chromodynamics. So we really only need to ask why one of them, the proton, is so light.Which is really a question for quantum chromodynamics and which has already been answered. Basically in quantum field theory, the smaller a particle is, the heavier it is. A proton's size is determined by the distance at which the gluon fields, being generated by the quarks inside the proton, reach a certain strength. Gluon fields get stronger away from the quarks (unlike an electric field, which gets weaker at large distances).When the gluon field is of a great enough strength it completely "seals in" the quarks in a self contained unit, the proton.However it takes a significant distance for the gluon fields to become strong, significant relative to the size of the quarks. This is because relativity and quantum mechanics together forbid the fields from growing more quickly than logarithmically in distance from the quarks.So the necessary strength isn't achieved until a very large distance, hence the proton is quite large and hence it has a low mass.Weakness of gravity explained.

This is not correct. When you switch to Planck units, rather than units that are an accident of human history, the Gravitational "strength" just disappears from every equation. The reason is essentially quite simple. In General Relativity mass and spacetime directly influence each other and both a measured in the same units, the meter.One meter of mass corresponds to one meter of curvature. No "strength" or anything. Mass simply causes an equivalent amount of curvature. You could say this several ways:
"Gravity has no strength" - Since there is no constant to adjust
"The strength of gravity is what it is" - Since you could consider it "fixed" at 1:1, between mass and spacetime curvature. This ratio is not adjustable. First of all, the distance over which a force acts has nothing to do with its strength, it has a more complicated origin, related to what is known as the symmetry group of the force.Secondly, gravity is not a force in General Relativity. There is no gravitational potential field acting on an object and causing it accelerate, unlike an electric field or a strong nuclear field.
This is stated in every single major textbook on the subject. If you want I'll provide you with quotes from the most commonly used graduate textbooks on General Relativity.

I'll explain things at a purely classical level, except at one point, since quantum mechanics doesn't really add much to this story.Okay the Strong Nuclear force and the Electromagnetic Force are indeed Forces in Modern physics. This is because they involve particles generating a potential energy field in their vicinity. Nearby particles that can interact with that field will no longer be able to remain stationary without exerting some energy. That is, remaining still is no longer the path of least resistance.Instead the path of least resistance will become some complicated trajectory dictated by the potential energy field. In particular a particle moving inertially (that is with no acceleration) will be forced to accelerate and change its trajectory.Under quantum mechanics these potential energy fields are composed of gluons for the strong nuclear force and photons for the electromagnetic force.So, particles have their trajectories altered by the presence of fields living in spacetime. Without these fields all particles would move on inertial paths, that is paths which involve no acceleration.General Relativity indicates that gravity is entirely different. Instead the shape of spacetime itself is distorted, in the presence of mass. However particles don't have their trajectories altered. They simply move along the usual inertial paths.The confusion of gravity being an actual force comes from the fact that when spacetime is only weakly curved, the inertial paths in the curved spacetime look very similar to non-inertial "force-caused" paths in flat spacetime. So you are able to pretend that gravity is a force living in flat spacetime.However a simple thought experiment reveals the different, "true", nature of gravity.Create a giant sphere the size of the Earth with a large positive electric charge and give yourself a negative electric charge. You will fall toward the sphere, just as you would fall toward the Earth from space under gravity. However you will feel this pull when it begins to accelerate you noticeably. You'll also notice objects heavier than yourself falling more slowly than you, as the same electromagnetic force strength cannot pull these objects quite as fast.Contrast this to gravity. While falling to Earth you feel nothing and more massive objects will fall at the same rate as yourself. This is not the behaviour of a Force tugging on you and the heavier objects, since the heavier objects would be harder to pull down.Instead you and everything else are simply moving on inertial paths in spacetime, you feel nothing, since nothing is actually acting on you. It's simply that spacetime has been distorted around the Earth so that a lot of inertial paths lead to its surface. However this no more a force than the fact that moving north on the Earth leads to the North Pole, which is just a consequence of the shape of the Earth. Falling is just a consequence of the shape of spacetime.Gravity is not a force and there is no gravitational field.

The problem in a way stems from the fact that, in a sense, entropy isn't "real" and is not part of the fundamental laws of physics.
(I'll just include an explanation of Entropy, sorry to bore anybody who knows this stuff.)
Essentially all of the fundamental laws are time reversible. Newton's laws will tell you how an object falls from space down on to the Earth, but it will also tell you how an object on the Earth will rise up into space, as time goes backwards. It doesn't seem to pick out either direction as the natural arrow of time. Same with General Relativity and most Quantum Field theories.Of course the difficult thing about applying the laws in reverse in the actual universe is that future states are more generic in real life. So if I have two rocks sitting on the ground, and if one fell from space and the other didn't, there won't really be much difference between them. I'll have to scrutinize the two rocks to see if I can detect traces of falling through an atmosphere on one of them. Only then can I apply the laws in reverse successfully and have the correct one rise into space.Imagine this experiment was done on a planet with a very thin atmosphere, so that the only difference between the rocks was some micrometer scale friction burns on one of them. This means I'd have to measure the rocks to a good degree of accuracy to reverse time. Compare this to the forward time description. One rock starts in space, the other on the ground, it's obvious what will happen as time flows forward. I don't need micrometer scale information about the rocks.Now take the extreme of the Sun. Try to reverse time there, it would be almost impossible to know which random atoms in the Sun should unmelt and reform into a comet that hit the Sun in the Devonian period. You'd need atomic level detail of the entire Sun! Again compare this with the forward time evolution, you start with a comet pointed at the Sun, it's easy to guess what will happen.The point being the difference between the two states, where the was Sun hit by a comet and the state where it was not, is at the atomic scale. They are very difficult to tell apart.The general point is that later in time states all tend to be difficult to tell apart. They are more generic. Entropy is just a measure of this generic-ness.This increase of generic-ness is what marks one direction of time from another in the real universe. However there are two problems with this:
1) Generic-ness is not a fundamental, physically real, quantity. It describes how difficult it would be to tell two states apart, but this isn't really a parameter that enters directly into the equations of General Relativity and Quantum Field theory.
2) The only reason this could work as a way to tell the directions apart, is if one end of time was in a highly non-generic state, you could then label that "the beginning" and define forward as the direction where generic-ness increases. There is no explanation for why this is true. Why was the Big Bang so non-generic (low entropy)?

The only problem is that from the point of view of the fundamental laws, there is no reason for the states in one direction of time to have lower entropy than the states in the other direction. The reason we can tell the direction of time via the events you describe is because the low entropy states always come first.The fact that low entropy states come first and that we can use this to tell the arrow of time has the immediate implication that states have lower and lower entropy as we go further and further back in time. Ultimately the state of the Big Bang had extremely low entropy.If the universe had began as a homogeneous soup of matter (which is "more likely", i.e. more generic/higher entropy), then the states in the past and the future would have similar amounts of entropy and neither direction would be distinguished.Without the Big Bang having low entropy, you wouldn't be able to use the methods you described above. Basically, the universe (down to a very fine scale) is the result of the interactions of quantum fields and spacetime. Those fields and spacetime itself do not have entropy as a property. It's a derived quantity, useful for discussing large scale objects, but as fundamentally real as temperature or tensile strength. In other words, entropy is an emergent quantity and since you use entropy to tell the direction of time, the arrow of time is itself an emergent property.Forwards or backwards in time, the fundamental quantum fields don't care, they literally can't tell the difference. However large scale objects built out of the fields do prefer one direction, for the reason that the large scale objects were in a very specific (non-generic) state at the big bang.Edited by Son Goku, : Typos

No real disagreement Percy, I'll just add some comments in case my post above was a bit unclear. Indeed, it probably should. One thing a lot of the quantum gravity theories (String, Loops, Causal networks, e.t.c.) have in common is that they all promote the number of possible states to being a fundamental property. So a lot of people would agree with you.I'm saying that current, verified physics does not do this and the number of possible states is not fundamental but derived. You might, and quite a few physicists do, think that this could be a flaw in current models. Again, this is what most people think. There is a tension between current physics and the arrow of time. Again since entropy is not fundamental under quantum field theory and General Relativity (which are current physics) and there is no selection mechanism for initial states (like that at the Big Bang), current physics would say all states are equally likely and since there are vastly more high entropy states than low entropy ones then, under current physics, a high entropy state is more likely.Of course this does not mean that a high entropy state is actually more likely. Quite probably there is some quantum gravitational effects controlling the initial state.However we don't have a quantum theory of gravity yet, so although almost all physicists would agree with you, the low entropy of the Big Bang is as of yet an unsolved problem. We still don't know why the universe has a preferred time direction even though many, including yourself, can guess at the probable form of the answer. That is, some deeper physics.