"Spontaneously broken symmetries require scalar particles/excitations with the quantum numbers of the broken Lie generators."
— Graffiti on a bathroom wall at Princeton
"Every continuous symmetry transformation under which the Lagrangian of a given system remains invariant implies the existence of a conserved function."
— Emmy Noether's Theorem
"All time is local."
— Einstein
Time, gravity and the speed of causality are manifestations of Noether's Theorem's conservation requirement. Broken symmetry may be the reason the arrow of time precipitated and gave rise to dimensionality or space-time. But in the larger Big Universe all functions are conserved, i.e. they sum to zero. This means that all space-time anomalies must remain local and self contained. They must have a boundary. Hence the speed of light, time and gravity are all connected and represent the side effects of the original broken symmetry. Eventually they may transpire to heal the break or they may simply continue to provide containment for the local space-time universe (small u).
The No-Time Before Time
For all practical purposes it will be impossible to prove that there was a beginning to time. Every experiment we can devise requires time as a component of measurement so no-time is irrelevant. Any timeless void preceding time by definition was infinitely short. There is no eternal wasteland preceding time. By definition it does not exist. It is dimensionless and unmeasurable. Now slowing or pausing time is a different issue. The potential pausing of time within a singularity such as a Black Hole may be a bit more accessible if we can measure the effect on something passing through or very close to the singularity. Extrapolation of relativistic equations hypothesize such a timeless point. In order for a singularity to contain the vast quantity of material that falls into an object like a black hole time has to cease for all practical purposes. This causes a collapse of dimensionality and a zeroing of any gauge fields1 leaving only probabilities but no actualities. It is unlikely though that time completely ceases in a singularity. If there is any spin whatsoever it would be impossible for dimensionality or time to zero out completely. Even if you had a black hole with no spin — which is highly unlikely because every particle falling into it would have to fall straight in or the sum of all particles entering the black hole would have to be zero angular momentum, otherwise the collapse would magnify even the smallest rotation — the constant bombardment of incoming material would keep the time/space rip open. To be a void-like singularity all forces must be in perfect balance. Otherwise the singularity becomes a furnace with pressures and temperatures beyond anything we can create in any lab imaginable. At this point even neutrinos should fuse into heavier particles.
According to Noether’s theorem, every continuous symmetry transformation under which the Lagrangian of a given system remains invariant implies the existence of a conserved function.
Noether’s Theorem may well describe the perfect ground state of the Universe (Big U) — that all functions are conserved, or sum to zero. But it has been observed in the study of quantum physics that quantum tunneling is inevitable i.e., stuff happens. This leads to the next theory that no ground state can contain exactly zero probability. This expands to the premise that in order for our universe (small u) to exist there can be no exact solution to a (Universal) Unified Field Theory. If such a solution existed then nothing would simply remain nothing, forever frozen in the perfect ground state. In the infinite expanse of no-time this is possibly true in a very limited local sense. But as one approaches infinity the probability of nothingness becomes incredibly small but never quite zero. A perfect state of nothingness may exist but it is as elusive as the Buddhist Nirvana. So any perfect perfect ground state that might exist is inherently unstable. Once an event occurs we leave the ground state and a new system that contains time becomes separated from the void of no-space/time.
It is possible that past the event horizon at the center of a singularity gravity simply brings time to a halt creating a ground state similar to what a true spaceless/timeless void would be. Dimensionality and time no longer have any meaning. All information about any matter or energy that fell into it remain engraved on the event horizon. Past the event horizon you enter into the realm of the naked singularity which is a region very similar to what the hypothetical eternity before time is like. Immense forces in a delicate balance.
In the early universe when everything was still under immense pressure time was reversible. No definite arrow of time had precipitated. Physical processes could not settle into a discernible linear causality. The probability of a process unfolding in one manner or an opposite manner were close to equal. Once expansion reached a point that cooling could begin then the probabilities of a process following one path of causality rather than its time opposite began to diverge. Matter began to condense and become stable. The probability of it remaining stable for more than a millisecond became greater than the probability of it breaking back into subatomic particles. Once the probabilities started to diverge an arrow of time precipitated.
At the extreme subatomic level chaos still rules and time in the sub-Planck reality is indeterminate. But as you move up the scale probabilities diverge and matter becomes stable. At the larger structure level that we inhabit there is the strong appearance of linear time. An example is the thought exercise of calculating the probability of a broken cup reassembling itself. Sure you can film a cup falling to the floor and breaking and the run the film backward and the physical processes would be equivalent in the abstract. But the probability calculations would diverge wildly. While the probability of the cup spontaneously reassembling would have a non-zero probability it would be absurdly small. However the probability of it remaining broken would be close to absolute. This divergence is what gives rise to the sensation of time at the macro level.
Another unusual property time exhibits is when an object falls into a black hole or approaches a large gravity well. Local time, that is time passage for the object under the influence of a large gravity well does not slow with respect to the object in its local frame. It only slows relative to an outside observer. The probability functions for the object still diverge up to the point the object comes under the intense pressure of the singularity which leaves the object’s probability function behind. Upon passing the event horizon divergent probabilities begin to converge. Now this would only be relevant at the subatomic level as all larger structures would probably have been shredded by the crush of gravity as the object approached the event horizon. Any information regarding the larger structure would have been turned into past history well before reaching the singularity. Only the most basic of particles would reach the singularity itself.
Anything passing through to the singularity itself would be stripped of any remaining information regarding its past. There would be no angular momentum, no spin, basically only the simplest and most non reactive particle would emerge from the other side into any theoretical “white hole” at the other side. If the energy density of the white hole is low enough, i.e. its Schwarzschild radius is large enough, then these new particles would remain in their simple non-reactive state. Possibly these would be neutrinos or some other very basic elementary particle. In a situation where the singularity is newly formed and its Schwarzschild radius is infinitesimally small then these elementary particles would experience immense gravitational pressure. Great enough that they might possibly be reduced to an even more elementary state. At this point we have a furnace hot enough to fuse neutrinos into more complex forms. A pure energy soup without dimensionality that cannot determine an arrow of time. A probabilistic struggle ensues and as soon as there is a symmetry break in the otherwise smooth probability function time arises, dimensionality appears and rapid inflation begins. This is inflation at all points, not just from a center.
Part of what might cause the probability symmetry to break is — if we follow the model of a black hole feeding a white hole on the other side — is the possibility of a discontinuous flow of matter and energy into the black hole. At the very earliest points before symmetry breaking occurs the singularity may be stable for an indeterminate moment but a sudden onrush of extra material may overload it and cause it to become unstable. Or the opposite, a temporary pause in the intake of new material may allow forces in the singularity to equalize and start to condense. Once this happens the processes of the Big Inflation takes hold.
Now as to dark matter and energy. It is proposed that they are composed of particles such as neutrinos or something even more basic. If the white hole model of the universe holds as true then more material may still be falling into the primordial singularity. It would manifest itself evenly throughout all of space as a continuous inflow of inflationary energy. Small fluctuations of material falling into the singularity during the very beginning while the universe was still quite hot could account for the slight energy density fluctuations that gave rise to the clumping of matter into stars and galaxies. After the universe had sufficiently cooled new material would simply continue entering the white hole but would not react with or form new matter. Although it would still have an effect.
The universe that we can see with our instruments is defined by the speed of light. The very early universe when light could still reach all corners is still perceivable. But once inflation had progressed far enough parts of the universe receded from view and we were left with a local light sphere. I do not like the idea of a light cone because it erroneously presupposes an identifiable center from which the cone began. Like Pascal's Sphere2 the universe has no center. It inflates evenly from all points.
This is all speculation. Attempts to pull back the curtain on the earliest time have led to an almost perfectly smooth and homogenous beginning. This would seem to jive with the possibility of the universe emerging from a singularity. Later clumping is still a bit of a mystery. The main reason for searching for primordial gravity waves is the possibility that something created a flux in the primordial soup that caused some localized clumping. The model proposed here would be consistent. The primordial singularity was fed by a steady diet of in-falling material. A pause ensued. It stabilized. And then a secondary shock of new material hit breaking the symmetry. This secondary shock went on for a brief period, long enough to create a few anomalies in the primordial soup and then paused again. By the time it restarted the universe had inflated phenomenally and any new material was not subject to the pressure of the primordial furnace and simply entered the universe in a fairly benign and non-reactive form. And it continues to do so to this day manifesting itself as inflationary energy.
– RD (2015)
1 Gauge Theory and Gauge Fields are an outgrowth of Natural Symmetry and are geometric differential equations that describe the relationship between forces and particles or particle like events, i.e., measurable events grounded in space-time. If time becomes indeterminate any force fields that govern interactions cease. There are no boundaries and no particles.
In short a Gauge Field describes a topological space that gives a good approximation of the probability and strength of an interaction between a topological structure and its interaction with another topological structure and the resulting space-time event that results from their interaction. — RD
“ The fundamental symmetries of nature could actually dictate the character of the force fields of nature.''
— Einstein
“For every conservation law, there is a symmetry. For every symmetry, there is a force field. For every force field, there is a conservation law.”
— Robert Mills
The comments below are excerpted from Quora: “What is Gauge Theory (Intuitively)?”
Curated and edited by: RD
(Leo C. Stein)
Summary: Gauge theory is any field theory in physics in which some global, continuous symmetry of the theory is promoted to a local symmetry. By doing so, a new field is introduced (the gauge field) which has its own dynamics and couples to the particles/fields which have the symmetry. Those particles are then said to be charged under the gauge field.
(Dan Piponi)
Quantum field theory is about fields. A field is some kind of quantity that varies over spacetime. A familiar example is a magnetic field. At each point in spacetime is a vector giving a magnitude and direction of the magnetic field there. Quantum field theory is about the dynamics of these fields.
Quantum field theory is also all about partial differential equations. What this means is that an important part of the dynamics is determined by the rate of change of the fields as you travel along a vector in spacetime. For example in the vicinity of a magnet, the field decreases as you move away from the magnet. This kind of rate of change plays a big role in quantum field theory (and also classical field theory).
But what does "rate of change" mean? Basically you need to compare the field at two different places in spacetime. In the example above I compared the magnetic field between two points, one nearer than the other to a magnet. That seems straightforward, you just measure the magnitude and direction in one place, measure it at another place, and compare the numbers.
But one thing Einstein taught us was that you can't compare things separated in spacetime. You can't even say when two events in spacetime are simultaneous. So we should question what it means to compare magnetic fields at different places.
If you want to compare two separated things, you need to drag one or both so that they both end up in the same place, or drag your measuring instrument from one place to the other. Then you can compare. So you need a rule that says if you measure X at one end of a path, then move along it to the other end, what's the equivalent measurement at the other end. Taking different paths from A to B might even give different results.
So if you have one of these rules, you can compute rates of change as you move along a path. But what should the rule be? You could imagine the rule itself might vary from path to path and depending on the endpoints and the path taken between those endpoints. It seems like there's a vast number of such rules but you can simplify things to the point where the rule is just described by a bunch of fields (known as gauge fields) that say what happens as you move around spacetime.
Now comes the weird bit: you consider the rule itself (or equivalently the set of gauge fields) to just be another part of the physical system with its own dynamics. That's Gauge Theory. It's a theory that involves varying fields and a bunch of varying rules for how those fields should be compared over spacetime.
For completeness I should point out some things that will allow you to compare with other people's descriptions. The rule for how to compare fields at different points is known as a Connection (vector bundle). The rule for how to use a connection to get rates of change is called a Covariant derivative. The quantities that you're comparing from one end of a path to anther live in a space called a Vector bundle.
I mentioned that the rule (i.e. the connection) can be described by a bunch of fields known as gauge fields. There's a bit of ambiguity here. Different gauge fields can describe the same connection. (It's the same as if we decided to redefine the dollar to be worth twice as much. Everything would cost half, but then our savings and earnings would be halved and it would make no difference.) This is a real pain in the ass. You have to do all kinds of complicated things to make sure you don't "double count" because you described the same thing in two different ways. For example BRST quantization with its Faddeev–Popov ghosts. When you study gauge theory you spend a lot of time dealing with this ambiguity. In fact, physicists sometimes spend so much time dealing with this issue that they think the ambiguity is what defines gauge theory. But this is putting the emphasis in the wrong place. Gauge theory is primarily about connections.
(Matthew Johnson)
A more intuitive, elementary, and hopefully, to many, a more accessible answer: gauge theory studies gauges, which are continuous changes of reference frames not only in 3D or 4D space, but in the 'state space' of a physical system. Gauge theory postulates that any meaningful relationships between physical quantities should be the same no matter what reference frame it is measured in, as an extension of Einstein's principle of relativity.
Towards A New Physics
2 Pascal’s Sphere “the center of which is everywhere, the circumference of which is nowhere” — In La cena de le ceneri he proclaimed that the world was the infinite effect of an infinite cause and the divinity was near, “because it is in us even more than we ourselves are in us.” He searched for the words that would explain Copernican space to mankind, and on one famous page he wrote: “We can state with certainty that the universe is all center, or that the center of the universe is everywhere and the circumference nowhere” ( De la causa, principio e uno, V). — Jorge Luis Borges commenting on Giordano Bruno’s comments about Copernicus.
Click here for the full text: Pascal's Sphere
Discussion to continue. . .