### Lightcone Structure of Spacetime

I want to start talking about some of the more philosophical aspects about physics but it won't be possible without going over important stuff. For this post I want to explain the lightcones that physicists use in relativistic physics. If you're already familiar with the concept of natural units you can go ahead and skip to the part labeled "lightcone structure of spacetime" and my feelings won't be hurt. But it may also help to watch Sabine Hossenfelder's video first. These are highly important to pin down in order to understand any branch of theoretical physics and what I discuss here is no exception.

Lightcone Structure of Spacetime

In mathematics and physics the metric of spacetime allows us to calculate the shortest distance between two points, the famous metric equation for Euclidean geometry and space is is the Pythagorean theorem for a flat two dimensional triangle

The theorem can be extended in three dimensions by adding a third dimension of space for a 3-dimensional universe but in special relativity this is still not enough. Space and time are combined into a single entity called "spacetime" so we need to modify the metric to include a variable for time as we have one dimension of time and three dimensions of space. We can easily do this but time is distinct from space. So our operation should be a negative rather than a positive sign

$(ds)^2 = (dx)^2 + (dy)^2 + (dz)^2 - (dt)^2$

For a geodesic in a spacetime described by this metric the proper time between two points is taken to be the integral

In special relativity the metric only describes flat spacetimes and doesn't add the scale factor or take into account any gravitational effects. For particles moving much slower than the speed of light their motion is well approximated by the physics of Galileo and Newton. But according to general relativity, however special relativity is wrong globally but correct in local regions of spacetime. In infinitesimal regions our spacetime is described as "Minkowskian" and described by the metric given above. This metric allows for three possible solutions

$\Delta s > 0$

In this case we interpret the two events as being separated through a distance just like ordinary Euclidean geometry and we say they are "space like" separated.

In this case our solution is less than zero and what's under the square root is an imaginary number. So we flip the sign and interpret the answer as a time value and we say these events are "time like" separated from one another.

In this case the events are not separated through time or space and we say they are "light like" separated. These different possible values are connected as different regions of a lightcone, the future and the past lightcone are regions which are time like separated from us whereas the region outside of the lightcone are regions which are space like separated from us. Only events which you can send or receive a light ray from are included in your lightcone. For practical purposes we ignore the present.

Any three dimensional space like surfaces in which the elements of the collection is labeled by real numbers and increases steadily from one surface to the next can be used to define what is "present" what is "past" and what is "future" relative to your reference frame. Each event on one surface is simultaneous to the events on that same surface. This kind of structure might lead one to believe that time is a block rather than just the present but that's a rather controversial topic for another time.

### William Lane Craig and the Hartle-Hawking No Boundary Proposal

Classical standard hot Big Bang cosmology represents the universe as beginning from a singular dense point, with no prior description or explanation of classical spacetime. Quantum cosmology is different in that it replaces the initial singularity with a description in accord with some law the "quantum mechanical wave function of the universe", different approaches to quantum cosmology differ in their appeal either to describe the origin of the material content of the universe e.g., Tyron 1973, Linde 1983a, Krauss 2012 or the origin of spacetime itself e.g., Vilenkin 1982, Linde 1983b, Hartle-Hawking 1983, Vilenkin 1984.

These last few proposals by Vilenkin, Hartle-Hawking and others are solutions to the Wheeler-DeWitt equation and exist in a category of proposals called "quantum gravity cosmologies" which make cosmic applications of an approach to quantum gravity called "closed dynamic triangulation" or CDT (also known as Euclidean quantum gravity). I&#…

### How Should Thatcherites Remember the '80s?

Every now and again, when I talk to people about the '80s I'm told that it was a time of unhinged selfishness, that somehow or other we learned the price of everything but the value of nothing. I can just remember that infamous line from Billy Elliot; 'Merry Christmas Maggie Thatcher. We all celebrate today because its one day closer to your death'. If it reflected the general mood of the time, one might wonder how it is she won, not one but three elections.

In an era when a woman couldn't be Prime Minister and a working class radical would never lead the Conservative party, Thatcher was both and her launch into power was almost accidental owing in part to Manchester liberals and the Winter of Discontent. Yet I'm convinced her election victory in '79 was the only one that ever truly mattered. Simply consider the calamity of what preceded it, the 1970s was a decade of double-digit inflation, power cuts, mass strikes, price and income controls, and the three…

### Creation Of Universes from Nothing

The above paper "Creation of Universes from Nothing" was published in 1982, which was subsequently followed up in 1984 by a paper titled "Quantum Creation of Universes". I decided it would be a good idea to talk about these proposals, since last time I talked about the Hartle-Hawking model which was, as it turns out, inspired by the above work.
Alexander Vilenkin also explains in a non-technical way the essential idea in his book; Many World's in One – one of the best books I've ever read – it mostly covers cosmic inflationary theory but the 17th chapter covers how inflation may have begun. In fact Vilenkin is one of the main preponderant who helped develop inflation along with Steinhardt, Guth, Hawking, Starobinsky, Linde and others.
Although I won't talk about it here, Vilenkin also discovered a way of doing cosmology by using something called "topological defects" and he has been known for work he's done on cosmic strings, too.
In ex…