How Math Might Reveal Quantum Gravity
quantamagazine.org
quantamagazine.org
EDIT: https://physics.stackexchange.com/questions/6530/rigor-in-qu... is pretty informative.
I am also much more pessimistic than Seiberg about the possibility that a priori mathematical investigation is going to say something useful about quantum gravity. The following essay gives a pessimistic point of view on a particular program to rigorize QFT, but the arguments generalize: http://philsci-archive.pitt.edu/8890/.
But, that's a long paper. For a super-condensed take on why the project might be hopeless, read section two of this paper: http://philsci-archive.pitt.edu/15296/1/qm-continuum%20revis....
\int Dx Exp[S[x]]
Where \int Dx is like a sum, x is a field (a thing that assigns numbers or an object to a point in space), Exp[S[x]] is a weighting. You sum over all possible field configurations weighted by S[x], which is called the action. You can feed in other fields to this sum and calculate expectations of events happening, a bit like a Fourier transform or Gaussian integral from statistics. Classical configurations (classical paths/trajectories) this is the biggest contribution, then all the quantum stuff gets weighted less.
Formalising this notion is complicated for the sorts of objects and spaces needed in physics.
This is also problematic when it comes to quantising general relativity, the gravitational field in a sense is not just a field on space, it's more like space itself, although you can try to describe that as a field. People get around this by summing over geometry. In a sense you can test what the geometry is by seeing what it does to objects, maybe a bit like forcing particles to interact with each other and seeing what gets produced says something about internal structure.
It is interesting of course that we try and use classical information plus some choices to build a field theory. In my opinion it is sort of unnatural to quantise, you are making choices. Broadly quantisation is sticking some commutative theory in a non commutative theory. But since we know the universe actually runs on those quantum rules, seems wrong to define it as like the embedding of a classical theory, it should go the other way, classical information should emerge naturally instead.
Perhaps the other issue is that field theories are effective in a sense. Much like fluid dynamics doesn't say anything about the internal molecular composition of water, fields are an effective theory. Perhaps string theory tries to get around this by having large scale dynamics and then saying what the micro local structure is, but that is even less of a well defined notion than a QFT.
They claim to have found a simple solution. Looks like Planck’s length was turned into a sphere, then they calculated how many of those spheres would fit inside a single proton. That was compared against how many Planck circles would fit on surface of single proton. From the ratio of the two they could solve size and critical mass of the universe, by looking at single proton. Quite amazing if that’s true. They think proton is a mini black hole and when it’s scaled up to size of the universe things match. And key to nailing it in the end was to consider volumes made from intersecting spheres (like flower of life pattern) instead of tiled cubes. The guy behind this certainly faced lot of criticism before but apparently now the math works. Anyways I don’t have skills to evaluate this by myself but maybe it’s worth checking out by someone who can do the math. Don’t shoot the messenger ok :)
What is represented by a mathematical field in the physical world?
Is the gravitational field a gas, ideal fluid, solid, crystal, or plasma? (IMHO, it's ideal fluid).
What causes it to release energy when two objects are attracted? Of course, it goes from higher energy state into lower energy state, but what state it is?
What causes attraction? It's because there is a gradient in the ideal fluid around every object, or because it's a form of interaction between particles of objects, or it's a something global, e.g. shadow, which blocks background radiation causing imbalance?
(Non-native speaker).
The fields (and their associated physical laws) accurately reproduce basically everything we've observed out there in the world in their respective domains. So regardless of some nebulous philosophical "ground truth", these mathematical laws provide a useful to way to think about these behaviors and make predictions of the future (and because these law are formulated mathematically, in many cases there are multiple entirely equivalent ways to work with them).
Analogies of these fields to less fundamental things (like fluids) are just that: analogies, and don't hold any fundamental meaning. The physics of (e.g.) electromagnetism is a thing in itself and requires new primitives to talk about -- there isn't necessarily some more familiar thing hiding underneath -- the gravitational field isn't a fluid or solid or gas, it is it's own thing.
We are not talking about an analogy. We are talking about representation.
A physical thing X is represented in physics as a field (3D array, [x,y,z]) of values of Y, so, if we have a field of Y, what is the X?
For example, height field represents the height of piles of rock and dirt about ocean average level, so, Y is height, and X is the rock.
What is represented by EM field, by gravitational field, etc.?
(Beware: non-native speaker).
1) The phenomena of electromagnetism and gravity are fundamental as far as we can tell -- there is no more familiar or more commonplace "thing" I can tell you that they are "made" of. In fact if you really pressed it, your concept of a "rock" or "water" as a solid, distinct object out in the world is probably better thought of as a manifestation of electromagnetic behavior.
That's just the way the world seems to be. If you drill down into it, our best physical theories describe everything in terms of fields defined over space (including all matter, like quarks, electrons, etc). So if you've a got a philosophical problem with fields for gravity and electromagnetism you've actually got a philosophical problem with basically all of our modern understanding of physics.
2) Whether our mathematics represents something intrinsic to the world rather than just providing a description of what we observe is a philosophical question (it's "ontological") that has no bearing of how well that description works.
So if you want to think of space being permeated by real fields like the electromagnetic and gravitational fields you're free to do so. It'll give a useful and extraordinary precise description of the bundle of phenomena we call electromagnetism and gravity. Conversely, if you want to think of these things as well built crutches that don't properly represent (some yet undiscovered) deeper reality, but nonetheless give a very accurate description of it -- you can do that to, it won't make any difference in the physics.
Modern OpenGL can be used to make astonishing predictions, but, IMHO, studying of OpenGL will not make me better at physics. However, if I will learn chemistry, optics, geology, fluids, mechanics, etc., then I will be able to make OpenGL better.
Modern math apparatus in physics does astonishing predictions, but it cannot explain the underlying mechanic.
IMHO, the solution is to make physical models, instead of mathematical models, of quantum objects, and study them with our own eyes, because it's easy to bend spacetime in math or OpenGL, but impossible in real physical world, so it forces making of realistic physical models.
2) I generated few ideas:
Maybe, a huge wave passed through our Visible Universe, and caused a pressure drop in the ideal fluid AKA Physical Vacuum, so bubbles are popped up, and they are merging now from subatomic particles and up to supermassive black holes.
Maybe, we are embedded into a huge massive object, so gravitation and EM are caused by rotation of this object, so gravitational attraction slowers rotation.
I don't know.
But, "energy is stored in 3D array of values, because 3D arrays are defined as foundational for mathematical apparatus of physics" - WTF it means?
I’d recommend khans academy if you want to learn more, as it’s really not that deep into the material at all. And if you dedicate a weekend to learning the subject matter you’ll not only get rid of the mystification you feel about the subject but have a really good understanding of it.
So, kinetic energy is stored as potential energy, and then released as kinetic energy again? Yes, it's true, but the question is: what stores this energy and in which form?
For example, when we use two electric magnets, when EM are attracted, energy for that is provided by grid, and when they are pulled apart, energy is returned back to grid.
In case of gravitation, the "grid" is unknown yet, but we can try to find it by tracking the energy.
Unifying gravitation and quantum mechanics amounts to asserting an equality we can never check because the numbers are tens of orders of magnitude too small to measure. People chasing unification have left off doing physics, because they have abandoned experiment. There is nothing wrong with engaging in maths for maths' sake; just don't call it physics.
There are whole worlds of physics still barely touched, because the maths have been too hard. There are plenty of open questions in solid state phenomena, in plasma fluid dynamics, in relativistic dynamics, and even in ordinary fluid dynamics.
We essentially have absolutely no fucking clue what is happening to the gravitational field when an object is in a super position of being in to different places. It definitely does something when an electron is in a superposition of different places and no one in the world can tell you what.
That is the point of unification - not some wild mathematical goosechase - we know quantum effects can do stuff to gravity (and vice-versa) and no one knows what is going on.
The last sentence of comment is reasonably true, but a lot of very, very smart people are working on all of those fields, its not like they're gonna stop because other people are working on quantum gravity.
The number of positions for post-docs in physics departments is capped by department budgets. Each seat given to a pure mathematician masquerading as a physicist is a seat not available to one who would rather do, you know, physics.
If, someday, it became possible to make progress on the topic, actual physicists would jump at the chance. Without possibility of an experiment, it is just maths. Maths departments welcome that, but don't get physics department budgets. For reasons.
What you seem to be saying is that you wish all three paragraphs were not correct. (I wish that myself.)
We already know people who have no expectation of ever being checked against experimental data are squatting Physics Department appointments, and will in time make gating decisions about grants, publications, and further appointments.