What is "the fabric" of space-time?

First let me return to physics as it currently stands in addressing the question, “what is the fabric of reality”.First of all, we have the basic revolutions of the 20th Century. Quantum Mechanics and Special Relativity. Quantum Mechanics is all about probabilities, e.t.c. I won’t go into it as it is tangential to the main issue here. Special Relativity is a theory which describes the structure of spacetime.(Part 1)
Okay as it currently stands in physics the world is described by two theories, General Relativity and the Standard model. General Relativity is an example of a classical field theory and the Standard model is an example of a quantum field theory.Classical field theory is a framework which describes fundamental forces using quantities defined everywhere in spacetime. An example is the electric field, which is defined at each point in spacetime and tells you the amount of Newtons per Coulomb, in a certain direction, at that location. How the field behaves is described by a set of equations, like Maxwell’s equations.Quantum Field Theory is another framework. Unfortunately I can not give a snappy description like the one above for classical field theory. The best way, where by best I mean “will lead to the least confusion”, is that quantum field theory is a language or mathematical syntax in which it is impossible to write down something which contradicts the basic tenants of special relativity and quantum mechanics. To do this the language makes use of “field operators” as its basic grammatical components. These field operators behave very similar to the fields of classical field theory to some extent. Obviously, since it is impossible to contradict special relativity in quantum field theory, quantum field theory uses the spacetime structure of special relativity rather than the absolute space and time structure of old Newtonian theory. An important point to stress is that quantum field theory is a language for writing theories; it is not (despite its name) a theory itself. If a theory is written down in the quantum field theory language it is called a quantum field theory or a QFT.(Part 2)
General Relativity updates the spacetime structure of special relativity to one where the shape of spacetime can change or be bent due to the presence of matter. The information regarding the shape of spacetime is stored in a quantity known as the metric tensor. This quantity is defined everywhere on spacetime and so General Relativity is a classical field theory, the field being the metric tensor.However if one wishes to perform particle physics then effects due to gravity are negligible so we can use special relativity’s flat spacetime structure. Since we are dealing with particles (quantum) at high speeds (relativity) we need quantum field theory.
Let us say we want to describe electrons interacting electromagnetically, we will need to write down a quantum field theory of the electromagnetic force. Roughly since we are dealing with two objects, the electromagnetic force and electrons, we need two “field operators”. A magical consequence of the QFT language is that when we write down the field operator for electrons, the same field operator also describes another particle which has opposite charge to the electron.* This particle is the “anti-electron” or positron. When we write down the field operator for the electromagnetic force it describes a particle called a photon.
This quantum field theory of photons, electrons and positrons is called QED or Quantum Electrodynamics.We then move on to the other forces and add field operators for quarks, neutrinos, e.t.c. As well as field operators for the other two forces, the weak and strong nuclear forces. Eventually we end up with a field theory with several field operators (17 or 20 in total, depending on how you count them**). This massive field theory is called the standard model and describes all particle physics ever observed.However what if we wanted to look at particle physics when gravity is strong and spacetime is curved? Then the language of quantum field theory can be updated so that it works with the spacetime structure of general relativity. This new language is known as quantum field theory in curved spacetime, but it is seldom used practically.This is where physics currently stands.*Quantum field theory basically explains antiparticles as being a consequence of causality. If you want to keep special relativity’s causality when you add in quantum effects you need antiparticles.**cavediver, I obtained this number by considering as a unique field, in the first case, each distinct rep of U(1)XSU(2)XSU(3). For matter this gives 16 fields. (2 fields per lepton generation, 3 per quark generation and Mr. Higgs all on his own) and all force fields as a single adjoint rep. The second figure is an attempt to be a little fairer to the forces and I’ve split the electroweak field into U(1)_e and the rest in order to reflect a little better the low energy world we live in.Edited by Son Goku, : Change of number

This deserves an explanation. Feynman worked during a period when QFT was very new and hence his way of thinking will seem a bit out of step with what we are saying.Basically Feynman came up with his diagrams, which you are familiar with. As you said these diagrams seem very particle based, not field based. That is what Feynman intended, he considered these diagrams as quantum mechanical descriptions of particle interactions of photons and electrons, nothing to do with fields.At the same time Julian Schwinger, who had just come out of working on radar research for the US government, had developed a quantum field theory of the interactions of photons and electrons.
Also at the same time Sin-Itiro Tomonaga, a Japanese physicist, had obtained a field theory identical to Schwinger's.The Schwinger-Tomonaga field theory gave identical predictions to the Feynman particle theory. Freeman Dyson eventually proved that Feynman's diagrammatic expressions are generated by the field theory. Of course many people were divided over which was primary. Did the field theory form the bedrock and generated the Feynman diagrams as a side bonus or were the diagrams all that matter and the fields only a pile of mathematical junk used to obtain them?During the 60s people veered in the direction of the later. Mainly because making Quantum Field Theory mathematically consistent seemed impossible* and field theory didn't seem to be able to describe the strong and weak nuclear interactions.However, ever since the 70s we've found several things (nonperturbative effects, certain bound states, e.t.c.) that the Feynman diagrams can't see/predict, which field theory does. Hence we now know that the Feynman diagrams are just useful mnemonic for field theory calculations when the interactions are weak.*In fact it still seems so. You can obtain $1,000,000 from the Clay mathematics institute if you can make it consistent.Edited by Son Goku, : Better title.

Here is how I think about it and to support it I'm going to take concepts first developed by Wilson. In my mind this has nothing to do with Platonism vs. formalism, since that is a mathematical question and this is a physical question. Take a river. Currently we know that a river is "really" a collection of atoms, an entirely discrete collection of quantum mechanical objects. It isn't "really" a smooth continuum fluid. Does this matter?
The answer is no, the reason being because at large scales all the atomic degrees of freedom smear into large scale continuum modes which transport energy and momentum density. On our scale water "is" a continuum fluid. All other degrees of freedom disappear and it is inappropriate to think of water as a discretum. Hence the model is a correct conception of the phenomena. Due to Kenneth Wilson's work we know that whatever the fundamental theory of reality, at low energy scales the degrees of freedom will "smear" together into a renormalizable quantum field theory. At our energy scales nature is a bunch of relativistic quantum fields. Think of it this way, just because a chair is made of atoms doesn't mean there is no chair. However nature is not a bunch of particle diagrams, a lá Feynman, at this scale.With regards to curved spacetime, you have asked is spacetime really curved. Well here is my opinion. First of all, at these energies I can take out a watch and ruler and measure distances and times between events. These events are recorded as real numbers; hence I can smoothly map spacetime points on to real numbers. That is one of the first conditions of being a manifold. Next I check with my friend to see the values of his measurements. Turns out my results can be expressed smoothly as a function of his results. That's basically all we need, spacetime is a manifold. From purely physical considerations I have deduced spacetime is a manifold on these energy scales. What else do I know? Well I can tell exactly how far away my friends are with my ruler. That is I can put a number to it, rather than just being able to say they are "near". So spacetime has more than just topological structure, it has a metric structure.
I can send a satellite into near Earth orbit to measure distances around the Earth with respect to me. Turns out the distance is given by a function. I check with my friends, with their own satellites, how they record the distance function. Their distance function can be related to mine in a certain way, making this function a tensor. Finally derivatives of this function, called curvature, correspond to gravitational stress the earth's ocean feels. Making these curvatures have a physical effect. So in what sense, at these scales, is spacetime not a curved manifold?Basically, can I say an apple is really 1 apple or is 1 just an accurate tool? Well at this scale, the scale we live at, there is 1 apple and I think that is true regardless of the quantum mechanics of the apples' atoms. Similarly matter is a quantum field at the compton scale and spacetime is a curved manifold regardless of what is going on at deeper scales.

First of all, to understand this post, you should know that it isn’t only mass that is supposed to cause spacetime curvature, but angular momentum, stress, even heat. You have recorded height as a function of time. The direct reading of the mathematics is that at "this time" you will have "this height" and that is exactly what you have. There is not a dynamic coupling between height and time, such as there is (vaguely speaking) between mass and time in GR. A function indicates some sort of dependence between quantities. For an actual coupling, where the quantities affect each other, you would expect a dynamical equation of motion, which would give functional solutions, something you have not recorded in your example. In fact you can easily see there is no coupling because in your example the time axis never changes, its values are simply mapped to height values. I appreciate though that “reading” maths is a skill that takes time to develop. I understand what you mean. However we have literally observed that objects near a large mass start having their clocks run slow, frequencies drop, in fact every physical process “slows down”. The effect is stronger nearer the mass and with increased density the effect becomes stronger. You also have to bear in mind that this isn’t an entirely philosophical issue. I can put statistical strength behind the assertion “mass affects time”. That is, with repeated measurement of various independent quantities the likelihood of the assertion being correct increases. It is now very, very likely to be correct.Also, to expand on my last post, there are in fact satellites in near earth orbit that use synchronised clocks and standard “rulers” to measure the spatial and temporal curvature near the earth. Even if you ignore for a moment the claim that mass causes spacetime curvature, we actually have observational evidence that spacetime is curved from these satellites. Which means we have empirical evidence that spacetime can be a dynamical entity and not simply a static observable. However, from the observations we then see that this curvature matches exactly (within observational error) the predictions of General Relativity of the effects of the Earth’s mass on spacetime. It even matches the predictions concerning the effects of the Earth’s angular momentum on spacetime.Also, unlike your example above, General Relativity is an entire framework which produces several consequences of the coupling of spacetime and mass. An example is neutron star orbit decay. All this stuff was predicted in advance as a consequence of the effects of this mass/spacetime interaction. It was not a case of us coming upon some kind of correlation between them and then assuming causation.Another thing to bear in mind is that mathematically speaking, if the equivalence principle is true and special relativity holds, mass has to affect spacetime. You can not avoid that conclusion mathematically.So, on a statistical, logical and observational front we have very good reason to conclude that mass causes spacetime to curve. A Tensor, physically, is a measurable quantity that has a definitive rule describing how it is viewed in one particular coordinate system (read reference frame, roughly speaking) compared to another. A simple example would be electromagnetic field strength. It takes six numbers to record electromagnetic field strength and those numbers measured in one frame can be related to the numbers measured in another frame. In fact you could see it as confirmation of special relativity. According to special relativity it is a tensor and observations confirm the fact that is a tensor.

The GPS satellite wasn't designed to directly test GR, so if you're looking for better experiments check out the PSR B1913+16 pulsar binary system experiments. There is also gavity probe a and more recently gravity probe b.
Also, one thing I cannot stess enough to people, is that we have directly measured that spacetime is curved. Even if somebody disagrees with GR's mechanism of mass causing that curvature, we know that the curvature exists. However I think the best way to see what GR proposes is to understand the Minkowski spacetime structure of special relativity. Then understand how an accelerated observer views the path of a light ray and finally combine this understanding with the equivalence principle and the realisation that there are no forces on you in free-fall. It soon becomes fairly clear that mass causes the curvature of spacetime.Basically an accelerated observer will see that light has a curved path. By the equivalence principle, light also has this path in a homogenous gravitational field created by a given mass. However the light is in free fall and has no forces on it and also from SR, the light simply follows null geodesics in spacetimes*. So the only way the curved path can occur is if the null geodesics themselves have become altered, which means the spacetime now has a dfferent shape due to the mass.** Several reasons. Mainly it's far too difficult to put in context for a child, since GR makes no sense without SR, pedagogically speaking.*Null geodesics are a kind of straight line in spacetime.
**Remember, in this example, the only thing I've put in the spacetime is the mass, so there is nothing else to "pin the mechanism on".Edited by Son Goku, : Slight addition.

Yes there is something similar in General Relativity, they're called the Penrose-Carter diagrams. A quick search on the net will give you a few images. It's also fairly easy to teach somebody how to read them, even if they haven't too much mathematical experience with GR.You mentioned the word "Isochronal". Just as isobars are surfaces of constant pressure, I'd imagine these would be surfaces of constant time, yes? If so, they're usually known as "spacelike hypersurfaces".

I just wanted to say that this is not true. Things are not made of energy. Energy is the ability to do work. It is a quantity an object can posses. Mass, the resistence to motion, is another quantity possessed by matter. Relativity states that these two quantities are the related. However nothing says that everything is made of energy.

Who knows? Depends on what you want. I could give an answer about particles being Poincaré irreps, e.t.c. However that's tangential to the thread. That is incorrect. You cannot "condense" energy and make it become matter. Show me a process where you take some "ability to do work" and condense it to make matter. If matter was only made of energy where would electric charge come from? In no theory in physics is matter made of energy. Again, there is no process where extremely disperse matter becomes energy. Name one, if you don't think this is the case. Which expresses how much energy a given amount of mass (the resistence to motion) is equivalent to. Not that matter is made of energy. True, but the same could be said of electric charge, color charge, momentum, spin, e.t.c. It doesn't mean matter is made of energy. There are several answers one could give, which may or may not be satisfactory. That doesn't change the fact that matter isn't made of energy.

Apologies for off-topicness. Ah, don't worry. The standard of this forum (in any area of discussion) is far too high for that to happen. Compare with another forum where I was recently accused of being a "dogmatic and textbook thumping member of the orthodoxy" for my "claim" that Neanderthals didn't land on the moon.

You do not need to know everything to know something. Given what energy actually is, it is a trivial deduction that matter is not made of it, regardless of one's knowledge of the actual constituents of matter.
Matter is not made of energy, just as it is not made of angular momentum. Both are properties of matter. Mass-Energy equivalence relates two properties of matter to each other. It still does not give a process where energy condenses and becomes matter. Where would every other property come from then? For instance charge.