Predicted in 1916 by Albert Einstein...

>Predicted in 1916 by Albert Einstein, there are gravitational waves: ripples in the metric of spacetime that propagate at the speed of light

What is the metric of spacetime? Is it analogous to a fabric extended throughout space? Is it space itself?

A metric is, pretty generally, a function ("bilinear form") that takes in two vectors in a space and produces a real number that we interpret as "distance".

The normal Euclidean metric in the plane is probably pretty familiar, ds^2 = dx^2 + dy^2. Curved space-time has somewhat more complicated metrics in the presence of mass.

Basically it's saying distances in space-time get warped by gravitational waves.

So it's a mathematical construct representing a geometric quantity?

A metric is essentially a set of definitions that let you input two quantities (vectors, usually indicating direction in spacetime) and outputting a quantitative relationship between those vectors, like the angle between them or the inner product.

If the metric is one that can be integrated, we can use this to define distances between two points on a manifold, providing we have a metric for every point in between.

In general relativity, the metric of spacetime is one of these sets of definitions for every point in spacetime. Treating it's components as fields that change from point to point in spacetime, we can derive equations of motion for the components (similar to Laplace's equation, in some sense) that restrict how they vary. The solutions to these Einstein Field Equations is what gives rise to a gravitational force which is felt by light or matter traveling through spacetime.

Is it possible that 'spacetime' is not itself curved or bent by the local presence of matter/radiation, but that matter/radiation causes objects in a gravitational field to behave as though spacetime were bent?

Gravitational field = curved spacetime

I don't understand your question.

I'm saying is it possible that spacetime does not inherently have geometric properties, but rather that a gravitational field makes matter/radiation BEHAVE as though spacetime had geometry (ie curvature)

In that model, you have no prevailing explanation for gravity.

also, one could say that if "behavior as if X existed" is indistinguishable from "X exists" then there's no real difference and X exists.

is wrong. It is perfectly possible to construct a mathematical model for general relativity in flat space-time, it's just a bit tedious. It is mathematically equivalent and makes the same predictions; Occam's razor is usually why people don't adhere to these models.

This is not true. It ignores what the words "general relativity" actually refer to.

Also
>[citation needed]

Guys I'm confused as fuck about what quantum fields are

Are these fields (electron field, Higgs field, gluon field) etc like overlapping mediums extending throughout spacetime? Wouldn't that make them like an ether of sorts? They have to have properties to encode their respective particles, right? So does a field have charge, momentum, etc?

I think of the field as available energy for things to happen under different circumstances.

Imagine completely empty space. There's nothing there, no forces acting on it. When the space is excited, either internally (quantum flucuation and virtual particles) or externally (particles or energy enter the space) then the fields respond according to their nature.

The concept that distinguishes a field from an ether is that of a preferred frame of reference. Fields do not have these, by construction.

And yes, a field is classified entirely by a few properties:
>mass
>angular momentum
These are actually called Casimir invariants. Fields are constructed as representation spaces of the symmetry group of spacetime, the Poincare group. It's an involved construction in group theory, but every one of these representations has associated with it a set of Casimir operators whose eigenvalues specify the field exactly. Technically they are the mass squared and the angular momentum eigenvalue "j(j+1)"

>momentum
Depends on frame of reference

>charge
exists if a field has what's called a "local gauge symmetry"

>I think of the field as available energy for things to happen under different circumstances.
This is not an accurate way to think of the field itself. maybe the dynamics OF the field, but not the fundamental component.

How can a field have mass though? Mass is just rest energy, correct? I thought mass was a property than only particulate matter can have. Or can radiation have mass too?

>So it's a mathematical construct representing a geometric quantity?
yes. thats where the analogy of space being bend = gravity derives from.

Also Einstein said that matter and radiation are just kinds of distributed energy, so is a physical field also a form of distributed energy? If so, how is it distinguished from matter and radiation?

>I'm saying is it possible that spacetime does not inherently have geometric properties, but rather that a gravitational field makes matter/radiation BEHAVE as though spacetime had geometry (ie curvature)
yes of course. thats what you call having a MODEL.

Particles arise from fields. No particles = ground state of the field, 1 or more particles = excited states of the field. The "mass" property of a field is called that because it is the mass of the field's particles.

So the field itself at ground state has no mass then?

Mass as in [math]\sqrt{({\rm energy}/c^2)^2 - ({\rm momentum}/c)^2}[/math]?
That's a bit tricky because if you try to calculate the energy of the ground state of the field, you get infinite energy. That's what all the people talking about "zero point energy" mean.

Okay but that's not renormalizable?

You can subtract it off to get the energy of the particles, if that's what you mean.

You need to stop thinking of things by their analogies. Spacetime is spacetime and it behaves like spacetime

That's circular logic you clown

it is not a wave. it is not a particle. wave-particle is just a model.

a photon is just a photon

Not all fields have mass. But some do, and we interpret that as a minimum energy requirement to "excite" the field.

Renormalization is different than any concept people have brought into this thread so far. It's not related to the concepts we've been talking about. The "zero-pint" energy is just a statement that the vacuum has energy associated with it. This is very different than renormalization.

So can physical fields interact with one another directly or only indirectly through particle interactions?

Particles are an emergent behavior of the fields. They're not separate entities. When particles of different types interact, it's because of an interaction between the fields.

Radiation is a type of interaction between physical fields then?

Lel

>counting Titanium twice

You mean like beta decay? If I'm understanding your question right, yes; everything other than particles moving inertially is due to the interactions between fields.

>Particles are an emergent behavior of the fields. They're not separate entities.

What does this mean (how do you formalize it)?

the art of tesla is dead. guys please :(

>Being AuTiSTiC

It means you start with a quantum theory for a field and you derive particles from it.

What the fuck are gravity waves?

t. brainlet