>Predicted in 1916 by Albert Einstein, there are gravitational

>>9117372

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.

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>>9117386

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

>>9117386

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.

>>9117441

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?

>>9117455
Gravitational field = curved spacetime

I don't understand your question.

>>9117458

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)

>>9117470
In that model, you have no prevailing explanation for gravity.

>>9117470
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.

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>>9117470

>>9117479 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.

>>9117492
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?

>>9117539
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.

>>9117539
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"

>>9117605
>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.

>>9117636

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?

>>9117413
>So it's a mathematical construct representing a geometric quantity?
yes. thats where the analogy of space being bend = gravity derives from.

>>9117753

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?

>>9117470
>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.

>>9117753
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.

>>9117769

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

>>9117771
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.

>>9117782

Okay but that's not renormalizable?

>>9117791
You can subtract it off to get the energy of the particles, if that's what you mean.

>>9117455
You need to stop thinking of things by their analogies. Spacetime is spacetime and it behaves like spacetime

>>9117802

That's circular logic you clown

>>9117827
it is not a wave. it is not a particle. wave-particle is just a model.

a photon is just a photon

>>9117753
Not all fields have mass. But some do, and we interpret that as a minimum energy requirement to "excite" the field.

>>9117791
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.

>>9117900

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

>>9118188
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.

>>9118211

Radiation is a type of interaction between physical fields then?

>>9117827

Lel

>>9117492
>counting Titanium twice

>>9120893
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.

>>9118211
>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 :(

>>9121455
>Being AuTiSTiC

>>9122269
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