Merged Relativity+ / Farsight

[Farsight]

Where was I?

There is no convention I'm aware of in which you can avoid considering some charges as negative. That we take the proton to have positive charge and the electron negative is indeed arbitrary, but that we take them to have opposite signs is not.

No problem with opposite charge. But you've heard me refer to chirality and topological quantum field theory, which relates to knots. You can tie your shoelaces left-over right to create a knot. Then on the other shoe you can tie your shoelaces right-over left to create an opposite knot. It's a "mirror image" knot, with the opposite chirality, but it isn't really a negative knot.

You're talking about extrinsic curvature. The intrinsic curvature of both bent rods is zero (assuming you mean to treat them as one-dimensional manifolds).

As I said the other day, I was referring to curvature in an electromagnetic context, as per Percy Hammond.

1D surfaces are fundamentally different to higher-dimensional surfaces - they are always intrinsically flat. When you go up to 2D, things get more interesting. See the following:

Left to right: Hyperboloid of one sheet, cylinder, and sphere.
[qimg]http://upload.wikimedia.org/wikipedia/commons/4/4a/Gaussian_curvature.PNG[/qimg]

The Gaussian (intrinsic) curvature can be negative (like a hyperboloid of one sheet), zero (like a cylinder) or positive (like a sphere), and there are important qualitative differences between the those cases.

Yes we know about this. You can draw a Euclidean triangle on a flat sheet of paper and roll the paper up into a cylinder without deforming the triangle. However the universe is not a sheet.

Triangles formed from geodesics give the best-known illustration: for a space of negative curvature the internal angles have a sum less than two right-angles, while for a space of positive curvature the sum is greater. To some extent it is conventional which type of space you call negatively-curved and which you call positively-curved, but that they are oppositely-signed holds for any useful definition of intrinsic curvature.

Sure they're opposite. But there's no evidence for any such curvature in the universe. The evidence suggests it isn't curved at all. That squares with my understanding of relativity. What doesn't, is the non-sequitur assertion that the universe must be curved, and that the radius of curvature must be huge.

 

[Farsight]

Given nothing except GR as a guide, a perfectly flat universe is exceedingly unlikely.

I beg to differ. Einstein described a gravitational field as inhomogeneous space, which you can equate to curved spacetime. The FLRW metric starts with the assumption of homogeneous space, and the universe didn't collapse under its own gravity. Ergo (expansion apart) spacetime is not curved. That's what WMAP indicated along with the Planck mission.

GR says the geometry of space is determined by the mass density.

No it doesn't. GR says the geometry of spacetime is determined by mass-energy density. The space around the Earth isn't curved, motion through it over time is curved. See this article on John Baez's website, where you can read this: "Similarly, in general relativity gravity is not really a 'force', but just a manifestation of the curvature of spacetime. Note: not the curvature of space, but of spacetime. The distinction is crucial."

There is 1 unique mass density that results in a perfectly flat universe. A razor edge. A myriad of other possibilities would appear flat unless the method of measurement is flawless.

Wrong. If the energy-density is uniform, there is no gravity. It doesn't matter what the energy-density is. Light goes straight.

The confidence level of the current flatness measurement is +/- 0.4%

That's pretty high. With the other things I've said, it ought to be enough for you to appreciate what I'm saying and why.

Not sure. If I'm visualizing it right, I suppose a flat triangle might be drawn on a doughnut-shaped surface. "Flat" in the sense that the internal angles sum to 180*.

When you draw a triangle on a sheet of paper and roll it up into a cylinder you don't deform the triangle. However when you turn the cylinder into a torus you do. It's all abstraction anyway, we have no evidence whatsoever that the universe is anything like that in a higher dimension. And nobody can actually explain to you how it would work. How can you see the back of your head?

But I'm not a fan of a toroidal universe. There is no data that calls for it.

Good stuff Toontown.

My understanding of GR is that the mass density determines the curvature.

Spacetime curvature. And it's actually "delta" energy density. If you send a light beam past a star, it curves. If you send a light-beam between two nearby stars, it goes straight as a die because there's no gradient in energy density. There is however a longitudinal energy-density gradient which result a "Shapiro" delay.

And "straight" is relative to the geometry of the space it's moving through, being the shortest path through the space.

Spacetime not space. And note that spacetime is an "all times at once" static mathematical model. Light doesn't move through spacetime. It moves through space.

Reflect off of what? Nothing?

The end of space. Imagine you're a microbe inside a water droplet and you send a ripple towards the edge of the droplet. That ripple isn't going past the edge of the droplet.

I think you've just invented a new something. A something called nothing. And that's been the problem with edged space all along.

I haven't invented the idea that space is a something. Einstein thought that you know. Go and read his Leyden Address.

If the universe is infinite, then it was never "small". Dense I'll grant, but never small. Just tightly packed.

How an infinite universe can possible square with the standard model of cosmology absolutely beats me.

A "singularity" is not necessarily a point, though it could be. "Singularity" means oneness - a singular entity. Size doesn't define what "singularity" means. A singularity can be infinite in size, as long as it's a singular entity - a oneness.

Jesus H Christ, Toontown, you don't really believe the expanding universe started out infinite do you? Because of "the oneness". Ohm, ohm, the oneness. Dearie me.

Sure, if you keep insisting that it started as a point singularity, in which case I suppose, given current observations, you need infinite expansion velocity or a replacement for GR.

I don't insist it started as a point singularity. I've referred to the original "frozen star" black hole interpretation. It doesn't have a point-singularity. Ditto for the early universe.

But the truth is, IF the universe is infinite, and if GR holds, then the universe did NOT begin as a point singularity - unless something wierd beyond my comprehension happened. A singularity, perhaps, in the "oneness" sense, but not a point. Meaning, in essence, that what changed was it's density, not it's size. And it transformed from oneness to a multiplicity of things. The "point singularity" was a speculation, not a necessity.

As for how or why the early "frozen star" universe changed and started expanding, I just don't know.

 

[edd]

Farsight, are you really still insisting that there are no curved solutions to GR where homogeneity and isotropy hold?

 

[Toontown]

I beg to differ. Einstein described a gravitational field as inhomogeneous space, which you can equate to curved spacetime. The FLRW metric starts with the assumption of homogeneous space, and the universe didn't collapse under its own gravity. Ergo (expansion apart) spacetime is not curved. That's what WMAP indicated along with the Planck mission.

Essentially wrong. Constant curvature is homogeneous. The curvature near a massive object is not constant, but that's a special case. I thought we were talking about macrocosmic space, which measures flat.

No it doesn't. GR says the geometry of spacetime is determined by mass-energy density. The space around the Earth isn't curved, motion through it over time is curved. See this article on John Baez's website, where you can read this: "Similarly, in general relativity gravity is not really a 'force', but just a manifestation of the curvature of spacetime. Note: not the curvature of space, but of spacetime. The distinction is crucial."

Again, you're using a special case of spacetime near a massive object. I'm talking about macrocosmic space, which measures flat and expanding. Imagine a photon moving through flat, expanding space, and you will see a curved spacetime path through flat space.

Wrong. If the energy-density is uniform, there is no gravity. It doesn't matter what the energy-density is. Light goes straight.

Wrong. Unless you're right and the cosmological consensus is wrong.

Again, light moving through flat, expanding space follows a curved spacetime path.

Spacetime not space. And note that spacetime is an "all times at once" static mathematical model. Light doesn't move through spacetime. It moves through space.

Light moves through space, and when macrocosmic space is flat and expanding, the light follows a curved path through spacetime.

No matter how many special cases around planets and stars you invoke.

The end of space.

What is the end of space? Is it the edge of space, or is it the edge of nothing? Pick your poison.

Imagine you're a microbe inside a water droplet and you send a ripple towards the edge of the droplet. That ripple isn't going past the edge of the droplet.

A droplet of water is not analogous to space in any way relevant to your claim. A droplet of water has a molecular skin, invoked by electromagnetic forces. Without the molecular skin, the droplet would disintegrate. There is something on the other side of that skin. Something the ripple would propagate into if the skin didn't stop it.

So, when light hits the edge of space, does it bounce off the space at the edge, or the nothingness at the edge?

I haven't invented the idea that space is a something. Einstein thought that you know. Go and read his Leyden Address.

I wasn't talking about space. You said the edge of space doesn't form a barrier, so I figured the light must be bouncing off the nothing at the edge.

How an infinite universe can possible square with the standard model of cosmology absolutely beats me.

Well, it doesn't seem to beat anyone else. The univese starts immeasurably hot and dense and starts becoming cooler and less dense, becoming measureable along the way.

Jesus H Christ, Toontown, you don't really believe the expanding universe started out infinite do you? Because of "the oneness". Ohm, ohm, the oneness. Dearie me.

Jesus H Christ, Farsight, are you trying to use peer pressure on me? May I remind you that you are a group of (1). I hear it's lonely at the top.

I said IF the universe is now infinite, then it started infinite. And why wouldn't it have been a "oneness"? What else would it be, before it was anything measurable? What do you think a "point singularity" is - a multiplicity? But then they'd call it a "multiplicity" instead of a "singularity", wouldn't they.

I don't insist it started as a point singularity. I've referred to the original "frozen star" black hole interpretation. It doesn't have a point-singularity. Ditto for the early universe.

Are you saying you are familiar with the concept of a singularity that isn't a point?

As for how or why the early "frozen star" universe changed and started expanding, I just don't know.

Maybe you'd know more if you started from different assumptions. If a black hole could empark upon a regimen of accelarating density reduction, it wouldn't be a black hole in the first place.

 

[Farsight]

With regards to what Farsight is insinuating about my opinions - I find them presumptive and insulting. I think what GR states is unambiguous and I do not have any particular problem with how some parties choose to express how that relates to conservation of energy. I think energy conservation is at a minimum an extremely important principle is almost all situations and is at worst something one should consider carefully in certain contexts by careful consideration of Noether's theorem and the rather clear cut laws of physics one would assume for them. I simply recognise why some parties may wish to encourage a, as I said initially, more nuanced view.

I didn't mean to be insulting edd. I just thought a bit of pointed criticism would help you think it through. Please accept my apologies.

 

[Farsight]

Such a viewpoint is incompatible with GR, the infinite FLRW solutions being among the counterexamples to your claim.

They aren't good counterexamples, in that the FLRW offers more than one solution, and they can't all be right.

"Finite universes with interesting topologies" includes several types of flat, finite universe.

But none that you can support defend with an explanation that Toontown can understand?

I think that makes about as much (and as little) sense as asking how a sphere "actually works", or finite flat space "actually works". Can you rephrase that question in a way that doesn't use the words actually or work?

OK, if light goes straight, how come I can see the back of my head?

That's your opinion, but that's not a prediction of GR, and it looks like your position is inconsistent. On no evidence at all, you positively reject infinite models

Expansion is the evidence. How many times do I have walk you through it?

yet on no evidence at all (and with considerably less theoretical support), you accept a finite flat model. I put it to you that your preferences on this matter are illogical, and based on nothing more than aesthetics.

Wrong. They're based on the expansion of the universe.

So you don't know whether momentum is conserved in your model, you merely imagine that it might be. This is just the tip of the iceberg, too. I think that there may be a rather serious issue with your model regarding this boundary.

Not as serious as those with an expanding universe that's always been infinite, or as those with a mystic torus universe.

For starters:

1. What boundary conditions apply to various fields (e/m, gravity, the various fermions, etc.)?

You'll be aware that I refer to an electromagnetic field as something akin to the gravitomagnetic field, involving frame dragging in three dimensions. At the boundary the field would be distorted, and largely hemispherical. I refer to a gravitational field as inhomogeneous space. At the boundary it would be simply truncated.

2. What shape does this boundary have, and why?

I can't say with any confidence. But I imagine it's spherical.

3. How does its shape and size vary with time, and why,

The shape remains spherical, and the size increases with time.

and how is its shape and size influenced by interactions with matter?

I can't say with any confidence. However given the wave nature of matter, I would expect the boundary to bulge momentarily during say an interaction with an electron.

 

[Farsight]

...Had Farsight understood the technical details of that Wikipedia article, he'd have learned that a negative value for the Ricci scalar means the volume of a ball with (sufficiently small) radius is larger than it would be in Euclidean space, while a positive value means the volume is smaller than it would be in Euclidean space...

And like I said, the volume of the ball isn't negative.

Farsight also believes he's giving me lessons on general relativity.

You got it Clinger. And lessons in electromagnetism.

 

[Farsight]

You have replied only to this part of my post:

What you actually said was this:

"Dropping a dimension think of a thin spring steel rod, then bend it into this shape U. Call that positive curvature. Then bend it into this shape ∩. This isn't less curved than the straight rod, you merely call it negative curvature by convention".

(My highlighting.)

You are clearly talking about curvature of some type in your rod example. If you didn't mean extrinsic curvature, as I originally thought, then all that is left is either (a) intrinsic curvature or (b) your private definition of curvature.

If (a), then you are wrong. You are wrong if you take the rods as 1D objects, because they both have an intrinsic curvature of zero, and you are wrong if you take them to be 2D surfaces, as they'd have the same intrinsic curvature at corresponding points (one is just a mirror image of the other). If you take them to be 3D objects in some way, then you must be using a private definition of curvature (see below).

If (b), then you should make your private definition public so we can properly understand what you're saying.

LOL, ctamblyn, you have an amazing ability to dig yourself into a hole. I said No, the rods were relevant to charge and chirality and curl and electromagnetism, not to intrinsic curvature. The curvature in the analogy is extrinsic curvature. See wiki, which includes this:

"In mathematics, curvature refers to any of a number of loosely related concepts in different areas of geometry. Intuitively, curvature is the amount by which a geometric object deviates from being flat, or straight in the case of a line, but this is defined in different ways depending on the context. There is a key distinction between extrinsic curvature, which is defined for objects embedded in another space (usually a Euclidean space) in a way that relates to the radius of curvature of circles that touch the object, and intrinsic curvature, which is defined at each point in a Riemannian manifold. This article deals primarily with the first concept".

The curved rods are an analogy for electromagnetic curvature as per Percy Hammond, not Riemann curvature as per general relativity.

 

[Farsight]

My opinion on the brick? It's boringly classical for the purposes of this discussion - in other words I think a conserved quantity can be easily defined for it for energy.

It isn't boringly classical edd. The mass of the brick at altitude is x. When you drop it, it exhibits a final kinetic energy of y. Once you've dissipated this, the mass of the brick on the ground is z, and z = x - y. The invariant mass varies. No way is that classical in the Newtonian sense.

Also, you aren't the expert. I would not wish to paint myself as a good cosmologist but I am not poorly educated in that way, and you persistently make extremely, quite plainly, basic errors.

Oh no I don't. Do you think I'm wrong about that brick? Go look up mass deficit. I'm right. Again.

 

[Farsight]

Could you please list the evidence for a finite universe?

1. Expansion

 

[Farsight]

Farsight, are you really still insisting that there are no curved solutions to GR where homogeneity and isotropy hold?

No. Those solutions are there, we all know that. We also know that they can't all be right. I'm saying that none of the curved solutions are right when it comes to the "shape" of the universe. And it would seem that WMAP and the Planck mission indicate that this is indeed the case.

 

[Toontown]

They aren't good counterexamples, in that the FLRW offers more than one solution, and they can't all be right.

But none that you can support defend with an explanation that Toontown can understand?

You're making me the guinea pig in your argument with ctamblyn?

I have no problem with the fact that geometry can be tortured into various forms that fit a widely accepted definition of flatness. I just feel no need to worry my pretty little head about all of them. If I worry my pretty little head about every little thing, I'll only get bogged down in details. No one can know everything. Fortunately, it isn't necessary to know everything.

Most cosmologists don't worry their pretty little heads about toroidal space and flat space with an edge, for a couple of examples, probably because it seems impossible to torture the known laws and data into forms which would invoke such space.

 

[Farsight]

Essentially wrong. Constant curvature is homogeneous. The curvature near a massive object is not constant, but that's a special case. I thought we were talking about macrocosmic space, which measures flat.

We are. It's flat. It isn't curved. And there's no justifiable intrinsic curvature either. Even ctamblyn said "Agreed" about the torus.

Again, you're using a special case of spacetime near a massive object. I'm talking about macrocosmic space, which measures flat and expanding. Imagine a photon moving through flat, expanding space, and you will see a curved spacetime path through flat space.

No problem. That's why I said expansion apart. Think of a little motor boat travelling on a straight line as it chugs across a puddle of treacle. It leaves a convenient wake behind it, marking out its path. This wake is straight. However when the puddle is expanding, the wake isn't straight.

Wrong. Unless you're right and the cosmological consensus is wrong.

I'm right.

Again, light moving through flat, expanding space follows a curved spacetime path.

And again, we set the expansion aside to see that in a homogeneous universe light goes straight. And note that you set the little motor boat down in the expanding puddle heading towards the edge, its wake is straight. It doesn't curve away from the edge, and it doesn't disappear from one edge and reappear on the opposite edge.

Light moves through space, and when macrocosmic space is flat and expanding, the light follows a curved path through spacetime.

But there's no gravity. The properties of space are varying over time, not across space.

What is the end of space? Is it the edge of space, or is it the edge of nothing? Pick your poison.

The edge of space. Like I said, Einstein thought of space as a something rather than a nothing.

A droplet of water is not analogous to space in any way relevant to your claim.

Yes it is. Waves run through it.

A droplet of water has a molecular skin, invoked by electromagnetic forces. Without the molecular skin, the droplet would disintegrate. There is something on the other side of that skin. Something the ripple would propagate into if the skin didn't stop it.

The "skin" doesn't stop it. There's no more water molecules to ripple.

So, when light hits the edge of space, does it bounce off the space at the edge, or the nothingness at the edge?

Neither. See above. There's no more space to ripple.

I wasn't talking about space. You said the edge of space doesn't form a barrier, so I figured the light must be bouncing off the nothing at the edge.

Don't. A ripple inside a droplet doesn't "bounce off" nothing, or the air.

Well, it doesn't seem to beat anyone else. The universe starts immeasurably hot and dense and starts becoming cooler and less dense, becoming measureable along the way.

It doesn't necessarily start off hot. Dense, yes. But heat is an emergent system property. The temperature of a gas is a measure of the average kinetic energy of the gas molecules. If they can't move because they're confined under enormous pressure, that "gas" isn't hot. It isn't even a gas either.

Jesus H Christ, Farsight, are you trying to use peer pressure on me? May I remind you that you are a group of (1). I hear it's lonely at the top.

Don't try to deflect attention from the issue. Do you seriously believe that the universe started out infinite? No.

I said IF the universe is now infinite, then it started infinite. And why wouldn't it have been a "oneness"? What else would it be, before it was anything measurable? What do you think a "point singularity" is - a multiplicity? But then they'd call it a "multiplicity" instead of a "singularity", wouldn't they.

Sorry Toontown, your "oneness" sounded like something out of an Eastern religion.

Are you saying you are familiar with the concept of a singularity that isn't a point?

Yeah sure. The Schwarzschild singularity is an example. I say it's something real, the other guys here dismiss it as a "coordinate artefact".

Maybe you'd know more if you started from different assumptions. If a black hole could empark upon a regimen of accelerating density reduction, it wouldn't be a black hole in the first place.

I try not to assume anything.

I hope you took on board what I said about space and spacetime. A lot of people confuse them. People who should know better.

 

[Farsight]

You're making me the guinea pig in your argument with ctamblyn?

Yep. I can explain things in terms that you can understand, and which make sense. A guy like ctamblyn will poo-poo what I say, but he can't offer an alternative explanation that you can understand, and which make sense. You should demand it from guys like him.

I have no problem with the fact that geometry can be tortured into various forms that fit a widely accepted definition of flatness. I just feel no need to worry my pretty little head about all of them. If I worry my pretty little head about every little thing, I'll only get bogged down in details. No one can know everything. Fortunately, it isn't necessary to know everything.

I'm sure that Catholic priests used to tell people not to worry their pretty little heads about things too. Just accept what they say, and let them do the thinking for you. Then when some guy challenges that thinking, don't worry your pretty little head about it.

Most cosmologists don't worry their pretty little heads about toroidal space and flat space with an edge, for a couple of examples, probably because it seems impossible to torture the known laws and data into forms which would invoke such space.

What you really mean if that you don't buy the toroidal universe, and you don't buy the infinite universe either. So voila, you find yourself in the same boat as me.

OK, gotta go. Nice talking to you guys as ever. Make sure you think about what I've said. And make sure you think for yourself.

 

[edd]

It isn't boringly classical edd. The mass of the brick at altitude is x. When you drop it, it exhibits a final kinetic energy of y. Once you've dissipated this, the mass of the brick on the ground is z, and z = x - y. The invariant mass varies. No way is that classical in the Newtonian sense.

Oh no I don't. Do you think I'm wrong about that brick? Go look up mass deficit. I'm right. Again.

I think mass defects are observed in systems of particles and the fields by which they interact. I'm not aware of evidence that the rest mass of bound particles varies in the way you seem to be implying, and yet again I worry about the blasé discarding of the equivalence principle when you suggest that sort of thing happens in a gravitational field.

 

[edd]

I didn't mean to be insulting edd. I just thought a bit of pointed criticism would help you think it through. Please accept my apologies.

Thanks, I understand what you intended better now and appreciate the explanation. I hope you understand that I personally obviously think conservation of energy holds in all non-cosmological situations. In others where GR I think the equations are clear and how one chooses to verbally describe those equations and their implications can be worded differently by different people, and as long as they imply the same observed result I tend not to worry too much. This applies to some other bits of cosmology too as it happens.

 

[ctamblyn]

No problem with opposite charge. But you've heard me refer to chirality and topological quantum field theory, which relates to knots. You can tie your shoelaces left-over right to create a knot. Then on the other shoe you can tie your shoelaces right-over left to create an opposite knot. It's a "mirror image" knot, with the opposite chirality, but it isn't really a negative knot.

But that's just in your view of the world. In physics, electric charge is described by a scalar number, and negative charges do indeed exist.

...
Sure they're opposite. But there's no evidence for any such curvature in the universe. The evidence suggests it isn't curved at all. That squares with my understanding of relativity. What doesn't, is the non-sequitur assertion that the universe must be curved, and that the radius of curvature must be huge.

Just to recap, for my benefit as much as anyone else's, we're talking about the possibility of negative curvature of spatial slices through spacetime.

Such a thing is possible, according to GR, on cosmological scales, though the evidence suggests that the large-scale curvature is very small (or zero) in our observable universe.

That aside, negative curvature in spatial slices on a local scale is actually commonplace. In the humble Schwarzschild metric, a constant-Schw.-time slice is a 3D version of a Flamm paraboloid, which has everywhere negative intrinsic curvature (which drops off as the cube of the Schw. radial coordinate).

 

[ctamblyn]

They aren't good counterexamples, in that the FLRW offers more than one solution, and they can't all be right.

That's not my point. My point is that they are all possible according to GR, and it is a matter of measurement to determine which is the best approximation to the universe around us.

But none that you can support defend with an explanation that Toontown can understand?

OK, if light goes straight, how come I can see the back of my head?

I covered that above. Remember that "straight" is defined with regard to the intrinsic geometry, not the particular choice of embedding in a Euclidean (which is just as well, as such embeddings are not always possible).

Expansion is the evidence. How many times do I have walk you through it?

Wrong. They're based on the expansion of the universe.

See above. The fact that a uniformly-dense universe is expanding does not make it spatially flat, except when the density has one particularly special value.

Not as serious as those with an expanding universe that's always been infinite, or as those with a mystic torus universe.

You underestimate the severity of the problem. At things stand, your model may not even be deterministic at the boundary, and whatever rule you apply will be additional to GR (and all the rest of physics), rather than derived from it.

You'll be aware that I refer to an electromagnetic field as something akin to the gravitomagnetic field, involving frame dragging in three dimensions. At the boundary the field would be distorted, and largely hemispherical. I refer to a gravitational field as inhomogeneous space. At the boundary it would be simply truncated.

I can't say with any confidence. But I imagine it's spherical.

The shape remains spherical, and the size increases with time.

I can't say with any confidence. However given the wave nature of matter, I would expect the boundary to bulge momentarily during say an interaction with an electron.

That's all lovely (though the last two statements contradict each other), but there isn't a shred of evidence for any of it. Why do you accept and actively promote it, even given the lack of either theoretical or experimental justification, while rejecting infinite models which are perfectly consistent with the evidence according to GR? There is a degree of hypocrisy in your position.

 

[ctamblyn]

LOL, ctamblyn, you have an amazing ability to dig yourself into a hole. I said No, the rods were relevant to charge and chirality and curl and electromagnetism, not to intrinsic curvature.
...

What you said in the post I actually responded to, as opposed to what you later claimed to have said, is there for everyone to see.

 

[ctamblyn]

We are. It's flat. It isn't curved. And there's no justifiable intrinsic curvature either. Even ctamblyn said "Agreed" about the torus.

The torus in question has zero intrinsic curvature.