Merged Relativity+ / Farsight

[Reality Check]

Farsight: Standard cosmology does not imbed the universe in a higher dimension

Au contraire, the evidence supporting big-bang cosmology suggests a finite universe. And whilst I'm on a roll, there is no evidence whatsoever to support the notion that the universe is somehow curved "in a higher dimension". Zip, zero, zilch. And as for PacMan world, pah.

Au contraire, the evidence supporting big-bang cosmology says nothing about whether the universe is infinite or finite. All it says is that universe is a lot bigger than the observable universe.
Is the Universe really infinite or just really big?

We have observations that say that the radius of curvature of the Universe is bigger than 70 billion light years. But the observations allow for either a positive or negative curvature, and this range includes the flat Universe with infinite radius of curvature. The negatively curved space is also infinite in volume even though it is curved. So we know empirically that the volume of the Universe is more than 20 times bigger than volume of the observable Universe. Since we can only look at small piece of an object that has a large radius of curvature, it looks flat. The simplest mathematical model for computing the observed properties of the Universe is then flat Euclidean space. This model is infinite, but what we know about the Universe is that it is really big.

And while you are still displaying some ignorance: there is no evidence whatsoever to support your imaginary notion that the universe is somehow curved "in a higher dimension". Zip, zero, zilch.
There may be some obscure cosmology theory out there that imbeds the universe in a higher dimension.
Standard cosmology does not imbed the universe in a higher dimension.

 

[Farsight]

That's not an assumption. The FLRW model assumptions are that the the universe is homogeneous and globally isotropic. If that's assumed, then the only possible flat spatial geometry is that of the (infinite) Euclidean plane.

It just isn't true, Vorpal. The universe can be homogeneous without being infinite. You cannot claim that the universe is not homogeneous on the grounds that something exists beyond the universe which is different. There's isn't anything beyond it, the universe is everything. So everything, the universe, is homogeneous.

But it's obviously not valid to say that just because the observable universe is pretty close to homogeneous and isotropic, then then whole universe must be so.

Sure thing. We can't be sure about the whole universe. And we can't be sure that it's infinite.

Fortunately, pretty much nobody actually made such a claim--the FLRW family is an idealization to simplify things, not a literal truth. Its actual physical relevance is only that the universe around us is close to a flat FLRW model; there is no suggestion that the universe arbitrarily far away must match the same FLRW model.

I tell you Vorpal, from my understanding of general relativity, the universe is flat, and was always flat. There's no overall gravity. It didn't collapse when it was small and dense, and it just had to expand. As for why Einstein talked about a hypersphere and a static universe, I don't know. It's as if his confidence in his own theory deserted him when it came to cosmology. Why oh why did he talk about a dusty universe instead of one comprised of space alone?

Notably, inflationary models of the Big Bang tend to explicitly break the assumptions of homogeneity and isotropy rather hard anyway.

I have no problem with inflation. Think in terms of a high energy density and extreme "gravitational time dilation".

I agree with the first statement. I don't agree with the rest--the evidence is pretty agnostic on the shape of the universe on the scale much larger than the observable universe. Because it's not observable, any claim about it is going to be based on assumptions that there is no evidence for.

The shape of the universe is perhaps misleading in that a "flat" universe might be a ball. But yes, we have no evidence for that. Just as we have no evidence for an infinite universe. IMHO the expansion is evidence against an infinite universe.

I don't know what you're talking about here. I don't recall this ever coming up as a claim by anyone.

ctamblyn referred to a PacMan world. It isn't his own idea. It's been bandied about by various "celebrity cosmologists". I'll dig up some references if you like, but tomorrow. Right now I'm off to bed.

 

[ctamblyn]

ctamblyn referred to a PacMan world. It isn't his own idea. It's been bandied about by various "celebrity cosmologists". I'll dig up some references if you like, but tomorrow. Right now I'm off to bed.

As I hope I made clear, I was simply explaining what a "flat torus" was, not making any claims about the topology of the universe.

 

[Reality Check]

I tell you Vorpal, from my understanding of general relativity, the universe is flat, and was always flat. There's no overall gravity. It didn't collapse when it was small and dense, and it just had to expand. As for why Einstein talked about a hypersphere and a static universe, I don't know. It's as if his confidence in his own theory deserted him when it came to cosmology. Why oh why did he talk about a dusty universe instead of one comprised of space alone?

Anyone who has studied GR and cosmology can tell you, Farsight, from their understanding of general relativity, that

• the universe is always "curved" and that curvature can be positive, negative or even zero.
• GR in cosmology indeed has no "overall gravity" because there is nothing outside of the universe to experience that gravity.
  There is however curvature as above (which may be zero). Note that this is intrinsic curvature.
• The universe did not collapse when it was small and dense - it expanded!
• The universe dis actually expand.
• A hypersphere is a common mathematical object so it is likely that Einstein talked about it.
• Einstein talked about a static universe because he wanted the universe to be static which was the theory at the time.
• Einstein was very confident about GR being used in cosmology, especially when many scientists developed cosmological models that fit current and future observations.
• Einstein talked about a dusty universe because he knew that this universe is not empty.
  I hope you know that, Farsight .
• Einstein would not have been silly enough to talk about a universe comprised of "space alone".
  He would have talked about a universe comprised of space-time only, i.e. he would set the RHS of his equation to zero to get Vacuum solution (general relativity).

 

[Reality Check]

IMHO the expansion is evidence against an infinite universe.

Sorry, Farsight, your humble opinion is just wrong because it ignores what the expansion of the universe actually is.
The expansion is an increase in distances as in the Friedmann–Lemaître–Robertson–Walker metric.
You can start with a finite universe, distances within it get bigger and finite universe expands.
You can start with a infinite universe, distances within it get bigger and this infinite universe expands.

Thus the expansion says nothing about the finiteness of the universe.

 

[Vorpal]

It just isn't true, Vorpal. The universe can be homogeneous without being infinite.

I have never claimed that homogeneity implies infinitude. Ever.
In fact, I very explicitly claimed that it can be homogeneous without being infinite just recently, in this thread, in one of the posts you've quoted me on (post #1011).

That was also half the point of the example of a flat torus. (And before you go off again, no one here claimed that the actual universe has this geometry.)

You cannot claim that the universe is not homogeneous on the grounds that something exists beyond the universe which is different.

Not only have I never made that claim, I've never observed anyone else make it either. I'm increasingly confused about why you're telling me this in a reply to one of my posts, since it has no apparent connection to anything in said post.

Sure thing. We can't be sure about the whole universe. And we can't be sure that it's infinite.

Of course.

I tell you Vorpal, from my understanding of general relativity, the universe is flat, and was always flat.

General relativity does not imply that the universe must have any specific geometry any more than Maxwell's equations imply that there is only one possible configuration for the electromagnetic field.

General relativity with observations of our universe do imply that the observable universe is very probably flat. That's as much as can be justified, as I've said that before.

As for why Einstein talked about a hypersphere and a static universe, I don't know. It's as if his confidence in his own theory deserted him when it came to cosmology. Why oh why did he talk about a dusty universe instead of one comprised of space alone?

A universe that is spatially a 3-sphere is a valid solution of general relativity. Of course, that doesn't mean that it is real. To continue the previous analogy, an everywhere-constant magnetic field is a valid solution of Maxwell's equations, but that doesn't mean the actual universe has such a field. The flip-side is that one can only say that it doesn't after one looks at the actual universe (which isn't that hard in that case).

As to why Einstein in particular thought 3-sphere was the right model for the universe, it's partly basically because he was enamored with his idiosyncratic interpretation of Mach's philosophy. But Mach's principle has little to do with GTR proper, and Einstein didn't seem to quite understand Mach anyway (Mach himself didn't think so, and looking at Einstein's paper, there's only the vaguest similarity between what Einstein called "Mach's principle" and Mach's philosophy, so he was probably right in that).

IMHO the expansion is evidence against an infinite universe.

This is a mistake.

 

[steenkh]

No, think of it as getting thrown out of a Roman Catholic church for refusing to accept something for which there is no supporting evidence, even though you give robust physics references to support your case.

That is really the problem: it is only in your imagination that you are giving robust physics references. Upon investigation, they always turn out to say something else or be quoted out of context. When you are given the chance to actually present the math that would prove you are right, you invariably decline.

All of your posts seem to show that you really cannot do the math yourself, you are keeping yourself well informed, but suffer from tunnel vision so that you only see what you want to see. This tunnel vision extends to posts by your opponents where you often attack straw men that nobody has argued for.

* sigh *

 

[Perpetual Student]

...
...
Not only have I never made that claim, I've never observed anyone else make it either. I'm increasingly confused about why you're telling me this in a reply to one of my posts, since it has no apparent connection to anything in said post.
...
...

This is one of Mr. Duffield's standard debating ploys. It has nothing to do with physics; it's his way of deluding himself that he has something meaningful to say.

 

[edd]

Challenge? That's no challenge? Why are you asking about temperature when I said the fine structure constant varies with gravitational potential? That's a straw man, not a challenge. One that attempts to defend the fantasy of a Goldilocks multiverse.

You've been talking about the running with energy. I'm suggesting you translate that to an energy scale and then justify the relevance of your arguments with that. I think you'll find it challenging to do so.

As for a change with gravitational potential that would as I've said before violate the equivalence principle as far as I could tell, but given recently published research I've found there are effects that might arise in the presence of a scalar field that would cause this, if such a scalar field existed. I do not believe you have been making these claims on the basis of the existence of such a field.

On a minor note sorry for taking a while to respond. I currently have limited internet and may take a while again next time too.

 

[Mister Earl]

Sheeesh. What's next? Ferrous solar surfaces?!

 

[Farsight]

I have never claimed that homogeneity implies infinitude. Ever.

In post #1016 you said this:

"That's not an assumption. The FLRW model assumptions are that the universe is homogeneous and globally isotropic. If that's assumed, then the only possible flat spatial geometry is that of the (infinite) Euclidean plane".

As it happens I'm happy that on a large scale, bigger than stars and galaxies and clusters, the universe is homogeneous and isotropic. However I'm not happy that the only possible spatial geometry is that of an infinite Euclidean plane. I think there's another possibility: that space is a 3-sphere, beyond which there is no space, so there is no beyond it.

In fact, I very explicitly claimed that it can be homogeneous without being infinite just recently, in this thread, in one of the posts you've quoted me on (post #1011).

You referred to a torus, which has the same topology as a chocolate teapot. We have no evidence for it, or for any intrinsic curvature in some higher dimension. The Planck mission looked for evidence of this and found none, see this paper which edd referred to in the Planck thread.

That was also half the point of the example of a flat torus. (And before you go off again, no one here claimed that the actual universe has this geometry.)

Sorry if I misunderstood what you were saying Vorpal. But read your posts again, it does rather sound as if you're claiming that the universe is either infinite or a torus.

Not only have I never made that claim, I've never observed anyone else make it either. I'm increasingly confused about why you're telling me this in a reply to one of my posts, since it has no apparent connection to anything in said post.

As above.

General relativity does not imply that the universe must have any specific geometry any more than Maxwell's equations imply that there is only one possible configuration for the electromagnetic field.

Actually, I disagree with both of those points. But since Einstein got his cosmology so wrong and failed to predict expansion, and failed to unify electromagnetism & gravity, I'm on a sticky wicket and won't push it.

General relativity with observations of our universe do imply that the observable universe is very probably flat. That's as much as can be justified, as I've said that before.

Fair enough. I was going to say a theory on its own isn't much use, you need evidence too.

A universe that is spatially a 3-sphere is a valid solution of general relativity. Of course, that doesn't mean that it is real.

Ergo then the only possible flat spatial geometry is that of the (infinite) Euclidean plane is not accurate.

To continue the previous analogy, an everywhere-constant magnetic field is a valid solution of Maxwell's equations, but that doesn't mean the actual universe has such a field.

I don't understand your analogy I'm afraid. The field concerned is the electromagnetic field. A "magnetic field" is the result of electromagnetic field interactions where linear forces cancel but rotational forces don't.

The flip-side is that one can only say that it doesn't after one looks at the actual universe (which isn't that hard in that case).

Agreed.

As to why Einstein in particular thought 3-sphere was the right model for the universe, it's partly basically because he was enamored with his idiosyncratic interpretation of Mach's philosophy. But Mach's principle has little to do with GTR proper, and Einstein didn't seem to quite understand Mach anyway (Mach himself didn't think so, and looking at Einstein's paper, there's only the vaguest similarity between what Einstein called "Mach's principle" and Mach's philosophy, so he was probably right in that).

I'm not fond of Mach's principle myself, or (cough splutter) Einstein's cosmology. I couldn't find my copy of The Meaning of Relativity to check it, but didn't Einstein proposed a 4-sphere rather than a 3-sphere?

This is a mistake.

I really don't think it is, Vorpal. The standard model of cosmology says the universe started small and has been expanding for 13.8 billion years. The stress-energy tensor features pressure. If that pressure is counterbalanced at all locations, it cannot result in expansion. I think the mistake is to claim that the expanding universe is infinite, and started out infinite.

 

[Farsight]

You've been talking about the running with energy. I'm suggesting you translate that to an energy scale and then justify the relevance of your arguments with that. I think you'll find it challenging to do so.

It's obvious edd. In physics conservation of energy is something we're used to. In cosmology we're accustomed to an expanding universe. And Λ is equivalent to an energy density in otherwise empty space. So the energy density of the early universe would have been high, so the fine structure "constant" would have been different. I can't explain why some cosmologists seem to disregard conservation of energy when it comes to say dark energy.

As for a change with gravitational potential that would as I've said before violate the equivalence principle as far as I could tell

I "root for relativity", but I just don't see how violating the equivalence principle is such a big deal. It only applies to an infinitesimal extent. That's a region of zero volume.

but given recently published research I've found there are effects that might arise in the presence of a scalar field that would cause this, if such a scalar field existed. I do not believe you have been making these claims on the basis of the existence of such a field.

I haven't, but I don't have a big issue with it. Google on gravity scalar potential.

On a minor note sorry for taking a while to respond. I currently have limited internet and may take a while again next time too.

Ditto, I've been busy of late.

 

[Farsight]

Sheeesh. What's next? Ferrous solar surfaces?!

Not from me. Take careful note of what I post. I'm more skeptical than a lot of the guys here, and get into fights with people like Perpetual Student peddling the multiverse, and people like sol invictus peddling the notion that a gravitational field is a place where space is falling inwards. If you want an iron sun, you want Oliver K Manuel mate.

That is really the problem: it is only in your imagination that you are giving robust physics references...

Oh puhlease.

As I hope I made clear, I was simply explaining what a "flat torus" was, not making any claims about the topology of the universe.

Duly noted.

This is one of Mr. Duffield's standard debating ploys. It has nothing to do with physics; it's his way of deluding himself that he has something meaningful to say.

See my response to Vorpal above. I don't use "ploys", I just talk physics and cosmology.

 

[Farsight]

Au contraire, the evidence supporting big-bang cosmology says nothing about whether the universe is infinite or finite. All it says is that universe is a lot bigger than the observable universe. Is the Universe really infinite or just really big?

"We have observations that say that the radius of curvature of the Universe is bigger than 70 billion light years. But the observations allow for either a positive or negative curvature, and this range includes the flat Universe with infinite radius of curvature. The negatively curved space is also infinite in volume even though it is curved. So we know empirically that the volume of the Universe is more than 20 times bigger than volume of the observable Universe. Since we can only look at small piece of an object that has a large radius of curvature, it looks flat. The simplest mathematical model for computing the observed properties of the Universe is then flat Euclidean space. This model is infinite, but what we know about the Universe is that it is really big".

I'm sorry RealityCheck, but this article is wrong. We know empirically that the universe looks "flat". We don't know that the volume of the universe is more than 20 times bigger than the volume of the observable universe. I'm sure that edd and Vorpal and others will back me up on this.

And while you are still displaying some ignorance: there is no evidence whatsoever to support your imaginary notion that the universe is somehow curved "in a higher dimension". Zip, zero, zilch.

Huh? I don't think the universe is curved in a higher dimension.

There may be some obscure cosmology theory out there that imbeds the universe in a higher dimension. Standard cosmology does not imbed the universe in a higher dimension.

See the doughnut universe and there's Perpetual Student's "hero of the multiverse", Max Tegmark. Also google on universe torus "higher dimension". As for whether this is deemed standard cosmology I don't know, but like I said above, the Planck guys looked for evidence of a toroidal universe and didn't find it.

 

[Farsight]

Sorry, Farsight, your humble opinion is just wrong because it ignores what the expansion of the universe actually is.
The expansion is an increase in distances as in the Friedmann–Lemaître–Robertson–Walker metric.
You can start with a finite universe, distances within it get bigger and finite universe expands.

No problem with that.

You can start with a infinite universe, distances within it get bigger and this infinite universe expands.

Oh no you can't. After what you were telling me about standard cosmology, do you really think standard cosmology tells us the universe started out infinite? Seriously?

 

[edd]

It's obvious edd. In physics conservation of energy is something we're used to. In cosmology we're accustomed to an expanding universe. And Λ is equivalent to an energy density in otherwise empty space. So the energy density of the early universe would have been high, so the fine structure "constant" would have been different. I can't explain why some cosmologists seem to disregard conservation of energy when it comes to say dark energy.

You'll find cosmologists have a more nuanced view of the conservation of energy. If you properly understood relativity this wouldn't be a problem for you. Anyway, it seems you want to talk about the energies of the early universe and the fine structure constant and not the low energy late universe where fine tuning is still a difficulty since the value of alpha barely varies for it.

I "root for relativity", but I just don't see how violating the equivalence principle is such a big deal. It only applies to an infinitesimal extent. That's a region of zero volume.

It is kind of fundamental to it, and the fact it is local isn't really a problem when your measurement of the fine structure constant is also reasonably local.

 

[edd]

I'm sorry RealityCheck, but this article is wrong. We know empirically that the universe looks "flat". We don't know that the volume of the universe is more than 20 times bigger than the volume of the observable universe. I'm sure that edd and Vorpal and others will back me up on this.

I'd say that the 20 times large number requires some assumptions that I would expect would be well stated in the relevant paper but might fail to make it to a press release. Those assumptions (if they are what I'd guess) would be reasonable but I don't think watertight?

 

[Farsight]

You'll find cosmologists have a more nuanced view of the conservation of energy.

What do you mean by that? Energy is fundamental, it's the one thing we can neither create nor destroy, matter is made of it. More generally we talk of Noether's theorem. Are you saying that some cosmologists think energy is not conserved?

If you properly understood relativity this wouldn't be a problem for you.

Come off it edd. I tell you about relativity and back it up with the Einstein quotes, and you dismiss 'em as cherry-picking. You're on the same side of the fence as Anders Lindman.

Anyway, it seems you want to talk about the energies of the early universe and the fine structure constant and not the low energy late universe where fine tuning is still a difficulty since the value of alpha barely varies for it.

Not really. What I said about alpha being a running constant was originally on Perpetual Student's multiverse thread. It got booted off. Talk about irony.

It is kind of fundamental to it

No it isn't. It applies to an infinitesimal extent. To no extent. Which means it doesn't really apply. It's as per the Synge and Ray quotes in Pete Brown's essay:

"I have never been able to understand this principle… Does it mean that the
effects of a gravitational field are indistinguishable from the effects of an
observer’s acceleration? If so, it is false. In Einstein’s theory, either there is
a gravitational field or there is none, according as the Riemann tensor does
not or does vanish. This is an absolute property; it has nothing to do with any
observers world line … The Principle of Equivalence performed the essential
office of midwife at the birth of general relativity, but, as Einstein remarked,
the infant would never have gone beyond its long clothes had it not been for
Minkowski’s concept [of space-time geometry]. I suggest that the midwife be
buried with appropriate honours and the facts of absolute space-time faced".

"It is very important to notice that in a freely falling frame we have not
transformed away the gravitational field since the Riemann tensor
(gravitation ←→ Riemann tensor) will not vanish and we will still measure
relative acceleration ….. The first thing to note about the 1911 version of
the principle of equivalence is that what in 1911 is called a uniform
gravitational field ends up in general relativity not to be a gravitational field
at all – The Riemann tensor is here identically zero. Real gravitational fields
are not uniform since they must fall off as once recedes from gravitating
matter."

and the fact it is local isn't really a problem when your measurement of the fine structure constant is also reasonably local.

The problem comes when you measure the fine structure constant at two different locations, and when they vary you claim it's a breach of the principle of equivalence and busts relativity. It doesn't. It's a principle that applies to a zero extent, not some sacrosanct golden rule.

 

[Farsight]

I'd say that the 20 times large number requires some assumptions that I would expect would be well stated in the relevant paper but might fail to make it to a press release. Those assumptions (if they are what I'd guess) would be reasonable but I don't think watertight?

The point is that we don't know that the actual universe is more than 20 times larger than the observable universe. Come on edd, you know I'm right about this. Back me up.

I'm off out.

 

[W.D.Clinger]

General relativity does not imply that the universe must have any specific geometry any more than Maxwell's equations imply that there is only one possible configuration for the electromagnetic field.

...snip...

A universe that is spatially a 3-sphere is a valid solution of general relativity. Of course, that doesn't mean that it is real. To continue the previous analogy, an everywhere-constant magnetic field is a valid solution of Maxwell's equations, but that doesn't mean the actual universe has such a field.

I don't understand your analogy I'm afraid. The field concerned is the electromagnetic field. A "magnetic field" is the result of electromagnetic field interactions where linear forces cancel but rotational forces don't.

As has been thoroughly documented within this thread, Farsight doesn't even understand freshman-level electromagnetism. Here's an example of an electromagnetic field that's a valid solution of Maxwell's equations but doesn't describe the entire universe:

E(t, x, y, z) = <0, 0, 0>
B(t, x, y, z) = <1, 0, 0>

(In the coordinate system of those equations, the electromagnetic tensor F^μν has only two nonzero components. Although Farsight continues to declare his inability to translate between the E, B and F^μν representations, that translation is easy.)

Repeating part of Vorpal's post for context:

A universe that is spatially a 3-sphere is a valid solution of general relativity. Of course, that doesn't mean that it is real.

I couldn't find my copy of The Meaning of Relativity to check it, but didn't Einstein proposed a 4-sphere rather than a 3-sphere?

No.

A 4-sphere is 4-dimensional. Einstein's theory of relativity assumes three spatial dimensions, not four.

I "root for relativity", but I just don't see how violating the equivalence principle is such a big deal. It only applies to an infinitesimal extent. That's a region of zero volume.

It is kind of fundamental to it, and the fact it is local isn't really a problem when your measurement of the fine structure constant is also reasonably local.

No it isn't. It applies to an infinitesimal extent. To no extent. Which means it doesn't really apply.

To explain why Farsight's reasoning is nonsensical, consider the definition of derivatives in calculus. They too are defined by taking limits, so they too apply only to an infinitesimal extent. If Farsight's reasoning were valid, derivatives wouldn't apply any more than the equivalence principle.

Yet Einstein's field equations, like Maxwell's, are expressed using derivatives. They are differential equations, which means they themselves apply only to an infinitesimal extent. If Farsight had a working knowledge of calculus and differential equations (or working knowledge of electromagnetism or relativity), he'd understand how local laws that apply only to an infinitesimal extent can constrain (but may not completely determine) global properties.

The equivalence principle says every free-falling observer can choose to use coordinate systems in which that observer is not being accelerated by gravity. The locality of the equivalence principle means those coordinate systems may not allow the observer to deny the effect of gravity (or curved spacetime) on other objects. Even so, it's quite useful to select coordinate systems in which one particular particle is free-falling (or stationary), as Farsight would learn by working through a few homework problems.