Where does new space come from as the universe gets bigger?

[Ken G]

But at least more and more physicists are realizing that a crisis does indeed exist in physics, that hard work is required and profound new ideas are called for.
We need to do a lot less scribbling and a lot more thinking.

I hope you didn't think my "crank" comment applied to you. It only applied to my uneducated reaction to you! But the point I was making still holds-- if all GR does is tell us ratios of scales, we can never know what is "causing" the ratios to change, be it changes in spacetime, changes in matter, or even if there is any meaning in that distinction. Would you say the situation is different in twistor theory?

 

[Frank Weyl]

You could achieve this by changing some of our constants of nature, to variables, with laws to describe how they evolve over time. We don't have a reason for why these constants exist anyway. They just happen to appear constant whenever we measure them.
Is it worth it? Of course not, as already explained, but it would be another way to formulate the models that we already have.

All four of the Planck constants mass, length, time and temperature are themselves defined by constants.
For example:
planck mass = √ hc/G = 5.56 X 10^5 gram...and so forth.

Allowing the constants to become variables would alter the complete structure of the universe.
Even altering just one would affect all the others and the universe would become chaotic for the first Planck-second and then all the atoms would simply disjunct.

 

[Ken G]

But we can agree that all the constants can be expressed in dimensionless form, for nature cannot care what a "gram" is. Hence having matter shrink (and clocks speed up) to match the usual changes in spacetime, the latter being our common arbitrary interpretation of the change in the metric, would not alter the constants in dimensionless form, any more than expanding space and redshifting light does.

Indeed, the current state of affairs is that we interpret cosmological redshifts differently from gravitational redshifts (the former is said to be due to "expanding space", the latter is said to be due to "clocks slowing down in a gravitational potential"). I think it's pretty clear that any physical description that claims such fundamentally different sources for cosmological vs. gravitational redshifts must be arbitrary convention, and perhaps not so well unified of a convention at that.

 

[Frank Weyl]

I hope you didn't think my "crank" comment applied to you. It only applied to my uneducated reaction to you! But the point I was making still holds-- if all GR does is tell us ratios of scales, we can never know what is "causing" the ratios to change, be it changes in spacetime, changes in matter, or even if there is any meaning in that distinction. Would you say the situation is different in twistor theory?

Thank you Ken,
The great triumph of Penrose's twistor approach has been the elegant new way in which it describes the various fields used in physics. As you know, fields have become one of the most important tools in modern physics. In the nineteenth century the electromagnetic field was created in order to explain the phenomena of light, electricity, and magnetism. Then at the subatomic level, the idea of the field was to reappear as quantum field theory.
Take as an example Schrödinger's equation that describes the motion of the electron. This equation does not in fact explain the electron's origins or properties. Something more is needed. Quantum field theory, an extension of the quantum theory of Schrödinger and Heisenberg, attempts to go deeper. It begins with "classical" fields for matter and force and then goes on to quantize them. The quantum excitation of the electromagnetic field, for instance, become photons of light, while the quantum excitation of the electron field are electrons and positrons. The unified field theories begin with a single grand field whose basic symmetry is then broken. The quantum excitations of these symmetry-broken fields are approximations of the various hadron and lepton elemental particles.
The field description is fundamental in both classical and quantum physics, and it is here that twistors are able to provide a powerful new formulation----fields appear in a particularly natural way in the twistor space picture. But since Penrose's approach is based on the proposition that mass is a secondary quality that arises in the interaction of more fundamental massless objects, the twistor formulation begins with massless fields such as those for the photon and graviton (at the time, the formulation included the neutrino, but the twister's mathematical resultant gave the neutrino mass..!) With luck, and some new insights, physicists may one day be able to discuss fields for massive particles within the same general formalism.
It turns out that these massless fields fall so naturally into the twistor scheme of things that it becomes possible to throw away the field equations themselves and discuss fields using a pictorial, geometrical approach!
Until Penrose and the twistor program came along, it was necessary to use what are called field equations in order to determine a field's behaviour. But today, with the help of the rich cohomology of twistor space. It becomes possible to get rid of the differential equations that determine the field. The twistor picture relies purely on the geometrical (or cohomological) properties of the field as it it expressed in terms of twistors and twistor space. This is a truly amazing result, for it means that the twistor approach can deal with the various fields of nature without ever needing to bother about field equations!
Your question, therefore, is mute in reference to twistor space, because the picture is radically different in Penrose's twistor approach, for the massless fields are now defined in (projective) twistor space. But since this space has only three complex dimensions, it turns out that the information about the field's structure will totally fill twistor space!
There is no room left in the twistor picture, nothing else for the field to do, no additional slice of space to fill...and, because twistor space is totally filled with the field's structure, there is no need for a field equation...the field along with all its dynamics is already totally defined, fully represented within the twistor picture.

 

[Ken G]

Thank you for the effort you put into that insightful summary. My next question is, how does the twistor picture account for the redshifting of the CMB?

 

[Mordred]

Also can you explain in more detail the amplituhedron? I understand that it simplifies the calculations to the eight fold way. But haven't understood how.

 

[Matterwave]

Notice that Ken G used the word 'matter', rather than 'elementary particles'. Basically any system of particles would get smaller.

You'd need to continously scale the range of the forces. You could achieve this by changing some of our constants of nature, to variables, with laws to describe how they evolve over time. We don't have a reason for why these constants exist anyway. They just happen to appear constant whenever we measure them.

Is it worth it? Of course not, as already explained, but it would be another way to formulate the models that we already have.

"Any system of particles would get smaller". Does that include the universe itself as a whole? Is the whole universe getting smaller? If so, doesn't that completely defeat the purpose of this model trying to describe an expanding universe? How about a galaxy cluster? A galaxy? Where do we draw the line of "any system of particles"?

 

[Chronos]

You can model our universe using shrinking matter and variable constants of nature, if you wish. Is that a 'simpler' model? I think not. Some, like Wetterich's model, can resolve certain issues - like a primordial singularity - but, at the price of introducing more issues than they resolve. I've always felt the goal of science is to model reality using the fewest possible variables.

 

[Ken G]

I've always felt the goal of science is to model reality using the fewest possible variables.

I don't see why there are any more variables. You write all the constants in dimensionless form, and you write the EFE. That's it, there's your physics, that's everything you can test. The metric is dynamical, the CMB is redder than when it was emitted.

Next you want to say in words what you are seeing there. So you say "something happened to space, relative to the matter", or you say "something happened to the matter, relative to the space." No more variables, no testable difference. Until we have a theory that says otherwise, I don't even see that any distinction exists at all between the two pictures. But only one answers the OP without another word.

 

[Ken G]

"Any system of particles would get smaller". Does that include the universe itself as a whole? Is the whole universe getting smaller?

In GR, bound systems don't "expand with space." That answers your question-- what would need to shrink, in the other picture, is bound systems. The universe is not one of those, so no, it does not shrink, it stays put. Nothing happens to it at all, that's kind of the point.

Where do we draw the line of "any system of particles"?

The same way you draw the line when you say "space expands"-- I could just as well ask you, "how about the space inside atoms?"

 

[Mordred]

roflmao, I didn't realize there was an actual model for this, learn something new everyday lol.

just had to google it and pulled a few arxiv articles.

In conclusion, we have constructed a “variable gravity universe” whose main characteristic is a time variation of the Planck mass or associated gravitational constant. The masses of atoms or electrons vary proportional to the Planck mass. This can replace the expansion of the universe. A simple model leads to a cosmology with a sequence of inflation, radiation domination, matter domination, dark energy domination which is consistent with present observations. The big bang appears to be free of singularities.

http://arxiv.org/pdf/1303.6878v4.pdf

just goes to show, metrics is capable of any descriptive lol. I would have to agree though Chronos I seriously doubt it would be simpler myself. Personally I don't think I'll waste much time studying this model except as an alternate viewpoint lol

 

[craigi]

"Any system of particles would get smaller". Does that include the universe itself as a whole? Is the whole universe getting smaller? If so, doesn't that completely defeat the purpose of this model trying to describe an expanding universe? How about a galaxy cluster? A galaxy? Where do we draw the line of "any system of particles"?

Current predictions are that our local cluster will become increasingly isolated. The rest of the universe would partiton off in the same way.

You can model our universe using shrinking matter and variable constants of nature, if you wish. Is that a 'simpler' model? I think not. Some, like Wetterich's model, can resolve certain issues - like a primordial singularity - but, at the price of introducing more issues than they resolve. I've always felt the goal of science is to model reality using the fewest possible variables.

Fewest variables, constants and laws? Even then we like our laws to have a degree of elegance to them. Laws that emerge from symmetry, ideally.

 

[Ken G]

It shouldn't be a different model, it should be the same model. Any model that makes all the same predictions is trivially the same model. All that is different is the language, and we should all know that language does not a physics model make. Certainly all the math should be the same. If any of their math is different, or any of their predictions are different, they should say so, and people should look for the differences. I doubt there are any differences, certainly not if they are talking about what I'm talking about, so it is not a different model. And finally, if all the math is the same, it is clearly not any "more complicated" than the usual arbitrarily chosen language.

 

[craigi]

roflmao, I didn't realize there was an actual model for this, learn something new everyday lol.
...
http://arxiv.org/pdf/1303.6878v4.pdf
...

Hah.

I thought we were just talking about some trivia that Ken G had just made up in the middle of this thread.

 

[Ken G]

Fewest variables, constants and laws? Even then we like our laws to have a degree of elegance to them. Laws that emerge from symmetry, ideally.

Indeed, the symmetries should be the centerpiece. The main symmetry in cosmology is translation symmetry, which is easier to support when nothing is going anywhere, i.e., when the matter is shrinking. If the space is expanding, it's of course the same thing, but a little harder to see that there is translation symmetry because the space is not just sitting there! If space is not said to be expanding, then clocks must be said to be speeding up, because it takes light more time to cross between galaxies. That is to say, the ratio of the time for light to cross between galaxies, and the time for an atom to oscillate, is increasing. The dimensionless speed of light stays the same (all dimensionless constants do), by which I mean, the ratio of the number of rulers crossed, to the number of atomic oscillations during the crossing, stays the same. That is all consistent with the rulers shrinking.

 

[Ken G]

I thought we were just talking about some trivia that Ken G had just made up in the middle of this thread.

Yes, I did just make it up, but then, so did whoever said space is expanding. How is that not just made up, can anyone cite evidence that is happening? Of course not, we have no model of space, we have only the predictions of GR. No part of the mathematics of GR says space is expanding, it's pure made-up language, accepted uncritically as if it was really saying something we could ever test, which then prompts people to ask "where does the space come from." That's my point here, the question emerges from a non-model, no part of GR asserts that space is actually expanding. Indeed, it seems to me one of the main points of all of relativity is noticing the difference between observations and coordinate systems!

 

[Mordred]

The problem is Ken is that it doesn't, stop and think about all the other models it influences, variable gravity? wouldn't that also affect Observation affects due to GR and SR.? This in turn implies remodelling QFT, QED, QCD etc after all we also have to include and describe a time component with an influence just to cover why particle sizes wouldn't be consistent. How many models would a varying Planck mass influence?
A quick google search showed me numerous articles he has written with unusual metrics, Cosmon inflation? "are galaxies Cosmon lumps", Cosmon dark matter the list goes on lol . Sounds to me that its not that simple if he has to redescribe everything we know

 

[Ken G]

The problem is Ken is that it doesn't, stop and think about all the other models it influences, variable gravity? wouldn't that also affect Observation affects due to GR and SR.?

No, it wouldn't affect a single observable that GR predicts, that's obvious because all GR predicts is the dynamics of the metric, and all a metric gives you is the number of rulers that could lay end to end between two events, or the number of times some atom oscillates. That's it, that's all you ever measure, and that's all the mathematics of GR ever refers to. If you doubt that, then feel free to tell me something else it refers to.

How many models would a varying Planck mass influence?

None, the Planck mass does not vary, if expressed in dimensionless form (like how many protons is it).

A quick google search showed me numerous articles he has written with unusual metrics, Cosmon inflation? "are galaxies Cosmon lumps", Cosmon dark matter the list goes on lol . Sounds to me that its not that simple if he has to redescribe everything we know

I don't know quite what this "cosmon" metric is, but if it's what I'm talking about, it cannot be the least bit different from the standard metric. Perhaps they are talking about something different, or perhaps they are talking about the same thing and don't realize it. I'm sure that what I'm talking about is the exact same metric, for the reasons I just gave.

 

[Mordred]

lol you should google the model name that Chronos mentioned then look at some of the arxiv articles listed. I nearly laughed my head off.

 

[Chronos]

Christof Wetterich is the leading proponent. He has a number of arxiv papers on the subject. The 'cosmon' is his terminology. It's unclear how his way of reformulating the cosmos actually accomplishes anything.

 

[Ken G]

The first question to ask is, if any of the predictions are different. If it does that, it's a different model. The second question is, if any of the math is different, that leads to those predictions (like Lagrangian physics starts with different math, and is better at different things, but is ultimately equivalent). If it does that, it's the same model, but useful in different ways. What would make cosmons laughable is if Wetterich can't tell the difference. I don't know.

What I am talking about is clearly neither of those, it is exactly the same predictions, using exactly the same math, but a different language for talking about what the math means. So when you say "look, space just expanded there", I say "no, a metric just changed, and you like to imagine that space did something." Pehaps I prefer to imagine that the matter shrank. I think we can all agree it is important to know the difference between a testable prediction, a different mathematical route to a testable prediction, and a simple pedagogical convention for talking about a testable prediction. It would also be laughable if we could not tell that difference!

 

[abitslow]

All models which predict the same things are NOT equivalent. Of course, that is by MY definition of equivalence.
If they were, all we need do is teach every grade school child about tensor calculus, and be done with it.
What is the tax on a bunch of bananas at 0.54$/lb, 3.27 lbs and 6.5% tax? Wait, I need to adjust for the local inflaton field, I'll get back to you once I get some supercomputer time. As simple as possible, but no simpler.

 

[Ken G]

All models which predict the same things are NOT equivalent. Of course, that is by MY definition of equivalence.

I would say they are equivalent, but can be distinguished. It's just semantics, if you'd prefer some other word for models that make all the same predictions, that's fine by me. It's actually not relevant to the picture I'm describing, as the steps for doing the math are precisely the same as for any GR solution. There is no difference at all until the mathematics, which leads to the predictions, is translated into words that say why the predictions come out the way they do. That's the part that isn't really physics at all, which is what I'm saying-- "space is expanding" is not physics, its social convention, much like a coordinate system. It can affect our cognitive resonance, but is ultimately subjective-- when we do an inclined plane problem, some people like to align their coordinate axes with gravity, others with the plane, but the physics is not different, and we do not say one picture is right and the other is wrong unless it yields an answer that does not predict the observations.

 

[guywithdoubts]

I'm still confused, it doesn't look like CosmicVoyager was having a problem with semantics. By space being a "thing," I'm sure he didn't mean a material object, as in made of particles or waves, but rather an entity of a different nature.
If space is not to be thought of as an entity (of whichever nature,) then why would two parallel lines eventually meet (given that the geometry of space allowed for it, I'm by no means trying to discuss this subject) if there is nothing but movement going on? I can understand space as simply being 'distances' between objects, and that gravity affects matter and energy directly, and that no 'actual' warping of a non-existing spatial entity occurs, and that all of this is an aid to help us visualize it. But what about two parallel laser beams? Why would they eventually meet, if all there is between them is distance, and no existing, warped space (as an actual entity)?
I though, precisely, that accepting the existence of an entity (distinct to matter and energy) would provide a mechanism (I'd say medium if it weren't for that darned aether) for this sort of things to happen.

 

[Mordred]

the volume of space is filled with energy-mass, the density influence of that energy-mass is what affects the path of light. In some ways like light passing through a prism or water.
The topography of the universe is determined by a comparison of the actual density (total density) as compared to the critical density. The critical density is represented by the following formula and is a calculated value to have a perfectly flat and static universe.

\rho_{crit} = \frac{3c^2H^2}{8\pi G}

P=pressure (change this to density
c=speed of light
G= gravitational constant.

density is represented by the Greek letter Omega \Omega so critical density is \Omega crit
total density is

\Omegatotal=\Omega_{dark matter}+\Omega_baryonic+\Omega_radiation+\Omega_{relativistic radiation}+{\Omega_ \Lambda}

this is a copy and paste from the Universe geometry article I posted earlier in this thread, from that you can see the density relations. Density has a pressure relation defined by the equations of state( cosmology) http://en.wikipedia.org/wiki/Equation_of_state_(cosmology)

so an easier way to think of it is the observations of light is influenced by the density influences of energy-mass, much like light flowing through an intergalactic medium. However space itself is best thought of as a change in distance or volume, that is simply filled with the contents of the universe

edit lol I just noticed a mistake in that article, I'm amazed I and other readers never caught it lol I had pressure instead of density for \rho should be density not pressure oops lol

 

[Mordred]

Universe geometry

The origins of the universe is unknown in cosmology. The hot big bang model only covers the history of the universe from 10^-43 seconds forward. Prior to that is described as a singularity. However its important to note that the singularity is not a black hole style. Instead singularity in this case simply means a point in time where our mathematics can no longer accurately describe it. Numerous youtube videos and pop media articles would have you believe our universe exploded from some super particle. This was never predicted by the hot big bang model.

The observable universe which is the portion we can see is a finite, sphere with a radius of 46 Gly, which is equal to 46 billion light years. The 46 Gly particle horizon refers to the today's distance of objects, whose radiation emitted in the past we receive today. The overall size of the universe is not known, it could be infinite or finite. If its infinite now then it would be infinite in the past, a finite value can never become infinite. So why is geometry so important to cosmology if we know the size of the observable universe? The answer to that question lies in how geometry affects the following aspects, Light paths, rate of expansion or collapse and overall shape.

In regards to light paths and geometry a closed universe described as a sphere will have two beams of light emitted at different angles eventually converge. An open hyperbolic universe such as a saddlebag will have those same two light beams diverge. A flat universe will have parallel light paths (provided the beams at emission were parallel to begin with)
You will notice on each image there is a triangle, this triangle represents how the geometry affects our measurements. In a flat curvature the three angles of a equilateral triangle will add up to 180⁰. A positive curvature will add up to greater than 180⁰, a negative curvature will add up to less than 180⁰

Image from http://universeadventure.org

The topography of the universe is determined by a comparison of the actual density (total density) as compared to the critical density. The critical density is represented by the following formula

\rho_{crit} = \frac{3c^2H^2}{8\pi G}

\rho=energy/mass density
c=speed of light
G= gravitational constant.

density is represented by the Greek letter Omega \Omega so critical density is \Omega crit
total density is

\Omegatotal=\Omega_{dark matter}+\Omega_baryonic+\Omega_radiation+\Omega_{relativistic radiation}+{\Omega_ \Lambda}

\Lambda or Lambda is the value of the cosmological constant often referred to as "dark energy" more accurately it is the vacuum pressure that attributes to expansion.
the subscript "₀"for \Omega shown in the image above denotes time in the present.

Energy-density is the amount of energy stored per unit volume of space or region. Energy per unit volume has the same physical units as pressure, the energy or mass density to pressure relations are defined by the equations of state (Cosmology). see
http://en.wikipedia.org/wiki/Equation_of_state_(cosmology)

\Omega=\frac{P_{total}}{P_{crit}}
or alternately
\Omega=\frac{\Omega_{total}}{\Omega_{crit}}

Geometry in 2D
In developing a theory of space-time, where curvature is related to the mass-energy density, Scientists needed a way of mathematically describing curvature. Since picturing the curvature of a four-dimensional space-time is difficult to visualize. We will start by considering ways of describing the curvature of two-dimensional spaces and progress to 4 dimensional spaces.
The simplest of two-dimensional spaces is a plane, on which Euclidean geometry holds.
This is the geometry that we learned in high school: parallel lines will go off to infinity
without ever crossing; triangles have interior angles that add up to 180. Pythagoras’
theorem which relates the lengths of the sides of a right triangle also holds:
c² = a² + b²
where c is the length of the hypotenuse of the right triangle, and a and b are the
lengths of the other two sides. One can generalize the Pythagorean theorem to three dimensions as well:
c²= a² + b² + c²
see image 2.0 below On a plane, a "geodesic" is a straight line(shortest distance between two points). If a triangle is constructed on a flat 2 dimensional plane by connecting three points with geodesics. The curvature can be represented in 2D, if you establish each angle of a equilateral triangle with
\alpha,\beta,\gamma for a flat geometry this follows the relation

\alpha+\beta+\gamma=\pi.

image 1.0

On a plane, (shown above) we can set up a cartesian coordinate system, and assign to every point a coordinate (x; y). On a plane, the distance ds between points (dx and dy) is given by the relation
d{s^2}=d{x^2}+d{y^2}

If a triangle is constructed on the surface of the sphere by connecting the angles will obey the relation

\alpha+\beta+\gamma=\pi+{AR^2}

image 1.1
where A is the area of the triangle, and R is the radius of the sphere. All spaces in which
\alpha+\beta+\gamma>\pi are called positively curved" spaces. It is a space where the curvature is homogeneous and isotropic; no matter where you draw a triangle on the surface of a sphere, or how you orient it, it must always satisfy the above equation.
"On the surface of a sphere, we can set up polar coordinates "north pole" and "south pole" and by picking a geodesic from the north to south pole to be the "prime meridian". If r is the distance from the north pole, and \theta is the azimuthal. angle measured relative to the prime meridian,"⁽¹⁾ then the distance ds between a point (r; \theta) and another nearby point (r+dr+\theta+d\theta) is given by the relation

{ds^2} = {dr^2} + {R^2} {sin^2}(r/R)d\theta^2

"An example of a negatively curved two-dimensional space is the hyperboloid, or saddle-shape. A surface of constant negative curvature. The saddle-shape has constant curvature only in the central region, near the "seat" of the saddle."⁽¹⁾. David Hilbert proved that a constant negative curvature cannot be constructed in a Euclidean 3D space. Consider a two-dimensional surface of constant negative curvature, with radius of curvature R. If a triangle is constructed on this surface by connecting three points with geodesics, the angles at its vertices \alpha
\beta,\gamma obey the relation \alpha+\beta+\gamma=\pi-{AR^2}.

{ds^2} = {dr^2} + {R^2} {sinH^2}(r/R)d\theta^2

image 1.2

A negative curvature is an open topography

If a two-dimensional space has curvature or flat which is homogeneous and isotropic, its geometry can
be specified by two quantities k, and R. The number k, called the curvature constant, R is the radius

k = 0 for a flat space,
k = +1 for a positively curved space,
k = -1 for a negatively curved space

Geometry in 3D
A two dimensional space can be extended to a three-dimensional space, if its curvature is homogeneous and isotropic, must be flat, or have uniform positive curvature, or have uniform negative curvature.

The 3 possible metrics for homogeneous and isotropic 3D geometries can be represented in the form ds²=dr²=S_k(r)²dΩ²

where
dΩ²=dθ²=sin²d\phi²<br /> S\kappa(r)=<br /> \begin{cases}<br /> R sin(r/R &amp;(k=+1)\\<br /> r &amp;(k=0)\\<br /> R sin(r/R) &amp;(k=-1)<br /> \end {cases}<br />

If a three-dimensional space is flat (k = 0), it
has the metric

ds² = dx² + dy² + dz² ;

expressed in cartesian coordinates or

{ds^2} = {dr^2} +{r^2}[d\theta^2 + {sin^2} d\phi^2]

If a three-dimensional space has uniform positive curvature (k = +1), its
metric is

{ds^2} = {dr^2} +{R^2}{sin^2}(r/R)[d\theta^2 + {sin^2}\theta d\phi^2]

A negative curvature in the uniform portion has the metric (k=-1)

{ds^2} = {dr^2} +{R^2}{sinH^2}(r/R)[d\theta^2 + {sin^2}\theta d\phi^2]

Geometry in 4D

Thus far we have discussed the 2 and 3 dimensional components. The Friedmann-Lemaitre-Robertson-Walker metric (FLRW) can be used to describe the 4D dimensions with the use of a(t). a(t) is the scale factor. See the redshift and expansion article for more information or the cosmocalc.
http://cosmology101.wikidot.com/redshift-and-expansion
http://cosmocalc.wikidot.com/start

Scale factor in a homogeneous and isotropic universe describes how the universe expands or contracts with time.
The FLRW metric can be written in the form

d{s^2}=-{c^2}d{t^2}+a({t^2})[d{r^2}+{S,k}{(r)^2}d\Omega^2]

references
(1)"Introductory to Cosmology" Barbera Ryden"
images 1.0,1.1 and 1.2 (see (1))
(2)"Modern Cosmology" Scott Dodelson
(3)"lecture notes, Introductory to Cosmology" Dr. Ka Chan Lu

 

[Mordred]

there corrections applied

 

[Ken G]

I can understand space as simply being 'distances' between objects, and that gravity affects matter and energy directly, and that no 'actual' warping of a non-existing spatial entity occurs, and that all of this is an aid to help us visualize it. But what about two parallel laser beams? Why would they eventually meet, if all there is between them is distance, and no existing, warped space (as an actual entity)?

It sounds like you are saying you want the spacetime manifold to be a real entity. What I'm saying is, we don't want to attribute it any real properties than are more than we need for it to support GR, since GR is the only tested theory we have here. I'm not a mathematician, and they are the ones who keep careful track of what aspects you need to keep the same on the various possible manifolds and metrics you could have that would induce all the same observable physics. All I'm saying is that there is one example which pretty obviously induces the same physics, which is a universe that globally respects a cosmological principle, and either has space expanding with age, or bound systems contracting with age. The "entity" of the spacetime manifold might sound like it is doing two different things in those cases, but it could just be the same thing seen from a different perspective. The distinctions are superfluous, like looking at a painting from different angles. What do we usually do with superfluous elements? Ask the aether!

 

[phinds]

I'm still confused, it doesn't look like CosmicVoyager was having a problem with semantics. By space being a "thing," I'm sure he didn't mean a material object, as in made of particles or waves, but rather an entity of a different nature.
If space is not to be thought of as an entity (of whichever nature,) then why would two parallel lines eventually meet (given that the geometry of space allowed for it, I'm by no means trying to discuss this subject) if there is nothing but movement going on? I can understand space as simply being 'distances' between objects, and that gravity affects matter and energy directly, and that no 'actual' warping of a non-existing spatial entity occurs, and that all of this is an aid to help us visualize it. But what about two parallel laser beams? Why would they eventually meet, if all there is between them is distance, and no existing, warped space (as an actual entity)?
I though, precisely, that accepting the existence of an entity (distinct to matter and energy) would provide a mechanism (I'd say medium if it weren't for that darned aether) for this sort of things to happen.

To vastly simplify Mordred's excellent exposition, your problem is that you are thinking of "parallel lines" as being Euclidean (in flat space) but in cosmology they are not. In the real world, things travel on geodesics (the cosmological equivalent of straight lines) and geodesics can diverge and meet in ways that Euclidean parallel lines cannot.

 

[Frank Weyl]

Even then we like our laws to have a degree of elegance to them. Laws that emerge from symmetry, ideally.

Hello craigi,
Could I ask if you were specifically referring to symmetry as: eightfold, global,local, patterns, symmetry break(ing) or symmetry groups per se?