Does this explain what generates gravity?

So, TNT, you're trying to "drum" up some further interest in the topology of the Universe?

The questions posed by the article are as follows:

If I analyse the sound of a drum can I infer the shape of the drum?

If I analyse the acoustic waves that left their imprint in the Cosmic Microwave Background can I infer the topology of the Universe?


Unfortunately, there's no conclusion in the article as to what the topology of the Universe actually is.

However, we've discussed the possible topologies of the Universe in this thread on several occasions.

The main contender we came up with is that the Universe is closed in on itself in all three dimensions like a three-dimensional torus.

A 3-torus is impossible to represent or imagine, but we can use the analogy of the 2-torus shown below instead.

1738012526695.png


A torus is in accord with a finite, unbounded Universe - one in which, if you travel long enough in the same direction in spacetime, you come back to where you began, rather than reaching the 'edge of the Universe'.

1738014236927.png


Your idea of a doughnut shaped universe is intriguing, Homer. I may have to steal it. - Stephen Hawking, The Simpsons.
 
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Remember... I also think I postulated that we should see the returning light.... but maybe the rond trip is too long or the light to "weak"...

Sat hat it is a 3-torus - how long is the round trip - could some resident mathematician calculate that please? 🙂

//
 
I also think I postulated that we should see the returning light

So, if we looked far enough we might see another Earth?

However, light rays would be emitted from the Earth in all directions, and on return each would arrive back at Earth from a different direction.

What we might see are multiple "weak" images, but not one unified image of the Earth.
 
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Having skimmed Einstein's original tome on all this Gravity and Cosmology lark, I thought it would be child's play to calculate the size of the Universe which he does in his last word... 😎

Size of Universe.jpg


Hard to read eh? This might help. Looks easy enough to me. I could have done that at O-Level 15-y-o. 😛

Size of Universe Expanded.jpg


Kappa is the Einstein version of Newton's G, 8 Pi G / c^4. So all I need now is Rho, the density of regular Matter-Energy which is actually mainly protons we now know, since Dark Matter and Dark Energy were not known about then. 😢

In fact nobody had a clue how big the Universe was in 1920, or that it was expanding, which was Hubble's red shift and Cepheid variable measurements in 1929.

It was not even then known that the Andromeda Galaxy was outside our own. Bitter rival Shapley still had doubts about an expanding Universe. "If it is expanding, what is it expanding into?". 🤣

Turns out Einstein couldn't calculate the size of the Universe at all. All he could do was add a fudge factor to make whatever size it was static.

Einstein Fudge Factor.png


https://en.wikipedia.org/wiki/Einstein's_static_universe

In fact the correction, aka The Cosmological Constant, comes to match Gravity over long range. Otherwise any homogenous and static Universe would all fall back into itself due to gravity.

Highly nonlinear over distance if you ask me. Every size Universe needs a different fudge factor.

Einstein Gravitational Cobstant K.png


It's all pretty hopeless. But TBH, adding modern fudge factors like Dark Energy and IMO the more justified Dark Matter is also a whopping fudge.

I feel far more comfortable with Particle Physics and The Standard Model. Dr. Becky can have this one. 🙂
 
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I thought it would be child's play to calculate the size of the Universe...

In an attempt to find clues as to the shape of the Universe, NASA's WMAP satellite took measurements of the CMB that placed the lower bound on the size of the Universe at about 78 billion light-years.

https://arxiv.org/pdf/astro-ph/0604616

How this should be compared with the radius (46 billion light-years) or diameter (92 billion) of the observable Universe I am not sure!

As I've said before, one must distinguish between geometry and topology (*see explanation below).

The WMAP data indicates that the geometry of space is very nearly flat, but it also provides information about the topology of the Universe.

*To illustrate the difference between geometry and topology, consider building the foundations of a house. Locally, the geometry of the ground is flat, but on a global scale the Earth has the topology of a sphere (or 2-sphere as the topologists call it).

1738085216914.png


The allowable topologies in a flat Universe are restricted to a set of eighteen possibilities. The WMAP and other independent analyses do not rule out a toroidal Universe, but don't support it either.

Heady stuff! :cheerful:
 
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I see that there is mention in Steve's previous post of Einstein considering both Euclidean and spherical (or elliptical) geometry.

Each geometry has its own possible universe topology attached to it.

Euclidean geometry introduces the topology of the 3-torus.

Elliptical geometry introduces the topology of the 3-sphere or 'glome'. This is the topology that Einstein assumed the Universe to have when he first solved his equations for general relativity.

3-torus or 3-sphere? Suffice it to say that the universe may be described as a 3-manifold! 😎

P.S. A 'glome' or '3-sphere' is a higher dimensional representation of the 2-sphere with which we are more familiar.

1738102598268.png

Unhelpful visualisation of a glome!

https://polytope.miraheze.org/wiki/Glome#:~:text=Formally, a filled-in glome is called a 4-ball,a 2-plane that intersects it is a circle
 
It is my stated view that most people don't know much, despite years of living on planet Earth. To prove this I asked my pub cronies "What is the correct way to boil an egg?"

They stumbled around with boiling from a pan of cold water for 5 minutes.... 🙄

NO, I said, you drop them into boiling water for 5 minutes! That way the white albumen doesn't stick to the shell, and you can easily peel them! 😎

What is the correct way to tie your shoelaces?

Well, you just sort of tie a knot in them.... 🙄

Incorrect, I said. You must tie a self-tightening Reef knot. A Granny knot will surely come undone. I then showed them the glaring difference between the two with my own shoes. 😎

Frankly I am amazed these people are still alive with so little knowledge. I expect they go out in storms in their cars, despite red warnings of falling trees, and end up "sadly" but inevitably deceased according to news items which usually express the horror in pictures of Dead Donkeys.

Dead Donkey.jpg


Consider then, the matter of Key, Cornish, Spergal and Starkman and their "What Shape is the Universe" nonsense:

https://www.quantamagazine.org/cosm...o-measure-the-shape-of-the-universe-20250127/

Raassuring images of learned researchers relaxedly calculating all this, against a background of learned books, which I very much doubt they have read. A device frequently employed by Politicians too.

The Well-Read Cosmologist.jpg


Whole thing reeks of hooey to me. Look at this idea:

WTF Topology.jpg


Let's hope it is a Reef knot, or our Universe will unravel.

Poincare Dodecahedron.png


Huh? How can a pointy thing be smooth?

A Child of Ten understands Gaussian Curvature, an intrinsic measurement that you can do at home, though Galu is very weak on this topic, which is the product of two orthogonal curvatures 1/R, leading to 1/R^2 and hopefully positive:

Gaussian Curvature in Geometry.jpg


And it is no coincidence that General Relativity is couched in the same units of curvature being inverse length sqaured:

Einstein Gravitational Cobstant K.png


That David Spergal (The President of a major funder of Quanta) is using Quanta Magazine for his own aggrandisement does not surprise me either.

I think it is much more fruitful to be reading useful science like this. As I am currently doing:

Paul Dirac TPQM.png


Feynman said that nobody understands Quantum Mechanics. It is my contention that Paul Dirac did. 😎
 
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A Child of Ten understands Gaussian Curvature [...] though Galu is very weak on this topic

I should like to hear your explanation of how curvature relates to the topology of the Universe! 😛

Geometry expresses the curvature of the Universe as permitted by the equations of general relativity. The geometry we are interested in is that of the flat Universe. Geometry looks at the Universe on the 'local' scale. Locally at least the Universe is flat.

Topology is also related to curvature, but looks at the Universe on the 'global' scale, providing a qualitative description of the actual shape of the Universe. An example of such a qualitative description would be that the Universe is shaped like a torus - or more accurately a 3-torus.

Should the possible topology of the Universe shown in your image (reproduced below) be regarded as "hooey"?

1738183947681.png


We can think about topology as determining whether the Universe contains holes which form closed loops.

Such loops would enable someone to travel out in the Universe without turning, yet end up back where they started.

P.S. Remember that it is the surface of the image that represents the Universe.
 
Oh, most definitely "hooey"! Some sort of Pretzel Universe? REALLY! 🙄

I might buy some sort of 3 or 4-sphere as a likely candidate for the topology or shape of the Universe:

3 Sphere.jpg


It is well known that there is a relationship between outer surfaces and their inner contents:

Greens Theorem.png


In fact, all these people have concluded is that the Universe is not a soccerball:

Extending the WMAP Bound on the Size of the Universe.png


Dirac would, of course, ask if that is a FIFA soccerball or a different Caribao Cup one?

Dirac the Magician.jpg


You might blame Ollie Watkins' astonishing Penalty miss against some Scottish team last night on the soccerball.

Ollie Watkins misses Penalty against Glasgow Celtic.jpg


But I know a bit about soccerballs, even 4 dimensional oines:

4D Polytopes.jpg


I blame the Turf Monster for making him slip. 🤣
 
I might buy some sort of 3 or 4-sphere as a likely candidate for the topology or shape of the Universe:

Topologists accept the 3-sphere as a possible topology of the Universe, while geometers would say 4-sphere.

Below are the two incompatible conventions for the meaning of 'n-sphere':
  • Topologists call the surface of a usual sphere a 2-sphere. One dimension up would be the 3-sphere.
  • Geometers call the surface of a usual sphere a 3-sphere. One dimension up would be the 4-sphere.
It is well known that there is a relationship between outer surfaces and their inner contents

Since we are talking about the outer surface being a representation of the Universe, I wonder what the "inner contents" would represent? :scratch2:

Note that talk of an interior does not relate to a "sphere", but to a "solid sphere", more usually called a "ball".

But I know a bit about soccerballs

All I know is that fitba' is a game played by players with truncated icosahedron shaped balls. ⚽
 
I've been looking into the infamous "soccer ball universe" model.

Because the panels of a soccer ball bulge due to the pressure of the air inside, the shape is a truncated icosohedron that is more spherical.

In 2003, an astronomy team from the Paris Observatory argued that a finite universe made up of curved pentagons joined together into a sphere would fit the WMAP observations.

1738252267168.png


The astronomers said that if you could step out of one pentagon, you'd step in on one on the other side. The team made the prediction that if the Universe does in fact fold back on itself, then there should be matching patterns of microwave radiation in corresponding areas on both sides of the sky.

The later 2006 research to which I referred earlier did not detect these matching patterns, or circles, of microwave radiation, thus ruling out the "soccer ball" model.
 
I really don't want to be spending time on wildly speculative notions of what topology the Universe has. Though I can see how on a 3-sphere, every direction we look leads back in time to the Big Bang and the CMB.

What we see is not how it is now, because the finite speed of light has delayed our view.

Clearly our Physics is in a total muddle anyway, Rather than ask Ethan Siegel or watch Doctor Becky explain Cosmology to people who can't even tie their shoelaces or boil an egg, I am reading Dirac and Feynman, who did ponder some of these issues in their own different ways.

Dirac and Feynman.png


I have even skimmed their papers on Relativistic Gravity that they presented in 1962 when this picture was taken. Which is more work than most of you have done, I'll wager.

Very interesting perspective on all this here:

https://ysfine.com/dirac/dirfeyn.html

And some of Dirac's wilder ideas about Lorentz Covariance in Special Relativity and Quantum Mechanics:

https://ysfine.com/dirac/dirk62.html

This is quite wild stuff, and Dirac didn't think much of Feynman's sloppy approach to it:

1 Invariant Lorentz.jpg


Relating circular and hyperbolic functions which are very much two sides of the same coin:

Lorentz Covariance and Quantum Mechanics.jpg


Covariance is just a fancy word for that which all observers agree on. Dirac actually had a notion of there being two sorts of time in his later years. Now I want to get back to Dirac's book on The Principles of Quantum Mechanics, and finish off the Feynman Bio one.
 
In 1986, Feynman was invited to give a Dirac Memorial Lecture entitled “Elementary Particles and the Laws of Physics”.

I don't know if you've listened to it, Steve, but I do know you like his lectures. He begins speaking at 3 mins, 45 secs:


EDIT:

I read in your second link above that 'Lorentz covariance' was Einstein's term for his theory of relativity.

Physical theories consistent with the principle of relativity must be covariant, meaning that they must have the same form in all frames of reference.
 
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I did, in fact, start to nod off during that lecture, and could not read the overhead projector on the precise maths. but since the first 15 minutes explained the need for antimatter virtual particles under Lorentz Covariance well enough, I think it is "Job Done".

I was, in fact, incapacitated from a surfeit of late-night "Haggis". On Manager's offer cheap at 'Spoons for a mere 5.49 for the large one with a cup of chocolate:

Haggis.JPG


It's quite nice with ketchup, but you don't want to know what it is made from. 😱

I was reading how Feynman discovered a new Physical Law in the 1950's, that of Charge Parity violation in the extemely interesting Weak Interaction, which everybody thought was a S-T thing, but was in fact a V-A thing:

The V-A Weak Interaction.png


I couldn't have put it better... 😎

On my way home I was still seeing stars, and photographed Mars for you in Gemini near Castor and Pollux, which means it is moving retrograde from Cancer and the Beehive cluster now:

Mars in Gemini.jpg


I have a map somewhere, ah, here it is:

Gemini Constellation.jpg


This is not its brightest opposition, which occurs in August in Aquarius.

Mars Orbital Properties.jpg


A good nights work, one feels. 🙂
 
I started to look at the video of the lecture. I can get completely mesmerised of hearing things I don't understand a single iota of... it is so very far out and it is seldom that I don't get a single word or aspect of what someone is talking about - I do hear what he is saying and I recognise most of the words... but still...gobbeldikgook.... ;-D

//
 
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Parity violation in the extemely interesting Weak Interaction

A simple explanation may be helpful as the mathematics in your book extract may appear to be gobbledegook, and not only to TNT! :scratch1:

The weak force is the only fundamental force that violates parity symmetry.

Parity symmetry means that every particle or interaction can be replaced by its mirror image counterpart.

1738340253732.png


The spin of the basketball above is reversed compared to its mirror image counterpart, but both spin versions are equally valid in parity symmetry terms.

However, particles produced during radioactive decay exhibit only one direction of spin and the opposite direction simply doesn't exist, i.e., parity is violated by the weak force which governs radioactive decay.
 
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