I like it 👍
I try to imagine it from the perspective of things moving at or near c. For those things (particles, radiation) the size and shape will be very different. The difference of course is how time passes for those things - for a photon it doesn’t so the cosmos is very small and it’s flat ie everything is squashed like a sheet of paper. As soon as something has mass (aka energy from E=mc^2), it has the property of experiencing time, so the cosmos looks to those things the way we see it - very big and very old.
I try to imagine it from the perspective of things moving at or near c. For those things (particles, radiation) the size and shape will be very different. The difference of course is how time passes for those things - for a photon it doesn’t so the cosmos is very small and it’s flat ie everything is squashed like a sheet of paper. As soon as something has mass (aka energy from E=mc^2), it has the property of experiencing time, so the cosmos looks to those things the way we see it - very big and very old.
So what makes such a structure keep its form and even expand... ?
and eventually collapse? 🙂
Would you say that the inflation set the stage to a toroid and BB filled the it with matter....
If so, why/how would an event like the inflation take that shape?
//
and eventually collapse? 🙂
Would you say that the inflation set the stage to a toroid and BB filled the it with matter....
If so, why/how would an event like the inflation take that shape?
//
I'm not entirely happy with your analogy, Steve.
In topology, 2-sphere refers to the 2-dimensional surface of a usual sphere (not to be confused with a solid sphere or ball).
So you are effectively representing the 3D Universe by the 2D surface of a round balloon - a common analogy.
As the surface of the balloon expands, all points on the surface move away from each other and there's no centre to the expansion.
Now, the CMB is everywhere in our universe - or as Wiki says, "fills all space in the observable Universe".
So it cannot simply be located at the "North Pole" of the balloon as you suggest, but must be present everywhere on the 2-dimensional surface of the balloon.
A work in progress?
I read that the topology of the Universe is thought to have been determined by quantum processes that unfolded in the initial moment of the Big Bang.
Let's take those "quantum processes" to mean cosmic inflation!
Then, as we've discussed before, a period of "reheating" is postulated to have occurred at the end of cosmic inflation that formed the particles, antiparticles and radiation that fed the hot Big Bang that filled the Universe with matter.
One of the areas of intense study in mathematics is topology and when you consider the shape of the universe, you can see why trying to imagine this in its entirety becomes such a difficult task. Add the multi-dimensional aspect I alluded to earlier and it is clear it is almost impossible for mere mortals.
Steve’s post I think was more of a prompt to highlight one possible view. If the cosmos is indeed donut or torus shaped and it is expanding, then all points will be moving away from each other.
A work in progress indeed.
Steve’s post I think was more of a prompt to highlight one possible view. If the cosmos is indeed donut or torus shaped and it is expanding, then all points will be moving away from each other.
A work in progress indeed.
Rather than represent the Universe by a 2-sphere, let's jump up one dimension to a glome!
In topology, the glome is the 3D representation of the 2D sphere and 1D circle.
The name derives from the Latin "glomus" meaning "ball of string".
In topology, the glome is the 3D representation of the 2D sphere and 1D circle.
The name derives from the Latin "glomus" meaning "ball of string".
Vaguely looks like something from an Andrew Wiles paper, Galu!
I am trying to imagine what a model (manifold?) would look like that fully represented the universe including how it appears to a photon, all other particles and all matter.
Maybe something like a torus, but instead of a doughnut shape like Steve showed, the centre bit would be a tiny point and it would then emerge from one side of the point and then all the way around back to the other side of the point. The tiny point is how photons experience the cosmos, but somehow it would have to show everything else as flat i.e. 2D. As soon as something has mass it experiences time, so it now moves in 4D (x,y,z and t) and has to traverse up away from the point - perhaps all the way around or just a loop around the inner part of the central bit for something moving at an appreciable % of c, like an accelerated particle.
Edit: Actually, looking at Steve's animation, I think it's pretty close. Personally, I would have flattened the whole thing out a bit just to make it a bit more pleasing to the eye aesthetically 😉
I am trying to imagine what a model (manifold?) would look like that fully represented the universe including how it appears to a photon, all other particles and all matter.
Maybe something like a torus, but instead of a doughnut shape like Steve showed, the centre bit would be a tiny point and it would then emerge from one side of the point and then all the way around back to the other side of the point. The tiny point is how photons experience the cosmos, but somehow it would have to show everything else as flat i.e. 2D. As soon as something has mass it experiences time, so it now moves in 4D (x,y,z and t) and has to traverse up away from the point - perhaps all the way around or just a loop around the inner part of the central bit for something moving at an appreciable % of c, like an accelerated particle.
Edit: Actually, looking at Steve's animation, I think it's pretty close. Personally, I would have flattened the whole thing out a bit just to make it a bit more pleasing to the eye aesthetically 😉
Be careful of what you read in the literature as geometers regard dimensions differently from topologists.
Geometers refer to the number of coordinates in the underlying space (thus a 2D sphere is a circle) and topologists refer to the dimension of the surface itself.
In geometry, the dimensions progress as follows:
0D: point
1D: line
2D: circle
3D: sphere
4D: glome
In topology, the dimensions progress as follows:
1D: circle
2D: sphere
3D: glome
Armed with the geometers way of thinking, perhaps its time to CUE THE TESSERACT!:
Geometers refer to the number of coordinates in the underlying space (thus a 2D sphere is a circle) and topologists refer to the dimension of the surface itself.
In geometry, the dimensions progress as follows:
0D: point
1D: line
2D: circle
3D: sphere
4D: glome
In topology, the dimensions progress as follows:
1D: circle
2D: sphere
3D: glome
Armed with the geometers way of thinking, perhaps its time to CUE THE TESSERACT!:
Well, one would have to decide which to use to envisage the cosmos. I'll leave that up to the geniuses to work out!
Did you open Steve's link from which the animation was taken? https://evolvingsouls.com/blog/toroidal-universe/
The Toroidal Universe Theory - for theory, read hypothesis of course!
The author admits, "I am not a physicist or a cosmologist, so this theory wasn’t conceived by studying data or devising complex formulas. I am an explorer of consciousness, and the idea came as a flash of inspiration while I was meditating and inquiring with a friend, Valerie."
I would file the hypothesis under Mumbo Jumbo. On the internet, other than that article, I can only find an incoherent two and a half minute video and several meditative diagrams like the one appended below.
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Indeed Galu - anyone who says a torus universe came to them while they were 'inquiring with Valerie' is on an outward-bound journey of some sort. I did not open the link. However, I'm only really interested in what the shape of the universe looks like for photons, stuff travelling at close to c and ordinary matter. I do get the feeling it is wrapped in on itself and distance/time take on very different shapes as an object or particles approach c. As a visual depiction, it ticked a lot of boxes.
Talking about that, what would a model like that make of entanglement? If for photons or particles moving at close to c, the cosmos is indeed very small and does not experience time passing, I would expect spooky action at a distance to be supported by such a view, ie it is a natural consequence of photons experiencing the cosmos as a point. We see the distance - the photon or entangled particles do not. Even the resulting wave functions, since they are propagating out at c, will not see any distance between them or their partners.
[We need to ask Steve If he got that thing from an Eastern meditation class that he hasn't told us about 🤣 ]
Talking about that, what would a model like that make of entanglement? If for photons or particles moving at close to c, the cosmos is indeed very small and does not experience time passing, I would expect spooky action at a distance to be supported by such a view, ie it is a natural consequence of photons experiencing the cosmos as a point. We see the distance - the photon or entangled particles do not. Even the resulting wave functions, since they are propagating out at c, will not see any distance between them or their partners.
[We need to ask Steve If he got that thing from an Eastern meditation class that he hasn't told us about 🤣 ]
You've pretty much covered the photon through what you said earlier.
For the photon, the Universe has no thickness and there is no time. I read that a photon would see the Universe as a bright spot of infinitesimal size.
Therefore to a photon the topology of the Universe would be a 0D solid sphere.
As for "stuff" traveling close to the speed of light, I read it would see the Universe behind it curving round in front of it.
I'm not sure what topology that indicates.
Best I've got! 🤓
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That’s precisely why trying to work out a topology that describes everything in the universe is challenging and interesting. You can’t IMV just consider matter and say that’s how the cosmos looks because that’s not everything - it leaves out radiation. The universe as we know it doesn’t work without radiation. It’s also why, like Lee Smolin, I have a particular fascination for time and how it arises and its relationship to energy and entropy. These things all seem to be linked. Maybe in the big scheme of things matter is just cosmological flotsam - the real important bit is radiation and energy.
TBH, I have dabbled in Eastern Mysticism and Astrology a bit myself, but prefer Physics and Astronomy. Even at Bedford College I discovered we had an observatory, and I would sometimes draw the key and go up there:
I didn't expect a sort of "Spanish Inquisition" when I said the Toroidal idea for the shape of our Universe "isn't bad at all!" 🙁
In fact the only reason I quoted a fairly mystical website in conjunction with that image was to credit my shameless lifting of the animation.
Which was fairly compact in size, thus minimising bandwidth requirements for our forum. I do try to reduce emissions in our current crisis.
If you want more reputable discussion of the idea, you will find it at Scientific American:
https://www.scientificamerican.com/article/how-many-holes-does-the-universe-have/
Or perhaps Quanta magazine:
https://www.quantamagazine.org/what-is-the-geometry-of-the-universe-20200316/
Now tireless self-publicist Ethan Siegel, and who doesn't look like a Proper Physicist* at all to me, feels the evidence is we live in a flat Universe.
https://www.forbes.com/sites/startswithabang/2021/03/05/ask-ethan-why-is-the-universe-flat/
The problem I have picked up with all this wretched Philosophical speculation is that 3-Toroids are not flat, but then neither are 3-Spheres. I am after all, quite comfortable in 4 dimensions. But it's all a bit confusing. 😕
* Proper Physicists look like this:
Not many people know that Wolfgang Pauli had a peculiar obsession with the number 137. Even thought it was the most important number in the Universe, whereas we know it's 1729. 🤣.
When sadly ill in hospital, he would ask his visitors if they found his room number (137) interesting. Arnold Sommerfeld (Here with his characteristic cigar) was sadly knocked over by a truck.
If I was writing the script, I would have had them both knocked over by the Clapham Omnibus shortly after this picture was taken. It would have made a good story at least. 😎
I will discuss entanglement, EPR and "Spooky Action at a Distance" when I have finished that chapter in Sean Carroll's book.
It is deep stuff. But perhaps more Particle Physics than Cosmology.
A photon will see the universe ‘passing’ it at c in an instant so the animation with everything rotating through the centre is excellent IMV.
(To be frank, I was expecting your music choices to be a bit more cerebral Galu)
(To be frank, I was expecting your music choices to be a bit more cerebral Galu)
When I hear about the ‘quantum foam’ that permeates the whole universe that we can never measure directly but provides a convenient way to describe how radiation or fields propagate through a vacuum, I am always lead to ask myself what is the difference between it and the luminiferous aether that Einstein threw out in c. 1905?
Seems we cannot envisage something propagating through a vacuum without some transport medium. Lex Fridman takes a dig at Sean Carrol and TP’s in one of his videos ‘you guys just create new fields whenever it suits you and look to quantise them to create new particles’ (I paraphrase a bit here). Lawrence Krause makes the point that particle physics has been spectacularly successful at explaining how matter and radiation arose out of the BB, but can it explain EMR propagation and gravity? Seems like it’s a difficult problem to solve.
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Cerebral Music uses the frequency, amplitude, and duration of musical sounds to move the brain from an anxious state to a more relaxed state.
I could use some of that!
Physicists describe the Universe as a manifold.
Mathematicians describe manifolds in terms of their geometry and topology.
As a non-mathematician, I find it is easy to get confused between geometry and topology, so let's examine the difference:
Geometry is a local quantity that measures the intrinsic curvature of a surface. (Intrinsic means detectable to the 'inhabitants' of the surface.)
Under the Standard Big Bang theory, the Universe could have one of three different curvatures: positive, negative and flat. The three curvatures create universes that are fundamentally different in their geometry. In positively and negatively curved universes, angles in triangles don't add up to 180 degrees and parallel lines are not really parallel.
Topology is a global quantity that characterises the shape of space.
The most studied topology of the Universe is that of the 3-torus which corresponds with the Euclidean geometry of a flat Universe. However, a 3-torus is hard to imagine so let's go down one dimension and consider the Universe as a 2-torus, i.e., as the surface of a doughnut. If you exist on the the surface of doughnut it seems to be flat locally. However, if you were to travel in any direction for long enough you would end up back where you began.
More here: https://web.archive.org/web/2007011...edu/home/web/olinto/courses/A18200/nbower.htm