Is Modern Physics Stagnant? A Deep Dive into Topology
Summary
At FriendZone | Make Friends ⋅ Fun Chill Active Chat ⋅ VC Social Gaming ⋅ Memes ⋅ Nitro Emojis ⋅ Anime, our community dives into complex topics beyond just gaming. This announcement sparks a heated discussion on the limitations of current cosmological models, questioning why mainstream physics avoids richer topologies like S3 or S4. It challenges the reliance on flat R3,1 space and explores how non-linear topological structures could solve modern scientific stagnation.
The simple idea of the universe being an R^3 space with a time dimension, typically represented by these people as the Minkowski R^{3,1}, is naive and ignorant given the problems with modern physics, bugging every field imaginable.
Firstly, we know (?) the universe should be finite, and expanding [whether the Hubble constant is in shambles due to the incompetence of cosmology is a different matter], thus, cosmologists love to create a hypothetical boundary pushed by dark energy leading to expansion. Why, firstly, is there even a need to construct an imaginary boundary in order to restrict the R^3 of space, when topological structures with such properties, including finiteness, are easily available ?
What's comical is that if the universe were to be of a richer topology, say S^3, or S^4, etc, trying to model it using three spatial dimensions is foolishness and would lead to unavoidable singularities !
Cosmologists love the dots-on-a-balloon analogy of the expansion of the universe, but the moment it comes to simulating the universe and developing theories and experimentation, they run back to the flat comfort of the R^{3,1}. Why, then, do you understand that analogy in the first place, and yet not try to implement it ?
The standard model already uses gauge groups to make sense of the fundamental particles and to explain their different symmetries, those are not flat, simple groups. Perhaps try that with the universe itself ?
Have they tried to formulate the universe with a richer topology that allows particles to exist and guarantees their topological existence ? That shall lead to solitons, and non linearity, which Physicists [mainstream] are for some reason hesitant to accept as a reality of this universe. If Physicists do not embrace non linearity, Physics shall continue to stay stagnant.
ill be honest i have zero clue what this is about but this seems really interesting sooo if you wanted to blabber on about this i dont mind learning. What is it again, topology? seems to be the idea of a space, and google seems to hint something at it
Bro youre cool
hell yeah he is, im curious to see what other things he knows
Thanks, I appreciate that !
Topology is the study of shapes and other geometric structures, and their properties under certain transformations or actions. It's one of the deepest, most crucial fields of mathematics.
oh interesting i can understand how it would be one of the most crucial fields in there considering youre taking a place and seehow when and how it reacts from A to understand its own self
I didn't quite get what you imply near the end 😅
"their properties under certain transformations or actions" under certain actions, so say for example space and the dark matter within it, how does the change if that dark matter for example was super charged? or this that and the other. So A is what changes the structure leading us to understand it better
i word things weird my fault mate
You're thinking of these actions as Physics, these actions are geometric.
They may preserve some properties but destroy others.
For example, if you have a knot in a closed threat, you cannot remove that knot without tearing the thread.
Imagine the threat itself to be highly stretchable.
Thus, think of stretching as an action, but it preserves some specific property/ies of the thread, here, the existence of these knots.
In this way, you can define your topological structures, and allow some specific actions over it, which gives rise to some interesting properties, including such invariants.
No worries, it's good enough that you're curious.
so could this be similar to a Möbius strip? In the sense that its similar to the knot analogy it bent as the action to connect both end points and preserves the property of strip itself while the existence of an infinite path is formed? Or did i not fully understand it?
Yes, the Mobius strip only loses its property if you tear it, that's another good example !
Similarly, topological theories regarding Physics use such properties to turn what we currently see as fundamental axioms or laws, into a property of the topology of our universe.
For example, some topologies allow something called solitons [think of them like vortices in a liquid] to exist, you can think of them as knots in a thread, they're topologically guaranteed to be conserved.
In this way, if you define particles as solitons embedded in such a topological space, they are guaranteed to not just disappear into nowhere.
In this way, you can also define charge as a winding.
Think of it as how many 'turns' you have in the knot.
By its definition, you cannot have half a knot, they can only exist in integer numbers [1 knot, 2 knots, etc]
Thus, charge is conserved, and so are the solitonic particles.
The orientation gives you the sign of the charge [like clockwise or counter-clockwise].
Thus, you can come up with rich topology and find a structure that mimics properties of particles as solitons embedded in it.
The problem is, it gets much more difficult as you try to unify everything into a single topology.
See thats very interesting to me, damn why dont they teach this in school
So theoretically could you impose a soliton in something? To keep something preserved so say another property of it can be focused on to change?
Basically from what im reading yap yap yap yapa yap to highest yap divided by the yappathon im I right 🥹
Well, firstly, topology is a quite advanced field well beyond schools, but, technically, a glimpse may be possible.
Solitons themselves are quite complex structures, waves themselves are taught quite later on with a mathematical focus.
😅
Im right or correct im confused
The word 'imposing' is wrong here. Solitons require some very specific conditions to exist, one of them is non linearity, in a way, you need exact balance between multiple properties of the medium.
As for your next question, yes.
Solitons and topology preserve properties like self energy/mass, winding/charge, and their own selves.
But, they can interact with each other, move through the medium/space, etc.
Well, yes, this is a yap about incompetence of Physics today.
[If that's what you were talking about]
I got timed out for some reason when asking my question which is interesting
are solitons the same or is each one different
Depends on what you mean.
Given one specific medium with its properties, the differential equation that governs these solitons is only one.
The type of soliton is unique to a medium, but it can have different winding, size, etc.
The underlying structure is the same.
But, if you change the medium, its properties, dimensions, etc, the equation changes and so does the soliton.
so if its unique to a medium would it be safe say that if two different mediums had the same size, then the soliton would be similar to a small degree?
Well, its not just size.
Properties of the medium is what shapes the soliton.
If two mediums have the same topology, but only their internal properties [like say, surface tension, elasticity, etc] the basic type is the same, they'll just look slightly different, yes.
Think of it as if two mediums are almost identical except their surface tensions are different.
Then the solitons might spin faster [if you think of them as vortices], but the basic type would be the same.
I should binge read this peak
a man taking notes gif
In my opinion we should legalise weed so I don't have to read this shit not high
basically you saying modern day physicist should stop being close minded and experience with different methods right
A lot of terminology. The second message could have been you explaining them so people can kinda grasp what you're saying
try to explain to me a guy who isn't well-versed in this topic in simple terms
At its core, yes.
They do not want to move on, as in cohesively, and abandon current theories that have, for some reason, become very dear to them.
Well, if so, it can get quite long, are you OK with that ?
Yes it fine
They have became a prisoner of sort
OK then.
Modern physicists and most of their equations and models are based on the universe being a flat 3-d space, + a time dimension to create spacetime.
Now, it might seem difficult to think of non-flat 3-d spaces. Think of it like this:
Let the universe be a flat 2-d plane and let us be 2-d lifeforms.
But, that 2-d surface we live on, could be curved, as in, the surface of a sphere, while we would not notice much as 2-d humans [we technically would realize distance calculations are not simple if the curvature was very large/the sphere was very small, that's a different story.
Thus, our 3-d universe may not be a simple R^3 [which is basically just a way to represent a space with three coordinates, x y and z], but it could be something much more complex, like the surface of a large 4-d sphere, and so on.
To unite spacetime, we represent it as R^{3,1} which basically is 3 spatial dimensions + 1 time dimension. We call this the Minkowski space which forms the basis of modern Physics.
However as I said earlier, this feels naive.
Because firstly, we believe the universe to be finite. And we know it expands.
[We attribute that to dark energy, that is, basically, implying we know nothing and decided to invent something rather than delve deeper]
But for this R^3 space to be finite, there has to be a boundary.
R^3 is normally an infinite 3-d flat space, and we're imposing a boundary over it, about which we know nothing, and neither about why it expands.
[The hubble constant is a measure of how fast the universe expands, when we calculate it using different methods, we get two completely different answers]
What I [and a lot of others within academia] argue is that, why are we using a flat 3-d space and creating a boundary over it to make it expand, when there are more interesting, non flat 3-d spaces where we don't even need a boundary, it can be finite by definition, and also expand ?
Think of the surface of a sphere [it is 2-d], it is finite, 2-d, does not need an imaginary boundary, and can expand.
Could the universe not be similar but in a higher dimension ?
The dots-on-balloon analogy is something physicists use to explain the expansion of the universe.
Think of a balloon with two points marked on it.
Now, blow the balloon so that its volume increases, so does its surface area.
The distance between the two points along the surface increases !
No boundary, and neither is there a center of expansion 'in' [that is, on the surface] the universe.
And yet, when it comes to model the universe and simulate it using computers, we go back to the flat universe.
Now assume that the universe was indeed not flat, and was something more complex, like the surface of a 4-d sphere.
In that case, if we tried to make it a flat 3-d space, a lot of problems happen.
In its 2-d equivalent, you can't capture the 2-d surface of the globe using a map without distorting something.
The north pole expands, sizes change, and the map abrupty stops.
In a way, this leads to mathematical singularities, as in, you can never capture a curved surface perfectly if you use a flat equivalent.
