Is quantum mechanics infinite dimensional?

[Read_this_post]

In a lot of debates i here quantum mechanics being used to say a verse is infinite dimensional. Ive also looked it up and found this and this just to see if it true and it seems to go with the idea that infinite dimensional hilbert space is tied with quantum mechanics. Does this mean any verse that has quantum mechanics has an infinite dimensional structure? or is infinite dimensional hilbert space something that doesnt have to be tied within quantum mechanics?

 

[ZacharyGrossman273]

Uh... No. Otherwise Gurren Lagann, Stellaris, World of Darkness, and Gravity Falls would all be high 1-B

 

[Read_this_post]

I dont actually recall them being based on quantum mechanics. But some of them dont even really scale to infinite dimensions even if their verses did run on those mechanics.

But regardless of verses, what is the actual debunk to this?

 

[DontTalkDT]

Just because something uses something mathematically, it doesn't mean that it proclaims that as its space-time construct.

CT scans, for example, also require mathematics in infinite dimensional spaces.

 

[Read_this_post]

Ct scans? What do you mean?

 

[DontTalkDT]

https://en.wikipedia.org/wiki/CT_sca

 

[Read_this_post]

Oh, i see. So what you are saying is that infinite dimensional is not actually referring to higher dimensions? but what about hilbert space? What tier would transcending that or existing in it equate to?

 

[DontTalkDT]

Infinite dimensional refers to higher dimensions, but not as space-time dimensions, but just as mathematical models.

A hilbert space can be a space of any number of dimensions.

Generally just existing in some mathematical space doesn't equate to anything btw.

 

[Read_this_post]

Im kind of confused. Wouldnt mathematical models be the thing used to describe/prove the existence of infinite higher dimensions in quantum mechanics?

 

[DontTalkDT]

There is a difference between describing something as infinite dimensional vector space and something being an infinite dimensional space-time.

Let me give an example (that is unrelated to the actual quantum mechanics thing, cause it's simpler):

Let's say we have some process, from which we know or suspect that it develops in a continuous fashion. For example, let's say the electrical field strength of some electrical field.

We do measurements of this process over a time of 1 hour.

Mathematically we model that as 0 being the moment we start gathering data and 1 being the moment we end gathering data. So we gather data over the interval [0,1].

Let's further suppose the electrical field strength only takes values between 0 v/m and 1 v/m.


That means the development of our electrical field is described by a continuous function that assigns each time value between 0 and 1 a strength value between 0 and 1.

That means mathematically we deal with a function that projects from the interval [0,1] unto the interval [0,1].


Now mathematically speaking there is a space of all continuous functions from [0,1] unto [0,1] and the dimensionality of said space is infinite.


If we now take measurements, we can actually only take some finite amount of measurements. From these we then want to find the function that best fits the measurements.

Finding this function in the infinite dimensional space of continuous functions is then an infinite dimensional problem, in which you have to operate in the infinite dimensional function space. (Finding the best such function usually means finding the function that in that function space is the least distance away from the actual function.)


But even though we are dealing with a lot of infinite dimensional stuff here, we have no infinite dimensional space, right? We only take measurements over some 1 meter distance in 3-D space, like normal.


So to summarize: Physics can at times use spaces of any given complexity and dimension as model for something, but that doesn't mean that it relates to the space-time dimensions of that something.

 

[Read_this_post]

I see. So would infinite dimensional hilbert space be mathematical as well?

 

[DontTalkDT]

In what you posted above? As the first answer in this says that seems to be about possibility spaces (probability functions) not spacetime dimensions.

 

[Read_this_post]

I see. One more question which is slightly unrelated. In this It was confirmed by staff that even viewing infinite dimensional beings as fiction would only infinite dimensional. but the tiering system appears to say that transcending infinite dimensions is outerversal (which would also upgrade many characters). Should this be changed or reworded?

 

[Antvasima]

It would be very appreciated if DontTalkDT would help us to modify our Hyperverse page based on the above information.

 

[Agnaa]

Our universe seems to operate through some form of quantum mechanics, but as far as I know, experimental observation on universal distances show the number of space-time dimensions to be roughly 4.0000

This is obviously pretty far off of "infinity".

 

[Sera_EX]

I agree with DontTalk. However, I just got home and am pretty busy, so I can't modify the page right this moment. But I will sometime later.

 

[Antvasima]

Okay. Thank you for the help.

 

[Antvasima]

I will just verify with DarkLK first.

 

[Udlmaster]

Okay, I have a Question, mostly because I read your Quora post and believe I'm getting a better understanding.

So, I was wondering, if Quantum Theory are stated to exist in a Verse, and something has Infinite Possibilities, then would that entail Infinite Dimensions existing within the Verse?

That's at least what I got out of it, mostly this part:

"So how many basis vectors are there in this Hilbert space? There is one for each possible outcome for the measurement. If the measurement yields only a small handful of possible outcomes (e.g., you are measuring the spin of the electron, which is either +1/2 or -1/2, with no other values possible) there are only two basis vectors. The abstract space that represents all the possible spin states of the electron will be two-dimensional.

But another measurement may have an infinite number of possible outcomes. Say, you measure the position or the momentum of a free electron. It can be anything. In between measurements, the electron is in a combination of all (infinite) possible position states or all (infinite) possible momentum states. The number of basis vectors (possible outcomes of the measurement) is infinite, hence the Hilbert space that describes the state of the electron is infinite-dimensional in this case."

So, in the case, let's change it to something much bigger, the Universe.

If in this verse, Universes are stated to come from Infinite Possibility and (again) Quantum Theory is stated to exist, would this entail Infinite Dimensional?

 

[Sera_EX]

A quantum multiverse can be visualized as being like a large tree with potentially infinite branches embedded in an infinite-dimensional sea (that does not make the quantum multiverse infinite-dimensional by necessity), where each possibility or choice results in a new branch forming on the "tree". This embodies many common multiverse descriptions within fiction with alternative timelines/realities.

A string multiverse describes a multiverse as described under modern String theories. Essentially, many quantum or lower-order multiverses could exist within one "vacuum", and there can be multiple vacua that embody many different physical constants, describing possible permutations in the nature of quantum mechanics.

Going by this, a String Multiverse is supetior to a quantum multiverse.

 

[Udlmaster]

Ah, so Hilbert Space is more so what can be while String Theory is what is?

 

[Sera_EX]

Pretty much.

 

[Udlmaster]

I see, thank you, also Sera, would it be okay if I ask you some question on your Wall?

I want to see what this would make a certain character.

 

[Sera_EX]

This is why I want to revamp the multiverse page to better describe how these types of multiverses can be applied by our system.

The idea that an 11-dimensional String Multiverse is the highest our theoretical multiverse has been described is false and an unscientific claim based on no evidence, since String Theory describes an 8, 10, 11, 12 or 26 dimensionality.

 

[Sera_EX]

@Udlmaster. Sure thing.

 

[ZacharyGrossman273]

...

Then why are homestuck god tiers listed as 12-D for transcending a string theory multiverse?

 

[Udlmaster]

Doesn't it go up to 32 dimensions as well?

 

[Sera_EX]

...

Then why are homestuck god tiers listed as 12-D for transcending a string theory multiverse?

Good question. Because we incorrecly assume String Multiverses to be 10/11-dimensional.

@Udlmaster

I've actually heard of 32-dimensional String Theory before, yeah. Also M-Theory describes at least 11-dimensions but M-Theory is not even finished so I don't even consider it.

 

[Udlmaster]

Sera EX >>> Sera (Base Form) >>> Tiering System

 

[DontTalkDT]

Regarding modifications to the hyperverse page: I don't think anything of what I wrote above is really relevant for the page. It basically was just confusion the mathematical model and reality.


That aisde, if one really wants to be scientifically correct I guess we should specify the fact that 11-D multiverse is one theory in many, as peope mentioned above.

There are lots of theories, many of which work without assuming multiverses or higher dimensions and at times one without the other and entirely different numbers. That's just the way it is with non-established / theoretical physics.

So first suggestion would be

In this wiki, a hyperverse is defined as a reality of a higher dimensional order than our own likely 11-dimensional multiverse.

to be changed to

In this wiki, a hyperverse is defined as a reality of a higher dimensional order than the 11-dimensional multiverse our own reality is assumed to be in some theories.

(Or similar)

Aside from that to be mathematically correct:

The mathematical concept of a "Hilbert Space" is an infinite-dimensional analog of Euclidean space.

should say

The mathematical concept of an infinite-dimensional "Hilbert Space" can be viewed as an analog of 3-dimensional Euclidean space in infinite dimensions.

(or similar)

 

[Antvasima]

@DontTalkDT

Okay. That seems fine. Feel free to make corrections and improvements to the Hyperverse and Multiverse pages.