QM and GR idea

[`hýsøŕ]

This is just a vague speculation but .. well I wanted to see if a similar idea has already been thought of and tested and failed by professional physicists.

 

With unifying quantum mechanics and relativity, I've heard the problem comes from trying to combine a smooth spacetime 'sheet' with a fuzzy, uncertain quantum mechanical mess.

What if general relativity is only an approximation to actual spacetime, and the fundamental description of spacetime is quantum mechanical.

So what I'm saying is that... could spacetime really be fuzzy and uncertain like QM says, but just appear smooth on large distance scales? (enough so that the calculations would work fine unless you go to like a singularity)

[swansont]

I think that's the exact problem people are dealing with.

[ajb]

The various approaches to quantum gravity do indeed suggest that space-time at some level should be fuzzy or discrete. Loosely we would expect space-time to be cut-up into fuzzy Planck-cells, which are the analogue of what you find on the phase space of quantum mechanics due to the uncertainty principal. Space-time should have some noncommutative structure to it.

 

If you want a not too hard to read introduction, try J. Madore, Noncommutative Geometry for Pedestrians, arXiv:gr-qc/9906059. It is a little old now but it will give you some feel for the ideas. I also think that Madore's book is okay for an introduction, he concentrates on the physics deformation-like theory of NCG rather than the c*-algebra approach of Connes, though both approaches are introduced in the book.

 

p.s.

 

Maybe this maybe be a rare thread that could be migrated from Speculations to Physics?

Edited June 26, 2014 by ajb

[Nicholas Kang]

When things get larger and wider in scale, they become more certain, vivid, clear and solid. When things are getting smaller and smaller, they become more uncertain. So, a possible consequence is that you can see a wide space-time vividly and clearly by Mathematical description with enclosed diagrams and visualizations but when you magnify the space-time continuum, it gets more incertain and uncertain until you reach a point which you can conclude that the space-time is uncertain. So, I don`t know.

 

I doubt the key to this question lies between the border between QM and GR. The grey area between these 2 theories is wide and not clearly understood. You can just investigate this field and find the answer to this question first before uniting them.

 

Yes, I am very sure this is the key to unting QM and GR. And he/she will get Nobel Prize.

Edited June 26, 2014 by Nicholas Kang

[`hýsøŕ]

@swans aha fair enough, I thought this seems too obvious to not already be thought of and being worked on

 

@ajb thanks for the link but I took one look at it and realised this is way beyond me at the moment hehe. looks like some knowledge of topology is needed, or perhaps one of these weirder areas of geometry. I'm still someway through getting the hang of set theory and basic group theory so thats a long way off.

 

@nicolas I .. half agree .. but I doubt that applies on all scales. what about if you compared the 'fuzziness' in a solar system with the 'fuzziness' in a galaxy? You could say the galaxy is much more complex and disordered than a solar system with just a star and a few planets, so in this case, in some sense, the 'fuzziness' has increased with zooming out. but i see what you're getting at xD

As for whether the key lies between GR and QM, I think its enjoyable to consider what happens between these two boundaries. imagine what weird physics could explain such a contemplated mystery o.o

 

I mean what if it is something like string theory that, say hypothetically, cannot be experimentally tested by any being in our situation? I guess then it'd forever remain an idea and never be that useful .. would be something of a shame, imo, if the answer to such a mystery doesn't open new roads into engineering or practical areas of science. I like when something seemingly useless allows you to build something really new/futuristic/useful.

[Nicholas Kang]

String theory is not the only theory claimed as a fundamental theory. But, I think this is to no end. What creates string theory and so on. Son sounds like nothing is fundamental in the world. Maybe our consciousness is the most fundamental one because it domainates everything.

[ajb]

@ajb thanks for the link but I took one look at it and realised this is way beyond me at the moment hehe. looks like some knowledge of topology is needed, or perhaps one of these weirder areas of geometry. I'm still someway through getting the hang of set theory and basic group theory so thats a long way off.

I guess a bit of knowledge of differential geometry is needed, together with algebra (fields, rings, modules etc) and a little topolgy and functional analysis. It depends on your tastes as to exactly what is needed.

 

The basic idea is to replace the functions (continous or smooth) on a manifold, which nessisarily is a commutative algebra, with a noncommutative algebra and treat that as if it were the algebra of functions on a "noncommutaive space". There are various ways of looking at this, but in physics it seems that the noncommutative algebras are usually deformations (formal maybe) of commutative algebras. The very mathematical treatment used c*-algebras and Connes spectral triples, which is really outside my area of expertese.

[ZVBXRPL]

The microcosmic is only microcosmic from our perspective and the macrocosmic is only macrocosmic from our perspective. There is no logical reason that the microcosmic and macrocosmic would follow different laws of Physics. The Universe is not confused. The Universe is not broken. The problem of trying to reconcile the two theories is of no concern to the Universe, it is only a problem for those trying to solve it.

[`hýsøŕ]

@nicolas consciousness i think will always be the hardest mystery to solve, i'm not convinced it can be solved but .. well maybe somebody will find a way eventually

 

@ajb im a first year student in a theorist's degree, the most maths i've learned so far is calculus 3, a little set theory/group theory, some complex numbers, so anything in diff-geo, manifolds, functional analysis all seems pretty far off to me. i mean whats a commutative algebra anyway? also topology looks really hard.. are all these subjects the kind of thing where it seems hard at first and then once you've got the hang of it you can do them in your sleep? (they certainly look way harder than anything i've learned in calculus)

 

@zvb aren't you basically just saying that its logical to assume a theory of quantum gravity, or something more fundamental, exists? (one set of laws that apply at all distance scales)

Edited June 28, 2014 by `hýsøŕ

[ajb]

i mean whats a commutative algebra anyway?

An algebra is a vector space for which you have a product of vectors two vector, which is again a vector. There is them some obvious compatability contidtions of the vector space structutre and this product. Usually one assumes the product to be associative: a(bc) = (ab)c.

 

By commutative we mean than we must also have ab = ba for all elements of the algebra.

 

An examlple of a noncommutative algebra you may have come across is the algebra of nxn matrices.

 

also topology looks really hard..

The basics of point-set topology are not very hard, but they are very abstract and not easy to follow (in my opinion) comming from a physics background.

 

Algebraic topology seems to be quite easy to define things, but very hard to calculate anything! (Well, I generalise here.)

 

I am not an expert in algebraic topology, I just take from it what I need when I need it.

 

are all these subjects the kind of thing where it seems hard at first and then once you've got the hang of it you can do them in your sleep? (they certainly look way harder than anything i've learned in calculus)

This depends on what you are doing. There are some fairly standard tools in algbera and algebraic topology that are used all the time.

Edited June 28, 2014 by ajb

[Nicholas Kang]

@nicolas consciousness i think will always be the hardest mystery to solve, i'm not convinced it can be solved but .. well maybe somebody will find a way eventually

 

Read Michio Kaku`s book-The Future of The Mind

[`hýsøŕ]

so in that sense, there isn't just one 'algebra' there are like.. algebras, each with different properties, and a commutative one is a particular algebra?

 

@nicolas i guess I should, from what I've heard he's attacking the problem of consciousness from a physical point of view, and i have some doubts this would ever work, since i don't see how matter could become conscious through physical processes

[Nicholas Kang]

Just read the book and your doubts are solved. But I shall remind you that most examples given are on experiment basis and not widely used, yet. So, it is still a far cry to control matter through consciousness.

[`hýsøŕ]

wow, if hes found some way around the problem i'd be glad to hear it o.o

 

but yeah i don't expect it to enable like.. malleable consciousness any time soon. though wouldn't it be cool if we could make our brains superpowerful and things

[Nicholas Kang]

If the brain is simple enough to be understood, we won`t be smart enough to understand it.

[`hýsøŕ]

I'm personally not a fan of that saying, not very rigorous...

[ajb]

so in that sense, there isn't just one 'algebra' there are like.. algebras, each with different properties, and a commutative one is a particular algebra?

 

Sorry I missed your question earlier on, I have been away for a week.

 

There are many associative algebras all of which share some basic properties that define what we mean by an associative algebra. In essence this is just a vector space for which we can multiply elements + some compatibility laws. A commutative algebra is an (associative)algebra for which the order of multiplication does not matter.

 

Examples commutative algebras (over the reals) that you know include;

 

1) The real numbers with standard multiplication.

2) Similarly the complex numbers.

3) Polynomials with real coefficients.

 

Noncommutaive (but still associative) examples include;

 

1) nxn matrices with real entries with standard matrix multiplication.

2) The quaternions (maybe you don't know this one yet).

3) Grassmann algebras (again, maybe you don't know this one yet).

 

We also have nonassociative algebras, that is we lose (ab)c= a(bc). These are less nice for generalising geometry, but I know that Beggs and Majid have looked into nonassociative geometry.

 

Now, there is a very very very important class of nonassociative algebras that you really must know about: the Lie algebras. These algebras are fundamental when describing infinitesimal transformations (and so symmetries) in geometry and physics. You should try to understand some basic ideas here.

[Nicholas Kang]

I'm personally not a fan of that saying, not very rigorous...

 

Why not rigorous? this is a quote form that book. And the author is anonymous.

[`hýsøŕ]

@ajb, i have heard lie algebras a lot on wikipedia pages but it all looks very advanced, i'll see if i can learn some of it at some point. atm i've just about gotten used to some of tensor calculus and im trying to tackle hilbert spaces, rather slow process lol

 

@nicolas well I just think a saying like that implies a deep knowledge of the brain which we don't have. saying 'if the brain could be understood by the brain, the brain wouldn't be smart enough to understand it' is vague and handwavy. there are other complicated things in life which the brain is very able to understand with training, how can anybody say that the brain couldn't be trained to understand anything at all without first understanding how the brain works?

[Nicholas Kang]

Personally, I thought this sentence implies that we are still a far cry to understand how the brain really functions, I mean from a biological and neuroscientific perspectives. Because we only started understanding the inner sanctum of the brain deeply and more precisely years ago. We still need to take time to fully understand the brain and along with that, the neuroscientific field matures. This sentence has a figurative meaning, not the one that you thought. I mean not to say training the brain, of course this sentence doesn`t tell/ask/advice you to train your brain. This sentence tells you if the brain was simple enough to be understood, then we won`t have the technology/technology is still immature to decipher the true meanings behind every neurons in your brain, so we are still a far cry from being smart enough to understand our brain even it is actually simple enough.

 

To me, the first part of the sentence is more of exaggerating than reality, if compared to the second part of the sentence which is more of a fact: The brain is hard to be understood and we are still unable to understand and study the brain NOW/CURRENTLY.

 

Finally, there is nothing to do with training.

 

Addendum: It is Nicholas not nicolas.