Exploring Physics in 2D Worlds: Ontology-Driven Investigations with VR/AR Tools

[nuno]

Our perception of the world would be very different were we to have access to only two dimensions, instead of three. Therefore, whatever laws of physics we would derive would also be quite different, being guided by experimental evidence collected in that twisted perception of the "actual" reality. The concepts, the ontologies of that world, being completely different, would give origin to laws expressed in equally different terms.

I've often though that an interesting investigation route for the true nature of reality, could be to try to compare the body of laws of physics derived in such world to ours, and then to try to extract some patterns from that comparison to extrapolate to the laws of higher dimensions than ours. This would allow the derivation to be more "natural", in the sense that it would be based in perceptual ontological differences in different dimensions, instead of mathematically-based ones. But I wonder if this approach makes any sense to the physicist mind and if so, whether he/she could benefit at all of the availability of some VR/AR tools to explore a two-dimensional world and derive the corresponding classical and relativistic physics compendiums, or if imagination and maths would be more than enough.

As a layman, I took a look at the paper from Einstein, where he explained restricted relativity, looking for concepts that were unique to the perception of a 3D world, but got lost in the maths really. Neverthless, I would suggest that even the concept of movement itself would have a different meaning in that world. I wonder if a scientist would find value in this as an investigation route and in the type of perceptual tools I mentioned, to help.

Thank you

 

[Nugatory]

Our perception of the world would be very different were we to have access to only two dimensions, instead of three. Therefore, whatever laws of physics we would derive would also be quite different, being guided by experimental evidence collected in that twisted perception of the "actual" reality.

Does the claim in the second sentence follow from the premise in the first? Fundamental laws such as conservation of energy and momentum operate unchanged when we restrict ourselves to two dimensions or even one; textbooks are full of exercises worked in one or two dimensions because it simplifies the math without losing the physics.

 

[Dale]

@nuno I suggest that you familiarize yourself with the physics literature a little more. There is a wide body of literature discussing laws of physics in fewer or more dimensions.

 

[nuno]

Does the claim in the second sentence follow from the premise in the first? Fundamental laws such as conservation of energy and momentum operate unchanged when we restrict ourselves to two dimensions or even one; textbooks are full of exercises worked in one or two dimensions because it simplifies the math without losing the physics.

Thank you for your considerate response. My point is that laws of physics are expressed as meaningful relationships between reality concepts that we take for granted because we were born into or can relate to them, so concepts like "momentum" and "energy", even if cultural constructions in the sense that they don't denominate anything immediately perceivable, express things that you have nevertheless learned to relate to through your senses. In that sense, you have the physics of the world you perceive, because that is the one that provides the basic vocabulary in terms of which you may express them. My claim is that trying to extrapolate multi-dimensional physics from our 3D concepts results in a body of physics that is completely different than the one you would derive if you were a native of the same world but had perception of lesser or bigger number of dimensions. My suggestion is that the insights you would get into the nature of reality in those other dimensions would be richer than if you took your "3D biased language" to those realms. Nowadays, I imagine that mathematicians already coin terms to denominate the constructs their intellectual explorations of higher dimensions take them through, terms that have no correspondence to our everyday senses, but are real according to deductive logic nevertheless. It's possible that whatever laws you derived from a fully sensitive immersion in how it would be like to actually be bound by two dimensional perception would be expressed in equally esoteric terms, but my proposition is exactly that that would not be the case, that the insights provided from immersing yourself in a completely different ontology would be richer than assuming that the same concepts apply in those lower dimensions while exploring them mathematically. Taking your example, momentum is an abstraction that you probably would not derive naturally in a 2D perception of things, but yet it's a useful intelectual construct. A "2D physicist" would probably derive some equivalent mathematical abstraction (whatever form math would take in that view of the world) that applied universally to all dimensions, but it would not give him the same immediate insights as if he could "feel it" in those extra dimensions, and exploring that reality beyond his senses would not be as fruitful or deep. Basically, my point is that we express our world in a vocabulary biased towards the 3D experience and that vocabulary is probably insufficient to write the sentences that describe a Nature that has more dimensions, which would make the possibility to extend that vocabulary through empirical sensitive exploration of lower dimensions worthwhile as an investigation path. Trying to figure out the ontological gap when moving towards lower dimensions, in order to learn some mapping rules that could be applied to extrapolate to higher dimensions. Does this make any sense to you ?

 

[nuno]

@nuno I suggest that you familiarize yourself with the physics literature a little more. There is a wide body of literature discussing laws of physics in fewer or more dimensions.

Thank you. Would you recommend some book on this topic that is not too mathematical in its approach ?

 

[Dale]

I don't have such a book, it is a topic that I am aware of but not interested in pursuing.

http://home.uni-leipzig.de/tet/?page_id=87

Might be a good start and includes some links with references. It is going to be math-intensive

 

[nuno]

So, you need maths to discuss the benefits of avoiding maths... I was coming to a physicists forum to avoid that...I guess I came to the wrong place then. I'll sign off.

 

[zwierz]

Perhaps the following observation will be of some fun in this context. Consider a Lagrangian system with $m$ degrees of freedom
$$L=\frac{1}{2}g_{ij}(q)\dot q^i\dot q^j-V(q),\quad q=(q^1,\ldots,q^m),\quad V>0.$$ This system is undergone with potential forces with potential $V$. It is clear. But one can consider this system as a result of the Routh reduction of the system with Lagrangian
$$\mathcal L=\frac{1}{2}g_{ij}(q)\dot q^i\dot q^j+\frac{1}{4V}(\dot q^{m+1})^2$$ The last system has $m+1$ degrees of freedom and consists only of kinetic energy.

 

[Drakkith]

Unfortunately we have no way of determining which laws in this imaginary "reality" are correct. Science is built on observation and experimentation and we cannot do either in any reality but our own. Searching for patterns in such an imaginary reality is just not the realm of science.

Thread locked.