[Pseudoscience-is-malarkey (OP)]

What would it possibly be like in a parallel universe where a third and forth dimension simply do not exist?

[Eternal Student]

Hi,

   Pick up any novel written by Jean Gaston^*.   There's no depth to anything or anyone.

Best Wishes.

* The name of the novelist was changed to avoid any lawsuits.

[alancalverd]

Or read Edwin Abbott's "Flatland" - a classic textbook combining maths, sociology and satire.

[Kryptid]

I've thought about this before. The inverse-square law would not apply. There is less room for light rays to spread out in two dimensions. The brightness of a light source would fall off in direct proportion to distance: twice as far away means half as bright. The same would be true for gravitational force. In our world, twice as far away means light and gravity are one-fourth as strong. I believe I've read before that orbits would not be stable in a two-dimensional universe for this reason.

[alancalverd]

Interesting thought! It also means that Coulomb forces would make atoms and molecules smaller. But would chemistry actually change?  Fortunately it's past my bedtime but the implications of living in a 4D world whilst only appreciating 3 of them will give me something to think about during boring lectures. 

[Kryptid]

But would chemistry actually change?

Given that there wouldn't be as much room around atoms to distribute electrons, I'm inclined to say yes. Bond angles would no doubt be different for at least some molecules, resulting in different dipole moments. No tetrahedral molecules like methane either. Since a planar molecule can't flip in two dimensions, chirality would be achievable with fewer total atoms. That would impact biochemistry.

[Eternal Student]

Hi.

I've thought about this before. The inverse-square law would not apply. There is less room for light rays to spread out in two dimensions...

    I do like that bit, I like it a lot.   Sadly or "interestingly" it won't actually gurantee that gravity would behave in a similar way.

Basically, if something (like a photon or particle of light) is emitted and moves away from the source with equal preference for any direction of emission then we would expect to obtain a 1/r² law for the intensity that hits an object at a distance r from that source, exactly as you stated.   I'm fairly sure you ( @Kryptid ) appreciate why or have seen some discussions with diagrams and mathematics for this before.
    However, it is just not clear that gravity is adequately explained or modelled as some sort of force carrying particle (like a graviton) that is emitted by a source and just radiated outward in all directions.

Let's just consider the most simple or basic issue:
   (i)  The total amount of light that hits an object will be influenced by the surface area that this object presents to the source of light.  So it makes some sense to consider the total solid angle over which our object can capture rays of particles emitted from the source.   From considering the capture over this solid angle, the 1/r² law emerges without difficulty.
      The total amount of gravitational force on an object would not be affected in this way.  We could have a lump of clay and mould it in various shapes presenting various amounts of surface area to the source.   Provided we keep the mass of the clay the same it doesn't matter at all what surface area is presented to the source of gravity.   Gravitational effects depend on mass not on the amount of space occupied by the object  (specifically,  the solid angle over which the object would be able to capture hypothetical rays of gravitons emitted by the source).   


More complex issues could also be raised:
   (ii)  Electromagnetic theories tend to have linear equations,  e.g.  Maxwells equations.    For these linear equations, sums of solutions are also solutions.  A principle of superposition and simple notions of linearity follows:   For example, we can reasonably assume that the electromagentic effect caused by two photons per second striking an object is twice the effect of one photon per second striking the object.    The electric (or magnetic) field produced by two charges that are a small distance apart from each other is just the sum of the electric (or magnetic) field produced by each one independantly  etc.    Many Quantum theories also have this property of linearity so that sums of solutions are also solutions  etc.    We need this notion of simple linearity to make sense of what we think is happening when we derive the 1/r²  laws from a simple consideration of rays of particles being thrown out by the source - specifically as the rays "thin out" the further away we move from the source, so their effect thins out in a linearly proportional way.   
    Meanwhile, the equations of General Relativity (e.g.  Einstein Field Equations) are non-linear.   A metric describing spacetime around one spherical mass is known - that's the Schwarzschild metric.   However, the metric describing spacetime around two spherical masses a small distance apart from each other, is some weird thing that is not like the sum of the metric produced by each mass independantly.   Most attempts at a quantised theory of gravity capture this non-linearity by recognising interactions occurr between one graviton and another graviton rather than just between gravitons and some mass.   To say that another way,  while one graviton per second hitting an object may cause a certain force of attraction toward that source of gravitons,  two gravitons per second may not cause twice the force - because the two gravitons can now interact with each oither in some complicated way rather than just being a simple superposition or summation.     Anyway, this means that we cannot assume that the overall effect of some gravitons ( e.g. an overall net force exerted on our object) will reduce in linear proportion with the way that the rays of gravitons are thinning out and spreading out over space.

...I've read before that orbits would not be stable in a two-dimensional universe for this reason...

    Ummm.... Maybe you have.   There's plenty of texts suggesting that the 1/r² law is important, I can verify that.    Whether the 1/r² law would be lost in 2D space is what I can't be sure of.

Best Wishes.

[alancalverd]

 

Gravitational effects depend on mass not on the amount of space occupied by the object 

Let's subject this to a variant of Galileo's thought experiment.

Consider a very large body (a star) of mass M and two smaller bodies (planets) m at distances r and R in the same direction.

Then to a first approximation  the force on M is GMm(1/r² + 1/R²).

The center of mass of the smaller bodies is located at (r+R)/2 so we could replace them with a single mass of 2m  at this distance, exerting a pull of 2GMm/((r+R)/2)² = 8GMm/(r² + 2Rr+ R²)

which is not the same. So a dumbbell is not the same as a blob of the same total mass.

Or have I lost my marbles?

[Eternal Student]

Hi,

    I'm not sure if I've understood exactly what you were implying @alancalverd but I think you're after something like this:

Yes, you're absolutely right.   Gravitational effects don't depend  ONLY  on mass.    They will depend on mass and position of that mass.    The only important point I was trying to make is that they do NOT depend on the surface area presented to the source of that gravity.
   Concrete example:   If your dumbell is a long way from the main source of gravity then we can assume all the appropriate masses were in the same basic place.   Let  r ≈ R and we obtain:

8GMm/(r² + 2Rr+ R²)  =   8GMm/4r²  =   2GMm/r² 
  =  GMm . (2 / r²)  =  GMm. (1/r² + 1/R² )

So it's all the same however we shape the test mass - but the surface area presented to the main source of gravity  (the big M)  will not be.   So we have no reason to assume the test mass (the dumbell or whatever) is simply collecting hypothetical graviton rays that were emitted from the main source mass.   Hence we have no reason to assume that gravity should be modelled as if some force carrying particles (gravitons) are being radiated out from the source mass.

   Another example to contrast the difference between gravity and electromagnetic radiation:
If gravity was modelled as rays that are emitted from a source,  then a flat pancake shape should fall to earth faster (has a higher acceleration) than a spherical ball of the same material -  simply because the pancake can collect a lot more of these gravitons due to the surface area it is presenting.   However, in the absence of air resistance, that is not what happens.    Meanwhile, an object like a "solar sailer" type of spacecraft will be propelled away faster from a star if we make the sails .. well you know, like proper sails.....    They ought to present a big surface area to collect the rays emitted from the source of light while a ball shaped sail would be an appalling choice of sail shape to use.  Light is well modelled as if some particles (photons) are being emitted by the source,  gravity is not.

Best Wishes.