How would gravity or any 1/r^2 force act in one dimension?

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Discussion Overview

The discussion explores how gravitational forces, or any force that follows an inverse square law, would behave in one-dimensional space. Participants are examining the implications of dimensionality on force laws, particularly focusing on the transition from three dimensions to one dimension.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant suggests that in one dimension, gravity would be proportional to distance, proposing the formula F = GMMR.
  • Another participant argues that in one dimension, the force would be constant, or 1/r0, implying that distance does not affect the force.
  • A later reply reiterates the idea that distance does not matter in a one-dimensional universe, finding this concept interesting.
  • One participant introduces the concept of 'flux' to explain force laws, using a fluid analogy to illustrate how the inverse square law arises in three dimensions and how it would translate to other dimensions, including one dimension.
  • This participant posits that in one spatial dimension, the condition of 'same flux at every distance' would imply a constant force at all distances.

Areas of Agreement / Disagreement

Participants express differing views on how gravity would behave in one dimension, with some proposing a constant force and others suggesting a proportional relationship to distance. The discussion remains unresolved, with multiple competing views present.

Contextual Notes

The discussion involves assumptions about the nature of force laws in different dimensions and the implications of the 'flux' concept, which may not be universally accepted or defined among participants.

zeromodz
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From what I know, in 2 dimensions gravity works as 1 / R, 3 dimensions is 1 / R^2, and in 4 dimensions 1 / R^3

But what about one dimension? Is it just proportional to R? So the formula would be

F = GMMR?

Please explain in detail, how gravity would behave in one dimension and how exactly we get 1 / R^2 in two dimensions. Thank you!
 
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In 1 dimension, it would just be constant (or 1/r0)
 
cjl said:
In 1 dimension, it would just be constant (or 1/r0)

Wow, so that means that distance doesn't even matter in a one dimensional universe. Thats pretty interesting.
 
zeromodz said:
From what I know, in 2 dimensions gravity works as 1 / R, 3 dimensions is 1 / R^2, and in 4 dimensions 1 / R^3

To discuss force laws in general let me first introduce the concept of 'flux'.

The word 'flux' comes from an analogy with the physics of fluids, so will use fluid as an example. Imagine a pool of fluid, and a tube extends into the pool, giving off a steady influx. Now surround the inlet with, say, a sphere that is made of a material that let's the fluid pass through. Clearly, the amount of fluid passing through the overall surface of the sphere is the amount that comes out of the inlet tube.
Surround with a yet bigger sphere: the same amount of fluid passes through the second sphere's surface. The surface area of a sphere is proportional to the square of the radius. This means that the velocity of individual fluid particles is inversely proportional to the square of the distance to the source.

Definition of 'flux':
In three dimensions of space an inverse square law has the following property: the flux of the force-field is the same at every distance to the source of the field.
(This 'flux' concept does not mean that gravity actually involves fluid flow, the analogy should not be taken literally.)


Now, one supposition (among other suppositions) is that whatever the number of spatial dimensions you want the force law to come out as a 'same flux at every distance' force.

Following that supposition you get 1/R for two spatial dimensions, and 1/R^3 for 4 spatial dimensions.

If you have just 1 spatial dimension, then 'same flux at every distance' means the same force at every distance.
 

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