Constructing a Different 4D Physics System: Inverse Square Law for Gravity

  • Thread starter Gold Barz
  • Start date
In summary: D universe is still an open question.Thanks for the clarification.So it is possible, but it is highly unlikely due to the problems with the critical acceleration.Thanks for the clarification.
  • #1
Gold Barz
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Is there any way to construct a fundamentally different physics system for the fourth dimension where gravity diminishes with an inverse square law instead of inverse cube law?

This was originally alkalines question
 
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  • #2
Hold on.What "inverse cube law" are u referring to...?

Daniel.
 
  • #3
3D = inverse square law
4D+ = inverse cube law

thus planets cannot form in 4D+ universes
 
  • #4
Is this (4D) a result of GTR...?What metric did they use...?Care to make a referece...?

Daniel.
 
  • #6
Interesting.I don't recall coming across the referred calculations in a GR book.Perhaps i didn't know where to look for.Let's hope that here,in GenPhys one of our experts in GR will provide more info on the calculations themselves (my interest) and the interpretation (yours).

Daniel.
 
  • #7
I'd expect gravity to drop off as an inverse cube in 4-d space based on the Newtonian limit. Basically, just Gauss's law - the force*area goes to a constant at large distances.

Something like MOND could change that, I suppose. I'm only vaguely familiar with MOND, so I looked it up. Based on the following


http://motls.blogspot.com/2004/10/mond-and-holography.html

The MOND theories, roughly speaking, say that the Newtonian laws are modified in such a way that the inverse square law (1/r^2) for gravity is continously replaced by the inverse distance law (1/r) for all objects whose acceleration is smaller than the critical value a_0.

It would appear to be possible for some sort of MOND-like theory to change the 1/r^3 force of gravity to something that allows stable orbits (anything slower than 1/r^3 will do) in a 4D universe. But the critical accleration value would have to be very large to allow stable planetary orbits (MOND for instance switches from 1/r^2 to 1/r only when distances are on a cosmological scale - Newtonian gravity works fine for planetary orbits. )

This would probably present some problems, becuase the critical acceleration is closely related to 1/H in current versions of MOND.

But if you're looking for something vaguely plausible (but highly unlikely), some sort of MOND-like gravity might work.
 
  • #8
Thanks, what do you mean by large acceleration values?
 
  • #9
And...so it is possible
 
  • #10
Gold Barz said:
Thanks, what do you mean by large acceleration values?

MOND in 3space+1time has a critical acceleration in which gravity changes from a 1/r^2 force to a 1/r force. (See the link I quoted). I was speculating that there is some 4space+1time version of MOND in which gravity changes from a 1/r^3 force to a 1/r^2 force below the "critical" acceleration. One problem with this idea is that it would be hard to make this work for planetary orbits with any value of the critical acceleration parameter that's similar to all to that in our universe.

I would stop well short of claiming that it's definitely possible to do what you want - just that I had this wild idea based on some promising but non-standard theories of gravity that might sort-of do what you want.
 
  • #11
But the problem with the whole inverse cube law thing is that they got the inverse cube law just by adding an additional dimension but applying the same geometry as before, wouldn't you have to do more than that? because 3D geometry and 4D geometry are different from each other
 
  • #12
Basically, the inverse cube law for gravity in 4-d space comes from the gravitational analog to Gauss's law.

See for instance http://hyperphysics.phy-astr.gsu.edu/hbase/electric/gaulaw.html
for more on Gauss's law - which is a law about electric charges.

While Gauss's law is a law about electric charges, Newtonian gravity also satisfies Gauss's law. General Relativity is more complicated than Newtonian gravity, but reduces to Newtonian gravity in the weak field limit. Thus we have GR satisfying Gauss's law in the weak field / low velocity etc. limit where it is the same as Newtonian gravity.

So in order to do what you want, you need gravity that does not satisfy Gauss's law, which means it can't be Newtonian in the weak field limit - the real problem isn't with Einstein, it's with Newton.
 
  • #13
So there's no way around it?

plus wouldn't the consenquences of adding an additional spatial dimension be emerging constants and effects we do not know of and cannot know
 
  • #14
You need something that modifies Newtonian gravity to get around your problem. MOND, which I mentioned, stands for "Modified Newtonian Dynamics". So it does modify Newton. It turns out that MOND even modifies things in the right direction. (Apparently, anyway - that's something I had to look up).

But in the form that's applicable to our universe, MOND is not nearly a strong enough modification to affect planetary orbits, it only shows up (in theory) over a much larger scale. And it's still quite a controversial idea - GR is still the standard theory of gravity.

Whether or not a form of MOND can be made to do what you want is somethign that I'm not familiar enough with the theory to answer.

Aside from modifying Gauss's law, it might be possible to make garavity anisotropic. Think of a gravity-like force that for some reason acted only in a specific plane in 3d space, and you'll get the basic idea. The 4-d equivalent would be a force that acted only act in a 3-d hyperplane. This idea is also pretty far out.
 
  • #15
So there is a way around the inverse cube law in a 4-D universe?
 
  • #16
I mean in a 4-D universe SHOULD there be the inverse cube law? but adding an additional spatial dimension changes things and probably change the extrapolation of inverse square law to the inverse cube law, I am guessing the laws would either change up or be tweaked
 

What is a 4D physics system and how is it different from traditional physics?

A 4D physics system is a theoretical framework that extends our understanding of the physical world beyond the three dimensions of length, width, and height. It involves incorporating the concept of time as a fourth dimension. This differs from traditional physics, which only considers the three dimensions of space.

What is the inverse square law for gravity and how does it apply to a 4D physics system?

The inverse square law for gravity states that the force of gravity between two objects is inversely proportional to the square of the distance between them. In a 4D physics system, this law still applies, but it is formulated in terms of four-dimensional spacetime rather than just three-dimensional space.

Why is it important to consider a 4D physics system and the inverse square law for gravity?

Studying a 4D physics system and the inverse square law for gravity allows us to better understand the behavior of objects in our universe. It also helps us to reconcile discrepancies between traditional physics and observations, such as the anomalous rotation of galaxies.

What are the potential implications of a different 4D physics system and inverse square law for gravity?

A different 4D physics system and inverse square law for gravity could lead to a better understanding of the fundamental forces of the universe and potentially revolutionize our understanding of space and time. It could also have practical applications in fields such as astrophysics and space travel.

What challenges are involved in constructing a different 4D physics system and incorporating the inverse square law for gravity?

Constructing a different 4D physics system and incorporating the inverse square law for gravity is a complex and challenging task. It requires a deep understanding of advanced mathematical concepts and rigorous testing and experimentation to validate the theories. It also involves reconciling new ideas with existing theories and making predictions that can be tested and verified through observation and experimentation.

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