4d object heavier then 3d object?

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Discussion Overview

The discussion revolves around the concept of mass and density in a hypothetical four-dimensional universe, particularly in relation to a four-dimensional version of the sun compared to its three-dimensional counterpart. Participants explore how such a four-dimensional object would interact with its surroundings and the implications of additional spatial dimensions on mass and density.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • Some participants propose that if a four-dimensional sun were to exist with the same size and atomic structure as a three-dimensional sun, it would have more mass due to the different definitions of density in four dimensions.
  • Others argue that if the atoms in four dimensions are the same size and mass as those in three dimensions, then the mass would remain the same, leading to a different representation of density.
  • A participant suggests that gravity in a four-dimensional world would follow an inverse cube law, contrasting with the inverse square law observed in three dimensions.
  • There is a discussion about the implications of adding dimensions and how mass might be affected, with some suggesting that time does not interact with mass in a measurable way.
  • Some participants express skepticism about the feasibility of discussing physical properties in a four-dimensional context, likening it to nonsensical questions about traveling faster than light.
  • Questions arise regarding the nature of atoms in four dimensions and whether they would retain the same mass as those in three dimensions.
  • One participant mentions theories involving additional small dimensions and how they might relate to the overall mass and volume of objects in higher dimensions.

Areas of Agreement / Disagreement

Participants do not reach a consensus, with multiple competing views on how mass and density would behave in a four-dimensional universe. The discussion remains unresolved, with differing interpretations of the implications of additional dimensions.

Contextual Notes

Participants highlight limitations in understanding how physical laws apply when considering hypothetical scenarios involving additional spatial dimensions, and there are unresolved questions regarding the definitions and interactions of mass and density in such contexts.

Cybervagabond
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Hello

I was sitting and thinking one evening and got this question.

In our 3 dimensional universe we have our sun, we know all the parts that makes the sun and how it interact with objects and space around it.

If we say that we have a 4 dimensional universe and have the same sun there but in 4 dimensional.

Would it have more mass, density and how would it interact with the objects and space surrounding it.

Hope for good answers
 
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three dimensions are length, width and height..
the forth dimension is TIME.

we all ready are in a 4-dimensional universe.. :)) you may browse more info by reading relativity.. :))
 
A temporal dimension is a dimension of time. Time is often referred to as the "fourth dimension" for this reason, but that is not to imply that it is a spatial dimension. A temporal dimension is one way to measure physical change. It is perceived differently from the three spatial dimensions in that there is only one of it, and that we cannot move freely in time but subjectively move in one direction.

So i am not talking about temporal dimension, but i am talking if there was a fysical forth spatial dimension and if it was. Would the cube contain more mass and density?
 
Time is not a spatial dimension. It only appears as a dimension in maths because the maths don't care about the physical interpretation what you're doing.
 
Hmmm I will assume you are describing an object at rest or to be more specific, not acted upon by any other force and that we are discussing its mass.

In purely technical terms this object already posses all the dimensional properties it ever can simply by virtue of its existential presence in a universe of n dimensions. Thus it is as massive as it is ever going to get without some additive process taking place.

Were you to add a dimension (because in math you are deific and can do such things) it would gain such mass as would describe the added dimension’s interaction with the existing dimensions where mass was concerned.

For instance Time, as a dimensional property, does not interact with any of the existing lower dimensions to affect mass at all (that we can currently measure). So even adding the dimension of time to the properties of the object does not increase its mass.
 
Cybervagabond said:
So i am not talking about temporal dimension, but i am talking if there was a fysical forth spatial dimension and if it was. Would the cube contain more mass and density?
In other words, what do the known laws of physics say will happen when something happens that the known laws of physics say can't happen?

Do you see the problem with your question?
 
Cybervagabond said:
Hello

I was sitting and thinking one evening and got this question.

In our 3 dimensional universe we have our sun, we know all the parts that makes the sun and how it interact with objects and space around it.

If we say that we have a 4 dimensional universe and have the same sun there but in 4 dimensional.

Would it have more mass, density and how would it interact with the objects and space surrounding it.

Hope for good answers
if 4D atoms are the same size and mass as 3D atoms and the 4D sun is the same size as a 3D sun
then yes it will have much more mass.

density of a 4D object would be defined as mass per 4D unit cube
density of a 3D object would be defined as mass per 3D unit cube.
you can't really compare one to the other.
its like comparing apples and oranges

gravity in a 4D world would follow an inverse cube law rather than the inverse square law of 3D
 
Last edited:
granpa said:
if 4D atoms are the same size and mass as 3D atoms and the 4D sun is the same size as a 3D sun
then yes it will have much more mass.

density of a 4D object would be defined as mass per 4D unit cube
density of a 3D object would be defined as mass per 3D unit cube.
you can't really compare one to the other.
its like comparing apples and oranges

gravity in a 4D world would follow an inverse cube law rather than the inverse square law of 3D


I considered this question. It is pretty much the same thing as saying, "what is the volume of a 2D plane?" Well, if it has zero extent in the third dimension then the volume is zero, unless you have an infinite plane and then the volume is undefined.

When I thought about this, it was in the context of theories that have 6 very small rolled-up dimensions. So consider the possibility that the Earth is really ten dimensional, with extent of each extra dimensions being the Plank length. That allows us to calculate a 10-volume for the Earth. If the extra dimensions somehow expanded to be of the same size as our usual three spatial dimensions, then the Earth would have a radius less than that of a proton.
 
When I thought about this, it was in the context of theories that have 6 very small rolled-up dimensions. So consider the possibility that the Earth is really ten dimensional, with extent of each extra dimensions being the Plank length. That allows us to calculate a 10-volume for the Earth. If the extra dimensions somehow expanded to be of the same size as our usual three spatial dimensions, then the Earth would have a radius less than that of a proton.

What makes you so sure that if the extra dimensions expanded the others would contract? I have heard of this in Greene's book on String Theory, but he didn't make it clear for me why, since you thought of the same thing maybe you could explain.
if 4D atoms are the same size and mass as 3D atoms and the 4D sun is the same size as a 3D sun
then yes it will have much more mass.

I don't understand this either, if 4d atoms are the same size and mass as 3d atoms, and the 4d is the same size(has the same number of atoms, since 4d atoms are the same size)
Then it would have the same mass, just a differently represented density, as it would be per m^4
 
  • #10
Zula110100100 said:
I don't understand this either, if 4d atoms are the same size and mass as 3d atoms, and the 4d is the same size(has the same number of atoms, since 4d atoms are the same size)
Then it would have the same mass, just a differently represented density, as it would be per m^4

if the radius of the 4D sun is the same as the radius of the 3D sun then the number of atoms will be proportional to r^4 in 4D rather than r^3 in 3D
 
  • #11
granpa said:
if the radius of the 4D sun is the same as the radius of the 3D sun then the number of atoms will be proportional to r^4 in 4D rather than r^3 in 3D

does an atom in R4 have the same mass as the one in R3?

This question makes no sense, all the talk is just nonsense, its just like the question "what will happen if you travel faster than light"
 
  • #12
whats an atom in R^4?
 

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