Important Math Question

XenoTheMorph · #1 November 3rd, 2003, 02:07 AM

Quote:

Originally posted by Grandpa Kim:

quote:
Originally posted by atari_eric:

Since we're on the subject of math, does anyone know the formula for finding the area of a 4-dimensional sphere? Assuming an equal radius for all 4 axes...

Sorry can't help you there but how about an additional question:

the formula for the 3D volume of a 4 dimensional sphere? This would be analogous to the area of a 3D sphere.

Well in anwser to these little questions:
wwwDOTbright.net/~mrf/hierarchy(1).html
(Yikes can't use links with brackets!!!! DOT is a ".")

1. A hypersphere (4D sphere) has a 4D "Area" of
V⁴ = π²r⁴/2

2. A hypersphere (4D sphere) has a 3D "Surface" of
S³ = 2π²r³

XenoTheMorph · #2 November 3rd, 2003, 02:43 AM

O.K. now onto the subject of infinite energy in an infinite universe.

Well Space is expanding due to the cosmological constant (vacuum energy, quintessance, so on whatever you call it or think it is, it all makes up the value of Lambda. If you followed that tell me how!

). This means that there is an edge to even an infinite universe, at least from our viewpoint, it is where the 'speed' of the expansion between the viewer and another point in space (whatever it happens to be) exceeds the speed of light.

This means that even though the both viewer and the other point are 'stationary' light cannot travel from one to the other (even over infinite time). The fact that nothing can travel faster than the speed of light (don't even say Tachyons

)is not a problem since nothing is, only the distance between the two points itself is changing.

Therefore even in an infinite universe you only get to see a finite volume of space. So only the Photons from objects in this volume can reach you, so no superheating problem! This also means that the cooling of space does not mean energy is being 'lost' only that the density of the energy is decreasing, same amount of energy larger volume.

Now i'm sure you are all wondering why I wrote all this, I don't know, no idea whatsoever.
Good Luck I hope you can follow this guys I'm not sure I can

[Edited for some clarity

]

[ November 02, 2003, 12:48: Message edited by: XenoTheMorph ]

Renegade 13 · #3 November 2nd, 2003, 04:24 PM

Quote:

Originally posted by XenoTheMorph:
Well Space is expanding due to the cosmological constant

Space is also expanding due to the mysterious force astronomers call "dark energy". It's an anti-gravitational form of energy that is accelerating the expansion of the universe. According to what I know of the theory, within several billion years, we will only be able to see stellar objects that are located in the Local Group, whose gravitational effects would overcome the anti-gravitational effects of dark energy.

This dark energy is believed to make up approximately 66% of the entire universe. Yet we know almost nothing about it. To say either that the universe is finite or infinite is pure guesswork. We know so little about the universe as a whole. For instance, only about 1% of the universe is made up of "normal" baryonic matter. The rest is dark matter and dark energy, which we know virtually nothing about. We need to find out more about these things before we can start formulating some hard theories about whether the universe is finite or not.

Don't get me wrong, I'm not discouraging debate and stuff like that. I'm just saying that even educated guesses are just that; guesses.

Renegade 13

Cyrien · #4 November 2nd, 2003, 04:45 PM

Quote:

Originally posted by deccan:

quote:
Originally posted by Cyrien:
Once again I am going to step in and say that we are making very big statements about EVERYTHING THAT EXISTS when we personally have observed about... less than .00001% of .000001% of .000001% (I am being generous tonight!(also assuming that it is finite and can have a percent value for it)) of everything in the Universe and then stating that we know that ALL OF THE UNIVERSE is cooling so it can't be infinite.

I don't disagree with logic of your statement, but I do disagree with the sentiment behind your statement. Certainly, all of our theories on the subject of cosmology (and much else besides) should always come attached with the caveat "so far as we can tell". But just because we cannot know for certain is no excuse for saying that we can never know and that we shouldn't speculate, build theories and try our best to extend our knowledge, imperfect as our methods are.

I never said we shouldn't speculate. I enjoy the speculation. The problem comes when, as I have often seen happen in other forums discussing this and other topics, people start pressing things across as facts to prove themselves when it is all just theory and speculation. IE: the number of atoms in the Universe, how old the universe is, background microwave radiation proves this or that... quite simply we don't know enough to be making any statements on these things based on what we can and can't know. All of this needs to be taken with a grain of salt when you start talking about infinite v finite universe.

Sorry if you took what I was saying the wrong way but I was simply trying to nip that in the bud, since normally as soon as people start posting cosmological data it rapidly approaches that path.

The basic problem is one you can see in every field of science. Older theories have prominence because they are the ones the scientists grew up with and their body of work is based on. If you say it might be wrong then you say that your whole body of work that you have worked on your whole life might be wrong. Most people just won't do this. You can see it historically with great resistance to new ideas and ways until overwhelming proof shows it to be truer and the old false and it can't be ignored anymore.

I wonder how much further along we could be if we as a species could simply admit to ourselves and others when something that we have worked on our whole lives might be wrong. Add up the decades of resistance you get to each new idea before it is accepted and I bet it is quite a alot.

Cyrien · #5 November 2nd, 2003, 04:49 PM

And Dark Matter theory is the perfect example of theories growing larger than maybe they should. It is the most largely accepted theory currently. But there are several other theories just as valid and accurate in the predictions for the actions of the universe that we can observe. They differ in what causes that and in their predictions for what we can't observe.

Yet Dark matter and energy is almost always what gets brought up. I know that we normally preface it as "this is just a theory" and quite correctly but the fact that we don't even bring up the others is itself a disturbing trend. If we don't even look at the alternatives will we notice when it starts being more accurate than the mainstream?

Suicide Junkie · #6 November 2nd, 2003, 08:53 PM

Quote:

I wonder how much further along we could be if we as a species could simply admit to ourselves and others when something that we have worked on our whole lives might be wrong. Add up the decades of resistance you get to each new idea before it is accepted and I bet it is quite a alot.

Of course, the flip side of that would be like societal ADD.
Everything in moderation...

deccan · #7 November 2nd, 2003, 11:20 PM

Quote:

Originally posted by XenoTheMorph:
Therefore even in an infinite universe you only get to see a finite volume of space. So only the Photons from objects in this volume can reach you, so no superheating problem! This also means that the cooling of space does not mean energy is being 'lost' only that the density of the energy is decreasing, same amount of energy larger volume.

Good points, and certainly true for a universe which is expanding at an accelerating rate, as our universe currently seems to be. Of course, in such a universe, the volume that we can interact with in any way is certainly very finite, so you throw away much of the appeal of having an infinite universe.