3-Dimensions Enough?

R

Reiku

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I have a question. Is evidence showing the existence of three-dimensions only evidence against the existence of any other dimensions?

On evidence for a three-dimensional object, apart from the obvious fact we observe three-dimensional objects in our minds, is the inverse-square law. For those who don't know about it, take a surface of a sphere, given as 4πr² and also when we have a ratio A2, A1

$$I_{1}/I_{2}=N/A_{1}/N/A_{2}=A_{2}/A_{1}=4pir2^{2}/4pir_{1}^{2}$$

then the following equation is solved by saying that the second surface is twice the distance from the source $$I=k/r^{2}$$ and is found to be in inversely proportional to the square of the distance.

$$I= r_{1}^{2}/(2r_{1})^{2}xI_{1}= r_{1}^{2}/(4r_{1})^{2}xI_{1}= I_{1}/4$$

And this is considered as proof of three dimensions. Since there is no experimental evidence to suggest extra dimensions, then isn't that evidence alone that there exists no other?
 
This is completely off-topic and I apologize in advance... but... Reiku is using tex tags?!
My god, it's full of stars...
 
Reiku said:
..there is no experimental evidence to suggest extra dimensions..
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Here are many, in fact. For example, the Casimir force (indirectly proportional to forth power of distance) or Lamb shift are direct evidence of hidden dimensions. The space isn't "just 3D", because for example the light wave has the spin and transfers moment at large distances. The "just 3D" environment cannot undulate in flat 3D Minkowski spacetime metric by such way. Can you imagine, how just 3D elastic material transfers spin at the distance? Me not. The symmetry or electron with respect of its spin is 720º - again, no body in "just 3D space" can have such degree of internal symmetry.

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I beg to disagree, i am sure we have no evidence of other dimensions. If this be the case, then string theory would also have this evidence, and it doesn't. We have not detected any other dimensions directly.
 
Reiku said:
I have a question. Is evidence showing the existence of three-dimensions only evidence against the existence of any other dimensions?
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What evidence do you have that the first three dimensions are things that physically exist?
 
zephir said:
Here are many, in fact. For example, the Casimir force (indirectly proportional to forth power of distance) or Lamb shift are direct evidence of hidden dimensions. The space isn't "just 3D", because for example the light wave has the spin and transfers moment at large distances. The "just 3D" environment cannot undulate in flat 3D Minkowski spacetime metric by such way. Can you imagine, how just 3D elastic material transfers spin at the distance? Me not. The symmetry or electron with respect of its spin is 720º - again, no body in "just 3D space" can have such degree of internal symmetry.
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I will ask you the same thing. What evidence do you have that the first three dimensions are physical things? There is no scientific reference that states that dimensions are things that actually exist. Can you show any evidence that a dimension is a physical thing?
 
zephir said:
Here are many, in fact. For example, the Casimir force (indirectly proportional to forth power of distance) or Lamb shift are direct evidence of hidden dimensions.
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This is wrong, since we can explain them using theories with only 3+1 dimensions of space-time. There exists an experimentally verified model (indeed, the Casamir effect was predicted before it was observed) which does it without extra dimensions.

Therefore the Casamir effect isn't evidence for extra dimensions.

Love waves in earthquakes decay like $$\frac{1}{\sqrt{r}}$$ but this isn't evidence the Earth hass 3/2 spacial dimensions.
zephir said:
Again, no body in "just 3D space" can have such degree of internal symmetry.
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This is the style of your arguments - or not?[/QUOTE]And your style is to not know anything about the Casamir force and to make incorrect claims about it.
 
AlphaNumeric said:
...we can explain them using theories with only 3+1 dimensions of space-time....therefore the Casamir effect isn't evidence for extra dimensions...
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Uhm, by the same logic, if we can explain many aspects of particle behavior without string theory, it means by your logic, any effect predicted by string theory isn't proof of hidden dimensions, because we can always construct another explanation of it (for example those based on LQG theory, which is operating in just 3D).

From my point of view, any violation of ISL in three-dimensional space can serve as an indicia of hidden dimensions. But as I stated previously, the number of dimensions differs by observational perspective and every theory can serve as such observational perspective. For example, from heliocentric model perspective the solar system is pretty 3D system, but from Ptolemy epicycle model it's apparent highly dimensional system. After all, this is why it was rejected because of Occam's razor principle.
 
mark 8 said:
What evidence do you have that the first three dimensions are things that physically exist?
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Good question. The inverse formula does predict three dimensions. That's the math. Observationally-wise, height, breadth and width are all qualities of three-dimensional objects, just like the dice you observe with six sides or even a sphere -- but not the surface alone obviously, because that is two dimensional. In four dimensions, objects look really strange. A cube for instance, will look more like an anvil, with both ends stretched out, looking more like a sand vase. A sphere though, would look more like it was elongated at the sides... just like a tic tack ;)
I suppose these are all evidences of three-dimensional things. But we have no direct observation of 5 dimensions and 6. Or any other.
 
Now... Zephyr... you said:

''By my opinion, the dimension itself isn't physical thing, but the space-time is.''

Do you know what dimension means? It's a freedom of movement and space. This is also time. Therefore, you would be saying that spacetime isn't a physical thing, because it consists of dimensions.

But spacetime is physical, and the dimensions are also physical. Spacetime is a physical sheet of infinitely spinning virtual and real particles.
 
Reiku said:
... you would be saying that spacetime isn't a physical thing, because it consists of dimensions....
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I don't think so. The dimensions are the abstract arbitrary concept. For example, the single space-time can have a different number of dimensions, depending on the character of energy spreading. Such number depends on the observational perspective, too.
 
zephir said:
Uhm, by the same logic, if we can explain many aspects of particle behavior without string theory, it means by your logic, any effect predicted by string theory isn't proof of hidden dimensions, because we can always construct another explanation of it (for example those based on LQG theory, which is operating in just 3D).
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But can you always construct a model which explains everything in just 3D? We have no evidence of that. Those models which use just 3+1 dimensions lead to field theory and relativity being incompatible.

LQG has even less success than string theory.
zephir said:
From my point of view, any violation of ISL in three-dimensional space can serve as an indicia of hidden dimensions.
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Then you'd be wrong. MOND is an example of an attempt to work in just 3 spacial dimenions but a violation of the ISL.
zephir said:
After all, this is why it was rejected because of Occam's razor principle.
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No, it was rejected on the grounds of evidence. You're the one who keeps talking about the phases of Venus and the shadow of Moon craters (or whatever it is).

You contradict yourself. Again.
 
AlphaNumeric said:
But can you always construct a model which explains everything in just 3D?
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This is just a dual stance, depending on the observational perspective. The Aether Theory describes the Universe as a system of infinitely nested density fluctuations of hypothetical infinitely dense environment, i.e. the Aether. From outside such model could always appear as a low dimensional stuff - it just depends on the number of hierarchy levels nested inside it. Or you can imagine, you're formed by some level of fluctuations in the middle of hierarchy and after then the same model would appear a highly dimensional for you.

Frankly, I don't believe in "just 3D Universe" at all, simply because I don't see any reason, why just number three should be so significant in explanation of space-time hierarchy, i.e. the anthropic principle strongly manifests here. The 3D space is most significant with respect of evolution of complex structures, because the system of just 3D hyperspheres is most compact with respect of energy spreading. This difference is quite subtle, but when extrapolated to very high density, it will reshape whole reality into 3D space-time foam for us. But I still believe, every particular view of the above model can be seamlessly converted into another, until we keep its implicit, recursive character.

AlphaNumeric said:
...no, it was rejected on the grounds of evidence...
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The situation isn't so transparent here. We can interpret the Ptolemy models by hidden dimensions as well simply by applying proper spatial transform into heliocentric model. After then even the Venus phases and Lunar crater shadows will fit the geocentric model well. It just will remain quite complex, but it's all just about imagination of the plural nature of reality.

The observation of the same situation from both sides becomes significant, when observing the boundary of Universe, because many black holes can be interpreted as manifestation of cosmological event horizon, just being observed from outside. By my understanding the Universe appears like multi-throat Klein bottle or nested foam from very distant perspective, where the outer and inner perspective, future or past, etc appear mutually interchangeable. The understanding of such model is not complex, but its nothing for schematically biased thinkers, who are believing in their "best explanation" of Universe.

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