- #1
phy
i understand the concept of dimensions until we get to 3 but having more than 3 dimensions is beyond me. anyone care to explain? thanks.
wow, you took the words from straight out of my mouth. someone enlighten me too.Hyperbolic said:I may be slow and i still don't understand these higher dimensions however i would still like to know the point of these higher dimensions. So far I haven't found out their names or what they actually are. Could someone please enlighten me?
Hyperbolic said:I may be slow and i still don't understand these higher dimensions however i would still like to know the point of these higher dimensions. So far I haven't found out their names or what they actually are. Could someone please enlighten me?
selfAdjoint said:Sol,
You have to understand that U(1)is a photon
U(1) is a group. It's actually the group you get be rotating a circle through angles. The angles of rotation represent the phases of the EM radiation (or photon, if you prefer).
Think of a sine wave along the x-axis, and somewhere you mark a zero and put in the y-axis. Now the sine curve repeats itself every length of [tex]2\pi [/tex] along the x-axis, because it's the stretched out equivalent of going around a circle where the circumference is [tex]2\pi [/tex] times the radius. So where the y-axis cuts in corresponds to some angle or other, which equals some group operation from U(1) or other. This is the phase angle.
Now it's important that we can't detect this phase angle! Or what's the same thing, Nature doesn't give us a fixed zero to measure the sine curve of EM from, it's just an arbitrary convention. So the theory of EM is the same whatever phase angle you pick, or in other words, the operations from the group U(1) don't affect the physics. This is GAUGE INVARIANCE, the big noise in physical principles of the last 50 years. And U(1) is the gauge group of electromagnetism.
sol2 said:I saw this as I was reading your post:
http://wikibooks.org/upload/e/e2/Emwave.png
If you were to look at the end of this wave, and imagine a circle then we would see what you were saying?
Can you help bring clarity to this.
selfAdjoint said:I'm going to leave the discussion of the Kalusza Klein geometry and compactification till another time, if you don't mind.
selfAdjoint said:Sol, while I was looking for good papers on branes and the Standard Model (I found one!), I also found this wonderful Visual QCD site . I don't know if you've seen it before, but it might be a candidate for a link from your website.
Dimensions refer to the measurable parameters or properties that describe the physical space in which we live. In our everyday experience, we are used to thinking of three dimensions: length, width, and height. However, in the scientific world, dimensions can refer to additional spatial or abstract concepts that are necessary to fully describe a given system or phenomenon.
While we may only experience 3 spatial dimensions in our daily lives, there are many theories and mathematical models that suggest the existence of additional dimensions. These extra dimensions may be too small for us to perceive or interact with directly, but they play a crucial role in understanding the behavior of particles and forces at a microscopic level.
Studying more than 3 dimensions allows us to gain a deeper understanding of the fundamental laws that govern our universe. It also helps us to explain and predict phenomena that cannot be fully understood using only 3 dimensions. For example, theories such as string theory and supergravity propose the existence of extra dimensions to reconcile inconsistencies between quantum mechanics and general relativity.
As of now, there is no scientific evidence or technology that allows us to directly observe or travel through more than 3 dimensions. However, scientists continue to explore and test theories that suggest the existence of additional dimensions, and advancements in technology may one day allow us to indirectly observe these dimensions.
The concept of more than 3 dimensions challenges our traditional understanding of the universe and forces us to think beyond what we can directly observe. It also has implications for various fields of science, such as cosmology, particle physics, and quantum mechanics. By studying more than 3 dimensions, we may be able to unlock new insights and potentially solve some of the greatest mysteries of our universe.