Arjun Artro Posted June 28, 2015 Posted June 28, 2015 I wanted to learn about 4d space and got curious why I cannot visualize it so I searched in the internet for some answers. I am not satisfied by how it is explained, especially the flatlander's theory. First of all, how can a 1d or 2d object exist? Lets take 1d for an example. Its called 1d because it only has length and no width. How can you see a line that has no width, even the slightest width and the slightest height? Okay, 3 dimensions might be needed to do the math but in reality , are dimensions real? And our theory about 4d, 9d and 25d might be just helping quantum physics and string theories but I dont think it's actually there.
Strange Posted June 28, 2015 Posted June 28, 2015 I wanted to learn about 4d space and got curious why I cannot visualize it You can't visualise it because we live in (and have only evolved to understand) three dimensional space! But I wonder if you mean 4D space-time? In which case there are the three spatial dimensions we are familiar with plus time. I am not satisfied by how it is explained, especially the flatlander's theory. First of all, how can a 1d or 2d object exist? Lets take 1d for an example. Its called 1d because it only has length and no width. How can you see a line that has no width, even the slightest width and the slightest height? I don't think any 1D or 2D objects actually exist. They are mathematical concpets. For example, the surface (area) of a sheet of paper or a sphere are two dimensional. And your height is one dimensional. Okay, 3 dimensions might be needed to do the math but in reality , are dimensions real? To some extent, this depends what you mean by "real". But I would say three spatial dimensions are real. You need to specify three spatial dimensions to identify a location (x,y,z or lattitude,longitude, altitude or left,right,up, etc). And if you want to meet someone at that location, then you need to specify the fourth dimension: when.
Arjun Artro Posted June 28, 2015 Author Posted June 28, 2015 Okay that's for locating an object. And I agree that dimensions are needed for that just like the latitude and longitude of the earth. But we never use the terms like "a latitude object" , a "longitude object" like we call 2d object, 3d object etc. I might be wrong, but imagine this- suppose there is another world which is 2 dimensional. And the projection of a 2d surface is a "line" right? Suppose there are two lines - red and blue. How would you know that one is red and the other is blue if those lines only have length and no width (even if it is negligible, width cannot be equal to zero) . Am I right?
ajb Posted June 28, 2015 Posted June 28, 2015 Nobody expects macroscopical physical objects to have zero width or height. Mathematically one can, sometimes under the right approximations, model objects as being 1 or 2d.
Arjun Artro Posted June 28, 2015 Author Posted June 28, 2015 That's all what I am saying here. It exists only in math. And objects like tesseract or 4d hypercube can only be modelled with certain assumptions and I don't we cannot visualize it because we live in a 3d world but because such objects only exist in math.
Strange Posted June 28, 2015 Posted June 28, 2015 Okay that's for locating an object. And I agree that dimensions are needed for that just like the latitude and longitude of the earth. But we never use the terms like "a latitude object" , a "longitude object" like we call 2d object, 3d object etc. I might be wrong, but imagine this- suppose there is another world which is 2 dimensional. And the projection of a 2d surface is a "line" right? Suppose there are two lines - red and blue. How would you know that one is red and the other is blue if those lines only have length and no width (even if it is negligible, width cannot be equal to zero) . Am I right? Correct. There are no real objects which have less than three dimensions. That's all what I am saying here. It exists only in math. And objects like tesseract or 4d hypercube can only be modelled with certain assumptions and I don't we cannot visualize it because we live in a 3d world but because such objects only exist in math. Space-time can be described as a four dimensional object. But whether you think that only exists in mathematics or is a real "thing" is not clear (as I say, it depends what you mean by "real" or "object").
ajb Posted June 28, 2015 Posted June 28, 2015 That's all what I am saying here. It exists only in math. Sure, but the mathematics can be very important in how we understand the real physical world.
StringJunky Posted June 28, 2015 Posted June 28, 2015 Correct. There are no real objects which have less than three dimensions. Graphene is an allotrope of carbon in the form of a two-dimensional, atomic-scale, hexagonal lattice in which one atom forms each vertex. It is the basic structural element of other allotropes, including graphite, charcoal, carbon nanotubes and … https://en.wikipedia.org/wiki/Graphene About as close to two dimensions as nature allows I think.
Strange Posted June 28, 2015 Posted June 28, 2015 About as close to two dimensions as nature allows I think. Close... And I'm not sure about electrons, for example, which appear to be zero-sized, point particles. Does that make them zero dimensional?
StringJunky Posted June 28, 2015 Posted June 28, 2015 Close... And I'm not sure about electrons, for example, which appear to be zero-sized, point particles. Does that make them zero dimensional? This is the thing, do they actually displace space?
Mordred Posted June 28, 2015 Posted June 28, 2015 Electrons being fermionic according to the Pauli exclusion principle do occupy space. https://en.m.wikipedia.org/wiki/Pauli_exclusion_principle
StringJunky Posted June 28, 2015 Posted June 28, 2015 Electrons being fermionic according to the Pauli exclusion principle do occupy space. https://en.m.wikipedia.org/wiki/Pauli_exclusion_principle Yeah, two electrons can't occupy the same position can they?
Mordred Posted June 28, 2015 Posted June 28, 2015 You should recall particles are both point like and wavelike. Wiki covers it fairly well. https://en.m.wikipedia.org/wiki/Point_particle Yeah, two electrons can't occupy the same position can they? Two electrons of the same quantum state.
StringJunky Posted June 28, 2015 Posted June 28, 2015 You should recall particles are both point like and wavelike. Wiki covers it fairly well. https://en.m.wikipedia.org/wiki/Point_particle Two electrons of the same quantum state. Yes, OK 1
Mordred Posted June 28, 2015 Posted June 28, 2015 "However, neither elementary nor composite particles are spatially localized, because of the Heisenberg uncertainty principle. The particle wavepacket always occupies a nonzero volume. " The quote is from the wiki article. Side note for other readers any number of bosons can reside in the same space. 1
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