What Is a Single Dimension and How Can We Comprehend It?

[timejim]

I do not understand and cannot comprehend anything existing in a single dimension. I have heard briefly that strings exist in a single dimension. How would you describe a single dimension? I understand 3 dimensions, length- height-depth. But wouldn't a single dimension object be invisible in two dimensions? Also, if it were a single dimensional object, how would it exist? I mean, if it were composed of "something" wouldn't it have to be more than one dimension? Any explanations would be appreciated.

 

[JonF]

A single dimensional object in 3-space or 2-space would be a point. You wouldn’t be able to see it in three dimensions or two dimensions. But, The idea of a 1 dimensional object (or a point) is represented all the time in math. If you want to know how an actual tangible thing would exist having only 1 dimension, as far as I know it would be massless. Flatland (I forgot who wrote it) is a great book that was written by some mathematician long that deals with observing lesser dimensional objects in greater dimensions.

 

[ZapperZ]

Originally posted by timejim
I do not understand and cannot comprehend anything existing in a single dimension. I have heard briefly that strings exist in a single dimension. How would you describe a single dimension? I understand 3 dimensions, length- height-depth. But wouldn't a single dimension object be invisible in two dimensions? Also, if it were a single dimensional object, how would it exist? I mean, if it were composed of "something" wouldn't it have to be more than one dimension? Any explanations would be appreciated.

The existence of 1D "objects" is more real than you think and certainly not confined to just "strings" (which, btw, can exist in many dimensions). A quantum wire is one clear example of a 1D object. You may read the link below as an example:

http://physicsweb.org/article/news/6/1/20/1

These are things that are being studied and fabricated, and there's a good chance that some time in the near future, some of your electronics may have them. What makes things 1D or 2D or 3D is the strength of the "coupling" or "overlap" of whatever object you are looking at in those various directions. A very thin wire with a diameter comparable to the deBroglie wavelength of an electron in the wire, and with no significant overlap from anything else beyond it qualifies as a "1D" object.

Studying reduced dimensional effects has intrinsic, fundamental value. Things like electrons behave very differently when you start restricting it to just 2D or 1D. We have already seen the fractional quantum hall/fractional charge effect for electrons in 2D. Things get even more interesting (weird?) in 1D where Luttinger liquid theory predicts a separation between the motion of the electronic spin and charge.

Zz.

 

[timejim]

Originally posted by ZapperZ
The existence of 1D "objects" is more real than you think and certainly not confined to just "strings" (which, btw, can exist in many dimensions). A quantum wire is one clear example of a 1D object. You may read the link below as an example:

http://physicsweb.org/article/news/6/1/20/1

These are things that are being studied and fabricated, and there's a good chance that some time in the near future, some of your electronics may have them. What makes things 1D or 2D or 3D is the strength of the "coupling" or "overlap" of whatever object you are looking at in those various directions. A very thin wire with a diameter comparable to the deBroglie wavelength of an electron in the wire, and with no significant overlap from anything else beyond it qualifies as a "1D" object.

Studying reduced dimensional effects has intrinsic, fundamental value. Things like electrons behave very differently when you start restricting it to just 2D or 1D. We have already seen the fractional quantum hall/fractional charge effect for electrons in 2D. Things get even more interesting (weird?) in 1D where Luttinger liquid theory predicts a separation between the motion of the electronic spin and charge.

Very interesting article, however, they spoke of the "diameter" of the wire, wouldn't that indicate it wasn't truly one dimensional??

Zz.

 

[ZapperZ]

Please take note that in my posting earlier, I specifically mentioned when something can be considered as "1D". I never said anything about anything having infinitesimal width or diameter. The same can be said about the so-called 2D objects such as the Cu-O planes in the cuprate superconductors. The charge carriers on those things are considered to be confined to the 2D planes because the perpendicular electrical resistivity is several orders of magnitude larger than the in-plane resistivity. There's nothing in here, nor in the 1D example I gave, that stated anything about "absolute" dimensionalities.

Zz.

 

[Entropee]

So how can something 1d vibrate in different directions, even if it exists in multiple deminsions, it still only exsists in those dimensions as a 1d object. so how do "strings" vibrate?

 

[nextone]

My theoretical example of one dimension is the space past the universe. If you believe the Big Bang theory, then you believe that the universe is still expanding. If you believe the universe is still expanding, you believe that the universe as it is has an end. But if the universe has room to grow, then there must be an infinate space beyond the universe. This space theoretically would have no matter in it, and there would be no end, therefore there is no possibility to measure the volume of that space, because there is no height, width, or depth.

 

[nextone]

So how can something 1d vibrate in different directions, even if it exists in multiple deminsions, it still only exsists in those dimensions as a 1d object. so how do "strings" vibrate?

String theory, for the reason you state, and for other reasons, cannot be proven with the technology we possesses at the moment, if ever.

 

[Dr Lots-o'watts]

Would you consider a painting as a 2D or 3D object? Strictly speaking, it may be 3D, but only 2D are relevant. The same with physical systems described as such.

 

[Drakkith]

Would a 1d object be a point or something like a line? Or am i getting confused with something here?

 

[cepheid]

Would a 1d object be a point or something like a line? Or am i getting confused with something here?

Something like a line. A point has no dimensions.

 

[Entropee]

I just don't get how something can have 1 dimension. If it has length but no width, then it doesn't exist, and vise versa. Something I just haven't quite grasped...

 

[Drakkith]

The existence of 1D "objects" is more real than you think and certainly not confined to just "strings" (which, btw, can exist in many dimensions). A quantum wire is one clear example of a 1D object. You may read the link below as an example:

http://physicsweb.org/article/news/6/1/20/1

These are things that are being studied and fabricated, and there's a good chance that some time in the near future, some of your electronics may have them. What makes things 1D or 2D or 3D is the strength of the "coupling" or "overlap" of whatever object you are looking at in those various directions. A very thin wire with a diameter comparable to the deBroglie wavelength of an electron in the wire, and with no significant overlap from anything else beyond it qualifies as a "1D" object.

Studying reduced dimensional effects has intrinsic, fundamental value. Things like electrons behave very differently when you start restricting it to just 2D or 1D. We have already seen the fractional quantum hall/fractional charge effect for electrons in 2D. Things get even more interesting (weird?) in 1D where Luttinger liquid theory predicts a separation between the motion of the electronic spin and charge.

Zz.

True, but those wires are still 3d objects. You are simply restricting the electrons to only be able to move in 1 dimension, right? The wires themselves are made of atoms, which are 3d objects.

 

[JDługosz]

If you believe the universe is still expanding, you believe that the universe as it is has an end.

No, it could be infinite and still expanding.

But if the universe has room to grow, then there must be an infinate [sic] space beyond the universe.

You are saying that as our universe expands, it must take away from some "other" space that is enough like our own that it makes sense to call it space. That does not follow directly, as you seem to think.

 

[Dr Lots-o'watts]

I just don't get how something can have 1 dimension. If it has length but no width, then it doesn't exist, and vise versa. Something I just haven't quite grasped...

The width is not relevant! It doesn't matter if there is a width or not. You may imagine there is one, but the physical effects of interest don't depend on it, they only depend on the 1D.

A 1D system is one where the other dimensions are irrelevant, not needed, not taken into account, negligible, or consciously overlooked in the math-theoretical framework.

 

[Tac-Tics]

I do not understand and cannot comprehend anything existing in a single dimension. I have heard briefly that strings exist in a single dimension. How would you describe a single dimension? I understand 3 dimensions, length- height-depth. But wouldn't a single dimension object be invisible in two dimensions? Also, if it were a single dimensional object, how would it exist? I mean, if it were composed of "something" wouldn't it have to be more than one dimension? Any explanations would be appreciated.

If you were a creature living in a two-dimensional world, Flatland, could you "see" lines?

Just something to think about. It really doesn't have a hard answer, because we don't know the physics of Flatland.

One dimensional manifolds (spaces) and objects are described perfectly well mathematically. Your intuitions don't really matter, because the laws of physics aren't concerned with what you think.

If you have trouble conceptualizing one-dimensional objects, string theory is far beyond your ability to grasp at the moment. General relativity is hard enough without having to worry about the extraneous theoretic nonsense string theory adds to it.

 

[DaveC426913]

If you were a creature living in a two-dimensional world, Flatland, could you "see" lines?

Yes. If for no other reason than the 1D line would block me from seeing (2D) photons coming at me from the other side of it.

 

[tomunc]

nextone wrote: "My theoretical example of one dimension is the space past the universe. If you believe the Big Bang theory, then you believe that the universe is still expanding. If you believe the universe is still expanding, you believe that the universe as it is has an end. But if the universe has room to grow, then there must be an infinate space beyond the universe. This space theoretically would have no matter in it, and there would be no end, therefore there is no possibility to measure the volume of that space, because there is no height, width, or depth."

One way around this, as described by Hawking, is the principle of the finite universe w/o boundary. He pictures it as like it is curved, closing on itself, similar to a planet.

It is believed by many that the universe will continue to expand forever...thinking that Dark Energy > Dark Matter (Repulsion > Contraction). However, what if say over a trillion years or so black holes continues to grow in number, and the larger of them continued to eat the smaller ones, increasing the size of their Event Horizons to the point of being able to eat entire galaxies. Then, over time the biggest of the biggest of the black holes ate the remaining black holes, and eventually EVERYTHING in the entire universe was sucked into this one humongous black hole, creating another Singularity...which BANGED again...and again...and again...for eternity.

Wouldn't this possibility also answer the God issue of what existed before the Big Bang...that the "Perpetual Universe" is in itself God, therefore not in need of a secondary creator?

So much of what we "believe" today is still theoretical. Over the centuries what we once believed has been replaced by something else, which has since been replaced, etc...

Maybe it's not as complicated as we think.

If someone absolutely knows WHY the possible answer I give here is unsound, please set me straight.

tomunc

 

[Drakkith]

It is believed by many that the universe will continue to expand forever...thinking that Dark Energy > Dark Matter (Repulsion > Contraction). However, what if say over a trillion years or so black holes continues to grow in number, and the larger of them continued to eat the smaller ones, increasing the size of their Event Horizons to the point of being able to eat entire galaxies. Then, over time the biggest of the biggest of the black holes ate the remaining black holes, and eventually EVERYTHING in the entire universe was sucked into this one humongous black hole, creating another Singularity...which BANGED again...and again...and again...for eternity.

This is nonsense. Black holes do not work this way and don't get nearly this big. The multi-million solar mass monster in our galaxy's center isn't even bigger than our solar system.

Wouldn't this possibility also answer the God issue of what existed before the Big Bang...that the "Perpetual Universe" is in itself God, therefore not in need of a secondary creator?

Please keep religious topics out of the discussion per PF rules.

So much of what we "believe" today is still theoretical. Over the centuries what we once believed has been replaced by something else, which has since been replaced, etc...

Maybe it's not as complicated as we think.

If someone absolutely knows WHY the possible answer I give here is unsound, please set me straight.

tomunc

You are partially correct. Science is constantly being updated with better and more accurate models. I think it's more correct to say that what we believe to be true is growing increasingly accurate as time passes, not that our previous ideas are being replaced. Calculating the flight time of a thrown baseball using classical physics will be just as accurate and correct now as it will be in 2,000 years. Baseballs don't start moving in spirals when thrown just because we come up with a new theory. Classical physics itself is 100% valid if used in the right context, it is in no way theoretical, as is Quantum Mechanics and General Relativity.

 

[tomunc]

This is nonsense. Black holes do not work this way and don't get nearly this big. The multi-million solar mass monster in our galaxy's center isn't even bigger than our solar system.

The universe is what...about 13.7 billion years old? Perhaps within a respective cycle this is but a drop in a bucket or a grain of sand on a beach of time relative to the duration of the cycle. Perhaps there are already existing black holes much, much larger than the one at the center of the Milky Way or any other galaxy we can see.

And besides, why would you use the term nonsense in reply to a question posed by a new member? Is it because you're so much smarter than I, and because you have all the answers? And how is it that you're such an expert on the nature of black holes?

 

[Drakkith]

The universe is what...about 13.7 billion years old? Perhaps within a respective cycle this is but a drop in a bucket or a grain of sand on a beach of time relative to the duration of the cycle. Perhaps there are already existing black holes much, much larger than the one at the center of the Milky Way or any other galaxy we can see.

There are, but not the size of what you suggested earlier. Plus they are expected to give off radiation over time, reducing their mass and causing them to shrink, making it unlikely for them to ever join together in huge numbers to form one massive one of that scale. Plus black holes do not suck in objects like a vacuum cleaner, they act like any other object that gravitates does.

And how is it that you're such an expert on the nature of black holes?

I am not an expert, I merely know the basics from reading up on them and learning here on PF.