Can a zero dimensional object exist? If you had the power to create an universe where you can choose its characteristics, is there a way you can create an universe that admits a zero dimensional object? If you were able to create a zero dimensional object, would every zero dimensional object be the same? In a zero dimensional universe, can there be only 1 zero dimensional object? I didn’t understand the concept of zero dimension really so these might be really dumb questions, I only know that a zero dimension point is just a mathematical concept, but I want to know if there could be something else
In: Mathematics
No, that’s it, it’s just a mathematical concept. It doesn’t even have a size.
You could imagine a 2D universe, or even a 1D universe (although commute there would be a mess), but a 0D universe would just be a point by itself.
An object with zero dimensions does not interact with space if an object does not interact with space then it does not exist.
Everything that exists has to be some place.
In physics this is called a singularity. We can model that under gravitational collapse you end up with one. It has neither height nor width but just a point with mass, angular momentum, and charge. Under these models there would be one at the centre of every black hole, but again they’re just models and we can’t actually know if they exist because they are beyond the event horizon which we can’t extract any information from and there could be new physics or exotic matter that prevents them.
In purer maths it’s called an infinitesimal. Calculus kinda got rid of the need for them in calculations, but they could still have their uses someday.
A universe that was just a singularity would be no different than the singularity as modelled by by that in a black hole, except it’s unclear how it could gain/lose mass, charge, and spin. If it couldn’t and didn’t start with any it basically wouldn’t be anything I guess is the best way to put it. No different than nothingness.
A zero dimensional object would be something like an empty list.
A box you could theoretically assign properties but that has none.
So… if it has no properties… does it exist? I’d say no. Maybe in some obtuse philosophical sense you could imagine an empty object, but in terms of actual existence I don’t think that’s the case.
The singularity at the center of a black hole is considered to be a single point. When we talk about black holes we usually consider the Schwarzchild radius of the black hole, which is the region of space around the singularity where any object which enters cannot exist, even moving at the speed of light.
For a 0-dimensional object that has mass, there will be at least some small region of space around it where gravity is sufficiently strong as to prevent light from escaping.
Now, things get more complicated when we consider very small particles under quantum mechanics. The electron, for example, is usually considered a point-particle, however we cannot pinpoint it’s precise location under the laws of quantum mechanics. Instead we are limited to considering the “probability cloud” where it is likely to be.
So as far as our modern theories of physics go, we can’t really study a 0-dumensional object. Point-particles such as the electron cannot be measured with enough detail due to quantum mechanics, and black hole singularities cannot be studied because we can’t measure anything within a the Schwarzchild radius of a black hole.
If you take some liberties with how you define words then yes. It would just be what we call space, Hindu would call it akash.
The easiest way to understand it is like infinite paper, remove it and then our reality can’t exist. After all you need something to draw on.
A dimension is just a way to measure things. Think about a graph: anything you can put on a graph can be called a dimension. Time, mass, velocity, energy, etc are all dimensions. The dimensions you’re thinking of (I assume), are the planes of physical space.
So, an object could exist that does not require physical dimensions. I would actually say that a magnetic field fulfills those requirements. Despite existing within physical space, it interacts without having a physical representation.
Let’s say you wanted to build a zero dimensional universe. Honestly, that’s really easy. If you run a video game on your computer, that’s basically a whole universe that’s made out of electrical signals.
That means there’s absolutely no reason there couldn’t be a universe with only energy inside it that creates extremely complex patterns like our own. There’s also no reason that our universe couldn’t be that exact thing, either. So, no, there wouldn’t only need to be a single object inside a universe with zero dimensions.
As others have mentioned, such objects are predicted in physics that do not have conventional 3 dimensions.
However such objects still contain information which basically has to exist in some other, non spacial, dimensions.
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