General Relativity is a local theory because it relates the local curvature to the local stress-energy tensor. So GR requires no extra dimensions to describe the universe, regardless of whether the universe is open or closed - current indications are that the universe is probably open. To learn more about what this means you might be interested in looking at the questions What is the universe 'expanding' into? and If the universe is expanding, what is it expanding into?. In general relativity no extra dimension is required because the curvature in intrinsic not extrinsic. All observers will agree there is one time dimension and three space dimensions, but they won't all agree on how those dimensions are defined.Īnyhow, you've undoubtably heard that spacetime is curved, and you've probably seen the rubber sheet analogies for spacetime, so it's natural to ask if there is a fifth dimension (fourth spatial dimension) for the universe to curve into. A vector that looks like a purely time displacement to me may look like a combination of a time and space displacement to another observer. This is because different observers will disagree about what bits are space and what bits are time.
It's important to note that while there are one timelike and three spacelike dimensions, you cannot uniquely split spacetime into separate time and space parts. The metric is the equation that tells us the distance between points. $t$, $x$, $y$ and $z$, to uniquely identify a spacetime point. We know there must be at least four dimensions because we need four numbers, e.g. This describes the universe as a four dimensional manifold equipped with a metric. If two theories make exactly the same predictions there is no way to distinguish between them, in which case physicists (being a down to Earth bunch) tend to choose the simplest theory.Īt the moment the generally accepted theory to describe the universe on the large scale is general relativity. Physics is a process of constructing theories to describe the universe, using those theories to make predictions, then doing the experiments to see if your predictions are correct. But then there's no experiment that we can do that could prove him right either, so as theories go it doesn't get us very far. Then no experiment we can do could prove him wrong. There's no way to detect the 4th (spatial) dimension
The scale of the sphere is far larger than the observable universe
The simple answer is that your cousin could be correct. So my question is: Is there a (as simple as possible) explanation/measurement/demonstration I could give/show to him to disprove his idea?Īlthough it's obvious, I confess I am definitely no expert, so please be forgiving to my formulations and assumptions. So it all looks very logical to him (and I admit, to me too).īut I am pretty sure this is incorrect as I don't recall reading anything about 4th spatial dimension (apart from String theory hidden dimensions), but I wasn't able to give him any kind of proof or counterexample.
That would allow the Universe to be both "infinite" and have its size, also questions like what's beyond the edge are not meaningful anymore. Then he came up with the idea (I'll rephrase it), that the Universe could basically be a 4d sphere which looks like 3d, but is warped into the 4th dimension, so it can form a 4d sphere - the same way as the Earth is 3d sphere which looks like 2d when you stand on it, but is warped ito the 3rd dimension, so it can form a sphere (hopefully the analogy makes sense as I seem to lack the proper wording). I was chatting with my 12yo cousin yesterday and we got to the Universe, its size and stuff like that.
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