Does the 4th dimension (and above) exist? Or is it just a human construct?

[Forogil]

It's not a theory. It's speculation without a basis in any physics or math, it just freely borrows words from both and combines them in ways that make progressively less sense.

For instance, carrying his analogy to time as the 4th dimension, he regards an element of the 4th dimension as a moment in the universe. This is a Newtonian way of looking at the world, where you could separate configurations of space into well defined moments in time. But this isn't possible in Special Relativity, where something can happen before or after something else, depending on choice of reference frame. This means that time itself is part of the description of events and you can't partition the universe into set slices of time anymore. This is basically a fancy way of saying that time doesn't behave like spatial dimensions, physically or mathematically.

I disagree somewhat, and think the error is deeper.

Newton's universe had space as being relative - so we can apply a rotation and transformation to switch between different reference frames.
In special relativity you can also do this; and in each reference frame each time-instance (in that reference frame) is a 3-dimensional spatial thing, and the before/after would be a set of spheres/circles/lines expanding like a cone. More commonly people use this with one spatial dimension combined with time.

But when transforming between different reference frames the time-axis doesn't behave as yet another spatial coordinate; and instead of staying 90 degrees apart the time and space axis can grow closer.

[Garnier Fructis]

I disagree somewhat, and think the error is deeper.

Newton's universe had space as being relative - so we can apply a rotation and transformation to switch between different reference frames.
In special relativity you can also do this; and in each reference frame each time-instance (in that reference frame) is a 3-dimensional spatial thing, and the before/after would be a set of spheres/circles/lines expanding like a cone. More commonly people use this with one spatial dimension combined with time.

But when transforming between different reference frames the time-axis doesn't behave as yet another spatial coordinate; and instead of staying 90 degrees apart the time and space axis can grow closer.

This is all true, but I think it over-complicates it. The idea in the picture that one can partition the universe based on time more naturally fits with the Newtonian view, as rotating or translating the 3-space doesn't change the time. Time is independent, so we can unambiguously associate to each time a configuration of space, up to rotation and translation.

This isn't possible in Special Relativity because the axes don't maintain 90 degree separation under all transformations, which means that to do the same thing with light cones we'd have to pin down a specific observer, first.

And this, I believe, is enough to show why the image is wrong. Because the image is clearly trying to carry forward the analogy in a Euclidean manner, and we know that the universe is at least Special Relativistic. And we usually understand SR to be non-Euclidean.

[Gamdwelf]

I'm an economist and I'm probably biased.

[Forogil]

This is all true, but I think it over-complicates it. The idea in the picture that one can partition the universe based on time more naturally fits with the Newtonian view, as rotating or translating the 3-space doesn't change the time. Time is independent, so we can unambiguously associate to each time a configuration of space, up to rotation and translation.

This isn't possible in Special Relativity because the axes don't maintain 90 degree separation under all transformations, which means that to do the same thing with light cones we'd have to pin down a specific observer, first.

But the fixed translations and rotations of 3-dimensional space are the same for Newton and special relativity. You only get the new problems with axes not maintaining 90 degree separation when the transformations include time.

If you squint and have one spatial dimension and one time dimension you have a Feynman diagram; it also has this problem of transformations etc.

And we usually understand SR to be non-Euclidean.

Yes, but we also have 2-dimensional maps of the Earth - even if spherical geometry is non-Euclidean and thus they misrepresent angles/distances/areas or more.

[Garnier Fructis]

But the fixed translations and rotations of 3-dimensional space are the same for Newton and special relativity. You only get the new problems with axes not maintaining 90 degree separation when the transformations include time.

And my point is that this is a huge problem. Because there's no good a priori reason to disregard transformations that affect time in the analysis of dimensions the image is trying to carry out.

[Forogil]

And my point is that this is a huge problem. Because there's no good a priori reason to disregard transformations that affect time in the analysis of dimensions the image is trying to carry out.

Yes, but I view it as a different problem. (His 5-dimensional analogy on the other hand makes no sense at all.)

In 4-dimensional space you can view what happens as different 3d-objects for each time-coordinate. And similarly we can remove one space-dimension and view a 2d-object changing over time as a 3d-object; or remove two space-dimensions and get a 2d-diagram. People actually do that.

The difference occurs when you try to change to a different reference frame (but before that there is no issue):
In a 4-dimensional spatial space all axis are the same.
In a Newtonian space the time-axis always stays separate.
In special relativity the time-axis combines with the spatial dimensions - but differently from the spatial axis.

[Deleted]

Time is not a spatial dimension. It's not even a dimension in full sense. More like a vector. Perhaps it's our perception of the spatial 4th dimension - but no one knows. As for not being the person from decades ago - that has nothing to do with dimensions.

Time is 4th dimension. To convince yourself, you just have to imagine that time is the third dimension of a movie.

[Deleted]

I don't know of anything that prevents more or less dimensions from existing. It's one of those questions like do multiple universes exist, can't be answered with our current knowledge and might not even be answerable at all.

But who knows maybe in a couple decades we figure out that all the dark matter/energy in our universe is actually a higher dimensional effect or w/e, you never know.