Do Higher Dimensions actually exist?

The problem with that philosophy is that understanding the core mechanism offers a more rigorous and comprehensive way of modeling (describing) the phenomenon. For instance, general relativity (GR) is a very good model for our observations of the behavior of gravity everywhere in the observable universe…save that it does not describe what happens when gravitational gradients are significant on the scale of the Planck length, nor does it provide a sensible explanation for what is termed “dark energy” or why there is such a massive discrepancy between the vacuum field energy predicted by quantum field theory and observed measurements of the cosmological constant. It is entirely possible that GR is as much of a “weak field approximation” to some higher order theory as Newtonian gravity and Galilean invariance are of GR.

Of course, M-theory with its infinitely tunable parameters and higher order dimensions which are compactified to a scale that we cannot plausibly be expected to probe are not particularly useful in terms of providing experimental or observational evidence, and should be regarded as mathematical ‘toy models’ which provide some conceptual way of linking the topology of spacetime to quantum field theories albeit in a not very likely to be accurate fashion, but they may lead to useful insights about how a practicable test could be constructed.

Stranger

The theorem that this is the densest possible sphere packing in 3 dimensions is called the Kepler Conjecture, first stated in 1611. Surprisingly for such a seemingly simple statement, it was not formally proven until 2014. Until then, I always thought it would be so cool if someone came up with a denser packing that had been overlooked for all those centuries.

These threads are so frustrating for me. I feel like it’s all just beyond my ability to grasp it. Maybe in my life in an alternate universe?

You’re in good company. Nobody else understands this either. Except Ed Witten and maybe Roger Penrose, and even they are probably mostly wrong.

Stranger

I would say the contrary: First, I have no reason to expect that general relativity would provide a description of the properties of a particular substance, and second, that despite those low expectations, GR provides a much better explanation for the cosmological constant than anything in quantum mechanics does.

Relativity can be understood, if you put your mind to it and are willing to re-evaluate what you think you know. But as Feynman once said, anyone who understands quantum mechanics doesn’t understand quantum mechanics.

General relativity provides a description of the properties of ‘normal’ spacetime but it really has no explanation for dark energy (or missing dark matter, either, although that may not be a problem with gravitation, just a bunch of weakly interacting mass that we can’t directly observe via electromagnetic interactions), which behaves in a way that is contrary to gravity as we experience it on everyday scales. And the cosmological constant is just an arbitrary parameter which was originally introduced to explain why the universe hasn’t collapsed upon itself; that it now has an apparent purpose in tuning GR to allow for the large scale expansion of the cosmos is a kind of happy coincidence, but it doesn’t explain where this energy is coming from or why it behaves this way. And that the cosmological constant produces a model of cosmology that is inconsistent with the vacuum energy predicted by quantum field theory (by 120 orders of magnitude) indicates that something is lacking in either QFT, GR, or (likely) both.

Theories of compactified or extra-universal ‘higher’ dimensions are a good place to hide that extra energy, but there is no experimental evidence of them, and GR has to be extended in non-intuitive (and largely non-falsifiable) ways to even accommodate such theories. But such concepts may be useful in guiding toward a practical theory (i.e. one that can be falsified) if it even exists.

Stranger