Ask Ethan # 104: what if we had four spatial dimensions?

There is a fifth dimension, beyond the limits known to man. This dimension is huge, like space, and timeless, like infinity. This is a neutral territory for light and darkness, for science and superstition.
- Rod Serling

We are quite accustomed to the three spatial dimensions of our Universe, to length, width and depth. We can imagine how things look in smaller dimensions - on a two-dimensional plane or on a one-dimensional line - but with higher dimensions everything is not so simple, since we cannot imagine movement in a direction that cannot be described by our usual space. In the universe there is a fourth dimension (time), and only three spatial. But among the questions this week, I saw an outstanding question in the “what if” series from writer Kelly Luke:

What would it mean for people if the number of measurements in our world would change as the seasons? For example, half of the year we have three dimensions, and half - four.

Imagine, if possible, that you have the ability to move in one additional direction - not included in the normal set up-down, north-south and west-east. Imagine that only you have this ability.



For a person from our three-dimensional world, your abilities will look amazing, and even, in a sense, godlike. After all, you can:
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• teleport from one place to another, disappearing in one place and appearing somewhere else,
• rearrange or remove the internal organs of a person, performing surgical operations without incisions,
• Remove anyone from his three-dimensional universe, and disembark a bit later at any other place of your choice.

How is this possible? Imagine that you, a three-dimensional creature, interact with a two-dimensional universe, for example, with a set of color forms [a toy in the manner of flat paper dolls that you need to wear in painted clothes - approx. trans.].



From the point of view of us with additional dimensions, we can climb inside a two-dimensional being and manipulate their insides without incisions. We can turn them inside out or swap left and right. We can lift them from the plane and move them to any place.

And if we, three-dimensional creatures, decided to enter the two-dimensional world, we would look strange, because at any moment they could only see our two-dimensional cut:

• at first we would appear as footprints,
• then would turn into two circles, moving down through their universe,
• circles would merge into an ellipse,
• then new (fingers) would appear,
• they would grow into two large circles (arms, shoulders),
• all this would be united into one big figure at shoulder level
• then it would decrease, grow again, and disappear (neck, head).



Fortunately, in our universe there are no four-dimensional creatures, because they would seem to us god-like creatures that violate physics. But what if we were not beings from higher dimensions, but in the Universe there would be more dimensions? And it is possible - it was shown that in the past the Universe could have more dimensions.



In the context of the general theory of relativity, it is quite simple to create a space-time in which the number of macroscopic measurements changes with time. We could have more dimensions not only in the past, but also in the future; moreover, we can construct a space-time, where this number fluctuates, and it becomes more and less.

So yes, in our Universe the fourth dimension can really begin to appear.


Tesseract


Icositrachor

All this is cool, but what would it look like? Usually we don’t think about it, but four fundamental interactions - gravity, electromagnetism, and two nuclear forces - have exactly these properties and quantities because they exist in the number of dimensions that exist in the Universe. If we reduce or increase their number, we will change, for example, the distribution of field lines.

Changing the electromagnetic and nuclear forces would lead to a catastrophe.



Imagine that you are looking at an atom, or at its inner part, nucleus. The nuclei and atoms are the building blocks of all the substance of which our world consists, and their scales are extremely small. The atoms - angstroms (10 ^-10 m), the nuclei - femtometers (10 ^-15 m). If these forces begin to flow into another spatial dimension, the laws governing them will change.

Simply put, these forces will have more distribution space, which means that they will weaken with distance faster. This will affect the cores not so much - their sizes will become slightly larger, and some cores will change stability. Stable nuclei can become radioactive, and vice versa. It's not so scary. But with electromagnetism there will be more problems.


Atomic orbitals table

Imagine that suddenly the forces connecting the electrons to the nuclei weaken. What will change the power of this interaction. At the molecular level, all that holds you in its entirety is relatively weak bonds of electrons and nuclei. If you change this interaction, the configuration of everything changes. Enzymes denature, proteins change shape, ligand-driven neurons no longer fit together, DNA will not encode molecules, as expected.

That is, if the electromagnetic interaction changes, penetrating into the fourth spatial dimension, which has reached the size of an angstrom, people will immediately die.



But all is not lost. There are many models, mostly inspired by string theory, in which these interactions, electromagnetic and nuclear, are limited to three dimensions. And then only gravity can penetrate into the fourth. For us, this means that gravity will flow into the fourth dimension, which is increasing in size (and in influence). And objects will become weaker than before.

As a result, many strange things will happen.



Rapidly rotating asteroids consisting of a loose substance will begin to decay. Their attraction will not be enough to hold stones and gravel on the surface. Comets approaching the Sun will evaporate faster and their tails will become more chic. And with a sufficiently strong fourth growth, the Earth’s gravity will fall, causing the planet to swell, especially along the equator.



People living closer to the poles will feel a decrease in gravity, and those who live closer to the equator will be in danger of flying into space. At the macro level, Newton's famous law, the inverse square law, will turn into the law of inverse cubes, and gravity will decrease more rapidly with distance.

With the growth of the measurement to the distance between the Earth and the Sun, everything in our solar system will come to the dressing. If this continues for more than a few days a year — even if gravity returns to normal for the remaining 50 weeks — our solar system will completely collapse in just one hundred years.



There will be periods on Earth when we not only can sense an additional direction for movement, but also when the properties of gravity change dramatically for the better. Not only will the jumps in length and height never be the same, the consequences for our dear stable Universe will be apocalyptic.

So be careful of your desires, Kelly, since the fourth dimension, growing to a large size, will not only bring amazing sensations, but will also drain a large part of the Earth, including the atmosphere and equatorial regions.

But there is a plus.



Global warming will stop worrying us, because an increase in the distance from the Sun will cool our world a lot, much faster than an increase in the amount of CO ₂ in the atmosphere will warm it up! All the minuses have their advantages, and although we will only have a few years to enjoy the new dimension, this experience may be worth the rest of our lives.