At the Planck scale, space is not smooth
The question about the unification of physics is a question about what happens at the Planck scale. How does nature look at the Planck scale? This basic question needs to be answered to unify physics.
Combining nature’s maximum speed, nature’s maximum force, and nature’s quantum of action yields a minimum length in nature, given by twice the Planck length. The value is tiny, about 3 ·10⁻³⁵m, and thus much smaller than everything ever measured. Exploring the properties of nature shows that the minimum length is also the minimum length measurement error and that no experiment can reach the minimum length.
So we are in a difficult situation. To unify physics, we need to find out how nature looks at the Planck scale, but we cannot reach the scale in any experiment. Only one option is left: we must think, guess, and check.
Thinking about the minimum length is fun. A minimum length in nature has some important consequences. First of all, a minimum length implies that space is not continuous. Did you learn something different in school? Of course, you did! However, the statement that space is continuous is wrong. Physical space is approximately continuous, but it is not exactly continuous. The lack of continuity is an unavoidable consequence of the unification of quantum theory and relativity.
To achieve unification, we have to eliminate continuous space. But there is more. A minimum length also implies that points do not exist. Points have no length, no diameter, and no size. In a universe with a minimum length, such points do not exist. Did you learn something different in school? Of course, you did! However, points are idealizations that do not exist in nature. Space is not made of points.
Therefore, to achieve unification, we must eliminate continuous space and points. But there is even more. A minimum length also implies that space is not discrete. Space is not made of point-like entities that form a crystal or a network. Space is not made of anything that is point-like or has a point-like cross-section.
Are we on the right track? Let us check. Our conclusion that there are no points in nature implies that all approaches to quantum gravity based on points cannot succeed. Let us check in detail. This condition eliminates a lot of attempts. It eliminates almost all attempts proposed so far! Indeed, no attempt based on points has been successful at unification.
But if points do not exist, what then is space made of? Space cannot have more dimensions, because dimensions require points. Instead, space must have three approximate dimensions. Space cannot have fermionic coordinates, as required by supersymmetry, because such coordinates again require the existence of points.
“Nature consists of particles and space”, we learned for over 2000 years. “Space differs from particles”, we also learned. But what happens at the boundary between space and particles if particles are not points and if space is not made of points? Nothing. At the Planck scale, space and particles do not differ.
How can space and elementary particles not differ at the Planck scale? Space is divisible, but elementary particles are not. Space is extended in three dimensions, but elementary particles are not.
We are left with one option only: elementary particles are only approximatively indivisible and only approximatively not extended in three dimensions. Likewise, space is only approximatively divisible, and only approximatively extended in three dimensions.
But we can say even more about the “stuff” that makes up space and elementary particles. This “stuff” must also make up black holes, wave functions, and interactions. Black holes have entropy, and the entropy value is due to processes occurring at the Planck scale. More precisely, the value of black hole entropy found by Bekenstein and Hawking proves that black hole entropy is due to constituents of Planck size.
A constituent of space can be of Planck size in three, two, or one dimension.
* Three Planck dimensions would mean that the constituents are little balls, little dodecahedra or some other little object moving around randomly. This is impossible because no such little objects could generate black holes, their entropy, or the various particles and forces observed in nature.
* One Planck dimension would mean that the constituents are thin fluctuating membranes moving around randomly. Again, this is impossible, because no such little objects could generate black holes, or the various particles and forces observed in nature.
* Two Planck dimensions would mean that the constituents are thin strands moving around. This is possible because thin strands indeed generate black holes, their entropy, and the various particles and forces observed in nature. This is told in this text.
Let us check the result. If both space and elementary particles are made of fluctuating strands with Planck radius, neither space nor particles are made of points, and space is not continuous — as we demanded. Likewise, elementary particles are only approximatively indivisible and only approximatively point-like — as we required. Moreover, space is only approximatively divisible, and only approximatively extended in three dimensions, as we deduced. Finally, if both space and elementary particles are made of strands with Planck radius, this yields general relativity and the impossibility of distinguishing space from elementary particles. In addition, we get all elementary particles and all interactions, as told here. No other approach ever achieved this. None.
In short, by describing elementary particles and space as made of fluctuating strands of Planck radius we get the description of nature at the Planck scale we were looking for.
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P.S. For explanations and publications on how strands lead to particle physics and general relativity, see this web page.
P.P.S. What happens if one introduces point-like quantities nevertheless? In that case, one is inventing and dreaming, i.e., adding ideas or properties that do not exist in nature. By doing so, one automatically gets processes, properties and consequences that do not occur in nature.
For example, singularities are such consequences. They do not occur in nature. But they occur if one “invents” the counterfactual idea that arbitrarily small distances can exist.
Whenever we allow for quantities or entities smaller than the Planck length, we are leaving reality. To put it simply: “continuous space” and “point-like quantities” are figments of the human mind. They do not occur in nature.