Theoretical Physicist, Professor Matt Strassler, recently described that SUSY (with s-particle) is a purely speculative idea. Luboš Motl (a physics blogger) wrote a negative comment about Matt’s usage of the word “speculation”: “Matt's adjective "speculative" makes SUSY – and all BSM physics research – sound like a speculative, philosophical, futuristic research or a research of unhinged crackpots. It's none of these things. … Supersymmetry is primarily a symmetry whose restoration seems inevitable at the Planck scale or lower in consistent theories of quantum gravity. It is also a symmetry that produces the most natural dark-matter candidates we know in literature.”
I strongly agree with Matt’s usage of that word. So, I wrote two comments on his blog (http://profmattstrassler.com/2013/07/31/a-few-stories-worth-a-comment/#comment-71566 ). The following is a rewrite of those comments which strongly refute Motl’s points.
First, we should examine what SUSY (with s-particle) is all about.
Let one ball (perfect sphere) rotating on its center and a very fine laser beam hits the ball while the beam reflects on a screen. During the rotation, if the laser dot on the screen does not move, then all those points which are swept by the beam are symmetrical somehow.
a. For a perfect ball, the laser dot on the screen will never move. This can be described in two ways,
i. infinite degree of symmetry,
ii. zero (0) point symmetry break.
b. If that perfect ball is punched and has a needle-hole, then we can find, at least, one occasion that the laser dot will move. That is, the infinite degree of symmetry is no more, and there is at least one (1) symmetry break.
c. If a few ditches are scratched on the ball surface (forming a soccer ball like pattern), we will notice that the “symmetry break” increases. That is, we will conclude that more patches on the ball the lesser degrees of symmetry.
For the Standard Model, it has 48 elementary particles which can be described as a (4 x 4 x 3) cube. And, this cube can be represented as a patched ball. If these 48 particles can be represented by a code of (3 x 3 x 2) cube, then this new cube has higher degrees of symmetry. On the other hand, if we double the 48 to 96, then the degrees of symmetry will be reduced.
With this understanding, no one can see that the SUSY (with s-particle) can be a higher symmetry. It should be a lower symmetry.
If this SUSY (s-particle) is not placed on the original ball but is on a new ball, then the entire system becomes a dumbbell which has very low symmetry from any “stand-point”. In fact, there is no way to convince anyone that SUSY (with s-particle) has higher degrees of symmetry than without it. If SUSY (s-particle) is not a higher symmetry, then what are all the hypes about it?
Second, can we refute Motl’s comment that SUSY (with s-particles) is absolutely necessary for the issues of dark-matter and hierarchy problem? This issue can be discussed clearly with a grandmother/boy dialogue.
Boy: grandmother, someone says that SUSY (with s-particles) is absolutely needed for dark-matter and the hierarchy problem. If the soccer-ball/laser-beam model cannot address these two issues, it must be wrong.
Grandmother: Exactly. The dark matter is about (5.8571428 – w) times the visible matter from this soccer-ball “calculation”.
Boy: Planck data is now public, and it shows (25.8/4.82) = 5.3526 times. Are you just making one up with this known data? By the way, I am not good at math at all. Thus, any complicate calculation will definitely go over my head. Just tell me some reasons behind the calculation.
Grandmother: No, not complicate calculation, just counting fingers. But, we first must get the “language” correct, a linguistic issue, you know.
A = matter/anti-matter symmetry
B = baryongenesis (matter/anti-matter symmetry-breaking)
Which one (A or B) has higher “degrees” of symmetry?
Boy: Come on! Of course, A has higher degrees of symmetry.
Grandmother: Indeed, this is “the” problem. Boy, you are wrong. Please see the following points.
a. If the ball is a “perfect” sphere, the laser dot will not move forever. Thus, it has “infinite” degrees of symmetry.
b. If there is one pin-hole on the ball, the laser dot will “eventually” make a jump (symmetry break). However big this “eventually” is, it is finite. So, it has much fewer degrees of symmetry than the first case.
c. If there are 24 pin-holes (patches) on the ball, the laser dot will jump (symmetry break) Y-times.
d. If there are 48 pin-holes (patches) on the ball, the laser dot will jump (symmetry break) Z-times.
It is very obvious that Z is larger than Y. Thus, the case c has higher “degrees” of symmetry than the case d. So, B (baryongenesis) must have higher degrees of symmetry than A (matter/anti-matter symmetry).
Boy: So what! What the heck is symmetry good for anyway! Why should it become a big deal, especially for the nature laws?
Grandmother: All is about the laziness. For example, there are 81 equations in the multiplication table. But, 5 x 8 = 8 x 5, thus, we need only memorize one-half (about 40) of these equations. So, symmetry is all about memory-management; the higher the symmetry, the lesser the memory-energy is needed. The universe is very huge and complicated while the Nature is very lazy. So, Nature plays this symmetry game, as it needs only to hold on one leash to control all. You kids can roam free but must obey the symmetrical rules. So, nature’s kids went out the world which is demarcated with many symmetrical-ditches.
Boy: Okay, okay. So, the ball is demarcated with symmetrical-ditches. What does this get to do with the dark-matter?
Grandmother: In order to increase the degrees of symmetry (tighten the leash), many ditches are filled while the lands are still owned by the symmetry-claimers. So, the laser dot will not move when it goes over those demarcations. That is, those lands become “dark-lands”, no laser-jumps (no manifested “particles [or ditches]”). Yet, while they turn dark (not manifested as particles), they still take up the land, still having the landmass, no difference from the visible particles in terms of the landmass. For the 48 SM particle-land-patches, 40 of them are dark-lands. Electron-neutrino is also dark. So, the total dark-lands are 41, that is, the dark/visible ratio is [(41/7 = 5.8571428) – w].
Boy: Why “-w”?
Grandmother: The playing of these visible-kids is often getting out-of-the-bound into the dark-lands, and it causes some sparks there. According to the AMS-2 data, the out-of-the-bound sparks account for (8 to 10%) of the dark-landmass. Thus, [41 x (100 – 9) % /7 = 5.3300] is almost identical to the Planck data [(25.8/4.82) = 5.3526].
Boy: Wow! You are really lucky and can make up numbers.
Grandmother: Well, the Alpha equation uses the same soccer-ball calculation.
Boy: How about the hierarchy problem?
Grandmother: Not today. But, there are no “fundamental” particles beyond the SM 48 particles on this soccer-ball, from here all the way to “the … energy”. Furthermore, the “infinite” degrees to “finite” degrees are a much bigger jump than the hierarchy problem.