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 at his blog (http://profmattstrassler.com/2013/07/31/a-few-stories-worth-a-comment/#comment-71566
). The following is a rewrite about 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 the 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 less
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 complicate 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 about (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.

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