Date post: | 03-Jul-2015 |
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What is Supersymmetry ?
1 kudayblog.wordpress.com What is
Supersymmetry ?
kudayblog.wordpress.com 2
What is Supersymmetry ?
Just a single ques:on for
crea:ng enough trouble.
What is Supersymmetry ?
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What is Supersymmetry ?
….But since people keep asking me a lot about it, I feel like explaining it in the simplest form here.
What is Supersymmetry ?
What is Supersymmetry ?
4 kudayblog.wordpress.com
So let me try….
What is Supersymmetry ?
Supersymmetry:
Assuming that the scalars we observed in real life (e.g: mass) is just projections of extra dimensional vectors of supersymmetric space, Supersymmetry searches for possible symmetries between those scalars and vectors.
kudayblog.wordpress.com 5 What is
Supersymmetry ?
Supersymmetry:
Assuming that the scalars we observed in real life (e.g: mass) is just projections of extra dimensional vectors of supersymmetric space, Supersymmetry searches for possible symmetries between those scalars and vectors.
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Scalars, vectors, extra dimensions, space, projec:on??
… Did you understand it
now??
What is Supersymmetry ?
Assuming that the scalars we observed in real life (e.g: mass) is just projections of extra dimensional vectors of supersymmetric space, Supersymmetry searches for possible symmetries between those scalars and vectors.
Supersymmetry:
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Me neither!!!
What is Supersymmetry ?
Assuming that the scalars we observed in real life (e.g: mass) is just projections of extra dimensional vectors of supersymmetric space, Supersymmetry searches for possible symmetries between those scalars and vectors.
Supersymmetry:
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Let’s draw a picture in other
words.
What is Supersymmetry ?
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This is Bob. He lives in a 4 dimensional (x,y,z,t) world like us. This means he can measure length, height, width of an object at any time. Here he has 3 vectors called x,y,z.
This is Alice. She lives in a 5 dimensional world. Because she can measure one extra dimension θ in addition to x,y,z,t. So she has 4 vectors called x,y,z,θ.
What is Supersymmetry ?
kudayblog.wordpress.com 10 kudayblog.wordpress.com 10
This is Bob. He lives in a 4 dimensional (x,y,z,t) world like us. This means he can measure length, height, width of an object at any time. Here he has 3 vectors called x,y,z.
This is Alice. She lives in a 5 dimensional world. Because she can measure one extra dimension θ in addition to x,y,z,t. So she has 4 vectors called x,y,z,θ.
What is Supersymmetry ?
Hushhhhh… Their rela:on has a strange story and I will tell you the reason why….
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Assume that this axis represents Bob’s world: (x,y,z,t) = xμ where μ = 1,2,3,4 So that x1 = x , x2 = y , x3 = z , x4 = t BOB
ALICE
What is Supersymmetry ?
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…and assume that this axis represents Alice’s world: (θ,x,y,z,t) = θa where a = 1,2,3,4,5 So that θ1 = θ , θ2 = x , θ3 = y , θ4 = z , θ5 = t
Xµ
BOB
ALICE
What is Supersymmetry ?
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Xµ
θa
Whenever they decide to measure the dimensions of an object, they can not find the same results.
BOB
ALICE
What is Supersymmetry ?
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Xµ
θa
Because Bob was measuring 4 dimensions -width, length, height, time- but Alice was measuring one more dimension called θ in addition to width, length, height and time.
Y
BOB
ALICE
Yµ
Ya What is
Supersymmetry ?
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Xµ
θa
Y
BOB
ALICE
Yµ
Ya
One day, Bob decided to do better than this. And he realised that he can also measure a scalar called Mass.
Mass of Y
What is Supersymmetry ?
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Xµ
θa
Y
BOB
ALICE
Yµ
Ya
He called up Alice and asked if she can measure any scalar feature of the same object Y. Alice told “What is a scalar?”
Mass of Y
What is Supersymmetry ?
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Xµ
θa
Y
BOB
ALICE
Yµ
Ya
She was completely unaware of SCALAR features of Y !!
Mass of Y
What is Supersymmetry ?
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Xµ
θa
Y
BOB
ALICE
Yµ
Ya
Bob thought “That is too much. She must have been LYING!! And this relation cannot go on with lies.”
Mass of Y
What is Supersymmetry ?
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Xµ
θa
Y
BOB
ALICE
Yµ
Ya
Then a physicist appeared. And warned Bob..
Mass of Y
Hey my friends, You’r ventured into Uncharted waters.
What is Supersymmetry ?
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Xµ
θa
Y
BOB
ALICE
Yµ
Ya
Mass of Y
There is a simple solution and hence the facts are always simple and understandable:
What is Supersymmetry ?
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Xµ
θa
Y
BOB
ALICE
Yµ
Ya
Mass of Y
“Alice” lives in an extra dimensional world so that she measures scalars (like mass) as vectorial dimensions.
What is Supersymmetry ?
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Xµ
θa
Y
BOB
ALICE
Yµ
Ya
Mass of Y
…But Bob measures some of her vectorial dimensions as scalars. So there is a naïve relation between Mass and θ.
What is Supersymmetry ?
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Xµ
θa
Y
BOB
ALICE
Yµ
Mass of Y
Years ago, Bob was living in Alice’s Extradimensional World. But his θ has collapsed into a scalar axis.
What is Supersymmetry ?
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Xµ
θa
Y
BOB
ALICE
Yµ
Ya
Mass of Y
Now you learned everything and i will tell you how you can relate your two different worlds with one equation.
What is Supersymmetry ?
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Xµ
θa
BOB
ALICE
Mass
Assume that a particle travel with a constant speed and it’s momentum is “p”. So length of its momentum vector will be |p|2 = 0
What is Supersymmetry ?
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Xµ
θa
BOB
ALICE
Mass
But Alice will write it as papa =0 and Bob will write it as pµpµ-m2 = 0 .
€
pa pa = 0
€
pµ pµ −m2 = 0
What is Supersymmetry ?
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Xµ
θa
BOB
ALICE
Mass
If we transform Bob’s scalar axis to Alice’s vectorial axis θ, only Alice’s equation would be valid and it means “supersymmetric transformation”.
€
pa pa = 0
€
pµ pµ −m2 = 0
What is Supersymmetry ?
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As a natural consequence of supersymmetry:
We should observe “scalar and vectorial partners” of elementary particles.
Vectorial Particle Scalar Particle electron selectron u, d, c, s – quark u, d, c, s – squark top quark stop bottom quark sbottom …(Fermions) ….(Bosons)
SUSY Transformations
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Assuming that the scalars we observed in real life (e.g: mass) is just projections of extra dimensional vectors of supersymmetric space, Supersymmetry searches for possible symmetries between those scalars and vectors.
Supersymmetry:
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I hope it is more apparent now.
What is Supersymmetry ?
The End
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