The Physics of Scales
Sanjit Shashi
1/24
Pushing a box
2/24
Force = (Mass) x (Acceleration)
Isaac Newton
Pushing a box
3/24
Force = (Mass) x (Acceleration)
Isaac Newton
Pushing a box
4/24
Force = (Mass) x (Acceleration)
Isaac Newton
Getting faster!
Pushing a box
5/24
Faster than light!
Pushing a box
6/24
Albert Einstein
Special relativity:
Speed of light is a speed limit
Faster than light!
When does Newton’s theory work?
7/24
Model that’s “good enough” (to a point)
8/24
Newton’s theory is “effective” (good at some scale)
Why are effective theories useful?
9/24
We don’t always know the completion
Gas with:
Need to look inside
Switching between effective theories
10/24
Let’s look at water at a bunch of different scales.
What are we looking at?
11/24
Distances ~ 1 meter
1 m
What are we looking at?
12/24
Distances ~ 10-3 meters (zoom in x1,000)
1 mm
What are we looking at?
13/24
Distances ~ 10-3 meters
World of bugs
Water is sticky
1 mm
What are we looking at?
14/24
Distances ~ 10-9 meters (zoom in x1,000,000)
Water molecules
Can line up ~420,000 across this hair!
1 nm
What are we looking at?
15/24
Distances ~ 10-9 meters
Electromagnetism in charge
1 nm
What are we looking at?
16/24
Distances ~ 10-15 meters (zoom in x1,000,000)
Oxygen nucleus: neutrons + protons
Strong force holding things together
1 fm
+
N
+
+
N
N
+
N
N
+
+
N
N
N
+
+
“Different physics” at different scales!
17/24
(Note: not to scale)
Wilsonian Renormalization
18/24
Ken Wilson
(Nobel 1982)
Mathematical framework for changing scales to switch between different effective theories
Ex: What is the charge of an electron?
19/24
Depends on the scale:
EM force is getting stronger here!
Unification of forces
20/24
𝜈
How has Wilson shaped modern physics?
“Four” fundamental forces:
+
N
+
+
N
N
+
N
N
+
+
N
N
N
+
+
1
3
2
N
+
-
4
Unification of forces
21/24
“Four” fundamental forces:
𝜈
2
N
+
-
1
Unification of forces
22/24
Sheldon Glashow
Abdus Salam
Steven Weinberg*
(Nobel 1979)
Focus on two fundamental forces:
At arbitrarily small distances, these forces are indistinguishable (electroweak force at about 0.01 fm)
𝜈
N
+
-
Unification of forces
23/24
Electromagnetism
Weak
Strong
Gravity
Electroweak
“Grand unified theory”
“Theory of everything”
Decreasing distance scales
Increasing energy scales
(Seen experimentally)
(Still theoretical)
To conclude…
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Physics is intricately tied to scale.
Don’t have a complete theory of nature, but we can inch towards it!
Thank you!
Can have a model that’s “good enough” (to a point)
Call these theories “effective” within some regime
NOT conceptually the same as “making an approximation!”
Gas with:
What are we looking at?
14/23
Distances ~ 10-10 meters (zoom in x10)
Oxygen atom (constituents not to scale)
Quantum electrodynamics + strong force
0.1 nm
+
N
+
+
N
N
+
N
N
+
+
N
N
N
+
+
-
-
-
-
-
-
-
-
What are we looking at?
15/23
Distances ~ 10-15 meters (zoom in x100,000)
“Inside” of a proton
Strong force holds quarks together
1 fm
What are we looking at?
Distances ~ 1 meter
Our world
Earth looks flat
What are we looking at?
Distances ~ 106 meters (one million)
Earth looks round
Only gravity matters
What are we looking at?
Distances ~ 1012 meters (one trillion)
Planetary motion
Gravity of the Sun
What are we looking at?
Observable universe
“Mostly empty” except radiation, dark energy
Distances ~ 1026 meters (one hundred-billion-quadrillion)
“Different physics” at different scales!
-
What is the charge of an electron?
Depends on the scale:
This change can be concretely calculated
To conclude…
Physics is intricately tied to scale.