The document describes a scenario where Earth is becoming uninhabitable due to environmental problems. NASA scientists have developed two plans to ensure humanity's survival: Plan A involves using a wormhole to transport people to a new planet, while Plan B involves sending frozen embryos to another habitable planet. 12 volunteers went through the wormhole to explore 12 possible planets, and 3 reported back to Earth. A new team is being sent to explore these 3 planets further and implement one of the survival plans. The document then provides background information on wormholes, black holes, gravitational time dilation, and tesseracts.

1. v
and Physics
Week 5

2. So that was kinda a long movie…
What happened again?

3. Due to a global crop blight and second Dust Bowl Earth
is slowly becoming uninhabitable. Nasa physicist are
working on plans to save mankind by transporting Earth's
population to a new home via a wormhole, called Plan A.
They have a Plan B, which is distributing 5,000 frozen
embryos on another habitable planet to ensure humanity's
survival.

4. 12 volunteers left to go through the wormhole to explore
12 possible inhabitable planets. 3 members sent
communication back to Earth; years later, another team is
being sent to explore the these 3 planets and carry out one
of the plans.

5. Worm hole?

7. Wormholes are “shortcuts” created by connecting
points in spacetime, where spacetime is the
combination of space and time to a single abstract
universe.

8. To get from North to
South Campus, you
usually have to walk
across the map, but
what if you could
just…

9. Skip Bruinwalk, and go
through everything.
Similarly to a map, we can
think of space as this 2D
plane, and if we fold it and go
through this folded surface,
we can travel normal euclidian
distances in little/no time.
These tunnels where we can
travel through the folded
maps are the wormholes.

10. Wormholes are theoretical, and have very little
physical or experimental support.
So how do we know?

11. Wormholes are theoretical, and have very little
physical or experimental support.
So how do we know?
MATH!!!

12. Certain types of traversable wormholes were
discovered as allowable solutions to the
equations of general relativity.
Thus, theoretically, this could all exist!
Primordial wormholes are predicted to exist,
and it’s possible that some have been stretched
as the universe expands.They also collapse
quickly.
It’s theorized that wormholes could eventually
be stabilized by adding exotic matter, like
negative mass, to keep them open long enough
for travel.

13. Very heavy mass
If there is a large amount of mass in space, it
creates this funnel, almost as if the mass is
weighing it down.With so much mass, it’d be
hard to keep the hole open as you get deeper.

14. Add negative mass
to keep it open!
Scientistic's theorize
that by adding exotic or
negative mass, it will
keep the hole more
stable and prevent it
from closing as quickly.

15. At the first planet, it is dangerously close to a black
hole called Gargantua, which affects the
gravitational forces and has severely dilated time.

16. Here’s a black hole.

17. Here’s a black hole.
Hehe…

18. What exactly is a black hole?
Consider this!

19. Remember, Newton’s Law, “what comes
up, must come down”?

20. What if there was so much gravity that
something couldn’t even go up?

21. • Black hole - mass in such a small space such
that a gravitational force is created that is so
strong not even light can escape
• large masses bends space time, and since light
is also a particle, it should bend around these
massive objects
• Space is bent so much that the light waves are
stretched out such that they loose all of
their energy by the time they emit from the
black hole
Black Holes 101

22. Black Holes 101
“a black hole is a
gravitational
singularity, a one-
dimensional point which
contains a huge mass in
an infinitely small
space, where density and
gravity become infinite
and space-time curves
infinitely”

23. Black Holes 101
According to general theory of relativity, gravity is
caused due to any mass that makes the space-time
curved. The high gravity of black holes is because of
the curvature of the space-time which becomes
infinite due to the mass of the black hole.
This is important and will come up soon again!

24. After we visit the first planet…

25. Gravitational time dilation is an actual difference of
elapsed time between two events as measured by
observers situated at varying distances from a gravitating
mass.The weaker the gravitational potential, the faster
time passes.This was predicted by Einstein’s theories of
general relativity.
1 hour (Miller’s Planet) = 7 years (Earth)

26. Instead of thinking about relative
amount of gravity, consider
relative points of view.

27. Bob is bouncing a ball on a train,
that’s moving right.
Bill
Bob

28. As the ball bounces, from Bob’s pov,
it goes like this:
Distance x

29. Bill sees something different
Bill
Bob

30. Bill
Distance y

31. ACCORDING TO THE DISTANCE EQUATIONS:
D = RXT
X = RT
Y = RT
WE KNOW THE BALL BOUNCES AT THE SAME RATE, THUS
SINCE X!=Y, THAT MUST MEAN THAT T (TIME) IS THE
CHANGING FACTOR!

32. • ALTHOUGH THIS EXAMPLE ACTUALLY INVOLVES
RELATIVE VELOCITY, BUT INSTEAD OF VELOCITY,
THINK OF GRAVITY.
• IF YOU HAVE AN EQUATION INVOLVING GRAVITY
AND A FIXED VALUE, SUCH AS THE SPEED OF
LIGHT, AND GRAVITY HAS DIFFERENT VALUES,
THEN THIS MEANS THAT THERE’S A THIRD
VARIABLE CHANGING; IN THIS CASE BEING TIME.

33. Distance y
Distance y
Bill and bob are seeing the ball
travel different distances
But the speed of the ball is the
same, so the times must be
different.
v = (r)(T)
Recall that black holes have an extremely high amount
of gravitational forces, so time will move slower from
an outsider person’s perspective.

34. Distance y
Distance y
Bill and bob are seeing the ball
travel different distances
But the speed of the ball is the
same, so the times must be
different.
v = (r)(T)
Skipping a few scenes… our main
character ends up in a…

35. Distance y
Distance y
Bill and bob are seeing the ball
travel different distances
But the speed of the ball is the
same, so the times must be
different.
v = (r)(T)
Skipping a few scenes… our main
character ends up in a…
Tesseract!

36. Mathematically, the tesseract is the four-
dimensional analog of the cube. In the movie,
this is how they represent the 5th dimension.

37. 1st Dimension: any kind of line
2nd Dimension: any kind of plane
3rd Dimension: space; height, width, depth
4th Dimension: time; like each moment of
your life strung together

38. 5th dimension: take a step out so that you are able to
view the 4th dimension. Being able to see all of the
past, present, and future as infinite collection of
moments strung together.

39. The End.

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recipient of the Presidential Medal of Freedom, the highest civilian award in the United States