Let's reproduce the calculations from Interstellar

Summary

This video explores the scientific accuracy of 'Interstellar', analyzing the ship's speed, artificial gravity, and black hole depictions. It delves into wormhole geometry, time dilation near a black hole, and the film's portrayal of gravitational anomalies. The video also discusses the theoretical physics behind the movie's climax, including the Tesseract and the potential for quantum gravity to save humanity.

Takeaways

• 🚀 *Interstellar* explores the realism of its scientific concepts, such as black holes and wormholes, with calculations to verify their accuracy.
• 🛰️ The ship in *Interstellar* travels at approximately 70,000 km/h, a speed feasible with advanced technology, taking two years to reach Saturn.
• 🌍 Artificial gravity is created on the spaceship *Endurance* through centrifugal force, with realistic dimensions of about 60 meters in diameter.
• 🌀 The movie's portrayal of a wormhole as a three-dimensional tunnel connecting two slices of space is consistent with theoretical physics.
• 🌊 On Miller’s planet, 1 km high waves result from tidal forces due to its proximity to the supermassive black hole Gargantua, though the time dilation portrayed is exaggerated.
• ⏳ Time dilation near Gargantua leads to one hour on Miller’s planet equating to seven years on Earth, achievable with a rapidly rotating black hole.
• 🌌 Gargantua’s visual effects include a plasma accretion disk with gravitational lensing and Doppler effects, though some aspects were altered for cinematic purposes.
• 🧑‍🔬 Professor Brand's equation suggests that gravitational anomalies may be caused by fields in a larger universe with extra dimensions.
• 🕳️ Cooper survives falling into the black hole due to a theoretical gentle singularity, and enters a four-dimensional tesseract created by advanced beings.
• 🏟️ The *Cooper Station* space habitat likely has a diameter between 50 to 100 meters, based on a baseball trajectory used to calculate its rotation and gravity.

Q & A

What is the main theme of the video 'Interstellar'?

The video discusses the scientific accuracy and concepts presented in the movie 'Interstellar', such as black holes, wormholes, and the behavior of time and space.

What is the estimated speed of the ship in 'Interstellar'?

The estimated speed of the ship in 'Interstellar' is around 70,000 km/h, calculated by dividing the distance of approximately 1.3 billion km by 2 years of travel time.

How does the artificial gravity system work in the ship Endurance?

The artificial gravity system in the ship Endurance works by using a rotating wheel, which creates a centrifugal force that pushes the characters against its outer walls, simulating gravity.

What is a wormhole and how does it appear in the movie 'Interstellar'?

A wormhole is a theoretical 'shortcut' through spacetime, connecting two distant points in the universe. In the movie, it appears as a three-dimensional tube connecting two celestial spheres.

What is the concept of time dilation as depicted in 'Interstellar'?

Time dilation in 'Interstellar' refers to the difference in the passage of time between two observers due to differences in their relative motion or gravitational fields. On Miller's planet, one hour corresponds to seven years on Earth.

How are the massive waves on Miller's planet explained?

The massive waves on Miller's planet are explained as tidal forces caused by the close proximity to the black hole Gargantua, which distorts the planet and creates immense waves.

What is the significance of the black hole Gargantua in 'Interstellar'?

Gargantua is a supermassive black hole with a strong gravitational pull that affects the time dilation experienced by the characters and the extreme tidal forces on nearby planets.

How does the Tesseract, a four-dimensional object, play a role in the movie?

The Tesseract in 'Interstellar' is a four-dimensional space that allows Cooper to interact with his past and communicate with his daughter Murphy, providing a means to send crucial data.

What is the role of the character Cooper in the movie 'Interstellar'?

Cooper, a former NASA pilot, plays the protagonist who embarks on an interstellar journey to find a new home for humanity and eventually interacts with a higher dimension to influence past events.

What scientific theories are explored in the movie's depiction of the universe?

The movie explores theories such as general relativity, quantum mechanics, and the possibility of extra dimensions, as well as the effects of black holes on time and space.

How does the movie 'Interstellar' visualize the scientific concept of gravitational anomalies?

Gravitational anomalies in 'Interstellar' are visualized as strange occurrences that guide characters to secret locations and are later explained as being influenced by higher-dimensional fields.

Outlines

00:00

🌌 Introduction to 'Interstellar' and Scientific Accuracy

The video script introduces a deep dive into the scientific accuracy of the movie 'Interstellar' directed by Christopher Nolan. It discusses the movie's realistic portrayal of a black hole and the various scientific concepts it explores, such as the speed of the ship, its dimensions, the behavior of time around a black hole, and the appearance of a wormhole. The script mentions a collaboration with Kip Thorne, the main scientist behind the movie, and the use of his book 'The Science of Interstellar' to verify the movie's scientific claims. The video aims to recreate some visuals from the movie and understand the technical aspects of the film, such as the travel time to the wormhole near Saturn and the artificial gravity on the spaceship Endurance.

05:03

🔭 Simulating the Wormhole and Black Hole in 'Interstellar'

This section of the script discusses the attempt to simulate the wormhole and black hole as depicted in 'Interstellar'. It explains the process of creating a realistic wormhole image using a method called ray tracing, which involves tracing the path of light rays through curved spacetime. The script also explores the appearance of the inside of a wormhole and how it was visualized in the movie. Additionally, it delves into the characteristics of the black hole named Gargantua, including its massive size, the extreme tidal forces it generates, and the significant time dilation near it. The script compares the simulated images with those from the movie to assess their realism.

10:04

🌊 Tidal Forces and Time Dilation on Miller's Planet

The script examines the extreme tidal forces and time dilation on Miller's Planet, which is depicted as being very close to the black hole Gargantua. It discusses how these forces create enormous waves and how time passes much slower on the planet compared to Earth. The calculations provided aim to estimate the distance at which a planet would need to orbit a black hole to experience such phenomena. The script also addresses the discrepancy between the movie's portrayal of time dilation and the actual calculations based on general relativity, suggesting that for the extreme time dilation shown in the movie to be accurate, the planet would need to be in an unstable orbit extremely close to the black hole.

15:14

🌒 Visualizing the Black Hole and Gravitational Lensing

This part of the script focuses on the visual representation of the black hole Gargantua and the surrounding environment in 'Interstellar'. It describes the use of ray tracing to simulate the gravitational lensing effects caused by the black hole, which distorts the light from the accretion disk and creates the shadow of the black hole. The script also discusses the Doppler effect on the appearance of the accretion disk, where one side appears brighter and bluer while the other appears darker and redder due to the movement of the disk relative to the observer. The video script compares these simulated visuals with the images from the movie to highlight the artistic choices made in the film.

20:15

🔬 Theoretical Physics and the Quest for Quantum Gravity

The script explores the theoretical physics behind the movie's plot, particularly the professor's quest to understand gravity and the nature of the universe. It discusses the idea of our universe being one slice of a larger multiverse with additional dimensions, and how this concept is used to explain the gravitational anomalies observed in the movie. The script also touches on the concept of singularities within black holes and the speculative idea that one might survive a fall into a black hole with a gentle singularity. It describes how Cooper, the protagonist, uses this knowledge to communicate with his daughter Murphy across time and space.

25:17

🚀 The Cooper Station and the Future of Humanity

In this final section, the script discusses the construction of the Cooper Station, a massive centrifuge designed to save humanity by lifting off into space. It provides a unique approach to estimating the dimensions of the station by analyzing a scene where a baseball is hit and travels the length of the station. The script uses the principles of gravity and motion to calculate the radius and rotation speed of the station. It concludes by reflecting on the movie's attention to scientific detail and the thought-provoking concepts it presents, encouraging viewers to delve deeper into the scientific aspects of the film.

Keywords

💡Interstellar

Interstellar is a 2014 science fiction film directed by Christopher Nolan that explores space travel, black holes, and the survival of humanity. In the video, 'Interstellar' serves as the central subject for mathematical and scientific analysis, where various scenes and concepts from the movie are scrutinized for their scientific accuracy.

💡Black Hole

A black hole is a region in space where the gravitational pull is so intense that nothing, not even light, can escape it. The black hole in 'Interstellar,' called Gargantua, plays a crucial role in the film’s narrative. The video discusses the visual and physical representation of Gargantua, including the gravitational effects, time dilation, and the accretion disk.

💡Wormhole

A wormhole is a theoretical tunnel through space-time that connects two distant points in the universe. In 'Interstellar,' a wormhole near Saturn allows the characters to travel to distant planets. The video examines the scientific plausibility of the wormhole’s visual appearance and discusses how light would behave when passing through such a structure.

💡Time Dilation

Time dilation is a consequence of Einstein’s theory of relativity, where time passes differently depending on the strength of the gravitational field or speed of movement. In 'Interstellar,' time dilation occurs near the black hole Gargantua, where one hour on a planet close to the black hole equals seven years on Earth. The video analyzes the accuracy of this effect and its implications.

💡Gravitational Anomalies

Gravitational anomalies in 'Interstellar' refer to strange events that occur due to disruptions in the gravitational field. Cooper discovers these anomalies early in the film, and they eventually lead him to NASA. The video suggests that these anomalies are tied to extra-dimensional forces, explaining how gravity may behave differently in higher-dimensional spaces.

💡Accretion Disk

An accretion disk is a rotating disk of matter that forms around a massive object like a black hole due to its gravitational pull. In 'Interstellar,' the black hole Gargantua is surrounded by a luminous accretion disk. The video explains how the light from the disk is distorted by gravitational lensing and why certain visual effects, such as the Doppler effect, were minimized for the movie.

💡Centrifugal Force

Centrifugal force is the apparent force that pushes objects outward when they are in a rotating frame of reference. In 'Interstellar,' the spaceship Endurance creates artificial gravity by rotating like a wheel. The video provides a mathematical explanation of how the centrifugal force on the spaceship mimics Earth’s gravity, making the environment comfortable for the crew.

💡Photon Sphere

A photon sphere is a region around a black hole where gravity is so strong that light can orbit the black hole. The video explains how the characters in 'Interstellar' would have to avoid this region to prevent unstable orbits. It also describes the theoretical effects of time dilation near the photon sphere and its relevance to the plot.

💡Tesseract

A tesseract is a four-dimensional cube, which serves as the key to the film's climax. In 'Interstellar,' Cooper enters a tesseract near the singularity of a black hole, allowing him to interact with different points in time within his daughter’s bedroom. The video explores the idea of higher-dimensional spaces and how the tesseract serves as a narrative device for explaining time travel and communication across time.

💡Singularity

A singularity is a point in space where gravitational forces become infinite, causing the laws of physics to break down. In 'Interstellar,' the singularity inside the black hole Gargantua plays a crucial role when Cooper plunges into it. The video delves into the various types of singularities, including the speculative 'gentle' singularity, which allows Cooper to survive, and discusses the challenges of understanding what happens inside a black hole.

Highlights

Interstellar, directed by Christopher Nolan, presents realistic images of a black hole and explores scientific concepts like time dilation and wormholes.

The video attempts to mathematically verify the accuracy of various concepts presented in the film.

The speed of the ship in the movie is estimated to be around 70,000 km/h, which is considered realistic given the context.

Artificial gravity in the ship is achieved through centrifugal force, calculated to have a radius of roughly 30 m or 60 m in diameter.

The appearance of the wormhole in the movie is simulated using a method called Ray tracing, which involves tracing light rays through each pixel of a camera.

The inside of the wormhole is explored, with simulations suggesting different visual effects based on the geometry of the wormhole.

The movie's depiction of extreme tidal forces on Miller's planet due to proximity to a black hole is analyzed.

Time dilation on Miller's planet is discussed, with the movie showing a factor of 60,000, which is higher than calculated estimates.

The visual appearance of the black hole Gargantua in Interstellar is examined, with simulations attempting to reproduce the movie's images.

The concept of a fourth dimension is introduced through the Tesseract, a four-dimensional object in the movie.

Cooper's survival near a black hole's singularity is explored, suggesting the possibility of a gentle singularity in older black holes.

The movie imagines gravity as the force that can cross dimensions and communicate across time.

Murphy uses the data sent by Cooper to understand how to control gravity, which is crucial for humanity's survival in the movie.

The dimensions of the space station in the movie are estimated using the trajectory of a baseball hit inside the station.

The movie's scientific accuracy is praised, with detailed calculations and simulations enhancing the understanding of complex concepts.

The video concludes by enjoying simulations built throughout, showcasing the intersection of science and cinema in Interstellar.

Transcripts

warning this video contains

spoilers here's what Interstellar could

have looked like

[Music]

[Music]

welcome back to science click today

let's try to remake the calculations

from

Interstellar released in 2014

Interstellar directed by Christopher

Nolan left its mark on audiences by

presenting realistic images of a black

hole but is the movie accurate what is

the speed of the ship what are its

Dimensions how does time behave around a

black hole what does the inside of a

worm whole look like in this video we

will go back over the Journey of the

film's characters and attempt to

mathematically verify the accuracy of

the different concepts we will also try

to rebuild some visuals from the movie

this may be a bit technical but just

keep in mind you don't need to

understand all the

calculations we will at times rely on

information from the book the science of

interstellar written by Kip Thorn the

main scientist behind the

movie this video was originally made in

collaboration with the French Channel

gab which talks about science in popular

movies he usually doesn't make videos in

English but kindly agreed to let us

translate his voice for this one so

don't be surprised if the visual style

of the video changes at times when we

present the

storyline at the start of interstellar

the situation on Earth is critical

humans are facing food shortages air is

close to unbreathable dust is

omnipresent the planet no longer seems

habitable on this apocalyptic Earth we

follow Cooper a former NASA pilot who

lives with his two children in the

bedroom of his daughter Murphy strange

events occur events that Cooper ends up

identifying as gravitational

anomalies one day one of these anomalies

mysteriously reveals coordinates which

once followed lead to a secret NASA base

as if the library had wanted to guide

them there in this NASA Center we learn

that a wormhole has opened near Saturn

forming a passage to planets and that

NASA is about to launch a critical

Mission a space crew will cross the

Wormhole and try to reach three

potentially habitable

exoplanets of course Cooper arrives just

in time for the adventure as a former

NASA pilot he is recruited and thus

embarks on an Interstellar Journey

aboard the

endurance after takeoff the crew goes

into hibernation the ship will take two

years to arrive at the Wormhole near

Saturn is this travel time

realistic we can roughly estimate the

speed of the ship by taking the shortest

straight line between Earth and Saturn

and factoring in the radius of their

orbits we can assume that the ship

travels approximately 1.3 billion km

divided by 2 years this gives us a speed

of around 70,000

kmph as a basis for comparison the

fastest ever manned flight was Apollo 10

with a speed of 40,000 km hour assuming

that interstellar's Technologies are

better than ours this 2-year duration is

therefore

realistic the characters need artificial

gravity to feel comfortable the inurance

forms a wheel which turns on itself and

pushes the characters against its outer

Walls by centrifugal effect the

centrifugal acceleration is given by 4K

^ 2 R / t^ 2 where R is the radius of

the wheel and T its period of rotation

in this scene we can time a half period

of 5.7 seconds which gives us a total

period of 11.4

seconds this must equal 9.8 m/s squared

the value of gravity on Earth we deduced

that the radius of the wheel must be

roughly 30 m or 60 m in

diameter a fairly realistic value given

the International Space Station is 70 m

cross the endurance's crew wakes up near

Saturn we observe For the First Time The

Wormhole that they will have to

cross a wormhole is a distortion of

space a sort of tube which connects two

slices of the

universe it is difficult to draw because

the surface of the tube is actually

three-dimensional a volume within which

the ship can move

light can also pass through it and we

can receive an image of what is on the

other

side but is its appearance in the movie

realistic to find out let's try to

simulate

it we start with a cylinder connecting

two sheets of space let's smooth out

this cylinder to have a better

transition for the movie Nolan chose a

very short cylinder and a relatively

quick transition to get the appearance

he

liked let's place a camera and choose

two images to represent the sky the

celestial sphere of each of these two

Universe

slices the camera receives light rays

some of which arrive directly from the

same slice it is on and others after

crossing the Wormhole all these light

rays arrive on the pixels of the

camera without going into details we can

perform a method called Ray tracing

which which involves sending a light Ray

through each pixel of the camera and

rewinding its trajectory to determine

where it came from in the sky and what

color is received by the camera on that

pixel in practice this amounts to using

the geodesic equation a general

relativity equation which allows us to

trace trajectories through curved

SpaceTime by repeating the operation for

each pixel we obtain an

image a result which when put in motion

is quite similar to that of the

movie we can now play around with

varying the geometry of the Wormhole to

see what it might have looked like if

Nolan had made different

choices with a very long Wormhole light

can orbit several times before reaching

us and we can observe an infinite number

of repeating images of the

[Music]

universe in interstellar the endurance

enters the Wormhole to cross it we

discover the inside of the

Wormhole is this scene

realistic to find out let's move our

virtual camera along the surface of the

tube this time around the images are

quite different from what the movie

shows us the visual effects team

probably wanted to help the viewer

better understand that the spaceship is

moving along the surface of a cylinder

and Crossing into a fourth

dimension if this scene had been

simulated we could have witnessed

hypnotizing images such as

[Music]

these exiting the Wormhole the Explorers

arrived near a super massive black hole

called Gargantua this black hole has

planets orbiting around it and our

crew's first destination is one of the

Millis

Planet this planet is very special it is

completely covered in water and its

orbit is very close to Gargantua so

close in fact that extreme phenomena

arise near a black hole tidal forces are

gigantic and Gargantua attracts the

planet more on one side than the other

distorting it and forming immense 1 km

high waves on its

surface because of its proximity to the

black hole time also passes more slowly

so much so that for each hour that

passes on this planet 7 years pass on

Earth in short Miller's planet is

mysterious and deserves our

attention let's start with the waves Kip

Thorn indicates that they stretch over 1

km in height how close to the black hole

would the planet need to be for such

waves to

form we can attempt a rough estimate we

can assume that these waves are in fact

Tides generated not by the attraction of

the moon but by that of the black hole

the waves in the movie look thinner than

simple Tides they might be closer to

what we call tidal BS but for a rough

estimate our approach should still work

the waves thus result from the

combination of gravity from the black

hole and the centrifugal effect produced

by the orbit of the planet we can

calculate the resulting net force with

Newtonian physics this is the tidal

Force

this Force displaces water from low tide

left and right to high tide up and

down the force supplies each water

droplet a certain energy which we can

calculate as the product of the vertical

displacement which is the radius of the

planet and the average value of the

force along this

path it is this energy brought by the

tidal Force which allows the water to

rise it must therefore equal the

gravitational energy that the water

acquires from this equality we can

deduce the distance at which the planet

should orbit for such tides to

form if the planet's dimensions are

similar to those of Earth knowing that

the black hole weighs 100 million solar

masses then the planet should orbit at a

distance of 4.5 billion

km to compare the spart Shield radius of

the black hole which we can deduce from

its mass is 300 million km across

if we bring this diagram to scale and

compare it to this image from the movie

showing Gargantua a scene from Millis

Planet the results seems

coherent but is this close enough to

also explain the strong time

dilation each hour that passes on the

planet corresponds to seven years on

Earth time passes 7times 365 time 24

times slower a factor of 60,000

for a static black hole this is the time

dilation experienced by a planet in

circular orbit if we insert the distance

obtained with the calculation of the

tides we get a time dilation of only 5%

far from what the movie shows us there

is an

incoherence to obtain a factor of 60,000

the planet would have to orbit just

above the photon sphere where light

itself can remain in orbit an absurd

result because any orbit so close is

inevitably

unstable but this calculation is only

valid for a static black hole general

relativity allows black holes to rotate

the faster a black hole spins the more

likely stable orbits exist near its

Horizon the calculations are more

complex but we can determine that it is

possible to reach a factor of 60,000

provided that the planet orbits 6,000 km

from The Horizon and that the black hole

spins at a trillion of a percent slower

than the speed of light extremely fast

but not impossible in theory of course

this situation remains incompatible with

what the movie shows

us the visual appearance of the black

hole is surely what brought attention to

Interstellar in France jeanpier Lum had

done a first simulation in 1979 but in

2014 it is the first time that we see

such images in theaters could we

reproduce these simulations at our

scale let's try the ray tracing method

we place a camera in the center of a

celestial sphere in front of a black

hole rotating almost at maximum speed

general relativity allows us to rewind

the trajectory of light rays to find

their origin in the sky some rays are

blocked by the black hole and the

corresponding pixels do not receive any

light in this way we can stru an

image the rays are deflected by

gravitational lensing causing Optical

distortions we observe the shadow of the

black hole the area from which we

received no light for a static black

hole this Shadow would be a disc but for

a spinning black hole it seems squashed

on one side because SpaceTime spins and

drags light with it in the movie this

phenomenon was reduced to render the

visual effect less strange

a round Gargantua orbits an extremely

luminous plasma disc let's place a disc

in our

simulation we see that its image is

distorted the back of the disc seems

folded above and below because the black

hole bends the Rays coming from

it in reality such an accretion disc

would be extremely hot it would emit

intense radiation which would instantly

destroy the ship the disc temperature

has therefore been drastically brought

down for the movie implying that it is

also very thin given its lower internal

pressure this plasma rotates very

quickly around the black hole such that

the light we received from it is

propelled on one side and slowed down on

the other this is the Doppler effect the

disc appears bright and slightly blue

where it moves towards us and dark and

red where it moves away from us this

effect was considered too strange and

was not included in the

film we can play around with comparing

our simulation to images from

[Music]

Interstellar here's what it could have

looked like if they had included the

asymmetry the Doppler effect and a

higher temperature dis

[Music]

[Music]

[Music]

while our Interstellar mission is going

on back on Earth the professor refines

his mathematical model trying to account

for the discovery of the gravitational

anomalies

this Quest had already led him towards a

very complex equation to solve and his

goal in solving this equation is to have

answers about the nature of gravity and

then use this new knowledge to launch a

gigantic spaceship into space and save

Humanity but we are not there yet at

this stage of the research the

professor's conclusion is that the

gravitational anomalies must be caused

by something outside our

universe according to him our space

could be one slice inside a larger

universe with one more Dimension the

anomalies would be caused by Fields

present in this bigger space outside our

world we see the details of this model

on Professor Bran's blackboards in the

movie The Universe would contain three

brains our brain a brain above and a

brain below forming a sort of Sandwich

between these two brains the geometry of

the universe would be curved into an

anti- deit geometry a geometry allowing

distances to be greatly stretched above

and below our universe such that gravity

cannot Escape in fact in our universe

gravity propagates in all directions and

its intensity is therefore distributed

over spheres which is why the force of

gravity is inversely proportional to the

square of the distance just like the

surface of a

sphere but if we were to add an extra

dimension of space gravity wouldn't form

spheres but hyperspheres extending

beyond our slice of universe

and gravity would decrease like the cube

of the distance which we obviously do

not

observe with the anti- deito warping

gravity remains confined near our

universe and still behaves as one/ r s

the other two brains help in delimiting

this warping leaving enough volume

outside for possible Adventures within

the fourth

dimension this is a necessary Precision

to justify the end of the movie

back on Earth Murphy has now taken over

from Professor brand in their quest for

Gravity it's now her task to find a

solution to the equation and describe

the nature of the fields to explain the

anomalies observed on Earth although the

professor's model seemed promising at

first no results follow and Murphy ends

up realizing what he had known all along

without telling her to complete the

model they need information about the

quantum nature of gravity Murphy must

understand what happens at a point where

gravity meets Quantum for example by

diving near the singularity of a black

hole coincidentally this is exactly what

her Father Joseph Cooper is doing in

another

[Music]

galaxy following tars Cooper detaches

himself from the endurance and Falls

towards the horizon of the black hole

can he survive without being

spaghettified up until the 1960s

singular ities were considered as

pointlike in the 1970s however

physicists understood that these

singularities undergo chaotic

distortions they are known as bkl

singularities in the 1990s researchers

discovered that when we fall into a

black hole all the matter falling behind

us seems to pile up because of the

slowing down of time we Face a mass

inflation

Singularity finally we discovered around

2010 that older black holes have a third

Singularity stemming from the

accumulation of matter that fell prior

this Singularity is gentle it generates

relatively weak tidal

forces while this is still highly

speculative it might be possible to

survive there but we would have to dive

almost at the speed of light to prevent

the other Singularity from catching up

with us this is precisely the advice

that romaly offers Cooper in the film

Gargantua is an old black hole

containing a gentle Singularity he could

survive it by diving at high

speed it is this possibility although

very speculative that Nolan chose for

his movie in a mysterious way Cooper

manages to accelerate enough to hit this

Singularity first and

survive no one knows what lies at the

center of a black hole we would probably

need a theory of quantum

gravity nonetheless in the movie Nolan

imagines that when Cooper hits the

singularity he is transported by a

four-dimensional object called the

Tesseract an object believed to have

been placed there by the same beings who

opened the

Wormhole this Tesseract is a sort of

four-dimensional cube while a

three-dimensional Cube's faces are

two-dimensional squares the Tesseract

faces are not squares but

three-dimensional cubes and this

structure allows for Koopa to stay

inside one of the faces of the Tesseract

while the tesseract transports him back

to Earth all the way to Murphy's room by

the way if this journey feels quite fast

despite the huge distance it is because

the Tesseract has been lifted above our

brain into the anti- DEA warping we

mentioned previously where distances are

greatly

contracted the Tesseract acts as an

elevator towards the fourth dimension of

space once he arrives Cooper can see

Murphy's room in the past which is

possible because light can travel within

the faces of the Tesseract up to his

eyes however in the model imagined by

Nolan light cannot go back in time from

Cooper to Murphy he therefore has no way

to communicate with her at least this is

until Cooper discovers that gravity can

cross this barrier and return to the

past an idea which is probably inspired

by the fact that in theories describing

universes with additional dimensions in

the context of brain cosmology all

fundamental interactions are generally

can find within the brains except

gravity which propagates through all

Dimensions Cooper can therefore send the

quantum data to Murphy using gravity

giving his daughter all the elements

necessary to solve the equation we

finally understand that he was behind

the gravitational anomalies from the

beginning recall once again though that

the things we have just described are

simply the physical rules set by Nolan

for this very speculative sequence of

the movie

thanks to the data Murphy understands

that it is possible to control gravity

we can reduce the intensity of gravity

on the surface of the Earth to lift off

a huge space station and save

Humanity the kooper station a large

centrifuge thus heads towards Saturn to

cross the Wormhole for our last

calculation let's try to determine the

dimensions of this space station we

could imagine several methods but let me

propose an unexpected Ed approach in

this scene of the movie we see a

baseball player hitting a ball which

travels through the entire station and

ends up breaking a window on the

opposite side above the field the ball

experiences no force and therefore moves

in a straight line at constant

speed but from the inside the trajectory

of the ball seems curved because we are

spinning with the

wheel at this stage we don't know the

param

of this trajectory the speed of the ball

the angle of the trajectory the radius

of the wheel and its rotation

speed but we see in the movie that the

gravity in the station is similar to

Earth's this gives us a restriction on

the rotation of the wheel it must spin

at a precise speed to generate this

gravity we also know that the ball ends

up breaking a window above the field we

can therefore restrict the angle of the

trajectory such that it reaches is a

point above the

field watching the scene we can time the

trajectory of the ball and measure 4.6

seconds between the hit and the impact

and we can then estimate its initial

speed by analyzing frame by frame and

comparing to the size of the player we

find an estimate of 30

m/s with all these restrictions we

determine the radius of the wheel

approximately 50 m or 100 m in diameter

for roughly 3 00 m in circumference a

relatively small station which would

rotate at four revolutions per minute

the trajectories of baseballs would be

chaotic to say the

least with other methods by comparing

with the size of a building for instance

we find very different values sometimes

even 1 km I'll leave it up to you to

develop your own techniques to estimate

these

Dimensions born from the creative mind

of an expert in relativity Interstellar

is a unique movie with breathtaking

visuals through these few calculations

we can appreciate the attention to

detail brought to the construction of

the scenario and delve deeper into

issues that may not seem obvious at

first viewing as a conclusion let's

enjoy once again some of the simulations

we've built throughout this video

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[Music]

[Music]

[Music]

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