I also love the movie, but there one thing with the time dilation I suspect does not add up. If the first planet is so deep into Gargantua's gravity well that it has such time dilation, would the energy required to get a spaceship out of the gravity well not be ridiculously huge? Given that they had limited energy, did it make sense to visit that planet first?

The thing about their energy budget was not well done. Why did they need rockets back on earth when they can mount the gravity well of a black hole and multiple planets afterwards? About your point with the order of visits though: I could see them using Gargantua for a slinghot maneuver after the first planet, which should work given the right constellation. It wasn't shown this way though.

Even with a ship capable of overcoming the gravity wells present in the movie, it would likely still make sense to launch from Earth with boosters/staging to increase the amount of fuel/energy available to the ship for the rest of the journey.

Yes, that's a valid argument I think. On the other hand, I'd imagine if our technological level is such that we have SSTO ships (with SSTO even for more massive gravity wells than Earth's), we'd probably not use rockets but have another SSTO tanker fueling up the ship in orbit. You could maybe argue that ressource constraints in their dire situation have forged a situation where they put everything they had into those ships and the rockets were just what they had still lying around from an older age, so they made use of it. It certainly was another artistic choice in order to give it a more familiar feel and I can respect that.

A rocket-scientist (ok, aerospace engineer by training) friend was recently surprised that he hadn't realized this:

"If the radius of our planet were larger, there could be a point at which an Earth escaping rocket could not be built. Let us assume that building a rocket at 96% propellant (4% rocket), currently the limit for just the Shuttle External Tank, is the practical limit for launch vehicle engineering. Let us also choose hydrogen-oxygen, the most energetic chemical propellant known and currently capable of use in a human rated rocket engine. By plugging these numbers into the rocket equation, we can transform the calculated escape velocity into its equivalent planetary radius. That radius would be about 9680 kilometers (Earth is 6670 km). If our planet was 50% larger in diameter, we would not be able to venture into space, at least using rockets for transport."[1]

[1] http://www.nasa.gov/mission_pages/station/expeditions/expedi...

Yeah this is indeed true, but sadly most movie plots treat distances badly for practicality reasons. The fact that they were able to leave the gravitational field of the planet they visited just using their "space shuttle" was also highly unrealistic, since that planet had about the same mass as Earth, whose gravity well they had to leave using a conventional rocket earlier in the movie. So this part definitely does not add up.

Wasn't the shuttle part of the older tech that was built on air decades ago, but the rocket on earth built out of the last pieces of scrap parts?

I attributed it to the fact that the black hole is very close, so it had a "helping hand". I'm not sure if it adds up though.

The time dilation was really quite fascinating. However, I assume that the entire planet would not behave as if it had the same time dilation all the time?

Considering the massive dilation (1 hour -> 7 years, a factor of 1 : 61320), wouldn't even relatively small distances on the planet surface create different dilation effects depending on an objects/individuals distance to the black hole?

I'm just wondering if there would not only be noticable effects from a distance (orbit -> planet), but also within visible distance on the surface itself.

If the dilation could act on scales such as the 200 meter wave, I'm having trouble imagining how it would look / behave, if for example the top of the wave was moving "slower" compared to the bottom of the wave.

Fascinating question, I'll have to look into this! I was considering writing a blog post about the movie physics already since there are so many fascinating things to be discovered, but I'll maybe check out Kip Thorne's book about the movie first ;)

The wormhole was perfect, except the travel bit bugged me. They use the 2d analog with paper. The second you pass through the hole in one location you emerge from the hole in the other location. In the third dimension, as they touch the sphere near Saturn they would be leaving the surface of the sphere on the other side. From their point of view they should be about to hit the 'ball' then all of a suddenly then are travelling away from the surface of another ball. Instead they had this tunnel thingy.

http://en.wikipedia.org/wiki/Wormhole would seem to indicate that there's a non-zero travel time through one.

> However, in 1962 John A. Wheeler and Robert W. Fuller published a paper showing that this type of wormhole is unstable if it connects two parts of the same universe, and that it will pinch off too quickly for light (or any particle moving slower than light) that falls in from one exterior region to make it to the other exterior region.

Imagine in the 2D analog, if there was a small gap of air between the 2 points on the paper.

Yea I was thinking about that, say a straw. A cylinder to us in the 3d world but in the 2d world one would just see themselves stuck in a circle for awhile. So to up a dimension a 4d whole in a 3d world would I guess appear to us to be a stuck in a sphere? Maybe that is what the movie tried to show, but it still looked like they were travelling in a tube.

It's a supermassive black hole, spinning at close to the maximum permitted (apparently there's a maximum, beyond which photons at either the photon sphere or an event horizon get dragged faster than the speed of light, and Gargantua's spin is ridiculously close to the maximum for the math on the orbit and time dilation to work out, but it does)

If you can find a copy of Thorne's book (it's already leaked to the web) and skim the appropriate sections, it'll clear up some things.

A relativistically spinning supermassive black hole might not be very unrealistic indeed, since it will have ingested the angular momentum of a whole galaxy during its growth and concentrated it in a very small region of space.

He addresses that in the book

> I found that Chris’s huge slowing of time requires Gargantua to spin almost as fast as the maximum: less than the maximum by about one part in 100 trillion. In most of my science interpretations of Interstellar, I assume this spin.

> In 1975, I discovered a mechanism by which Nature protects black holes from spinning faster than the maximum: When it gets close to the maximum spin, a black hole has difficulty capturing objects that orbit in the same direction as the hole rotates and that therefore, when captured, increase the hole’s spin. But the hole easily captures things that orbit opposite to its spin and that, when captured, slow the hole’s spin. Therefore, the spin is easily slowed, when it gets close to the maximum.

> Ultimately, when the hole’s spin reaches 0.998 of the maximum, an equilibrium is reached, with spin-down by the captured photons precisely counteracting spin-up by the accreting gas. This equilibrium appears to be somewhat robust.

In essence, the necessary spin (for an object to stably orbit at a distance for the time dilation needed for the plot), while possible, is not sustainable, based on what we know about physics. But it's allowable as real physics, because there could be some exotic physics involved in keeping Gargantua spinning that fast, possibly intervention by the civilization that created the tesseract.

> here we have to assume that the black hole is not rotating very fast

I read that, for Interstellar, it's actually very important to include rotation of the black hole: http://www.slate.com/blogs/bad_astronomy/2014/11/09/interste...

> which offer great 'Fermi problems'

An aside, but I'm curious. I see this mentioned a lot more often lately, and I know Randall Monroe talks about them a lot in his 'What if?' series, so I'm not sure if it's because of that popularising the term, or if it's just the Baader-Meinhof phenomenon on my part. A Google Trends search suggests increased interest, but it could just be coincidental.

Fermi problems are discussed a lot in Physics, and as a working physicist you always need to be able to quickly estimate the order of magnitude of something when developing ideas for experiments, since calculating everything in detail is usually too time-consuming. So I'd say that this is not a hype but rather a pretty useful skill for any scientist.

Wait what? What about sending "quantum data" back from the black hole? The point is that no information can leave.

Also, from what I learned in high school physics, the body of a human would completely fall apart if it's falling to the black hole, because of the difference in gravity between proximal and distal parts.

These are just the 2 things I noticed and I'm far from a physicist. Basically, it got a couple of things right and a bunch of things wrong. There was a clear preference of emotion over science. It just seemed like "The Core" Version 2.0, but here love and reading books conquers all and is beyond the forces of nature.

I liked Europa Report a lot more even though they didn't invest nearly as much into special effects.

That's an interesting point! The fact that our current theories suggest that no information can ever leave a black hole entails a paradox which is known as the "Black hole information paradox" (https://en.wikipedia.org/wiki/Black_hole_information_paradox). In the movie they resolve this by resorting to gravitational waves, which can "permeate" through space and time by a mechanism not explained in the film. In real physics, there is actually an ongoing debate in the community about whether information can escape from black holes or not, which resulted in a famous bet between Stephen Hawking and Kip Thorne on one side and John Preskill on the other. The fact that Thorne suggests that information can be sent out from a black hole might therefore be a small stab at John Preskill ;)

Concerning the second point, there is actually a pretty fascinating explanation: For a small black hole, the "tidal force" when entering the black hole (i.e. the force difference between your feet and your head) would be so enormous that you'd probably get ripped apart (so-called "Spaghettification" - https://en.wikipedia.org/wiki/Spaghettification). However, the Schwarzschild radius (or event horizon) increases linearly with the mass of a black hole, whereas the gravitational force declines with the square of the radius. Hence, for a supermassive black hole with 10 million solar masses, the tidal force is not bigger than the one you experience here on Earth (https://en.wikipedia.org/wiki/Supermassive_black_hole), and you would probably not even notice when you cross the event horizon. Fascinating stuff.

They glossed over the tidal force in the movie and I assumed it was a deus ex of sorts (in fact, I assumed the whole final act of the movie was more concerned with resolution of the story than with proper Physics). Thank you for this explanation, this is fascinating stuff.

It's still a gloss over, but one of the characters does mention it early on, which I took as indication that it was going to end up being important.

I remember having a similar thought process to all of the above, but they even explicitly call it out as "gentle" with maybe a single really simple sentence on why it was. I don't remember if they made the direct connection to it being supermassive (like they did with its rotation), but it was in the same bit of dialog.

Maybe black holes are nature's true-random-number-generator (via hawking radiation). Energy comes in, energy eventually comes out, but there's no relation as far as wavelength, direction etc.

No idea, I'm an EE not an astronomer, just guessing out of my back end.

I don't know why you're being downvoted, so I'm going to give you a proper reply instead.

Actually, the 2 things you noticed are not that hard to resolve:

- The quantum data was most likely never going to get out of the black hole. They executed the plan on the off chance that TARS was able to figure out how to do it if he had the quantum data. It's not impossible that there is a way to do it, we just don't know it yet.

- Your concern about spaghettification is valid, but the risk of that happening also decreases with the size and mass of the black hole. A stellar mass black hole would rip you apart instantly, but around a supermassive black hole the gravity gradient is a lot gentler. It wouldn't be comfortable per sé, but definitely survivable. You would get ripped apart inside the event horizon, but you could cross it pretty safely.

There is actually a much bigger problem than the spaghettification: every black hole has a shell of light orbiting it at the event horizon. It's light that came in tangentially, and doesn't have enough speed to escape, but is fast enough to keep orbiting. In a black hole of considerable age (like the one in Interstellar), that shell would be very very energetic. I don't know if the ships they were in would be able to survive a blast of radiation that intense, let alone the human and robot inside.

I don't think it's fair to say that they went for emotion over science. They tried to do both, and wanted at least an inclination of accuracy from the start. That's laudable in itself, in a time where most wouldn't bother with that.

Wouldn't spaghettification happen anyway, but at a later point? Maybe everything after he fell in was a dream of his? This would actually make it much more interesting for me although many people probably wouldn't like this sort of ending.

It would happen, but for a black hole massive enough, that point would be well inside the event horizon. We don't know how deep they actually went into the black hole, or even whether or not the 4D structure was inside the black hole or somewhere else entirely. Everything inside the event horizon is essentially unknown to us, both as scientists and as movie-goers, but the trip up to that point is survivable.

That was what bothered me, there would be a zone of high energy particles that you could not pass without severe damage to your ship and your tissues.

They did show his ship being shredded by a bunch of glowing particles...

I'm not going to comment on the "cosmic censorship" hypothesis of black holes since that's actually an incredibly difficult topic, but regarding the tidal forces that would rip you apart, there are certainly large enough black holes that would allow you to comfortably enter the event horizon without being ripped apart. But just to give you a taste of how counter-intuitive this subject can be, consider that despite the fact that light cannot escape a black hole it is conjectured (by Hawking no less) that black holes can emit radiation! (The mystifying mechanism of this involves, very roughly, quantum fluctuations at the event horizon spontaneously giving rise to particle/anti-particle pairs, with one particle of negative mass falling into the horizon and the other of positive mass going out.)

The event horizon is only the "point of no return" insofar as it's the imaginary boundary inside of which even the forward light cones are oriented towards the center of the sphere (so that light cannot escape no matter what direction it's emitted in). It's not the point at which the tidal forces are so strong that matter is ripped apart (or even just your macroscopic body).

Gargantua is a spinning "Kerr" blackhole in the movie. The nearly maximally spinning blackhole is central to the movie plot as it is the reason Miller's planet can be in the orbit it is claimed to be, tidally locked to the spin direction of the blackhole. And the "accretion disc" is not really accreting into the blackhole but is just in orbit around the blackhole, cooling off. The accretion discs and the polar ejections we know from astronomy are energetic medusas that'll fry anything that so much as glances in its direction.

I haven't checked the numbers in any way, but is it safe to assume that the black hole is not rotating "very fast"? In the news covering the render software and papers that will be/have been published, it was mentioned that they were surprised to see the effect the rotation of the black hole has on the accretion disk -- that it bends and twists space and light, so insted of a flat, Saturn-ring-lik disk, you end up with the thing you see in screen.

> here we have to assume that the black hole is not rotating very fast

From the article: "The black hole needs to be spinning very fast"

Calculations about time dilation become enormously more complicated in a system where the black hole is spinning, because you get effects like frame dragging that influence the orbits and time. For the purposes of the parent poster, a ball-park number of distance is enough, they don't need the whole shebang.

> For the purposes of the parent poster, a ball-park number of distance is enough

Citation needed.

It's been said repeatedly that considering the strong rotation of the black hole is critical for the situation in the movie to be possible. "It's hard" is not an excuse to ignore a strong effect.

ThePhysicist talks about using the bits of information provided in the movie to learn about the basics of some of the physics behind it. That's why he points to the formula for calculating a Scharzschild radius and not the complicated solutions of Einstein's field equation for Kerr (rotating) black holes. As a learning experience, you don't want to dive into the hardest stuff right away. As a you learn, you'll also figure out what was a ball-park number and what wasn't.

Also, the effect is strong, but in all of the formulas you're already guessing factors such as mass of the black hole, which have a far bigger influence on the end result.

Remember a black hole will crush a galaxy, but not a dude in a space suit.

Don't forget to put the tarp over the ham basin before departing for olfactory shoes.