Would it be worth the money?

If you could describe this film in one word other than "Epic" what would it be?

So one of the big-ish questions in theoretical physics is why gravity seems so weak relative to the other forces. This may sound like a weird question, since in our daily lives, we're much more likely to be held down by gravity than be picked up by a magnet, but that is an artifact of the scale of things that we interact with on a daily basis! Think about how huge our planet has to be even to hold down something as small as a paperclip, and then think of how tiny of a magnet you need to pick up that same paperclip! However unlike other forces that we deal with, gravity really only serves as an attractive force, instead of having both attractive and repulsive interactions. So as you add more stuff together, gravity tends to increase, whereas the attractive and repulsive forces of, say, magnetism, tend to average out, so we perceive gravity to be stronger. But....it's really really not (for comparison, take two hydrogen atoms in an H2 molecule - the gravitational attraction between them is approximately 1000000000000000000000000000000000000 times weaker than the electric force between them), and so we're left with the question of why it's so much weaker.

The other relevant idea here is what is meant by the word "dimension" - there are two common definitions: "an aspect or feature of a situation, problem, or thing." and "a measurable extent of some kind, such as length, breadth, depth, or height.".

Old-school goofy/cheesy sci-fi will sometimes use "dimension" in the sense of the first dimension as sort of a synonym for "place where the laws of physics are different", but that usage isn't well defined in a proper science conversation, and leads to confusion.

The second definition is the one that relates more directly to the mathematical/scientific usage of the word (and correspondingly, the use in Interstellar). Essentially something lives in an "n-dimensional space" if n is the number of variables you need to give all of its measurements. So, for example, things that are 1-d might have only length, where as things that are 3-d might have length, width, and depth. However it's important to realize that dimensions aren't necessarily intuitively geometric and the variables used for measurement can be more abstract ideas! So for example, in my image processing class this semester we talk about a 16 x 16 image living in a 256 dimensional space, because you need a separate variable for each pixel! However, in the context of physics, it is very common to talk about time as representing a 4th dimension, so objects have length/width/height, and also a duration! This was formalized in Einstein's theory of relativity, when he proposed the idea that we really do live in a 4-dimensional universe, where space and time are all mixed up together, and measuring them can only be done relative to your frame of reference, but where the laws of physics appear to be the same in every frame of reference. This is where the notorious speed of light as a universal speed limit comes from, and the idea that you can travel backwards in time if you exceed the speed of light come from, but also that traveling faster or slower can make time speed up or slow down. This is pretty much known to be true at this point, by very rigorous experimental validation (for example, your GPS relies on these sorts of calculations to even be able to accurately tell you where you are!), even though it is very counter-intuitive to our daily experience of traveling very slowly.

Now, where the two things tie together in Interstellar:

We know that if you have something with a small number of dimensions, not only can you "fit it" into a larger number of dimensions, but that you can do so in many many different ways, by folding or curving it into different shapes within that space. For example if you're a person trapped in a piece of paper, or a string, it doesn't matter how crazily that string or paper is curved, unless two points are touching that shouldn't touch (like with the wormhole analogy they did with paper and pencil in the movie), everything will seem normal to the person living in it, because they can't observe that higher dimensional twisting. What they can observe however is stretching, if distances that they know should be short are suddenly much longer, they know that something is stretching them out in some higher dimensional space. Moreover, this is exactly what is happening with gravity!

So one theory (or rather, one idea that is common to several theories) that ties all of this together, is that perhaps the reason gravity appears so weak relative to all of the other forces is because the particles that carry gravitational force really live in some higher dimensional universe that we can't observe through the other forces, and transmitting gravity in those other dimensions as well! Thus gravity is weaker because it "leaks out" across dimensions, but electromagnetism is strong because it is "stuck in this dimension" (This last paragraph conveys ideas that are theoretical in the "we have a model and haven't tested whether it actually works, but the math seems nice" sense, rather than theoretical in the "we have model, and the predictions it makes actually check out in the real world" sense).


The idea of embedding time into a spatial dimension that we could explore goes back to the embedding and spacetime stuff and isn't really related to gravity. Basically, even though we live in a universe where space and time are all mixed together and tangled up, when we actually go to measure them, we find a small but significant difference:

You might remember the Pythagorean theorem from math class. If you have a right triangle whose legs are of length A and B, then the third side, of length C, satisfies the equation A^2 + B^2 = C^2. This carries over to measure distances in higher dimensional spaces too (or at least in ones with relatively flat curvature, which we'll take as an approximation of our universe for the sake of a simple explanation), so if you're separated from something else by distances x, y, and z in three different (orthogonal) directions, the total distance, d, by which you are separated satisfies d^2 = x^2 + y^2 + z^2. But when you add a timelike dimension, you end up using a minus sign instead! So if you are separated from an event by x,y,z,t, then d^2 = x^2 + y^2 + z^2 - t^2. (t can be converted from a "time measurement" into a "distance measurment" by multiplying by the speed of light). Of course imagine for that x,y,z are all 0! Then your d^2 will be a negative number, and the square-root of a negative number is imaginary! So the thing that makes timelike dimensions different from spacelike dimensions is that they contribute "imaginary distance"! And obviously you can't just walk 5i feet, because that doesn't even make physical sense (until you use it as time, and square it properly and all that good stuff).

The movie tries to visualize the idea that the future society helping them out is, by virtue of their control over higher dimensions, is able to "embed" our timelike dimensions into a physical spacelike dimension which Cooper is then able to explore. I haven't thought through the math here closely enough to decide if that's even a sensible/plausible thing for them to be able to do, from a mathematical/geometric perspective, but that is at least the idea that the movie was attempting to convey. Remember that embedding low dimensional things in high dimensional spaces, allows you to curve them and rotate them in all sorts of funny ways, and that in complex space, imaginary numbers are just a 90degree rotation from real numbers, so maybe the future high-dimensional society is able to "rotate" our timelike dimension into a spacelike one, because they live in a space where they can rotate our 4 dimensions at will.

Of course, they don't need the weird embedding stuff for stock time-travel, a simple wormhole is good enough for that, because it allows you to simulate traveling faster than the speed of light without having to actually do it, but they did need it for him to be able to explore the timeline of Murph's bedroom interactively!

resulting in an end product that pleases nobody.

it seemed like the original goal was to make a "super serious" science fiction story that was plausibly in line with modern scientific theories, but that this was retroactively fitted with things like drawn out, simplified explanations, a half-arsed attempt at drama, "love solves everything!!!", "HACKING!!!", "I WILL DO SCIENCE TO IT!!!", and inexplicably powerful AIs for comic relief.

by "hacking", i was referring mostly to the bit where the main character points an old laptop at a drone flying overhead and, minutes later, has complete control over it via touchpad, despite their flyovers happening very rarely, if ever, judging by everybody's reaction.

this, coupled with the fact the lockheed martin has already basically solved the problem of compact fusion, would mean that this future has an abundance of cheap, clean energy to fulfill any needs.

Oh yeah, I had forgotten about that. Just to throw an excuse out, if something is that old there are likely known vulnerabilities to exploit in the software and "catching" one must be pretty important to life in this age to go through your field of corn crop in chase. Thus, any hobbyist or someone looking to make a quick buck (or whatever they are for) has the software and/or knowledge to exploit such a vulnerability. I do call BS on the method of flying the drone once it was captured though; he was able to use a finger to control direction and altitude. I would have loved more backstory but not knowing is almost as interesting as well.

Compact fusion is certainly an awesome leap forward. But if something is up in the air for 100 years, it's not going to see an upgrade in terms of propulsion. I'm not saying the movie is 100 years in the future but the technology likely wasn't miniaturized enough to fit in a high altitude drone by the time it was being engineered and/or manufactured. And if the military was receiving cuts on the scale of NASA, they'd likely reuse older drones and technology than spending the money to retrofit new tech into them. Now, having a small space station operate for 23 years is another story. Compact Fusion could have gone into that as I don't recall seeing any solar panels on it.

The area where they lived was a dust bowl. I'll recede and admit I would have liked a more global picture. Was there some metropolitan cities on Earth or was it all farm land? I would have welcomed the bigger picture at times but it didn't affect the movie for me one way or another.

The character names are not the actor names. There is no Matthew in this movie, it's Cooper.