Movies Part 1: Ex Machina and Primer, Safety Not Guaranteed

As a young child, I loved the novel the Man who Folded Himself by David Gerrold. And Primer, at some very basic level, reminds me of that novel.

Both of these movies were low budget. (I can hear, in my imagination, the creators of Primer laughing their heads off. They probably wish they had had one month’s budget of Ex Machina and one tenth of the studio time these lucky sons of guns got and deserved.) So some allowances have to be made and a lot of eye squinting is needed.

First, let me say that the special effects of Ex Machina were superb as was the acting, set design and camera work. The DP was a genius. The editing was fantastic. Primer had practically no special effects and the one that they did do could not be seen against the actors white/blue shirt. The acting was decent. The set design was barebones. The camera work raw and the editing good. However, Primer was one of the best time travel movies I have ever seen. Like the shadows under the sleds in the original production of Star Wars, the rawness worked for the movie and worked well.

I found the story in Primer to be confusing. The plotting at times was a little intertwined and involved but that also worked for the movie. After all, it is a time travel movie, of course the timeline of the plot is going to look like spaghetti. Amazingly enough, continuity was good for a low budget time travel movie.

(Spoiler Alert. Skip this paragraph if you have not seen the movie Safety Not Guaranteed.) Now compare this to Safety Not Guaranteed, about a guy who puts an ad in the paper for a time traveling partner. In Safety Not Guaranteed one never knows what is real and what is fake until the end. And even at the end, one has to wonder if they really traveled in time or simply disintegrated. More on this movie later. Since the science was not the centerpiece of the movie and was only hinted at, there isn’t much to say about it except, “A laser.” After all, it is a comedy.

The reason I loved Primer, besides its gritty nature and its in the face time travel, was the scientific premise. They were trying to build an anti-gravity device. A device that affected the gravity and therefore the weight of a payload. (This is where they make their biggest faux pas. In the movie, they say that the object’s mass, the Weeble’s mass was decreasing, which is wrong. It wasn’t the mass that was decreasing but rather the weight of the mass in a gravity well. mass equals Force divided by acceleration. m = F/a.) (Sorry, folks, you can’t skip the math in this post.)

I have been playing with the notion of time dilation. A clock in a moving frame will be seen to be running slowly, or dilated according to the Lorentz transformation. The time will always be shortest as measured in its rest frame.

A clock in a gravitational field runs more slowly according to the gravitational time dilation relationship from general relativity:

Thus the faster you are going the slower time flows or the heavier the gravity the slower time goes. The reason that time slows in gravity is very similar to the Bernoulli principle but in reverse, (don’t get excited, this is a metaphor,) because the speed of light is constant. Because gravity bends space-time and because the speed of light is constant, time must slow down in order for light to travel the greater distance around the bend. In other words, because gravity bends space-time, it elongates space, causing the light to have to travel father and because you are actually bending both space and time, it takes longer but only from the reference frame of an outside observer. Basically, gravity is stretching both space and time. Time is, after all, just geometry. Click here and read this Quora post for a beautiful explanation. Read at least three different responses in the Quora post for detail on gravitational time dilation.

For the person in the moving frame or the higher gravity frame, time does not appear to slow down. It is only in comparison to another frame of reference, and by comparing clocks, that one notices the difference in the march of time. Click here for a video explanation.

By the way, a science fiction story was written about this. A starship cruise line sold tickets with the advertising gimmick that your orgasms would be an hour long. (I forget who wrote it.) Of course, on the ship the people having the orgasm experienced it in normal time but to a person on Earth, it looked as if the orgasms were an hour long. Customers felt that they had gotten cheated. This was a very interesting subplot or sub-theme wound throughout the story.

If we have a velocity of c, the speed of light, time goes to infinity. If we have a velocity greater than c, we get the square root of a negative number. In other words, our time component becomes imaginary.

Now, in the Lorentz invariant theory, the same formulas that apply to ordinary matter, bradyons, apply to tachyons, the faster than light particles. This means that the energy-momentum relation holds:

(where p is the relativistic momentum of the braydon and m is its mass.) The formula for the total energy of the particle still applies.

If you will notice, if v is greater than then the denominator becomes imaginary and this means that m, the mass, of the particle must also be imaginary in order for the total energy of the tachyon to be real. According to the formula, as the energy decreases, the speed of the particle increases. Also note, that just like it’s real counterpart, the bradyon, c is a barrier for the tachyon. Tachyons can never go just the speed of light but only faster than light. This would also mean that the tachyon would move backwards in time because the result would be negative. For the math, click here to read about the tachyon anti-telephone.

Now for the speculative part pertaining to the movie Primer. What happens if rather than increasing gravity we decreased gravity? By analogy to the faster than light tachyon, and this is not speculation but rather just wishful thinking, the anti-gravity would not slow down time but send it backwards. However, if you look at the math, the formula does not allow one to simply plug in a negative number whether it is velocity or gravity or mass. Because in the first set of time dilation equations, the velocity is squared and will always be positive. In the gravitational time dilation equations, you are subtracting from one. And if you subtract a negative number it is like adding a positive number. (1 – -1 = 2) Time would speed up. Thus, anti-gravity is not going to cause time to move backwards. In the movie, time is also looping. This is Gödel’s solution to the General Relativity equations, which allows, well, actually insists that there are closed timelike curves. (Timelike as opposed to space like.) So this is a possibility though highly unlikely. Click here and here for more information.

However, if we look at the math, if the gravity and mass of an object, like say a black hole, becomes so great then conceivably we will be taking the square root of an imaginary number. So, what happens, then, inside a black hole? Does time go backwards? Since I’ve never been inside a black hole, I don’t know. But then for T to come out real, T₀ would have to be imaginary. Mostly likely, the relativistic equations and perhaps the laws of physics itself in this universe would break down.

If you are confused, just watch this very instructional video, click here.

(Spoiler: Don’t read this next paragraph if you haven’t seen Ex Machina! Say, “Good-bye,” watch the movie and I’ll see you in my next post.) The writing in Ex Machina was good. The plotting was strong and straightforward and the half twist at the end of the movie, while not a complete surprise, was interesting. However, I am going to stop here and continue my train of thought in my next blog post. I want to include in my follow-on post the movies Robot and Frank and Loopers and I have not watched them yet.