Back To The Future - Resolving The McFly Conjecture

I was thirteen years old when the original Back To The Future film was released, the film in which everybody's favourite '80s actor, Michael J. Fox plays the likeable teenager, Marty McFly. In the film McFly travels back in time to 1955, using a DeLorean modified by his friend Doc Brown. The film, as you'd expect with a Hollywood movie, takes certain liberties when it comes to closed-loop time travel.

These discrepancies were easily ignored by my thirteen-year-old brain, that is, right up until the end when Marty decides just before he is supposed to travel back to 1985, to set the timer for fifteen minutes before he originally left. He does this because just before jumping back thirty years, he sees his friend Doc, being gunned down by some bad guys. Thus he travels back in time knowing that his friend has been killed. After meeting with Doc in 1955, he tries to warn him, but Doc, ever mindful of disrupting the spacetime continuum, refuses to listen to Marty.

Okay, so far so good. Except no, Marty's decision to come back before he left, produces a paradox my tiny little brain just couldn't ignore, and because my brain tends to lean towards the obssesive, I have conducted a thirty-seven year thought experiment which I like to call, The McFly Conjecture.

A Universe Of Infinite McFlys

The problem with coming back fifteen minutes before he left, is that Marty eventually runs into himself at the point he decides to go back in time. Therefore, Marty Number One arrives fifteen minutes early and sees Marty Number Two go back to 1955 and presumably do all the things the first Marty has done in the film, including coming back fifteen minutes early, only to find Marty Number Three going back in time and carrying on the whole loop.

At first, I thought this would lead to an ever-increasing amount of Martys building up until they filled the entire United States and then the world. The reason I thought this was because when Marty arrives back in 1985, he is some distance from the street where he originally left. When the DeLorean materialises back in 1985, he is immediately out of gas, this means he has to dash across town on foot. The dash takes him approximately fifteen minutes, thus he is not in time to give his friend Doc a verbal warning about his assailants.

So I imagined another Marty jumping out and doing exactly the same thing, however I realised just the other day, whilst watching an unconnected YouTube video on time travel paradoxes, that whilst there would be an ever-increasing amount of Martys going into the past, they wouldn't get a chance to multiply in the way I had first thought.

And that's where Einstein enters the room or rather, his equation.

The McFly Collision

Now I am become Death, destroyer of worlds.

The above words were purportedly said by Oppenheimer upon viewing the first nuclear detonation on Earth. But perhaps those words would be echoed by Marty McFly if he realised the catastrophic chain reaction he put into motion when he made the fateful decision to come back fifteen minutes early.

Einstein's famous equation tells us that the total energy contained in any one object, is equivalent to the object's mass, multiplied by the speed of light squared, famously notated as E=mc2. This is relevant because as we've seen, Marty going back to 1985 fifteen minutes before he left, creates another version of himself, which is doomed to also create another version of itself and so on.

This means at precisely 1.24 a.m. the time Marty decides to return to 1985, not just one Marty appears at the spot where the DeLorean runs out, but they all do. We can see this if we take it step-by-step.

When Marty appears at 1.24 there is another version of himself making his way, with Doc, to the teleportation site, fifteen minutes later, the new (or old, depending on which way you look at it) Marty teleports, but he teleports back to 1.24 a.m. the very same time at which the first Marty appears, therefore two objects are teleported to the same place, at the exact same instance. Which any good thermodynamics student will tell you, will result in the complete and utter annihilation of both objects, releasing all of their energy in an instant. Resulting in a catastrophic explosion.

To calculate just how devastating the explosion would be, I asked GPT 4 and some of his plugin buddies, to crunch some numbers for me. I'm assuming that Marty McFly is roughly seventy kilograms in weight and from the DeLorean car specs for that particular model, the weight is 1,233 kg. With no idea how much extra weight the eponymous flux capacitor adds, I'm just going to say the combined weight of McFly and DeLorean (McD) is 1300kg.

So the mass-energy equivalence principle is given by the equation:

E=mc 2

where: E is the energy, m is the mass, and c is the speed of light.
Given that the speed of light c is approximately
3×10^8 m/s, and the total mass of D is

2×1300 kg, so we can calculate the energy release as:

E=2×1300kg×(3×10^8 m/s) 2

This means that the energy released when two DeLorean-driving Marty McFlys, both arrived at 1.24 a.m., each weighing 1300 kg, colliding instantly will be 5.6×10 ^6 times more powerful than the energy released by the atomic bomb dropped on Hiroshima.

In other words, the energy released from the McFly collision would be equivalent to the detonation of about 5.6 million Hiroshima bombs. To put this into further perspective, let's look at just how much an explosion equivalent to over five and a half million Hiroshimas would destroy.

To estimate the area affected by such an energy release, we can use the concept of energy density. The energy density is defined as the amount of energy per unit area. For simplicity, let's assume that the energy is distributed uniformly over a circular area.

The energy density (D) can be estimated using the formula: D= A/E

where:
D is the energy density,
E is the total energy, and
A is the area.

Given that we have an energy release of 2.34×10^20 joules, and assuming that the energy density is similar to that of the Hiroshima bomb, we can estimate the affected area.

The Hiroshima bomb affected an area of approximately 13 km². The energy of the Hiroshima bomb was 4.18×10^13
joules. So, the energy density of the Hiroshima bomb is:

D-Hiroshima =4.18x10^13J/13km2
Now, assuming that the energy density D for our hypothetical scenario is similar to D-Hiroshima, we can estimate the affected area (A) by dividing energy (e) over density (D) A= E/D

So using those calculations, the energy released from the collision of two objects, each weighing 1300 kg, if distributed uniformly over a circular area with a similar energy density to the Hiroshima bomb, would affect an area of approximately 7.278^10 square kilometres. Roughly equivalent to half the land mass of Earth.

McFly's First Paradox

If Marty McFly time travels to 1955 and then comes back to 1985 fifteen minutes before he originally left the eighties, then he will run into himself causing an explosion that would wipe out half the land mass on Earth, which in turn would put us out of our nice regular orbit around the sun and inevitably would lead to the destruction of the planet and everything on it.

Okay, but that would all happen fifteen minutes before Marty left for the past, thus preventing him from going into the past in the first place. It's getting a bit complicated so allow me to illustrate using a simple graphic representation.

In the first figure, we see what would happen if Marty travelled back to 1955, did his business there and then returned to 1985 after he originally left.

Fig. 1

In the above image, the blue trail represents Marty travelling back to 1955.

The thick red line represents the time he spent in 1955.
The thick blue line to the right of the image, represents his life up until the point at which he left. Notice there is no thick red line between 1955 and 1985, because Marty did not exist for all of that time, presumably being born around 1970.

Also notice there is no thick blue line after the point at which he left 1985, because at that point, Marty ceased to exist in 1985.

The red trail represents his return leg and it lands after the moment he originally left, the amount of time doesn't matter, it could be one second or one year, it doesn't break causality because he is coming back to a Martyless universe.

Now let's look at what actually happened in the film.

Fig. 2

As we can see from viewing the above diagram (and the film itself), by returning 15 minutes (or any amount of time) earlier, Marty comes back to a universe where he already exists.

In the film he appears at a different physical location to where he was originally, so he has to run across town to warn Doc. There, he sees himself, going back in time to 1955 and as we can see from the diagram, that version of himself, will go back in time and return fifteen minutes before he left.

The only problem is, if the observed Marty does what our original Marty does, then they will both appear at the same spot because there is only one timeline, therefore there can only be one instance of 1.24 am. This means that two Martys (and their DeLoreans) will collide and obliterate each other. Which will release enough energy to blow up half the Earth, which is problematic, because that will also obliterate the location from which Marty leaves in the first place.

But let us suspend our belief for a second and assume that 1.24 am can happen 'twice'. The first time, only one Marty McFly exists and he travels back to 1955 and comes back fifteen minutes before leaving, only to see another version of himself leaving, to come back to 1.24 am the 'second time'. Then that space would be occupied by the first Marty and KABOOM!

Check Yourself Before You Wreck Yourself

So perhaps we have discovered a law of closed-loop time travel, if it is indeed possible, then one thing that can't be possible is coming back before you leave because that would create a closed time loop, whereby you will be destroyed by your other returning self.

But of course that is not the only paradox when it comes to closed-loop time travel, The Grandfather Paradox notwithstanding. The type of time travel where you can break causality by going back and killing your grandfather, or even leaving yourself a note, seems impossible. If it is possible, then we can assume that some time traveller in the future has already travelled back along their own timeline, which depending on what they did, could very well break the universe and cause us all to cease existing in the blink of an eye.

In truth the only way any kind of sub-superluminal-closed-loop time travel is possible would be if you could simply travel back as an observer who couldn't interact with the world you saw around you, thus preventing you from killing your grandfather (or an earlier version of yourself), or taking part in any other universe-breaking activities.

I strongly suspect that if time travel is possible, then it is either of the type where near-lightspeed travel is involved, allowing for a time-dilated trip to the future. The sci-fi type of time travel I suspect would only be possible if when the traveller jumped back in time, he was creating or travelling to a new universe, one in which the original protagonist now exists.

So in that way you can travel back in time and kill your grandfather, thus instantly creating a universe where your mother was never born and so neither were you. However, the original universe you came from still exists and carries on just fine.

McMega Death

As far as Back To The Future is concerned, the film should have ended in a colossal Earth-destroying explosion as two Marty McFlys, both driving Flux Capacitor-enabled DeLoreans, both appeared at the same spot, at the same time, giving us a wonderful example of Einstein's E=mc2 equation.

But then the sequel would have just been a shot of a burnt husk of an Earth wandering through the galaxy having been ejected from its star. Which let's be honest, would have completely bombed at the box office.

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