This week Dr. Faraday did a simple time dilation test, time as it is perceived by two different observers (the rocket and himself). His results were astounding, the time dilation between the island and thw outside world was 31 minutes. Now just looking at the number 31 is interesting in and of itself, but the big deal is the ratio yielded in the experiment which is about 5/6.
How big is the dilation?
If the time dilation is a constant and depending on where it started the island can be in a completely different time. If it started when they crashed on the island (“The Economist” is on the 94th day, that is Christmas Eve), then real world time has elapsed 111 days. If it only started after the hatch implosion then (27 days have gone by since then), real world time has elapsed 99 days since the crash. Although, with the dilation being constant, we would notice a difference in the radio contact between the island and “Not Penny’s Boat.”
What does it all mean, Basil?
There are multiple ways of explaining the phenomena that is occurring that would cause this kind of dilation on the island. For starters, we bring back an old friend, Closed Timelike Curves.
Last week, we examined the idea of a CTC enveloping the island due to the strong electromagnetic field. The island’s CTC could be running parallel with the rest of the world, but it is off by just a little bit. This would cause the time dilation that Faraday observed, and would also mean that the dilation is constant and has been going on for some time.
Now if the CTC has been around since Ben came to the island (about 30 years), then Ben is about 5 1/2 years behind the rest of the world. The dilation would also allow Ben to get the footage of Juliet’s sister (giving the false idea that time moves at the same speed on island and off) with ease, since Juliet was on the island for three years.
Behind door number 2 is the island has an Event Horizon. An Event Horizon is a boundary in space-time (we are hinting towards Minkowski again). The rocket would have been slowed when it entered the event horizon. This theory would, like the CTC, peg the dilation as being constant, but has a way around the problem with the radios. The frequency change is explained by a Cauchy Horizon (pronounced Ko-shi), but if it contains the Casimir Effect (Orchid Station) this change will not happen.
The island has a fluctuating electromagnetic field. And by fluctuating, I mean fluctuating in multiple ways (strength, direction, and velocity). But how exactly does time change with the electromagnetic field?
Let’s take a look at Einstein’s Special Relativity, his whole theory is hinged on the fact that light is the fastest anything can go. Time dilation, as explained by special relativity, two clocks moving in motion of each other will see the others clock as being dilated. The effect is reciprocal. This is shown by the Lorentz factor blow:
Where the speed of light is depicted by c and the relative velocity is v. Now James Clerk Maxwell said that electromagnetism also moves at the speed of light (since it is made of photons, like light). So theoretically we could replace the speed of light with the speed of electromagnetism, and with some basic algebra we will get the following:
So with Daniel Faraday being one observer and the rocket being the other, the electromagnetic field of the island would be traveling at half the speed of light. Crazy, huh? But thats not all, the field (since velocity is determined by multiple factors) will be fluctuating as found by Maxwell’s equations:
The Dharma Initiative found this field on the island, and tried to tap into it. When they had failed, they decided to cork the field by installing the hatch. This allowed them to release the field in small doses and study its time dilating effects. Then the hatch imploded, and the field was partly sealed which would keep the field from going completely out of control. But the field is still leaking out, which would account for the strong electromagnetic field that is surrounding the island and its fluctuating attribute.
Daniel may have found an area where the field is not present, and was telling Frank to fly there so that his helicopter would not be not affected by the field.