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An explanation of Faraday's journal

IdoruFM April 20, 2010 User blog:IdoruFM

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As Sean Sheep has posted in a blog, I am as well keen on finding an scientific explanation to the series plot(or at least to some part of it). Here is mine based on one of the Faraday's journal pages which was shown to us in season 4 and season 6. I am not scientist so I will try to put it simple while tonight's episode is airing (I am not from US).


First some definitions quoted from Wikipedia

In physics and mathematics, Minkowski space or Minkowski spacetime (named after the German mathematician Hermann Minkowski) is the mathematical setting in which Einstein's theory of special relativity is most conveniently formulated. In this setting the three ordinary dimensions of space are combined with a single dimension of time to form a four-dimensional manifold for representing a spacetime.

In physics, the world line of an object is the unique path of that object as it travels through 4-dimensional spacetime.

light-like curves(or lines), having at each point the speed of light. They form a cone in spacetime, dividing it into two parts. The cone is a three-dimensional hyperplane in spacetime, which appears as a line in drawings with two dimensions suppressed and as a cone in drawings with one spatial dimension suppressed.

time-like curves(or lines), with a speed less than the speed of light. These curves must fall within a cone defined by light-like curves. In our definition above: world lines are time-like curves in spacetime

space-like curves falling outside the light cone. Such curves may describe, for example, the length of a physical object. The circumference of a cylinder and the length of a rod are space-like curves.

In a Euclidean space, the separation between two points is measured by the distance between the two points. A distance is purely spatial, and is always positive. In spacetime, the separation between two events is measured by the interval between the two events, which takes into account not only the spatial separation between the events, but also their temporal separation. The interval between two events is defined as:


  S^{2}= \Delta r^{2} - c^{2}\Delta t^{2} (spacetime interval)


Minkowski Space

320px-World line2.svg
We are used to represent objects and their positions in an Euclidean space with two or three coordinates(x,y,z) with a metric(distance between two objects) but in fact the special relativity doesn't represent positions but events, that is, positions of objects in a concrete time and separated by a spacetime interval. That is why a Minkowski space is comfortable to represent events or a sucession of events in spacetime. The image on the left shows how a Minkowski space is look like, we can see an observer of an event and the series of events that form/affect the past and the future of that event. We see two cones, the future light cone and the past one, which delimit the series of events that can form/affect the future of the past of that event, cause none can move to a speed higher than that(remember we are representing position against time).







Faraday's journal

180px-6x11 DanielsJournal
(A larger picture can be seen here [1]) Maybe this is easier to see in the two dimensional representation we can see on Faraday's journal. There we can see that Faraday has represented a triangle which is formed by the axis of space(aka position) against time, being the hypotenuse the edge of the light of the cone. Each dashed line called time-like in the figure is a succession of events from the origin differentiated by their speed (read for speed their position in space time), with the edge being the edge of the cone and and the travel at the speed of light. As time passes in a different form to a traveller depending on its speed, a succession of events at different speed leads you to a different position in space time and makes possible time travelling. Faraday is theorizing that there is a space-like curve called in the journal "space time invariance", which is an area where the spacetime interval/difference/separation between two events is 0 (\Delta r = c\Delta t, ct is called imaginary time as time is an imaginary number), which means the difference between their positions in spacetime is equal to the speed of light multiplied by their difference in time. That means that if we travel at the speed of light or lower speeds to a concrete position and time in spacetime inside that area, the result of the travel can not be an alteration of events as their spacetime interval is 0, basically, the two time-likes aka timelines resulting are the same (whatever happened, happened). Faraday theorized that there is an area outside this space time invariance that will allow you to change the difference/separation between events, so if you travel to a concrete point in spacetime inside that area, you will be allowed to change an event from the past or the future. Faraday found that one of those points outside that area is 1977 on the island and the series of events that lead to the detonation of Jughead.


Propagation of changes and explanation of the two realities

Quoting from Wikipedia:

The future of the given event is formed by all events that can be reached through time-like curves lying within the future light cone.

The past of the given event is formed by all events that can influence the event (that is, which can be connected by world lines within the past light cone to the given event).

The present is the region between the two light cones. Points in an observer's present are inaccessible to her/him; only points in the past can send signals to the observer. In ordinary laboratory experience, using common units and methods of measurement, it may seem that we look at the present, but in fact there is always a delay time for light to propagate. For example, we see the Sun as it was about 8 minutes ago, not as it is "right now." Unlike Galilean/Newtonian theory, the present is thick; it is not a sheet but a volume.


That means that we are humans and so perceive and have an interpretation of reality according to what we see and our brain thinks. When we are staring at our monitor we are not seeing the present of it, just a past image of it. This is so cause the light is fast but its velocity has a finite value and is not until the light reflected and emitted by the monitor arrives to our eyes and is processed by our brain that we are aware of it, it doesn't exist for us until then. Of course, when light has to travel through small distances that difference in time between the past image and the present image is not significant but what about if light has to travel a distance equivalent to 2007-1977 = 30 years through time and space? When the losties time travelled to 1977 changed their past and so the light cone of their Minkowski space, but they travelled back to 2007. They are both the cause of the 1977 event and the observer in their Minkowski space, they have travelled at a higher speed than the propagation of the changes from the past and so in 2007 can only see their past and not their real present. That is why people in the FST seem to have memories or deja vu of the other reality, cause both realities are merging slowly, the FST is swallowing the OT as time passes and propagation of events occurs cause two objects can not co-exist in the same spacetime. Eloise said to Desmond that he is not supposed to look for Penny, at least not yet, not until the FST has swallowed all the OT until 2007, moment when the OT will be over. That is why when the characters die or are near to die are near the other reality, cause the merging stops and only the alive version in the OT or the FST is the version prevailing.


Forget about all of this and watch lost tonight, this has never happened (or maybe is just that has not propagated to the present yet :))


Links:

Wikipedia's article about Minkowski space [2]

Wikipedia's article about Spacetime [3]

Wikipedia's article about Worlines, time-like, space-like, past, present and the future [4]

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