In the Season 4 Trailer involving Dr. Marvin Candle posing as Edgar Halowax he says he is at a DHARMA station the Orchid. The Orchid is portrayed as a botanical research station but is later proved to be not true. It in actuality houses a number of white rabbits each with a number on their backs. Most importantly in this little clip is the reference to the Casimir effect. This has quickly become a very popular theory in possibly what the island is or how it is related to this force. The Casimir effect is a very complicated and complex theory and therefore is very difficult to summarize however I will do my best to do so in as little space as possible. This effect was developed by physicist Hendrik B. G. Casimir. "The Casimir effect can be understood by the idea that the presence of conducting metals and dielectrics alter the vacuum expectation value of the energy of the second quantized electromagnetic field. Since the value of this energy depends on the shapes and positions of the conductors and dielectrics, the Casimir effect manifests itself as a force between such objects." I didn't write that last part. The Casimir effect is related to the show in many ways and in one way it is somewhat of an electromagnetic phenomena. Electromagnetism receives credit for many of the islands strange properties. For example; tidal anomalies, healing properties, and the "monster." To try and better explain the Casimir effect I will use layperson terms. Basically through the Casimir effect a wormhole or blackhole could be created. A wormhole potentially created could make it possible to travel in time, or alternately travel across dimensions. A theory is that what if Naomi was telling the truth about the plane being found and there being no survivors, this theory accounts for that. If the plane while off course and in the air, neared the wormhole, the plane split into two planes and one crashed in the ocean and another crashed on the island. While on one of them all the passengers died and the other they made it onto the island. This could have been the purpose of the Swan station was to control this wormhole, and when Desmond left the station and the anomaly happened it opened the wormhole up and that is when the plane made it through. And now that the Swan station imploded they have no control over the wormhole. Going along with this theory, the Hanso Foundation sent the DHARMA Initiative to the island through there own version of a wormhole to study these traits on the island. Since the DHARMA people were purged is Ben keeping more people from the Hanso Foundation from returning to the island. In regards to electromagnetism, James Clerk Maxwell is a real life expert in the area of electromagnetism.
At this point this is irrelevant however if you play the ARG Find815 then you find out that the main character of the reality game is receiving encoded emails from a Maxwell Group. The Maxwell Group in the ARG is a group who is also funding the search for the Black Rock. The Maxwell Group is a division of Widmore Industries. This is Penny's father's company. Penny is the girlfriend of Desmond Hume. Widmore Industries are supposedly tied to the Hanso Foundation, as well as the Paik Heavy Industries. Widmore Industries appears to have its hand in many business ventures as it's logo or name is seen in many episodes on a variety of products. In a flashback to a Driveshaft video shoot a banner for Widmore Construction is seen in the background. The Widmore logo is also found on the hot air balloon of Henry Gale as well as the pregnancy tests taken by Sun and Kate.
Other things that are seen in episodes throughout the series are the recurrences of the "Lost Numbers" which are 4 - 8 - 15 - 16 - 23 - 42 of which the sum total = 108.
- The Flight Number was Oceanic Air 815
- The news station at Hurley's lotto interview was KSVU-8
- The appointment when Claire wanted to sign the adoption form was at 8:15AM
- The number of the safe deposit box that Kate robbed is 815
- The number of people that die in Hurley's shoe factory fire is 8
- The Number of Michael and Walt’s room is 815
- The number on the Old Scooter Man's hat in the Sydney Airport is 8 (who Hurley buys the scooter from for $1600)
- Kate and Tom Brennan buried the time capsule on 8/15
- The copiers that Charlie was trying to sell were model # C-815
- Adam Rutherford's time of death was recorded in St. Sebastian Hospital at 8:15
- Anthony Cooper's safety deposit box was #1516
- According to the driver's license found by Sayid, The Real Henry Gale lived on 815 Walnut Ridge Rd
- The September 22nd System Crash occurred at 4:16
- Kate has a $23,000 bounty on her head
- Danielle askes Sayid where Alex is 23 times
- The number of the departure gate of the flight is 23
- Hurley's hotel room in Sydney was number 2342
- The temperature in Sydney the day Flight 815 departed was 23°C
- The number of people who survived the crash in the tail end of the plane according to Libby was 23
- Part of the video reel #23108-42 that Kelvin shows to Sayid
- Munson's 10 Million was hidden in unit 23c
- Karl was being held in room 23 in the Hydra prison
- Juliet enters 1623 into the sonic fence keypad
- The radio volume in the van is set to level 23 when Driveshaft's song starts playing
- Ana Lucia - Sat in seat 42F
- Hurley's car has gone 42km when it breaks down on his way to the airport
- Number of original passage survivors at the end of Season 1 in the the middle section was 42
- Desmond looks at letters he sent to Penny while he was in jail, and the address of Southway Garrison, Desmond's jail, is 42 Berechurch Road
- Desmond tells Libby that he needs $42,000 to buy a boat
- The number of moves to inevitable mate of the computer on the chess game Locke played in the Flame is 42
- Leonard Simms was playing the game Connect Four
- 42 is the number of cells in Connect Four.
- 4:8:15 can be seen carved into Eko's stick upon close examination
- Nikki had a role in the 4th Season of Exposé
- Ben's tumor was growing around his L4 vertebra
- Number of years old the girl that Jack did his first solo operation on was 16
- Sawyer needed $160,000 for his con of Jessica
- Number of weeks since someone had won the Lottery before Hurley did was 16
- Number of miles/hr Desmond was peddling the exercise bike was 16
- The September 22nd System Crash occurred at 4:16
- When Hurley rides past 6 players of a girls' soccer team in the airport, each uniform has one of the Numbers
- 7418880 (the product of the Numbers, which appeared on the computer screen at the listening station before the discharge