Electromagnetism is a fundamental force in physics, the interplay between the phenomena of electricty and magnetism.
Electromagnetism broadly refers to the properties of electric and magnetic fields. Many of the events witnessed on the show are a result of electromagnetic phenomena inherent to the Island. Electromagnetism is one of the DHARMA Initiative's fields of study (as stated in the Swan Orientation Film).
The Island exhibits a number of unique anomalies suggestive of magnetic phenomena. The cause and exact nature of these anomalies is presently unknown. We know of at least two locations on the Island that have electromagnetic anomalies in their vicinity: The Swan and The Orchid. It appears a previous civilization on the Island was aware of at least one of these pockets. The construction of the frozen wheel suggests that they also were aware of how to tap into it.
There have been many instances of navigational issues that suggest the disruption of compass bearings on and around the island. Near the Swan station, Sayid informed Jack that his compass did not read a true magnetic north ("Hearts and Minds"). Desmond Hume also had difficulties navigating at sea, claiming that he sailed straight away from the Island but somehow ended returning to it. Oceanic Flight 815 also experienced difficulties in navigation, causing the plane to travel several thousand miles off course. In order to leave the Island, Ben told Michael to follow a bearing of 325 degrees("Live Together, Die Alone")
The DHARMA Initiative, and later the Others, used a sonar beacon to allow submarine navigation to the Island, suggesting that other means of navigation might be unreliable ("Enter 77"). Later, when the helicopter traveled to the island, Frank Lapidus followed a bearing of 305 degrees, as instructed by Daniel Faraday, who made sure he flew back following the same bearing ("The Economist").
After Ben turned the wheel beneath the Orchid station and the time shifts began, Daniel told Juliet that if they wanted to leave he would have to calculate a new bearing, and to do that he would need to know what time they were presently in ("The Lie").
See also: Mid-air break-up
According to the producers, the high field magnetic surge that occurred during Desmond's system failure at the Swan station caused Oceanic Flight 815 to crash. They also went so far as to state that this surge also caused the disruption or destruction of electronic systems on the plane itself. (Lost: The Answers)
It is possible for high amounts of magnetism to destroy avionics equipment, although it is unknown if extremely high amounts of electromagnetism could cause a catastrophic mid-air break-up.
That said, the strength of magnetism required to cause avionics failure depends on the plane's altitude at the time of the magnetic event, which, in the case of Ocean Flight 815's crash, is ambiguous. In "Pilot, Part 1", Jack suggests that the plane was at 40,000 ft AGL when the failure began. The horizon, visible from inside the airframe after the loss of the tail in this same episode, is clearly above the cloud ceiling; the horizon is likely above 10,000 ft AGL, but not near 40,000 ft. Yet, "A Tale of Two Cities" shows the plane breakup at a significantly lower altitude, well below the cloud ceiling, probably under 5,000 ft AGL.
At an altitude of about 40,000 ft AGL, sufficient magnetic strength to cause avionics failure might be possible through highly advanced artificial means, but it is not geologically possible. Disruption of avionics at about 5,000 ft AGL is within the realm of field strengths reachable in special laboratories - but, it is still tens of thousands of times stronger than geologic causes. The electromagnetism on the Island, however, has unique properties and, as it is implied that a large discharge could have catastrophic consequences, it clearly has immense magnitude. Using this information, we can tell that the Island has extremely powerful magnetic forces, since no magnetism known to science could tear apart a plane, even if it was flying below cloud level.
In "Greatest Hits", Juliet stated that the Looking Glass station is responsible for blocking outgoing electric communications signals. Sayid also states that the broadcast from the radio tower is causing interference with the satellite phone.
It is difficult to imagine why this would occur. The radio tower presumably is broadcasting longwave radio signals, which are well outside the spectral bandwidth of a gigahertz-range microwave phone. Likewise, a submerged station is an exceedingly poor location for broadcasts of any type, except for ULF and similarly low frequencies, and regardless wouldn't be capable of causing inference in a usable frequency range.
Thus, the exact nature of how signals from the Island are blocked is inadequately explained. Given that the signal from the radio tower has been picked up unblocked on the Island on multiple occasions, the Island must be outside the radius of the signal blocking. But, to accomplish that sort of block, requires facilities encircling the Island at a reasonable distance from the Island. It also uncertain how so much broadcast bandwidth can be effectively blocked.
It has been suggested that the invisibility of the Island is caused by its incredibly strong magnetic field. Conventional physics suggests this is theoretically possible, but would require such a strong electromagnetic and gravitational field that it would wipe out all life on the planet. Also, any complete "cloak" would block contact in either direction, making the radio tower useless. Thus, the Island might be obscured through hindrances to navigation, such as a local magnetic field.
An alternate explanation is revealed when Daniel Faraday notices that "light scatters different here." This scattering is due to the "Faraday Effect," in which a magnetic field will rotate a polarized light source. The Island's strong magnetic field has this effect on the light. This could explain why the Island is "invisible" to outsiders: light scattered through the earth's atmosphere is (partially) polarized. If the light reflected by the Island is rotated by the magnetic field, then it is possible the Island is difficult to view until you are within the magnetic field's range. This would also explain why the sky turned "purple" during the discharge event (e.g. due to light scattering effects). Similarly, a strong magnetic field can rotate radio waves. This effect could explain how the Looking Glass station "jammed" radio signals off the Island.
The potential scientific explanation for the invisibility of the Island, however, does not explain how notoriously difficult it remains to be found; i.e., why it is apparently impossible to leave or return to the Island except by a specific bearing, nor does it explain how the Island "moves".
The tidal anomalies seen in "Whatever the Case May Be", which are unusual for a near-equatorial land mass, have sometimes been attributed to magnetic effects. Magneto-hydrodynamic  effects could account for this; still, under normal circumstances, water is not responsive to magnetism.
The presumed healing properties of the Island have also been attributed to magnetic effects. Magnet therapy, magnetic therapy, or magnotherapy, as it is more commonly referred to, is "new-age" alternative medicine claiming to effectively treat certain medical disorders through exposure to magnetic fields. There is current research into, but no precedent for, miraculous cures caused by magnetism in scientific literature. . Why some inhabitants of the Island would be affected (ex: Locke, Rose) and not others (ex: Ben), however, is unknown.
In describing how the DHARMA Initiative originally found the Island, Eloise Hawking explained that beneath the Island is a "unique pocket of electromagnetic energy. That energy connects to similar pockets all over the world." The DHARMA Initiative built a station known as the Lamp Post on one of these sites: a pocket located underneath a church in Los Angeles, California. The purpose of the station was to identify the location of the Island - which is always moving. Isaac of Uluru also referred to certain places in the world with great energy, spots on the Earth such as Uluru in Australia. He speculated that this energy may be geological or magnetic. ("S.O.S.") ("316")
As mentioned in the Swan Orientation Film, and seen various times in the 1970s timeline, electromagnetism was a subject of study by the DHARMA Initiative. The Swan station was intended to serve this purpose before the Incident.
As Stuart Radzinsky states, the purpose of The Swan was to "manipulate electromagnetism in ways we never dreamed of."("The Incident, Parts 1 & 2"). The Swan site was one of the most accessible sectors of the Island where magnetism was found. It was the focal point for at least three cataclysmic events linked to electromagnetism: The Incident, Desmond’s system failure, and the Discharge (see below). Similarly, the station contained many subtle hints about the source and nature of the magnetism on the Island.
Main article: The Incident (event)
The Incident occurred in July of 1977, during the Swan's construction. The DHARMA scientists, led by Stuart Radzinsky, set up a drill to bore directly into a massive pocket of electromagnetic energy. On the fourth day after Jack, Kate, Hurley, and Sayid arrived in 1977, the drill reached the pocket, releasing the energy. The result was a catastrophic event similar to a massive system failure in that everything metal was pulled toward the magnetic anomaly. Guns, tool chests, rebars, iron beams, scaffolding, oil drums, bulldozers, cranes, and industrial drills were all pulled into the shaft. Juliet, dragged into the shaft by a chain wrapped around her, then detonated a hydrogen bomb. It is not entirely known what happened after the hydrogen blast. ("The Incident, Parts 1 & 2")
According to the Swan Orientation video, the Swan was "originally constructed as a laboratory, where scientists could work to understand the unique electromagnetic fluctuations emanating from this sector of the Island." An unspecified incident, however, required the implementation of a certain protocol. This protocol was to be executed every 108 minutes, by entering a series of numbers in the Swan's computer (see pushing the button).
Kelvin Inman remarked in "Live Together, Die Alone" that a "charge" progressively “builds up” in or near the Swan, with an accompanying magnetic field. The procedure of "pushing the button" effectively discharges the amassed energies. Through this containment mechanism, the Swan appears to exercise some control over the electromagnetic field. In the event of a failure of the protocol, a fail-safe mechanism was installed.
Naturalistically speaking, magnetic fields are not "cumulative," though a field's strength can be varied by a corresponding physical change or a change in the associated electric field. Fields of the strength seen normally in the Swan are geologically impossible, but could be artificially produced (except for the high fields seen during system failures).
An unobserved theoretical particle predicted by many superstring theories, known as a magnetic monopole, could hold a "magnetic charge" greater than zero. Nearby high-energy subatomic collisions could produce these particles, which could be used to explain the periodicity of the magnetic field.
Normally, the magnetic field was depicted as relatively benign and apparently did not affect daily activities in most parts of the Swan. The only area where it was shown notable was in the main corridor, near the concrete barrier. However, there were no clear indications of exactly how strong the field was there during non-catastrophic operation. Desmond's comment in "Orientation" about "pain in his fillings" – ostensibly, gold, silver, tin, copper, or zinc amalgam, all nominally paramagnetic or diamagnetic – suggest that the field is still fantastically strong. Likewise, the degree of attraction shown three times (see photos and captions) is fairly strong. These observations are probably suggestive of the >1 tesla range.
However, when attempting to excavate the concrete barrier in "Everybody Hates Hugo", Sayid notes that the titanium plane part he used had "very little magnetic attraction" to the walls. He guesses the concrete seal is six to eight feet thick.
The electromagnetic forces under the Swan are extremely powerful. They were strong enough to tear apart a 777 passenger plane during the System Failure and pull heavy industrial equipment down a narrow shaft in The Incident. No electromagnetic force on earth is known to be that immense in strength.
The normal level in the station is higher than that of an MRI. This would cause anyone who had a tattoo (Jack) to have the metal ripped out of their skin. This is a very painful process and obviously had no effect on him. It pulled a key from his neck but didn't affect his tattoo.
Some have suggested that the metallic geodesic dome of the Swan computer room was a Faraday cage, which would protect the electronics inside. Conceptually, a Faraday cage would suppress the transit of electric fields through a given region of space; however, this does not extend to magnetic fields. For a Faraday cage to function properly, the metal blast doors must be shut (e.g. sealing the room) to create the shielding effect.
Alternate theory: This shape of this dome enables the dome to be held by gravity. This eliminates the need for a pillar in the middle of the room. A flat roof would require support in the middle. This forces all the weight to the sides, providing more room for the equipment. In addition, it is actually more stable and provides greater protection than a flat roof.
Main article: Blast door map equations
Several equations, likely related to electromagnetism, were written on the blast door map. Two notations potentially alluded to fields with strengths of "104 T" and "106 T," (T is the SI abbreviation for tesla), though the exact interpretation of these two writings is somewhat unclear. If these referred to magnetic field strengths, they were unimaginably strong. Interestingly, 106 tesla is easily sufficient field strength to crash an airplane through shearing forces but the effects of such a field on the Island would involve actions unseen, such as levitation and destruction of non-metallic objects (likely the death of all life on the Island).
Main article: System failure
In "Live Together, Die Alone", after Kelvin's death, a "system failure" occurred at the Swan as the button was not pushed in a timely manner. The Pearl station printout also indicated the same "system failure" and confirmed the correct date and time, which corresponded to the crash of Oceanic Flight 815. A huge surge of magnetic field strength occurred during this time connected to a considerable earth tremor across the Island. Desmond successfully entered the Numbers and pressed Execute which ended the system failure. Operations at The Swan appeared to return to normal with no visible change.
Main article: Discharge
Locke's destruction of the computer in "Live Together, Die Alone" effectively ended DHARMA's protocol and triggered a system failure after the countdown timer reached zero. When the system failure occurred, the magnetic field strength subsequently grew to enormous levels (easily >100 tesla), resulting in the Swan's gradual destruction as ferromagnetic items aligned within the field.
Desmond's activation of the Swan station’' fail-safe mechanism during this system failure caused a phenomena collectively known as "the discharge." Inside the Swan, this was seen as a white flash, similar to a nuclear double-flash. Outside, this was characterized as: loud low-frequency sound wave, earthquake, and bright pink/lavender spectral discharge in the atmosphere above the Island for several seconds. The hatch door was subsequently ejected along with a number of other items. The discharge was also detected at the tracking station in Antarctica. ("Live Together, Die Alone")
Locke, Eko, and Desmond, who were all inside the Swan during the discharge, were subsequently seen in "Further Instructions", largely unharmed and distributed throughout the jungle. Desmond's clothing and Eko's stick were ejected in this process. Later in the episode, the Swan's remains are seen as a deep crater, with metallic debris (or possibly rock) compacted at the bottom. Locke (and later Desmond) remark that the station apparently "imploded." Desmond further remarks that the "fail safe key must have detonated the electromagnetic anomaly" - although this brief explanation is scientifically meaningless.
In "Every Man for Himself", Tom remarked to Ben that the Other's have "been blind" and that their "comms are all down" and he couldn't "get them back up" since "the sky turned purple." Similarly, in "Not in Portland", Tom explains that "ever since the sky turned purple," some disruption precluded taking Ben off the island for medical treatment of his tumor. Sayid refers to the discharge in "Enter 77" in a similar way, and Mikhail in "Par Avion" refers to it as an "electromagnetic pulse" and confirms that it caused a disruption in the Others's communications equipment and capabilities. However, in "Through the Looking Glass", it is implied that the communications disruption may have been unrelated to the Discharge - being caused instead by jamming all communications from the Looking Glass station.
Based on Kelvin's comments, the activation of the fail-safe presumably ended the need for ongoing "containment" procedures. Additionally, this may have resulted in fundamental changes to the Island’s magnetic phenomena, although no persistent effects have been noted outside the Swan to date.
According to "Access Granted" on Lost: The Complete Third Season (DVD), the DHARMA Initiative broke into an electromagnetic anomaly on driling. The break allowed the magnetic field to leak out and the Swan was constructed over this area to serve as a sort of cork in the dam. DHARMA then formulated the Swan protocol as a means of temporarily closing the leak, but with the drawback that the field would would continue to build up and eventually break it. The fail-safe system permanently "sealed" the leak.
The science of the discharge is currently unknown and very difficult to explain. If the discharge is considered an instance of the magnetic field growing to enormous strengths and then shrinking to zero (or "normal") strengths, the "implosion" can be understood as the alignment of ferromagnetic and paramagnetic items with the field in that time period. The huge magnetic force required to "implode" the Swan would also compact nonmetallic matter (such as moist dirt), possibly to very high densities. The subsequent expansion of this material upon release of the field could explain the ejecta observed and the excavation of topsoil around the Swan station remains. Additionally, diamagnetic effects could be responsible for the apparent ejection of nonmetallic material. How Locke, Eko and Desmond survived is unknown.
Similarly, such a strong magnetic field can induce significant electric eddy currents in conductive materials, if the flux strength varies rapidly enough. This is often referred to as "electromagnetic pulse" or "EMP." Solid-state electronics are particularly sensitive to these effects and can be disrupted or damaged if the pulse is sufficiently energetic. Based on the observed magnitude of the discharge, it is plausible to assume that this could have occurred on many parts of the Island. Comments about the disruption of the Others's communications equipment can be understood in this manner.
The DHARMA Initiative also discovered another energy pocket on the Island there anothe station, The Orchid was later built. The DHARMA scientists, however, were using this pocket to conduct experiments in time travel. Pierre Chang noted that he was brought to the Island to research the Kerr Metric Equations, which some physicists believe could allow time travel, a property that the Island is known to have. Additionally in the Orchid Orientation Video, Dr. Chang notes that the energy pocket is "negatively charged exotic matter" which produces a Casimir Effect that allowing "unique experiments in both space and time". He also warns that the Island's electromagnetic properties are "highly volatile and unpredictable", a possible reference to The Incident. In the film's first "demonstration", the scientists attempt to shift a white rabbit 100 milliseconds in four dimensional space. ("There's No Place Like Home, Parts 2 & 3")
For reference, the energy at the Swan Station was considered about 30,000 times more powerful than that at the Orchid. ("The Variable")
In turning the frozen wheel beneath the Orchid station in "There's No Place Like Home, Parts 2 & 3", a sound is heard similar to that of the Discharge. A brilliant white light is also seen, reminiscent of the purple sky seen at the end of the second season. It is unknown if and how these events may be related.