In a previous post "No Cause to Dispute Einstein" I explained that travel faster than the speed of light c is not forbidden by Einstein's theory of special relativity, despite recent media reports. I pointed out that the real problem with superluminality is the way it can interchange cause and effect. Let me try to illustrate how this comes about, using my example of the 1804 duel in which Aaron Burr killed Alexander Hamilton.
Please refer to the figure FTL on my website. This is a space-time diagram in which the vertical axis is time and the horizontal axis is the distance along a line between Burr and Hamilton. The black dots represent two events is space-time: Burr firing a bullet toward Hamilton and Hamilton catching in his lower abdomen. The red line represents the path of the bullet in space-time. In this diagram, the paths of particles traveling at the speed of light are 45-degree lines. The dashed blue lines are the paths of photons. Since the bullet is moving at less than the speed of light, the slope of its paths is greater than 45-degrees.
The green line represents the paths of a tachyon traveling faster than the speed of light. Its slope is therefore less than 45-degrees.
The dashed blue line farthest to the left is the path of a photon from the place and moment that Burr fires his gun. It crosses the green line at the place and moment the tachyon sees Burr fire.
The next dashed blue line shows the path of the photons from when and where Hamilton gets hit to when and where the tachyon sees that event. Note that the tachyon sees the events in the order that we expect: Burr fires and later Hamilton gets hit. You can imagine a whole series of parallel blue lines allowing the tachyon the witness the whole flight path of the bullet.
However, now look to the right of the red line. There we see two additional dashed blue lines emanating from the same two events. Since the tachyon is going faster than c, it is able to overtake those photons and so it sees the two events again. Only this time it sees them in reverse order! The tachyon observes the bullet leave Hamilton's stomach and travel back into Burr's gun.
Suppose Burr had been brought to trial for murdering Hamilton. His defense attorney could have argued: "A witness moving faster than the speed of light would have seen the bullet go from Hamilton to Burr. So how can my defendant be held responsible?"
This is the paradox that Einstein dealt with by adding his principle of causality, which postulated that cause must always precede effect. However, in the years following Einstein physicists and chemists realized that no distinction is made between cause and effect in fundamental processes and, indeed, many seem to proceed spontaneously, that is, with no predetermined cause at all. So doing away with causality is no longer such a big deal.
This is not to say that causality is not still a useful concept in all branches of science including physics and chemistry, as well as everyday life. It's just that we cannot assume that it is a universal principle that applies in all circumstances.
For example, for years theologians have used the Kalam Cosmological Argument for the existence of God:
- Everything that begins must have a cause
- The universe had a beginning
- Therefore the universe must have had a cause
That cause is then assumed to be a personal God, although it seems to me that a natural cause is not logically ruled out.
On any case, the first premise fails because not everything has a cause. The second premise also fails because the universe need not have had a beginning, but I will leave than for another day.