304. Science in Watchmen. How Ozymandias prevented Dr. Manhattan from seeing the future
Save This Post as PDFIf you have already seen “Wathchmen” (and/or have read the Moore’s graphic novel), recall that one of the main pillars of the storyline is the fact that Adrian Veidt (Ozymandias) used generators of tachyons located in his playboy hideout in Antarctica to prevent Dr. Manhattan from seeing the future and being able to affect Veidt’s plot of saving humanity from self-destruction.
So, how did the trick work exactly (and does it have any meaning to even talk about tachyons in the real world)?
Tachyons are hypothetical particles moving with the speed faster than the speed of light in vacuum 
km/s. Probably, the first person who thought about them in a constructive way was Eugene Wigner (photo on the left), a genius (well, almost every physicist of that generation was genius, isn’t it true? 
) who was also the first to introduce group theoretical methods in physics. He has basically figured out that one of the irreducible representations of the Lorentz group contains tachyons.
But physics of tachyons is surely more interesting than their history… The first interesting feature of a tachyon is that its mass is actually imaginary. Let us check this explicitly. The relativistic relation between the energy 
of the particle and its momentum 
reads
,
where 
is the velocity of the particle. The mass of the particle squared is in turn given by
.
Therefore, if the velocity of the particle 
, then 
, and the mass of the tachyon itself is indeed imaginary.
This is actually a very serious problem since the energy of the tachyon decreases with velocity growth:
(note that 
is real and positive in the formula above). So, it is energetically favourable for tachyons to move faster and faster (infinite speed 
corresponds to vacuum 
!), and it is possible for us to steal energy from tachyons – and provide an infinite source of energy for Humanity’s needs. Maybe that’s exactly how Veidt wanted to solve energy problems of the Mankind in the movie
Anyway, let us now see how he tricked Dr. Manhattan using generators of tachyons. The reason why Dr. Manhattan played damn fool is a contradiction between existence of (free) tachyons and causality. What does exactly the word “causality” mean in special relativity? The meaning is actually very simple: the timing (sequence) of two events related by a signal exchange can never be inverted by a coordinate transformation (that is, transformation of the reference frame). In other words, cause is always earlier than the effect in arbitrary frame of reference, which sounds quite reasonable, doesn’t it?
Let us now see explicitly how tachyons allow to violate causality. Let us consider two spacetime events 
and 
related by a tachyonic signal exchange:
, 
.
In the reference frame that moves with a velocity 
such that
we have
,
i.e., cause and effect were exchanged. That’s exactly the reason why Dr. Manhattan could not foresee the future. The poor guy was probably able to see all events but wasn’t able to rearrange them into a sequence – to figure out what causes what
Well, let me ramble a little bit more… Tachyons, if they exist, cannot carry information. They can connect events, though, if by connection we understand that events are equivalent (whatever this crap means). For example, there is always a reference frame where the tachyon propagates with infinite speed, i.e., it is emitted and absorbed in different space points at the same moment of time 
(so yes, if you allow tachyons, then relativity is dead as a concept and we are back to Galileo era).
Via Abstruse Goose.
To conclude this rambling, let me mention that the lowest energy state in non-critical string theory (as well as critical bosonic string theory) is a tachyon (its ), which allows many people to argue that the vacuum of non-critical string theory is unstable and may only achive stability after tachyon condensation.
So, if Adrian Veidt was able to figure out how non-critical string theory works and even get string theoretic effects in the lab, he could indeed be considered as the smartest man in the world
Update (by Haelfix): For completeness sake, the story doesn?t quite end there and makes for further interesting scifi possibilities, though of course it does becomes more and more controversial depending on who you talk with. You could mention the Feinberg reinterpretion of tachyons, where such things do NOT violate causality b/c they do not carry information into their past light cone.
Scalar fields in spontaneous symmetry breaking are also examples of the condensation and vacuum instability.
Update (by Lubos Motl): The “stealing” of energy from tachyons is pretty much the same process as the tachyonic fields rolling down from the hill, signaling the instability.
Tachyons? energy cannot be kept positive in a Lorentz-invariant way – whether it?s positive or not depends on the reference frame. So the fastest way to steal energy is to give tachyons a huge negative energy. Because it can be much greater than the absolute value of the tachyon rest mass, tachyonic particle-antiparticle pairs can be spontaneously created from the vacuum (with momenta which are spacelike and opposite; there is no separation between the set of positive-energy and negative-energy momenta for them).
A (multiple pair) creation of tachyons is a microscopic description of the process of rolling down the hill. In a fock basis, the coherent states moving the tachyon field away from the unstable maximum correspond to many particle excitations.
Only theories which contain at least metastable minima of the potential, aside from the unstable maxima, can support a world where physicists have enough time to make experiments. 
Further reading
1. Brian Greene. Elegant Universe. Superstrings, hidden dimensions and the quest for the ultimate theory.
2. Barton Zwiebach. First course in string theory (2nd Edition).
Update: In order to check how carefully you read the post, I’ve planted a picture of Enrico Fermi instead of Eugene Wigner in the earlier version of the post Kudos for discovering my terrible plot go to Massimo Bedini.
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For completeness sake, the story doesn’t quite end there and makes for further interesting scifi possibilities, though of course it does becomes more and more controversial depending on who you talk with. You could mention the Feinberg reinterpretion of tachyons, where such things do NOT violate causality b/c they do not carry information into their past light cone.
Scalar fields in spontaneous symmetry breaking are also examples of the condensation and vacuum instability.
Hi Dmitry, nice writing and a funny cartoon.
The “stealing” of energy from tachyons is pretty much the same process as the tachyonic fields rolling down from the hill, signaling the instability.
Tachyons’ energy cannot be kept positive in a Lorentz-invariant way – whether it’s positive or not depends on the reference frame. So the fastest way to steal energy is to give tachyons a huge negative energy. Because it can be much greater than the absolute value of the tachyon rest mass, tachyonic particle-antiparticle pairs can be spontaneously created from the vacuum (with momenta which are spacelike and opposite; there is no separation between the set of positive-energy and negative-energy momenta for them).
A (multiple pair) creation of tachyons is a microscopic description of the process of rolling down the hill. In a fock basis, the coherent states moving the tachyon field away from the unstable maximum correspond to many particle excitations.
Only theories which contain at least metastable minima of the potential, aside from the unstable maxima, can support a world where physicists have enough time to make experiments.
Hi Dmitry, great post … but isn’t that Enrico Fermi ?
Haha, yes, it is
Kudos to you, you were the only one who noticed 
Actually, kudos goes to my brother that pointed this out to me.