I apologize if this is ill defined or overly speculative.(adsbygoogle = window.adsbygoogle || []).push({});

As far as we know, mass is a permanent characteric of all particles, so we have three disjoint possible categories of particles: bradyons (particles with timelike world-lines), luxons (lightlike world-lines), and tachyons (spacelike).

I assume that all users of PF are human beings, so presumably you're an observer made out of bradyons. You can therefore verify empirically that it's possible to make an observer out of bradyons under the conditions that pertain in the present cosmological epoch, in 3+1 dimensions.

What about luxons? There's the dictum that you can't make a clock out of photons, which is based on the fact that Maxwell's equations in a vacuum in 3+1 dimensions are conformally invariant. You would think that any set of ingredients too impoverished to make a lowly clock wold surely be too poor to build an observer. But this thread https://www.physicsforums.com/showthread.php?t=514558 clarified for me that "you can't make a clock out of photons" really just means that without massive particles, you can't define a persistent, universal *standard* for measuring time. Based on arguments given in that thread, it seems clear to me that, starting with just photons, you can build up massive objects, and out of these massive objects you ought to be able to make observers. Such an observer would presumably have a center of mass with a timelike world-line, since lightlike frames of reference don't exist (in the limit of [itex]v\rightarrow c[/itex] a Lorentz transformation isn't one-to-one). This seems reasonable, since the sum of non-parallel lightlike vectors from the future light-cone is a timelike vector.

In clarifying my own ideas, I found it helpful to apply this to Penrose's conformal cyclic cosmology (CCC), even though that theory no longer seems viable. In CCC, there's a phase where the universe "recycles" itself. It doesn't seem like it would make sense to have an observer around to observe the recycling, since it's hard to imagine how that observer's observations would be consistent with any laws of physics. But that's probably OK, because in an open universe with a nonzero cosmological constant, only a finite number of computations is possible (Krauss, http://arxiv.org/abs/astro-ph/9902189 ).

I'm curious about the tachyonic case. Tachyons are different from luxons in that the sum of non-parallel spacelike vectors can still be spacelike. Therefore it seems reasonable that, if tachyons existed, there could be tachyonic observers whose centers of mass were tachyonic. But Gorini has proved a no-go theorem that says that tachyonic frames of reference are impossible in 3+1 dimensions (V. Gorini, "Linear Kinematical Groups," Commun Math Phys 21 (1971) 150, open access via project euclid: http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.cmp/1103857292 ). Therefore it seems that in 3+1 dimensions, nature must somehow conspire to prevent a system of tachyons (even assuming, hypothetically, that they exist) from interacting so as to form an observer with a tachyonic center of mass. I don't see what it is that prevents this.

Tachyons aren't consistent with causality, in the sense that in any classical or quantum-mechanical system containing tachyons, we probably don't have existence and uniqueness for solutions of Cauchy problems. It's not obvious to me what it would mean to be an observer in a universe without causality. An observer is someone who measures things, and a measurement has a cause (the thing being observed) and an effect (the storage of information that can be remembered in the future but not in the past).

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# What ingredients can make an observer?

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