Using different theories at the same time

Scientists, especially astronomers, use several incompatible theories in their calculations.  How?  And why?

“Doublethink,” a term coined in George Orwell’s novel 1984, means holding two contradictory ideas in your head at the same time.  The phenomenon certainly didn’t begin with him, though he showed how terrible it could be.  (We suspect that few people have bothered to read the book since its eponymous year.  If many had, there’s no possibility of a hit TV show being named “Big Brother.”)

Stepping back and thinking about it, our astronomer noticed that his peers may, at various times, use any one of several theories to work out what’s happening (or might happen) out there somewhere.  A short list:

• Newtonian mechanics, the physics you learned in school if you learned anything.  Forces change an object’s momentum; mass is conserved, as is energy, separately.
• Quantum mechanics (QM), which gives the right answer for things like atoms when Newton gives the wrong one.  A scientist uses an operator on a wave-function to work out what will probably happen.
• Special relativity (SR), Einstein’s 1905 work, necessary with high speeds; time and space can get traded off against each other, and mass can get converted to energy (and vice versa).  It teaches you to think in four-dimensional space-time.
• Electromagnetism (EM) in the “classical” form, which is not very compatible with QM but is completely in harmony with SR.  Lots of vectors.
• General Relativity (GR), which includes gravity; SR is GR without any gravity.  You have to think in four-dimensional curved space-time.
• Quantum Field Theory (QFT), which is QM expanded to include SR.  It can be unsettling because almost every number you calculate turns out to be infinity.

You could divide up theories and techniques in a different way, but this gives the general picture.  The important points are (i) you have to think in an entirely different way about a given situation when using a different theory, and (ii) the answers you get disagree among themselves, sometimes drastically.

And yet, astronomers in particular switch between them without bother.  One could deduce from a spectrum of a certain galaxy (using QM and EM) what it’s made of and how strong its magnetic field is.  The speed of its various parts (QM and SR) can be used to work out how its mass is distributed (Newton), which when placed within a cosmological model (GR) can help place bounds on some exotic particle (QFT).  And if anyone wants to make further observations, the coordinates of the galaxy are given in a geocentric form (which is, admittedly, not quite using Ptolemaic theory).

How could this possibly work?  In principle, you’d think that the theories that have been proven most accurately correct (QFT and GR) would be used all the time.  Well, the best answer is that the more accurate the theory, the harder the mathematics.  For example, to work out the possible orbits of two bodies around each other is an undergraduate exercise for a Newtonian; it’s impossible in the general case for GR (so you have to spend a lot of computer time to work out your specific case).  So you look for something good enouth: if you’re working with things much larger than atoms, you can generally use something simpler than QM or QFT.  If all your speeds are much slower than light, you needn’t bring in SR.  And if your gravitational fields aren’t really, really strong you can ignore GR.  Most of the time.  Knowing when you can use a simpler theory and still be accurate enough for your purpose is a learned skill.

But it’s still kind of amazing that an astronomer can switch between such different ideas and approaches all the time, without even thinking about it.  It must bewilder any tidy-minded philosopher.