Sometimes in Physics one builds a toy model to study some more complicated phenomenon. One example would be the Gross-Neveu model and its relation to QCD.

Now, consider the following situation in the context of the General Theory of Relativity (https://arxiv.org/abs/gr-qc/0612131, https://arxiv.org/abs/0901.2298):

One considers two equal masses connected by a massless rod. The lenght of the rod isn't fixed, but varies periodically with time so that the masses start together, get apart at a maximum distance, and get back together.

One finds that in that case, depending on how this internal movement is performed, the two massess have their fall accelerated or deaccelerated.

Now, I was given this to work with. I've questioned my advisor: what is the physical motivation behind it? His answer was: "because theoretical physics is this - we imagine one exercise and solve it, there has no physical motivation for it, it is because we want to compute things".

I've insisted, but he said he had no idea what this system could actually represent.

I don't know, but I don't like much this approach. It seems like math: we want to compute things, so we take one exercise out of our heads and do it. I believe that when we set out to research something there should be physics motivation for it. Why this system is important? Is it an approximation for something more complicated that needs understanding? Does it shed light on the understanding of some fundamental physics concept? These things.

So the question here is: this particular example, in the way I've described, is it in the end, some simplification to some real system that occurs in nature? Does it have some real physical relevance to be studied, or is it just one exercise to compute things really?

I've read the answer on this question of mine suggesting that it is somehow related to the so-called EMRIS (extreme mass-ratio inspirals). I've asked to my advisor about this, but he doesn't even know what is an EMRI, so he didn't know if it is related somehow.

  • $\begingroup$ By "have their fall accelerated" do you mean that if allowed to fall in freefall near the surface of the Earth the acceleration will vary? $\endgroup$ – garyp May 10 '18 at 18:55
  • $\begingroup$ Possibly related: Papapetrou, Proc. Royal Soc. London A 209 (1951) 248. MTW, p. 1121. arxiv.org/abs/gr-qc/0612131 arxiv.org/abs/gr-qc/0510054 Scientific American, Eduardo Gueron, Aug 2009 $\endgroup$ – user4552 May 10 '18 at 21:02
  • $\begingroup$ @garyp yes, that's the point. If that system is in free fall in Schwarzschild spacetime, falling radially, the acceleration will vary according to the oscilation pattern. $\endgroup$ – Gold May 10 '18 at 21:12
  • $\begingroup$ @BenCrowell, the first arxiv paper you quote (The relativistic glider) describes the system and the result in question, about which I'm asking here. $\endgroup$ – Gold May 10 '18 at 21:12
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    $\begingroup$ @user1620696: So...I'm confused. Did you already know that people had previously worked on this? Your description made it sound like a new research program. Are you asking what is the physical motivation for a preexisting research program? Is it a situation where you've read all this other literature on this topic, but you feel that the topic is poorly motivated? If that's how you feel, then maybe you should just tell your advisor that this doesn't seem like an interesting topic, and you don't want to work on it. $\endgroup$ – user4552 May 11 '18 at 3:56

Toy models like this are typically used to help understand the "problem of motion" in general relativity, which is not as intuitive as you might think. They typically describe a simplest possible model with certain attributes (in this cases a system with a time dependent quadrupole moment). They can be used to scope out different effects.

For example, in this particular toy model one finds that the radial free fall acceleration can be modified by adjusting the frequency of the oscillating dumbell. The immidiate question that comes to mind is whether this effect can be big enough to to completely cancel the radial free fall. If answer in positive this would have huge implications (you have just found away to make a levitating car!).

However, in this case the answer is negative, which is a lot less useful as it is unclear if this is due to a fundamental limitation of GR or due to an arbitrary constraint of the toy model.


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