Gravity Shambles

I have been listening to the enjoyable podcast book shambles with Robin Ince and Josie Long. The episode with Fay Dowker, a cosmologist, had me scratching my head at one point. She was discussing how, if people payed attention more carefully to their direct experience of the world, this could have helped them to understand some physical laws quicker. As a general point this doesn’t seem too controversial, though runs counter to what I have always thought of, and read about, as the prevailing trend in the history of science. That is that we need to overcome our naive experience of the world to see a little deeper. Obvious examples being the shift from a kind of Aristotelean physics to that of Newton, or Galileo’s use of a telescope to view the sky rather than just trusting his eyes. Nonetheless that the opposite can also be true sometimes seems quite reasonable.

It was the example given that confused me. I will try and summarize it here, hopefully not doing a disservice to it! Imagine you are sitting on a chair, without thinking about it one should say what you are feeling in your bottom. Most people will say that the chair is pushing up on them, and this is indeed the desired answer. At this point I thought the point was going to go onto Newton’s third law – that when one body exerts a force on another, there is an equal and opposite force being exerted in return. (The chair is pushing you up as you are pushing down on the chair.) I was quite spectacularly wrong with that guess! Instead Fay Dowker then asked what do we not feel? Well, we don’t actually consciously feel anything pulling us down. We don’t experience gravity in this situation, not as a force. This was proposed as an insight which tells us that there is something wrong with Newtonian physics which relies on forces, whereas in Einstein’s theory of gravitation no mention of forces is made, which we now know to be a more complete theory of gravity.

I have a major problem with this line of argument though. It is true that normally one does not talk about forces in Einstein’s general theory of relativity (the name for his theory of gravity). Instead space and time themselves are described as distorting and curving around mass, and objects are just trying their best to follow straight paths in this space-time. This is where talk of rubber sheets and weights normally comes in, which I have always found a little unsatisfactory as the weight is only distorting the rubber sheet because of gravity. What kind of explanation of gravity relies on gravity! (I am only being half serious here…)

But what does the general theory of relativity have to say about the situation at hand, you sitting on a chair. Well, it has to agree with Newton’s theory of forces doesn’t it! If it didn’t it wouldn’t agree with everything we have learnt about gravity in the time since Newton that we see played out in the world around us. Differences between the theories, though they may be metaphysically quite distinct, only show up in observation and experiment at large scales or with very large masses. Not between the earth, a chair, and you (or me).

In fact it is not so difficult to start with Einstein’s theory and derive Newton’s for a simple set up. For example just you and the earth, at some distance from each other. (This is obviously a very specific meaning of “not so difficult” which assumes one has already spent half a year learning the maths needed to do general relativity, once you’ve got that bit done you are almost home and dry!) How does one go from distorted and curved space, to a force? Well, on the scale we are talking about most of this curvature just can not be seen, it is just too small, and we can safely ignore it. What we are left with is a quantity which varies in space which we call a ‘potential’, which depends on where you are, and where the earth is. The way in which this potential varies tells us what the force of gravity looks like, and of course this ends up agreeing with Newton’s law. If it didn’t Einstein’s theory would have been abandoned long ago, probably by Einstein himself!

So, if our experience does not agree with Newton on this thought experiment, then it doesn’t agree with Einstein either! It can’t possible favour one theory over the other, and it certainly isn’t telling us that forces aren’t real. So what is going on? Well, probably it is entirely down to how your brain works. Bearing in mind that we feel the effects of gravity all the time, it would be rather odd of the brain to be constantly telling us that we are being pulled down, but I am straying rather too far into conjecture now. As a last thought I don’t think it is so hard to find scenarios where we do feel the effects of gravity as a force… can you think of any?

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