There isn’t much to check at the most basic level (m_i L theta” = - m_g g theta, where m_i is the inertial mass, m_g the (passive) gravitational mass, L the length of the pendulum, so the period depends of sqrt(m_i/m_g)), but the fun is to find out what the most important systematics can be. There are TONS of systematics affecting the system enough that you need to model them, even to 10^-3 in relative error in m_i/m_g. That’s the pedagogically useful part imho. As for the possibility of finding new physics: clearly very low, bet here: https://manifold.markets/mariopasquato/will-i-find-a-violation-of-universa?r=bWFyaW9wYXNxdWF0bw
Edit: current theories of gravity may well be wrong in some regime (as in making predictions that contradict experimental results). We can assign a low probability to that, but certainly not zero. The question is whether theoretical predictions will depart from empirical results _in this regime_. We can’t possibly know that until we actually try. A positive result (a violation signal) is not that unlikely to emerge (manifold has it at 5% which still seems high to me, but we know that prediction markets struggle with low probabilities) but will probably be due to systematics. Still, until you fully understand those systematics or redo the experiment with a more sensitive setup, you can’t possibly know whether that’s a genuine violation instead! That’s the beauty of empirical research. Conversely a null result is a worthwhile result (contrary to what you say). It means that there is no detectable violation at this level of error. That is also something we would not know before running the experiment.
> We can’t possibly know that until we actually try.
Yes, we can, that's kind of the point of modern science. We can't know everything, but we do definitely know some things.
You might as well put together an experiment where you ship people two sets of a billion M&Ms and ask them to put them together in a pile and count them to empirically verify that 1 billion + 1 billion = 2 billion.
The fun fact is that if you actually attempt this even for much smaller numbers (say in the thousands) you will find that in fact quite often arithmetic predictions are disproven by experience (though we choose to say that people make mistakes in counting, that is we consider a physical theory made up of arithmetics + assumptions about people's counting abilities and conclude that this theory is disproven by experience, while we suspect that arithmetics + some different way to operationalize "counting" would not). At any rate the "adding M&Ms" thing is a strawman: there is clearly much more uncertainty around theories of gravity than around adding M&Ms. Furthermore a violation of universal free fall may be due to a fifth force, which would not necessarily require us to question our understanding of gravity.
There isn’t much to check at the most basic level (m_i L theta” = - m_g g theta, where m_i is the inertial mass, m_g the (passive) gravitational mass, L the length of the pendulum, so the period depends of sqrt(m_i/m_g)), but the fun is to find out what the most important systematics can be. There are TONS of systematics affecting the system enough that you need to model them, even to 10^-3 in relative error in m_i/m_g. That’s the pedagogically useful part imho. As for the possibility of finding new physics: clearly very low, bet here: https://manifold.markets/mariopasquato/will-i-find-a-violation-of-universa?r=bWFyaW9wYXNxdWF0bw
Edit: current theories of gravity may well be wrong in some regime (as in making predictions that contradict experimental results). We can assign a low probability to that, but certainly not zero. The question is whether theoretical predictions will depart from empirical results _in this regime_. We can’t possibly know that until we actually try. A positive result (a violation signal) is not that unlikely to emerge (manifold has it at 5% which still seems high to me, but we know that prediction markets struggle with low probabilities) but will probably be due to systematics. Still, until you fully understand those systematics or redo the experiment with a more sensitive setup, you can’t possibly know whether that’s a genuine violation instead! That’s the beauty of empirical research. Conversely a null result is a worthwhile result (contrary to what you say). It means that there is no detectable violation at this level of error. That is also something we would not know before running the experiment.
> We can’t possibly know that until we actually try.
Yes, we can, that's kind of the point of modern science. We can't know everything, but we do definitely know some things.
You might as well put together an experiment where you ship people two sets of a billion M&Ms and ask them to put them together in a pile and count them to empirically verify that 1 billion + 1 billion = 2 billion.
The fun fact is that if you actually attempt this even for much smaller numbers (say in the thousands) you will find that in fact quite often arithmetic predictions are disproven by experience (though we choose to say that people make mistakes in counting, that is we consider a physical theory made up of arithmetics + assumptions about people's counting abilities and conclude that this theory is disproven by experience, while we suspect that arithmetics + some different way to operationalize "counting" would not). At any rate the "adding M&Ms" thing is a strawman: there is clearly much more uncertainty around theories of gravity than around adding M&Ms. Furthermore a violation of universal free fall may be due to a fifth force, which would not necessarily require us to question our understanding of gravity.