Right, I asked myself the same question when writing my comment. I mean that infinities cannot be measured and that the current observations can be explained with infinity-free models, though sometimes not as elegantly.
There are no intensive infinities in physics.
That roughly means you cannot have an infinite amount of something in a finite volume of space. It doesn’t stop you you having an infinite amount of space.
Which kind of model does an instrumentalist use to guide their actions in this situation? The ones with infinities, the ones without, or a probabilistic mixture of the two kinds? It seems like you’re saying just use the ones without infinities (since in either of the other two cases we do have to deal with Boltzmann brains). But how do you justify that?
Which kind of model does an instrumentalist use to guide their actions in this situation?
In what situation? Calculus of infinitesimals is a convenient tool invented by Newton and Leibnitz to calculate planetary orbits and other things. The same can be done with differences and not differentials (and is, for numerical calculations), but requires more work. The situation is similar in most other areas. Kronecker delta is a convenient tool in physics and electrical engineering, without necessarily meaning that there is an infinitely strong and infinitely short spike of current somewhere in your circuit.
The original concern was that the evidence points to the infinite universe, therefore everything imaginable happens somewhere. While this can be a fun speculation, I am merely pointing out that the evidence so far points to a very large universe, but not necessarily infinite or even close to large enough for Boltzmann brains.
Right, I asked myself the same question when writing my comment. I mean that infinities cannot be measured and that the current observations can be explained with infinity-free models, though sometimes not as elegantly.
There are no intensive infinities in physics. That roughly means you cannot have an infinite amount of something in a finite volume of space. It doesn’t stop you you having an infinite amount of space.
Which kind of model does an instrumentalist use to guide their actions in this situation? The ones with infinities, the ones without, or a probabilistic mixture of the two kinds? It seems like you’re saying just use the ones without infinities (since in either of the other two cases we do have to deal with Boltzmann brains). But how do you justify that?
In what situation? Calculus of infinitesimals is a convenient tool invented by Newton and Leibnitz to calculate planetary orbits and other things. The same can be done with differences and not differentials (and is, for numerical calculations), but requires more work. The situation is similar in most other areas. Kronecker delta is a convenient tool in physics and electrical engineering, without necessarily meaning that there is an infinitely strong and infinitely short spike of current somewhere in your circuit.
In the situation that infinite and finite cosmological models can both explain all current observations. Isn’t that the topic of this thread?
The original concern was that the evidence points to the infinite universe, therefore everything imaginable happens somewhere. While this can be a fun speculation, I am merely pointing out that the evidence so far points to a very large universe, but not necessarily infinite or even close to large enough for Boltzmann brains.