Recent content by Demystifier

In order to better explain all this to myself (and hopefully to others as well), I will present a simple toy model. Consider two point particles with positions ##q_1(t)## and ##q_2(t)## moving in one dimension. Suppose that the Lagrangian has the form $$L = \frac{m_1\dot{q}_1^2}{2} +...

@Dale and @PeterDonis I'm still somewhat confused, so I will ask a slightly more general question. Consider a Newton-like theory of gravity, but with inertial mass different from the gravitational mass. In such a theory, is the "gravitational" force a true force or a fictitious force? Can such a...

I still disagree to some level. If we define force as mass times acceleration, the acceleration is always relative to a specified reference frame, so even the electric force is relative in this sense. Of course, you are right if by acceleration you mean proper acceleration, which is not...

That works for a macroscopic body, but not for a microscopic particle.

How would you measure the electric force, without a reference to a frame? Note that the Coulomb theory of electric force is almost identical to the Newton theory of gravitational force.

I think we disagree on what does it mean to measure something. In my view, to measure something means to infer it from observing something else, which is correlated with the thing one wants to measure. So inferring the force from the motion, or from the position of a static object, is measuring...

E.g. by weighing scale.

As Einstein said, it is theory which determines what is measurable. According to the Newtonian theory of gravity, the gravitational force can be measured. GR, on the other hand, reinterprets this same measurement by claiming that such a measurement does not measure the gravitational force, but...

Well, for those who like Albert's style of writing, it's probably good. Personally I'm not a fan of his style, but I believe there is nothing wrong in it.

The Albert's Chapter 8 is very interesting on its own right. It considers a version of the Wigner's friend thought experiment, by which one can, in principle, simultaneously determine two non-commuting observables, thus violating the uncertainty principle.

The geodesic equation $$\frac{d^2x^{\mu}}{d\tau^2} + \Gamma^{\mu}_{\alpha\beta} \frac{dx^{\alpha}}{d\tau} \frac{dx^{\beta}}{d\tau} = 0$$ can be written as $$m\frac{d^2x^{\mu}}{d\tau^2} = F^{\mu}$$ where $$F^{\mu} \equiv - m \Gamma^{\mu}_{\alpha\beta} \frac{dx^{\alpha}}{d\tau}...

A lot of modern research papers investigates the possibility of aether. https://arxiv.org/search/gr-qc?query=aether&searchtype=title&abstracts=show&order=-announced_date_first&size=50

That's infinite for any ##N##, not only for ##N=3##, due to the infinite last term ##i=N## in the sum.

That is in accordance with the result by OP, who obtained ##KE=E-M=M##, which implies ##E=2M##. This demonstrates that my removal of the ##N##-th ring with the speed of light is justified. With bigger ##N## one should get a result even closer to 2. Indeed, ##N=10^4## gives 1.979...

Interesting! How much the last term ##i=N## contributes to the full sum? What happens if you take ##v=1## but compute the sum only up to ##N-1##? What happens with larger ##N##, say ##N=10^4##?