Recent content by Roberto Pavani

My fault. I didn't realize you meant a constant "cosmological constant".

Doesn't this requires that ## \int_{t_0}^{\infty}\frac{dt}{a(t)} ## to be finite ? Acceleration itself doesn't allow this. As an example: Suppose ## a''(t)>0 ## but ## a(t)=t\log(1+t) ## gives: ## \int_{t_0}^{\infty}\frac{dt}{a(t)} =\int_{t_0}^{\infty}\frac{dt}{t\log (1+t)} =\infty. ## In...

Strongly agree

Yes, we can Note: acceleration is ## \approx 9.81 \frac m { s^2 } ## because ## g \propto \frac 1 { R^2 } ##

V = 0 doesn't matter. Throw C upward: at the top ## v=0 ## for an instant, but C ir's still free-falling all the time (accelerometer = 0). This video can provide a rough idea:

I never specified the height where the stones are, A can be on the ground, while B and C on the rooftop with C falling from there. In that case your question is just a relabeling of B <-> C

You have to specify the reference frame to define motion, that's the key. Here perhaps a too simple explanation: Three stones: A and B rest on the ground, C falls. A: "B is at rest relative to me, we both feel an acceleration (## F/m = g ##), and C falls toward us." C: "I feel nothing (## F/m...

I think the two spaces have to be kept separate, like Fourier space vs the function space the transform acts on. Then you can set up a relation pairing each ## (x,E_i ) ## in ## \mathbb{R}^4 ## with a ## ( y, M_i ) ## in ## \mathbb{R}^{3,1} ##. However, the Lorentzian structure would still live...

Only if you solve the problem of time, as PeterDonis pointed out, in R4 you have four spatial directions and no time. Some related work: analogue gravity (Barceló, Liberati & Visser, Analogue Gravity, Living Rev. Relativity 14, 3, 2011), effective Lorentzian metrics emerging from...

That's a good question. Within the Standard Model, fields are simply part of the starting assumptions of the theory; they are not explained in terms of something more fundamental. Whether they are ultimately fundamental or emergent is unknown. In short: I don't know.

I don't think it is correct to say that particles and fields are made of mass. In the Standard Model, fields are the fundamental ingredients, particles are excitations of those fields, and mass is one of their physical properties.

Fair point, let me be precise, because I mean something stronger than ordinary indirect inference. With a microscope, the object and the probe live at the same level: light reaches the cell. That's indirect observation of something in principle accessible. What I have in mind is the case...

Fair enough, I missed a comma. “We have an upward proper acceleration, with ‘upward’ defined relative to a local freely-falling frame.”

A single self-report is only one output of the system. In the systems-theoretic sense, observability requires that the internal experiential state be uniquely reconstructible from a sufficient history of inputs and outputs.

I think the phrase "we are accelerated upward" can be misleading if taken too literally. We are not moving upward relative to the Earth. Rather, we have an upward proper acceleration relative to a local freely-falling frame.