Why is gravity a fictitious force?

[Demystifier]

Okay, then we're back to my original criticism: the first particle, not the second, is the one that's affected by the electric field. So any acceleration measured by the accelerometer should be assigned to the first particle, not the second, since it's the one that feels a force.

I don't see any problem with that. The second particle is a measuring "apparatus", which measures a property of the first particle. All measuring apparatuses are of this form. (Of course, the second particle also feels a force, the one due to the interaction with the first particle, but the second particle does not feel the force of the external electric field.)

I believe my toy model is a good model of an accelerometer, in the sense that it captures all essential properties of the real accelerometer, and yet does it in a very simple way.

 

[PeterDonis]

I don't see any problem with that.

But it's not what your description said. You said:

by observing the relative position $q_2-q_1$ one can determine the acceleration $\ddot{q_2}$. That's how the accelerometer measures the acceleration.

That says that the accelerometer is measuring the acceleration of particle 2. But now you appear to be agreeing with me that it's measuring the acceleration of particle 1. That means the math you should be showing should be for $\ddot{q}_1$.

 

[Demystifier]

But it's not what your description said. You said:


That says that the accelerometer is measuring the acceleration of particle 2. But now you appear to be agreeing with me that it's measuring the acceleration of particle 1. That means the math you should be showing should be for $\ddot{q}_1$.

You are right, I should have been more precise about that. In a direct sense it determines $\ddot{q}_2$. But indirectly it determines also $\ddot{q}_1$. How? Because I assume that the spring does not oscillate, i.e. that $q_1(t)$ and $q_2(t)$ are comoving, so $\ddot{q}_2=\ddot{q}_1$. That's what I tacitly assumed when I said that it is an accelerometer, because that is essentially how the real accelerometer works. To provide that there are no oscillations of the spring I could have added a dumping term which dumps the oscillations after a short time, which would make the model even more realistic, but I felt that this detail is not essential for my point. Now I see that maybe it is.

 

[Demystifier]

One additional note. My model of the accelerometer with only one apparatus degree of freedom $q_2$ is analogous to the von Neumann model of the measuring apparatus for quantum measurements, which also involves only one apparatus degree of freedom. The need for a dumping term to make the accelerometer more realistic is analogous to the need of decoherence to make a model of quantum measurement more realistic.

I could have made the analogy even more explicit by taking a different model of an accelerometer, by introducing the interaction Hamiltonian of the form
$$g(t) p_2 a_1$$
where $g(t)$ is a time-dependent coupling. Such an interaction establishes a direct correlation between the apparatus pointer variable $q_2$ (conjugated to the momentum $p_2$) and the acceleration $a_1$ of the measured object, in exactly the same way as in the von Neumann model. However, such a model would less resemble the working of the real accelerometer.

 

[PeterDonis]

To provide that there are no oscillations of the spring I could have added a dumping term which dumps the oscillations after a short time

I think you mean damping here, and yes, that is important, for the reason you give (and it's the reason why real accelerometers have damped springs).

 

[Demystifier]

I think you mean damping here, and yes, that is important, for the reason you give (and it's the reason why real accelerometers have damped springs).

Yes, sorry for the misspelling!

 

[Demystifier]

Where did Einstein say this? Since many things were measured prior to the development of the corresponding theory, that seems like a pretty difficult claim to justify. Even if Einstein did say it.

A quote from the book A. Becker, What is Real?

Safely ensconced in his apartment, Einstein finally asked Heisenberg what he really wanted to know.
"You assume the existence of electrons inside the atom, and you are probably quite right to do so. But you
refuse to consider their orbits.… I should very much like to hear more about your reasons for making such
strange assumptions."
"We cannot observe electron orbits inside the atom," replied Heisenberg. He pointed out that only the
spectrum of light from an atom is really observable and concluded with a rather Machian statement.
"Since a good theory must be based on directly observable magnitudes, I thought it more fitting to restrict
myself to these."
In Heisenberg's later retelling of this encounter, Einstein was shocked at this. "But you don't seriously
believe that none but observable magnitudes must go into a physical theory?”
"Isn't that precisely what you have done with relativity?" replied Heisenberg.
"Possibly I did use this kind of reasoning, but it is nonsense all the same," said Einstein. "In principle, it is quite wrong to try founding a theory on observable magnitudes alone. In reality the very opposite happens. It is the theory which decides what we can observe."

 

[PeterDonis]

"Possibly I did use this kind of reasoning, but it is nonsense all the same," said Einstein. "In principle, it is quite wrong to try founding a theory on observable magnitudes alone. In reality the very opposite happens. It is the theory which decides what we can observe."

Sounds like typical Einstein, like when someone asked him what he would have done if experiments had not confirmed the predictions of relativity, and he said he'd feel sorry for God, but the theory is correct.

https://skeptics.stackexchange.com/...ld-feel-sorry-for-the-good-lord-the-theory-is

 

[PeterDonis]

"In principle, it is quite wrong to try founding a theory on observable magnitudes alone. In reality the very opposite happens. It is the theory which decides what we can observe."

One could interpret this as saying that the theory might have to make use of unobservable quantities, but it will predict what we will and will not be able to observe. But we still have to test those predictions.

 

[Dale]

A quote from the book A. Becker, What is Real?

Which is not a professional scientific publication.

It is the theory which decides what we can observe

And this remains a false statement. Many seminal observations were made prior to the existence of the relevant theory.