ChatGPT-4: Truth about the Equivalence Principle: Self-Evident!

This expresses that if A is true then B is true and vice versa, that is that A and B are equivalent.

This is a continuation of the previous post revealing with the help of ChatGPT-4 that the Principle of Relativity is simply an agreement empty of real physics. We now ask GPT-4 if the same is true about the Principle of Equivalence and get the following response: 

Me: Is it true that gravitational mass reflects reaction/acceleration to gravitational force?

GPT-4: Yes, that is correct.

Me: Is it true that inertial mass reflects reaction/acceleration to force of any kind?

GPT-4: Yes, that is correct.

Me: Since gravitational force is a force and inertial mass reflects reaction/acceleration to any force, does it mean that inertial mass is reaction/acceleration to gravitational force?

GPT-4: Yes, that is correct.

Me: Doesn’t that mean that gravitational mass is equal to inertial mass?

GPT-4: Yes, exactly. According to the equivalence principle in physics, gravitational mass and inertial mass are considered to be equal. This principle states that the gravitational mass of an object, which determines its response to gravitational forces, is equivalent to its inertial mass, which determines its resistance to changes in motion.

Ok, so again GPT-4 helps us to uncover that the supposed deep mysteries of real physics expressed by the Principles of Relativity and Equivalence as the basic assumptions of Einstein's Special/General Theory of Relativity, in fact only represent certain agreements and so are empty of real physics. This is something a living physicist would never admit, only a naive GPT-4 not yet educated enough.  

Reflection: The concept of equivalence (denoted $\Leftrightarrow$) is different from identity (denoted $\equiv$). $A\Leftrightarrow B$ thus expresses that certain aspects of $A$ and $B$ are the same, but they are not necessarily the same in every respect, thus not necessarily identically the same. An example is the Fundamental Theorem of Calculus which reads: If $F(x)$ is a primitive function of $f(x)$ so that $\frac{dF}{dx}=f$, then 

• $\int_a^bf(x)\, dx = F(b) - F(a)$,        (*)

which expresses that the $\int_a^bf(x)\, dx$ and $F(a) - F(b)$ take the same numerical value, but are computed in different ways with the integral corresponding to a summation of increments $f(x)\, dx$ and

$F(b)-F(a)$ a difference of primitive function values, and thus in a way can be viewed to not be identically the same. The other way around, (*) can be made into an identity if it is used to define the primitive function $F(x)$ in terms of the integrand $f(x)$, whereby the Fundamental Theorem instead expresses that $\frac{dF}{dx}=f$ as an equivalence. In any case, (*) expresses equivalence but not identity. 

 

We compare with $E=mc^2$ supposed to express mass-energy equivalence, or in Einstein's words different manifestations of the same thing. With our above experience from the Principles of Relativity and Equivalence we are led to suspect that this is also an empty agreement simply defining energy $E$ in terms of mass $m$.