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 $m$. 

ChatGPT-4 Truth about Special Theory of Relativity: Self-Evident!

In a conversation with GPT-4 about the meaning of the Principle of Relativity underlying Einstein's Special/General Theory of Relativity as a foundation of modern physics, GPT-4 reveals the following from reading physics literature:

• The principle of relativity, which asserts that the laws of physics should appear the same to all observers in inertial reference frames, is often considered self-evident or intuitively reasonable. It is a foundational principle that underlies our understanding of physical phenomena.
• In the context of special relativity, the constancy of the speed of light is derived as a consequence of the principle of relativity. By assuming that the laws of physics should be the same for all observers, regardless of their motion, it can be deduced that the speed of light must be constant for all observers.
• So, from the perspective of special relativity, the constancy of the speed of light can be seen as a consequence of the self-evident principle of relativity.
• In summary, the principle of relativity is often considered self-evident, and the constancy of the speed of light is derived as a consequence of this principle in the framework of special relativity. 

Let me summarise what GPT-4 has learned by reading physics literature:

• The Principle of Relativity is self-evident: Physics cannot be changed by non-interacting observers. Self-evident!
• The Constancy of the Speed of Light is a consequence of the Principle of Relativity.
• Conclusion: Constancy of the Speed of Light is self-evident = agreement!

To save modern physics from a collapse into something merely self-evident = agreement = tautology, GPT-4 presents the following caveat: 

• However, the constancy of the speed of light itself is supported by empirical evidence rather than being self-evident in the same direct sense as the principle of relativity.

This is the trick borrowed from Einstein: The constancy of the speed of light is both an agreement, and a physical fact. Einstein played this trick in such a masterful way that everybody was fooled.

If you are a modern physicist, you will worship this trick as a deep scientific insight. If you are a mathematician understanding the difference between a definition or agreement, which is true by logic or the use of words, and a proposition or conjecture which may be true or false, you will find this deep insight to be empty. Your choice. 

In any case, GPT-4 gives a valuable insight into the minds of modern physicists without the the cover-up typically met in a conversation with a living modern physicist. Enlightening! 

You can test your understanding by answering the following question: Is the fact that there are 100 centimeters on a meter (i) a definition/agreement true by logic, or (ii) is it a physical fact which can be confirmed by physical experiment inspecting meter sticks?  

Helpdesk:  Recall that in the 1983 SI standard the meter as unit of length is defined in terms of a certain fraction of a lightsecond, which means that the constancy of the speed of light is an agreement: All observers following the SI standard agree on the same speed of light, exactly equal to 299.792.458 meter/second by definition/agreement. Physics by agreement! You can then get experimental support by inspecting a meter stick to see that is is exactly 100 centimeters long. Relativity theory in a nutshell.