Can ChatGPT Handle Complex Physics Questions Accurately?

[Demystifier]

Perhaps that says something about the relative difficulty of those two topics!

See my #89.

 

[martinbn]

Mathematica, on the other hand, can answer high school math questions, but can't write articles on quantum foundations. Those are simply different tools, it doesn't follow from it that one thing is easy and the other hard.

No, Mathematica cannot answer high school questions.

 

[Demystifier]

No, Mathematica cannot answer high school questions.

It can't if the questions are written in normal English. But it can if they are written in formal Mathematica language. For example, instead of asking "What is the solution of ...", in Mathematica you write something like "Solve[...]".

 

[martinbn]

It can't if the questions are written in normal English. But it can if they are written in formal Mathematica language. For example, instead of asking "What is the solution of ...", in Mathematica you write something like "Solve[...]".

What if the problem is "the room is 5 by 8 the price of carpet is 3 per m^2. What is the cost?" Or some geometry problem which reaquires for the solution to prove something.

 

[Demystifier]

What if the problem is "the room is 5 by 8 the price of carpet is 3 per m^2. What is the cost?" Or some geometry problem which reaquires for the solution to prove something.

I believe we are not far from a tool which will combine ideas of systems such as ChatGPT and Mathematica to solve such problems.

 

[Haelfix]

There are AIs that do approximately average (amongst a select group of high achievers!) on high school math olympiad level questions. It does particularly well where things require formal proofs (its less good with geometry).

ChatGPT right now produces essays roughly at the first year undergraduate level (less in some respects, better in others) and can generalize concepts in essays at roughly the same level (although it is confidently incorrect a good percentage, where perhaps a human might be more cautious).

The way this stuff is scaling, I don’t think its very long (<10 years) before they are solving properly formulated physics/math subproblems (the type we give students for research projects).

I suspect it will be somewhat field dependant for awhile. One thing I have come to expect with this revolution, is that it struggles in places where naively I would have thought it would be strong, and does far better where I would have expected it to be weak.

 

[Morbert]

Me:"Write a python script that characterizes a quantum particle in a well using the consistent histories formalism"

ChatGPT:"Sure! Here is a python script that characterizes a quantum particle in a well using the consistent histories formalism

import numpy as np # Define the Hamiltonian for the quantum particle in a well def Hamiltonian(x, p, mass, well_width): H = (p**2) / (2 * mass) + (well_width**2) * (x**2) / 2 return H # Define the decoherence functional for the quantum particle in a well def decoherence_functional(x1, x2, t1, t2, mass, well_width): delta = x1 - x2 prefactor = (mass / (2 * np.pi * (t1 - t2)))**0.5 exponent = - mass * delta**2 / (2 * (t1 - t2)) D = prefactor * np.exp(exponent) return D # Define the function that computes the probabilities for the quantum particle in a well def probabilities(x1_values, x2_values, t1, t2, mass, well_width): prob = [] for x1 in x1_values: for x2 in x2_values: D = decoherence_functional(x1, x2, t1, t2, mass, well_width) prob.append(D) return prob # Define the initial and final times for the quantum particle t1 = 0 t2 = 1 # Define the mass and well width for the quantum particle mass = 1 well_width = 1 # Define the values of x1 and x2 to compute the probabilities for x1_values = np.linspace(-5, 5, 100) x2_values = np.linspace(-5, 5, 100) # Compute the probabilities for the quantum particle in a well probs = probabilities(x1_values, x2_values, t1, t2, mass, well_width)

This script defines a function for the Hamiltonian of a quantum particle in a well, a function for the decoherence functional of the particle, and a function for computing the probabilities of the particle being in different positions at different times using the consistent histories formalism. It then sets the initial and final times for the particle, the mass and well width, and the values of x1 and x2 to compute the probabilities for, and calls the probability function to get the probabilities."I haven't reviewed the script yet but it's interesting that it at least gets the jist.

 

[martinbn]

Me: Solve $x^5=1$
ChatGPT:
If $x^5 = 1$, then $x$ is one of the fifth roots of $1$. The fifth roots of $1$ are $1, -1, i, -i$, and $-i^2$. Note that $i^2 = -1$. Therefore, the solutions to $x^5 = 1$ are:
$1, -1, i, -i$, and $-i^2$
So, $x$ can be any of these values.

Me: Solve $x^5=x$
ChatGPT:
To solve $x^5 = x$, we can use the fact that $x^5 - x = 0$. We can then factor this equation as follows:

$(x^5 - x) = 0$

$(x^4 + x^3 + x^2 + x + 1)(x - 1) = 0$

Therefore, the solutions to $x^5 = x$ are $x = 1$ and $x = -(x^4 + x^3 + x^2 + x + 1)$. The first solution, $x = 1$, is a real solution. The second solution, $x = -(x^4 + x^3 + x^2 + x + 1)$, is not a real solution.

 

[vanhees71]

So cheating using the bot in a math exam for the 1st semester might not be the best idea ;-).

 

[Demystifier]

Me: Solve x^5=0.

Me: Explain Galois theory such that an average physicist can understand it.

I will not copy paste the answer, but let me just say that now I understand Galois theory better than before.

 

[vanhees71]

Are you sure that the bot explained it right to you? Given the answer to $x^5=1$, I'd be very skeptical.

 

[physika]

Dr. House.

AI model determines cardiovascular risk from routine chest X-ray

https://physicsworld.com/a/ai-model-determines-cardiovascular-risk-from-routine-chest-x-ray/

Single MRI scan of the brain could detect Alzheimer’s disease

https://physicsworld.com/a/single-mri-scan-of-the-brain-could-detect-alzheimers-disease/

 

[Demystifier]

Are you sure that the bot explained it right to you? Given the answer to $x^5=1$, I'd be very skeptical.

I don't understand your point. Maybe I should ask ChatGPT to explain me what you meant?

 

[martinbn]

Me: Explain Galois theory such that an average physicist can understand it.

I will not copy paste the answer, but let me just say that now I understand Galois theory better than before.

It obviously gave the wrong answer. The correct answer is that the average physicist cannot understand Galois theory.

 

[martinbn]

I will not copy paste the answer...

Out of curiosity, is this the answer?

Galois theory is a branch of mathematics that deals with the study of field extensions. Specifically, it studies the conditions under which a field can be obtained as an extension of another field, and the properties of these extensions.
One of the main results of Galois theory is the Galois correspondence, which gives a one-to-one correspondence between subgroups of the Galois group of a field extension and intermediate fields of the extension. This result allows for a deep understanding of the symmetries inherent in field extensions, and has numerous applications in mathematics and physics.
Galois theory has found applications in a wide range of fields, including number theory, algebraic geometry, and the study of elliptic curves. It also has applications in physics, particularly in the study of quantum mechanics and the theory of solitons.
Overall, Galois theory is a fundamental tool for understanding the structure of field extensions and their symmetries, and has had a profound impact on a wide range of mathematical and physical disciplines.

 

[martinbn]

Me: What is the Galois group of x^2+1?

ChatGPT:
The Galois group of a polynomial is a group of symmetries of the polynomial, which consists of all the permutations of the roots of the polynomial that can be obtained through field automorphisms.
In the case of the polynomial x^2+1, the roots of the polynomial are complex numbers i and -i, which are not real numbers. Therefore, the Galois group of the polynomial x^2+1 is a subgroup of the group of all automorphisms of the complex numbers, which is known as the Galois group of the field extension of the real numbers by the roots of the polynomial.
The Galois group of the polynomial x^2+1 is a finite group of order 2, and consists of the identity automorphism (which leaves the roots unchanged) and the automorphism which swaps the roots i and -i. This group is known as the Klein four-group, and is isomorphic to the group of symmetries of a square.
The Galois group of a polynomial is a fundamental concept in Galois theory, and is used to study the symmetries and properties of the roots of the polynomial, as well as the structure of the field extension generated by these roots.

I was reading is as it was typing it, and I thought "Damn it it is OK. I cannot complain about it." But then it wrote about Klein and the Square and I was happy again.

 

[martinbn]

It always says that the Galois group of a polynomial is a group of order the degree of the polynomial.

 

[Morbert]

"Explain Galois theory with a peanut butter analogy"

Sure! Galois theory is a branch of mathematics that deals with the solution of polynomial equations. Here's an analogy to help understand it:
Imagine you have a jar of peanut butter and you want to spread it evenly on two slices of bread. You could use a knife to do this, but it would be difficult to get the peanut butter evenly distributed.
Instead, you might choose to use a spoon. This would make it easier to spread the peanut butter evenly, but it would still be a bit of a challenge.
Now, suppose you had a special tool called a "peanut butter spreader." This tool would make it much easier to evenly distribute the peanut butter on the bread. In the same way, Galois theory provides a "tool" for solving polynomial equations in a systematic and efficient way.
I hope this analogy helps! Let me know if you have any questions.

 

[PeroK]

It obviously gave the wrong answer. The correct answer is that the average physicist cannot understand Galois theory.

@Demystifier is not your average physicist!

 

[Devin-M]

“Physics professors are quite a sight

They study day and night

Their work is never done

But they're always having fun

They teach us about energy and mass

And how to calculate the speed of light's pass

They explain the laws of motion

And solve problems with precision

Their minds are sharp as a knife

They're experts in their life

But they don't just teach and lecture

They also love to conduct experiments, in nature

So let's give a round of applause

To all the physics professors

For all the knowledge they impart

And the joy they bring to the heart
In labs and classrooms they do dwell

Physics professors, smart as hell

Their minds are sharp, their theories sound

They'll leave you dizzy, spinning round

They study particles, both big and small

From atoms to galaxies, they know it all

They delve into the depths of space and time

Leaving no mystery behind

Their equations, formulas, and laws

Are complex, but they're the masters of them all

So if you want to learn about the ways of physics

Just find a professor, they'll be oh so prolific

They'll teach you about the speed of light

And all the forces that take flight

They'll show you how the universe works

And leave you with a sense of awe, it's quite a perk

So don't be afraid, give physics a try

With a professor by your side, you'll surely fly

Through the mysteries of the natural world

Your knowledge will be unfurled”

 

[Demystifier]

@Demystifier is not your average physicist!

But I'm average (in the population of theoretical physicists with PhD) in my abilities to understand abstract algebra.
I was always an analysis-rather-than-algebra guy.

 

[Demystifier]

I was reading is as it was typing it, and I thought "Damn it it is OK. I cannot complain about it." But then it wrote about Klein and the Square and I was happy again.

Me: Why are some people happy when others are wrong?

ChatGPT:
There could be a variety of reasons why some people might feel happy when others are wrong. Here are a few possibilities:

1. Schadenfreude: This is the feeling of pleasure or joy that comes from seeing someone else experience failure or disappointment. Some people might feel happy when others are wrong because it gives them a sense of superiority or validation.

2. Competition: If someone views a situation as a competition, they might feel happy when others are wrong because it gives them an advantage.

3. Personal biases: People may feel happy when others are wrong if it confirms their preexisting beliefs or biases.

4. Misunderstandings: Sometimes, people might feel happy when others are wrong simply because they misunderstand the situation or the intentions of the other person.

It's important to note that feeling happy when others are wrong is not necessarily a healthy or positive reaction. It's usually more productive and empathetic to try to understand others' perspectives and find common ground, rather than taking pleasure in their mistakes or failures.

 

[Demystifier]

Out of curiosity, is this the answer?

No, mine was different, and more illuminating to me.

 

[martinbn]

No, mine was different, and more illuminating to me.

Interesting. So it does not always generate the same answer.

 

[martinbn]

Me: Why are some people happy when others are wrong?

ChatGPT:
There could be a variety of reasons why some people might feel happy when others are wrong. Here are a few possibilities:

1. Schadenfreude: This is the feeling of pleasure or joy that comes from seeing someone else experience failure or disappointment. Some people might feel happy when others are wrong because it gives them a sense of superiority or validation.

2. Competition: If someone views a situation as a competition, they might feel happy when others are wrong because it gives them an advantage.

3. Personal biases: People may feel happy when others are wrong if it confirms their preexisting beliefs or biases.

4. Misunderstandings: Sometimes, people might feel happy when others are wrong simply because they misunderstand the situation or the intentions of the other person.

It's important to note that feeling happy when others are wrong is not necessarily a healthy or positive reaction. It's usually more productive and empathetic to try to understand others' perspectives and find common ground, rather than taking pleasure in their mistakes or failures.

Oh come on. The previous posts were jokes. Wasnt it clear? I even put one of those faces.

 

[Demystifier]

Interesting. So it does not always generate the same answer.

True. You even have a button "Regenerate Response" that gives you a different answer to the same question.

 

[Demystifier]

Oh come on. The previous posts were jokes. Wasnt it clear? I even put one of those faces.

If it was clear that you were joking, why do you think that I was not joking too? I'm sure you had a good reason.

 

[martinbn]

If it was clear that you were joking, why do you think that I was not joking too? I'm sure you had a good reason.

Because you put a "I am sad" response on my post. I expected a "haha".

 

[Demystifier]

Because you put a "I am sad" response on my post. I expected a "haha".

You are good in math, but bad in rationalization.

 

[timmdeeg]

Me: how would you explain "quantum spookiness" with an every day analogy?

ChatGPT:
Quantum mechanics is a fundamental theory in physics that describes the behavior of matter and energy at the atomic and subatomic scale. One of the most striking and counterintuitive aspects of quantum mechanics is the idea of "quantum superposition," in which a quantum system can exist in multiple states simultaneously. This concept is often referred to as "quantum spookiness."

To understand quantum superposition, it might be helpful to consider the following everyday analogy: imagine you are playing a game of "rock, paper, scissors" with a friend. At any given moment, your hand can be in one of three states: rock, paper, or scissors. But in the world of quantum mechanics, a quantum system can be in multiple states at the same time. It's as if your hand could be both rock and scissors simultaneously, and only when you make a choice and "measure" the state of your hand does it become one or the other.

This strange behavior is a consequence of the fundamental uncertainty principle in quantum mechanics, which states that it is impossible to know the precise state of a quantum system with complete accuracy. The idea of quantum superposition helps to explain many of the strange and counterintuitive phenomena that are observed at the quantum scale, such as the fact that particles can be entangled and can seemingly communicate instantaneously over vast distances.