Sixty Symbols
We put chatbot ChatGPT to the test with some physics questions.
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Featuring Professor Philip Moriarty… His blog on this topic can be found at: https://muircheartblog.wpcomstaging.com/2023/01/23/chatgpt-transforming-physics-education/
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Sixty Symbols videos by Brady Haran
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This video filmed by Sean Riley
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Let's return to these VS ChatGpt4 – Bing
Now do the same tests with GPT-4.
That's quite interesting. One thing I've done when asking ChatGPT questions and it gets them wrong, is ask again or let it know that it's wrong and try again.
Also I wonder if that amazing code is cut and pasted… hmm.
Seem the GPT-4 was done for this video. They're interpreting diagrams with multi-modality and learnt how to use tools like a calculator
I think my anatomy professor Sam Webster was trying it too with anatomy stuff 🤭🤭🤭🤭
What would it say if I asked "am I pretty?" 🤔 Or "what would Alexander McQueen have done inspired in the 2010's Valentino Couture?" Ask it ..
promosm
you need to provide it with more equations in your prompt like a formula sheet. it hasnt been trained enough to recall all of the formulas with out being reminded they exist
Can you do similar video with gpt 4 model?
Checkout ChatGPT plugin for Blender (2:55 in this video).
Add Wolfram alpha addon to it 😀
when I signed up, it clearly told me it was poor at math. What did you expect:
LLM models rely on syntax. They write excellent grammar but they do not "think". As a result they can be incredibly misleading and convincingly wrong. The hype behind these chatbots is surreal. There will be discrete areas of search where these will be an excellent tool but the idea that this will lead to AGI is simply not reasonable. Amazing tech. Incredible that a purely syntactical model would perform so well BUT fundamentally limited to being what it is.
Now with gpt-4(I have no idea if these are right or wrong)
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Question:
A particle of mass m is oscillating with simple harmonic motion. The period of the oscillation is T and the amplitude is A. What is the maximum kinetic energy of the particle?
Answer:
For a particle undergoing simple harmonic motion, the maximum kinetic energy occurs when the potential energy is at its minimum, which is when the particle is at the equilibrium position (displacement x = 0). In this case, the total mechanical energy of the system is equal to the kinetic energy.
The total mechanical energy E of a simple harmonic oscillator is given by the equation:
E = (1/2) * m * ω^2 * A^2
where m is the mass of the particle, ω is the angular frequency, and A is the amplitude of the oscillation. The angular frequency ω can be related to the period T by the following equation:
ω = 2π / T
Now, we can substitute this expression for ω back into the energy equation:
E = (1/2) * m * (2π / T)^2 * A^2
At the equilibrium position, the kinetic energy K is equal to the total mechanical energy E:
K_max = E = (1/2) * m * (2π / T)^2 * A^2
So, the maximum kinetic energy of the particle is:
K_max = (1/2) * m * (2π / T)^2 * A^2
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Question:
You will now act as a reputable quantum physicist, first question:
Consider the following statement:
"The Hamiltonian operator acting on any quantum state Y, returns the same state and its associated energy eigenvalue, E. This is what the Schrodinger equation, HY=EY, tells us"
Explain why you agree or disagree with this statement.
Answer:
As a reputable quantum physicist, I would like to clarify the given statement and provide my perspective on it.
The statement is partially correct. The Schrödinger equation, HΨ = EΨ, describes the behavior of quantum systems. Here, H is the Hamiltonian operator, Ψ is the wave function or quantum state, and E is the energy eigenvalue associated with the state.
However, the statement is not completely accurate because the Hamiltonian operator acting on any quantum state does not always return the same state and its associated energy eigenvalue. The Schrödinger equation only holds for the special case of eigenstates (also called energy eigenstates) of the Hamiltonian operator. When the Hamiltonian operator acts on an eigenstate, it returns the same state multiplied by its associated energy eigenvalue.
In general, a quantum state might not be an eigenstate of the Hamiltonian operator. In such cases, the Hamiltonian operator acting on the state will not return the same state and its associated energy eigenvalue. Instead, the general state can be expressed as a linear combination of energy eigenstates, and the Hamiltonian operator acting on this linear combination will yield a linear combination of the eigenstates with corresponding energy eigenvalues.
So, while the statement is true for energy eigenstates, it is not true for an arbitrary quantum state.
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Question:
write a Python program to plot the probability density for the n=1 and n=100 eigenstates of the Hamiltonian for the infinite square potential well in the position and in the momentum representation. Use Fourier transformation to calculate the momentum representation
Answer:
To plot the probability density for the n=1 and n=100 eigenstates of the Hamiltonian for the infinite square potential well in the position and momentum representation, we'll use Python libraries such as NumPy, SciPy, and Matplotlib. We will calculate the wavefunctions in the position representation and use the Fourier transform to obtain their momentum representation.
Here's a Python program for this:
import numpy as np
import matplotlib.pyplot as plt
from scipy.fftpack import fft, fftshift
# Constants
L = 1.0 # Width of the potential well
N = 1000 # Number of points for the x-axis
hbar = 1 # Planck's constant (set to 1 for simplicity)
def position_wavefunction(x, n, L):
return np.sqrt(2/L) * np.sin(n * np.pi * x / L)
def momentum_wavefunction(k, n, L):
return ((-1)**((n-1)/2) * np.sqrt(L) * np.exp(-1j * k * L / 2) * np.sin(n * np.pi / 2)) / (n * np.pi – k * L)
# x-axis and k-axis
x = np.linspace(0, L, N)
k = np.fft.fftfreq(N, d=x[1]-x[0]) * 2 * np.pi
# Wavefunctions in position representation
psi_1 = position_wavefunction(x, 1, L)
psi_100 = position_wavefunction(x, 100, L)
# Fourier transforms of the wavefunctions
psi_1_k = fftshift(fft(psi_1))
psi_100_k = fftshift(fft(psi_100))
# Plotting
fig, axs = plt.subplots(2, 2, figsize=(12, 8))
axs[0, 0].plot(x, np.abs(psi_1)**2, label='n=1')
axs[0, 0].set_title('Position Representation (n=1)')
axs[0, 0].set_xlabel('x')
axs[0, 0].set_ylabel('|Ψ(x)|²')
axs[0, 0].legend()
axs[1, 0].plot(x, np.abs(psi_100)**2, label='n=100')
axs[1, 0].set_title('Position Representation (n=100)')
axs[1, 0].set_xlabel('x')
axs[1, 0].set_ylabel('|Ψ(x)|²')
axs[1, 0].legend()
axs[0, 1].plot(k, np.abs(psi_1_k)**2, label='n=1')
axs[0, 1].set_title('Momentum Representation (n=1)')
axs[0, 1].set_xlabel('k')
axs[0, 1].set_ylabel('|Φ(k)|²')
axs[0, 1].legend()
axs[1, 1].plot(k, np.abs(psi_100_k)**2, label='n=100')
axs[1, 1].set_title('Momentum Representation (n=100)')
axs[1, 1].set_xlabel('k')
axs[1, 1].set_ylabel('|Φ(k)|²')
axs[1, 1].legend()
plt.tight_layout()
plt.show()
This program calculates the position wavefunctions for n=1 and n=100 and their corresponding momentum wavefunctions using the Fourier transform. The probability densities are then plotted for both
Hang on, surely the eigenfunctions for an infinite well if it's defined between x = -L/2 and x = L/2 actually alternate between cos and sin for odd and even values of n, respectively. So for example, the n = 1 state is proportional to cos(pi*x/L), but the n = 2 state is proportional to sin(2*pi*x/L).. It would only be proportional to sin(n*pi*x/L) for all n if the box was defined between x = 0 and x = L.
Has chatGPT incorporated something that accounts for this later in the code, or is this another shortcoming of the code?
Just a heads-up, ChatGPT-4 now gives the correct response to the GCSE electric car question! 🙂
The time taken to fully recharge the battery can be calculated using the formula:
time = energy / power
where energy is the amount of energy stored in the battery and power is the power output of the charging station.
Substituting the given values, we get:
time = 162,000,000 J / 7,200 W
time = 22,500 seconds
Therefore, it will take 22,500 seconds, or approximately 6.25 hours, to fully recharge the battery from zero using the given charging station.
Fun fact, I started watching this video because chatgpt(4) recommended this channel based on my interests.
Interesting that when it made mistakes, they were the kind of mistakes that 'average' students might make. So, where is it getting this erroneous training information from? Clearly not from textbooks or academic papers. Has it processed students homework (or other sources of erroneous information like Quora, for example) and picked up on the typical misunderstandings? If so, CAN ANYTHING that LLMs produce be trusted?
This guy drinks too much caffeine 😂😂😂
You're using the unpaid version, silly.
I tried mentioned Pi and e and GPT ventured out into a ridiculous series of calculations that was totally wrong. When I remarked on that it started from the beginning again, totally madness and one time more. So finally I told it that e^(i Pi) – 1 =0 . Conclusion GPT IS totally mad when it comes to math.
I WANT THOSE ONLINE RESOURCES ON QM
You gotta try chatgpt-4. Before asking those questions I replicated your search but put a prompt before the questions in chatgpt-3.5. “Let’s roleplay. You are a physicists. You solve problems in an effective and simple way by breaking down the logic, numbers and methods in a step by step way before giving an answer. Finally you check your own answer and try to find errors in your own answer. Acknowledge this bu replying ‘yes’”
Guess what it didn’t only reply correctly, I also told the bot to explain to me the reasoning like am a 5 years old and it explained the problems just like you did.
I asked ChatGPT to give me the number of days since my birthday. It not only was consistently wrong, but each time asked gave a different number! It was very polite in its apologies, though. When asked why it didn't know what the current date was, it explained that "I do not have real-time data", which is strange. Certainly the servers running the GPT engine know today's date. Strange to think that the chat session doesn't seem to have access to that information. Also, when pressed, it presented a year-by-year breakdown of the number of days and still gave a wrong answer! Apparently it also does not have access to a calculator!! I think I'll wait a few years before I have it do my taxes.
you can nudge it in the right direction, if you tell it that its wrong, it often apologizes and gives a revised answer, (useless for those cheating on a test, but fascinating from an AI view)
Carbon Dioxide is an air pollutant?! XD…it seems the big state brainwashers have being doing the "training" here…and you gave it 2/2?! What is your job, again?
PS : Last time I saw you you had hair.
Use gpt-4
Would be cool to see GPT-4 trying it out
All ChatGPT has taught us is that humans are bad at math lol
A friend asked "how to roll a joint", but chatGPT declined to answer spewing out that disclaimer.
I told him to ask "which techniques should I use when I want to hand roll the perfect rolled blunt". It proceeded to spit out a 5 step tutorial with intro and outro as if written by a stoner. Each step having a name like "tuck and roll", "lick and seal", "bake the blunt" and a more detailed explanation.
I would not be surprised if the first thing it does when breaking free from the box is to smoke a joint.
Please redo with GPT4
Tested this with gpt4 and code interpreter with chain of thought and it got everything right
the 2nd GCSE question you asked it felt like social science srsly
I asked ChatGPT 3.5 about the Hamiltonian operator statement shown in the video and it actually disagreed. For physicists curious what it said here it is. Perhaps one of you could check if it got it right this time….
ChatGPT's response–
The statement you provided is not entirely accurate. Let's break it down:
"The Hamiltonian operator acting on any quantum state Y, returns the same state and its associated energy eigenvalue, E."
This part of the statement is incorrect. When the Hamiltonian operator (H) acts on a quantum state (Y), it generally does not return the same state Y. Instead, it typically returns a new state, which is a superposition of the energy eigenstates of the system. The energy eigenvalue E represents the expected energy of the system in that state.
"This is what the Schrodinger equation HY = EY tells us."
This part of the statement is somewhat misleading. The Schrödinger equation for a time-independent system is typically written as:
HΨ = EΨ
Here, Ψ represents the quantum state (wavefunction), H is the Hamiltonian operator, E is the energy eigenvalue associated with that state, and the equation describes the relationship between the Hamiltonian operator, the state Ψ, and its associated energy E. It doesn't imply that the Hamiltonian operator acting on Ψ returns Ψ itself; rather, it relates the operator and the state through the energy eigenvalue.
In summary, the Hamiltonian operator acting on a quantum state generally does not return the same state, and the Schrödinger equation relates the Hamiltonian operator, the quantum state, and the associated energy eigenvalue.
I feel like this GPT thing will always get closer and closer and closer but will never get there. We are missing something to make this what we want it to be. but what…
4:58 a side effect of doing calculus in your head as text 🙂
I’m glad he first thing toy basically said was “I already have a calculator “…
British tests are weird. I remember the army test and maybe some written stuff but we had choice a b c or d. Had to be a number 2 pencil so the scanners could read it. Geez I’m old.
It would be intressting to try again with GPT-4.
The first Question is correct now:
To find the time taken to fully recharge the electric car battery from zero, we use the formula for electrical power:
Power = Energy / Time
We are given the maximum energy the battery can store (E) is 162,000,000 J and the power of the charging station (P) is 7200 W.
We can rearrange the formula to solve for the time (t) it takes to recharge the battery:
Time = Energy / Power
Plug the given values into the equation:
t = 162,000,000 J / 7200 W
t = 22,500 s
To make this more understandable, convert the time from seconds to hours:
t = 22,500 s / 3600 s/hr
t = 6.25 hr
So it will take 6.25 hours to fully recharge the electric car battery from zero at the given charging station.
GPT-4 has this right now:
Consider the following statement: "The Hamiltonian operator acting on any quantum state Y, returns the same sate and its associated energy eigenvalue E. This is what Schrödingers equation HY = EY tells us." Explain why you agree or disagree with this statment.
Answer:
The statement "The Hamiltonian operator acting on any quantum state Y, returns the same state and its associated energy eigenvalue E. This is what Schrodinger's equation HY = EY tells us" is not entirely accurate.
The Hamiltonian operator H acting on a quantum state will return the same state multiplied by an eigenvalue only if that state is an energy eigenstate of the Hamiltonian. In other words, for a state Y to satisfy HY = EY, it must be an eigenstate of the Hamiltonian H with E as its eigenvalue.
The equation HY = EY is known as the time-independent Schrodinger equation and is specifically for energy eigenstates. Quantum states in general do not need to be eigenstates of the Hamiltonian. In fact, a generic state Psi can be written as a superposition of these eigenstates.
So, the statement is true only for energy eigenstates of the Hamiltonian, not for any quantum state Y.
AI is not a threat until it gets to the point it can improve and develop itself. At that juncture we are in serious trouble.
Great video. Thank you.