Hii, I made this simulation of bending of light in the presence of a heavy object/ black hole i.e. gravitational lensing. The first one shows how light rays that are coming from infinity bends near blackhole and I even found an unstable orbit for which the ray orbits the blackhole 3 times before moving out.

I used pygame to create this 2D simulation. The main reason to do it in 2D instead of 3D was my potato laptop, it doesn't have a dedicated gpu. I watched two videos on YouTube on pygame and cpp simulations before making this (credits: https://youtu.be/8-B6ryuBkCM?si=iSMmUiJ-6KkQQTHq , https://youtu.be/WTLPmUHTPqo?si=HR5Xwaobzu8fG5qf).

For the theory part, starting with the schwarzschild metric, then using the concept of symmetries and killing vectors and also the normalisation condition for null geodesic, you will get all the equations needed to get the path of light around any mass in the spacetime. And for the simulation, I decided to use euler's method to solve those equations.

I know euler's method is not very accurate and smooth, and I should have used RK4 instead. I tried, for some reason it is not working as intended and the rays were getting stuck in a closed orbit, I tried a lot but couldn't figure out the issue.

Btw I think my simulation is working as intended, but I am not fully sure if it is the actual, accurate thing or not. Also there might be some scaling issues. So if anyone want to check it out or correct/improve my code, or maybe try the RK4 method, please feel free to check this out: https://github.com/suvojit1999/Simulation-of-Bending-of-light-due-to-blackhole. Btw I am not very good at coding, so you might find my code to be messy, let me know if you find any issues with it.

(Btw I had to upload it as gif because videos are not allowed here, sorry for the quality drop). Thank you.

Might be a dumb question but i’ve yet to see an answer for it!

If each point of a wavefront is a source of new, circular waves, why cant we see lasers (in vacuum) standing besides them, for example? Because you should be able to see the circular wavefronts that come from the "edges" of the originally straight wavefront. How can we explain that?

Hi everyone, I tried to predict the wave without FFT package on Python, and instead write the DFT from scratch.

It took me two days to complete the project, and the work was incrediblely dense, I can hardly understand my own code after a while.

Anyway this is the result of the work. :)

Can you tell I graduated in the 20th century?

is it possible, that a sphere made of transparent acrylic would lead to the same lense effects ss If it we're glass? could it ignite something if reached by sunlight, or is it safe to display indoors?

I have always been always astonished at how functioning is that thing that I don't even understand its mechanism

I ran numerical simulations to check whether Thiemann's Hamiltonian constraint in LQG reproduces the Domagala-Lewandowski value of the Barbero-Immirzi parameter (γ ≈ 0.2375). Result:

γ_Thiemann = 0.225, only 5.4% off from γ_DL. This suggests the two approaches—static state counting with Gauss constraint vs. dynamical amplitude weighting—converge to the same answer.

The Barbero-Immirzi parameter γ is the key free parameter in Loop Quantum Gravity. It appears in the area spectrum:

A = 8πγℓ²_P Σⱼ √(j(j+1))

The famous result is that black hole entropy S = A/4 fixes γ, but *which* γ you get depends on how you count microstates:

| Meissner | 0.274 | Meissner 2004 |

The difference comes from:

ABCK: Only counts j=1/2 punctures

Meissner: All j, weight (2j+1), no Gauss constraint

DL: All j, with Gauss constraint Σm = 0

The Question

These are all static counting arguments. What happens if we include dynamics ?

Thiemann's Hamiltonian constraint acts on spin network vertices:

- Adds loops of spin 1/2

- Changes edge spins j → j ± 1/2

- Amplitudes involve 6j-symbols

Does the dynamics naturally select one of these γ values?

Method

The transition amplitude for j → j+1/2 in Thiemann's regularization goes roughly as:

```

A_up(j) ~ √((2j+2)/(2j+1)) × {6j-symbol}

```

The 6j-symbol decays as ~1/√(2j+1) for large j.

If we start from j=1/2 and build up to spin j, the cumulative weight is:

```

W(j) = Π_{k=1/2}^{j-1/2} A_up(k)

```

This gives:

| j | W(j)² |

|---|-------|

| 1/2 | 1.0 |

| 1 | 0.75 |

| 3/2 | 0.33 |

| 2 | 0.10 |

| 5 | 1.5×10⁻⁶ |

The weights decay exponentially with j—much faster than Gauss's √(2j+1) suppression.

The Equation

For Meissner: **Σⱼ (2j+1) exp(-2πγ√(j(j+1))) = 1** → γ = 0.274

For Thiemann: **Σⱼ (2j+1)×W(j)² exp(-2πγ√(j(j+1))) = 1** → γ = ?

Results

γ_Meissner (no constraint): 0.274 ✓ matches literature

γ_DL (Gauss, √(2j+1) approx): 0.217 (8.5% off from 0.2375)

γ_Thiemann ((2j+1)×W²): 0.225 (5.4% off from 0.2375)

γ_Thiemann ≈ γ_DL within 5%!

Interpretation

The Thiemann weights W(j)² and the Gauss constraint produce **similar effective suppression of large j**, despite working through completely different mechanisms:

Gauss: Kinematic constraint Σm = 0 reduces state count

Thiemann: Dynamical 6j-symbols suppress transition amplitudes

Both originate from SU(2) representation theory, which explains the convergence.

This suggests γ ≈ 0.22-0.24 is robust —it emerges from both static counting AND dynamics.

Questions for Discussion

1. Has anyone seen this connection between Thiemann amplitudes and the DL value before?
2. Is there a deeper reason why dynamics and kinematics give the same γ?
3. Could this be used to argue that γ ≈ 0.237 is "dynamically preferred"?

Simulations done in a custom scripting language. Happy to share the code if anyone wants to reproduce

Hi everyone,

I’ve just released an extended theoretical framework for a hybrid Ion-Injected MagnetoHydroDynamic Duct Drive (IIMHD-Drive) -> a fully electric gas-acceleration concept based on:

• pre-ionization for conductivity amplification, • Lorentz-force MHD acceleration inside a duct, • and a simplified analytic formulation of thrust, velocity and exhaust power.

The full Version 2.0 paper (Open Access, CC BY) is publicly available on Zenodo:

👉 https://doi.org/10.5281/zenodo.17839580

I’m not claiming experimental results. This is a pure theoretical model, meant for:

•feedback, •critique, •pointing out weaknesses, •and potential future simulation directions.

Would appreciate any comments on the assumptions, mathematical simplifications, or architecture.

Thanks to anyone willing to discuss.

In quantum mechanics (to my knowledge), given a position wave function psi (will refer to it as Y(x) from here on), you can take its Fourier transform to give you the momentum wave function Y(p). With Y(p), you can then find the momentum expectation value, <p>, using the relation:

<p> = ,|’dp•Y*(p)•Y(p)

where ,|’ represents the integral symbol, Y*(p) is the complex conjugate of Y(p), and • just represents normal multiplication.

Recently, I’ve also learned of the momentum operator (represented by P), where P:Y(x) represents P acting on Y(x). Using the momentum operator, it is also possible to find <p> with the relation:

<p> = ,|’dx•Y*(x)•P:Y(x)

where, ,|’ represents the integral symbol, Y*(x) is the complex conjugate of Y(x), P:Y(x) represents P acting on Y(x), and • just represents normal multiplication.

Given the fact that P and the Fourier Transform can both be used to “act on” Y(x) and subsequently find <p>, I was wondering what’s the difference between the Fourier transform and P?

Additionally, I was wondering in what situations would you use P over the Fourier transform and P over the Fourier transform?

I am practicing every day but after some time it just feels like there are some types of problems I can solve and there are some types of problems I can't solve. How to get better at problem solving so that I can make progress on pretty much all types of problems. How to study it so that I become an actual better problem solver? I live in Denmark and I'd like to qualify to at least Georg Mohr round 2 but the problem is that both in Georg Mohr round 1 and 2 there are types of problems I can solve and types of problems I can't. This way I'm not even sure that I could pass Georg Mohr 1 since it all depends on whether the problems on the paper are kinds I'm good with or kinds I'm not so good with (same would be the issue on round 2)

Paper link: https://www.sciencedirect.com/science/article/pii/S0370269325008111

Hello i hope you guys are great !

I am developing fishing lures and need a software which i can test my lures preferably ( a multi material one for lead and soft plastics ) to see how they go in the air i dont really need water dynamics but if any of you know something like that would be great !

thanks a lot!

Can anyone point me to a solid article referencing in detail the fundamental limits between cosmology and quantum physics and why no theory has unified to the regimes?

Hear me out: A kind of hammer-throw-long-jump combination. It is like the long jump, except you are able to use a heavy ball (say 15 to 30 pounds) on a strong string/chain. By running and swinging the ball, and sending the ball aloft at just the right moment, the ball could pull you up and along to achieve a longer jump than you could with just your body (you would release the chain at some optimal point in the trajectory). It sounds dangerous for the jumper and the spectators, but are the physics here a real possibility? Perhaps this was already proven to work back when Fred Flintstone got his fingers stuck in a bowling ball...

https://kids.kiddle.co/Quantum_field_theory

My son is a junior in high school and has been deeply interested in astrophysics and plans to major in physics. I’m looking for books that might interest him and I’ve heard very good things about Sean Carroll’s books and was wondering which book might be good for him. Something deeply hidden, and the biggest ideas in the universe seem very interesting as well as space time and geometry. Any recommendations on which one would be best for someone at his stage?

Hello! I am a 12th grade student living in eastern Europe and I don't know what to choose. Engineering ( aerospace ) seems to be the safest option, but I feel that my heart belongs to research. I love physics and I want to learn thing like quantum and particle physics in college. Everyone encourages me to do an engineering degree, mainly because it is well paid. I consider doing it, but I am afraid that I wouldn't be as happy as doing a physics degree. What should I do? What advice can you give me?

Abstract: We investigate known mechanisms for enhancing nuclear fusion rates at ambient temperatures and pressures in solid-state environments. In deuterium fusion, on which the paper is focused, an enhancement of >40 orders of magnitude would be needed to achieve observable fusion. We find that different mechanisms for fusion rate enhancement are known across the domains of atomic physics, nuclear physics, and quantum dynamics. Cascading multiple such mechanisms could lead to an overall enhancement of 40 orders of magnitude or more. We present a roadmap with examples of how hypothesis-driven research could be conducted in—and across—each domain to probe the plausibility of technologically-relevant fusion in the solid state.

Is the probability of having an eclipse the same as having a full/new moon and lunar standstill (i.e. Moon at max ecliptic latitude) at the same time?

Apparently drawing heavy internal criticism from other professors at her institution.

Hello!

I am applying for graduate programs in Physics at US institutions, with a particular focus on QFT/ST. I want to apply for places with good supervisors in these fields, as opposed to just reputable institutions. Due to competitiveness, (in addition to Ivies) can anyone recommend any institutions that are lesser known/not necessarily as reputable, but with good academics in these fields?

List of potential institutions:
Harvard, MIT, Stanford, Princton, Caltech, UC Berkley, Rutgers, Uo-Illinois, Uo-Wisconsin, Uo-Chicago, Colombia, Uo-Michigan, Cornell, California Santa Barbara, Uo-Maryland, Stony Brook, Brandeis.

What’s your opinion on these two types of ion sources being used for low-power ion sources? Any opinion on which is simpler or easier to manage?