Recent content by Trysse

I have been wondering what it would take to send a radio signal that could be detected from a neighboring star system (for example, Alpha Centauri, ~4.3 light-years away). Transmitter size: How large would a transmitting antenna or array need to be for such a signal to be detectable above...

Right. Didn't pay attention

Why ? For ##c+v## and ##c-v##, the arithmetic mean is $$\frac{(c+v)+(c−v)}{2}$$ The geometric mean is $$\sqrt{(v+c)\cdot (v−c)}$$ so I can write the two as a ratio: $$\frac{\sqrt{(c+v)⋅(c-v)}}{\frac{(c+v)+(c−v)}{2}}$$ which simplifies to $$\frac{\sqrt{c^2-v^2}}{c}$$ I bring ##c## under the...

In the scenario of inertial motion, there’s a straightforward formula for the required speed ##\beta##: $$\beta=\frac{d}{\sqrt{\Delta \tau^2+d^2}}$$ This follows directly from the invariant interval. The proper time ##\Delta \tau## is related to the coordinate time and spatial distance by...

I use ChatGPT a lot to review the texts I write and read. The obvious part is copy editing—finding grammatical errors and making formulations smoother. But I also use it to summarize texts, both ones I get and ones I write. If it’s a text I receive, I want to see if it’s worth my time before...

I don't draw the circle. The circle is constructed from intersecting the cone and the plane. All you see above is the same GeoGebra model. In some pictures I have only removed some elemnts. The 2d pictures are from the 2d view of GeoGebra. So it is always the same circle. Overall it is not...

Imagine an event ##O##: Next, construct a future light cone for ##O##: Then construct some plane that intersects the light cone of ##O## in a circle ##o##: Now select two points that lie in the plane. One inside the light cone (##E_T##) and one outside (##E_S##). Both points represent events...

Thank you for your responses. The method using the hyperbola is also what at least two LLMs suggested. Given my original question and the discussion so far, this might sound like a naive question, but I’ll ask it anyway—sincerely: How sure are you that it is impossible to measure the...

I have checked several textbooks but haven't found a method to measure the spacetime interval directly with a ruler in a Minkowski diagram. Various LLMs also couldn’t provide a reference. All sources I found define the interval algebraically and emphasize that it differs from Euclidean...

@weirdoguy I think I got your point. However, I take it more as a personal position than an argument in this discussion. Although the problem of distorted graphs is mostly discussed in the context of statistical data and not in the context of mathematical functions, I believe the same principle...

Thanks a lot!

I have an overleaf-project in which the bibliography is not displayed. The project has a MyBib.bib. The error message says: Citation 'alstein_teaching_2021' on page 1 undefined on input line 28. link‪./main.tex, 28‬ You have cited something which is not included in your bibliography. Make...

There might be other fields, but right now I am interested in this one. So what is the intuition you want convey to your students? Or what do you think is the intuition they build? What do you think students remeber 10 years after having learned about relativistic effects if Special Relativity...

I am not sure the distortion of the graphs poses no problem. Consider the following question: What is the didactic intention of putting the graphs into the textbooks? I assume it is to build intuition in students. So the question is, what intuition do students get from a distorted graph? If I...

Thank you for your answers so far! I appreciate the feedback. Since nobody has so far pointed this out, I have a question: Has anyone noticed that the scales in these graphs are distorted? If yes, what did you think about it? If no, what do you think about this now? Do you think it’s a problem...