Recent content by Trysse

Do Authors have a say on how their books are priced? Or how the priceis adjusted over time? Do you have any ideas on how many of those niche books are sold? I asked Google. It said between 200 and 3000. Sounds like barely viable for authors. I also wonder if those books are nowadays actually...

In a recent thread @bhobba suggested the book "Fields and their Quanta" with the hint "It's a bit pricey". I was just wondering what he meant so I looked it up. When I saw the price I was impressed: 160,-€ for around 200 pages. That got me thinking: Any idea what makes this particular book so...

I am not sure if this was meant as a rhetorical question. But I think this is the right question to ask. I would reformulate it slightly: Is the Lorentz factor i.e. the expression $$\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$$ fundamentally necessary to do the math of Special Relativity?

I had a look at a number of books that deal with Special Relativity. Many, if not most, textbooks on the theory of Special Relativity introduce the Lorentz factor ##\gamma## $$\gamma=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$$ Different textbooks introduce ##\gamma## differently; some use it only as a...

The question is designed to suprise you. To regain a feeling of intuition you can take the numbers and apply them to da different scenario. Imagine you have a box with 10×10=100 compartments. In each compartment you put a white ping-pong ball (100% white ping-pong balls). Next you replace one...

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...