# Angle in a space time diagram

K

#### Kashmiri

##### Guest
Kashmiri Asks: Angle in a space time diagram

FIGURE 4.13 A Lorentz boost as a change of coordinates on a spacetime diagram. The figure shows the grid of $\left(c t^{\prime}, x^{\prime}\right)$ coordinates defined by $(4.18)$ plotted on a $(c t, x)$ spacetime diagram. The $\left(c t^{\prime}, x^{\prime}\right)$ coordinates are not orthogonal to each other in the Euclidean geometry of the printed page. But they are orthogonal in the geometry of spacetime. (Recall the analogies between spacetime diagrams and maps discussed in Example 4.1.) The $\left(c t^{\prime}, x^{\prime}\right)$ axes have to be as orthogonal as the $(c t, x)$ axes because there is no physical distinction between one inertial frame and another. The orthogonality is explicitly verified in Example 5.2. The hyperbolic angle $\theta$ is a measure of the velocity between the two frames.

The transformation is given as

\begin{aligned} c t^{\prime} &=(\cosh \theta)(c t)-(\sinh \theta) x \\ x^{\prime} &=(-\sinh \theta)(c t)+(\cosh \theta) x \\ y^{\prime} &=y \\ z^{\prime} &=z \end{aligned}

To find the angle $x'$ axes makes with $x$ axes I use

$0=(\cosh \theta)(c t)-(\sinh \theta) x$ to get its slope as $Tanh(\theta)$ and hence the angle is ${Tan}^{-1}(Tanh(\theta))$ but the book says the angle is $\theta$ ? What did I do wrong?

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## Unreplied Posts

#### Debug assertion failed when trying to delete array from heap

Hofbr Asks: Debug assertion failed when trying to delete array from heap
I have a sub-optimal solution to return two variables from a function by creating a pointer to an array with two indexes. (just using my current knowledge base from class. I know vectors or std::pair would be a better solution)

However, when I try to delete the array via the pointer, I'm getting the below error.

Am I misunderstanding the procedure? Don't know I need to delete the array created in heap?

Code:
#include <iostream>
#include <cmath>

double* quadraticEquation(double a, double b, double c) {
double x1, x2;

x1 = (-b + sqrt(b * b - 4 * a * c)) / (2 * a);
x2 = (-b - sqrt(b * b - 4 * a * c)) / (2 * a);
double arr[2] = {x1, x2};
return arr;
}

int main()
{
double* solution = quadraticEquation(3, 5, -8);

double x1 = solution[0];
double x2 = solution[1];
std::cout << "x1 = " << x1 << std::endl << "x2 = " << x2 << std::endl;

delete[] solution;
solution = nullptr;
}

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#### Apache - I can open every file except the index

Doctore Asks: Apache - I can open every file except the index
Fresh Apache install on Fedora Server.

After replacing the default index.html with one of my own (just a boilerplate html with "Test" in the body) - I am unable to open it. I get Forbidden/You don't have permission to access this resource.

The real kicker is, I have two other files in the /var/www/html folder, one html the other php, and I can open both of them.

Apache is listening on port 80 and the port is open in the firewall. Permissions for all 3 files are exactly the same, along with owner/group.

Btw, I can't access the index.html either from the browser of another computer on the same network, or directly at the server cli with wget.

Any ideas what's going on here?

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#### Using MySql for a backend for flutter app?

Dumb Nerd Asks: Using MySql for a backend for flutter app?
Been doing some deep diving in regards to building a backend for my flutter application. The premise and requirements I am looking for are something that is self-hosted and ultimately free (no monthly charges, overuse, etc like firebase) only the essentials such as storage that I would pay for IF AND ONLY IF required; in other words, it's my responsibility. I just downloaded MySql, my only question is how should I go about what APIs I could use for caching and passing data to the application, or do I even need a middleman to pass data? Input is much appreciated.

SolveForum.com may not be responsible for the answers or solutions given to any question asked by the users. All Answers or responses are user generated answers and we do not have proof of its validity or correctness. Please vote for the answer that helped you in order to help others find out which is the most helpful answer. Questions labeled as solved may be solved or may not be solved depending on the type of question and the date posted for some posts may be scheduled to be deleted periodically. Do not hesitate to share your thoughts here to help others.

I get this error when I run my code on an iOS 14 device using XCode 14.

Code:
  dyld: Symbol not found: _\$s7SwiftUI15GraphicsContextV4fill_4with5styleyAA4PathV_AC7ShadingVAA9FillStyleVtF
Referenced from: ******
Expected in: /System/Library/Frameworks/SwiftUI.framework/SwiftUI

I do not get any errors when I run the same code on an iOS 16 device.

How do I resolve this issue?

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#### How do I resolve Java Eclipse command errors that do not meet the conditions?

Soohyun Kang Asks: How do I resolve Java Eclipse command errors that do not meet the conditions?

It works well if I type the word that has more than 6 characters in the console, but if I type the word that has less than 6 characters, an error appears as shown in the picture. In this case, how do I solve this problum on words with less than 6 characters?

SolveForum.com may not be responsible for the answers or solutions given to any question asked by the users. All Answers or responses are user generated answers and we do not have proof of its validity or correctness. Please vote for the answer that helped you in order to help others find out which is the most helpful answer. Questions labeled as solved may be solved or may not be solved depending on the type of question and the date posted for some posts may be scheduled to be deleted periodically. Do not hesitate to share your thoughts here to help others.