29
votes
What is the cause of the constancy of the speed of light in vacuum?
The invariance of the speed of light follows from the principle of relativity. This says there is no experiment that can distinguish between inertial reference frames: physical laws are the same in ...
- 786
18
votes
What is the cause of the constancy of the speed of light in vacuum?
The constancy of $c$ is an experimental result, verified to great precision. When we make mathematical models that assume the constancy of $c$, we get predictions that match other experimental results ...
- 13.2k
9
votes
What is the cause of the constancy of the speed of light in vacuum?
This is not a question of cause and effect, but a question of definition. A local inertial frame is defined as one where locally you measure the speed of light to be $c$ (among other properties). So ...
- 81.7k
7
votes
Accepted
Length contraction in special relativity- from a sphere to an ellipse
You're using coordinates named $(x_0,y_0,z_0)$ for both the primed and unprimed frames in the first two equations. Never do that or you will become hopelessly confused. I'm going to use $(t',x',y',z')$...
- 22k
6
votes
Accepted
Lorentz transformation and special relativity: Why the equations must be linear?
A linear transformation maps straight lines to straight lines, that is a straight line in the $(t, x)$ coordinates maps to a straight line in the $(t', x')$ coordinates.
This is required because a ...
- 343k
5
votes
Time dilation and contradiction
The mistake is that you cannot substitute the deltas, as they refer to different quantities in each of the two equations. In the first equation, delta t refers to a time interval between two events ...
- 22.3k
4
votes
What is the cause of the constancy of the speed of light in vacuum?
Five year old kids asks the question "Why?" time and time again. In the Toyota production model there is an accepted way to handle root causes known as "Five Whys".
What is the ...
- 804
4
votes
What is the cause of the constancy of the speed of light in vacuum?
The constancy of light is that in free space the 3rd along with the 4th Maxwell's equation produce a wave equation which depends only on the electric and magnetic permeability of the medium and ...
- 128
3
votes
Length contraction in special relativity- from a sphere to an ellipse
In the frame S, the object is smaller by a factor of
$$\gamma=\frac{1}{\sqrt{1-(v/c)^2}}>1$$
In the frame S', $x_0=R,y_0=0,z_0=0$ is a solution. We want the obect to be shorter in the frame S, so $...
3
votes
What is the matrix for change of basis from unrotated to an airplane with yaw, pitch and roll?
There are two equivalent ways to perform the rotations. The approach you describe I would call the moving axes convention: at each step we rotate the coordinate system and perform the next rotation ...
3
votes
Accepted
Time dilation and contradiction
A Lorentz transformation (for simplicity: 1 spatial dimension) is generally given by
$$\left(\begin{matrix}ct'\\x'\end{matrix}\right)=\left(\begin{matrix}\gamma&-\beta\gamma\\-\beta\gamma&\...
- 185
2
votes
The average of a continuous value: $\overline{O} = \int O(x) \rho(x) dx$, but coordinate invariant
lpz is correct that you are including an erroneous factor of $|dy/dx|$ in your transformation of $O(x)$. You may be getting misled by the transformation of the density, which uses the same symbol for ...
- 546
2
votes
Decomposing a force vector at an arbitrary angle
You have to calculate the projection of the force vector on the direction vector (i.e. norm one) you are interested in. The projection of vector $\mathbf{v}$ on the vector $\mathbf{n}$ is the scalar ...
- 569
2
votes
Accepted
Decomposition of 3D rotation (in analogy to translation)
You are probably asking about the Gibbs composition of rotations (1884), an idiosyncratic non-abelian law. If you describe a rotation by a Gibbs vector
$$ \mathbf{g} = \hat{\mathbf{e}}\tan\frac{\theta}...
- 54.1k
2
votes
What is the cause of the constancy of the speed of light in vacuum?
The physical reason for the constancy of the speed $c$ of light in free space (i.e. perfect vacuum) has nothing to do with Special Relativity but rather with the vacuum itself and Maxwell's ...
- 3,404
2
votes
Transformation of basis vector in Kruskal coordinate
When specifying partial derivatives it is important to specify what coordinate is being keeping fixed in addition to what coordinate is being varied. Without this information the partial derivative ...
- 9,357
1
vote
Why the divernce of this magnetic field is not zero?
I confirm that the divergence of
$$\tag{1}
\vec{B}_{X,Y,Z}=\frac{B_0 R^3}{(X^2+Y^2+Z^2)^{5/2}}[-3X Z\, \hat{I} -3YZ\, \hat{J}+(X^2+Y^2-2Z^2)\hat{K}],
$$
which I prefer to write as
$$\tag{2}
B(x,y,z)=\...
- 1,289
1
vote
What is the matrix for change of basis from unrotated to an airplane with yaw, pitch and roll?
You have described the following steps to pitch/roll/yaw your hand:
Face some direction that we will take as North, raise your hand flat and level in front of you, this is the start position.
Sweep ...
- 36.5k
1
vote
Accepted
How do I convert vectors between rotated cartesian coordinate systems?
For this specific problem involving aircraft relative to Earth, you have chosen a decent frame: North East Down (NED), which is a local tangent plane: https://en.wikipedia.org/wiki/...
- 28.2k
1
vote
How do I convert vectors between rotated cartesian coordinate systems?
This problem can be solved in a general way via a basis change, where one basis is related to the other via a 90° rotation. More about this can be found on the following wiki page: https://en....
- 41
1
vote
What is the cause of the constancy of the speed of light in vacuum?
The physical meaning of it is that everywhere in spacetime, and in every direction, there exists a special speed, which you can measure with local experiments. You can imagine that spacetime is ...
- 22k
1
vote
Accepted
How to exactly determine the position and sign in vector quantity like displacement?
I assume that you have chosen a unit vector, $\hat {\mathbf w}$ that points along the ruler towards the wall. In that case you should have found the resultant displacement to be +32 cm $\hat {\mathbf ...
- 31.6k
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