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5 questions
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Forces that are invariant under Galilean spacetime rescaling $\mathbf x' = \lambda \mathbf x$, $t' = \lambda^2 t$
Consider a force of the form
$$
m \ddot{\mathbf x}(t) = -k\frac{\mathbf x(t) - \mathbf x_0}{|\mathbf x(t) - \mathbf x_0|^d}.
$$
For what values of $d$ is this force invariant under the Galilean ...
- 12.8k
9
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2
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Can Galilean transformation be derived from length invariance?
Given length invariance in Euclidean 3D space between two inertial frames:$$ds^2=ds'^2$$
Can Galilean transformation be derived like Lorentz transformation derived from space-time interval invariance?
- 25.4k
2
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1
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What is actually meant when it is said Scalar is invariant?
As far as i know a quantity is called invariant if it satisfies some specific transformations.
Now,Suppose a body is moving with velocity $\vec{v}$ as measured from the lab frame.Its non-relativistic ...
- 52.2k
2
votes
1
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976
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Newton's theory of gravity is covariant under Galilean transformations
We know from classical mechanics that the gravitational field equation for the scalar potential takes the form $$\nabla^2\phi=4\pi \rho,$$ where $\rho$ is mass density (which, can depend on time and ...
- 103
0
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How length is an invariant in Euclidean space?
The special theory of relativity shows that intervals are invariant under Lorentz transform in the Minkowski space -time.
But how can we prove (any postulates or theory) that the length is an ...
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