40
votes
Why are there so many objects perfectly orbiting each other? Isn't it infinitely more likely that two random objects crash/fly apart?
Your intuition that two isolated objects approaching each other and not already in a closed orbit will either collide or will fly apart again is substantially correct. If the objects are not already ...
- 47.7k
26
votes
Why are there so many objects perfectly orbiting each other? Isn't it infinitely more likely that two random objects crash/fly apart?
Btw, here's an expertly drawn diagram that took 1000 hours in MS Paint to show things visually.
None of your three pictures really illustrates the actual physical scenario very well. (OK, picture B ...
- 13.4k
11
votes
Why are there so many objects perfectly orbiting each other? Isn't it infinitely more likely that two random objects crash/fly apart?
they can either miss each other and fly apart (if the velocity is enough and there's not enough gravitational attraction between them), or they can be attracted enough to each other that they ...
- 94.6k
7
votes
Why are there so many objects perfectly orbiting each other? Isn't it infinitely more likely that two random objects crash/fly apart?
Partly it's about how galaxies form (see another excellent answer about that).
But do also consider that you're seeing the survivor bias of 13.8 billion years. If they weren't in a stable orbit, the ...
- 2,531
7
votes
Accepted
Are there torques affecting Earth?
Earth Rotation Variations from Hours to Centuries (Dickey) has some analysis of these variations and states that they are mainly due to interactions with the atmosphere and with the earth's core.
...
- 38.4k
6
votes
Has a heavier atmosphere and the relocation of oil around the Earth had a measurable effect on the rotation of the Earth?
The effect is minuscule, because:
Oil and gas and coal do not come from "the center of the Earth", they come from relatively close to the surface. The deepest oil wells in existence are &...
- 47.2k
4
votes
Why are there so many objects perfectly orbiting each other? Isn't it infinitely more likely that two random objects crash/fly apart?
chausies asked: "Why are there so many objects perfectly orbiting each other?"
Apart from the fact that most orbits are not perfectly circular but more or less elliptical: if two objects ...
- 11k
4
votes
Stern–Gerlach experiment - what's so strange?
When a magnetic dipole is deflected by the magnetic field it releases the potential energy as light as it comes to rest. We measure the amount of deflection and therefore the initial orientation of ...
- 857
4
votes
Accepted
Lorentz group representation of spin 2 particles
Note that
$$(a,b) \otimes (c,d) = (a \otimes c, b \otimes d) \tag{1}$$
so
$$(1/2,1/2) \otimes (1/2,1/2) = (1/2\otimes 1/2, 1/2\otimes 1/2)$$
$$ = (1 \oplus 0, 1/2\otimes 1/2)$$
$$ = (1, 1/2\otimes 1/2)...
- 1,185
4
votes
Why are there so many objects perfectly orbiting each other? Isn't it infinitely more likely that two random objects crash/fly apart?
And yet there are a zillion celestial objects perfectly orbit each other
This is survivorship bias. Based on our current model of how we think planets form, there were many orders of magnitude ...
- 879
3
votes
Accepted
Confusion with Hund's rule
Hund's first rule is based on non-relativistic quantum mechanics without any spin-orbit interactions. Since the non-relativistic Hamiltonian (in the absence of magnetic fields) is spin-independent, ...
- 1,197
3
votes
Landau QM Angular Momentum Eigenvalues Derivation
The argument is that (single particle) wavefunctions should satisfy $\psi(\phi)=\psi(\phi+2\pi)$ since rotating a distribution by $2\pi$ about the $z$ axis should leave the distribution invariant.
...
- 45.1k
3
votes
Accepted
Commutation of the Hamiltonian with the generator of boost
...From the above, we see that $$\{M^{0i}, H\} = P^i$$
No, you should have:
$$
\{M^{0i}, H\} = -P^i
$$
...Why is it that $\frac{d}{dt}M^{0i}\neq \{H, M^{0i}\}$? Can someone please explain?
It's ...
- 17.7k
2
votes
Why are there so many objects perfectly orbiting each other? Isn't it infinitely more likely that two random objects crash/fly apart?
At first glance it may seem this way, but conservation of angular momentum sort of acts as a "restoring pseudoforce" to make orbits more likely.
If one object is traveling towards another ...
- 7,382
2
votes
Lorentz group representation of spin 2 particles
This isn't a complete answer, but
Just by counting dimensions, $(0,1)\oplus (1,0)$ is correct. $(1/2,1/2)$ has dimension 4. So $(1/2,1/2)\otimes (1/2,1/2)$ dimension 16. In the decomposition, $(0,...
- 244
2
votes
Why does torque increase with radius or distance from the centre?
As with everything in physics, it's about modelling the real world, based on experiments.
We all experienced that, e.g. for turning a screw, the same force applied to a longer lever has a better ...
- 2,836
2
votes
Linear Momentum conservation
Since there is a hinge at the end of the ruler, linear momentum is never conserved because the hinge is applying force on the ruler when acted by a force. However, angular momentum is conserved about ...
- 152
1
vote
Angular momentum operator in second quantization
Well, actually, it is nothing surprising. The second quantized form of a general first quantized one-body operator $\hat{A}$ is
$$
{\cal{A}}=\sum_{p,q}\langle \phi_p|\hat{A}|\phi_q\rangle a_p^{\dagger}...
- 1,197
1
vote
Regarding Clebsch-Gordan Coefficients using Recursive method
You are told
$$
J=\ell +1/2, \\
m= m_1+m_2= m_1+1/2, \\
\implies ~~ m-1/2= m_1,
$$
obviously an integer, no?
- 60.5k
1
vote
Accepted
Lorentz Transformations and Angular Momentum unclear derivation
Depending on the type of transformation, the infinitesimal parameter can be a scalar, vector, tensor etc.
We parameterize the change in the field as
Scalar: $\delta \phi = \alpha \Delta \phi$
Vector: ...
- 933
1
vote
Accepted
Vanishing of angular momentum with scale
… the whole universe doesn't possess an angular momentum. It can't: If it had one, the centre would be a special point (which isn't allowed) and the velocities of the outer regions would easily become ...
- 15.4k
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