Many are the Mysteries of the Universe. I can scarcely keep up with them all, except by bringing Clarity to the individual matters.
Even the Kepler problem of Planets under the inverse square Law is little understood, which is why I try to find time for Lectures about the central inverse-square force:
https://johncarlosbaez.wordpress.com/2015/03/17/planets_in_the_4th_dimension/
What is boils down to is that Energy and Angular Momentum is Conserved. But a Third more abstract Quantity is also Conserved, and we don't often think about this:
https://en.wikipedia.org/wiki/Laplace–Runge–Lenz_vector
This, in a nutshell, is the Eccentricity of the Orbit. And it relates to a symmetry of Time itself, IMO. Amazing!
Even the Kepler problem of Planets under the inverse square Law is little understood, which is why I try to find time for Lectures about the central inverse-square force:
https://johncarlosbaez.wordpress.com/2015/03/17/planets_in_the_4th_dimension/
What is boils down to is that Energy and Angular Momentum is Conserved. But a Third more abstract Quantity is also Conserved, and we don't often think about this:
https://en.wikipedia.org/wiki/Laplace–Runge–Lenz_vector
This, in a nutshell, is the Eccentricity of the Orbit. And it relates to a symmetry of Time itself, IMO. Amazing!
There's a high degree of eccentricity in this thread!
I'll study your attempts at clarification later.
Right now, the giant fusion reactor in the sky is shining and I'm off for a ramble. 😉
I'll study your attempts at clarification later.
Right now, the giant fusion reactor in the sky is shining and I'm off for a ramble. 😉
Considering the Kepler problem in spacetime allows the reparametrisation of time?
Sorry, I'm simply not having it. My time is too precious! 😉
yes and the hair on your head(if you have any) and your toenails are growing at relatively different rates. 😵
True, but that's an entirely different topic from the one referred to in Steve's link.
There's two effects.
First is Velocity, which is Special Relativity so the guy on Earth ages faster:
Second is Gravity, which is General Relativity and the guy on Earth ages slower:
https://www.space.com/36273-theory-special-relativity.html
Quite tricky to calculate, IMO. These effects work in opposite directions, don't they?
A comparison between fingernail and toenail rates of growth would be far more appropriate.
That's a dimensional problem. Energy = A/r in terms of potential Energy. Familiar equation, The Hamiltonian of central forces. It's in the Woit book.
https://johncarlosbaez.wordpress.com/2015/03/17/planets_in_the_4th_dimension/
Now this is interesting:
What else is inversely proportional to distance in the Kepler problem?
These TWO effects are taken care of satellites of the GPS system.
If they were not, positioning should not work at all because of two much clock drift. A nano second is a foot long.
Aa, so Cosmos is the "biggest" entity we talk about. So thats everything?
Cosmos -> Universe -> Visible universe -> ... OK?
//
Part of the extract reads "different universes within the overall cosmos".
The definition of "cosmos" is "the universe, especially when it is understood as an ordered system".
So, perhaps Morison considers that the cosmos is an ordered system of universes? 🤔
The definition of "cosmos" is "the universe, especially when it is understood as an ordered system".
So, perhaps Morison considers that the cosmos is an ordered system of universes? 🤔
Define "familiar"! 😀
The Hamiltonian is associated with orbits in central force fields.
I read that the Hamiltonian description is especially useful for finding conserved quantities, which play an important role in describing orbits.
I also read that Hamiltonian mechanics is a reformulation of Lagrangian mechanics.
However, it's all Greek to me! 😵 https://en.wikipedia.org/wiki/Hamiltonian_mechanics
Its crazy that cristal osccitate at relatively different frequency in same circuit .in different time conditions. Not saying its miracle . But relativity is wonder of nature
I had to duck out last night. Decided I would learn more about the Universe from a good Physics book than listen to the random remarks here.
Shame on you! Lazy students!
Aside all the interesting considerations of Gravity, Relativity and Quantum Mechanics, you need a reset in your thinking.
Only 5% of the Universe is Particles. Mainly Protons by mass. Photons and electrons are a tiny fraction of that, but are what we mostly see in our lives. The Electromagnetic force is 99%.
20% may or may not be Dark Matter. Maybe massive right-handed Neutrinos. Nobody knows. If Dark Matter disappeared tomorrow, we wouldn't notice for millions of years, so slowly does our galaxy rotate.
75% is Dark Energy, which may or may not be the Energy of Space-Time itself.
What it boils down to, is it is Fields that make up the Universe. Particles are just a sugar-dusting on the main event. Excitations of the Field.
Shame on you! Lazy students!
Aside all the interesting considerations of Gravity, Relativity and Quantum Mechanics, you need a reset in your thinking.
Only 5% of the Universe is Particles. Mainly Protons by mass. Photons and electrons are a tiny fraction of that, but are what we mostly see in our lives. The Electromagnetic force is 99%.
20% may or may not be Dark Matter. Maybe massive right-handed Neutrinos. Nobody knows. If Dark Matter disappeared tomorrow, we wouldn't notice for millions of years, so slowly does our galaxy rotate.
75% is Dark Energy, which may or may not be the Energy of Space-Time itself.
What it boils down to, is it is Fields that make up the Universe. Particles are just a sugar-dusting on the main event. Excitations of the Field.
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