Light may well mean the diameter of the universe is 96 billion LY, but that doesn’t mean matter is spread across 96 billion LY.
I do wonder where you get your ideas sometimes, @Bonsai!
I thought we had established the radius of the Cosmic Microwave Background is currently 46 Bn Light Years...
Think of it as a sort of Photon Event Horizon beyond which we cannot see with optical telescopes, and it is all pretty straightforward, IMO.
In the foreground is Matter and Galaxies amongst other things.
I was struck by this image purportedly showing The Horsehead Nebula in Orion:
Where have I seen this before?
Surely it is Crow the Robot from MST3K photobombing the picture? 🤣
Teenagers from Outer Space shocks from the outset when Betty's plucky dog Sparky gets capriciously disintegrated by heartless aliens just for barking at them:
I just knew the aliens were up to no good:
Their evil rampage continued, though Betty is seemingly unaware at this stage that she is dating an alien:
Though I thought they had the alien look in the first reel:
The entire $14,000 budget schlock movie can be reviewed here, and certainly an interesting way to spend time:
But what I really wanted to talk about here was the Time Independent Schrodinger Equation:
I solved this one for the 1s Hydrogen atom one hot summer in my teenage years. The left hand side is the Hamiltonian for the sum of Kinetic and Potential energy in spherical coordinates. It is easier than it looks once you guess that it's going to come out at 13.6 eV, and you can plot it for radius r. mu is the electron mass in the simple case, we can then ignore centre of mass corrections for the finite proton mass.
It is a sort of exponential function. Where you have to be careful is allowing for the way the electron seems to be likely to be found at the centre r = 0.
This is not true, because the volume falls off at the centre as inverse cube, reducing the probability, so it looks like this as you have seen before:
Hope I got that right. Schrodinger's Equation in two minutes! 😎
Best, Steve.
I thought we had established the radius of the Cosmic Microwave Background is currently 46 Bn Light Years...
Think of it as a sort of Photon Event Horizon beyond which we cannot see with optical telescopes, and it is all pretty straightforward, IMO.
In the foreground is Matter and Galaxies amongst other things.
I was struck by this image purportedly showing The Horsehead Nebula in Orion:
Where have I seen this before?
Surely it is Crow the Robot from MST3K photobombing the picture? 🤣
Teenagers from Outer Space shocks from the outset when Betty's plucky dog Sparky gets capriciously disintegrated by heartless aliens just for barking at them:
I just knew the aliens were up to no good:
Their evil rampage continued, though Betty is seemingly unaware at this stage that she is dating an alien:
Though I thought they had the alien look in the first reel:
The entire $14,000 budget schlock movie can be reviewed here, and certainly an interesting way to spend time:
But what I really wanted to talk about here was the Time Independent Schrodinger Equation:
I solved this one for the 1s Hydrogen atom one hot summer in my teenage years. The left hand side is the Hamiltonian for the sum of Kinetic and Potential energy in spherical coordinates. It is easier than it looks once you guess that it's going to come out at 13.6 eV, and you can plot it for radius r. mu is the electron mass in the simple case, we can then ignore centre of mass corrections for the finite proton mass.
It is a sort of exponential function. Where you have to be careful is allowing for the way the electron seems to be likely to be found at the centre r = 0.
This is not true, because the volume falls off at the centre as inverse cube, reducing the probability, so it looks like this as you have seen before:
Hope I got that right. Schrodinger's Equation in two minutes! 😎
Best, Steve.
Regarding "the distribution of charge density within the orbitals" (your first graph):
According to Wiki, the electron's charge acts like it is smeared out in space in a continuous distribution, proportional at any point to the squared magnitude of the electron's wave function (ψ).
I found this nice illustration:
"(a) The density of the dots shows electron probability. (b) In this plot of Ψ^2 versus r for the ground state of the hydrogen atom, the electron probability density is greatest at r = 0 (the nucleus) and falls off with increasing r. Because the line never actually reaches the horizontal axis, the probability of finding the electron at very large values of r is very small but not zero."
Read (lots) more here: https://chem.libretexts.org/Courses/Howard_University/General_Chemistry:_An_Atoms_First_Approach/Unit_1:__Atomic_Structure/Chapter_2:_Atomic_Structure/Chapter_2.5:_Atomic_Orbitals_and_Their_Energies
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Indeed, Steve.
The CMB is the farthest and oldest light any telescope can detect.
It is impossible to see further beyond the time of its release because then the Universe was completely 'opaque'.
“I thought we had established the radius of the Cosmic Microwave Background is currently 46 Bn Light Years...”
To my point, that is radiation, not matter.
To my point, that is radiation, not matter.
You are a man of few words, Bonsai!
It appears you are correcting my Wiki quote which said that the CMB radiation was emitted by matter.
You would be correct in stating that the radiation was present from the beginning of the Universe, but was simply unobservable.
Check out the following description for me, inspired by this: https://www.esa.int/Science_Explora...anck_and_the_cosmic_microwave_background#TK1b
Photons were created in the Big Bang along with a hot plasma of particles (mostly protons, neutrons, and electrons).
At first, the photons could not travel any distance before interacting with free electrons, so the Universe was opaque.
It took about 380,000 years for the Universe to cool down to a temperature at which neutral atoms can form.
Photons could then travel freely and the Universe became transparent. The CMB is the relic of that first light.
I must say I enjoyed "Teenagers from Space", even if some of them seemed a lot older than that.
One gripe. "Derek" did seem an unlikely name for an alien. Surely he might have been called something like "Klaatu", which sounds more, well, alien.
I think @Bonsai posts from one of those stupid mobile 'phone thingies... I mean REALLY! I don't care if they have 100M pixel cameras, I can never even read the small letters on them without a magnifyimg glass.
@Galu. I think "the matter" is resolved to our satisfaction. We can leave it there, IMO. 😎
@TNT raised the question of troublesome singularities within Black Holes. I don't worry about them much.
Often, and I leave this for the interested student, IMO, singularities go away with the correct treatment.
For instance, here is the Hydrogen 1s (Ground State) wavefunction:
Clearly a negative exponential times a constant, which we know all about:
It only remains to know what the Bohr radius is and all falls into place:
TADA!
Not quite sure where I am going on that, TBH. And apologies if that doesn't display too well on mobile 'phones. Serves you right! 😀
Of course a child of ten knows that Schrodinger's Equation has theoretical limitations. It is not relativistic, nor does it directly include spin.
For that we need Dirac and later Quantum Field Theory:
As usual, I am doing all the heavy lifting on this interesting topic. 🙄
One gripe. "Derek" did seem an unlikely name for an alien. Surely he might have been called something like "Klaatu", which sounds more, well, alien.
I think @Bonsai posts from one of those stupid mobile 'phone thingies... I mean REALLY! I don't care if they have 100M pixel cameras, I can never even read the small letters on them without a magnifyimg glass.
@Galu. I think "the matter" is resolved to our satisfaction. We can leave it there, IMO. 😎
@TNT raised the question of troublesome singularities within Black Holes. I don't worry about them much.
Often, and I leave this for the interested student, IMO, singularities go away with the correct treatment.
For instance, here is the Hydrogen 1s (Ground State) wavefunction:
Clearly a negative exponential times a constant, which we know all about:
It only remains to know what the Bohr radius is and all falls into place:
TADA!
Not quite sure where I am going on that, TBH. And apologies if that doesn't display too well on mobile 'phones. Serves you right! 😀
Of course a child of ten knows that Schrodinger's Equation has theoretical limitations. It is not relativistic, nor does it directly include spin.
For that we need Dirac and later Quantum Field Theory:
As usual, I am doing all the heavy lifting on this interesting topic. 🙄
It's a struggle following your argument at times.
For instance, it is only in your last post that it is made clear that the a0 in your graphs of posts # 4,252 and #4,262 refers to the classical Bohr radius!
All terms must surely be defined at the appropriate stage if understanding of this complex subject is to be achieved.
@Galu, I made it clear what the Bohr radius was last year. Almost 2,000 posts back in this thread! Had you forgotten?
Anyway, it is an unambiguous physics constant.
https://www.diyaudio.com/community/...enerates-gravity.393908/page-120#post-7504052
Apropos the first physics statement, it really is true that the square root of (510.999 keV / 27.2114 eV) = 137.036, aka the (inverted) fine structure constant alpha, often abbreviated to 1 / 137! Which I find interesting. 🙂
Anyway, it is an unambiguous physics constant.
https://www.diyaudio.com/community/...enerates-gravity.393908/page-120#post-7504052
Apropos the first physics statement, it really is true that the square root of (510.999 keV / 27.2114 eV) = 137.036, aka the (inverted) fine structure constant alpha, often abbreviated to 1 / 137! Which I find interesting. 🙂
You may attempt to obfuscate, but the fact is that you posted graphs employing the symbol 'a0' (a subscript 0) without defining the meaning of the symbol.
That bewildered me at the time and delayed my understanding. I should have asked for a definition, but didn't want to show my ignorance! 🤓
Interesting if we click on Hartree and Rydberg energy, which I may do later!
You'll remember we discussed the fine structure constant at some length earlier in the thread.
Let's hear it for Arnold Sommerfeld (who worked in electrostatic CGS units).
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Hartree energy is just twice the Rydberg energy. It is actually the potential energy of the Coulomb field ignoring the Kinetic energy 13.6 eV. You can check my calculation on your pocket calculator.
You have probably been as concerned by our wretched cloudy North Westerly weather lately as I have been. Happily we may have turned the corner into "Flaming June" now.
I have decided that ISO 800 camera setting is optimal for my nightly Nova hunting:
https://en.wikipedia.org/wiki/T_Coronae_Borealis
TBH, I have my doubts. It's historically 80 years between Nova explosions. Why the boffins get 78 years now, well, I just don't know. 🙁
You have probably been as concerned by our wretched cloudy North Westerly weather lately as I have been. Happily we may have turned the corner into "Flaming June" now.
I have decided that ISO 800 camera setting is optimal for my nightly Nova hunting:
https://en.wikipedia.org/wiki/T_Coronae_Borealis
TBH, I have my doubts. It's historically 80 years between Nova explosions. Why the boffins get 78 years now, well, I just don't know. 🙁
From your current position on Earth, consider standing on a planet on one of those far distant galaxies. You take your torch, turn it on, and point it in any direction you care. The light leaves the torch at 298 million m/sec. From here on Earth it may seem that both planet and light beam are moving at c, but on the distant planet they are not. The light beam is racing away from the planet. One of SR’s paradoxes and why light is probably what sets he outer bounds of the cosmos, not matter. Which raises all sorts of interesting questions about the age of the universe a photon experiences (it’s not as old as matter aka mass experiences it) and its diameter (it’s not big and it’s two dimensional like a sheet of paper), both subjects we have touched upon earlier in this thread or its predecessor thread - I can’t exactly recall.
Our observable universe is a sphere around 92 billion light-years in diameter.
However, we should not regard our planet as being at the centre of the Universe.
Nor should the inhabitants of a planet in a distant galaxy who have their own observable Universe.
You speak of the Universe having "outer bounds" when it could actually be infinite in extent.
We and the aliens can really only conclude that the Universe is much larger than the volume that can be directly observed.
Well, I didn’t say we were the centre (we are sort of to ourselves and I suppose the same for aliens on the distant planet in the galaxy that is now similar to the age of our galaxy). I simple made the point that the outer bounds of the cosmos, wherever that may be, we’ll be where light is and not mass. There is no proof btw that the universe is infinite. If it started 13.8 billion yrs ago then it can’t be.
Whether the Universe is finite or infinite depends on its shape. We've described the three possible topologies of the Universe before.
There is mounting evidence that the Universe is flat. This indicates that the Universe is infinite and doesn't curl up into a closed ball.
https://www.astronomy.com/science/i...f,that the universe is flat and thus infinite.
I admit to being slow on the uptake! Can you explain in more detail why you think that "light is probably what sets the outer bounds of the cosmos, not matter".
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It could be flat but still have an "edge". An edge that would be impossible for anything to pass. Outside this edge it is 0K so no time passes. No material or light pass this edge as they can not conquer gravity of universe. Still, there is someting there.... but it is beyond the expansion of inflation. Inflation also stopped at this edge. Eventually the edge will fall back on its origin and it all starts again 😉
All agree? ;-D
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All agree? ;-D
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We do not know. But if the universe started a finite time ago, how can it be infinite?