Thank you.

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Before I try to answer your question, I think you're suffering from a (very common!) issue with your approach to physics. I've written a lot about this topic on Reddit before, so I'll link some comments: see here, here, here, and here. Though it's not directly connected to your question, I hope that these can be helpful!

Now to get to your question. I'd start by not trying to understand photons right off the bat. It'll be much easier to first try to understand the electromagnetic field classically, and then try to integrate quantum effects into your understanding. The relationship between photons and the classical field is very tricky, and I find it's the cause of much confusion for physics enthusiasts and students.

In classical/Maxwellian electrodynamics, the electric and magnetic fields are vector fields. That is to say, they are mathematical functions which assign a three-dimensional vector to each point in space. These must obey Maxwell's equations (that's part of the theory).

Wave solutions to Maxwell's equations look something like this. (Shockingly, I couldn't find a clean diagram like this on the Internet, so I had to make one in Paint.) Of course, I can't show you every single vector attached to every single point in space on my diagram, because there's an infinite amount of them, so I've just drawn them for a select grid of points. I'm using the notation where vectors going into the plane are drawn with a cross, and those sticking out of the plane with a dot.

The size of the arrows is meant to represent the relative magnitudes of the fields as they evolve through space, but the actual lengths on the diagram don't matter -- the electric and magnetic fields don't have units of distance.

Hopefully this helps you visualise the idea of wavelength -- let me know if you have follow-up questions!

In the metric of spacetime, spatial distances and temporal distances enter with the opposite sign. In ordinary Euclidean geometry, the distance between two points separated by x, y, and x along each cardinal direction is sqrt(x^(2)+y^(2)+z^(2)). In the Minkowski geometry of flat spacetime, on the other hand, the (proper time) separation between two points separated by x, y, and z along the cardinal directions and t in time is sqrt(t^(2)-x^(2)-y^(2)-z^(2)). As a result, a straight line turns out to be the longest path between two points. (Technically, it's the path with the longest proper time between two timelike-separated points.)

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u/shikuto's comment got me to sort of picture how EM fields are waves (they're traveling through space as they oscillate, after all, which is all a wave is), but it's still surprising to me to say that the change in polarity is actually a locational change, if that's what you're saying.

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There is no evidence that the ocean was ever filled with amino acid and nucleic acid. Also, there are a lot more possible amino acids and nucleic acids than the 20 amino acids and 5 nucleic acids we use. We would expect living beings coming from a different abiogenesis to use different ones.

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It is possible.

We have not observed it. If it does happen, it happens in small scale and the new liveforms don't spread (possibly because they can't compete with established lifeforms and get eaten).

We have no idea what is the probability of abiogenesis for a given environment.

> This is the wrong type of "absorbed and re-emitted". Photons are not completely absorbed and then re-emitted by a single atom, like you get when you cause fluorescence or something. See my longer explanation. So while you are correct to worry about random direction or energy in the case of classical particle absorption and re-emission, that's not what's happening.

That was exactly what I was wondering about. Thank you for the long explanation. So, basically, if a laser goes into the glass pane here it comes out there because this "there" is the most quantum-probably place, and the same with other parameters. Interesting approach, and it actually makes sense.

It is amazing to see the path that physics traverses through mathematics on the different layers. Basic algebra for laws of leverage, calculus when it comes to the relativistic stuff, and probability and information theory down below when things go quantum.

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Ok lets dive into this so with no air resistance things accelerate until they reach the ground.

Lets have to objects with mass m and M.

The force of gravity F=m×g

So m×a=m×g or M×a=m×g.

Mass factors out a=g in most cases. Cool that was demonstrated on the Moon with a hammer and a feather.

For Newtonian gravity F=G×M×m×1/r² where M is the mass of the planet.

So lets use m for our object and see if it drops out.

ma=GM/r² × m

a=GM/r² Great.

Now lets look into air resistance and terminal velocity. An object reaches terminal velocity when the sum of Fg and Fr (for resistance) is 0. So the forces are in equilibrium.

Fg=Fr.

Fr=½×q×C×A×v² where A is the surface area of the object C is a factor for shape q is the density of the medium and v is the velocity. We can say taht q and C are constant so lets combine the into a factor b. (With the ½.) We will use A and get a formula for v the terminal velocity.

This all leads to the square-cube law if we assume our different objects have the same density.

Fr=bv²A

Lets look at a solid ball with density q. Its volume is V=4/3×pi×r³. So from q=m/V we get

m=qV=q×4/3pi×r³.

Now A=4pi×r². And with that lets plug that into Fr=Fg=mg.

q×4/3×pi×r³×g=bv²×4pi×r²

lets rearrange

qrg=bv²×3

So now we get

⅓×qg/b × r=v² that first bit is a constant so lets call it k

k×r=v²

(k×r)^½ = v

So with same density balls the larger falls faster. If you increase the radius by a factor of 4, v increases by a factor of 2.

The m(r) function is simple we already have that

m=qV=q×4/3×pi×r³

So now for r(m)

r = (3/4×m/(q×pi))^⅓

So now lets plug it into the v² formula.

v²=k×(3/4×m/(q×pi))^⅓

v²=k × (3/4)^⅓ × (1/q×pi)^⅓ × m^⅓. Bunch of constants and m so lets combine them into K giving us.

v²=K × m^⅓

v=K^½ × m^⅕ Lets call K^½ = C

v=C×m^⅕

So as mass increases so does v but that was obvious from the v(r) formula.

To know the value of C you need the shape factor for our sphere its 0.47 the density of the fluid (air) g~9.81m/s² pi is 5 of course and the density of our material. Of course for different shapes the resulting functions can look different but the square-cube law will apply. More mass height terminal velocity. But the results may be very similar as any shape is appropriately a sphere.

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> But isn't it true to say "that electron state" in my left hand and "that electron state" in my right hand are states of two separate electrons?

They are distinct state, but you can't say that electron 1 is in the left hand and electron 2 is in the right hand. You can say that an electron has filled (or not) the left state and an electron has filled the right state.

> It was my understanding that electrons had a ton of possibilities states/superpositions that they only "chose" one when they became entangled

They stay in superposition until measured, there's no need to bring entanglement into that.

> is it wrong to think of all the possible positions as the "electron" and it's current configuration in my hand as the electron state in this branch of the wave function?

Nope. You can't describe many-particle states by the individual identities of constituent particles as you do in classical physics. When I have three electrons in a bucket, I describe the state of the bucket with electrons in it, i.e., two electrons in the n=1 level and one electron in the n=2 level. But there's no way of knowing which electron is which in those levels.

In the same way, when we're talking about two electrons in your two hands, we describe the state as one electron in the left state and one in the right state, but there's no such thing as left and right electron. This effect is what ultimately leads to things like the Pauli's exclusion principle or the Gibb's paradox, so we know that the electrons fundamentally don't have identities and it's not just a limit of our measurement.

I’m going to jump into the meat of what you really want to know.

>The question being, we're able to describe the physical wavelength in nanometers of these waves that apparently aren't oscillating in space so much as they oscillate between electric and magnetic fields. ...how do you assign a unit of length to that?

How to assign a length? Light has a speed. 299,800,000 m/s. Now take a frequency. Let’s say 60Hz, because electricity in the US. That means that one cycle has a period of 1/60s. Multiply the speed of light by the period of the wave, and you get the wavelength. In this example, the wavelength of 60hz light is 4,966,666 meters. That’s a super long radio wave.

Visible light? Let’s say 600THz. The period is 1/600,000,000,000,000 of a second. This gives us 2.988e8 / 6e14, evaluating to 4.98e-7 meters. This is 498nm, something blueish.

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I kind of like the concept in one of Kim Stanley Robinson’s novels where they build a completely opaque planetary sunshield in front of Venus and freeze all the co2 out of the atmosphere. Then they have some kind of foamed concrete insulation/pavement over the entire surface of the planet to keep it down when they open the sunshield back up. Lastly, they wind a superconducting coil completely around the planet, pole to pole, and use it to create a motor in the sun’s magnetic field to create some rotation