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It certainly depends on a belief in the waviness of light—if light were particulate, it could just go blasting through empty space with no need for any Æther to carry it.

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Vanderjuice hits upon one of the greatest oddities in physics: the wave-particle duality. We now know light goes blasting through empty space. But it still acts like a wave in so many other regards. I don't know anything about physics (except how to strike a pool ball a certain way to get it to go where I want!) and even less about quantum physics. Maybe quantum physics explains this odd duality better, where something acts like a particle on Tuesday and then a wave on Thursday. But it seems to me there must be a third thing that is both somehow and we're all just too stupid to come up with an satisfying equation for it. It's probably because you can only understand the properties of the warticle when observing it from a higher dimension. Like in a balloon. Man, I sure miss the easy reading of the Chums of Chance chapters!

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 Sir Oliver Lodge defined it as 'one continuous substance filling all space, which can vibrate light . . . be sheared into positive and negative electricity,' and so on in a lengthy list, almost like the Apostle's Creed.

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"Sir Oliver Lodge"
Vanderjuice probably found this quote in Modern Views of Electricity from 1889 but I'm not going to read that book just to verify it. Sir Oliver Lodge also wrote a book in 1925 called Ether and Reality in which he defends his definition of Æther even though it was already a scientific relic of the last century. His need to believe in an invisible substance with a major effect on reality probably stemmed from his deep conviction in the afterlife, having been convinced by several mediums that he could speak with his son Raymond who had died in the First World War. His belief in spiritualism was seen as quite a flaw in the scientific community because Sir Oliver Lodge had pushed the knowledge of electricity and electromagnetic fields forward by some distance. He even received a patent used in radio which Marconi ultimately had to pay him to use. And spark plugs! His family sold spark plugs!

"one continuous substance filling all space"
For some reason, this brings to my mind this quote from Gravity's Rainbow: “If there is something comforting - religious, if you want - about paranoia, there is still also anti-paranoia, where nothing is connected to anything, a condition not many of us can bear for long.” It's as if Lodge's view of Æther is that of the paranoiac: the connection of everything to everything else via some invisible substance gives comfort. It is all connected. There's a strong meaning to be found in having things connected.

"which can vibrate light"
I suppose the vibrations of the Æther is what supposedly propagates the waves of light.

"be sheared into positive and negative electricity"
Is that how we get electricity? Shine light into a razor sharp angle so that it is split into positive and negative charges? It doesn't seem right but then it also kind of seems right in that static electricity is pretty much the shearing off of electrons onto something that isn't particularly capable of holding strongly onto those electrons and, as such, you shock the face of your cat and it gets pissed at you.

"Apostle's Creed"
First off, Mr. Pynchon, it is "Apostles' Creed." Normally I would put this blame on Vanderjuice, the speaker, but since there's no audible difference between the versions, I'm going to have to blame Pynchon, the colossal hack writer. Anyway, I only know that because being raised an areligious person, I had to look up what the hell the Apostles' Creed was. It's just a litany of "I believe" statements. I guess, in religion, that's how you argue logically. You just keep restating to yourself, again and again, that you believe in nonsense because if you ever stop declaring you believe it, you might actually think about it and see the pure nonsense yourself. So what Vanderjuice is saying is that Lodge's writing about Æther pretty much just amounts to a bunch of "I believe" statements without seeing any need to back them up with evidence. The colossal hack!

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 Lord Salisbury said it was only a noun for the verb 'to undulate.'

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"Lord Salisbury"
Robert Arthur Talbot Gascoyne-Cecil, 3rd Marquess of Salisbury. He was Prime Minister of the United Kingdom three times in the latter half of the 19th Century. I don't know why he was weighing in on the possible existence of Æther except that people sometimes want to know what powerful politicians think. This guy seemed pretty smart if absolutely a model of conservative British politics. My favorite bit about him was his credo: "Whatever happens will be for the worse, and therefore it is in our interest that as little should happen as possible." Being the leader of the greatest imperial country of the 19th Century, this motto did not stop him from winding up with the most territory in the Scramble for Africa. I suppose that was more a case of the worst happening and less a case of as little should happen as possible. Because, you know, Britain could have sat out plundering Africa with the other imperialists, could they have not?

This guy looks like his credo.

"a noun for the verb 'to undulate.'"
I don't know if he really said this or this is just Pynchon fictionalizing some possible dialogues surrounding Æther at the time but it definitely sounds good! The main reason for Æther's existence was to give light waves something to travel, or undulate, through. The movement of light waves simply needed a medium, or noun, to make sense.

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 Some don't believe in it, some do, neither will convince the other, it's all faith at the moment.

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Think about science as theories based on observations and we can understand the kind of "faith" Heino means. If early "scientists" (just meaning curious people who actually consider the world around them rather than horny people just trying to get laid (which we need too! I'm not judging!)) were to first observe fish, and the only thing they knew was that they, and most animals they knew of, would drown underwater, they would probably come up with a story, or theory, as to how the fish survives. Religion is theory based on observation without evidence. That's where faith actually lies. Science is theory based on the current best understanding of what's being observed and which everybody knows is liable to change with new evidence. That's hardly faith! But back to the fish watchers! A theory one of the early scientists might come up with is that fish don't need to breathe. They're just different. Everybody might nod their heads and say, "Yeah, yeah! That sounds reasonable. They seem fine underwater yet no animals we know of can breathe underwater. Therefore fish don't breathe." Belief in that story would be Heino's version of faith. It makes sense through observation and an understanding of the world around them. But as soon as somebody takes a fish out of the water and sees the way it gasps and eventually dies, the theory would immediately change. Obviously the fish is trying to breathe! But it drowns on land the way people drown underwater! So they do breathe but they seemingly breathe water. Boom. That's the new story that some will believe, some won't, and nobody will convince the other because the evidence to support either assertion isn't in yet. It's all faith.

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 "You're quite right, of course, the Æther has always been a religious question.

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"a religious question"
I suppose all scientific theory must be born from faith or we would ultimately learn nothing. If we only believe what we see evidence of without somebody extrapolating further on their observations, then nobody would ever come up with theories to test. At what point does a scientific theory go from the religious to the scientific? It seems to me what's most religious in the arena of science is when the evidence has stacked up against a long-held theory and yet adherents continue to cling to it.
    Here Heino agrees with Merle that Æther has been a religious question because it has merely been theorized as something needed to uphold scientists' views on light and its properties. Kind of like how String Theory's multiple dimensions haven't been proved in any actual way but are only theorized because of the math. Or maybe dark matter is a closer comparison, pretty much being the modern day equivalent of Æther in that it seems to be needed for the current model of the universe and general relativity to work.

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 They strolled among the elm-shadows, eating sandwiches and apples out of paper bags, "a peripatetic picnic," as the Professor called it, slipping thereupon into his lecture-hall style.

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"elm-shadows"
Elm trees create plenty of shade and are one of the most popular trees to be used in public landscaping, often planted as boundary markers for paths, creating tunnel-like effects when planted to either side of a path. The elm is both a symbol of pastoral peace and death. Perhaps Heino and Merle are walking in the shadows of these border trees because they are, technologically speaking, crossing from a time of pastoral peace, where technology has begun to make impacts in our lives and seen as improving them, toward a time when technology will begin its decent from the peak of improvement, hurtling toward the ground as it becomes destructive and deadly, until it finally crashes beyond the zero into nuclear annihilation.
    Or maybe its just a bit of descriptive tat.

"eating sandwiches and apples"
Apples being the symbolic fruit of which Eve partook. Yeah, I know the fruit is never actually described but instead of being a pedantic nerd on the Internet, how about understanding the cultural symbols all around you. There's a reason the Apple logo is that of an apple with one bite taken out of it. And it's not because it's the mark of the beast and an indication of man's inability to resist temptation! It's about gaining knowledge! Maybe those are the same things though. See my comments on "elm-shadows."

"out of paper bags"
They didn't have plastic bags yet! If you want to learn more about the history of plastics, Pynchon covers that topic in Gravity's Rainbow.

"a peripatetic picnic"
This is a pun. The Professor is commenting on how the picnic is a traveling picnic but also it's a picnic where they discuss philosophical matters as they eat. So peripatetic as the adjective in that they're traveling but also as in The Peripatetic school founded by Aristotle, as we see Heino begins to lecture Merle as they walk.

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 "Guess I'd better go take a look. Probably that gear train again."

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The guy just came out with singed hair and smelling of burning flesh and cleaning products. I don't think it was the gear train. I think the Professor decided to try holding the Leyden Jar in his non-cranking hand. He may also have been re-attempting the "What happens if the jar is down my pants?" experiment. Maybe he was rubbing the glass spheres against his scrotum to generate the static electricity? Am I projecting too many of my own kinks onto the Professor? Although his name is Heino Vanderjuice. There's got to be a semen joke in their somewhere.

Maybe the more important part of Merle's response is for the reader to understand that Merle has the know-how to build and fix an electrostatic generator!