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No, spectral lines have finite width for a variety of perfectly good reasons. (Finite line width means there is a range of absorbing or emitting frequencies of course.) These include the Doppler effect, from motion of the emitters relative to absorbers, and uncertainty broadening, due to finite lifetime of the excited state leading to uncertainty in its energy, by Heisenberg's Uncertainty Relations. In gases, this can be a function of pressure, cf. "pressure broadening", since collisions may shorten lifetimes of excited states and also alter their energy, due to transient proximity of second atoms, thereby disturbing the potential experienced by the electrons. And for matter in condensed states, atomic lines tend to get broadened into bands anyway, due to the overlay of vibrational and/or rotational fine structure. If you read up a bit about spectroscopy, there is quite a bit to it besides simple line emission and absorption.

Great stuff. Bach innovated in so many ways, counterpoint, modulation, four part harmony, use of dissonant chords, even in stepping back to Dorian mode and others. Always a fan. And provider of Bach jokes.... Why did Bach have 20 children? Because there were no stops in his organ.

I'm a little late, I think all aspects are sorted out already. But I had started drawing a picture of different aspects of the relative velocities in the scenario. Posting in case anyone finds it helpful: Rocket A is traveling from space station a at velocity VAa (Aa denotes that the velocity is the relative velocity between a and A) Rocket B travels from station b at velocity VBb . The rockets will meet head on and VAa=-WBb Equations: 1: a and b (the space stations) are at rest relative one another, in the same inertial frame of reference 2: When each rocket's crew measures the velocity of the other approaching rocket, relative to their own rocked, the velocity does not match the sum of velocities relative their starting points. (Assuming the correct sign is used since velocity is vector) 3: for low speeds the sum of velocities is a reasonable approximation 4: Rocket A will measure its speed relative its starting point to be the same (with negative sign) as the rocket B will measure relative it's starting point 5: Rocket A will measure leaving a with the same velocity that it is approaching b (minus the sign) 6: In any case the relative velocities between the rockets, measured by crew on board A, is greater than the rocket's velocity relative it's starting point a (and symmetrical for rocket B and crew) 7 (now shown) observers on a or b will agree that the rockets will meet half way between a and b. The sum of distance traveled by A plus B can be more than a light signal could travel in the same amount of time. (did this in a bit of a hurry between other things, please point at errors)

for the differential aging in the twins' paradox, not the acceleration, nor the frame change. Yes, when the orbiting twin turns his gaze around, he will appear to be approaching instead of receding. So the redshifted view of the tower clock will change to blue shift, the difference being purely Doppler effect in both directions. The dilation is due to speed, and speed isn't affected by where anybody is looking, so the dilation is unchanged at the far side of the planet. Yes, there is acceleration, but all of it orthogonal to motion, so since the 'twins' are at the same potential, the dilation is constant for the entire orbit. It is objective. The orbiting twin will be younger when the meet again, just like the one that goes out and back to the distant star. To do this in special relativity, the planet can have no mass, and the 'orbiting' twin would need to curve his path via say a string tied to the center of Earth to get him to curve is path like that. Rockets also works, but the engineer in me hates to waste fuel when there's a better way.

Yes Bach seems to be a great inflexion point in the evolution of Western music. All the pros play Bach, even rock musicians. I remember once talking to a Thai pianist, playing jazzy hotel stuff in a hotel bar in Bangkok. My colleague asked him what music he played for pleasure at home and he replied "Bach". I tried to persuade him to play some for me, as he was taking requests, but he said the hotel management wouldn't like it (!) and I could not convince him. I also recall once listening to an organ performance of the Art of Fugue in my room in Oxford, when a fellow chemist came in who was a jazz clarinettist (He had been a member of the Kent Youth Orchestra before coming up). One of the weirder fugues was playing and he couldn't make it what it was. He thought it sounded so edgy it must be some c.20th composer - Messiaen or something. He was amazed when I told him. But if you liked what I posted, this (opening chorus, 1st 7 mins) is another of my all time favourites as a choral singer, from Part V of the Christmas Oratorio (apologies if I've posted this one before at some point): You have to click the "watch on YouTube" link to see it. This is also in 3/4. My impression is Bach does not often use that time signature and when he does, he often thinks it's time for some gaiety. In the video you can actually see the musicians enjoying it. They are making eye contact with each other and smiling.

Just to link it up for Moontanman, the bits I bolded above are worked examples (reverse order) of what I described in the 3rd post:

It was, because otherwise one rocket's relative speed to the other one is equal and opposite to the converse, no matter what relativity principle you use (Galilean or Einsteinian). It's exactly as Swansont said with 0.5, 0.5, giving 0.8 (in units of c) It's perhaps an illuminating exercise to do it with 0.99999 and 0.99999. It gives (0.99999+0.99999)/(1+0.99999*0.99999) = 0.9999999999 (in units of c) which is practically just c. But, and here's what interesting, with small velocities as compared to c. 0.00001, 0.00001, it gives (0.00001+0.00001)/(1+0.00001*0.00001)=0.00002000000000 which is so close to the simple addition of velocities that nobody could tell the difference. That's why our intuition tells us velocities are additive.

Fantastic indeed. Thank you. The Suite muffled by the voices was great for setting the mood. I've long felt that all music gravitates towards Bach... or emanates from it. Or something like that. I feel that music before Bach is a preamble to Bach. And music after Bach is a corollary to Bach. Even atonal music seems like an attempt to break the shackles of Bach while still doing music. Like 'how little Bach can one get without making just noise?' I'm very partial about Bach, you see. I'm very Bach-centred. So thank you.

RIP Dickey Betts

If two rockets each approached the space station at 0.5c, from opposite directions, they would be approaching each other at 0.8c (.5 + .5)/(1 + 0.5*0.5) (Galilean addition would give you c)

There are some attempts in that direction, mostly targeted at toxic VOCs. From what I recall, it seems that likely microbes are responsible for oxidizing some of the VOCs and breaking them down . But I don't think that algae were shown to do that. Conversely, I vaguely remember that some algae actually release VOCs (though I cannot recall whether those were in any form harmful). The provided link paints a very poor picture of the capabilities of the company, considering they are conflating CO2 capture with capture of harmful substances (via photosynthesis, no less). Failing that much at basic biochemistry does not inspire confidence. The blurb also seem to suggest that this is just an exhibit, likely putting some algae (or even just a green liquid) into a stand. A real bioreactor for cyanobacteria or algae needs quite a bit more to work. And randomly growing cyanobacteria can also produce toxic microcystins. So there is also that. From what I remember the carbon yield (for fuel or plastic production) was also rather low. I am also skeptical that oxygen production from those volumes would be significant, but I may be wrong.

Your right I didn't bother responding to your logic. As I stated I lost interest. Particularly when you have statements such as information travelling faster than c that you cannot back up with any real physics or mathematics. This includes your holonomic toroid allowing a faster than c wave. This runs counter to well known and understood physics. So any logic based on this is meaningless if you cannot show how that's even possible under mathematics using known physics. Another example is some mysterious toroid travelling at c. It must be something massless to do that. However you can't describe it beyond your verbal claims. I also have no interest in downloading a paper from an outside source when the rules requires that material to presented here.. Who knows you might catch my interest once you start applying some real physics or mathematics. Rather than nothing more substantial than your logic

The comments are helpful,the latex and machete,I will try where I can or mayb try to reverse engineer my own ideas and theories,to be on the same table rather than light-years away to avoid a hangman noose. All the same I thought I hand tried to step away from diagrams for simple brains to mathematics...and mayb the input of likes of Mordred, sincerely talking not trivializing others,in my other thread, simplified quantum gravity, he had a lot of input and i had been waiting for him to come back on the forum to just get his take, brilliant brains seems to vanish away with age i.e you can't ask today Higgs a question regarding Higgs boson. and after reviewing my former thread i saw a need for mathematics to bring clarification to my thinking and to tackle Genady on issue concerning geodesic paths and finally settled the issue on faster than the speed of light that unsettled exchemist and others.sometimes whining help but in this form 😂😂😂 or rather 😭 to clean the eyes.