Strange

They have nothing in common because you have chosen two different lines (with different values of m and b). As a real mathematician would know, if we have a single straight line, we cannot determine the value of m and b from a single pair of x and y values. However, if we have two pairs of x and y values then we can solve for m and b. One simple way of calculating b is to set x to zero. And then the value of b is just the y-intersect at x=0. Contrary to your ludicrous claim: THIS DOES NOT MEAN THAT THE VALUE OF b IS ONLY CORRECT WHEN x=0; it always has that value in the equation. So this mathematically proves that you claim that we cannot use a "special case" more generally is wrong. We can, of course, calculate the values of m and b using any arbitrary x and pairs (just as we can derive the the Lorentz transform using any combination of frames in relative motion). It just becomes slightly more complicated.

That could change the initial rate of acceleration of the lead (or whatever). Depending on what the mass and radius actually are. I'm not sure if lead is a good candidate for fusion at all. It would require a significant input of energy, rather than releasing energy. Although the result would almost certainly be unstable and start to decay by fission. Like the LHC? (which achieves much, much higher speeds, and therefore energy, than your scenario.) We have detailed mathematical descriptions. But none of them are testable because we cannot get any information from inside a black hole. But as current theories predict infinite density at the centre, they are assumed to be wrong/incomplete. For a rotating (ie. real) black hole, the structure is quite complex with multiple zones outside and inside the event horizon: https://www.forbes.com/sites/startswithabang/2019/06/01/ask-ethan-whats-it-like-when-you-fall-into-a-black-hole/

“2–8 years (occasionally much longer)”

In linguistics, this is called "intonation". (Inflection is modifying the word for grammatical reasons, like adding an 's" to indicate plural in English.) There is some background here: https://en.wikipedia.org/wiki/Intonation_(linguistics) but any introduction to linguistics (and some language-learning texts) should cover it.

Wouldn't that be weird, though, if they were. Even weirder if everyone in a society ended up synchronised as well!

From Wikipedia: https://en.wikipedia.org/wiki/Hair_follicle#Timeline

I can see that this might work (qualitatively, at least) if you just consider two objects. But say you have three objects: the Earth, the Moon and a meteor in space falling towards the Earth. If we describe gravity in terms of the objects getting bigger (and so the relative distance decreasing) doesn't this imply that the meteor will also be getting closer to the Moon?

No, it is one problem (the relationship between two frames of reference in relative motion). The three cases are just ways of eliminating one of the variables at a time in order to solve the equations with multiple unknowns. It is a completely standard technique. As any mathematician could tell you. As mathematicians and physicists have been examining this for over 100 years, and none have spotted this "error" I don't think that suggestion is particularly useful. (Apart from the fact that swansont is a physicist, of course.)

Right. We have shown you where you have gone wrong in your criticism of [7]. There is clearly nothing more to say (because you refuse to acknowledge your error). So lets move on to your analysis of the derivation here: https://thecuriousastronomer.wordpress.com/2013/03/10/derivation-of-the-lorentz-transformations-from-first-principles/

I agree that "model" might be a better description I'm sure something like this could be the basis of model, bit it would probably require all sorts of ad-hoc things added, because what you are actually modelling is the way gravity works! For example: Why would that slow down the expansion of the grid? There is nothing inherent in the grid model that requires this; it is just added because it seems to be necessary to make the model accurate. There are a few other things like that. But it may not be a completely mad idea. After all, in GR, when you are stationary on the surface of the Earth you are accelerating upwards continuously (which is why you feel like you are being pressed into your chair: just like when a car accelerates). It isn't obvious (to me) that "things getting bigger" is equivalent to "things staying the same size but moving closer together". (I can't think of a compelling counter-argument either. ) It may just be a change of coordinates. But how does it fit with the inverse square law? And would things free-falling at different distances need to be expanding at different rates (because they are approaching each other at different rates)? How would orbits work in this model? The size of the orbit would have to increase at the same rate that things were expanding; is there a mechanism for that? The model might work conceptually, but I would like to see some quantitative results from it. You might also want to look at the "waterfall" model of space where, instead of representing gravity as spacetime curvature it is represented as space "falling" towards massive objects.

Interesting. I didn't know there was so much variability.

! Moderator Note Moved to Speculations. Please read the specific rules for this section of the forum, particularly the need to provide evidence or other support.

Baking powder is a mixture of sodium bicarbonate and tartaric acid

10 amps at 10 volts? That's 100W; something should be getting very hot. Not sure it is relevant, but that will react in water to produce CO2 gas (and leave sodium tartrate dissolved in the water).

hipster doofus suspended for 3 days for repeatedly spamming the forum with their pet idea

Clearly you are not willing to listen to anything that contradicts what you believe. As I said, you can easily derive the same equations without assuming x'=0, it is just a simplification. See the link provided by swansont, for example. You haven't shown that is wrong.

! Moderator Note Do not bring this subject up again unless you have something more than opinion to back up your claims. Science doesn’t care about “reality”, only what can be modelled and tested. Until you can model and test your claims, they are not science and do not belong on this forum.

You can continue to assert that but it isn't true. You can easily derive the same equations without assuming x'=0, it is just a simplification. They are not experiments. I think you are the one who needs help from a competent mathematician. Well, it is a proof that the mathematics is correct, because thousands (probably millions) of real mathematicians have looked at it. There are regular claims from crackpots that it is wrong, but that is always because they have failed to understand it. It is obviously not proof that the theory is correct because, as Hawking says, that is not how science works.

I did (Eqn 2.5 does not involve x' and so cannot be dependent on the value of x') You are. No one will. After 115 years of mathematical development and experimentation. You are clearly wrong. You do not have the right to dictate that. (If you think that people are taking the thread off topic by referencing sources that show you are wrong, feel free to report the thread, using the Report Post link.)

"Applies to" is not correct. It uses x'=0 as a simplifying assumption. The equations derived from this do not only hold when x'=0 (for example, x' does not appear in eqn 2.5; it is generally true, for all x'). You can do the derivation without making that simplifying assumption, it is just more complicated. (That seems to be the approach taken by the page that swansont linked to.) I think it shows that your claim to be a mathematician is somewhat exaggerated. That is a reasonable description of how the equations of SR were derived. And, as already noted, it is consistent with experiments. Pleas show what you think the error is in that third one.

Then you would (I guess) find that energy is decreasing as the universe expands. Although, there is the zero-energy universe hypothesis.... It is the change in scale factor; in other words, just the expansion of the universe (you can think of it as stretching the wavelength of the photon).

That is not a frame of reference, it is the measurements that are used (in any frame of reference). For example, two people in relative motion will be in different frames of reference (even though they both use space-time to measure things) and they may each say that a given system have different energy. In the case of the universe, light from the past comes from a frame of reference that has a different scale factor. Energy is not well defined. Would you add up the energy as you see it? Or as someone at the source of those photons measured it? Or ...? Nothing impacted the photon (or we wouldn't see it).

! Moderator Note And I think that is a good time to close this.

It is hard (maybe impossible) to say. I don't think it is possible to quantify the total energy of the universe because energy is dependent on the frame of reference so you can't just add up the total energy in the universe. And we know some matter is continually being converted to energy (and some energy is being converted to matter). For example, the photons we receive from distant galaxies are red-shifted (lower energy). But that energy has not gone anywhere, it is just because we are observing it in a different frame of reference from where they were emitted.

! Moderator Note If you are worried, you should see a doctor. We cannot give medical advice.