That is not how I remember physics (former PhD student here):
The speed of light has a dimension, so it in itself does not change physics (thought experiment: everybody switches to feet-per-decade as the unit of choice, nothing really changes). It is the dimensionless constants that determine the real physics.
Have not heard the statement that is alpha was a tiny factor larger/smaller that would make atoms no longer exist. It's this were true, this would actually be a way to actually calculate it from first principles ('at which value of alpha are there solutions to this equation').
Edit: typo
There is the Hoyle state, a peculiar resonance state that is very important for nucleosynthesis. Without it, stars would not produce a lot of carbon. It appears to be finely tuned for complex chemistry and thus life to evolve.
The speed of light does change physics, as does any fundamental constant. Expressing a speed in different units does indeed yield different numbers, but that is not equivalent to a change of speed.
Changing alpha means that electromagnetic force get stronger or weaker, thus the atoms still exist but with different orbital levels. Considering how intricate the orbital levels of atoms are, it's not shocking that a tiny change in alpha completely redefines chemistry, but chemistry would still exist.
The point is that all of the speeds we measure are actually measured in units of the speed of light, if you go right down to it (seconds and meters are defined in terms of the speed of light). So, the value of the speed of light doesn't really matter - which is why c=1 is often used in many kinds of physics.
The fine structure constant is dimensionless and would be different if c were different. When doing a unit conversion, one also has to alter other constants so as to be consistent with observed reality; whether one alters other constants or not is the difference between talking about a change in units and a change in c.
It looks like this still doesn't cancel out? It's an interesting point as to whether our hypothetical change in c would affect the relationship between photon energy and wavelength, but either way we get a nonzero power of c.
Solutions to D(x)=C is probably something like p_a^a * p_b^b * … * p_n^n with a+b+d+…+n (yes, I am skipping c) equal to your constant C, and p_a, p_b etc all prime.
No, that looks wrong. Take c = 2, for example. You seem to be saying that p^2 ought to be a solution. But D(p^2) = 2p (because D(p^2) = D(p) p + p D(p) = p + p = 2p).
One idea, but people will probably hate me for it:
If you return to e.g. the google search site (hence: when the long click metric would be triggered) have a dialog on top saying ‘result great / OK / bad-or-confusing’.
Can probably be gamed (bot nets trying to destroy the reputation of others) but at least a long time would not automatically mean ‘great result’. (In the arms race to combat destruction, it could be so that a ‘bad-or-confusing’ click would not actually push a value down, just not make it go higher).
I disagree. Reading lecture (! not literature or study books) I read 15 books each weekend in my teens, reading all science fiction and fantasy books in the town's library. And no, not all where 1000 pages long. But they weren't all shorter then 300.
And yes, I regurarly went back during the week to catch an extra book or two.
I realize I might be a relatively fast reader, and this fast reading I only did in English (while my mother tongue is Dutch), but do not underestimate how quick some people can read?
I suppose I can concur in your 'low complexity' argument: I did not read Tolkien in my teens, and probably would have skipped all the poetry while reading.
Edit: Clarification: 15 books each weekend should be read as ==>> I traded my 15 books for 15 new books each weekend, reading them during the weekend and when not in school
> 15 books each weekend should be read as ==>> I traded my 15 books for 15 new books each weekend, reading them during the weekend and when not in school
So you mean 15 books each week, not each weekend! I was surprised when I read that, but this makes more sense.
I stopped agreeing when reading nr 7.
Einsteins notation (X_n Y^n being defined as sum over ‘n’ of X_n times Y^n) is one of the most elegant and simple solutions that really work.
If if you need x_n = y_n * z_n, you would write just that. Only when you write y_n * z^n would the notation imply summation over n.
> Einsteins notation (X_n Y^n being defined as sum over ‘n’ of X_n times Y^n) is one of the most elegant and simple solutions that really work.
Yes, but that notation still includes the indexes being summed over, which I think is the point that no. 7 was trying to make. What doesn't work is a notation that just says XY, without any indexes whatsoever. The ordering of indexes and the specification of which indexes are being summed over matters, so a notation that leaves those things out doesn't work.
A PalmOs user myself, I remember thinking the iPhone should have had no chances against the Palms.
Although, might be the reason I went the Android way when that arrived;-)
Former physicist myself:
Not sure I understand your (and parents) argument.
Given the Suns gravitational field, and the orbit that Mercurius has, the speed of the planet can be determined. So the argument that a point mass would have the same precession does not dispute the argument that it is the relativistic mass of the point mass/planet that determines the precession.
I will not venture into arguments* whether grandparents explanation is ‘correct’, ‘best’ or ‘useful’, there is an equivalence between ‘gravitational field + orbit’ being the reason and ‘(relativistic) speed + orbit’ being the reason.
* A sybling comment states that relativistic mass is avoided in modern physics. As someone who did physics 30 years ago, I can not deny or corroborate this statement. And indeed, the explanation of grandparent is not the way I myself think about the perihelium precession. But that does not make me certain enough to say it is ‘wrong’.
Just think about it. If relativistic mass (a term that indeed tends to be avoided by actual physicists for good reasons, because it confuses concepts of mass and energy which are clearly defined in relativity) was the explanation, then the shape of the planet's orbit itself would influence the anomalous precession component from General Relativity. And you would see no relativistic effect at all for perfectly circular orbits with zero eccentricity. That is simply not the case.
The explanation of grandparents for the perihelium effect of Mercury tried to explain the 'overshoot'. And yes, in a perfectly circular orbit there would be no overshoot??
I do not think grandparent tried to say that all relativistic effects were caused by the increase of the 'relativistic' mass, just that the overshoot was.
So I am sorry: I cannot see how this argument disproves the explanation of grandparent. And just to be clear: I do not think in the way of grandparents argument myself.
>And yes, in a perfectly circular orbit there would be no overshoot??
That's where you and the other comment are wrong. The only way to get a stable circular two body orbit is for newtonian potentials which are exactly 1/r shaped. Add any other term (like 1/r^3 for General Relativity) and you essentially get more or less chaotic movement over time, similar to the three body problem in newtonian gravity. See Betrand's theorem [1].
