Yes. But I understand that Newton was off because he wasn’t aware of certain factors that, if he had been aware of them, he would have simply made accommodation for them in his formulas. Or is there something I’m missing?

# Theory of Everything?

Okay, so Newtonian mechanics has been disproven to instrumental precision, which is one part in one thousand billions.

If you want to change Newtonian mechanics to something else that accommodates the observations, then that’s a different story. Newtonian mechanics itself is not on “pretty good footing”.

Now if you agree up to there, then suppose Newton knew of these modern experiments. How do you expect him to “simply made accommodation for them in his formulas”?

I’m not a physicist so I haven’t a clue. But assuming that he came up with so accurate formulations that are still used to this day to send people to the moon, it seems like he would probably be up to the task.

I just can’t imagine accounting for such minute differences would be such a monumental task. At least it seems like it should be possible, wouldn’t you agree?

Newton’s equations are a practical and acceptable approximation for the values involved in a moon mission.

Unless I am seriously mistaken, there is no way no how you would run a particle accelerator using Newton’s equations.

I knew you’re going to bring up sending people to the moon. This is somehow always a layperson’s response. The moon is a big target, and the distance to it isn’t very far, it’s completely within the error budget of Newtonian mechanics. This is not the case with comporting to the strictest instrumental bounds.

Perhaps you should learn physics first before making such claims. The corrections to Newtonian mechanics from general relativity is an infinite sum, called the Post-Newtonian expansion. It cannot be done without taking infinite amount of time and effort.

That’s interesting; I’d never heard of this. Obviously this is only when trying to write it as a correction to newtonian mechanics in the general case, right? Since there are some solutions with closed form expression where we can compare GR and Newtonian mechanics directly.

Which solutions are you referring to? When we learn how to compare closed form expressions between GR and Newtonian mechanics in textbooks, there are hidden assumptions that hides the infinite sums, e.g. using the test particle approximation.

I was thinking of idealized cases like the Schwarzchild solution. I’m guessing the test particle assumption is where you compute geodesics for particle motion assuming the particle mass is infinitesimal and doesn’t affect the geometry? That is what I had in mind, basically.

Correct. When the test particle is not affecting the geometry, we can write the motion of the particle in a “Newtonian”-like way that is closed form for some special spacetimes. But this is not true in reality: any particle has backreactions to the underlying spacetime, either by e.g. gravitationally tugging on the black hole on the Schwarzschild spacetime, or generating wakes of gravitational radiation as it travels the spacetime.

The amount of complexity hidden in the Einstein field equations always amazes me. That is some compact notation, alright.

For kicks, because this is the kind of nerd I am, I once tried writing the EFEs out in terms of the metric tensor components… in the equations editor in Microsoft Word… it bogged down the app so hard I couldn’t even get halfway finished, and I probably spent over an hour just getting that far.

I must admit that I find the elegance of the EFEs to be probably the strongest argument in favor of four-dimensionalism.

OK. So I think I remember reading that there is some kind of pull from the sun, electromagnetic(?) or something to that effect, that is only strong enough to be felt by Mercury that causes Newtonian calculations to be off by 43 seconds per century. Is that correct?

PdotdQ in another thread pointed my to this series of lectures. I found them to be pretty well put together, and pertinent to your line of questioning.

Gravity Near a Massive Body

Thanks @RonSewell. However, I don’t know if that really addressed my question. From looking at the article it seems it’s saying that a curvature in spacetime accounts for the discrepancy. But what is the cause of the curvature? It seems to suggest the sun’s gravity is bending spacetime?

So is the answer to my question that it’s the gravity of the sun pulling on space that is somehow enough to be felt by Mercury as it travels close enough to that space that accounts for the discrepancy?

Pretty much. The quote you always hear is that mass tells space-time how to curve, and space-time tells mass how to move.

So would it be fair so say that it could be translated into Newtonian Mechanics by saying that if there is a large enough mass it’s gravitational pull can have an affect on surrounding space up to a certain point which can also have an affect on any objects in the immediate vicinity of that space?

However practical the utility of Newtonian Mechanics is in the workaday world, General Relativity has superseded it and passed test after test. Do you have a partiality to Newtonian Mechanics? Is so, why the appeal?

I believe the Newtonian concept of reality makes much more sense. Though I’m not disputing Einstein’s calculations, I am especially disputing his assumption that there is no absolute space, time, or simultaneity which, as far as I can tell, he based solely on verificationism. Though an accepted philosophical view at the time, it is no longer considered valid by most all philosophers.

As far as I can tell, the idea no absolutes in time, space, or simultaneity leads to absurdities. And it seems plausible to me that the conflicts between macro and micro physics could be resolved by returning to Newtonian concepts of reality on the macro level, and adopting a pilot wave theory at the quantum level.

I can only wish you good luck. Do not be surprised if it is not only difficult to find people prepared to support this, it might be even difficult to find people prepared to argue against you. To have a seat at the table there is no shortcut, you need the advanced math, differential geometry and some alien algebras, and that is only a necessary but not sufficient qualification to be taken seriously. I think I have enough science to at least discern whether someone knows what they are talking about and maybe pose some decent questions, but nowhere near the math to enter into any disputation or offer any path forward. I’m afraid your intuition will not get you far.

Not so sure about that. Don’t see why Einstein’s formula for the perihelion shift per revolution could be added as an additional formula to correct Newtonian Mechanics on the large mass issue, and neo-Lorentzian SR is already compatible as far as I know. I think those are two of the main issues. Are there any other major issues to be dealt with?

I’m lost here. If the equations of Newtonian Mechanics are correct, why would they need correction? You cannot be a little bit pregnant.