A Purely Newtonian Universe

[Eternal_Freedom]

This idea arose from this mornings Cosmology lecture. Basically, let us suppose that we are living in a Universe described perfectly by Newton's laws and principles. Relativity was never dreamt up because there was no need for it; all observations could be explained by the physics of the 17th century. Hence:

-Gravity is an inverse-square law that acts instantaneously over infinite distance between two points.
-Light travels at c but there is no time dilation/length compression/mass gain asscoiated with near-c velocities.
-FTL is easy; just keep accelerating.
-You can can accelerate smoothly for infinity, if you have the fuel/energy.
-There are no other dimensions/other universe/parallel worlds.
-Space is infinite.

How different would this world be to us? Astronomers and cosmologists would probably shit themsevles, but woudl it affect any parts of "the real world?"

Also, feel free to add any other principles that I omitted.

[Kuroneko]

This idea arose from this mornings Cosmology lecture. Basically, let us suppose that we are living in a Universe described perfectly by Newton's laws and principles. ... How different would this world be to us? Astronomers and cosmologists would probably shit themsevles, but woudl it affect any parts of "the real world?"

How much large-scale cosmology changes really depends. For example, the Friedmann equations describing the the evolution of standard Big Bang models can be exact in a Newtonian universe as well. The physical meaning of the terms is subtly different. Of course, the observations required to confirm them would have to be different, but the Newtonian analogues exist.

Modern electronic technology is then outright impossible. Even at the most basic semiconductor notions like the band gap and the valence/conduction bands, are explicitly non-classical. It's likely that matter on the microscopic scale is fundamentally continuous and not at all like what our universe has, because the stability and solidity of matter, and even covalent bonds themselves, are due to the spin 'exchange force' that has no classical counterpart.

If you meant to say only relativity is excluded from this hypothetical world, despite quantum mechanics being very non-Newtonian, then that situation is quite a bit more subtle. But some of the physical properties of the heavy elements are affected by relativity. Famously, gold is yellowish and mercury is liquid because of relativity, so in a sense even ancient observation falsify a Newtonian universe.

[Eternal_Freedom]

Yes, only omitting relativity is more what I had in mind.

Fascinating; I had thought that only large scale cosmology woudl differ. Thank you kuroneko.

Although that does answer one of the other quesitons that arose in the discussion; what if we were in a purely classical universe.

[Kuroneko]

I've tried to find some other results just now, and though there are some, most of the relevance to everyday life is unclear (not to say there necessarily isn't any, just that I'm not competent in chemistry to say). But there's one fascinating one that stuck out: Relativity Powers Your Car Battery.

[Eternal_Freedom]

Awesome. Thanks for that, I'm sure the rest of my group will find that fascinating.

[Sriad]

IIRC/Speculate Correctly we'd see a lot more supermassive black holes/great attractor type bodies.

It's hard for me to imagine what instant gravity over infinite distance would do to macro cosmic structures... overall the infinite universe averages out but LOCALLY it seems like we'd see the galactic equivalent of solar systems. Dense regions of the primordial plasma would exert influence instantly instead of within only their own light cones, collapsing into black holes or ultra-dense clusters of super-galaxies, with the standard galactic structures we're used to forming in orbital bands around the attractors.

Or maybe that effect would just lead to abundant primordial black holes.

[NoXion]

IIRC/Speculate Correctly we'd see a lot more supermassive black holes/great attractor type bodies.

It's hard for me to imagine what instant gravity over infinite distance would do to macro cosmic structures... overall the infinite universe averages out but LOCALLY it seems like we'd see the galactic equivalent of solar systems. Dense regions of the primordial plasma would exert influence instantly instead of within only their own light cones, collapsing into black holes or ultra-dense clusters of super-galaxies, with the standard galactic structures we're used to forming in orbital bands around the attractors.

This idea sounds utterly fascinating, mind if I steal/adapt it? Sounds like a such a universe could be at least partially fractal in structure...

[starslayer]

IIRC/Speculate Correctly we'd see a lot more supermassive black holes/great attractor type bodies.

It's hard for me to imagine what instant gravity over infinite distance would do to macro cosmic structures... overall the infinite universe averages out but LOCALLY it seems like we'd see the galactic equivalent of solar systems. Dense regions of the primordial plasma would exert influence instantly instead of within only their own light cones, collapsing into black holes or ultra-dense clusters of super-galaxies, with the standard galactic structures we're used to forming in orbital bands around the attractors.

Or maybe that effect would just lead to abundant primordial black holes.

It wouldn't really happen that way, actually. You can simulate most aspects of sturcture formation in the universe using Newtonian gravity; the fields are so weak and operate over such long distances that the only real difference between GR and Newtonian gravity is the travel speed. Remember also that conservation of angular momentum and energy haven't gone away, so galaxy clusters and such would probably largely have the same forms they do today. Black holes would be somewhat different in both formation and appearance, I think. More on that later, when i have some time.

[Omeganian]

How are the stars going to shine without E=MC^2?

[starslayer]

10 My is basically the Kelvin-Helmholtz (thermal) time of the Sun, so it would shine for about that long after it formed due to gravitational energy alone; you didn't fudge anything, DXIII. It would practically shine for somewhat longer than this, since as it lost energy, it would cool and contract, and thus have lower luminosity as it did so.

Energy release in nuclear fusion actually isn't much of an issue; the nuclear binding energy is present without needing to invoke relativity (it comes from the strong nuclear and electromagnetic forces). However, since the mass defect would be nonexistent, the energy would have to come from some other source within the nucleus. Just where I'm not really sure.

[SpaceMarine93]

Heard they have their equivilant of Black Holes in the form of Dark Stars. Don't ask me how it works though.

[Simon_Jester]

Yeah. Other people mentioned it earlier, though, and they do know how it would work.

[Kuroneko]

IIRC/Speculate Correctly we'd see a lot more supermassive black holes/great attractor type bodies.

Black holes as such cannot exist in Newtonian gravity, though 'dark stars' may or may not, depending on the details of how light works in this universe.

How are the stars going to shine without E=MC^2?

Of course nuclear processes in this hypothetical world cannot be even remotely like the real ones, because those are relativistic, but the basic mechanism of some underlying fields rearranging and this showing up as an energy difference in independent of relativity. To see this, first realize that chemical processes already do exactly the same thing: the electrons react in a variety of ways, and the difference in chemical potentials also shows up as a mass difference in our world.

In other words, the hypothetical world can easily have a high-energy "nuclear chemistry" analogous to, but different from, our nuclear physics.

Actually, there's no reason it can't show up as a mass difference in the Newtonian universe as well. For example, if you assume Maxwell's electromagnetism in some frame and calculate the inertial mass of a stable configuration electromagnetic particle(s), you'll find from conservation of electromagnetic energy that
[1] Mphysical = Mbare + U/c²,
where U is the total electromagnetic field energy and Mbare is the inertial mass of the body without the field. That is because the electromagnetic field has an energy density and momentum density determined by the Poynting vector E×H, so that accelerating a stable configuration of charged particles would involve also changing the electromagnetic momentum and require more force. In other words, there is an additional mass caused by the self-interaction of the body--the interaction of the body and its own field. One way to interpret the "classical electron radius"
[2] re = (1/4πε₀)(e²/mec²)
is that this is the radius of a sphere with surface charge only such that half the electron mass comes from its electromagnetic field, the other half being its bare mass.

There is nothing in the above reasoning that depends on relativity (i.e., invariance of c with respect to inertial frames, or equivalently, that of vacuum permittivity/permeability). The simplest historical change would be if the 1851 Fizeau experiment had a negative result and the 1887 Michelson-Morley experiment both had positive one, in exact reverse of the actual ones. Things can get really strange if only one of them was different.

I figure the sun has ~ 10^41 J of gravitational energy in there... shining as brightly as it does in real life, that should last for thereabouts a ten million years (unless I fudged something).

Yes, though it would have rather variable luminosity, that's close enough. A while ago I calculated 6.1E41J based on a detailed 2000-layer numerical simulation of solar physics someone published in ApJ.

[Cykeisme]

Famously, gold is yellowish and mercury is liquid because of relativity, so in a sense even ancient observation falsify a Newtonian universe.

That's interesting! Briefly, why is that?
I'd try and look it up, but I'm not even sure what to start searching for!

[Grandmaster Jogurt]

The term you're looking for to find stuff about this is relativistic quantum chemistry. As a rough and brief starting summary, electrons orbiting higher elements need so much velocity due to the high charge of the nucleus that they experience relativistic effects of various kinds. As an example, higher relativistic mass can shrink the radius of orbitals. Mercury doesn't bond easily or strongly because its outer orbital is contracted, and the relativistic effects on gold shift its reflectance curve such that it primarily reflects yellow.

[Simon_Jester]

IIRC/Speculate Correctly we'd see a lot more supermassive black holes/great attractor type bodies.

Black holes as such cannot exist in Newtonian gravity, though 'dark stars' may or may not, depending on the details of how light works in this universe.

One key question is whether light is actually affected by gravity at all. Newton would have said "yes, it will be," but Maxwell would say "no, it isn't."

[starslayer]

Yes, light would be affected by gravity. The Newtonian result is actually only a factor of two off from what GR obtains in the weak-field limit, and only requires that light comes in the form of photons rather being a pure electromagnetic wave (which, since non-relativistic QM is still intact, is still true). The gravitational potential and acceleration generated by a massive body only depend on its own mass, not on the mass of the body it's interacting with, so masses can still affect massless objects like photons.

[Kuroneko]

That's interesting! Briefly, why is that?

To add to the Jogurt's post, metallic bonding involves electrostatic forces between delocalized electrons, no longer attached to any particular atom. Relativistic shrinking of the electron orbitals means the atoms 'hold on' to their valence electrons more, making bonds between the atoms weak, allowing it to melt at lower temperatures. Similarly, relativistic corrections adjust the energy levels, making gold absorb blue light. Without it, gold would be absorb light outside the visible band, making it the typical metallic grey color.

One key question is whether light is actually affected by gravity at all. Newton would have said "yes, it will be," but Maxwell would say "no, it isn't."

Right. Newton's conception of light was corpuscular. Though Maxwell doesn't determine whether light couples to gravity.

Yes, light would be affected by gravity. The Newtonian result is actually only a factor of two off from what GR obtains in the weak-field limit, and only requires that light comes in the form of photons rather being a pure electromagnetic wave (which, since non-relativistic QM is still intact, is still true).

That's not really accurate. Quantization has nothing to do with that comparison, and while there are precise ways in which the "Newtonian result" is half GTR's, ascribing them to actual Newtonian gravity involves dubious handwaving. For example, one can...

1. In a Galilean background and Newtonian gravity, calculate the deflection of of a hyperbolic orbit with speed c at infinity, or some such similar setup. Note that this assumes that Newtonian gravity deflects light in the same way as massive particles, and then derives that the deflection must be half the GTR's prediction. If the assumption is not granted, nothing more can be said.

2. Take the static, weak-field limit of GTR, and observe that O((Φ/c²)²,(v/c)²) terms in the Lagrangian are irrelevant to reproducing Newtonian orbits in v/c ~ 0 (alternatively, the spatial terms in the resulting metric). If you simply drop them from the dynamics, you get half the GTR deflection, but the gravity an analogue of Newton on a Lorentzian background rather than Galilean as true Newtonian gravity. On the other hand, if you take the Galilean limit, v/c→0, there is something decidedly odd about then plugging in v = c afterwards.

The gravitational potential and acceleration generated by a massive body only depend on its own mass, not on the mass of the body it's interacting with, so masses can still affect massless objects like photons.

You're assuming this hypothetical world is some limit of GTR, whereas no such assumption is justifiable, nor even that gravitation follows the equivalence principle, which is something Newtonian gravity does not address. But even if this world is a limit of some (Lorentzian-)relativistic gravitational theory that satisfies the equivalence principle, that does not imply that light must gravitate, because there are myriad of possible alternatives to GTR. For example, if mass induced spatial curvature opposite that of GTR, there would be no gravitational deflection of light. One of the simplest such theories would be some variation of conformal gravity, e.g.,
[1] ds² = exp[-Φ/c²][-(cdt)² + dx² + dy² + dz²], Φ gravitational potential,
which reproduces Newtonian gravity in the static, low-velocity limit, but does not allow gravity to affect the light-cone structure at all.

But more to the point, the Galilean-relativistic theory of Newtonian gravity to compare is Newton-Cartan, rather than GTR, and NC is completely agnostic as to how light propagates.