# Is it possible to have a Newtonian universe but everything else behave the same way as this universe? What adjustments to physics is necessary?

Man would never travel beyond his interstellar neighborhood in his lifetime. He can, but he'll never return home in the lifetime of everyone he knows. If he travels further, he will return to find even his home is long gone. This is due to one vicious supervillain ruling our universe. A supervillain named "c". "c" is a velocity, a velocity impossible to surpass. What's even more cruel about this supervillain is that it will outsmart you no matter how you wanna outsmart it. Yes, all methods of FTL can and will lead to causality violations, and there's no way around it. However, this villain is also the backbone of why everything in this universe behaves as it does. Unless...

This supervillain c will make interesting sci-fi plots such as galactic empires completely impossible. You can't keep an empire united when even a simple "execute political dissidents" message takes multiple hundreds of lifetimes to reach the "rural" areas of said empire. So i propose a Newtonian universe where the speed of light and other massless propagation is infinite. I know this would cause Olber's paradox of infinitely bright sky but we can solve that by saying this universe is not infinite, and non homogenous at all scales. However, this universe is huge. 21st century humans might as well think it's infinite. The furthest galaxy as of 2022, called HD1, lies 13.5 billion light-years away in light travel time. The luminosity distance, i.e. the distance based on the observed brightness of the galaxy alone, if it wast't subject to cosmological redshift, is 650 billion light-years. This is thus the distance humans with 21st century technology can observe, the actual universe is much larger.

As the speed of light is infinite, the concept of "light-year" might as well not exist. Instead, I'll imagine people using parsecs instead when referring to interstellar distances. 1 parsec is approximately 31 trillion kilometers or 19.3 trillion miles.

Now this is all settled, the supervillain c is gone. You can travel however fast you want. There won't be black holes anymore though, but an infinitely dense singularity tearing apart everything that comes near it is still possible, so quasars can still be a possibility. Only difference is that it's theoretically possible to escape it no matter how close you get. And also, no time dilation, the whole universe shares one universal time.

Wait, didn't i say this supervillain c is also the backbone of why everything in this universe behaves as it does? Now that it's gone, what adjustments to physics do I need to make in this universe in order to have it behave the same as this one macroscopically? As in, if I get teleported there right now, I won't detect any difference except that the speed of light is infinite. Every physical, chemical and biological experiment I do there yields the same results as if I'm doing it here, except the ones related to relativistic velocities. Do i need to rewrite all the fundameltals in the universe in order for my idea to work?

• @Eumel: You may want to check your arithmetic. To reach 300,000,000 m/s at a measely 1 g (assumed to be 10 m/s²) you need 30,000,000 seconds, which is 83,333 hours, which is 3,472 days, which is 9.5 years. Jun 7 at 7:45
• @AlexP you are absolutely correct, i must have mistyped somewhere on the calculator. You are still looking at tavel times of many years to even the closest stars and many lifetimes to get across the galaxy. Jun 7 at 7:52
• 30,000,000 seconds is just under a year, but yeah that's a technical challenge humans in that universe might have to find a way around, at least it's not a fundamental impossibility. Maybe for the first few thousand years individual humans can only visit nearby stars in their lifetimes. Until the invention of anti-gravity devices that can allow them to accelerate at 10 or 50 gs without feeling anything, and as technology advances maybe the anti-gravity device can withstand millions of gs, who knows? Jun 7 at 11:52
• The problem here is that Special Relativity was how certain contradictions in classical mechanics were resolved. Specifically the contradictions between Newton's laws of motion and Maxwells equations of Electromagnetism which had been extensively tested by Einstein's time. Einstein resolved them by basically saying the Maxwell had it right and that Newton's laws had to be modified. Going the other way amounts to discarding Maxwell's equations which is a really big problem. Jun 7 at 15:08
• @NeilMeyer one where Newton's laws of motion hold regardless of the speeds involved. In our universe they only hold at non-relativistic speeds.
– M.D.
Jun 9 at 6:44

1. "All methods of FTL can and will lead to causality violations": Not true.

The simple way out is to require that all FTL travel be done with respect to one "special" frame of reference; this takes care nicely of any paradoxes and violations of causality.

In physicists' speak, that's called a distinguished frame of reference. Now we know that within our understanding of physics there is no distinguished frame of reference, that is, we cannot distinguish between being in motion in a straight line with constant speed, and being absolutely at rest. But then, within our understanding of physics we cannot travel faster than light. The distinguished frame of reference would obviously be introduced by whatever new physics allows us to accelerate to such immense speeds.

Other more complicated workarounds exist, such as Penrose's cosmic censorship hypothesis, or Hawkings's chronology protection conjecture.

2. "Do i need to rewrite all the fundamentals in the universe in order for my idea to work?" Yes, obviously.

The problem is not mechanics, it is electromagnetism. The entire point of Einsteinian special relativity is to reconcile mechanics with electromagnetism. In fact, Einstein's paper in which he introduced special relativity has the title "On the Electrodynamics of Moving Objects".

(Before that, physicists had tried to reconcile them by actually postulating a distinguished frame of reference, called the luminiferous aether¹; unfortunately, Michelson and Morley's 1887 experiment had proven that it did not actually exist.)

¹) "Luminiferous aether" is Anglicized Latin for light-bearing godly air. 19th century physicists loved the classics.

The problem arises because the speed of light in a vacuum, $$c$$, is directly linked with the strength of electromagnetic forces via the electric permittivity of the vacuum $$\varepsilon_0$$ and the magnetic permeability of the vacuum $$\mu_0$$: $$c = 1 / \sqrt{\varepsilon_0 \mu_0}$$. If you make $$c$$ infinite you automatically make at least one of them zero; this would, just for example, have very baddd effects on chemistry. (Baddd effects such as atoms cannot exist.)

• Comments are not for extended discussion; this conversation has been moved to chat.
– L.Dutch
Jun 8 at 20:18

The three legs of pre-relativistic physics were

1. Newton's laws of motion
2. Maxwell's equations
3. Laws of thermodynamics

The problem is that an object that moves according to Newton's laws and radiates according to Maxwell's equations can not conserve energy according to thermodynamic laws.

It was Newton's that were, not as much wrong, as a special case where relativistic effects are negligible.

Either Maxwell's equations would have to not correctly describe electromagnetism, or thermodynamics would have to not correctly describe energy conservation and entropy.

Both of those are fundamental to many other things, so changing either would be big.

• By your 'the problem is [...]' quote are you talking about the UV catastrophe? If not, what did you mean? Jun 7 at 8:15
• There would need to be a different explanation of why the UV catastrophe doesn't happen.
– Mary
Jun 8 at 21:55
1. Any amount of mass would correspond to an infinite amount of energy.

Unless you eliminate mass-energy equivalence, and just allow mass to be an independent inherent property of fundamental particles, like spin or charge, completely unrelated to energy. Gravitational and inertial mass may remain identical... or not.

Mass and energy would need to be separately conserved, which has all sorts of interesting consequences for nuclear reactions and particle production.

1. No magnetism, no magnets.

Atoms could still exist, with slightly simpler structures due to the lack of magnetic energy-level splitting effects. Electrical technology could even still exist, with electrical power generation done with influence machines rather than dynamos. But no stellar, planetary, or galactic magnetic fields.

1. No electromagnetic waves.

But that doesn't mean no equivalent of light; there would still be purely electric waves. These could either travel instantaneously, or be associated with a massive "luxon". In the latter case, the speed of light would depend on its energy, leading to far-away objects being chromatically distorted, with blue components of the image being newer than red components. This would also lead to changes in the behavior of the electric force, such that it is no longer infinitely ranges. Atoms and chemistry could still exist as long as the luxon mass was small, so the electric force range remains much larger than the size of an atom. How you conserve mass in luxon production remains an open question... you might need to allow negative-mass particles, with luxons always produced in pairs. And negative mass has all sorts of interesting implications...

• But it doesn't have to be that way. They can just exist. Jun 7 at 15:57
• @user253751 Yes; as I said, you can just have independent sources of the magnetic field. And, as long as we are working in 3D space, you can just declare that magnetic fields also bend the paths of charged particles. But the connection between currents and fields is fundamentally a relativistic effect. Without relativity, if you want magnetic fields, you need inherently magnetically charged matter. Jun 7 at 16:37
• Magnetic fields can just exist (for no reason) and be related to electric currents (for no reason). Jun 7 at 16:42
• @user253751 Only if the universe has a preferred rest frame for electrodynamics. In which case you get really weird effects, like molecular stability depending on orientation and the apparent laws of chemistry changing with the seasons, or with the speed and direction of high-speed travel. Jun 7 at 17:44
• @Vikki Maybe, but they conflict with the point of the exercise: if traveling at large fractions of the speed of light kills you because chemistry stops working, it doesn't matter that individual particles can have arbitrary velocities--your space opera still won't happen! Jun 8 at 1:58

# No

$$E = mc^2$$

Replace $$c$$ with infinity in that formula and even a neutrino would obliterate galaxies it passed through.

Your universe would never form even the most basic particles.

• How would that formula come about in a world where Galilean relativity is true? Jun 6 at 21:13
• @AlexP good point. I think your answer is on point when you say all fundamentals have to be rewritten. Jun 6 at 21:41

Another problem: Our everyday world has objects with substantial relativistic effects: the electrons around heavy atoms are moving at a good chunk of lightspeed. (At least as much as they can be said to be moving.)

While the only effects I know about from this are gold is golden (Newtonian gold would be silver color) and your car wouldn't start (the battery would put out about 20% of the voltage it does now) I'm sure there are plenty of edge cases where reactions that work in our world wouldn't, and reactions that don't happen here would happen there.

And yet another problem: E=mc^2. If you wave that away by separating energy and mass you just killed both chemistry and nuclear physics: You'll find E=mc^2 lurking at the heart of every reaction that produces or consumes energy--any energy-producing reaction has products that are ever so slightly lighter than what went into it. (.7% for hydrogen->helium fusion, lesser amounts for every other reaction.) Every energy-consuming reaction has products that are more massive than what went into it. Without the ability to interchange mass and energy why would there be any such reactions?

You probably need to do something.... if you want, but it is your story.... and there is plenty to do without worrying about the details of absolutely everything.

Take the hydrogen atom when looking at how it works at a fundamental level with quantum mechanics you can do a set of calculations to find the energy levels of the electron without thinking about relativity and you will get pretty good answers.

However, when you look at the atomic spectra more closely you will find that the energy levels are off by just a tiny amount, or that in some cases the spectra has two lines very very close together where you think there should only be one.

This is becasue there needs to be a relativistic correction for the electron. Instead of having just a kinetic energy term, in the equations, the electron needs to have an additional term that comes from special relativity. This is a small correction but it turns out that when looking at this splitting closely the splitting is proportional to a something called the 'fine structure constant' that is one of the fundamental constants of the universe. Looking at the spectral lines of elements and these little details was how quantum mechanics got started.

The reason you might care about the the fine structure constant is that it pops up when trying to understanding how particles and fields interact. The value of the fine structure constant is about 1/137....

It is coupling constant measure of the strength of the electromagnetic force that governs how electrically charged elementary particles (e.g., electron, muon) and light (photons) interact.

So if you get rid of special relativity, you might not care if you can see two spectral lines instead of one, but you might care a lot if it means that how all charged particles interact.

For example, if you changed the value of the fine structure constant it might mean the protons in the nucleus might not stay together, or electrons might orbit atoms at a different radius etc.

As other answers to this question have pointed out, physics has to be rewritten at a pretty fundamental level to make it Galillean-invariant instead of Lorentz-invariant. However, there is a way to do this for electromagnetism that keeps most of the effects needed to make light and chemistry work the way they need to in order to have a fairly recognizable universe (at least at the solar system level, and assuming quantum mechanics is still a thing). The trick is to add a good old-fashioned aether, with local velocity $$u$$. The electromagnetic constants (and therefore the speed of light) may also depend on the aether state.

The aether determines the auxiliary fields $$D$$ and $$H$$ through constitutive equations:

$$D = \epsilon_0 (E + u\times B)$$ $$B = \mu_0 (H - u\times D)$$

Then Maxwell's equations can take their traditional forms:

$$\nabla \cdot D = \rho$$ $$\nabla \times H = \frac{\partial D}{\partial t} + j$$ $$\nabla \times E = -\frac{\partial B}{\partial t}$$ $$\nabla \cdot B = 0$$

The Lorentz force on a particle of charge $$q$$ and velocity $$v$$ still has the form:

$$F = q(E + v \times B)$$

This is all invariant under a Galillean transformation, with the fields in particular transforming as: $$E' = E + v \times B$$ $$B' = B$$

And you get electromagnetic waves that propagate at speed $$c$$ relative to the aether.

Note that this theory can be derived from the same action as classic electromagnetism if we replace $$E^2-B^2$$ in the Lagrangian with $$E\cdot D - B\cdot H$$.

Actually the supervillain c is not as powerful as you may think. The restriction on faster than light travel is only a local restriction not a global one. As far as our understanding of physics go there is nothing preventing seemingly distant points to be connected through a wormhole if you are willing to give up to think about the universe being an euclidean space, and instead allow more complicated topologies.

Traveling through the worm hole to get somewhere faster than light traveling another route is no contradiction with this, since a light beam traveling through the worm hole following the same path as you will still be faster.

In a certain sense faster than light travel is already possible in this universe in the neighbourhood of a black hole. For example light takes several days to travel around Ton 618-the largest currently known black hole. So traveling for one hour in one direction along the photon sphere around Ton 618 near the speed of light will make you arrive at your destinations days before light traveling around the Ton 618 traveling along the photon sphere in the other direction, so you will have arrived at your destination faster than the light traveling in the wrong direction.

I don't think you can have stars in a non-relativistic (Newtonian) universe. At least not ones that look like ours. In the proton-proton chain that provides most of the energy powering stars the size of our Sun (which is a pretty average star) one step is $$p + p + e^{-} \to {}^2\text{He}^+ + \nu_e \, . \tag{1}$$ The sum of rest masses on the left is greater than the sum of rest masses on the right. Therefore this reaction is not allowed in Galiliean relativity ("Newtonian physics") It is allowed in Einstein relativity because then the mass of a composite system is not the sum of the masses of its constituents. Rather, the mass squared $$M^2$$ is given by $$M^2 = \big(\sum_i E_i \big)^2 - \big( \sum_i \mathbf{p}_i \big)^2$$ where $$E_i$$ are the energies (including rest energy) and $$\mathbf{p}_i$$ the momenta of the constituents. The reaction (1) is allowed because $$M^2$$ can be kept constant by giving the He-nucleus and the neutrino some kinetic energy and momentum. Indeed it releases some energy that contributes to making stars glow.

Even if you came up with some way of powering stars, supernovae are going to have very different physics and you won't get any neutron stars (the Chandrasekhar limit is a relativistic effect).

In any case, the non-relativistic theory of gravitation is, well, Newton's theory. So in your universe you don't get any general relativity effects like (roughly ordered by the order in which they became possible to detect)