Implications of Newtonian universe

Question

I'd like to remove the speed of light limit from my world. However I don't want to just hand-wave the consequences. How should my universe look if:

• light travels at infinite speed, and so do gravity waves and magnetic fields
• there is no limit to relative speed between two objects
• energy cost to accelerate doesn't depend on speed

Would I need to change something else to make such a world work? I am interested in consequences in outer space, space travel and observation of space, rather than consequences on microscopic scales.

To narrow down what I'm after, I'd also like to point out that the world is a game, which involves people traveling between planets in their ships while obeying the rules of orbital mechanics. Therefore I need to know about:

• Does anything change in the way rockets and related tech work because of my change?
• Will the background sky look different? I assume the same amount of light arrives at the observer as in our universe, but suddenly we watch the universe as it looks right now, rather than a million years ago.

Answer 1

First is the speed of light is not the speed of light, it is the speed of causality. PBS Space Time has a great video about this. Light goes at this speed because that's as fast as events are allowed to propagate in our universe. Make the speed of light infinite and now the speed of causality is infinite. This means events which happen here can affect distant parts of the universe instantaneously. This has serious consequences.

The speed of light/causality is also a sort of universal conversion factor between mass and energy, and space and time. If it's infinite then mass, energy, space, and time are now four separate things, not two. This also has serious consequences.

In our universe we have 4 dimensional "spacetime". A Newtonian universe has 3 dimensional "space" and 1 dimensional "time". The speed of light is the conversion factor between space and time. If it's infinite there's no conversion. Space and time are now fundamentally different things. This has deep consequences for how our universe works, such as gravity. For example, gravity is not a force, but it's curved 4D spacetime. This solved many small discrepancies in planetary and stellar observations. That's easily handled by saying discrepancies simply wouldn't exist in your universe. Ok, but astronomy is really the least of the problems.

Mass and energy would be different things. E = mc^2, the mass-energy equivalence, would not be. This has deep, deep consequences. The mass-energy equivalence doesn't say that mass can be converted into energy, it says mass is a property of energy. There is no such thing as "matter", it's just a special form of energy. So much of our physical world relies on this. In a Newtonian universe matter and energy are separate things. Here's more about the significance of E = mc^2 from PBS Space Time.

Since matter and energy are now non-convertible, both energy and matter would always be conserved. Fusion, which converts part of the rest mass into energy, would not be possible. No fusion, no heat from stars. No heat from stars, no life. Stars just collapse under gravity into lumps of matter initially heated by gravitational collapse but eventually going cold. Neutron stars (and regular stars) require quantum effects which don't exist in a Newtonian universe.

In a relativistic universe, because of the mass-energy equivalence, energy has "mass". A box containing 1 gram of matter and one containing 9x10¹³ J of energy have the same mass-energy and the same gravitational pull. In a Newtonian universe this is not so. There is no mass-energy equivalence so energy does not exert nor feel gravity. No gravitational lensing. No black holes. Energy can only be absorbed and reflected.

The speed of light shows up in many equations, even those they appear not to. Many of the physical equations we learn in school are actually non-relativistic versions only for use at low relative velocities. For example, the kinetic energy equation: 1/2 m * v^2 is far more complicated in relativity and uses the speed of light. Making the speed of light infinite changes all this.

Then there's the question of time. If light, energy, and causality travel at infinite speeds, we have no "past" and no "future". Everything happens in the "present" all at once. If the speed of light/causality is infinite, we have no time. Again, here's PBS Space Time on the origin of time and why speed of light is necessary for time to exist.

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There you have it. No space-time. No mass-energy equivalence. No fusion. No stars. No time. A Newtonian universe would be very, very, very different.

That's just the broad overview. Many, many everyday equations change, or must be derived in a radically different way. I also didn't get into the lack of quantum mechanics which eliminates everything from transistors to stars (again). There's more about that on Physics.SE. For your universe to work and be consistent you'd have to re-engineer a significant portion of reality so the macroscopic world still works as it does now.

Alternatively you leave your world at the 18th century level of understanding. Stars shine, there is time and causality, they don't know how or why, and you don't need to explain it. The linear relationship between velocity and kinetic energy allows spaceships with far simpler technology.

Or you just don't let anyone with a decent physics background play. :)

Answer 2

Given that we are not sure of exactly how big our universe really is, because of the speed of light only allows us to observe so far, it could be that the night sky would be blindingly bright, with the light of stars in every direction extending off into infinity.

Essentially we're looking at a universe without relativistic effects. No time-travel. However, if the mass of an object did not increase with it's speed, then we could have some interesting theories about space travel, but nothing within the reach of our technology in the next hundred years or so. Also, because light travels anywhere instantly, we can communicate across any distance with no latency, so the internet would be happy :)

Answer 3

The biggest difference is that all of chemistry would depend on your current velocity.

In Newtonian mechanics, you have what is called a "Gallilean transformation". This describes how to change reference frames. For example, if I am standing in an airplane, I can toss a football to you easily, even though we are both moving at a very fast speed. I don't need to consider the speed of the airplane, determine where you are, then aim the football at where you will be in 2 seconds. I just pretend that the airplane is motionless and throw the ball to you. This works because the Laws of Motion do not change when applying a Gallilean transformation.

In a non-Newtonian universe, such as the one we live in, the Gallilean transformation is not perfectly accurate. When you get close to the speed of light, you need a "Lorentz transformation". This has the same concept, making the airplane look at though it is stationary, but works with special relativity.

Now we get to Maxwell's Equations. These describe electricity and magnetism. Now, unlike the Laws of Motion, these change under a Gallilean transformation, but not under a Lorentz transformation. In our world, an electric motor performs identically regardless of whether it is stationary or moving very fast on an airplane, because our universe uses the Lorentz transformation. In a Newtonian universe, using the Gallilean transformation, electricity would work differently in the two cases.

Now, what effects would that have? Well, change the relative strengths of electricity and magnetism, and the atom changes size. The fine structure constant also would change, so all of your elements would start having different chemical properties.

• A factory in which some critical step occurs at high velocity, where a chemical reaction can occur that wouldn't otherwise happen.
• A speed limit of safe travel in outer space. You could continually accelerate, but eventually you would reach a velocity at which the chemical processes in your body no longer function.
• The military would develop supplements that would allow their ships to travel at a faster speed, by replacing the proteins that your body can no longer produce.
• An alien civilization, traveling through the same space as us, but at a different velocity, might be based on their different chemistry. Trade would therefore be very difficult, if not impossible.
• Planets closer to their star, having a wide range of absolute velocities throughout their orbit, would be much less hospitable. Life there would need to survive at a wide range of possible chemistries.

Answer 4

If your universe is bounded but the speed of light is infinite, then you have to worry about what happens when light hits the edge, which of course it does instantly. And what does that do to conservation of energy? If it's not bounded, then you have to worry about Olbers' Paradox.

Astronomy and cosmology will be greatly handicapped by the inability to see into the distant past and by the lack of red shift (I assume there will be no red shift, since the formula for red shift depends on the ratio of the speed of recession to the speed of light).

Answer 5

Trying to come at this from a different angle than all the awesome physics based ones and focus on a couple of points from the game aspect:

A) Assuming we hold to your "ignore the microscopic implications" (meaning things like computers and related are a thing), I think scanners are a bit more realistic in your universe than a lot of other video game universes (in the sense that a probe near Earth would be able to detect a big ship near Jupiter in real time versus an multiminute delay that generally doesn't show up in most video games) although I'd be willing to be corrected; my assumption for having a scanner in solar system being able to detect stuff in an adjacent solar system would still be unlikely due to the power of the signal falling off with square of the distance (although I could see some interesting things with mirrors if light travels infinitely fast)

B) Likewise, Laser-based weapons would seem to be even more desirable (and force shields to be even more critical). If light has a finite speed and aliens in a galaxy 10 lightyears away want to declare war by launching a massive laser blast, it still takes 10 years for that to happen which is rather uninteresting for most games; if the speed of light is infinite, then I would expect if shields aren't always on, war devolves into galaxy wide MAD... although again I'd be willing to admit I don't know if even a perfectly coherent laser doesn't lose potency over that distance.

C) Rocket-wise, for manned rockets I wouldn't think a lot changes (again assuming we ignore the micro-effects); you're still going to want to limit the G forces human pilots/passengers endure. For unmanned drones, you again can build a super weapon by taking a big hunk of rock, boosting it arbritarily fast at the enemy planet, and even if the scanner system could detect it, given that there would still be some sort of reaction delay, unless the enemy planet has always on deflectors, I would expect they'd be having a bad day.

Answer 6

At low speeds (low including the velocity that stars and planets moving with relation to each other) you will see basically no changes. Newton's laws are a good enough match that it took a long time before we needed relativity.

The main difference to the larger universe is that there will be no such thing as black holes, it is always going to be possible (although it may be very difficult) to escape.

Rockets and suchlike will work just as they do now, we've never tried to accelerate anything to the point where relativity starts to be a problem. Constellations would look different as they would reflect current positions in the sky but that's only going to matter to people looking in detail.

You should also consider the effect of gravity on light, for example will you still have gravitational lensing? If you have it then a black hole could still look like this:

(The fictional black hole "Gargantua" from the movie Interstellar produced in association with physicist Kip Thorne)

But you would need to think about how gravity can bend something moving at infinite speed.

Answer 7

If you try to just look at what happens to Maxwell's laws of electromagnetism in the limit as the speed of light approaches infinity, one problem is that in Maxwell's theory all electromagnetic waves are produced by accelerating charges, but if you look at the Larmor formula which is derived from Maxwell's laws, as c approaches the infinity the power radiated by an accelerating charge should approach zero, so there should be no measurable electromagnetic waves at all in this universe.

An alternative you might want to consider would be to use something like the old luminiferous aether theory that physicists tended to assume prior to the Michelson-Morley experiment which produced results inconsistent with it. In this theory, it's assumed that electromagnetic waves are a type of sound wave in a medium pervading space, the luminiferous aether. It's assumed that Maxwell's laws only hold exactly in the rest frame of the aether, in other frames would have to be modified by a Galilean coordinate transformation. For example, just as it's true that all sound waves in air travel at the same speed in the rest frame of the air, but not as measured in the frame of an observer moving relative to the air, the same would be true for the aether: an observer moving at speed v relative to the aether would measure light waves to travel at speed v+c in one direction and v-c in the opposite direction.

One assumption here is that it's possible to create some sort of physical ruler which isn't observed to undergo length contraction when it's moving relative to the observer, and clocks which aren't observed to undergo time dilation when moving relative to the observer. Perhaps this would entail that they are held together by non-electromagnetic forces; the microscopic structure of matter would have to change in a non-relativistic world. But note that there is a non-relativistic quantum model of atomic structure based on the Schrodinger equation which is invariant under the Newtonian coordinate transformation (which does imply that rulers and clocks whose structure was determined by these laws would undergo no length contraction or time dilation), so you could assume that if you only want your universe to be "Newtonian" at macro scales but allow it to be quantum at micro scales. Though I don't know of any non-relativistic version of nuclear physics, so that would imply that stars radiate just due to some combination of chemical reactions and thermal radiation (assuming they form in a hot state), in which case they would cool down more quickly--the physicist William Thompson (or 'Lord Kelvin') once calculated an upper bound of about 20 million years of heat for a non-nuclear Sun.

If you assume your universe is infinitely old as in the steady-state theory, rather than the current state having resulted from the expansion of space since the Big Bang as in the cosmology of general relativity, you are also going to have a problem with Olber's paradox, which says that in a universe with infinite stars distributed throughout space and radiation obeying an inverse-square law, one would expect the entire night sky to be lit up no matter what direction one looked. Since the steady state allows new matter to be created, perhaps you could just assume the universe was empty and then the matter-creating process "booted up" some finite number of years ago, then if you combine that with the idea that light travels at a finite speed as in aether theories, that would explain the mostly-dark sky.

As for gravity, it could just follow the Newtonian formula, whose results are a bit simpler to calculate than with relativity (note that if you combine with an aether theory for electromagnetism, electromagnetic waves would not be affected by gravity, unlike in relativity, so there'd be no black holes or gravitational lensing). And macro objects in such a universe would obey Newtonian kinematics and the Newtonian laws of collisions, even if they obeyed non-relativistic QM at a micro level, due to the correspondence principle. This implies that if you have a rocket using up a constant amount of potential energy per unit time to fling exhaust backwards at a constant rate, its velocity will also change at a constant rate as seen in the frame of any given inertial observer (constant acceleration in their frame). So, in this sense it would be true as you said that "energy cost to accelerate doesn't depend on speed" (at least if you are looking at the energy cost for observers on board the accelerating object, as measured in their instantaneous inertial rest frame at any given moment), and also that "there is no limit to relative speed between two objects" since velocity in the observer's frame can get arbitrarily large as long as the rocket has enough fuel (so, a rocket could overtake light waves in much the same way an aircraft can break the sound barrier--this would presumably lead to a sort of electromagnetic "boom" similar to Cherenkov radiation). This is in contrast to relativity, where although an observer on board the rocket would measure a constant proper acceleration, the coordinate acceleration measured by an inertial observer would continually decrease as the rocket approached a speed of c in the observer's frame.

Answer 8

If gravity also travels at infinite speed, then we would probably have a Big Crunch due for the universe.

Also, solar sails would be much more efficient in that universe for space travell.

I have no idea if the mysteries of dark matter and dark energy would still exist in the universe. In general, newtonian physics is much simpler than modern physics.

If intelligent life does exist on other planets, we probably would already have had made contact with them, considering that communication speed would be infinite.

Although the night sky would be much brighter than it is today, I don't think it would be blindingly bright. Light disperses a lot with distance, but then again, all of the universe would be in instantly observable range. I think starlight alone would be as bright as twice the full moon.

Last but not least, I would not be posting this answer here, as Andromeda would already have had collided with Milky Way since a long time ago ...

Answer 9

The really big implication of this would be losing randomness in such universe. Everything would be perfectly predicable, down to the subatomic level. (Assuming by Newtonian universe you also mean quantum mechanics do not exist.)

There would be no transistors and all computers would be based on some other sort of method to compute numbers (whether digital or analogue).

If people in such universe would be able to build a supercomputer that can approximate the universe, they would find out that they lack free will and consciousness, since everything will be predictable and everything in the past would be known, just by running a simulation.

See https://en.wikipedia.org/wiki/Uncertainty_principle and https://en.wikipedia.org/wiki/No-cloning_theorem

both principles are fundamental to how our universe work.

Basically it is very hard to say if everything would change, as you removed a huge chunk of the physics in our universe. We can only hypothesize, and we can't even know if such universe would exist or stay stable.

Answer 10

If the speed of light is infinite then there's no relationship between frequency and wavelength of electromagnetic energy, e.g., radio waves. So radios and antennas and related technology (wifi, radar, microwaves, etc, etc, etc) either don't work at all or work (and look!) really differently than they do in our universe. Light would also be very different but I haven't taken the time to figure out how.