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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.
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In terms of on/off topic I think on balance it's ok, especially now you've narrowed it down. – Tim B Mar 24 at 10:58
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I feel that the narrowing of the specific issues at hand is sufficient. Unfortunately, I have no idea how to construct an answer! – CAgrippa Mar 24 at 11:01
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@GnoveltyGnome : I guess light would be a wave propagating through the luminiferous aether, without the wave-particle duality. – vsz Mar 24 at 16:07
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@Twelfth Those are most likely problems with instruments. Much like this one. – jpmc26 Mar 26 at 3:47
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Fun fact: Newton knew that light moved at a finite speed. AFAIR, he thought that light particles were accelerated when they entered a denser medium, to explain refraction phenomena. – nikie Mar 26 at 7:56

10 Answers 10

up vote 41 down vote accepted

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.


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. :)

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+1 for the last line. :-) Seriously, though, I like the focus on the implications of fusion. Sometimes it's hard to realize just how much $E=mc^2$ affects us. – HDE 226868 Mar 24 at 22:57
    
You say no fusion but you missed some related things: No chemistry. No elements. I'm not sure if you even have gravity. – Loren Pechtel Mar 25 at 3:46
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Without watching a whole 12-minute video, the claim that without relativity there would be "no time" sounds like obvious nonsense--Newtonian kinematics and Newtonian gravity are well-defined mathematically, and the equations tell you how the positions of different objects vary as a time parameter is varied. And there is also still causality in the sense that the state of the universe at later times can be inferred from its state at earlier times, although causality is non-local. – Hypnosifl Mar 25 at 4:58
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@Hypnosifl The host is a professor of astrophysics, I'm inclined to believe him. Newtonian physics are observational in nature, not derived. They match mid-scale, non-relativistic observations, but they don't explain why things are the way they are. It turns out the speed of light and space-time are a big part of that "why". As to there being causality because there's a "before" and "after", that is a tautology. If you change the rules of the universe, linear time can go away. One thing is for sure, when you start looking at how the universe works nothing is obvious. – Schwern Mar 25 at 7:41
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While all this is true about relativity, and relevant to q. gravity, in no way does it call into doubt my statement that Newtonian physics is a mathematically well-defined model of objects whose position changes with time, even though it lacks this neat notion of the causal structure being reducible to events connected by light-like paths (and in Newtonian physics, two events at exactly the same time can be having a causal influence on each other, so you can't have a nice causal ordering where every single event must be either in the past or future of any event it's causally connected to). – Hypnosifl Mar 25 at 15:00

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 :)

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Are you sure instant light would have that effect on the sky? I'm playing with the thought that the light that arrives should be the same ammount, just at different time. – Tomáš Zato Mar 24 at 10:36
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@TomášZato Read up on Olbers' Paradox: en.wikipedia.org/wiki/Olbers%27_paradox – Mike Scott Mar 24 at 10:51
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Nah I wouldn't think so. There are plenty of stars within the observable universe that we can't see with the naked eye. The luminous intensity that we observe decreases with the square of our distance from it, meaning beyond a certain distance (much less than the boundary of the observable universe), stars would have to be unrealistically bright for us to see them with the naked eye. – Devsman Mar 24 at 17:37
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the "no latency" is a fallacy. There would still be router and machine delays. – Mindwin Mar 24 at 21:09
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@Devsman - You're missing the point of Olber's paradox--if you divide space into concentric spherical shells of finite thickness (say, a shell consisting of the space between 1 and 2 light years from us, another consisting of the space between 2 and 3 ly from us, etc.), then if we assume stars are distributed with approximately uniform density on large scales, just by geometry the total number of stars in each shell will be roughly proportional to the square of the shell's distance from us, canceling out the inverse-square dimming of individual stars so each shell emits the same light. – Hypnosifl Mar 25 at 5:12

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.
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Could you explain more why does electricity and magnetism change under Gallilean transformation? I see no reason for it. – Tomáš Zato Mar 24 at 15:02
    
Sure, though I won't be able to get to it until later today. All the sources I am finding simply state that Maxwell's Equations are not invariant under the Gallilean transformation, but don't go into detail. When I have a chance later today, I'll see if I can derive exactly what the effects would be. – Eldritch Cheese Mar 24 at 16:22
    
@TomášZato PBS's Space Time Youtube channel did an excellent video explaining this. youtube.com/watch?v=msVuCEs8Ydo – asgallant Mar 24 at 21:52
    
Chemical reactions involve matter<->energy conversions--they won't happen in a world where such conversions are impossible. – Loren Pechtel Mar 25 at 3:46
    
This is not correct. The Maxwell equations change under the Galilean transformation BECAUSE there is a factor of the speed of light involved in the equations. If you let this go to infinity, the equations change such that they are invariant under the Galilean transformation. What does happen is that there will be no interaction between the electric field and the magnetic field, and as such no electromagnetic radiation (just electric or magnetic radiation). Light will be just a standing wave, instead of a traveling wave. – Rob Mar 25 at 12:36

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).

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The universe doesn't have an edge anymore than the surface of a sphere does. The problem is what happens when all the photons wrap around the whole universe and are simultaneously at all locations at once? – Schwern Mar 24 at 20:08
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Note that if the universe was unbounded and the speed that gravity propagated was infinite, nothing could move. Everything would have an infinite gravitational attraction along every possible vector. – Comintern Mar 27 at 18:03

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.

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A and B would seem to contradict each other. If you can focus a laser well enough to do damage to a planet 10 ly away, you can focus a much lower power LIDAR sensor to scan it. – Schwern Mar 25 at 0:09
    
Scan the planet: seems doable with some hand waving; scan the entire next solar system seems to be problematic – Foon Mar 25 at 0:16

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:

enter image description here

(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.

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Could you add details about the image (including source)? Is it an "artists impression", or based on observations - or even an actual photography? – Volker Siegel Mar 24 at 19:45
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@VolkerSiegel That's the black hole Gargantua from Interstellar. It's so accurate they produced a paper about it. I've edited the link into the answer. It only has one ring (accretion disk) which we're viewing nearly edge on like a typical view of Saturn. What we see as a circle around the hole is actually the light from the ring on the other side being bent around the edge of the event horizon. – Schwern Mar 24 at 21:07
    
There is at least one case where we accelerate things enough such that relativity causes issues: satellites have to have their clocks adjusted for relativistic effects. Their speed is roughly constant, but since they are constantly changing direction relative to an observer on Earth, they are constantly changing velocity (accelerating and decelerating). – Aurast Mar 24 at 21:44

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.

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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 ...

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Would solar sails be more efficient, or would they be moot? In fact, a lot of this answers feels speculative without any justification for whats claimed.. – James Trotter Mar 24 at 13:21
    
Don't fear galaxy collisions! Gallaxies ar almost empty space - there is not that much chance for anything solid actually colliding. – Volker Siegel Mar 24 at 19:50

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.

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A perfect simulation still wouldn't be possible for a computer within the universe, since every particle of the computer itself would have to be represented by some physical computing element, and each such element would be presumably made up of many particles, or at minimum one. A hypothetical Laplacian demon that could observe the universe from the outside universe could still make perfect predictions, but this would just be a philosophical thought-experiment, not something the inhabitants could realize in practice. – Hypnosifl Mar 25 at 19:38
    
As for lacking "free will", there are plenty of philosophers who adopt 'compatibilist' definitions of free will that don't require indeterminism. Likewise, plenty believe a deterministic computer program could have subjective experience, which is what is usually meant by "consciousness". – Hypnosifl Mar 25 at 19:40

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.

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