Can I keep our universe, but without the speed limit (of light)?

Question

It seems like nothing can move faster than light and this is quite bothersome for interstellar travel. It takes decades in the best case to get anywhere interesting in our little Milkyway (Many thousands of years to travel an appreciable distance within it) and unless we find some loopholes traveling between galaxies seems off the table entirely.

I want to have a universe where there is no maximum speed but that is otherwise relatively similar to ours. Is this possible?

Preferably this universe would have:

• A beginning (a big bang?)
• galaxies
• stars
• planets

That will do for now. How can I make this possible with a well defined rule-set and what notable, large differences would there be between our universe and this universe?

Some things to get started:

• Forces and all massless particles (like light) might travel at infinite speed.
• Special relativity likely doesn't hold.
• The big bang and what happens in the following moments are probably immensely important.
• Can I still have quantum stuff?

Answer 1

Yes, you can! You could imagine a universe where physics is based on Galilean relativity instead of special relativity. I'll skip over the mathematical details (unless you're interested), but basically Galilean relativity describes a spacetime that has one universal axis of time, which never mixes with the dimensions of space as it would in special relativity.

In Galilean relativity, there would not be any invariant speed that is the same for all observers. Specifically, the speed of light (by which I mean the actual speed that light travels, not the constant $c$) would be different depending on the conditions under which it was measured.

There are some different ways you could make this work. Probably the simplest is filling your universe with some medium that light travels through, and it always travels at a fixed speed relative to the medium. (This was a real scientific theory in the late 1800s; the medium was called the luminiferous aether.) Light in this model would behave a lot like sound, for which air is the medium. Objects like planets and solar systems could affect the motion of the medium, just like mountains and buildings affect wind, and you might even have aether-weather phenomena if the dynamics of the medium are complicated enough.

An alternative would be that light simply moves at a certain speed relative to whatever emitted it. In this model light would behave like a projectile, e.g. a bullet from a gun, so it is a natural match to a particle model of light (though you could do it with a wave-particle dual model of light too). The speed at which light is emitted might depend on the energy of the photons, and/or on the mechanism by which they are produced. It would probably be quite natural to have higher-energy photons, corresponding to higher frequencies of light, travel at higher speeds. If you do this, you would have an interesting effect where you'd see a faraway object at different times in different frequencies - for example, a brief flash of white light would be seen from afar first as purple, then transitioning through blue, green, yellow, orange, and red.

Galilean relativity would not require forces to propagate at infinite speed, but they could. In other words, you would be able to have two kinds of forces in this universe. One kind is the ones which are carried by fields, the way forces work in our universe. The object that exerts the force actually triggers some kind of propagating disturbance in the field, and then the object that feels the force reacts to the disturbance. These disturbances would propagate at some speed characteristic to the field - but note that all the discussion from earlier paragraphs still applies, concerning how the speed would change depending on the conditions under which it was observed. Depending on how you want it to work, you can achieve a wide variety of effects, including the "temporal chromatic aberration" from the last paragraph, except now with forces: if gravity worked this way, then a sudden change in a mass distribution (assuming such a thing were possible) would have a prolonged effect because gravitational waves at different frequencies would arrive at different times.

The other kind of force is that which instantaneously affects the entire universe. Actually you could think of this as a subset of the previous kind of force, where the natural speed of the force is infinite. The existence of this kind of force would allow for instantaneous communication between widely separated locations, although if the distances involved are large enough, the people in your universe might have technological problems detecting a signal because it would simply be too weak. The phenomenon where a signal weakens in proportion to $1/r^2$ would still apply in Galilean relativity, or at least it could, though I think it would be possible to have a force that does not weaken over distance, if it's not carried by a field.

You could still have a big bang, which would represent a definite beginning of time. Everything in the universe would start out moving away from everything else, though you wouldn't have a good answer to the question of why it started doing that in the first place. Anyway, afterwards, the evolution of the universe could proceed much the same way it did in the real world; you'd still get galaxies, stars, and planets, for example, though not until some hundreds of millions (or billions) of years after the beginning. Special and general relativity actually aren't that important for most of the universe's history.

Your universe could have a finite size, in the sense that there is only a finite region of space filled with stuff, although with a big bang-like event at the beginning, that region would change size over time. You could set it up so that characters in your universe could travel beyond the edge of this region (assuming they have the technological means to get to the edge), into an endless void; or the edge could be a hard wall that they run into; or anything that hits the edge could just vanish. The latter two options are a bit tougher to reconcile with existing physics though. Depending on the details of how light and forces travel, and the size of the universe, characters in your universe may or may not realize that the universe is finite. Naturally the closer they are to the edge, the easier it is for them to tell.

If your universe is infinite, on the other hand, depending on how light behaves, it might be subject to Olbers' paradox, which basically points out that in an infinite universe filled with stars, the entire night sky would be lit up because there is no direction you would look that would not run into a star eventually. However, if you have a beginning to your universe and light travels at finite speed, this argument wouldn't hold. So you could still have a dark night sky.

If gravity (or some other attractive force) travels at infinite speed in your universe, the expansion will slow down over time, and will eventually stop and reverse. So your universe is doomed to collapse in on itself at some point in the possibly distant future. If gravity does not travel at infinite speed, then it may or may not collapse, depending on the details.

Lastly, none of this invalidates quantum mechanics. You wouldn't have quantum field theory, but there could still be nonrelativistic quantum effects and so a lot of quantum phenomena we are familiar with would still be possible.

Answer 2

To answer (finally) your question. Safest assumption is: No ... but ... who cares?

I am not physicist. I just tend to "procrastinate" on interesting questions and thinking of how to make it possible. So, I will list my possibilities:

Stick to loopholes: Do not rebuild whole universe just because you need faster than light travel. Yes, loopholes are no longer funny (link to codegolf is intentional), but they are safe. I came here from Writers and so I take every question as "story background". So, If you put Enterprise in your universe, yes it will be no longer funny. But everyone will instantly know how space travel is done and you can focus on story itself

Make tachyons possible Tachyon is theoretical particle which should be faster than light. And bonus: Thanks to New-Age culture, loads of people know about them. (watch on your own risk. You have been warned).

And one purely Writer-like answer

Do not care about details, just describe it in plausible way Look, if you go to common household and ask them how microwave oven works, they will maybe have just idea about it. Ask them about Induction cooking and you will quite possibly hear about "magic" in it. The same goes for computers, cars or GPS device in your pocket.

So, if you need it to happen, let it happen. Make captain of ship say "thanks to this FTL drive, we will be in Omicron Persei 9 in 10 minutes" and never explain what the heck FTL stands for or how does it even work.

Answer 3

First, the good news: You still can have quantum stuff. All the quantum weirdness already exists in non-relativistic quantum mechanics.

Without the speed limit, full relativity is, of course, out of question. Therefore let's look at the alternatives:

Preferred frame of reference

Assumptions: Matter behaves as in non-relativistic quantum mechanics, while unchanged electrodynamics holds for electromagnetic fields. This is basically the aether theory of before Einstein, except of course they didn't know about quantum mechanics yet.

Note that in this case the sped of light would be $c$ only in the preferred frame. The speed of light would not be a limit for particle movement, though.

Let's look at what would happen with atoms at high speeds. To get a feeling of what is bound to happen, let's first use a classical model of the atom, before taking a closer look at quantum mechanics.

As custom when looking at atomic physics, we approximate the nucleus as charged point particle. We will also neglect any spin/magnetic moment of the nucleus.

The fields of a moving electric point charge are

$$\vec E = \frac{q}{4\pi\epsilon_0} \frac{\gamma}{r^3\left(1+\gamma^2 \frac{v_r^2}{c^2}\right)^{3/2}} \vec r$$ $$\vec B = \frac{\vec v\times\vec E}{c^2}$$

Here $q$ is the charge (for an atom with atomic number $Z$, we have $q=Ze$ with $e$ the elementary charge), $r$ is the distance from the (moving) charge, $\vec v$ is the velocity of the charge, and $v_r$ is the radial component of that velocity. Moreover we have the gamma factor $$\gamma=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$$

If you object that the calculation on the linked page was relativistic: Electrodynamics is inherently Lorentz invariant, therefore those calculations are still valid in the hypothetical non-relativistic world, as long as we are in the preferred frame.

Now let's look at a classical electron (charge $-e$) orbiting the nucleus in a plane orthogonal to the velocity, in a circular orbit. If that electron is at radius $r$, its velocity $\vec v_e$ has the component $\vec v$ as it moves with the atom, and additionally the tangential component for orbiting.

Now let's calculate the force acting on that electron. First, the electric field causes a force $\vec F=-e\vec E$. Since we are perpendicular to the velocity, $v_r=0$, and the only correction compared to the field of a charge at rest is the gamma factor. So we get an attractive radial force with strength $$F_E = -\frac{Ze^2}{4\pi\epsilon_0} \frac{\gamma}{r^2} = \gamma F_0$$ where $F_0$ is the absolute value of the force an electron orbiting an atom at rest would experience at the same radius. The minus indicates attraction.

On the other hand, the electron moves through the magnetic field of the moving nucleus with velocity $\vec v_e$, giving rise to a Lorentz force $\vec F_B = (-e)\vec v_e\times \vec B$. Since the orbital component of $\vec v_r$ is in the direction of $\vec B$, only the component $\vec v$ due to the atom velocity would enter the formula. This gives a repulsive force of the strength $$F_B = \frac{v^2}{c^2} eE = \frac{v^2}{c^2}\gamma F_0$$ Together we therefore get $$F = F_E + F_B = -\left(1-\frac{v^2}{c^2}\right)\gamma F_0 = -\sqrt{1-\frac{v^2}{c^2}}F_0$$ We see that the attractive force is reduced as we get faster. Quantum mechanically this means the atoms will get wider in the orthogonal direction.

More importantly, we see that as soon as we reach the speed of light, the force will go to zero. In other words, the electron will stop being bound.

So in short, while this model would allow acceleration of particles beyond the speed of light, matter would disintegrate as soon as passing the speed of light. So from a practical point of view, the speed of light would still be a limit; indeed, it would not even be safe to just come close to it.

Taking the limit $c\to\infty$

Another option would be to remove the speed limit by letting it go to infinity. Indeed, the Minkowski spacetime of Special Relativity would then transform to the Galilean spacetime of Newtonian physics. The electric field would work as instantaneous force following the Coulomb law, analogous to Newtonian gravitation. There would be an absolute time, but no preferred frame.

However, when looking closer at Maxwell's equations, one recognizes that this would also mean that there are no magnetic fields.

Also, quite obviously there could be no light waves. It would be a dark universe.

As before, but adding "Newtonian light"

We can fix the last issue by simply going back to Newton's idea of light: Just postulate light particles that are emitted from light sources. Thanks to quantum mechanics, we don't even need to forego interference. To work without relativity, those light particles would need to have mass.

However this would likely give a very different universe from ours.

Answer 4

Just increase the constant

All kinds of interesting border cases of our universe may behave wacky if time and relativity would function in a fundamentally different way. For example, having one fixed time masure for everything in universe, being able to calculate how much is the "absolute speed" of earth since there would be a concept of absolute speed, etc. This is tricky, has not been explored much, and probably would not add anything useful to the story.

However, there are no reasons why you coudn't simply assume a world where c isn't 300,000 km/s but, say, 300,000,000 km/s. It wouldn't change the fundamental principles of how the world works (it would alter the details of atomic weights of isotopes and nuclear reactions), but would allow a slower-than-light travel that is still fast enough.

Answer 5

Remember that the speed of light also affects other physical processes than just space travel. Let's take Einsteins famous formula

$e=m c^2 $

(energy is equal to mass multiplied with the speed of light squared)

This formula doesn't just govern how much energy you need to approach the speed of light. It also governs how much energy you obtain from nuclear fission, fusion or matter/antimatter annihilation.

What would this mean in a physics system where $c$ is infinite? It would mean that nuclear fusion creates infinite energy. And what is the energy source of stars again? Nuclear fusion. Any stars would be infinitely bright.

So nuclear fusion doesn't work anymore in your universe. But fusion in stars is the process which created any elements than hydrogen and any visible energy in the universe.

So a universe without a speed of light would be a very dull universe.

Answer 6

There are attempts by people, who should know better, to re-formulate physics without relativity, and explaining effects that we currently attribute to relativity in different ways. In effect, they are trying very hard to maintain classical Newtonian physics as the "correct" backbone for all things.

I am in no way supporting this as a correct worldview, however this kind of thinking (which I consider just plain wrong physics) turns up in a few places, often with similar agenda as creationism and other religiously-motivated rebuffs of science. On the plus side from your point of view, there is a substantial amount of this content. It contains some grave errors, but it takes a qualification in physics to spot them. A lot of the maths is worked through with correct substitutions for instance. As a writer, you could buy in to the fantasy, and have plenty of esoteric material and arguments that sort-of work, and give you a universe like ours, but with no upper speed limit.

To answer your main question, the simplest answer is "no, it is not possible to have our universe with no upper speed limit". But more concretely, it is very hard to figure out the consequences of such a universe, and what else you would need to alter. It is simplest to have physics as we understand it in place, and add something that allows for exceptions. Or alternatively, hand-wave away the inconsistencies as "resolved behind the curtain" - i.e. assert that it is possible to construct a universe like ours, but without requiring anyone to do the maths.

Answer 7

An alternative solution to the problem is to say that the speed of light still exists, light and forces and almost everything that is not concerned with mass moves at the speed of light.

However, that is not to say that in your universe the speed of light has to be 'the universal speed limit'. You could simply say that things can move faster than the speed of light under special circumstances or that it does not become harder to accelerate objects as they get closer to the speed of light.

Both these proposals lead to other weird physics but you could more easily ignore these side affects and keep things plausible.

Answer 8

You can keep all the physics but allow certain conditions for different properties of space. Wormholes and stuff. Space what is not Euclidean. Can be folded to create shortcuts.

Like Newton's physics describes universe close enough when objects move around slowly (up to say hundred miles per second), Einstein's world could be valid unless some other special properties of space are involved. We did not discarded Newton's physics when we learned Relativity. We just know that Newton's laws are enough to calculate stress on a bridge, or trajectory of a bullet, but when you want to find coordinates using GPS signals, you need to account also for Relativity.

It might be that in our part of Galaxy/Universe FTL (Faster-Than-Light) travel is not possible. It might be that elsewhere conditions are different, and so are the rules.

Answer 9

A couple more problems come to mind:

As Philipp pointed out, an infinite c means E = mc² breaks horribly. However, it's not just nuclear reactions that blow up, even chemical ones do. The mass loss in a chemical reaction is far smaller than in a nuclear one but it's still there.

Going a little farther your hard drive fails for the same reason. See this post: http://www.ellipsix.net/blog/2009/04/how-much-does-data-weigh.html

Even if you ignore this you'll find the chemistry of the heavier elements altered. Heavy elements have electrons that orbit at relativistic velocity. Put them in a Newtonian world and your car doesn't start—because the battery is only turning out .4V per cell rather than the 2.1V it really does (although by the time you draw any substantial power from it you only get 2.0V.) I'm sure there are a lot more changes but I'm not qualified to figure them out.

Answer 10

Look at Greg Egan's The Clockwork Rocket and sequels. He has stuff on his website about his universe and the ramifications worked out, including quantum mechanics! In Yalda's universe, as it is called, there is infinite velocity to a given reference frame.

Answer 11

What about living beings with higher lifetimes and different perception of time? It seems it is quite possible to imagine a being living in our universe for whom a million of years would be just as short as a day for us.

Of course such a slow person may be subject to various dangers (our own perception of time evolved from the need to react faster). But the level of danger may deminish as the universe cools, temperature falls and average power of energy sources falls as well. Thus the rate of diffusion, decay and erosion would deminish, reducing the need for food consumption and mobility.

Answer 12

I think you'd have to redefine matter for this to work.

The two constraints:

1 - mass is dependent on its speed compared to the speed of light. As you approach the speed of light, your mass begins to approach infinity...and no amount of energy can increase the speed of something with an infinite mass. But the other relation goes...our current speed in relation to the speed of light is what defines our existing mass as well. Lets say you can just increase the constant that is the speed of light and you don't change our speed at the same ratio, we lose mass. As the speed of light approaches infinity, our mass will approach 0.

2- Time is also dependent on the speed of light. If we could accelerate a ship to 99.9999% the speed of light, for every day that passes to a person on that ship, nearly 2 years will have passed for the rest of us...hitting the speed of light would suggest 1 day that you experience is an infinite amount of time for the rest of us. Once again, the inverse exists...if the speed of light were to increase, the greater the delta in our speed to the speed of light, and the slower our time will pass...as the speed of light approaches infinity, the flow of time will approach 0. (oddly enough, this does come with the conclusion that it may take decades for a ship to get out of our galaxy, but if it was going fast enough, those decades would feel like a couple days to those on the ship itself)

Prior to the big bang, something at 0 speed would also be timeless (which would be true regardless of the speed of light). Soon after the big bang, the speed of the mass ejected was limited by its increase in mass as defined by the speed of light. A speed of light that is twice that it is currently would ultimately see the masses ejected not gain mass until a higher speed. I'm sure I can't prove it, but I think a higher speed of light would result in a much quicker expanding universe and the distance between objects would be significantly greater (the earth would either be faster moving at a ratio equivalent to the speed of light increase or would loose mass at a proportion of the speed of light increase compared to its existing speed...in either event I think this puts Earth further away from our sun). This is pure speculation...but it's a little defeating to the idea that this would help space travel as the worlds and galaxies would be further apart.

An infinite speed of light sees massless particles at an infinite speed...starlight would be to our eyes instantaneously (instead of the 'historic' view we currently get when looking at stars). Hoepfully this doesn't have the effect of instantaneously irradiating us with all of the combined light in the universe (At an infinite speed, would it stand to reason that all light would be everywhere simultaneously?)

With all that said...this is how it works in our world, in our universe, in our existence. In a different setup, one must assume they exist and therefore whatever got them there has to be possible...those questions are left to the physicists in their universe to explore in the same ways ours here would.

Added

Would it stand to reason that stars relying on fusion that release energy based on e=mc² be hotter or very least contain more energy? Might have a big impact on star lifecycle.

Answer 13

What would be the reason for positing limitless speed?

If you are trying to build a whole universe based upon this premise, you will have to accept some limitations. One is the big bang: if time is absolute, not relational, then it makes no sense for it to have a start. You can perhaps still have a local big bang for our sector of the universe, but it would have to be situated within time, not outside of it.

If on the other hand you just want for your spaceships to travel at any speed, free from the Einstenian limitation to 300,000 km/s, I would say you would be trying to kill a fly with an atomic cannon.

First, you can move your spaceships at any speed you want with unobtainium - white holes, space portals, eleventh dimension gaps, ninth dimension folds, etc.

Second, moving your spaceships around without such pseudoscience is actually less credible, or would necessitate a bigger amount of handwaving. That's because our physiological limitations regarding acceleration are narrower than cosmic limitations regarding speed.

A recent question asked about the effects a 1.5 g gravity would have on us. The consensus is that it would be very bad for our health. We live well on an 1 g environment.

Now, gravity is an acceleration like any other. If we are going to travel long distances in space, we will need to do that accelerating at 1 g. Which is to say, at 10 m/s. A simple calculation will show us that a year has 31.536.000 seconds - so, if we accelerate at 1 g for one year, we will reach light speed. Which further means, to attain a speed significantly bigger than light speed, we would need to travel for considerably more than two years (considering that we would have to de-accelerate at the other end of the travel). Considering our life span limitations, we would still be trapped within a very small sector of the universe. Realistically, the closest star is about 4 light years from Earth. You would take √2 years, or about 16 months, to travel to it (and further 16 months to come back). So the shortest far-space trip we could make would take 2 years and eight months. The closest star known to have a planet - probably the closest thing we would want to visit - is at 10 lyghtyears distance; a trip to there and back again would take us 6 years and four months.

Answer 14

You do live in a universe in which the speed of light is not constant - it varies with the speed of the light source, as predicted by Newton's emission theory of light. That is what the Michelson-Morley experiment showed in 1887, but then FitzGerald and Lorenz advanced the ad hoc length contraction hypothesis and changed the interpretation of the experiment:

http://www.philoscience.unibe.ch/documents/kursarchiv/SS07/Norton.pdf John Norton:

"These efforts were long misled by an exaggeration of the importance of one experiment, the Michelson-Morley experiment, even though Einstein later had trouble recalling if he even knew of the experiment prior to his 1905 paper. This one experiment, in isolation, has little force. Its null result happened to be fully compatible with Newton's own emission theory of light. Located in the context of late 19th century electrodynamics when ether-based, wave theories of light predominated, however, it presented a serious problem that exercised the greatest theoretician of the day."

http://books.google.com/books?id=JokgnS1JtmMC "Relativity and Its Roots", Banesh Hoffmann, p.92:

"Moreover, if light consists of particles, as Einstein had suggested in his paper submitted just thirteen weeks before this one, the second principle seems absurd: A stone thrown from a speeding train can do far more damage than one thrown from a train at rest; the speed of the particle is not independent of the motion of the object emitting it. And if we take light to consist of particles and assume that these particles obey Newton's laws, they will conform to Newtonian relativity and thus automatically account for the null result of the Michelson-Morley experiment without recourse to contracting lengths, local time, or Lorentz transformations. Yet, as we have seen, Einstein resisted the temptation to account for the null result in terms of particles of light and simple, familiar Newtonian ideas, and introduced as his second postulate something that was more or less obvious when thought of in terms of waves in an ether.