# Speed of Light As a Maximum Speed Limit [duplicate]

I know the speed of light problem has been beaten do death by hundreds of questions and answers, but I wanted to explore a new possibility and perhaps show an indication that light-speed as a constant is a man-made theoretical limit.

Would you please tell me if my musings are incorrect?

Now onto the subject at hand.

Suppose somewhere in the universe there are about 5000 different celestial bodies in a gargantuan solar system, each spread out the distance between the earth and the moon, each weighing approximately the size of 1 earth.

If by certain miracle, the orbits of those celestial bodies (planetoid objects) are arranged as such that 1) they are on the same plane, and b) all bodies line up almost perfectly with one another (at the time of the experiment).

It follows that if we launch a space vehicle, say a shuttle, and use gravity assist around those celestial bodies, we could theoretically increase the speed of that vehicle (provided that it doesn't rip itself apart from the inertia) 5000 times. As we have already achieved speeds of 150,000 mph using gravity assist in the past - wouldn't it follow that doing this 5000 times in sequence would eventually break the light speed barrier?

• You have successfully argued that if you assume Newton's laws are correct, then you can exceed the speed of light. If, instead, you assume that relativity is correct, then of course your argument, which uses Newton's laws, does not apply. – WillO Sep 26 '18 at 0:03
• I believe the answer here is quite relevant to this question: The one thing to keep in mind is that in order to perform a gravity-assist maneuver, you need to be able to enter a hyperbolic orbit around a given body that is moving relative to your destination. And, in order to be in such an orbit, there is a specific range of velocities for every object that you must have (dependent on mass of the object). ... – Alfred Centauri Sep 26 '18 at 0:19
• ... So the fastest you can get to by gravity-assist is much less than relativistic speeds because at relativistic speeds, you would not be able to enter into a proper hyperbolic orbit. – Alfred Centauri Sep 26 '18 at 0:19
• @AlfredCentauri: Your comments convince me that my earlier comment ("You have successfully argued...") was much too hasty. – WillO Sep 26 '18 at 2:29
• A superluminal speed is not something that hypothetically exists, but is prohibitively hard to achieve. Local superluminal speeds just don't exist in the hyperbolic geometry of our spacetime, so there simply is nothing to achieve. It is like going to the North of the North Pole. Such a direction simply doesn't exist. Every road from the North Pole goes South. – safesphere Sep 26 '18 at 8:21

Without seeing the math in relativity, it's hard to see where you're going wrong.

In relativity, the kinetic energy of an object is given by:

$$KE = (\gamma-1) m v^2$$

where $$v$$ is the object's velocity, $$m$$ is its mass, $$\gamma$$ is $$\sqrt{\frac{1}{1-v^2/c^2}}$$, and $$c$$ is the speed of light.

You can do gravitational assists to increase the body's kinetic energy, but the faster the body goes, the larger $$\gamma$$ gets, and the more energy you must put into the body to make it go even faster. You can never actually reach the speed of light: at that point $$\gamma$$ is infinite and you need an infinite amount of energy.

The gravitational assist scenario you describe just adds energy to the object. You can't add an infinite amount, so you can't reach the speed of light. You'll indeed go faster and faster, but while the first round of acceleration might add 5000mph, the second won't - it'll be less. This is because the formula for addition of velocities changes at relativistic speeds.

tl; dr: you can't break the light speed barrier with gravitational assists.

No, as you approach the speed of light relative to any of those bodies, that body's ability to accelerate you decreases according to the parameters of relativity.

Maybe a helpful analogy will be to think of yourself sailing and each of those bodies to be a 30mph gust of wind. The first gust you get a 2mph speed boost. But as you keep going you get less and less of a speed boost from each gust, with an eventual limit of 30 mph that you can never cross.

• That's not a good analogy since there is no such limit to a sailboat's speed. The current world speed record over a 500m course is 65.45 knots, by SailRocket, set in winds estimated to be about 25 knots. – D. Halsey Sep 25 '18 at 23:49
• @D.Halsey that's only possible with tacking. The analogy is fine if you exclude tacking (which most people don't know about anyway) – Señor O Sep 26 '18 at 0:40
• The analogy is only good going perfectly straight downwind. Tacking is something else altogether. – D. Halsey Sep 26 '18 at 1:57

It is important to understand that the speed of light is not a limit the way you think of it. The speed of light is c when measured locally, in vacuum. It is the same speed for EM waves and gravitational waves.

It is a common misconception to think that you can speed up to the speed of light. That is not correct. SR tells us three things:

1. anything with rest mass travels with a speed less then c, and will always do so

2. anything with no rest mass travels with the speed of light, and will always do so

3. anything that travels faster then the speed of light will always do so.

People usually do not even know about 3.

It is not that the speed of light is the maximum speed limit. It is just that anything that has rest mass will always travel slower then light (in vacuum when measured locally).

Now you are thinking about this the wrong way. You think you can speed up, but it is actually the other way around. The only speed is the speed of light. Light does not move in the time dimension, its speed in the time dimension is 0. Light does not experience time the way we do. If you want to experience time, you need to slow down in the spatial dimensions. The way to do that is to gain rest mass. If you gain rest mass, you will start moving in the time dimension, and start experiencing time the way we do.

In your case, your spaceship has rest mass. Let's assume it has unlimited fuel. As it starts to speed up, at about 0.8c, relativistic effects will become dominant, and ass the spaceship tries to speed up, it gains more mass. Having more rest mass will make it even harder for it to speed up. At this point, as it nears the speed of light, it would need infinite energy to speed up, so it becomes impossible.

Now there is an easy way to think about this. Anything in the universe has a speed relative to the speed of light (in vacuum when measured locally). Your spaceship has a speed of let's say 0.8c. When you do the slingshots, you just increase the speed to 0.81c etc. The increments in the speed of the spaceship are also relative to the speed of light. Even the lightest thing, the neutrino is traveling at a speed relative to the speed of light. As you go closer to the speed of light, the relative increases will need even more energy, and after a while, they will need infinite energy, so your spaceship will not speed up anymore, but will just gain more mass.

This form of use of relativistic mass is not in use in particle physics anymore, because it becomes confusing. In particle physics, they use rest mass, invariant mass.

I am using this example only for your question with the spaceship.

And I would like to mention a nice example for you. The way you describe it, imagine a neutrino traveling through space from far away, lets say passing by black holes, starts etc. Every time it passes by a star or black hole, it might do a slingshot, and speed up. By the time it gets to Earth, it would be possible to find a neutrino that has done slingshots the way you describe it and has sped up to speeds more then c. But we have not found any so far, and that is because even if the neutrino would do slingshots and speed up, it would still just speed up relative to the speed of light, and would always still travel slower then light.