Can Staging Rockets Achieve Faster-Than-Light Travel Despite Relativity?

[benss]

I have heard this before many times, ‘we can’t reach some parts of our universe because of expansion’ but can we launch a massive rocket and then launch a rocket from the first rocket in the same direction and then again and again? Due to relativity.

 

[PeroK]

I have heard this before many times, ‘we can’t reach some parts of our universe because of expansion’ but can we launch a massive rocket and then launch a rocket from the first rocket in the same direction and then again and again?

With what purpose?

 

[FactChecker]

I have heard this before many times, ‘we can’t reach some parts of our universe because of expansion’ but can we launch a massive rocket and then launch a rocket from the first rocket in the same direction and then again and again? Due to relativity.

Good question. But relativity says that speed does not simply add like that. In fact, the spacetime geometry of Special Relativity does not have a speed greater then the speed of light. A famous test by Michelson and Morley showed that. They didn't like their result and tried for years to get a different answer. They never could and the results they didn't like have been confirmed by many things..

 

[Ibix]

can we launch a massive rocket and then launch a rocket from the first rocket in the same direction and then again and again?

Yes. But it isn't any different from launching a single-stage rocket, except more fuel-efficient because you dump a load of empty fuel tanks. It doesn't get round the theoretical limitations because it's just an engineering change.

 

[benss]

With what purpose?

I suppose, to help a simpleton understand relativity better. If the earth is in motion in a specific direction, then we would have different maximum velocity depending upon whether we launched with or against the earth’s direction of travel.

 

[phinds]

I suppose, to help a simpleton understand relativity better. If the earth is in motion in a specific direction, then we would have different maximum velocity depending upon whether we launched with or against the earth’s direction of travel.

No, the maximum velocity is c. Period.

 

[Ibix]

I suppose, to help a simpleton understand relativity better. If the earth is in motion in a specific direction, then we would have different maximum velocity depending upon whether we launched with or against the earth’s direction of travel.

The limit to how far you can travel is imposed by the speed of light being finite and how that interacts with an expanding space. Launching a rocket in the direction of motion of Earth (relative to the CMB rest frame, for pedants) will let it travel a fraction further than launching one in the opposite direction, but neither can get further than a light ray launched at the same time. Launching multiple stages still won't let you overtake that light ray because they still can't go faster than light.

 

[PeroK]

I suppose, to help a simpleton understand relativity better.

That's a good objective. The expanding universe is covered by the theory of General Relativity (GR). That's required to explain the universe as a whole.

If the earth is in motion in a specific direction, then we would have different maximum velocity depending upon whether we launched with or against the earth’s direction of travel.

From an practical point of view, you want to launch your rocket with the maximum speed away from the Sun (assuming you are trying to escape the solar system). Launching the rocket in the direction of the Earth's orbit is, therefore, a good idea. But, the maximum speed the rocket can achieve relative to the Sun is always less than the speed of light in vacuum $c$.

 

[jbriggs444]

Good question. But relativity says that speed does not simply add like that

To make this more concrete, suppose that you have a rocket that can reach half the speed of light. On the tip of this rocket you mount another rocket that can reach half the speed of light relative to the first. On the tip of this second rocket you mount a third that can reach half the speed of light relative to the second.

One is tempted to think that this achieves one and a half times light speed. But it does not. Under the rules of special relativity, velocities add according to the rule:$$u = \frac{v+u'}{1 + (vu'/c^2)}$$Here $u$ is the resulting speed of a second stage as measured in the original rest frame, $v$ is the speed of the first stage in the original rest frame, $u'$ is the speed of the second stage as measured relative to the first stage final rest frame. and $c$ is, of course, the speed of light.

If we plug in the numbers we get:$$u = \frac{0.5c + 0.5c}{1 + (0.5 \times 0.5)} = \frac{1c}{1.25} = 0.80c$$We had expected to get $c$ but we only got $0.8c$.

The reason that the velocity addition of $u' = 0.5c$ does not get us the full $0.5c$ is because that additional $0.5c$ is measured using a different reference frame than our starting $v = 0.5c$. Distance is contracted, time is dilated and simultaneity is affected. One cannot expect both the first stage frame and the original rest frame to get the same number for the separation rate $u'$ between the first and second stages.

Velocities and separation rates add in the ordinary way if all are measured against a common rest frame. When velocities and separation rates from different rest frames are combined, it is a little like adding apples and oranges.