# A question about constant acceleration close to the speed of light

• ledopmi
In summary, an accelerating object will still feel the same acceleration, but will be further away from the speed of light than it was before.

#### ledopmi

If a spaceship was to accelerate forever, at a constant rate that allowed the pilot to feel 1g, would he still feel 1g when the spaceship was close to the speed of light?
I know that it will never reach the speed of light so the acceleration must slow as the ship speeds up, so I assume that close to the speed of light the pilot will be mostly weightless.

Is this true or will he still feel the same acceleration?

ledopmi said:
If a spaceship was to accelerate forever, at a constant rate that allowed the pilot to feel 1g, would he still feel 1g when the spaceship was close to the speed of light?
I know that it will never reach the speed of light so the acceleration must slow as the ship speeds up, so I assume that close to the speed of light the pilot will be mostly weightless.

Is this true or will he still feel the same acceleration?
Your question is most likely based on the incorrect assumption that an accelerating object is in some way "catching up" with the speed of light.

It is not, even if it accelerates for 10 million years with 1G, it is still just as far removed from the speed of light as it was before.

Contrary to what is often claimed, even in the limit (except when we decrease the mass to zero) it would not reach the speed of light!

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ledopmi said:
I know that it will never reach the speed of light so the acceleration must slow as the ship speeds up, so I assume that close to the speed of light the pilot will be mostly weightless.

Is this true or will he still feel the same acceleration?

No, the pilot continues to "feel" the same acceleration, and his ship's rocket engines continue to produce the same amount of thrust (burn fuel at the same rate), even though in any inertial reference frame his speed asymptotically approaches the speed of light and becomes nearly constant.

As others have already stated, the pilot won't notice anything different in empty space. This follows from the basic principle that there is no way to determine one's "absolute" velocity without something to compare it to.

The standard reference with detailed formulas for velocity vs 'time' is http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html [Broken]
(there are actually a couple of types of time that are interesting, proper time and coordinate time).

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jtbell said:
...even though in any inertial reference frame his speed asymptotically approaches the speed of light and becomes nearly constant.
It actually depends on the direction of acceleration.
To some intertial frames his speed can even approach zero.

MeJennifer said:
Your question is most likely based on the incorrect assumption that an accelerating object is in some way "catching up" with the speed of light.

It is not, even if it accelerates for 10 million years with 1G, it is still just as far removed from the speed of light as it was before.

Contrary to what is often claimed, even in the limit (except when we decrease the mass to zero) it would not reach the speed of light!

I do not understand. I realize that it will never reach the speed of light but I do not understand how it will be just as far removed from the speed of light as it was before it started to accelerate.

ledopmi said:
I do not understand. I realize that it will never reach the speed of light but I do not understand how it will be just as far removed from the speed of light as it was before it started to accelerate.

If the observer on the hypothetical spaceship measures the speed of light from any source, including a source that was initially stationary with respect to him when he began accelerating, he will measure the speed of light from that source as being equal to 'c' (using his local clocks and rulers).

Therefore he is just as far away from the speed of light as he ever was, even after he accelerates. Before he accelerates, the light was coming towards him at 'c'. After he accelerates, the light is still coming towards him at 'c'.

If you read the FAQ entry I quoted earlier, you'll see a lot more info, including some interesting things about what parts of the universe the accelerating observer can and cannot see.

Any light that the observer on the rocket can see, however, will always be measured as traveling at 'c', no matter how long he accelerates.

ledopmi said:
I do not understand. I realize that it will never reach the speed of light but I do not understand how it will be just as far removed from the speed of light as it was before it started to accelerate.

It depends on whose point of view (reference frame) you're talking about. From an earthbound observer's point of view (or indeed any other inertial observer), the ship's speed gets closer and clooser to the speed of light. From the pilot's point of view, the speed of any light pulse, including the one he's "chasing", is still c.

http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/einvel.html

The relativistic velocity addition equation not only guarantees that the relative velocity of two material objects can never exceed c, it also guarantees that the speed of a light pulse relative to any inertial observer is always c. Let one of the velocities being "added" be c, and calculate the result.

Can i think in this way??

In the instantaneous co-moving frame of the spaceship, the pilot feels his acceleration (1g). However, he never admit that his speed has become closer to the speed of light as the relative speed he measure between light and him is always c.

In the Earth-frame, um...how can i think for it more iteratively?

jtbell said:
From an earthbound observer's point of view (or indeed any other inertial observer), the ship's speed gets closer and clooser to the speed of light.
Sorry jtbell, but as I wrote a few posting earlier, what you write is simply not true.

For some intertial observers that is the case but you cannot say that that is the case for all observers. For some inertial observers the ship's speed will actually approach zero.

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ledopmi said:
I do not understand. I realize that it will never reach the speed of light but I do not understand how it will be just as far removed from the speed of light as it was before it started to accelerate.
You are always at rest with respect to a photon. If you weren't, you wouldn't always measure C to be C.
In the instantaneous co-moving frame of the spaceship, the pilot feels his acceleration (1g). However, he never admit that his speed has become closer to the speed of light as the relative speed he measure between light and him is always c.

In the Earth-frame, um...how can i think for it more iteratively?
The word "admit" seems strange there, but in any case, if a spacecraft accelerates away from Earth at 1g (according to the pilot), an observer on Earth will see him get closer and closer to C without ever reaching it and the pilot will look back at Earth and see it receeding at closer and closer to C without ever reaching it. But he'll still always measure light to travel at C.

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MeJennifer said:
jtbell said:
...even though in any inertial reference frame his speed asymptotically approaches the speed of light and becomes nearly constant.
It actually depends on the direction of acceleration.
To some intertial frames his speed can even approach zero.

I assumed that ledopmi is talking about a ship that is accelerating in the direction of its motion. Most people who haven't been thoroughly indoctrinated into the physicist's mindset, use "decelerate" when referring to acceleration in the opposite direction.

ledopmi said:
I do not understand. I realize that it will never reach the speed of light but I do not understand how it will be just as far removed from the speed of light as it was before it started to accelerate.
Motion in relativity is a relative concept not an absolute one. You can only move relative to something else, and that something else must have mass.

Suppose you are the only ship in the universe, nothing else but you, and you would accelerate for say 10 billion years. Then what is your motion in space-time? The answer is that there is no point in even asking that question, since you have no way to measure your motion against.

What about your position? You position is in the middle of the universe! You are always in the middle, wherever you go.

Space seen as a 3 dimensional hypersurface of space-time is not Euclidean but hyperbolic. Hyperbolic space is "weird" for instance you can pack an infinite number of spaceships with an equal distance from each other inside a sphere with a radius the size of the distance traveled by a photon of a given time interval. The volume of this region is infinite!

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