Falling Object at c: Relativistic Position Expression for the Attracted Object

In summary, the conversation discusses the relativistic position expression for a falling object that could reach the speed of light, the equations for acceleration, speed, and position in non-relativistic and relativistic scenarios, and the need to measure acceleration in a non-accelerating frame of reference traveling at the same speed as the object.
  • #1
Imagine
Gedenke experiment: Falling object upto c?

Bonjour,

I would like to know the relativistic position expression for a falling object that could reach the speed of light.

Thanks.

P.S.: Suppose the only things, that exist in the universe, are a BIG attractive mass and the attracted "object".
 
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  • #2
Nothing with mass could be accelerated to c.

Even if it were to go into a black hole, starting an infinite distance away, once it crosses the event horizon, it is in a different spacetime.
 
  • #3
Gedenke experiment: Falling object upto c?

Bonjour Brad,

I shall agree with your mass issue.

Suppose, isolated in the universe , a small energetic object, with zero initial relative speed, somewhere far-far-far away from a non-negligeable gravitationnally attractive accumulation of energy (both with mass equivalence (m & M) for gravitational purpose ).

"m" shall be accelerated by "M", following gravitational effect, right?

While m's speed is within non-relativistic speed, I got no problem to express acceleration, speed and position equations.

What would be these equations when relativistic speed's effect is non-negligeable? (Should I ask this in Theoretical forum?)

P.S.: ............
 
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  • #4
For relativistic versions of those, some tinkering with the equations here: http://www.wikipedia.org/wiki/Relativistic_equation

might help you to get them.

Also, http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html

note that it has the equations you are looking for.
 
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  • #5
Welcome to Physics Forum, Imagine! :smile:
 
  • #6
Originally posted by Brad_Ad23
For relativistic versions of those, some tinkering with the equations here: http://www.wikipedia.org/wiki/Relativistic_equation

might help you to get them.

Also, http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html

note that it has the equations you are looking for.

Phobos, merci pour votre mot de bienvenue.

Brad, I red the rocket page. I also understand the origin of the following restriction: "The acceleration of the rocket must be measured at any given instant in a non-accelerating frame of reference traveling at the same instantaneous speed as the rocket".

Thanks, that was exactly what I searched.
 
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1. How is the position of a falling object at relativistic speeds expressed?

The position of a falling object at relativistic speeds is expressed using the relativistic position expression, which takes into account the effects of time dilation and length contraction.

2. What is the equation for the relativistic position expression?

The equation for the relativistic position expression is x = x0 + v0t + (1/2)(at2), where x is the position of the object at time t, x0 is the initial position, v0 is the initial velocity, a is the acceleration, and t is the time.

3. How does the relativistic position expression differ from the classical position expression?

The relativistic position expression takes into account the effects of time dilation and length contraction, which are not accounted for in the classical position expression. It also includes a correction factor for the increase in mass at high speeds.

4. Can the relativistic position expression be used for any falling object?

The relativistic position expression can be used for any object falling at relativistic speeds. However, it is most accurate for objects with significant mass and velocity, such as planets or satellites.

5. How is the relativistic position expression related to Einstein's theory of relativity?

The relativistic position expression is a consequence of Einstein's theory of relativity, which states that the laws of physics are the same for all observers in uniform motion. This theory explains the effects of time dilation and length contraction, which are taken into account in the relativistic position expression.

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