Perpetual Acceleration: Questions for Beginners

[Gingermolloy]

Hi Guys,

I am new here and this is my first post so be gentle!

I have been recently trying to increase my knowledge of relatively.

I have a few questions to ask but here is my first? Hope you guys can help me.

If a body is in a gravitational field (like everything on earth) then it is accelerating through space-time right??

If this is the case then that body is in a state of perpetual acceleration through space-time forever.

My understanding is that everything is moving at the speed of light in space-time.

If this is the case how can something be accelerated from the speed of light.

Where am I getting muddled up here??

Help please

Ginger

 

[A.T.]

1) You have to differentiate between:
- moving through space, where c is the maximum speed (in respect to a clock at rest)
- advancing though space-time, where c can be considered the constant advance rate of all objects.

2) Acceleration doesn't imply an increase of speed. An object in circular motion experiences acceleration despite constant speed, because it's spatial path is not straight. In GR an object resting in a gravitational field experiences acceleration, because its path through space-time is not straight (geodesic).

You can play around with this applet to get a rough idea:
http://www.adamtoons.de/physics/relativity.swf

 

[Dale]

If a body is in a gravitational field (like everything on earth) then it is accelerating through space-time right??

If this is the case then that body is in a state of perpetual acceleration through space-time forever.

My understanding is that everything is moving at the speed of light in space-time.

If this is the case how can something be accelerated from the speed of light.

Where am I getting muddled up here??

Hi Ginger, welcome to PF!

Don't forget that something can accelerate without changing speed. For example, in uniform circular motion an object is constantly accelerating but never changing speed.

In space-time the same thing happens. The four-dimensional analog to acceleration (four-acceleration) is always perpendicular to the four-dimensional analog to velocity (four-velocity). The result is that the magnitude of the four-velocity remains constant, but your direction in spacetime changes.

 

[Gingermolloy]

Thanks Guys,

So when a body is accelerated through space it is still moving through space-time at the speed of light. Think I get that bit now.

Not sure I understand the concept of a bodys path in space-time changing direction.

I thought that the curved path of a body though space is a concequence of a body moving in a straight line through curved space-time.

Do all bodys move in straight lines through space-time??

 

[Dale]

Thanks Guys,

So when a body is accelerated through space it is still moving through space-time at the speed of light. Think I get that bit now.

Not sure I understand the concept of a bodys path in space-time changing direction.

I thought that the curved path of a body though space is a concequence of a body moving in a straight line through curved space-time.

Do all bodys move in straight lines through space-time??

No, not all bodies. The generalization of a "straight line" to curved spacetime is called a "geodesic". Free-falling bodies follow geodesics. For any such body, an onboard accelerometer will read 0 proper acceleration. However, it is also possible for a body to have an onboard accelerometer that does not read 0. These bodies are not following geodesics. So a curved path in space can result from either following a geodesic in curved spacetime (free fall) or from proper acceleration.

 

[A.T.]

Not sure I understand the concept of a bodys path in space-time changing direction.

This is indeed tricky, because in curved space-time "changing direction" can mean "staying at the same space coordinate". An object resting on your table changes its direction in space-time with respect to the locally straight (geodesic) path, in order to stay at the same space coordinate.

I thought that the curved path of a body though space is a concequence of a body moving in a straight line through curved space-time.

This is true for free falling objects. But an object resting in space in a G-field is not moving on a straight path through space-time. The normal force of the table pushes it away form that path.

Check out this:
http://www.relativitet.se/spacetime1.html

And chapter 2 of this (Figure 2.20 & 2.21):
http://www.relativitet.se/Webtheses/tes.pdf

 

[stu dent]

if you imagine looking at an object in orbit from a top down view, it looks like the object is moving at a constant rate.

acceleration is to do with vectors, with direction. an object in orbit is continuously changing direction.

if you take the same object in orbit that you are looking at from a top down down view, and put it on its side, then you will observe the object accelerating to the center, towards the thing it is orbiting, and then decelerating out from it, stopping, and coming back. the object is continuously doing that, on any angle you can look at it from at any given time.

only light or possibly other zero mass energies travel at the speed of light.

all objects of mass must travel at a speed lower than that.

gravity works similar to a bowling ball in a trampoline, this curvature of space-time results in the altered path of things traveling through it.

 

[Gingermolloy]

http://www.relativitet.se/Webtheses/tes.pdf

This ws hugely helpful!

Thanks

A. T.