Understanding Proper Acceleration and Four-Acceleration in Special Relativity

In summary, the conversation discusses the confusion surrounding the concepts of four-acceleration and proper acceleration as described in Wikipedia articles. It is clarified that the proper acceleration within a co-moving inertial reference frame is equal to the proper acceleration felt by a moving particle along its world line. Additionally, it is noted that the formula for proper acceleration is incorrectly stated in one article, but is correctly stated in another article. A request is made for someone to double check the edits made to the articles.
  • #1
granpa
2,268
7
does anybody besides me find the following wikipedia articles confusing?

http://en.wikipedia.org/wiki/Four-acceleration
a=du/dτ
γu is the Lorentz factor for the speed (coordinate velocity) u
In an instantaneously co-moving inertial reference frame u = 0, γu = 1 and dγu/dτ = 0, i.e. in such a reference frame
A =(0,a)
Therefore, the four-acceleration is equal to the proper acceleration that a moving particle "feels" moving along a world line.

should read:
Therefore, the four-acceleration within that co-moving inertial reference frame is equal to the proper acceleration that a moving particle "feels" moving along a world line.http://en.wikipedia.org/wiki/Proper_acceleration
The proper acceleration 3-vector, combined with a null time-component, yields the object's four-acceleration. (this is just plain wrong)

even though below that:
http://en.wikipedia.org/wiki/Proper_acceleration#Viewed_from_a_flat_spacetime_slice
it correctly states:
proper acceleration α and coordinate acceleration a are related[6] through the Lorentz factor γ by α=a*γ^3
Hence the change in proper-velocity w=dx/dτ is the integral of proper acceleration over map-time t (coordinate time)
and gives these formulas:
http://upload.wikimedia.org/math/f/3/f/f3fd7fcce9b254111e10ca5bae382511.png

you can check that the derivative of proper velocity with respect to coordinate time is a*gamma^3 by entering v[t]/sqrt[1-((v[t])^2)] into this http://calc101.com/webMathematica/derivatives.jsp#topdoit
 
Last edited:
Physics news on Phys.org
  • #3
I have edited the 2 wikipedia articles in question. I would very much appreciate it if someone would double check my work.
 

1. What is proper acceleration in special relativity?

Proper acceleration is a measure of how quickly an object's velocity changes with respect to its own frame of reference in special relativity. It is also known as the acceleration measured by an observer who is co-moving with the object.

2. How is proper acceleration different from coordinate acceleration?

Proper acceleration takes into account the effects of time dilation and length contraction in special relativity, while coordinate acceleration only considers the change in velocity in a specific coordinate system.

3. What is the formula for calculating proper acceleration?

The formula for proper acceleration is a = γ^3 * (dv/dt), where γ is the Lorentz factor and dv/dt is the coordinate acceleration.

4. How does proper acceleration affect the concept of simultaneity in special relativity?

Proper acceleration can cause a difference in the perception of simultaneity for observers who are in different frames of reference. This is due to the effects of time dilation and length contraction on the measurement of time and distance between events.

5. Can proper acceleration be greater than the speed of light?

No, according to the laws of special relativity, the speed of light is the maximum speed that can be reached by any object. Therefore, proper acceleration cannot exceed the speed of light.

Similar threads

  • Special and General Relativity
5
Replies
144
Views
6K
  • Special and General Relativity
Replies
11
Views
938
  • Special and General Relativity
Replies
33
Views
1K
  • Special and General Relativity
Replies
30
Views
3K
  • Special and General Relativity
2
Replies
36
Views
3K
  • Special and General Relativity
Replies
3
Views
1K
  • Special and General Relativity
Replies
29
Views
1K
  • Special and General Relativity
Replies
15
Views
2K
  • Special and General Relativity
Replies
1
Views
1K
  • Special and General Relativity
3
Replies
75
Views
3K
Back
Top