Acceleration Frame in SR: References for Research

In summary: From haushofer's notes:(4) If the object experiences a uniform acceleration, then its velocity will change continuously according to the following equation:v(t) = v0 + a(t)dt(5) If the object experiences a non-uniform acceleration, then its velocity will change according to the following equation:v(t) = v0 + a0 t2 + a1 t + a2 t2 + .... + aN tN(6) If the object experiences a constant acceleration, then its velocity will be constant.(7) If the object experiences an instantaneous acceleration, then its velocity will be zero at the instant of the acceleration.
  • #1
Haorong Wu
413
89
TL;DR Summary
References of acceleration frame in SR
Hi. I am looking for some references of acceleration frame in SR, such as an accelerating rocket problem.

I have some equations regarding the time, distance, velocity measured in the Earth frame, etc. But the reference I have does not provide the derivation of those equations, so I need some more references.

Thanks!
 
Physics news on Phys.org
  • #2
Recently I wrote up some notes for myself. There are some typo's in it (the last version is at my home pc), but maybe it is of some help for you.
 

Attachments

  • Accelerated Observers.pdf
    329.9 KB · Views: 232
  • Like
  • Love
Likes etotheipi, PAllen, vanhees71 and 1 other person
  • #3
haushofer said:
Recently I wrote up some notes for myself. There are some typo's in it (the last version is at my home pc), but maybe it is of some help for you.
Thanks! Great notes! It just has what I need.
 
  • #4
Haorong Wu said:
Summary:: References of acceleration frame in SR

Hi. I am looking for some references of acceleration frame in SR, such as an accelerating rocket problem.

I have some equations regarding the time, distance, velocity measured in the Earth frame, etc. But the reference I have does not provide the derivation of those equations, so I need some more references.

Thanks!

Misner, Thorne, Wheeler (MTW) has a treatment of this in "Gravitation". But it uses tensors. Most treatments of accelerating frames that I've seen use tensors. Rindler has another (more dated) treatment, I believe in his GR textbook. I imagine there are others.

However, if you drop the "frame" part and are just interested in acceleration in special relativity, the "relativistic rocket" FAQ might be helpful. See https://math.ucr.edu/home/baez/physics/Relativity/SR/Rocket/rocket.html for instance.
 
  • #5
pervect said:
Misner, Thorne, Wheeler (MTW) has a treatment of this in "Gravitation". But it uses tensors. Most treatments of accelerating frames that I've seen use tensors. Rindler has another (more dated) treatment, I believe in his GR textbook. I imagine there are others.

However, if you drop the "frame" part and are just interested in acceleration in special relativity, the "relativistic rocket" FAQ might be helpful. See https://math.ucr.edu/home/baez/physics/Relativity/SR/Rocket/rocket.html for instance.
Hello, @pervect. The equations I got are from the same page. Equations (4) to (8) in that page are just given without the derivation. Gladly, @ haushofer 's notes fill this gap.
 

1. What is an acceleration frame in special relativity?

An acceleration frame in special relativity refers to a reference frame in which an object is accelerating. This means that the object is experiencing a change in velocity, either in magnitude or direction. In special relativity, acceleration frames are important because they can affect the perception of time and space for an observer.

2. How does acceleration affect time dilation in special relativity?

In special relativity, time dilation is the phenomenon where time appears to pass slower for an observer in one reference frame compared to another. When an object is accelerating, it experiences a change in velocity, which can cause time dilation to occur. This means that time will pass at a different rate for an observer in an acceleration frame compared to an inertial frame.

3. What is the difference between an inertial frame and an acceleration frame in special relativity?

An inertial frame in special relativity is a reference frame in which an object is either at rest or moving at a constant velocity. In contrast, an acceleration frame is a reference frame in which an object is accelerating. Inertial frames follow the laws of special relativity, while acceleration frames require the use of more complex equations to account for the effects of acceleration.

4. How does an observer in an acceleration frame perceive space in special relativity?

In special relativity, an observer in an acceleration frame will perceive space differently compared to an observer in an inertial frame. This is due to the effects of acceleration on the perception of distance and length. For example, an object may appear to be shorter in the direction of its motion for an observer in an acceleration frame compared to an inertial frame.

5. What are some real-world applications of understanding acceleration frames in special relativity?

Understanding acceleration frames in special relativity is important in many real-world applications, such as space travel and GPS systems. In space travel, the effects of acceleration on time and space must be taken into account for accurate calculations and predictions. In GPS systems, the satellites are constantly accelerating, so the effects of acceleration on time and space must be accounted for to ensure accurate location data.

Similar threads

I Is an accelerating frame the same as an inertial frame at a point?
    • Special and General Relativity
Replies
11
Views
1K
I SR textbooks discussing accelerated reference frames without delving into GR
    • Special and General Relativity
2
Replies
36
Views
2K
I Principle of relativity for proper accelerating frame of reference
    • Special and General Relativity
5
Replies
144
Views
6K
B Differences in Predictions between SR and LR?
    • Special and General Relativity
Replies
20
Views
1K
I Hafele-Keating Exp: Balancing SR Effects in Plane Ref Frame
    • Special and General Relativity
2
Replies
54
Views
2K
I Galilean relativity in terms of homogeneity
    • Special and General Relativity
2
Replies
51
Views
2K
I Momentary Co-Moving Reference Frame in SR
    • Special and General Relativity
Replies
3
Views
1K
I About inertial reference frames and logical deduction
    • Special and General Relativity
Replies
26
Views
2K
I About global inertial frames in GR
    • Special and General Relativity
3
Replies
78
Views
4K
B What is x' for Moving Rocket from P?
    • Special and General Relativity
Replies
2
Views
1K

Hot Threads

Recent Insights

Back
Top