Distance between two events w.r.t. two frames

In summary, the conversation discusses the distance between events in different frames of reference and how a person on a train may perceive the train to be accelerating even though it is not actually moving. It is concluded that in the train frame, the train is stationary and therefore not accelerating. This conclusion is reached by the definition of the train frame.
  • #1
Pushoam
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51

Homework Statement


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Homework Equations

The Attempt at a Solution


Distance between events w.r.t. Earth frame,

De = | (1/2)w(t+Γ)2 - 350 - (1/2)wt2 | = 242 m

Distance between events w.r.t. train frame,
Dt =350 m , correct?
As w.r.t. train frame , the train is not moving.

But, a person on the train will observe that the train is accelerating.
But , if the train is not moving, then how will this person observe that the train is accelerating. Here , I am doing some mistake. Please help me.W.r.t. Earth's frame, the two events occur at (x1,t1) and (x2,t2)
such that x1 - x2= 242 m
and t2 - t1 = 60 s

At t = 0 s, origin of both K's and Earth's frames meet each other.
W.r.t. K's frame, the two events occur at (x'1,t1) and (x'2,t2)
such that x'1 - x'2= 0 m
and t2 - t1 = 60 s
x'1 - x'2= 0 m = x1 - Vt1 - x2 + Vt2

x1 - x2 = - V( t2 - t1 )

V = 242/60 = 4.0 m/s
 
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  • #2
Pushoam said:
But, a person on the train will observe that the train is accelerating.
No it will not. The train frame is a non-inertial frame.
 
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  • #3
Orodruin said:
No it will not. The train frame is a non-inertial frame.

How can I,too, reach to this conclusion?
If a person sitting in an accelerating train wants to measure the acceleration of the train, won't he measure the acceleration to be nonzero?
 
  • #4
Orodruin said:
No it will not. The train frame is a non-inertial frame.

How can I,too, reach to this conclusion?
If a person sitting in an accelerating train wants to measure the acceleration of the train, won't he measure the acceleration to be nonzero?
 
  • #5
Pushoam said:
How can I,too, reach to this conclusion?
If a person sitting in an accelerating train wants to measure the acceleration of the train, won't he measure the acceleration to be nonzero?
This depends on what you mean by "measuring the acceleration". An accelerometer will give you a non-zero value, but it will read the same in all frames. By definition of the train frame, the train is stationary in that frame and therefore not accelerating.
 
  • #6
Orodruin said:
An accelerometer will give you a non-zero value, but it will read the same in all frames.
Does "all" imply both inertial and non-inertial frames?
Orodruin said:
By definition of the train frame, the train is stationary in that frame and therefore not accelerating.
So, we reach to that conclusion by definition.
 

1. What is the concept of distance between two events with respect to two frames?

The concept of distance between two events with respect to two frames refers to the measurement of the space or interval between two events as observed from two different reference frames. This is based on the theory of relativity, which states that the measurement of time and space is relative to the observer's frame of reference.

2. How is the distance between two events measured in special relativity?

In special relativity, the distance between two events is measured using the Lorentz transformation equations. These equations take into account the relative motion and time dilation between the two frames to calculate the distance between the events in each frame.

3. Is the distance between two events the same for all observers?

No, the distance between two events is not the same for all observers. According to the theory of relativity, the measurement of distance is relative and depends on the observer's frame of reference. Different observers will measure different distances between the same two events.

4. Can the distance between two events be negative?

Yes, the distance between two events can be negative. This can happen when the events occur at different times and the observer's frame of reference is moving in the opposite direction. In this case, the distance is measured as a negative value, indicating that the events are moving away from each other.

5. How does the distance between two events affect the perception of time?

The distance between two events can affect the perception of time due to time dilation. This means that the time interval between events will appear different for observers in different frames of reference. The closer the events are in space, the shorter the time interval will appear for the observer in that frame.

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