Consistent with special relativity?

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Discussion Overview

The discussion revolves around the scenario of two identical spacecraft moving in opposite directions at 0.80c, as observed from the ground, and the implications of their separation rate being perceived as 1.60c. Participants explore how this situation aligns with the principles of special relativity, particularly concerning velocity addition and the nature of speed measurements.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants assert that the separation rate of 1.60c does not imply a physical object is moving faster than light, as it is a measurement between two objects from a third observer's perspective.
  • Others discuss the application of relativistic velocity addition to clarify how speeds are perceived differently depending on the observer's frame of reference.
  • A participant notes that while the observer on the ground sees the spacecraft separating at 1.60c, an observer in one of the spacecraft would measure the other moving away at 0.976c.
  • Some participants emphasize that special relativity allows for two separate objects to have a net speed greater than c, but not a single object exceeding the speed of light.
  • There is a mention of a potential typo regarding the term "contradiction SR," indicating a need for clarification on that point.

Areas of Agreement / Disagreement

Participants express varying interpretations of how the separation rate relates to special relativity, with some agreeing on the distinction between relative speeds and others questioning the implications of the observed rates. No consensus is reached on the interpretation of the separation rate as it pertains to special relativity.

Contextual Notes

Participants acknowledge the complexities of applying relativistic velocity addition and the nuances of speed measurements between multiple observers. The discussion reflects a range of assumptions and interpretations that remain unresolved.

ZephyrWest
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Here's the problem:

Two identical spacecraft are moving in opposite directions each with a speed of 0.80c as measured by an observer on the ground. The observer on the ground measures the separation of the spacecraft as increasing at a rate of 1.60c.

Explain how this observation is consistent with the theory of special relativity.

I know that nothing can exceed the speed of light c. So is it consistent with special relativity because it is not a physical object that is moving at 1.60c? I'm asking because I'm really not sure if I'm correct.

Thanks for your help.
 
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I understand relativistic velocity addition but am not sure how to apply it to this situation. Can you please explain?
 
Explain how this observation is consistent with the theory of special relativity.
Are you asking how the space can be increasing by that much & yet none of those two spaceships measures a superluminal speed ... ? Ordinary velocity addition doesn't apply.
 
Well, the simple answer here is that "separation rate" is not a speed. Speed is measured between two objects, not three. So it is perfectly fine to say that according to the 3rd observer, the two spacecraft are separating at 1.6C. That isn't contradicting SR because it isn't saying anything about a speed.
 
Last edited:
Hmmm... ok. From the frame of reference of one of the spacecraft s, is the separation rate, or speed, this?

[tex]\frac{0.80c + 0.80c}{1 + \frac{(0.80c)(0.80c)}{c^2}} = \frac{1.60c}{1.64} = 0.976c[/tex]

And, what is "contradiction SR"?
 
ZephyrWest said:
Here's the problem:



I know that nothing can exceed the speed of light c. So is it consistent with special relativity because it is not a physical object that is moving at 1.60c? I'm asking because I'm really not sure if I'm correct.

Thanks for your help.

1. SR precludes one massive object from moving at a speed equal or larger than c.(photons having zero mass move at c)

2. In your example you are dealing with two separate objects closing on each other at a net speed v>c. SR does not preclude this, actually speeds as large as 2c are acceptable in SR.
 
ZephyrWest said:
Hmmm... ok. From the frame of reference of one of the spacecraft s, is the separation rate, or speed, this?

[tex]\frac{0.80c + 0.80c}{1 + \frac{(0.80c)(0.80c)}{c^2}} = \frac{1.60c}{1.64} = 0.976c[/tex]

And, what is "contradiction SR"?

This example above simply says that if a rocket flies in the +x direction at 0.8c and you are observing it from another rocket flying at 0.8c in the -x direction, you would measure the other rocket receding from you at 0.976c.
The observer in your original problem sees you and the other rocket receding away from each other at 1.6c.
The difference is quite clear now, right?
 
Yes, so if I was in one of the rockets, I would see the other moving traveling away away from me at 0.976c.

The external observer on the ground would see the two rockets traveling away from each other at 1.6c. This is possible because special relativity permits two separate objects to have a net speed greater than c, but not one object.

Did I get it right? :)
 
  • #10
ZephyrWest said:
Yes, so if I was in one of the rockets, I would see the other moving traveling away away from me at 0.976c.

The external observer on the ground would see the two rockets traveling away from each other at 1.6c. This is possible because special relativity permits two separate objects to have a net speed greater than c, but not one object.

Did I get it right? :)

perfect :-)
 
  • #11
ZephyrWest said:
And, what is "contradiction SR"?
A typo... (fixed)
 

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