Lorentz transformation for an approaching observer

In summary, the conversation discusses the Lorentz factor and its application in a formula. It is mentioned that the Lorentz factor can have both positive and negative values, which constitutes a sign change. The conversation also touches on a previous discussion about Lorentz boost speed or velocity. The conversation ends with a humorous exchange about a nickname and a goodbye message.
  • #1
sukmeov
10
2
Homework Statement
Let O and O' be observers both moving along the x-axis at constant velocity. Assume O and O' meet at the origin. Suppose also that O' moves towards O with relative velocity v. O reference frame has coordinates (x,t) and O' reference frame has coordinates (x',t') What is the Lorentz transformation for the two coordinate frames. ( I only care about the relationship between the time coordinates)
Relevant Equations
Lorentz transform for positive velocity: t' = Lorentz factor * (1-v/c)t
I think this should be t'= Lorentz factor* (1+v/c)t, but that doesn't make sense to me.
 
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  • #3
Many thanks. So there is no sign change in the formula, even if v is negative? Also it's not a nickname it's my surname.
 
  • #4
sukmeov said:
Many thanks. So there is no sign change in the formula, even if v is negative?

You're right that ##v## can indeed be positive or negative; that constitutes the sign change. There was actually a thread about this a short while ago: https://www.physicsforums.com/threads/lorentz-boost-speed-or-velocity.988183/

sukmeov said:
Also it's not a nickname it's my surname.

:eek:

I don't know what to say... goodbye PF it's been nice knowing you all :doh:
 
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  • #5
Very helpful. Thank you.

Ukan Sukmeov.
 
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  • #6
I KNEW it! :mad:
 
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Related to Lorentz transformation for an approaching observer

1. What is the Lorentz transformation for an approaching observer?

The Lorentz transformation is a mathematical formula used in special relativity to describe how the measurements of space and time change for an observer who is moving relative to another observer. It takes into account the effects of time dilation and length contraction.

2. How does the Lorentz transformation account for an approaching observer?

The Lorentz transformation includes a velocity term, which represents the relative velocity between the two observers. This velocity term affects the measurements of both time and space for the approaching observer, resulting in different values than those measured by the stationary observer.

3. What is the difference between the Lorentz transformation for an approaching observer and a receding observer?

The Lorentz transformation is symmetrical, meaning it works the same for both approaching and receding observers. However, the velocity term will have a different sign depending on whether the observer is approaching or receding, resulting in different values for time and space measurements.

4. How is the Lorentz transformation related to Einstein's theory of relativity?

The Lorentz transformation is a key component of Einstein's theory of special relativity, which revolutionized our understanding of space and time. It allows for the prediction and explanation of various phenomena, such as time dilation and length contraction, that are observed in experiments and are essential to the theory of relativity.

5. Can the Lorentz transformation be applied to any observer in motion?

Yes, the Lorentz transformation can be applied to any observer in motion, as long as the relative velocity between the observers is less than the speed of light. It is a fundamental principle of special relativity and has been extensively tested and confirmed through experiments.

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