Does Light Reach Objects Moving at High Speeds?

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Discussion Overview

The discussion centers on the question of whether light can reach objects moving at high speeds, particularly when those objects are moving away from the light source. Participants explore the implications of relativistic effects on the perception of time and distance in different frames of reference.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant questions how light can reach an object moving at 50% of the speed of light if the light is emitted from behind it, suggesting that the distance light must travel would exceed 300,000 km.
  • Another participant introduces the concept of time dilation using the formula t=t0/(sqrt(1-(v/c)^2)), indicating that in the object's frame, the distance light travels is perceived differently.
  • A third participant mentions the Lorentz transformation, emphasizing that the speed of light remains constant due to the principles of relativity and causality.
  • A later reply reiterates the initial question and provides a mathematical approach to analyze the situation, suggesting that in the frame of the moving object, light still approaches at speed 'c' despite the object moving away.
  • One participant seeks clarification on whether the distance light must travel increases when the object is moving away from it.

Areas of Agreement / Disagreement

Participants express differing views on how to interpret the relationship between the motion of the object and the light reaching it. There is no consensus on whether the distance light must travel increases or remains constant in the context of relativistic effects.

Contextual Notes

The discussion involves complex concepts such as time dilation, Lorentz transformations, and the relativity of simultaneity, which may not be fully resolved within the conversation.

Who May Find This Useful

Individuals interested in the implications of special relativity, the behavior of light in different frames of reference, and the mathematical foundations of these concepts may find this discussion relevant.

themaster1j
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As I just registered as a member, I don't know if this question has been asked before on this forum, and I'm sorry if I'm asking it again.

From what I understand, even if an object is moving away from light with a significant speed, the light would still approach that object as if it would be standing still.
If an object travels at 50% of the speed of light and a light beam is emitted at ~300,000km behind that object, how can the light reach the object in 1 second if the object is moving away from the light? Doesn't it mean that the distance the light would have to travel would be more than 300,000km?

I apologize for my basic understanding of Physics.
 
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Well for the object with speed 50% of speed of light time will increase will increase by the formula t=t0/(sqrt(1-(v/c)^2)), where t0 is original time.Similar way is for distance.The distance from your frame will have increased so that light cover's only 300000 km in one second.
 
Read about Lorentz trans formation. Speed of light is postulated to be constant by relativity because of causality. Lorentz transformation is what makes speed of light constant.

Last but not least, welcome to PF!
 
themaster1j said:
As I just registered as a member, I don't know if this question has been asked before on this forum, and I'm sorry if I'm asking it again.

From what I understand, even if an object is moving away from light with a significant speed, the light would still approach that object as if it would be standing still.
If an object travels at 50% of the speed of light and a light beam is emitted at ~300,000km behind that object, how can the light reach the object in 1 second if the object is moving away from the light? Doesn't it mean that the distance the light would have to travel would be more than 300,000km?

I apologize for my basic understanding of Physics.

In the frame where the object is moving away, it does takes more than one second. In fact you can write

x1 = -3e8 m + 3e8(m/s) * t
x2 = 1.5e8 (m/s) *t

and solve for the value of time at which x1 = x2 as t=2

However, it is still true that if you transform to the frame of the moving object, so that it is standing still, the light beam still approaches it at 'c'. You have to be careful how you analzye this, becuase the notion of simultaneity is the moving frame is different - specifically, the coordinates of the object (t=0, x=-3e8 meters) transform to something like (t=.5*gamma seconds, x = -3e8*gamma meters), where gamma 2/sqrt(3).

This is done via the Lorentz transform
[tex] x' = \gamma \left( x - v\,t\right)[/tex]
[tex] t' = \gamma \left( t - \frac{v}{c^2} \, x\right)[/tex]
 
So the distance the light has to travel to reach the object doesn't increase, even though the object is moving away from the light?
 

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