What Color Would a Light Beam Appear While Chasing It at 0.999c?

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Discussion Overview

The discussion revolves around the hypothetical scenario of observing a light beam while traveling towards it at 0.999c, focusing on the implications of the Doppler effect and relativistic physics. Participants explore the visibility of the light beam and the resulting color shift, if any, under these extreme conditions.

Discussion Character

  • Exploratory
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants question the feasibility of seeing a light beam while traveling towards it at 0.999c, suggesting that one would never catch up to it and therefore never see it.
  • Others propose that if it were possible to see the light, the Doppler shift would lead to an infinitely redshifted appearance due to time dilation effects as one approaches the speed of light.
  • A participant mentions the use of the relativistic Doppler shift formula to calculate the redshift when moving away from a light source, indicating that the frequency observed would depend on the relative velocity.
  • One post humorously asserts that if it were possible to see the light, it would appear black, followed by a playful poem.

Areas of Agreement / Disagreement

Participants generally disagree on whether it is possible to observe the light beam at all, with some asserting that it cannot be seen while others explore the implications of the Doppler effect if it were possible.

Contextual Notes

There are unresolved assumptions regarding the nature of light and observation at relativistic speeds, particularly concerning the limits of visibility and the application of the Doppler effect in this scenario.

Quantum1332
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This might be a stupid question, but it came to me the other day while reading. Since the speed of light is the same in all frames what would happen if you were chasing a light beam at .999% c, so you were heading right for it (but could never catch it) and it is ahead of you traveling at c. If you were to include the doppler effect what color would the light beam appear?
 
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Since you'd never catch up with the light, you'd never see it at all!
 
I don't understand the scenario. If the "light beam" is moving away from you, you won't see it at all.

[jtbell beat me too it!]
 
if it were possible to see it?
 
Quantum1332 said:
if it were possible to see it?
The doppler shift equation is based partly on the time dilation of the source in your frame--in other words, if a source is emitting wave peaks at a frequency of 5*10^14 per second (visible light) in its own rest frame, then because of time dilation, when it's moving with respect to you it will emit less peaks per second in your frame. In the limit as the velocity of a clock in your frame approaches c, the time between ticks of the clock approaches infinity, no matter how long between ticks in the clock's own frame...so analogously, in the limit as a source's velocity relative to you approaches c, the time between peaks of any signal it emits in your direction approaches infinity too. So I think the answer you're looking for is that the light from a source moving at c would be infinitely redshifted, even though that only makes sense as a statement about limits since a massive light-emitting source cannot actually move at c.
 
Last edited:
Quantum1332 said:
if it were possible to see it?

Black.

Black is black,
But I want my baby back.
For grey is is grey,
Since you went away.
 
If you were heading away from the source emmiting light of a known frequency at .999c, so that the light from the source could catch up with you, then you would just use the relativistic doppler shift formula to convert the velocity into a redshift:

http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/reldop2.html

You would compute

<br /> \sqrt{\frac{1+\beta}{1-\beta}}<br />

to get sqrt(.001/1.999) and a redshift frequency factor of .022 (or a wavelength incrase of 44.7).

As various posters have pointed out, it doesn't make any sense to ask what the frequency is if you can't observe it.
 

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