Is Length Contraction Accounted for in the Analysis of a Moving Clock?

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Discussion Overview

The discussion centers on the analysis of a moving clock within a spaceship traveling at a steady speed, specifically addressing whether length contraction should be accounted for in the timing of light travel between points in the clock. The scope includes theoretical considerations of special relativity, the behavior of light, and the perspectives of different observers.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant presents a mathematical analysis of the time taken for light to travel in a moving clock and questions the necessity of accounting for length contraction.
  • Another participant queries whether the time measured is the same for observers inside and outside the spaceship, suggesting that both would observe the clock's movement relative to the photons.
  • It is noted that from an external observer's viewpoint, the spaceship is shorter due to length contraction, yet the time for light's round trip remains the same across frames.
  • Concerns are raised about the concept of a "rest frame" for photons, with some participants arguing that photons do not have a rest frame and thus cannot be used as a reference for movement.
  • Participants discuss the invariance of physical laws across different frames of reference and the implications of time-dependent properties of photons, such as frequency changes due to the Doppler effect.
  • One participant asserts that the analysis differs for observers inside and outside the spaceship, emphasizing that the internal observer does not perceive the mirror's movement.
  • Length contraction is described as observable only by observers moving relative to the spaceship, with references to cosmic ray muons as practical examples of length contraction effects.
  • Relativistic effects, including length contraction, are acknowledged as integral to the framework of Special Relativity.

Areas of Agreement / Disagreement

Participants express differing views on the implications of length contraction and the perspectives of various observers. There is no consensus on whether the initial analysis is correct, and the discussion remains unresolved regarding the interpretation of the clock's behavior in different frames.

Contextual Notes

The discussion highlights the complexity of relativistic effects and the assumptions underlying different observers' perspectives. There are unresolved questions about the nature of light and its interaction with moving frames.

Ross B
Hi

Is this analysis right

A spaceship is traveling at a steady speed V in the direction shown. Inside the spaceship is a simple clock of length L and consisting of a light source at “a” and a mirror at “b”. The light leaves “a”, bounces off the mirror at “b” and goes back to “a”, which counts as a single tick of the clock.

As the spaceship is moving the clock is shown at times t1, t2, and t3. At time t2 the clock which was originally at a and b will now be at a' and b'. Time t2 is the time the light reaches the mirror.

The mathematical analysis for the time taken for one tick to occur is

T = ((L – vt)/c) + ((L + vt)/c)

(L – vt)/c = is the time taken for the light to leave the light source and travel to the mirror.

(L + vt)/c = the time to do the return trip.

vt = the distance traveled by the clock in the time it takes for the light to travel the length of the clock.

do I have to allow for length contraction? Is the above correct?
 

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It looks right. Is this the time measured by an observer watching the spaceship go by or is it the time measured by an observer inside the spaceship. Does it matter?
 
it is the time measured by both and the same would be observed by both. If that is the case it appears the observer inside the spaceship would observe the clock, and thus the spaceships, movement relative to the photons in the clock!
 
Ross B said:
... would observe the clock, and thus the spaceships, movement relative to the photons in the clock!
Remember that the speed of light is c regardless of the frame of reference.

You asked if you have to allow for the length contraction of the spaceship as seen by an observer who watches it go by. Obviously, from the viewpoint of that observer the spaceship is shorter by a factor of γ. If the spaceship is shorter and the speed of light is c, why does light take the same amount of time for the round trip in the two frames? I think the answer to that question is the lesson to be learned in this problem.
 
ah yes, thanks for that

will both observers observe the movement of the clock relative to the photons within the clock, it appears to me they will?
 
Please don't say things like "the movement of the clock relative to the photons". There is no such thing as a "rest frame" of the photons. So there is no movement "relative to them". The photons move at the speed of light, c, relative to the clock and relative to any other frame one might think of, including the observer and the spaceship. They also move at speed c relative to other photons.

On Edit: The last sentence is withdrawn; it should not have been written. :oops:
 
Last edited:
a rest frame is where one frame is at rest wrt another frame isn't it?

But won't the observer external to the spaceship observe the clock is moving relative to the photons?

How come photons are not affected by the change of time? Photons have time dependent properties that seem to be immune to the change in time. It appears other phenomena "know" when they are in a moving frame of reference but photons are completely oblivious!
 
Last edited by a moderator:
Ross B said:
But won't the observer external to the spaceship observe the clock is moving relative to the photons?
The observer on the ground will see the clock move at speed v and the photons at speed c.
The observer in the spaceship will see the clock at rest and the photons move at speed c.
Ross B said:
Photons have time dependent properties that seem to be immune to the change in time.
What kind of properties are you thinking of that are time-dependent?
Ross B said:
It appears other phenomena "know" when they are in a moving frame of reference but photons are completely oblivious!
The laws of physics are invariant under a coordinate transformation. This means that two physicists moving relative to each other will deduce the same laws of physics after observing the same phenomena.
 
time dependent velocity, frequency, I don't know that much about photons but there are probably many others, entropy, do photons age?
 
  • #10
One more time, the photon velocity is not frame-dependent or time-dependent; it is fixed and equal to c. Frequency can change due to the Doppler shift. Photons do not "age" which or decay. Be patient and learn some more physics. By the time you get to Quantum Mechanics, you will be more comfortable with photons.
 
  • #11
kuruman said:
Please don't say things like "the movement of the clock relative to the photons". There is no such thing as a "rest frame" of the photons. So there is no movement "relative to them". The photons move at the speed of light, c, relative to the clock and relative to any other frame one might think of, including the observer and the spaceship. They also move at speed c relative to other photons.

I think your last sentence contradicts what you say in your 2nd and 3rd sentences?

.
 
  • #12
Mister T said:
I think your last sentence contradicts what you say in your 2nd and 3rd sentences?
I agree, I should have not written it.
 
  • #13
so just to clarify my analysis is right?. The person inside the spaceship would use the same analysis?

and length contraction is only observed by and observer moving relative to the space ship
 
  • #14
Ross B said:
so just to clarify my analysis is right?. The person inside the spaceship would use the same analysis?
No. The person inside the spaceship does not see the mirror move. Therefore, the time for the round trip is T = 2L/c however the "go" trip takes the same amount of time L/c as the "return" trip. That is is not true for the person on the ground. Although the time for the round trip is the same, the "go" trip takes less time than the "return" trip as you have calculated.
Ross B said:
and length contraction is only observed by and observer moving relative to the space ship
Yes, although it is better to say that length contraction is observed in the frame with respect to which the spaceship is moving.
 
  • #15
Tanzeel said:
Have anyone has observed length contraction?
Cosmic ray muons which are detected at the Earth's surface in greater than expected numbers will have observed a length-contracted atmosphere.

http://hyperphysics.phy-astr.gsu.edu/hbase/Relativ/muon.html
Tanzeel said:
Is length contraction theoretical or practical ?And what’s its scientific implications?
It is part and parcel of Special Relativity. Length contraction, time dilation and the relativity of simultaneity are all part of the Lorentz transformation.
 

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