Lorentz contraction of a light pulse

• Thecla
In summary, the ET, Earth, and moon are in an equilateral triangle with the Earth emitting a laser pulse for .01 seconds to the moon. The ET, who is monitoring the conversation, sees a 1,862 mile long "blip" travel to the moon in 1.3 seconds due to the light scattering off dust particles. However, the ET expected the pulse to be shorter due to Lorentz contraction, but the pulse is not affected by this because it has no rest frame. Therefore, the length of the pulse is dependent on the velocity of the source, but not through the traditional length contraction relationship.
Thecla
Suppose the earth, moon, and an extraterrestial observer(ET) are at the corner of an equilateral triangle. The Earth observer points a laser at the moon and emits a powerful laser pulse for exactly .01 seconds. The 1,860 mile long pulse travels to the moon in about 1.3 seconds. The ET knows that the pulse is .01 seconds long because he has been monitoring the Earth scientists' conversations, but the ET can't see the pulse in the vacuum of space. Suppose, however, there is a low density of dust particles in space that scatters some of the light in the direction of the ET(similar to the visualization of a searchlight beam on a foggy night). The ET will see a 1,862 mile long "blip" travel to the moon in 1.3 seconds.
Or will he?
The pulse is moving at the speed of light and the ET knows the pulse lasted for.01 seconds(1,862 miles long). Knowing that Lorentz contraction always shrinks an object in the direction of motion, the ET was expecting the Lorentz contrcted pulse to be shorter than 1,862 miles.What is the reason the light pulse is not Lorentz contracted? Is it because the pulse is not a material object and is therefore exempt from relativistic effects?

Thecla said:
Suppose the earth, moon, and an extraterrestial observer(ET) are at the corner of an equilateral triangle. The Earth observer points a laser at the moon and emits a powerful laser pulse for exactly .01 seconds. The 1,860 mile long pulse travels to the moon in about 1.3 seconds. The ET knows that the pulse is .01 seconds long because he has been monitoring the Earth scientists' conversations, but the ET can't see the pulse in the vacuum of space. Suppose, however, there is a low density of dust particles in space that scatters some of the light in the direction of the ET(similar to the visualization of a searchlight beam on a foggy night). The ET will see a 1,862 mile long "blip" travel to the moon in 1.3 seconds.
Or will he?
The pulse is moving at the speed of light and the ET knows the pulse lasted for.01 seconds(1,862 miles long). Knowing that Lorentz contraction always shrinks an object in the direction of motion, the ET was expecting the Lorentz contrcted pulse to be shorter than 1,862 miles.What is the reason the light pulse is not Lorentz contracted? Is it because the pulse is not a material object and is therefore exempt from relativistic effects?

What is ET's relative motion to all this?

Thecla said:
What is the reason the light pulse is not Lorentz contracted?

Length contraction is always relative to the proper length of an object: the length of the object in its rest frame (the inertial reference frame in which it is at rest). But a pulse of light has no rest frame! It moves at speed c in any inertial reference frame.

The length of the pulse does depend on the reference frame, nevertheless. First consider the rest frame of the source. Let the time interval that the source is "on" be $\Delta t_0$. Then the length of the pulse in this frame is $L_0 = c \Delta t_0$. We can't call this the "proper length" of the pulse, but I'm going to call it $L_0$ anyway for convenience.

Now consider what this looks like in a frame in which the source is moving. Suppose the source is moving in the +x direction, and it emits the light in that direction, too. In this frame, the time duration of the pulse is greater because of time dilation: $\Delta t = \gamma \Delta t_0$ where as usual

$$\gamma = \frac {1} {\sqrt {1 - v^2/c^2}}$$

Also suppose that in this frame, the source starts emitting when it's at x = 0. It stops emitting after time $\Delta t$. At this time, the front edge of the pulse is at $x_{front} = c \Delta t$, and the rear edge of the pulse is at $x_{rear} = v \Delta t$ because that's where the (moving) source is at that time. So the length of the pulse in this frame is

$$L = c \Delta t - v \Delta t = (c - v) \Delta t = (c - v) \gamma \Delta t_0$$

After some algebra we get

$$L = \sqrt { \frac {c - v} {c + v}} (c \Delta t_0) = \sqrt { \frac {c - v} {c + v}} L_0$$

So the length of the pulse does depend on the velocity of the source, but it's not the length-contraction relationship.

Last edited:
If the ET is at rest wrt the other observers involved then it will measure the same length as they do.

FYI, in general I discourage the use of the time dilation and length contraction formulas. I think it is always best to use the full Lorentz transform equations. The length contraction and time dilation formulas then automatically pop out whenever appropriate simply by setting certain terms equal to 0.

The ET the Earth and the moon are all at rest. The only thing moving is the light pulse.

1. What is Lorentz contraction of a light pulse?

Lorentz contraction of a light pulse is a phenomenon described by the theory of relativity, where the length of an object appears to decrease in the direction of its motion as its velocity approaches the speed of light.

2. How does Lorentz contraction affect the speed of light?

Lorentz contraction does not affect the speed of light, which is always constant at approximately 299,792,458 meters per second in a vacuum. Instead, it affects the perceived length of an object in motion relative to an observer.

3. What is the formula for calculating Lorentz contraction?

The formula for calculating Lorentz contraction is L = L0 * √(1 - v2/c2), where L is the contracted length, L0 is the rest length, v is the velocity of the object, and c is the speed of light.

4. Does Lorentz contraction only apply to light pulses?

No, Lorentz contraction can occur with any object or particle that travels at high speeds close to the speed of light. However, it is most commonly observed and measured with light pulses due to their incredibly high velocity.

5. What are the implications of Lorentz contraction in the theory of relativity?

Lorentz contraction is an important concept in the theory of relativity as it helps explain the observed phenomenon of time dilation and the relativity of simultaneity. It also highlights the fact that space and time are not absolute, but rather are relative to the observer's frame of reference and the speed at which objects are moving.

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