# Length contraction and Time dilation for LIGHT?

• Stephen Bulking
In summary: Yeah it's CIn summary, the conversation discusses the concept of time and distance in relation to a particle traveling at near light speed in the Earth's rest frame. It is mentioned that there is no frame of reference for light, and the proper time for a particle moving at near light speed in the Earth's rest frame would be less but not zero. The question asks for the time and distance calculations in the Earth's rest frame, and the correct answer is option C.
Stephen Bulking
Homework Statement
A message is sent via radio wave (λ = 10 m) from Earth to a nearby star, Proxima Centauri, which lies 1.3 parsecs from Earth. A parsec is a unit of length and 1 parsec = 3.1 × 10^16m. How long will it take the message to reach Proxima Centauri traveling through vacuum?
(a) 0 yrs, the message arrives instantly.
(b) 1.38 yrs
(c) 4.26 yrs
(d) 255.0 yrs
(e) 1.38 × 108 yrs
Relevant Equations
t = t0/γ (time dilation)
l = γl0 (length contraction)
t0: proper time
l0: proper length
Radio wave travels at the speed of light 3x10^8 (m/s)
Converting the distance to meter: 1.3 x 3.1x 10^16 = 4.03x10^16m
The time it takes in our Earth frame of reference is: 4.03x10^16m/3x10^8 (m/s) = 4.26 years
But wouldn't the time in light's frame of reference be 0 and it's length be infinite?
If it was another particle traveling at near light speed than it it's frame of reference, the time and distance it has to travel are still given by time dilation and length contraction formulas right?

The question is just asking for ##\Delta x = c \Delta t##, nothing more.

There's no such thing as the frame of reference of light! But for a particle with ##v## very close to ##c##, everything works just fine.

Stephen Bulking
Stephen Bulking said:
But wouldn't the time in light's frame of reference be 0 and it's length be infinite?
If it was another particle traveling at near light speed than it it's frame of reference, the time and distance it has to travel are still given by time dilation and length contraction formulas right?

The question ought to state that these measurements are in the rest frame of the Earth.

There is no frame of reference for light, or inertial reference frame moving at ##c## with respect to another.

The proper time for a particle (i.e. in its reference frame) moving at near the speed of light in the Earth's reference frame would indeed by less - and, in fact, can be made arbitraily small; but not zero.

Stephen Bulking
Stephen Bulking said:
traveling through vacuum?
If you needed one, there is a hint there. The message is "traveling". If the message were stationary while the endpoints moved then the endpoints would have been "traveling".

It is sometimes useful to look at the problem statement to see if a particular frame of reference is implied.

Stephen Bulking said:
But wouldn't the time in light's frame of reference be 0 and it's length be infinite?

Whether or not that is well-defined (and it's not), at no point were you asked that.

Stephen Bulking said:
Radio wave travels at the speed of light 3x10^8 (m/s)
Converting the distance to meter: 1.3 x 3.1x 10^16 = 4.03x10^16m
The time it takes in our Earth frame of reference is: 4.03x10^16m/3x10^8 (m/s) = 4.26 years
B? Not C?

etotheipi, Delta2 and SammyS
vela said:
B? Not C?
Yeah man I got B, there's no given answer to check with but from my calculations I got B

Stephen Bulking said:
Yeah man I got B, there's no given answer to check with but from my calculations I got B
You said you got 4.26 years, which is option C.

PeroK said:
You said you got 4.26 years, which is option C.
Oh right, sorry, typo.

## 1. What is length contraction for light?

Length contraction for light is a phenomenon in which the length of an object appears shorter when it is moving at a high speed relative to an observer. This is due to the fact that the speed of light is constant and cannot be exceeded, causing the object to appear compressed in the direction of its motion.

## 2. How does time dilation affect light?

Time dilation is a concept in which time appears to pass slower for objects moving at high speeds. This means that the time taken for light to travel a certain distance may appear longer for an observer who is moving at a high velocity relative to the light source. This is due to the fact that the speed of light is constant and cannot be exceeded, causing time to appear slower for the moving observer.

## 3. Can length contraction and time dilation occur simultaneously for light?

Yes, length contraction and time dilation can occur simultaneously for light. This is because they are both consequences of the constant speed of light and are dependent on the relative velocity of the observer. As an object's velocity approaches the speed of light, both length contraction and time dilation become more significant.

## 4. How is length contraction and time dilation for light related to Einstein's theory of relativity?

Einstein's theory of relativity explains the relationship between space and time and how they are affected by the speed of light. Length contraction and time dilation for light are both consequences of this theory, as they demonstrate how the perception of space and time can change for observers who are moving at different velocities.

## 5. Is there a limit to how much length contraction and time dilation can occur for light?

According to Einstein's theory of relativity, there is no limit to how much length contraction and time dilation can occur for light. As an object's velocity approaches the speed of light, these effects become more significant. However, the speed of light is the ultimate limit, and it cannot be exceeded, so there is a limit to the amount of contraction and dilation that can occur.

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