# Length contraction and Time dilation for LIGHT?

• Stephen Bulking
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. f

#### 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
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
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.

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.

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
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