Length Contraction of Particles & Photons in Relativity

In summary, the distance between 2 photons seen from S' is less than the distance between the same photons seen from S.
  • #1
pieterdb
3
0
I'm trying to teach myself special relativity. I use the book 'Introduction to Special Relativity' by Wolfgang Rindler. I have a question about length contraction.

We consider 2 particles traveling along the x-axis of a reference frame S with a constant distance between them. We can always go to the rest frame of the particles. If the distance between the particles as seen from their rest frame is L_0, then the distance between the particles as seen from any other inertial frame moving with a velocity v in the direction of the x-axis of S is calculated by L = L_0 / gamma. This length contraction formula originates in the relativity of simultaneity.

If we now replace the 2 particles by 2 photons, it is no longer possible to go to the rest frame of the photons (since the speed of light is c in every inertial frames). Likewise it is impossible to calculate the distance between the photons as seen from another reference frame with the length contraction formula, since gamma always leads to a division by zero.

So apparently there is a difference between the length contraction of the distance between two particles and the length contraction of the distance between 2 moving photons. I guess the 2 moving photons are the limiting case ?

I don't understand this. Is there a length contraction for the distance between 2 moving photons or is this distance the same in all inertial frames (I guess there should be a length contraction since the relativity of simultaneity) ? If yes, how can we calculate this length contraction ?
 
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  • #2
pieterdb said:
If we now replace the 2 particles by 2 photons, it is no longer possible to go to the rest frame of the photons (since the speed of light is c in every inertial frames). Likewise it is impossible to calculate the distance between the photons as seen from another reference frame with the length contraction formula, since gamma always leads to a division by zero.
When you calculate how something is seen from another (inertial) reference frame, the gamma factor is the one defined by the velocity difference between the two frames. In this case however, since the two objects that have constant velocity in the first frame aren't at rest in the other frame, you can't just use the Length contraction formula. You should start by drawing the world lines of the photons in a spacetime diagram, and then draw a simultaneity line for the frame that you going to transform to. Check where it intersects the world lines of the photons. You need to determine the coordinates of these two events in both frames. When you've done that, it shouldn't be hard to find the distance between the photons in the other frame.
 
  • #3
Thx, I understand it now.The motion of a photon seen from S is given by :

x = x0 + ctUsing the standard Lorentz Transformation formulas, I can express the motion of a photon seen from S' by :

x' = [tex]\gamma[/tex]x0 + [tex]\gamma[/tex](c-v)(t'/[tex]\gamma[/tex](1-v/c) + vx0/c2(1-v/c))This eventually leads to the distance between the 2 photons seen from S' :

L' = L (c+v)1/2(c-v)-1/2
 

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1. What is length contraction in relativity?

Length contraction, also known as Lorentz contraction, is a phenomenon predicted by Albert Einstein's theory of special relativity. It states that the length of a moving object will appear shorter to an observer in a stationary frame of reference compared to an observer in the moving frame of reference.

2. What causes length contraction?

Length contraction is caused by the effects of time dilation and the constancy of the speed of light in all inertial frames of reference. As an object approaches the speed of light, its time slows down and its length appears to contract in the direction of motion.

3. Does length contraction apply to both particles and photons?

Yes, length contraction applies to both particles (such as electrons) and photons (particles of light) in special relativity. However, it is important to note that length contraction is only observed in objects traveling at speeds close to the speed of light.

4. How is length contraction different from regular contraction?

Length contraction is a result of the changes in space and time that occur at high speeds, while regular contraction is a change in an object's physical size due to external forces or factors. Length contraction is also only observed in objects traveling at speeds close to the speed of light, while regular contraction can occur at any speed.

5. Can length contraction be observed in everyday life?

No, length contraction is only significant at speeds close to the speed of light, which is much faster than any object can travel in everyday life. Its effects can only be observed in experiments involving particles or objects that are accelerated to high speeds. However, the concept of length contraction is important for understanding the principles of special relativity and its applications in modern technology.

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