Relative visit of photons

[logearav]

Two photons are travelling, one in the east and another in the west. Then the relative velocity between two is

(a) 2c (b) c/2 © c^2 (d) c

I know the velocity of light is constant, i presume the answer is option (d). But the term relative velocity confuses me.

I look forward for revered members' help in this regard

[ajb]

Photons do not have a rest frame, thus asking what is the speed of one photon relative to another is not well posed.

 

You could consider the relative speed of a photon with respect to some object travelling at near the speed of light (wrt to some frame). You will see that the relative speed of the photon is c. So, one could then consider the limit in which the object travels at c, again you will get c as the relative speed.

 

Thus, the "hand waving" answer to your question is (d), but this is not very well defined.

[DrRocket]

Two photons are travelling, one in the east and another in the west. Then the relative velocity between two is

(a) 2c (b) c/2 © c^2 (d) c

I know the velocity of light is constant, i presume the answer is option (d). But the term relative velocity confuses me.

I look forward for revered members' help in this regard

 

What ajb told you is correct.

 

But your question is rather awkwardly worded and confusing. It occurs to me that you might, by using the expression "The relative speed between the two" be trying to describe the closing speed of two photons approaching one another as determined in some inertial reference frame. In that case the answer is 2c. This is the upper limit for closing speeds in special relativity. This does not in any way contradict special relativity, as there is nothing that is actually moving at 2c.

 

It is possible to have "speeds" that exceed c in special relativity. Closing speeds are one example. Another is the "speed" of motion of the spot of light generated by sweeping a searchlight across a distance screen, which can be arbitrarily large with sufficient distance between the screen and the searchlight. These do not contradict special relativity since nothing is actually moving at greater than c and no information-carrying signal is being transmitted superluminally.

[michel123456]

Two photons are travelling, one in the east and another in the west. Then the relative velocity between two is

(a) 2c (b) c/2 © c^2 (d) c

I know the velocity of light is constant, i presume the answer is option (d). But the term relative velocity confuses me.

I look forward for revered members' help in this regard

 

Reminds me the riddle

The captain of a ship was telling this interesting story: "We traveled the sea far and wide. At one time, two of my sailors were standing on opposite sides of the ship. One was looking west and the other one east. And at the same time, they could see each other clearly."

In your case, if the 2 photons are going away from each other, I am not aware of any mean to observe directly the phenomenon: you can only observe the photons that reach you.

If one takes the opposite question (see the riddle's solution), then it is about closing speed and the answer has been given already.

 

solution

 

The sailors were standing back to the edge of the ship so they were looking at each other

 

Edited December 11, 2011 by michel123456

[logearav]

Thanks for the replies. But i have reproduced the question asked in competitive exam held for recruiting teachers , verbatim. No additional details are given either. To ease out the confusion, i posted in this forum so that learned members can clarify

[swansont]

If the problem is meant for an observer of the two photons, the observer will see the photons closing or departing with a speed of 2c, as DrRocket has mentioned , That is, after time t, the photons will be a distance d=2ct further apart or closer together. (a) is the only answer you can build a case for, IMO. It's a poorly phrased question.

[ajb]

The phrase "relative velocity" is the trouble here. It is not very clear if we mean some "external observer" or one of the photons.

 

The "approaching or separating speed" as seen by an external observer is 2c, as stated by DrRocket and swansont. But we need to be very careful here. This is not a relative velocity, the observer will not measure relative to themselves any of the photons to be moving at a speed 2c. Photon to photon "point of view" is poorly defined, as I outline.

 

So, overall the question is poorly worded.

Edited December 12, 2011 by ajb

[A Tripolation]

It is possible to have "speeds" that exceed c in special relativity. Closing speeds are one example. Another is the "speed" of motion of the spot of light generated by sweeping a searchlight across a distance screen, which can be arbitrarily large with sufficient distance between the screen and the searchlight. These do not contradict special relativity since nothing is actually moving at greater than c and no information-carrying signal is being transmitted superluminally.

 

I have heard mention of this, but I never quite understood. Perhaps you can explain it for me. Does "phase velocity" also fall under this category? What is meant by "closing speed"? Am I correct in thinking about it the same way they tell you to think about a giant pair of scissors closing in space at the speed of c? The tips will be moving at "superluminal" speeds but they are just arbitrary points?

[DrRocket]

It's a poorly phrased question.

 

Yep. The formulator of the question should flunk.

 

Special relativity (and really all science) requires precision in the use of language, else confusion arises and one gets an answer to the question as interpreted by the reader (or just a justified huh ?) rather than the question that the interogator intended to pose.

 

This one calls for a "huh ?", which should receive full credit.

[imatfaal]

I have heard mention of this, but I never quite understood. Perhaps you can explain it for me. Does "phase velocity" also fall under this category? What is meant by "closing speed"? Am I correct in thinking about it the same way they tell you to think about a giant pair of scissors closing in space at the speed of c? The tips will be moving at "superluminal" speeds but they are just arbitrary points?

 

The way I remember the explanation -

 

if the scissors are actual concrete solid scissors then no matter how quickly they are closed at the hinge the tips will close at a slower than subluminal speed (they are actual stuff moving through space on a circular course as viewed from the hinge) - you just cannot multiply up the speeds for further away from the hinge. in any real scissors the circular motion to close will not be instantaneously transmitted through the blade - in fact it will move at way below the speed of light at around the speed of sound in the material - the blades will deform as the information/force travels up the blade.

 

if alternatively the scissors are merely two beams of light - then you can go as faster as you like as no information can be transmitted, and nothing is actually travelling in a circular motion - they are arbitrary points.

[DrRocket]

The way I remember the explanation -

 

if the scissors are actual concrete solid scissors then no matter how quickly they are closed at the hinge the tips will close at a slower than subluminal speed (they are actual stuff moving through space on a circular course as viewed from the hinge) - you just cannot multiply up the speeds for further away from the hinge. in any real scissors the circular motion to close will not be instantaneously transmitted through the blade - in fact it will move at way below the speed of light at around the speed of sound in the material - the blades will deform as the information/force travels up the blade.

 

if alternatively the scissors are merely two beams of light - then you can go as faster as you like as no information can be transmitted, and nothing is actually travelling in a circular motion - they are arbitrary points.

 

The usual scisor illustration is this: The tips of the scissors cannot move faster than c, but the point of intersetion of the cutting blades (the cutting point of the scissors) can move arbitrarily quickly. But that point of intersection is not a physical point, and does not carry information so that there is no contradiction of relativity. A similar analogy is made with the point of intersection of a guillotine blade with the cutting plane.

 

Now, you may object that the scissors could cut a wire and thereby send a signal. The answer to that is that we are not talking about a real pair of scissors made from real material, and in the case of such a physical pair of scissors, the rigid body idealization breaks down, and the scissors cannot really perform per the idealization. In reality the stress wave that propagates down the blades to cause them to close travels at about the speed of sound in the material.

[imatfaal]

The usual scisor illustration is this: The tips of the scissors cannot move faster than c, but the point of intersetion of the cutting blades (the cutting point of the scissors) can move arbitrarily quickly. But that point of intersection is not a physical point, and does not carry information so that there is no contradiction of relativity. A similar analogy is made with the point of intersection of a guillotine blade with the cutting plane.

 

Now, you may object that the scissors could cut a wire and thereby send a signal. The answer to that is that we are not talking about a real pair of scissors made from real material, and in the case of such a physical pair of scissors, the rigid body idealization breaks down, and the scissors cannot really perform per the idealization. In reality the stress wave that propagates down the blades to cause them to close travels at about the speed of sound in the material.

 

 

Yes, yes, that makes sense. thanks