Q14CQ Suppose you measure the red shif... [FREE SOLUTION]

Chapter 34: Q14CQ (page 1237)

Suppose you measure the red shifts of all the images produced by gravitational lensing, such as in figure below. You find that the central image has a red shift less than the outer images, and those all have the same red shift. Discuss how this not only shows that the images are of the same object, but also implies that the red shift is not affected by taking different paths through space. Does it imply that cosmological red shifts are not caused by traveling through space (light getting tired, perhaps)?

Short Answer

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Images with the same redshift imply that the distance travelled by light from the object is the same for all sources, implying that the object is the same. Furthermore, the fact that all of the redshifts are the same suggests that redshift is a path-independent value. On the other hand, it has no bearing on the mechanism for gaining redshift; it just means that it is independent of the path travelled. More measurements would be required to draw conclusions regarding the mechanism.

Step by step solution

Definition of cosmological red shifts.

The wavelength at which the radiation is originally emitted gets stretched because it travels across (expanding) space in cosmic redshift. Cosmological redshift occurs due to the expansion of space rather than by the motion of a single body

Does the cosmological red shifts are not caused by travelling through space?

The middle image's redshift is that of the intervening galaxy, which is closer than the one being lensed. Because they are further away, the lensed images (those on the side) have a larger redshift. The fact that they all have the same redshift indicates that the item that produced the image was equally distant for all photographs, implying that it was the same thing.

The intriguing part is that upon lensing, the rays do not pick up any additional blue/redshift. This is because they gain blue shift when they enter the gravitational