Red shift of light and expanding universe - Your help needed.

[royp]

This relates to Doppler's effect.

The phenomenon: It is quite simple and says that light emitted from a moving object will be redshifted when the object is moving away from us (earth) and blueshifted when the object is moving towards us (earth). I was thinking of this phenomenon and arrived at some unexplainable conclusions. Looks like there are some flaws in the reasoning but I am unable to find it.

I need your help in uncovering the flaw.

The scenario: We will consider the following hypothetical scenario. A star is moving towards the earth. Then the light coming from the star will be blue-shifted.Now, more formally, suppose, an element X on the surface of the star is in state S and emitting monochromatic Red light with frequency v1. If we write the corresponding energy equation,

E1 = hv1 (from Planck's law, h is Planck's constant)

Now, due to reference frame invariance, had we brought the same element X in state S on the surface of the earth, it will emit the same red light with the same frequency. In other words, had it been brought to earth, it would have satisfied the same energy equation viz.

E1 = hv1.

Now, as the star is moving towards us, this red light emitted from element X will appear to an observer on Earth as blue-shifted Suppose. the frequency of the light beam is v2. So, the corresponding energy equation is:

E2 = hv2

Now, v2 > v1 (As the light is blue-shifted)

=> hv2 > hv1

=> E2 > E1

In other words, the beam of light (appears to) have more energy when received on Earth than when it started from the star.

But the question is: who has provided this additional energy and when?

There is quite likely some flaw in the above line of thought. But assuming that the above reasoning is correct, then we will be forced to conclude that so called blue shifting is not happening.

Then, as a logical extension of the above reasoning, red-shifting is also not tenable.

Which will bring us to the big question: Is the universe really expanding? Or at any rate, Is there sufficient evidence to conclusively say that the universe is really expanding? That in turn, will bring in bigger questions on Big Bang etc.

 

[alxm]

But the question is: who has provided this additional energy and when?

The kinetic energy of the emitting system, which decreased by the same amount due to the recoil from the momentum of the photon.

 

[royp]

Guys,

Thanks for your help. Some of you have gone through the above post. I presume that you didn't find the argument presented is flawed. That boosted my confidence. I have now rearranged things more formally and would be sending as a paper for publication.

royp

 

[tom.stoer]

Two comments:

Energy alone is not conserved when changing reference frames; energy and momentum are subject to Lorentz transformation; their values change in a similar way as time and distance change in special relativity.

Even if it may not be obvious: the relativistic Doppler effect due to relative motion between source and detector and cosmological redshift due to expansion of space are two different effects and results in different formulas!

http://en.wikipedia.org/wiki/Redshift#Difference_from_a_Doppler_effect