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TrickyDicky
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Is photon energy conserved for comoving observers in redshifted light from receding galaxies?
And in the case of gravitational redshift?
Thanks
And in the case of gravitational redshift?
Thanks
nutgeb said:Photon energy is strictly conserved, if you look at it from the correct perspective. If you consider galaxies to be moving through space (as opposed to space itself expanding), then redshift is merely an accumulation of tiny Doppler shifts along a photon's trajectory through space. Doppler shifts do not constitute a loss of energy per se, rather the redshift occurs as the photon loses momentum relative to the observer, or its wavelength physically stretches as each wavecrest takes longer to arrive, as it chases and enters successive reference frames that are receding ever faster away from the emitter.
The cosmological redshift is a function primarily of location -- that is, the proper distance traveled away from the emitter, which in turn determines the changes in its proper velocity (c + H * D) it experiences in each successive reference frame. (H is the then-current Hubble rate and D is proper distance from the emitter). The photon of course always travels at a local (peculiar) speed of c, but its proper velocity relative to the emitter progressively increases with distance due to Hubble's Law. Note that at large cosmic distances, the accumulation of tiny Doppler shifts along the photon's trajectory yields a much different total redshift figure than would a single end-to-end Doppler shift velocity calculation. The accumulation of redshifts along the trajectory is incremental because the photon must adjust its proper velocity (relative to the emitter) to maintain a local speed of c in each successive recession frame it travels through, even though the photon is not absorbed in any of those frames until it reaches the ultimate observer.
The basic concept of cosmological redshift as Doppler shift, and the implications for conservation of energy, are the subject of the cover article of the current issue of Scientific American, authored by Tamara Davis. You can read it at www.sciam.com. As she points out, even in the recent past many authors have written as if the cosmological redshift somehow violates energy conservation, and they often resort to unhelpful platitudes such as "General Relativity does not require energy to be conserved in an expanding universe". But really it is just a failure to take the Doppler velocity differential of the observer and emitter fully into account. The photon's momentum relative to its emitter (redshift) decreases with distance; but its proper velocity relative to its emitter increases with distance, and in exactly the same proportion. Therefore at each location along the photon's trajectory, multiplying momentum and proper velocity together always yields a constant. That constant relates the photon's energy conservation back to the emitter's reference frame. An increase in proper velocity doesn't come as a free lunch; the price paid for it is the loss of momentum observed as redshift.
You also asked about gravitational redshift. From the perspective of the observer, gravitation causes blueshift, not redshift, as the photon is accelerated toward the observer by the sphere of cosmic mass energy defined by the photon's radius from the observer at each instant in time. However, if redshift is treated as Doppler shift in the FRW metric, then gravitational blueshift is already subsumed in the Doppler shift, so it is not a separate factor in the calculation. The effect of gravitation is reflected in the decrease of the Hubble rate over time. As a result of this decrease, the photon's accumulated proper velocity (H * D) increase relative to the emitter is less than it would have been if gravity weren't progressively slowing down the Hubble rate. Since energy conservation is maintained by the Doppler shift formula, the gravitational contribution is already captured in the overall energy conservation.
But the mathematical role of gravity is coordinate-specific. If Schwarzschild coordinates are used instead of FRW coordinates, then gravitational blueshift becomes a discrete element of the redshift calculation, and it is multiplied by an element equivalent to the accumulated Special Relativistic Doppler shift. In Schwarzschild coordinates, all of the cosmic mass in the sphere defined by the emitter's radius from the observer is considered to be concentrated at the observer's location. Therefore clocks run slower at the observer than at the emitter, and the observer sees more wavecrests arriving per beat of slower local clock time (i.e., higher frequency), which is observed as blueshift. The total energy of a system comprised of a Schwarzschild mass and a photon (or any object) freefalling radially toward it is strictly conserved.
That's a tricky question to answer. In general I would say no, but like so many aspects of relativity, the answer is dependent on which coordinates you choose.TrickyDicky said:From this energy conservation considerations, can we properly say that in every instance, a redshift (either cosmological, gravitational, Doppler in case you distinguish it from the cosmological) of incoming light implies that the observer local clock goes faster than at the source and therefore time dilation is directly linked to redshift?.( that can be observed too in the lightcurves of supernovae Ia, I think)
To expand on nutgeb's comments, here's what we'd get for the doppler frequency shift if it was due "only" to time dilation (in flat spacetime inertial coordinate systems):TrickyDicky said:Ok, so I understand we can observe redshifts that are not associated to time dilation.
Can you provide me with some specific example?
Thanks
TrickyDicky said:Is photon energy conserved for comoving observers in redshifted light from receding galaxies?...
Marcus, I think your answer, while superficially accurate in a certain narrow sense, misses the point of Tamara Davis' article in Scientific American. Although an observer receiving light from a moving emitter will measure and calculate that the photon has less energy than when it left the emitter, that does not represent a true loss of energy for the system as a whole, only a shift from the perspective of one participant to the perspective of another participant. After all, how can the observer talk about the supposedly higher energy of the photon when it left the emitter, except by shifting his own perspective to the emitter's reference frame?marcus said:I think you are asking about the photon energy as it would be measured by successive comoving observers along the path. The answer is clearly NO. The energy of the photon does not remain constant. It decreases in proportion as the wavelength increases. Each successive observer would see it as less.
JustinLevy's answer explains very crisply what I was alluding to. Thanks for that!TrickyDicky said:Ok, so I understand we can observe redshifts that are not associated to time dilation.
Can you provide me with some specific example?
Thanks
In http://www.astro.ucla.edu/~wright/cosmo_01.htm" , more than 99% of the observed redshift are not due to time dilation. Is that what you wanted to know?But I am now more specifically interested in the link between time dilation and redshift, that is why I asked for some example of observed redshift not associated with some quantifiable time dilation?
Ich said:In http://www.astro.ucla.edu/~wright/cosmo_01.htm" , more than 99% of the observed redshift are not due to time dilation. Is that what you wanted to know?
TrickyDicky said:Thanks for the replies. I think I get the picture about the energy part, even if it looks more complex than I thought.
But I am now more specifically interested in the link between time dilation and redshift, that is why I asked for some example of observed redshift not associated with some quantifiable time dilation?
Photon energy conservation is a principle in physics which states that the total energy of a system consisting of photons remains constant over time.
Photon energy conservation is important because it helps us understand and predict the behavior of light and other forms of electromagnetic radiation. It also plays a crucial role in various technological applications, such as solar panels and lasers.
Photon energy is conserved through various processes such as reflection, refraction, and absorption. When a photon interacts with matter, its energy can be transferred to the matter, but the total energy of the system remains constant.
Yes, photon energy can be converted into other forms of energy, such as electrical energy in solar panels or heat energy in solar water heaters. This conversion process does not violate the principle of photon energy conservation, as the total energy of the system is still conserved.
The energy of a photon is directly proportional to its frequency, according to the equation E = hf, where E is energy, h is Planck's constant, and f is frequency. This means that higher frequency photons have higher energy and vice versa.