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Hubble's Law conundrum 
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#1
Jan1612, 03:40 PM

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Imagine this;
Two planets and a star separated by cosmological distances that share an amost linear positional relationship  the star is not in the middle and both planets have a direct eyeline to it. Both planets have intelligent life and both are observing the star's redshift. Two photons leave the star's surface from almost the same place and at almost the same time (relative to each other). Each of the planets receives one of the photons and notes the redshift. Hubble's Law requires that the planet further away should note a greater redshift. How is it that the photons contain different information for different observers? 


#2
Jan1612, 07:08 PM

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The planets are not equidistant from the star in question.



#3
Jan1612, 08:31 PM

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Sure, this is a condition for the question. The crux is this. When the photons were emitted they had the same information, they were emitted under the same conditions  the Doppler effect is the stretching (or compression) of the photon at the time of emission. Once free of the emitter's (sun's) gravitational influence the photons can no longer gain information from their source and are just travelling as you would expect light to travel. But to satisfy Hubble's Law they must still arrive at their respective destinations with different information. Begging the question; Did the information change enroute? 


#4
Jan1612, 09:46 PM

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Hubble's Law conundrum
This is a common mistake. The redshift is not a simple Doppler effect depending merely on relative velocities at time of emission and or time of reception. The usual way one calculates the redshift uses to ratio of distance now (at reception) to distance then (at emission). The wavelenths are stretched out by the same factor that largescale distances are stretched out during the time the light is in transit. The standard cosmo model (Friedmann equations) determines a time dependent quantity called the scalefactor a(t). It is an increasing function of time, normalized so that a(now)=1. Distances between stationary observers increase in proportion to a(t). The definition of the cosmo redshift z is by this equation: 1+z = a(now)/a(then). In other words if distances have doubled during the photon's flight, then its wavelength will be stretched out by a factor of 1+z = 2. That is, redshift z=1 If distances have tripled during the photon's flight, then its wavelength will be stretched out by a factor of 1+z = 3. That is, redshift z=2. These are just conventions, how redshift is defined in relation to the scalefactor a(t). ========================= a(t) is the basic output of the model (which is derived from the Gen Rel equation, and fits data excellently). a(t) does not grow at a constant rate. Its growth is determined by the Friedman equation (a specialization of GR). So the redshift is the cumulative effect of the whole history of the expansion of the universe during the time the photon is in flight and that rate of expansion varies. There is no simple relation between the stretching of wavelength and one or two relative velocities! Lightwaves are stretched just the same as largescale distances are. By changing geometry. (As distances are between things that are not locked together by physical forces and are free to be at rest relative to the cosmic microwave background.) 


#5
Jan1712, 05:31 AM

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You can also get 90% of cosmology doing things Newtonian with a bit of SR.
This means that wavelength (and hence energy) isn't an intrinsic property of a particle. 


#6
Jan1712, 11:19 AM

P: 37

I was separating out the 'emission' part of the Doppler effect for demonstration purposes and rereading my post it seems that I implied that the whole of the Doppler effect occurs at that point. It was unintentional. Thankfully the guy with answers, marcus, read through that. No. I have to disagree with this. Imagine again the above emission of a photon except at a small enough distance away from the receiving planet so as to have an immeasurably small cosmological red shift. All we are considering then is the Doppler effect. Once away from its emitter the wavelength of the photon is intrinsic. The intrinsicity of wavelength is lost (changed) when the photon is observed (stopped). In an inertial frame of reference that has the emitter as stationary  observers moving toward it note a shorter wavelength (blue shifted) and observers moving away note a longer wavelength (red shifted). In fact, in the case of the Doppler effect alone the intrinsicity of the wavelength can be said to be the wavelength noted by an observer that is stationary with respect to the emitter. Obviously, over vast distances intrinsicity is lost as wavelength is constantly lengthening through the cosmological red shift. But your post was clearly concerned with the Doppler effect and it's that to which I respond. Reply to marcus in process. ch@rlatan. 


#7
Jan1712, 03:42 PM

P: 37

But there is still a question of the mechanism for the information exchange between the 'in transit' photon and the space through which it is transmitted. I'm not really sure what this means. Can you please elaborate on this? ch@rlatan. 


#8
Jan1712, 04:29 PM

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Bear in mind that expansion increases with cosmological distance. Relative to the star, the planets are receeding at different 'speeds'. Let's say planet A is twice as distant from the star as planet B. This means the recession component of planet A's velocity is twice that of planet B. Now imagine the star is a quarterback, the planets are receivers, and the photons are footballs. The quarterback throws a football to both receivers at the same time at the same velocity. Receiver A is receeding more quickly from the quarterback than receiver B. Which receiver feels more 'sting' upon catching the football?



#9
Jan1812, 02:31 PM

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#10
Jan1812, 05:13 PM

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The quick and dirty answer is energy is not conserved in GR. But, the deeper explanation is [of course] more complicated. There is no unambiguous description of energy in GR, which makes it quite difficult to even entertain the notion of global energy conservation. An analogy [admittedly flawed] of cosmological redshift would be a sine wave drawn on a rubber sheet. If you stretch the rubber sheet in every direction [mimicking expansion of the universe], the sine wave also stretches.



#11
Jan1812, 09:00 PM

P: 37

This is the question of energy exchange that I am posing, except you are asking 'where has it gone?' and I am asking 'how was it taken?'. Logically, if something is acting upon the photon to change it then it must do it by applying a force  in this case it would seem that only a very weak force is needed. Also, that force must act constantly upon the photon throughout its passage in space. If it didn't, the information we infer from redshift data would be compromised. There is only one 'thing' that constitutes a weak force and which permeates all of space and by deduction it must be the same thing that is acting upon the photon  the cosmic microwave background radiation (CMBR). Does the expansion 'steal' energy from the photon to create space and thus maintain a stable CMBR? There are models, based on laws of thermodynamics, that eventually see a completely cold and empty universe which is consistent with the idea of 'energy theft'. Matter converting to energy and energy converting to space. Maybe it's the very reason for the expansion itself and our notion of cause and effect needs reversing. The analysis of such an idea is frustrated as we don't know what energy is. Particle / wave duality is a question of form only. We're great at measuring energy and getting it to do the stuff we want it to do but its true nature eludes us and probably always will. Nevertheless, if you can take Hubble's Law and information about the CMBR then deduce a mathematical proposition based on the idea of energy theft and expansion. Then show that to be consistent with Einstein's highly trusted and predictive General Theory of Relativity. Well, there's a $1,000,000 prize waiting for you in Switzerland. There's definitely a paper there. Good luck with that. ch@rlatan. 


#12
Jan1912, 12:36 AM

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#13
Jan1912, 02:40 AM

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I know.....that's what I'm saying?? Not at all. Dark energy is a hypothetical concept  thought by many to be the effect of the cosmological constant and is a measure of what we don't know. On the other hand the CMBR is very real and measurable. What's more it's the same stuff as a photon  electromagnetic radiation. It's a logical deduction. If it is erroneous in construction then logic can destroy it. I'm always happy to hear your argument. The cosmological hypothesis called the 'Big Rip'.....and.......I know.......you don't seem to be seeing a lot of things that don't involve them. OMG!!!!! You got me!!! I could make the lame excuse that earlier I was looking at the CERN website brushing up on my quantum chromodynamics but....I know....it's unforgivable. I'll be sure to hang up my physics apron. ch@rlatan. 


#14
Jan1912, 12:30 PM

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This is what has me baffled  the CMB is comprised of the most ancient photons in the universe and is afflicted with most severe case of cosmological redshift [z~1100] in the universe, so, how can the CMB be stealing energy from less ancient photons emitted from less distant sources?



#15
Jan1912, 10:01 PM

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#16
Jan1912, 10:17 PM

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If you are on a beach, and you sail a boat either toward the waves or away from them, the length of the waves change in your new reference frame. 


#17
Jan2012, 06:35 AM

P: 37

Hey Chronos, I think the best example to give here is Young's doubleslit experiment which provides a clear demonstration of the interference of lightwaves (interference fringes). The age of the light is not a property of it  though time is inferred from its energy. The significant difference in energies (wavelength) of the CMBR and the 'new' light may  and I am not beholden to this notion  constitute a small interference. That interference must mean that both parties have exchanged information (that which we measure as cosmological redshift in the observed light) whilst in contact through the void. ch@rlatan. 


#18
Jan2012, 08:01 AM

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I'm amazed that this thread has carried on as long as it has without someone requesting the OP provide a precise definition of information. Although I think this might be moot at this point...



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