
#19
Jan1310, 04:44 PM

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#20
Jan1410, 12:48 AM

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Gravity works both ways, matter on the far side counters gravitational effects from the near side. A net zero effect. Expansion is the only logical explanation.




#21
Jan1410, 04:10 AM

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Lets look at this in two ways. The simplest way is to place to origin of some coordinates at the reciever such that they remain fixed. Imagine a spherical region around them with the emmitter at the edge of that region. When they fire the photon towards the centre they are moving away from the reciever. Since the reciever is always fixed, this means there is a redshift from the original motion so it doesn't matter that later on the emmitter starts moving towards the observer when the Universe begins contracting. The gravitational blueshift, in this case, exactly cancels this original redshift. It looks like this: Motion at emmission causing a Doppler redshift Obs . . . . . . Em > Photon is falling towards the bottom of the potential well, causing a blueshift Obs . . . . . . << Photon We can instead define the coordinates to be centred on the emmitter. In this case it remains fixed. If you think about this it means that compared to the rest frame of the emmitter, the observer will be moving towards the emmitter when the photon is observed. Thus you will have a blueshift due to motion. This might be confusing, until you realise that in these coordinates, the photon is moving away from the origin, climbing out of the potential well we have define, and therefore in this system the effect of gravity is to cause a redshift, in this case exactly cancelling the Doppler blueshift. It looks like this: Motion at reception, causing Doppler blueshift Em . . . . . . < Obs Photon is climbing out of potential well, causing gravitional redshift Em . . . . . >> Photon We could also place the origin between the emmitter and observer. In this case the relative motion cancels out, so there is no Doppler contribution. But also, we now define the bottom of the potential well to be between the two, so the photon picks up a blueshift falling in, which exactly cancels the redshift of it climbing out. It looks like this Motion at emmission <Obs . . . . . . O . . . . . . Em > Motion cancelled at reception, no net Doppler effect Obs > . . . . . . O . . . . . . < Em Photon falls into potential well, gaining energy . . . . . . O . . . . . . << Photon But then loses the same amoung climbing out again << Photon . . . . . . O . . . . . . This might sound like a bit of mathemagic, but it is all just coordinate tricks with classical physics. As with any problem to do with energy, you have to be very careful about where you are defining the arbitary zero point, and make sure you are referencing everything consistantly with respect to that. 



#22
Jan1410, 04:20 AM

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In any case, these things are vastly easier to understand if you just take them in comoving coordinates, where both the emitter and observer are stationary (up to local peculiar velocities). In comoving coordinates, the only source of redshift is the overall expansion, and so the redshift is simply:
[tex]z + 1 = \frac{a_{obs}}{a_{emit}}[/tex] 



#23
Jan1410, 04:35 AM

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But hang on, we know that we can always just use these coordinates. The question is what the hell do they mean? The OP asked how motion and or gravity is responsible for causing redshift, which is a very reasonable question. Simply stating the above equation tells you how to calculate it, but it doesn't tell you what that means and doesn't answer the question. Reducing everything to the effect of 'the overall expansion' leaves you at sqaure one; what precisely is that motion, and how does it cause redshift? In fact the 'motion' implied by looking at da/dt is nothing like the intuitive motion we see in day to day life, since it encodes gravitational effects as well. This is very very convenient for cosmologists, since it reduces everything to the single function a(t), but it is horrible for people new to the area trying to work out what that function means in terms that are familiar.
Ich and I explained how you can understand the interplay between motion and gravity by looking at how the more familiar Newtonian physics gives you the same answer, but more obviously demonstrates how both motion and gravity are both at work, even in a homogenous universe. Writing down a simple relation, and really understanding what that means are two vastly different things. 



#24
Jan1410, 05:24 AM

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#25
Jan1410, 06:07 AM

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Well then I have to disagree. When you say 'photons are expanded along with space' you are talking about something that is only true for one specific set of coordinates and you also imply a false causality; that there is a physical effect called 'expansion of space' which causes photons to stretch.
Simply saying 'there are many ways of looking at this, so none of them mean anything' is not very useful. In fact, as has been explained, the physics is universal, and can be seen readily by looking at the Newtonian picutre, to which all coordinate descriptions will converge to for small distances. The coordinates are what are malleable, yet you want to fix on just one coordinate system and force the physics to conform to that (since you remove gravity and motion and invent a new placeholder fictious effect which acts for both). I'm afraid that is bassackwards. As can be readily evidenced in this forum, blanket use of this phrase without context leads to much wailing and nashing of teeth, such as 'why don't galaxies get expanded by space?' 'does the expansion of space drive electrons further from the nucleus of atoms?'. These are reasonable questions to ask when you've been told to just think of everything in terms of some illdefined 'expansion of space' but the are easily done away with when you break it down into the simple underlying physics. Again, I go back to the OP. It was asked whether motion and/or gravity is responsible for the observed redshift of galaxies. How does writing down 1 + z = a/a_0 and saying 'the photons get stretched by expanding space' answer this question? Redshift can be understood in simple well understood terms like motion and gravity, I see no reason to force people to abandon these intuitive notions in favour of a coordinate dependant mathematical function which has no universal physical meaning. It depends on what we are trying to help people with. If you want to learn how to calculate cosmological quantities, then you need to learn the maths behind comoving coordinates, and learn the easiest way to make calculations. If someone wants to a good nonmathematical intuitive understanding in terms of familiar concepts, then this is clearly not the best way to go. 



#26
Jan1410, 08:36 AM

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Your description is no less coordinatedependent and has no greater universal physical meaning. I just don't think your description is any more intuitive, though it is certainly more convoluted.




#27
Jan1410, 09:53 AM

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At least this time I dropped out of the discussion in time.




#28
Jan1410, 10:13 AM

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:sigh: I should know better than to continue, but "Once more unto the breach"....
The only reason any of this got at all convoluted is because you were incorrectly applying Newtonian physics, and thus I had to explain in gory detail how your recollapsing dust ball example was perfectly consistant with a Newtonian description. Remember that you introduced the recollapsing idea, and when doing so failed to correctly apply Newtonian physics. If we just return to the original question, how to understand how gravity and motion play a role in the redshifts we see in the Universe, we see that there is one single unique way to describe this using Newtonian physics (we don't have general covariance in Newtonian physics, so it all becomes much simpler). Now, even given the gauge freedoms in GR, all coordinate systems will converge for small distances to satisfy the equivalence principle. Hence, the Newtonian description tells you clearly how the underlying physical mechanism are at play, in a way free from coordinate transformations. You don't even need to define any coordinates, you can just use words, but when you do so you are using words that have a direct physical meaning; gravity, motion etc. On the other hand, when you wrap everything into a(t) and repeat the phrase 'expansion of space' to explain anything without any context you aren't learning, teaching or understanding anything more than the properties of one arbitrary foliation of the FRW spacetime. I'm not against the use of the phrase 'expansion of space' or the analogies that go along with it, I just object to their misuse in contexts where it is not appropriate. When someone has asked how gravity and motion play a role in redshift, then this is clearly not the time to be invoking this concept. 



#29
Jan1410, 10:16 AM

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#30
Jan1410, 10:20 AM

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I'm speaking up here, because it was a previous time you explained this that represents for me one of the latest AHA moments which come at me from time to time as I'm trying to deepen my own understanding. Grasping this point has meant several aspects of cosmology and relativity now click together better for me. Cheers  sylas 



#31
Jan1410, 10:22 AM

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Posts #17 and #19. You were commenting and making predictions based on the Doppler + gravitational explanation Ich and I gave ("whereas by your claim" etc). In doing so you incorrectly applied basic Newtonian physics, making a false prediction and thus claiming that the physics was in error.




#32
Jan1410, 10:26 AM

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The problem is that there are some very bad misconceptions thouroughly ingrained in the modern popsci view of cosmology. It is so very difficult to remove some of these, because there is a constant feedback loop of people telling each other they are so right about an entire false lexicon that has replaced understanding of physics with a canonical verbal description at odds with some fundamental (and very important!) concepts in GR. Then again I do have a tendancy to suffer from this syndrome 



#33
Jan1410, 10:54 AM

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So even though these descriptions may provide the impression of understanding, they don't provide any real understanding because none of the extra statements made are nonarbitrary (e.g. gravitational vs. doppler redshift). 



#34
Jan1410, 03:14 PM

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and what Chalnoth did say does not, as far as I can see, imply a false causality; that there is a physical effect called 'expansion of space' which causes photons to stretch. What it seems to me that Chalnoth did do was give a straightforward response to the OP by confirming what anya already offered as an intuitive explanation. That expansion of wavelength correlates pretty much exactly with expansion of distance (that occurred while light was in transit.) This is a relation which I believe we do well to stress to newcomers, before delving into more complicated matters. It refers to the standard FRW metric and standard model cosmo. 



#35
Jan1410, 05:37 PM

P: 87

to do this exercise in another thread last year, and I see no reason to reiterate it here. Rather I give part of the result, which is that for FRW models with flat or spherical spatial sections, the contribution to spectral shift from motion in flat spacetime is 0%, and the contribution from spacetime curvature is 100%. Another way of arriving at this result can be found in arXiv:0911.1205. Using the fact that the geometry of the FRW models is preserved under certain holonomy transformations that change the topology, it is shown that the interpretation of spectral shift as a Doppler shift in flat spacetime leads to a mathematical contradiction if the spatial sections are flat or spherical. This applies to all distances, i.e., for arbitrary close comoving observers. models. 



#36
Jan1510, 03:53 AM

P: 16

Wow, this thread gave me a headache. Some say thats an indication I've learned something but who knows.
The first answer to the question of anya was in regard only to the space between the observer and the observed object. My question is "What about the rest?" What I mean is, if the universe is much bigger compared to the observable universe, and keeping in mind gravitational waves never fully stop, they are endless and just decay over distance, isn't the pull from OUTSIDE to observable universe, that can potentially be HUGE, isn't it's pull going to always EXCEED the gravitational lensing that occurs inside the bubble of observable universe, that could be tiny compared to the whole universe? In other words, it might not be the universe thats expanding, but gravity pulling light back outside the observable universe, creating similar effect to the proposed expansion? And just to illustrate my point: If the universe is infinite, then it's pull will always exceed the pull of the finite, visible universe. So, in the center, our point of observation gravity from the whole universe is equally pulling light, neutralizing it's effect. But if we observe distant objects like A and B, the center of gravity will shift relative to our POV and the further the observed object, the more it's light will be pulled in direction, opposite of our observation. B will appear more redshifted than A not because space between has expanded, but because it is more affected from the pull in the direction, opposite to our POV. Now if the universe is endless, every point in it can be seen as it's center, so the effect exhibited is only present relative to our position and the position of the observed object. In other words  no expansion redshifts, only gravitational. 


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