## Expansion of the universe

 Quote by Lino Wow! Thanks George. I think that I understand what you are saying and it gives me a lot to target my reading at. But there is one concept that is very alien to me, so in prep, can I confirm, are you saying that when such measurements are taken here and now, it is the history of the input variables that cause the results - not just the "final" value of the variables. Is that correct?
It is a curve-fit to a large number of individual point measurements. When we look at a distant galaxy and see a supernova in it, we can measure both the redshift of the galaxy or the supernova and also the brightness. That gives us one point on the curve. Hunderds of such measurement pairs give us the relationship which we can then fit by adjusting parameters in the equations.

 (I'm trying to understand / compare it to other measurement processes: for example, is this the equivilant to conducting a litmus test and based on the single result being able to understand the history of the acidity of the solution?)
No, it's like making lots of individual measurements of skin colour versus sugar content of a particular type of apple at different stages of ripening and plotting a graph. Going back to your original question, the graph then lets you estimate the relative difference in sugar content of two apples based on the difference in skin colour even if neither is fully ripe. Similarly, we could tell how far apart two distant supernovae were from their redshifts and our graph of the scale factor.

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 Quote by MDEarl ... In 1922 Alexander Friedmann came out with equations for an expanding universe which still form a basis for GR and cosmology today. To do this he employed Newtonian gravitation and conservation of energy principles, probably assuming they were universally applicable.
Friedmann did not "employ Newtonian gravitation..." Einstein's GR equation came out in 1915 and Friedmann was using it.
Friedmann equation is a simplification of the Einstein GR equation derived by making the simplifying assumption that the universe is approximately uniform (matter evenly distributed, more or less). If it is close enough to uniform, at very large scale, e.g. with same number of galaxies per unit volume everywhere, then you can TREAT IT AS IF IT WERE perfectly uniform and then General Rel geometry simplifies enormously and you get Friedmann equation.

You also get a concept of "universe time" or "Friedmann time" as it is sometimes called, and you get a concept of the scalefactor a(t) that shows how distances increase with time. The Hubble rate H(t) is defined to be a'(t)/a(t). That is the time derivative of a(t) divided by a(t) itself. It is is always changing and in the past has fallen off very rapidly. It is still changing but more slowly now.

 Hubble’s law has the form of a simple growth equation, HoR = dR/dt which mathematically requires an exponential value for R.
Ah! I see you use R(t) for the scale factor, instead of a(t). Both notations are in use.

No, the facts do not require exponential growth of R(t). Because H(t) is not constant.
When people write H0 they mean the CURRENT value of H(t) that it happens to have at present. If H(t) were constant, then you would get an exponential solution for R(t).
But it isn't constant. For about half the history of expansion the R(t) curve has been convex (decreasing slope) and then it had an inflection point and became concave (increasing slope). Far in the future it may have approximately an exponential growth shape. But if you are talking past and present then what you say runs against what's been learned so far.

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 Quote by mufa Sometimes electron has wavelike behaviour,and photon behaves like a particle. I am still can't make out how photons loose momentum provided that the speed is stable, whereas in your example the relative speed of the electron decreases.Thanks.
Think of it this way. Because the photon cannot lose speed, it MUST lose momentum by losing energy, and since the photon's energy and momentum is determined by it's frequency, it redshifts to a lower frequency. Now, realize that the photon isn't doing anything itself, it is merely a consequence of your frame of reference being different than the frame of reference that emitted the photon.

 But photons speed is stable.Does n't frequency reduction meaning an energy reduction too?
Yes. A lower frequency has less energy than a higher frequency. Just like a moving object has less kinetic energy when viewed from something moving away from it's source, the photon will have less energy when viewed from something moving away from it.
 Yes,I understand this.My petition is other:Why photon should not be an ultra small particle behave as a wave,like the electron does? Why we claim that it is a wave with particle properties and not the opposite,such as the electron?This model,as suggested above by elias2010 not leads to dark energy.
 Thanks George. (Kinda understand and just the info I was looking for.) Regards, Noel.
 De Broglie equation has experimentally confirmed.Why we have to reject the hypothesis photon have a mass instead of the possibility being wrong the relativistic formula for energy?

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 Quote by mufa De Broglie equation has experimentally confirmed.Why we have to reject the hypothesis photon have a mass instead of the possibility being wrong the relativistic formula for energy?
Because experiments have failed to detect a photon mass greater than $10^{-27}$ eV (see http://en.wikipedia.org/wiki/Photon#...on_photon_mass.)

 Quote by GeorgeDishman No. The simplest way to think of a photons is as a short burst of waves encapsulated in a form that can only interact as if it was a particle, i.e. all or nothing. It's equivalent to thinking of it as a particle which has an intrinsic phase which changes at a rate given by its angular frequency. .
George,I read your posts.Can you explain to me what an elegtromagnetic pulse is? Because I thought that is a wave with only one peak represents a big quantity of photons.
 My confusion comes from whether objects in space are moving apart, or whether space itself is getting larger. The distinction seems less than clear in most discussions I've seen. http://en.wikipedia.org/wiki/Accelerating_universe http://en.wikipedia.org/wiki/Metric_expansion_of_space

 Quote by Landrew My confusion comes from whether objects in space are moving apart, or whether space itself is getting larger. The distinction seems less than clear in most discussions I've seen. http://en.wikipedia.org/wiki/Accelerating_universe http://en.wikipedia.org/wiki/Metric_expansion_of_space
They're indistinguishable, it's just more convenient to think of it as space expanding.

Quote by harve
 Doppler effect appears in waves produced by oscillators witch have “peaks” and “hollows”. These peaks can be condensed or diluted by the Doppler effect. In the light case, a peak represents an amount of photons
No. The simplest way to think of a photons is as a short burst of waves encapsulated in a form that can only interact as if it was a particle, i.e. all or nothing. It's equivalent to thinking of it as a particle which has an intrinsic phase which changes at a rate given by its angular frequency.
George,I read your posts.Can you explain to me what an electromagnetic pulse is? Because I thought that is a wave with only one peak represents a big quantity of photons.
I've added some context as the quotes are quite old.

A single pulse has a DC component so can't be a simply EM signal in space say. If it was a switched DC signal on a wire, you'd have to look at the components of the Poynting Vector and it all gets complicated, however I understand what you are asking. You can consider instead a rectangular wave with narrow, widely separated pulses and zero average value.

A square pulse is the sum of many sine waves, you can get the pattern by taking a Fourier Transform. For a regular series of pulses there are discrete harmonics while for a single pulse you get a continuous spectrum. Either way, you can then break down each sine wave into numbers of photons by dividing the portion of the pulse energy in that frequency by the energy of a single photon. As you say, ultimately you will get a burst of photons but of a mixture of frequencies. Again, each photon can be thought of as a burst of waves and they overlap to create the macroscopic, measurable, sine wave.

That's very different to what the O.P. was saying, that "a peak [of a sine wave] represents an amount of photons".