Redshift and energy conservation

[garyburk]

The subject line gives away my question. No matter if the result of stars moving or cosmological expansion, and no matter if approaching (blue shift) or receding (red shift) , we know that E = hf where f=frequency, therefor E varies with any wavelength shift. But, conservation says that E is invariant.

Is energy conservation wrong (perhaps only true in specific frames of reference), or is the delta E transferred to something else?

What is the "correct" equation and/or rule?

Regards,
Gary Burk
garyburk@hotmail.com

[Chris Peterson]

The subject line gives away my question. No matter if the result of stars moving or cosmological expansion, and no matter if approaching (blue shift) or receding (red shift) , we know that E = hf where f=frequency, therefor E varies with any wavelength shift. But, conservation says that E is invariant.

Is energy conservation wrong (perhaps only true in specific frames of reference), or is the delta E transferred to something else?

What is the "correct" equation and/or rule?

Conservation of energy, as generally presented, is a Newtonian concept. General relativity treats this very differently, and in fact, energy is not conserved over relativistic distances. Or maybe a better way of saying it is that there isn't some global value of E that can be defined over relativistic distances; conservation of energy is a local phenomenon.

[RJN]

http://adsabs.harvard.edu/abs/2008AmJPh..76..265N

[Chris Peterson]

http://adsabs.harvard.edu/abs/2008AmJPh..76..265N

Adventures, indeed!

[garybur1]

Thank you gentle-people, this may keep me busy for a while.

[neufer]

The subject line gives away my question. No matter if the result of stars moving or cosmological expansion, and no matter if approaching (blue shift) or receding (red shift) , we know that E = hf where f=frequency, therefor E varies with any wavelength shift. But, conservation says that E is invariant.

Is energy conservation wrong (perhaps only true in specific frames of reference), or is the delta E transferred to something else?

What is the "correct" equation and/or rule?

Conservation of energy, as generally presented, is a Newtonian concept. General relativity treats this very differently, and in fact, energy is not conserved over relativistic distances. Or maybe a better way of saying it is that there isn't some global value of E that can be defined over relativistic distances; conservation of energy is a local phenomenon.

The conservation of energy relies on time invariance;
our expanding universe (among other things) is NOT time invariant.

<<Amalie Emmy Noether (23 March 1882 – 14 April 1935) was brought to Göttingen in 1915 by David Hilbert and Felix Klein, who wanted her expertise in invariant theory to help them in understanding general relativity, a geometrical theory of gravitation developed mainly by Albert Einstein. Hilbert had observed that the conservation of energy seemed to be violated in general relativity, due to the fact that gravitational energy could itself gravitate. Noether provided the resolution of this paradox, and a fundamental tool of modern theoretical physics, with her first Noether's theorem, which she proved in 1915, but did not publish until 1918. She solved the problem not only for general relativity, but determined the conserved quantities for every system of physical laws that possesses some continuous symmetry.

Upon receiving her work, Einstein wrote to Hilbert: "Yesterday I received from Miss Noether a very interesting paper on invariants. I'm impressed that such things can be understood in such a general way. The old guard at Göttingen should take some lessons from Miss Noether! She seems to know her stuff."

For illustration, if a physical system behaves the same, regardless of how it is oriented in space, the physical laws that govern it are rotationally symmetric; from this symmetry, Noether's theorem shows the angular momentum of the system must be conserved. The physical system itself need not be symmetric; a jagged asteroid tumbling in space conserves angular momentum despite its asymmetry. Rather, the symmetry of the physical laws governing the system is responsible for the conservation law. As another example, if a physical experiment has the same outcome at any place and at any time, then its laws are symmetric under continuous translations in space and time; by Noether's theorem, these symmetries account for the conservation laws of linear momentum and energy within this system, respectively.

Noether's theorem has become a fundamental tool of modern theoretical physics, both because of the insight it gives into conservation laws, and also, as a practical calculation tool. Her theorem allows researchers to determine the conserved quantities from the observed symmetries of a physical system. Conversely, it facilitates the description of a physical system based on classes of hypothetical physical laws. For illustration, suppose that a new physical phenomenon is discovered. Noether's theorem provides a test for theoretical models of the phenomenon: if the theory has a continuous symmetry, then Noether's theorem guarantees that the theory has a conserved quantity, and for the theory to be correct, this conservation must be observable in experiments.>>

[neufer]

http://adsabs.harvard.edu/abs/2008AmJPh..76..265N

Adventures, indeed!

Alexander Alexandrovich Friedman or Friedmann (Александр Александрович Фридман) (June 16, 1888, Saint Petersburg, Russian Empire – September 16, 1925, Leningrad, USSR) was a Russian and Soviet cosmologist and mathematician. Alexander Friedmann lived much of his life in Saint Petersburg. He fought in World War I (on behalf of Imperial Russia) as a bomber and later lived through the Russian Revolution of 1917.

He discovered the expanding-universe solution to the general relativity field equations in 1922, which was corroborated by Edwin Hubble's observations in 1929. Friedmann's 1924 papers, including "Über die Möglichkeit einer Welt mit konstanter negativer Krümmung des Raumes" (On the possibility of a world with constant negative curvature of space) published by the German physics journal Zeitschrift für Physik (Vol. 21, pp. 326-332), demonstrated that he had command of all three Friedmann models describing positive, zero and negative curvature respectively, a decade before Robertson and Walker published their analysis. This dynamic cosmological model of general relativity would come to form the standard for the Big Bang and steady state theories. Friedmann's work supports both theories equally, so it was not until the detection of the cosmic microwave background radiation that the steady state theory was abandoned in favor of the current favorite Big Bang paradigm. Another famous physicist, George Gamow, was a student of Friedmann.

In addition to general relativity, Friedmann's interests included hydrodynamics and meteorology. In July 1925 he participated in a record-setting balloon flight, reaching the elevation of 7,400 m (24,300 ft). Friedmann died on September 16, 1925, at the age of 37, from typhoid fever that he contracted during a vacation in Crimea.>>

<<George Gamow (March 4 [O.S. February 20] 1904 – August 19, 1968), born Georgiy Antonovich Gamov (Георгий Антонович Гамов), was a Russian-born theoretical physicist and cosmologist. He discovered alpha decay via quantum tunneling and worked on radioactive decay of the atomic nucleus, star formation, stellar nucleosynthesis, big bang nucleosynthesis, cosmic microwave background, nucleocosmogenesis and genetics.

Gamow was born in the city of Odessa, Russian Empire (now in Ukraine) to mixed Russian-Ukrainian parents. He was educated at the Novorossiya University in Odessa (1922–23) and at the University of Leningrad (1923–1929). Gamow studied under Alexander Friedmann for some time in Leningrad, though Friedmann died in 1925. At the University Gamow made friends with three other students of theoretical physics, Lev Landau, Dmitri Ivanenko, and Matvey Bronshtein (who was arrested in 1937 and executed in 1938 by the Soviet regime). The four formed a group known as the Three Musketeers which met to discuss and analyze the ground-breaking papers on quantum mechanics published during those years.

Gamow then worked at a number of Soviet establishments before deciding to flee Russia because of increased oppression. His first two attempts to defect with his wife, Lyubov Vokhminzeva, were in 1932 and involved attempting to kayak: first a 250-kilometer paddle over the Black Sea to Turkey and then from Murmansk to Norway. Poor weather foiled both attempts. In 1933, the two tried a less dramatic approach - Gamow managed to obtain permission for himself and his wife (who was also a physicist) to attend the Solvay Conference for physicists in Brussels. The two attended and promptly defected. In 1934, they moved to the United States. He began working at The George Washington University in 1934. Gamow became a naturalized American in 1940.

Gamow produced an important cosmogony paper with his student Ralph Alpher, which was published as "The Origin of Chemical Elements" (Physical Review, April 1, 1948). This paper became known as the Alpher-Bethe-Gamow theory. Gamow had the name of Hans Bethe listed on the article as "H. Bethe, Cornell University, Ithaca, New York" to make a pun on the first three letters of the Greek alphabet, alpha, beta and gamma. Bethe had no other role in the α-β-γ paper. The paper outlined how the present levels of hydrogen and helium in the universe (which are thought to make up over 99% of all matter) could be largely explained by reactions that occurred during the "big bang". This lent theoretical support to the Big Bang theory, although it did not explain the presence of elements heavier than helium (this was done later by Fred Hoyle). In this paper, no estimate of the strength of the present day residual cosmic microwave background radiation (CMB) was made. Shortly thereafter, Alpher and Robert Herman predicted that the afterglow of the big bang would have cooled down after billions of years, filling the universe with a radiation five degrees above absolute zero. Astronomers and scientists did not make any effort to detect this background radiation at that time, due to both a lack of interest and the immaturity of microwave observation. Consequently, Gamow's prediction in support of the big bang was not substantiated until 1964, when Arno Penzias and Robert Wilson made the accidental discovery for which they were awarded the Nobel Prize in Physics in 1978. Their work determined that the universe's background radiation was 2.7 degrees above absolute zero, just 2.3 degrees lower than Gamow's 1948 prediction.

Gamow published another paper in the British journal Nature in 1948, in which he developed equations for the mass and radius of a primordial galaxy (which typically contains about one hundred billion stars, each with a mass comparable with that of the sun).>>

[rstevenson]

Thanks Art. It was very pleasant to be reminded of George Gamow, who unknowingly contributed greatly to my interest in mathematics and science at a tender age, back in the mid-60s. For reasons I cannot now recall I purchased a paperback copy of his book "One, Two, Three...Infinity". (I don't think I can adequately convey how odd it was for me, at that time, to do that.) It took me quite a while to read it -- not because it was hard going but because I felt I had to stop every few pages and let my brain expand to find room for what I was learning. I was newly out of high school, and my reaction to Gamow's book may reflect more on the paucity of my schooling than on anything else, but that's another story. I've clung to very few artifacts of my early life in the intervening years, but that tattered copy of Gamow's book is one of them I cherish.

Rob

[Ann]

I, too, enjoyed reading about George Gamov.

As a person who fails to find any pleasure in math, I wouldn't read a book by George Gamov myself. That doesn't mean that I don't admire people who can spot fantastic patterns and connections in nature thanks to math.

To me, George Gamov is mostly one of the "Alpha-Beta-Gamma" gang. All I remembered about it was that George Gamov had cooperated with Ralph Alpher, and they just thought it would be fun to name Hans Bethe as a contributor to their work. You know, to get the "Alpha-Beta-Gamma" sound of it! I didn't remember what the "Alpha-Beta-Gamma" work was about, so thank you very much for reminding me!

Ann

[bystander]

Alpher–Bethe–Gamow (αβγ) paper

... αβγ paper ... argued that the Big Bang would create hydrogen, helium and heavier elements in the correct proportions to explain their abundance in the early universe. While the original theory neglected a number of processes important to the formation of heavy elements, subsequent developments showed that Big Bang nucleosynthesis is consistent with the observed constraints on all primordial elements.
...

The results of these calculations were first announced in a letter to The Physical Review, April 1, 1948. This was signed Alpher, Bethe, and Gamow, and is often referred to as the 'alphabetical article.' It seemed unfair to the Greek alphabet to have the article signed by Alpher and Gamow only, and so the name of Dr. Hans A. Bethe (in absentia) was inserted in preparing the manuscript for print. Dr. Bethe, who received a copy of the manuscript, did not object, and, as a matter of fact, was quite helpful in subsequent discussions. There was, however, a rumor that later, when the alpha, beta, gamma theory went temporarily on the rocks, Dr. Bethe seriously considered changing his name to Zacharias.

The close fit of the calculated curve and the observed abundances is shown in Fig. 15, which represents the results of later calculations carried out on the electronic computer of the National Bureau of Standards by Ralph Alpher and R. C. Herman (who stubbornly refuses to change his name to Delter.)

The Origin of Chemical Elements - R Alpher, H Bethe, G Gamow

• Physical Review Letters 73(7) 803 (Apr 1948) DOI: 10.1103/PhysRev.73.803

[Beyond]

I wouldn't change my name to 'Delter' either.

[Drewster]

Suppose there are two rocks, galaxies, whatever. They are a certain distance apart, and falling towards each other. This system has a potential and a kinetic energy and the total energy of the system remains constant.

Now suppose I reach in and drag the two farther apart. There is now more potential energy in the system, but that doesn’t violate conservation of energy because I had to put that amount of energy into the system to drag them farther apart.

Now suppose they get further apart due to the space between them expanding (i.e. due to expansion of the universe). They are further apart so there is more potential energy in the system, right? Where did that energy come from?

I can think of two explanationss but see holes in both.

Drew Sullivan

[Drewster]

I did read this thread before posting and from the fact that my question got moved here I gather the answer may be here somewhere but if so I don't see/understand the answer.

Any insight into this? Are you implying that there is a GR solution?

Drew Sullivan

[bystander]

Your post was merged into this discussion because expansion of the universe is redshift. Same topic.

[Chris Peterson]

I did read this thread before posting and from the fact that my question got moved here I gather the answer may be here somewhere but if so I don't see/understand the answer.

Any insight into this? Are you implying that there is a GR solution?

GR does not require conservation of energy. In general, conservation of energy is probably not a universal law.

With respect to your problem with the galaxies, I'd start by considering the mechanisms causing the galaxies to get farther apart. One is not a force, but might be thought of as analogous to inertia; energy released during the Big Bang and the inflationary period set space into expansion. There should be no major energy concerns here. The other mechanism is analogous to a force, and is causing the expansion rate of the Universe to increase. The proposed cause of this is dark energy, and I'd note that the term "energy" is used here for a reason.

[Drewster]

Are any or all of these statements true:

1) The first law of thermodynamics isn't really a law. (I know it doesn't apply at very small scales where virutal particles can appear/disappear but this is a macroscopic, long lasting system. Is the first law just a Newtonian approximation?)

2) The answer to my question about the rocks/galaxies is that the expansion itself is part of the system, so you have to take the expansion into account at the first (closer together) and second (farther apart) states of the system and if you do that energy is conserved.

Are statements 1 and 2 conflicting?

Drew S.

[Chris Peterson]

Are any or all of these statements true:

1) The first law of thermodynamics isn't really a law. (I know it doesn't apply at very small scales where virutal particles can appear/disappear but this is a macroscopic, long lasting system. Is the first law just a Newtonian approximation?)

2) The answer to my question about the rocks/galaxies is that the expansion itself is part of the system, so you have to take the expansion into account at the first (closer together) and second (farther apart) states of the system and if you do that energy is conserved.

Are statements 1 and 2 conflicting?

I'd say neither statement is entirely accurate, and there is no conflict between them as stated.