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Old 06-December-2003, 03:33 AM
Oops Oops is offline
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Default Cosmological Constant

How does this fit into current science?
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Old 06-December-2003, 03:37 AM
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That Einstein--a hundred years ahead of the game...
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Old 06-December-2003, 03:40 AM
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Didn't Einstein call it his greatest mistake?
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Old 06-December-2003, 03:42 AM
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Also didn't he just put it in as a fudge factor because the calculations weren't working out right?
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Old 06-December-2003, 03:43 AM
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I read that he used it to explain why no one had observed that the Universe was expanding or contracting. He got rid of it when someone discovered it was expanding.
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Old 06-December-2003, 05:28 AM
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Originally Posted by Oops
I read that he used it to explain why no one had observed that the Universe was expanding or contracting. He got rid of it when someone discovered it was expanding.

Back around 1915, most astronomers and physicists still believed the universe was stationary and “static”, non-expanding and non-contracting, with all the stars not having much motion. A problem with this type of universe is that it should collapse in on itself, due to all the gravity of all the massive bodies.

This problem had confounded Newton more than 200 years earlier.

I haven’t been able to find any mention of the idea of “expansion” of the universe in any of Newton’s writings, but I have an 1803 astronomy book, titled “Natural Theology”, by William Paley, Arch-Deacon of Carlisle, which contains the following quote on page 276:

“But many of the heavenly bodies, as the sun and fixed stars are stationary. Their rest must be the effect of an absence or of an equilibrium of attractions. It proves also that a projectile impulse was originally given to some of the heavenly bodies, and not to others. But further; if attraction act at all distances, there can be only one quiescent center of gravity in the universe: and all bodies whatever must be approaching this center, or revolving around it. According to the first of these suppositions, if the duration of the world had been long enough to allow it, all its parts, all the great bodies of which it is composed, must have been gathered together in a heap round this point.”

Well, here we have the basic “big bang” theory in a single paragraph, complete with all the mass of the universe gathered together around a “point”, and a “projectile impulse” that caused the universe to start expanding.

Interestingly, it was the Belgian Catholic priest, Georges Lemaitre, working for a Vatican observatory, who developed the first modern “big bang” theory in 1927, and this is the same basic theory we have today, with some modifications added over the years.

But back in 1915, Einstein’s “solution” to the mystery of why the universe didn’t collapse in on itself was taken basically from Poincaré’s idea about a four-dimensional “hypersphere” universe (with 4 spatial dimensions and one of time). This is from Poincaré’s 1902 book:

”Let us imagine to ourselves a world only peopled with beings of no thickness, and suppose these "infinitely flat" animals are all in one and the same plane, from which they cannot emerge. Let us further admit that this world is sufficiently distant from other worlds to be withdrawn from their influence, and while we are making these hypotheses it will not cost us much to endow these beings with reasoning power, and to believe them capable of making a geometry. In that case they will certainly attribute to space only two dimensions.

But now suppose that these imaginary animals, while remaining without thickness, have the form of a spherical, and not of a plane figure, and are all on the same sphere, from which they cannot escape. What kind of a geometry will they construct ? In the first place, it is clear that they will attribute to space only two dimensions. The straight line to them will be the shortest distance from one point on the sphere to another—that is to say, an arc of a great circle. In a word, their geometry will be spherical geometry. What they will call space will be the sphere on which they are confined, and on which take place all the phenomena with which they are acquainted. Their space will therefore be unbounded, since on a sphere one may always walk forward without ever being brought to a stop, and yet it will be finite; the end will never be found, but the complete tour can be made.


Einstein copied this idea in his 1916 book, when he said:

”Let us consider now a second two-dimensional existence, but this time on a spherical surface instead of on a plane. The flat beings with their measuring-rods and other objects fit exactly on this surface and they are unable to leave it. Their whole universe of observation extends exclusively over the surface of the sphere. Are these beings able to regard the geometry of their universe as being plane geometry and their rods withal as the realisation of " distance " ? They cannot do this. For if they attempt to realize a straight line, they will obtain a curve, which we " three-dimensional beings " designate as a great circle, i.e. a self-contained line of definite finite length, which can be measured up by means of a measuring-rod. Similarly, this universe has a finite area that can be compared with the area, of a square constructed with rods. The great charm resulting from this consideration lies in the recognition of the fact that the universe of these beings is finite and yet has no limits."

Well, this 1902 Poincaré concept, adopted by Einstein in 1915, in order to keep the universe from collapsing, turns the universe into a strange thing – a 5-D “hypersphere” – that can’t be imagined, described, or drawn or made into a 3-D or 4-D model.

This is where our modern and puzzling conception of "Einstein’s curved space” comes from. The “cosmological constant” was added to the theory to keep gravity from acting in a way that would cause the universe to collapse. So Einstein never did “predict” that the universe was “expanding”, and in fact he said in his 1916 book that all the distant stars of the universe were “fixed”, and he did not mention the “galaxies”, which, in 1915, many scientists thought might be small things that probably resided inside our own Milky Way.

After Lemaitre published his theory in 1927, and after Hubble published his famous paper about the redshifts of the distant galaxies that he believed were well outside our Milky Way, Einstein retracted his “curved space” and “5-D hypersphere” idea in a paper he wrote with de Sitter in 1932. In the paper, Einstein said:

“There is no direct observational evidence for the curvature, the only directly observed data being the mean density and the expansion, which latter proves that the actual universe corresponds to the non-statical case. It is therefore clear that from the direct data of observation we can derive neither the sign nor the value of the curvature, and the question arises whether it is possible to represent the observed facts without introducing a curvature at all.”

“Although, therefore, the density corresponding to the assumption of zero curvature and to the coefficient of expansion may perhaps be on the high side, it certainly is of the correct order of magnitude, and we must conclude that at the present time it is possible to represent the facts without assuming a curvature of three-dimensional space. The curvature is, however, essentially determinable, and an increase in the precision of the data derived from observations will enable us in the future to fix its sign and to determine its value.”


Inexplicably, Einstein’s original 1915 5-D “curved space non-expanding universe hypersphere” theory is still taught in some physics books, even though Einstein disavowed the theory in his 1932 paper, after he learned of the evidence of “expansion”. In fact, I’ve got several books from the 1950s through the ‘90s that relate the old theory as if it is still in effect and as if there is no “expansion” going on.
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Old 06-December-2003, 05:47 AM
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Quote:
Originally Posted by Sam5
Einstein copied this idea in his 1916 book
Quote:
this 1902 Poincaré concept, adopted by Einstein in 1915
The idea of a curved unbounded but finite space arose long before Poincare.
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Old 06-December-2003, 06:01 AM
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Oops,

Evidently Einstein got some of his ideas from the 1884 fairytale, “Flatland”, by A. Abbott:

Abbott, 1884 –

”I call our world Flatland, not because we call it so, but to make its nature clearer to you, my happy readers, who are privileged to live in Space.

Imagine a vast sheet of paper on which straight Lines, Triangles, Squares, Pentagons, Hexagons, and other figures, instead of remaining fixed in their places, move freely about, on or in the surface, but without the power of rising above or sinking below it, very much like shadows -- only hard with luminous edges -- and you will then have a pretty correct notion of my country and countrymen. Alas, a few years ago, I should have said "my universe": but now my mind has been opened to higher views of things.

In such a country, you will perceive at once that it is impossible that there should be anything of what you call a "solid" kind; but I dare say you will suppose that we could at least distinguish by sight the Triangles, Squares, and other figures, moving about as I have described them. On the contrary, we could see nothing of the kind, not at least so as to distinguish one figure from another. Nothing was visible, nor could be visible, to us, except Straight Lines; and the necessity of this I will speedily demonstrate.



Einstein, 1915 –

”In the first place, we imagine an existence in two dimensional space. Flat beings with flat implements, and in particular flat rigid measuring-rods, are free to move in a plane. For them nothing exists outside of this plane: that which they observe to happen to themselves and to their flat " things " is the all-inclusive reality of their plane. In particular, the constructions of plane Euclidean geometry can be carried out by means of the rods e.g. the lattice construction, considered in Section 24. In contrast to ours, the universe of these beings is two-dimensional; but, like ours, it extends to infinity. In their universe there is room for an infinite number of identical squares made up of rods, i.e. its volume (surface) is infinite. If these beings say their universe is " plane," there is sense in the statement, because they mean that they can perform the constructions of plane Euclidean geometry with their rods. In this connection the individual rods always represent the same distance, independently of their position.
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Old 06-December-2003, 06:10 AM
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Quote:
Originally Posted by Sam5
Evidently Einstein got some of his ideas from the 1884 fairytale, “Flatland”, by A. Abbott:
Everyone's read Flatland, even my kids, at school. But those ideas predate even Flatland.
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Old 06-December-2003, 01:29 PM
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Originally Posted by Oops
I read that he used it to explain why no one had observed that the Universe was expanding or contracting. He got rid of it when someone discovered it was expanding.
I am of the understanding that his GR theory revealed an expanding universe. This was contrary to their understanding in their day so he added the constant to offset the expansion. There is a famous 1929 picture of him with Hubble and Walter Adams which shows him looking through the 100" Mt. Wilson scope. This was due to the great interest in discovering evidence of an expanding universe.

Once the universe was shown to be expanding, Einstein said it was his biggest blunder. However, I don't think he had his tail tucked much as it did honor his GR equations greatly! Once again, he broke the "you must be nuts" barrier. =D>

I'm curious why he hasn't received another Nobel for relativity. Anybody know? #-o
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Old 06-December-2003, 01:52 PM
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I'm curious why he hasn't received another Nobel for relativity. Anybody know?
As you infer, Einstein did not receive a Nobel for either special or general relativity. He received it for his work on the photoelectric effect, I believe. However, I think only four people have received more than one Nobel, and only two of them have received more than one in the same category--Bardeen in physics for the transistor and superconductivity, and Sanger in chemistry for sequencing amino acids, and a virus DNA. And you can't receive one after your death, so the case has been closed since 1955. At the time of his death, the only person who had been awarded two was Madame Curie, with prizes in physics and chemistry. Pauling received a chemistry prize, and a peace prize.
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Old 06-December-2003, 02:15 PM
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The cosmological constant has been revived recently as one possibility to account for the accelerating expansion of spacetime.
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Old 06-December-2003, 02:57 PM
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Originally Posted by George
I am of the understanding that his GR theory revealed an expanding universe. This was contrary to their understanding in their day so he added the constant to offset the expansion. There is a famous 1929 picture of him with Hubble and Walter Adams which shows him looking through the 100" Mt. Wilson scope. This was due to the great interest in discovering evidence of an expanding universe.
Small correction: it was 1931. From Ken Croswell's cosmology book The Universe at Midnight:

"In early 1931, Albert Einstein visited Mount Wilson Observatory and met Edwin Hubble. There Einstein threw out the cosmological constant, the `antigravity' force that had allowed the universe to be static. With the discovery that the universe was expanding, Einstein no longer needed the cosmological constant, and he later called it the biggest blunder of his life.

"At Mount Wilson, Einstein's wife was shown the mammoth 100-inch telescope with which astronomers like Hubble were determining the universe's structure. She was not impressed. `Well, well,' she reportedly said, `my husband does that on the back of an old envelope.'"
--From Ken Croswell's The Universe at Midnight, page 35.
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Old 06-December-2003, 03:40 PM
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"In early 1931, Albert Einstein visited Mount Wilson Observatory and met Edwin Hubble. There Einstein threw out the cosmological constant, the `antigravity' force that had allowed the universe to be static.
Einstein invented the cosmological constant because he thought the universe was static. The constant was his way of explaining why the “static” universe didn’t collapse in on itself. When he discovered that the universe was “expanding”, he was quite surprised. He went to meet Hubble for the publicity and media photo opportunity so he could try to salvage his reputation, after he had claimed for many years that the universe was static.
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Old 06-December-2003, 03:46 PM
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he had claimed for many years that the universe was static.
Except, that was not "his" claim, that was the generally accepted position.
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Old 06-December-2003, 04:01 PM
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Quote:
Originally Posted by George
I'm curious why he hasn't received another Nobel for relativity. Anybody know?
As you infer, Einstein did not receive a Nobel for either special or general relativity. He received it for his work on the photoelectric effect, I believe. However, I think only four people have received more than one Nobel, and only two of them have received more than one in the same category--Bardeen in physics for the transistor and superconductivity, and Sanger in chemistry for sequencing amino acids, and a virus DNA. And you can't receive one after your death, so the case has been closed since 1955. At the time of his death, the only person who had been awarded two was Madame Curie, with prizes in physics and chemistry. Pauling received a chemistry prize, and a peace prize.
It was for the photoelectric efect. Also noone can receive more than one anymore from what I remember reading. However, I can't seem to find it in writing at this moment.

Also Linus Pauling was awarded the Nobel Prize in Chemistry in 1954 and the Nobel Peace Price in 1962 he is the only one to receive 2 unshared prizes Curie's were shared. The Curie's however were a main stay of the prizes for a while:

Pierre Curie 1903
Irène Joliot-Curie 1935
Marie Curie 1903,1911
Frédéric Joliot 1935

Double Nobel Prizes are listed below:
Marie Curie received the Nobel Prize in Physics 1903 and the Nobel Prize in Chemistry 1911.


John Bardeen received the Nobel Prize in Physics 1956 and 1972.


Frederick Sanger received the Nobel Prize in Chemistry 1958 and 1980.


Comité International de la Croix Rouge received the Nobel Peace Prize in 1917, 1944 and 1963.


Office of the United Nations High Commissioner for Refugees received the Nobel Peace Prize in 1954 and 1981.


Linus Pauling received the Nobel Prize in Chemistry 1954 and the Nobel Peace Prize 1962.
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Old 06-December-2003, 10:50 PM
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As you infer, Einstein did not receive a Nobel for either special or general relativity. He received it for his work on the photoelectric effect, I believe...
Yes, it was for the photoelectric effect. This greatly helped awaken entrenched scientists to Planck's idea of quantum mechanics which was a number of years old already. Planck had come up with the idea to explain the odd blackbody curve (higher frequency energy should dominate the curve but it doesn't).

I still, however, do not know why Einstein's relativity work is not considered worthy of a Nobel and was curious if there was more to this issue. #-o

Crimson. My reference stated 1929 and another time of 1931. I am not clear if both dates are correct. You may be right.

Quote:
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The cosmological constant has been revived recently as one possibility to account for the accelerating expansion of spacetime
Would this mean the constant will be significantly different as it will no longer counter expansion but boost it along?
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Old 07-December-2003, 03:40 PM
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Quote:
Originally Posted by George
Crimson. My reference stated 1929 and another time of 1931. I am not clear if both dates are correct. You may be right.

Quote:
Originally Posted by chaotica
The cosmological constant has been revived recently as one possibility to account for the accelerating expansion of spacetime
Would this mean the constant will be significantly different as it will no longer counter expansion but boost it along?
The year was indeed 1931--see Ken Croswell's book. The cosmological constant is the same (though its numerical value differs). Einstein invented it to keep the universe from contracting. Now, it is boosting the expansion. Thus, the present expansion of the universe has two causes:

1. The initial kick given by the big bang, and
2. The cosmological constant, which boosts the expansion.
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Old 07-December-2003, 05:55 PM
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Thus, the present expansion of the universe has two causes:

1. The initial kick given by the big bang, and
2. The cosmological constant, which boosts the expansion.
The cosmological constant doesn’t do anything to the universe. A math equation can’t “boost the expansion”.

This “expansion” has gone through many changes in physics