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jamesabrown
2009-Apr-27, 06:20 PM
(Sorry for the weird title. Apparently the BAUT forum chokes if the word 'time' is used in the title.)

So I found a copy of Stephen W. Hawking's A Brief History of Time at a used bookstore on sale for $1.00. At that price I felt an obligation to purchase it, of course. I read it years and years ago and didn't understand most of it, but I've learned a few things since then.

Now I want to read it again, but slowly this time. Slow enough to think about what I'm reading, to digest it. And I'm asking you fine folks for help.

In essence, this thread will be me reading through this ground-breaking book. When I come to a passage I don't understand, or if a question is raised in my mind, I'm going to ask it here, and I'm hoping you can answer my questions using Small Words. If I don't understand your answer, then someone else will have to explain using Even Smaller Words. And I won't continue with, say, Chapter 2 until I understand Chapter 1, etc., no matter how long it takes.

So then, I'm doing good until Chapter Two: Space and Time (p. 18 in hardcover) where I read this:


The fact that light travels at a finite, but very high, speed was first discovered in 1676 by the Danish astronomer Ole Christensen Roemer. He observed that the times at which the moons of Jupiter appeared to pass behind Jupiter were not evenly spaced, as one would expect if the moons went round Jupiter at a constant rate. As the earth and Jupiter orbit around the sun, the distance between them varies. Roemer noticed that the eclipses of Jupiter's moons appeared later the farther we were from Jupiter. He argued that this was because the light from the moons took longer to reach us when we were farther away. His measurements of the variations in the distance of the earth from Jupiter were, however, not very accurate, and so his value for the speed of light was 140,000 miles per second, compared to the modern value of 186,000 miles per second. Nevertheless, Roemer's achievement, in not only proving that light travels at a finite speed, but also in measuring that speed, was remarkable--coming as it did eleven years before Newton's publication of Principia Mathematica.

So first question. What does this mean, "the eclipses of Jupiter's moons appeared later the farther we were from Jupiter"? A moon--say, Ganymede--passes behind Jupiter, and Roemer observes it in his telescope. Six months later he sees the same thing, and he figures out it's happening later? Later than what? Isn't the light coming from Jupiter's surface and Ganymede's surface traveling roughly the same distance (Roemer's eyeball)?

grant hutchison
2009-Apr-27, 06:28 PM
So first question. What does this mean, "the eclipses of Jupiter's moons appeared later the farther we were from Jupiter"? A moon--say, Ganymede--passes behind Jupiter, and Roemer observes it in his telescope. Six months later he sees the same thing, and he figures out it's happening later? Later than what? Isn't the light coming from Jupiter's surface and Ganymede's surface traveling roughly the same distance (Roemer's eyeball)?Rømer had a table of eclipse predictions (by Cassini, IIRC), worked out on the basis of Kepler's laws and prior observation.
Trouble is, the visual appearance of the Galilean satellites doesn't behave in strict accordance with Kepler: sometimes eclipses come early, sometimes late. The late eclipses are all when Jupiter is on the opposite side of the sun from Earth. Rømer figured out that the eclipses are actually following Kepler plus a delay for light travel time. The light from a maximally "delayed" eclipse has an extra 2AU (16 minutes) to travel, equivalent to the width of Earth's orbit.

Grant Hutchison

cjameshuff
2009-Apr-27, 06:31 PM
So first question. What does this mean, "the eclipses of Jupiter's moons appeared later the farther we were from Jupiter"? A moon--say, Ganymede--passes behind Jupiter, and Roemer observes it in his telescope. Six months later he sees the same thing, and he figures out it's happening later? Later than what? Isn't the light coming from Jupiter's surface and Ganymede's surface traveling roughly the same distance (Roemer's eyeball)?

The lightspeed lag between Jupiter and Earth changes by about 16 minutes depending on their relative locations. If you start watching at the closest approach, at the furthest point, you will see the eclipses happening 16 minutes later than expected.

01101001
2009-Apr-27, 06:31 PM
What does this mean, "the eclipses of Jupiter's moons appeared later the farther we were from Jupiter"? [...] Isn't the light coming from Jupiter's surface and Ganymede's surface traveling roughly the same distance (Roemer's eyeball)?

I expect something probably made Roemer go, "Hmm..." Satellites passing behind Jupiter should be periodic events with regular frequencies. When measured, with clocks ticking away on Earth, the period varied. That would be because sometimes the event happened nearer Earth and sometimes much farther away. The events were quite periodic in the frame of Jupiter, but the varying distances at which they were observed, because the events' images had to travel to Earth only at the speed of light, made them seem to happen at odd times on an Earth-based clock.

Edit: There you go: 3 different flavors of the answer. Who else wants to give the reason?

astromark
2009-Apr-27, 07:07 PM
No. I will not answer the already well dealt with question..., but a little free advice (worth as much as you pay ).
The author of this excellent book writes in a very calculated way. He chooses his words with deliberate and calculated finesse. Unlike I who just blither on at random, blurting on uncontrolably... Mr Hawking's use of English is very good. Read what he says and except it as true... it is. Most has been well tested and challenged as required. You will not find him wrong. Asking us for clarity and endorsement is flattering and good on you for the effort. Never stop asking the questions. Good luck to you.

jamesabrown
2009-Apr-27, 07:46 PM
Okay, let me repeat your answers back to you and see if I understand it right, because I think I'm missing something. So Roemer has a chart that predicts that on, say, January 10, 16xx, Ganymede will wink out of sight at 10:10 pm. Roemer watches, and it actually eclipses at 10:12 pm. Now since Earth is at the same point in space as the last January tenth, that shouldn't matter, but because Jupiter takes over eleven years to orbit the sun, the giant planet's going to be in a much different position on the same date year to year.

So if Kepler's prediction is for a close Earth-to-Jupiter distance, and Roemer's observation is for a distant Earth-to-Jupiter distance, then that would be enough for him to figure out that light is taking time to travel the extra bit (rather than traveling instantaneously), and calculate the speed.

Is that right? If yes, then that makes perfect sense, and I can move on.

If no, then use Smaller Words.

grant hutchison
2009-Apr-27, 08:08 PM
The author of this excellent book writes in a very calculated way. He chooses his words with deliberate and calculated finesse.Well ... I completely disagree. :)
In my opinion he writes very badly, to the extent of being utterly opaque on many occasions. It's almost impossible to understand him if you don't already have some background in the subject. So people shouldn't be discouraged if they don't understand the book, and certainly shouldn't buy the book as an introductory text.
In fact, I'm not sure under what circumstances I'd recommend buying the book. Perhaps as an example of how not to write a popular science book?

Grant Hutchison

grant hutchison
2009-Apr-27, 08:16 PM
So if Kepler's prediction is for a close Earth-to-Jupiter distance, and Roemer's observation is for a distant Earth-to-Jupiter distance, then that would be enough for him to figure out that light is taking time to travel the extra bit (rather than traveling instantaneously), and calculate the speed.

Is that right?Yes. Rømer had a table of Cassini's predictions for Galilean eclipses spanning several years, which Cassini had calculated using simple Keplerian orbits. The tacit assumption in Cassini's tables was that the speed of light was effectively infinite, so that we would see an eclipse the moment it occurred. But Rømer noticed that eclipses came later than predicted when Earth and Jupiter were far apart. He made a specific prediction that an eclipse of Io would occur ten minutes later than Cassini's tables predicted. He was right, and was able to use the mismatch to calculate the speed of light.

Grant Hutchison

Nick Theodorakis
2009-Apr-27, 08:20 PM
Yes. Rømer had a table of Cassini's predictions for Galilean eclipses spanning several years, which Cassini had calculated using simple Keplerian orbits, and (tacitly) assuming that the speed of light was effectively infinite, so that we would see an eclipse the moment it occurred. But Rømer noticed that eclipses came later than predicted when Earth and Jupiter were far apart. He made a specific prediction that an eclipse of Io would occur ten minutes later than Cassini's tables predicted. He was right, and was able to use the mismatch to calculate the speed of light.

Grant Hutchison

Was the scale of the solar system known that well at the time, or did he express c in terms of AU/sec (or something similar) instead of m/sec?

Nick

Edit: nevermind, if I read the whole thread first I would have seen the answer

Argos
2009-Apr-27, 08:20 PM
Well ... I completely disagree. :)
In my opinion he writes very badly, to the extent of being utterly opaque on many occasions.

I agree. It´s bad in English, and it´s a translator´s nightmare. The Portuguese language edition is almost unintelligible, and, thus, almost worthless, if the intent is to make things clearer to the layperson.

grant hutchison
2009-Apr-27, 08:29 PM
Was the scale of the solar system known that well at the time ..,The initial measurement had recently been made, though not by Rømer: Hawking is little misleading in that regard. In fact, Richer and Cassini had triangulated the approximate distance to Mars during the opposition of 1671 1672. Rømer announced his results, building on theirs, in 1676.
Cassini's table of Galilean phenomena, used by Rømer, had in fact been drawn up to allow Richer (in Cayenne) to synchronize his pendulum clock with an identical clock used by Cassini (at the Paris Observatory). Of course, the systematic errors Rømer discovered didn't materially affect the original triangulation, because all that was required was that Richer and Cassini had made simultaneous observations. Any errors arising from light travel time across the figure of the Earth were very small compared to their acknowledged errors in synchronization and triangulation.

Grant Hutchison

jamesabrown
2009-Apr-27, 08:53 PM
Next question, page 31:


Light rays too must follow geodesics in space-time. Again, the fact that space is curved means that light no longer appears to travel in straight lines in space. So general relativity predicts that light should be bent by gravitational fields. For example, the theory predicts that the light cones of points near the sun would be slightly bent inward, on account of the mass of the sun. This means that light from a distant star that happened to pass near the sun would be deflected through a small angle, causing the star to appear in a different position to an observer on the earth. Of course, if the light from the star always passed close to the sun, we would not be able to tell whether the light was being deflected or if instead the star was really where we see it. However, as the earth orbits around the sun, different stars appear to pass behind the sun and have their light deflected. They therefore change their apparent position relative to other stars.

Okay, what does that actually look like through the eyepiece of a telescope. Does the star jump from one position to another as it's light moves away from the gravitational influence of the sun? Or does it slide across space rapidly for a bit, then come to a relative stop? Is there a video demonstration of this I can see; some recording that someone made through their telescope?

Gillianren
2009-Apr-27, 08:57 PM
I agree. It´s bad in English, and it´s a translator´s nightmare.

See, now I'm going to have to read it. But it's going to wait a bit. I've got a lot of other dense nonfiction piled up, not to mention The Canterbury Tales. Too much at once.

hhEb09'1
2009-Apr-27, 09:02 PM
Okay, what does that actually look like through the eyepiece of a telescope. Does the star jump from one position to another as it's light moves away from the gravitational influence of the sun? Or does it slide across space rapidly for a bit, then come to a relative stop?I can't tell what you're asking with these questions. What is the difference between those two?

Maybe use smaller words. :)
Is there a video demonstration of this I can see; some recording that someone made through their telescope?The first time it was done, the stars were photographed very close to the sun--so it had to be done during a solar eclipse. Solar eclipses do not last very long, so the observation of the close-in stars did not last long enough to take a video.

The change in position is very small, so you wouldn't see large jumps, or rapid movement, anyway. As the image of the star gets nearer to the sun, the effect is stronger.

Argos
2009-Apr-27, 09:06 PM
See, now I'm going to have to read it. But it's going to wait a bit. I've got a lot of other dense nonfiction piled up, not to mention The Canterbury Tales. Too much at once.

I think I´ve beaten you Gillian. I´m going through Finnegans Wake. A pain and a delight at once. :)

George
2009-Apr-27, 09:50 PM
Okay, let me repeat your answers back to you and see if I understand it right, because I think I'm missing something. So Roemer has a chart that predicts that on, say, January 10, 16xx, Ganymede will wink out of sight at 10:10 pm. Roemer watches, and it actually eclipses at 10:12 pm. Now since Earth is at the same point in space as the last January tenth, that shouldn't matter, but because Jupiter takes over eleven years to orbit the sun, the giant planet's going to be in a much different position on the same date year to year. The history can be every bit as interesting as the science. :)

You have the right idea, but, in case you are wondering, the time variation from the predicted time would be seen monthly, if not weekly for many weeks. The time variation would be cyclical and this was corelated to the change in distance between Jupiter and Earth.

It, apparently, was Cassini that was first to suggest that the slight time variations were due to the finite speed of light, and stated it in a 1675 publication. However, he seems to have not held to this view and the credit went to Romer, who published in 1676 with better data, which came from himself and a non-captain Picard. [Or was he a captain? :) ]


So if Kepler's prediction is for a close Earth-to-Jupiter distance, and Roemer's observation is for a distant Earth-to-Jupiter distance, then that would be enough for him to figure out that light is taking time to travel the extra bit (rather than traveling instantaneously), and calculate the speed.
Apparently, he didn't bother to do the calculation, though, if true, is quite suprising. Using their data, it was Huygens that did the first speed of light calculation, but slightly muffed it.

Interestingly, it was Galileo that calculated the ephemerides of his Medician moons and came close to selling these to Spain for navigational purposes. Assuming a navigator could observe the relative positions of these moons, he would know what time it was more accurately than any chronometer known. Spain had recently been burned on another scientific deal, I think, and was dubious it would work. Also, observing moons from a rocking ship wouldn't be a simple task, no doubt.

grant hutchison
2009-Apr-27, 10:38 PM
Apparently, he didn't bother to do the calculation, though, if true, is quite suprising.Rømer's notebooks show that he did, in fact, do the calculation, coming up with a figure of 1091 Earth diameters per minute, distinctly on the low side of the modern value. Huygens came up with an even lower figure of 16⅔ earth diameters per second.

Grant Hutchison

George
2009-Apr-27, 11:39 PM
Rømer's notebooks show that he did, in fact, do the calculation, coming up with a figure of 1091 Earth diameters per minute, distinctly on the low side of the modern value. Huygens came up with an even lower figure of 16⅔ earth diameters per second. That makes more sense. He actually did the calculation, but I assume he did not publish it.

There was some controversy about the speed of light, naturally. Hooke claimed it was instaneous, and Newton stated in Principia (1st edition, 1686) that the speed was one Earth orbital diameter per 22 minutes, as per the claim of Huygens 9 years earlier.

However, there seems to be some conflict in stories as to whether it was Huygens or Romer that calculated the 22 minute time for light to cross Earth's orbital dia. Wiki (http://en.wikipedia.org/wiki/Ole_R%C3%B8mer), *cough*, shows Romer as having the 22 min. value, and another site (http://www.rundetaarn.dk/engelsk/observatorium/light.htm) shows it was Huygens that found this value. If ther later is true, then Huygens value is more accurate than Romer's, contrary to my earlier muffing comment, which means, of course, Wiki *breath taken* would be wrong here too.

Regarding Hawkin's quote, "His measurements of the variations in the distance of the earth from Jupiter were, however, not very accurate, and so his value for the speed of light was 140,000 miles per second, compared to the modern value of 186,000 miles per second." It seems to me that Romer's value would have been closer to 135,000 miles per second given that 1019 Earth diameters per minute equates to 134,558 miles per second, and the diameter of the Earth was fairly accurate back then, I would assume. Was the orbital distance fairly accurate back then?



tide for him. {Care to rate that pun? :) Of course, the acceptance (by the Church) of the Tychonic model would still have likely kept him struggling with the doubters.}]

Hornblower
2009-Apr-28, 02:04 AM
tide for him. {Care to rate that pun? :) Of course, the acceptance (by the Church) of the Tychonic model would still have likely kept him struggling with the doubters.}]
This time variation would not distinguish between a heliocentric and a geocentric model. In the latter, Jupiter would be moving in a large epicycle, the center of which would be moving in the deferent orbit around the Earth. The variation in distance between Earth and Jupiter would be the same either way.

Cougar
2009-Apr-28, 02:28 AM
Well ... I completely disagree. :)
In my opinion he writes very badly, to the extent of being utterly opaque on many occasions. It's almost impossible to understand him if you don't already have some background in the subject. So people shouldn't be discouraged if they don't understand the book, and certainly shouldn't buy the book as an introductory text.
In fact, I'm not sure under what circumstances I'd recommend buying the book. Perhaps as an example of how not to write a popular science book?

Well, I've got to stop my reading of this thread right here and respond to Grant's characterization of Hawking's A Brief History of Time. I completely and totally agree. :exclaim: I have read well over 100 contemporary popular science books in the last decade or so, and Hawking's Brief History is quite poor in comparison to the many excellent books available that describe to a lay audience the fairly current state of knowledge of... what field would you like? Physics? Astronomy? Cosmology? Astrophysics? Hawking is well known for his brilliance as a theoretical physicist, but not so much for his writing. Pick up something by Timothy Ferris or Paul Davies or Rocky Kolb or any of the Nobelists - Lederman, Gell-Mann, Feynman (well, he didn't write, he was collected), Weinberg, Schwinger, Mather, Smoot, t'Hooft....

...or there's always The Thermodynamics of Pizza, Essays on Science and Everyday Life [1991] -- Harold J. Morowitz. :)

AndrewJ
2009-Apr-28, 04:46 AM
I enjoy Hawking's writing style. Apart from that thing about "the mind of God" (I would add a puke smiley if I knew how).

George
2009-Apr-28, 04:58 AM
This time variation would not distinguish between a heliocentric and a geocentric model. In the latter, Jupiter would be moving in a large epicycle, the center of which would be moving in the deferent orbit around the Earth. The variation in distance between Earth and Jupiter would be the same either way.
Good point, and he understood this Ptolemaic model. I had not considered that the model was not only quite good at relative positioning of the planets, but also good with relative changes in distances, though actual distances were not accurately determined then for Jupiter.

George
2009-Apr-28, 05:01 AM
Well, I've got to stop my reading of this thread right here and respond to Grant's characterization of Hawking's A Brief History of Time. I completely and totally agree. :exclaim: I have read well over 100 contemporary popular science books in the last decade or so, and Hawking's Brief History is quite poor in comparison to the many excellent books available that describe to a lay audience the fairly current state of knowledge of... what field would you like? Physics? Astronomy? Cosmology? Astrophysics? Hawking is well known for his brilliance as a theoretical physicist, but not so much for his writing. Pick up something by Timothy Ferris or Paul Davies or Rocky Kolb or any of the Nobelists - Lederman, Gell-Mann, Feynman (well, he didn't write, he was collected), Weinberg, Schwinger, Mather, Smoot, t'Hooft....

...or there's always The Thermodynamics of Pizza, Essays on Science and Everyday Life [1991] -- Harold J. Morowitz. :)
I feel better that so many feel as do I regarding his works. They seemed to be teasers for the heavy hittters, more than informative about modern physics. Perhaps sitting in Newton's chair and understanding Principia has something to do with it.:)

Tog
2009-Apr-28, 06:33 AM
Next question, page 31:



Okay, what does that actually look like through the eyepiece of a telescope. Does the star jump from one position to another as it's light moves away from the gravitational influence of the sun? Or does it slide across space rapidly for a bit, then come to a relative stop? Is there a video demonstration of this I can see; some recording that someone made through their telescope?

I'll take a stab at this one.

The change in position would be very small as has been said, but it would also be a gradual thing.

Let's say you were to take a yard or meter stick and nail it to a door frame so that one end can't possibly move. Sighting down the stick points from the door frame to the kitchen light switch. The end of the stick as seen from the switch is the position of the star as seen from Earth.

Now, exert a small force on the middle of the stick. This is the gravity of the Sun. From Earth it seems the star shifted to one side, but only a bit. We know the end of the stick lines up exactly with the door frame, but when we look at it with the pressure applied, the end of the stick is closer to the source of the gravity (further from the finger doing the pushing).

For the speed at which this all happens, consider the angular speed of the Earth as it orbits. On June 1 the star looks like it's where it belongs. One June 2nd, it's still where it belongs. On June 3rd (Eclipse day) it seems to be a bit closer to the sun than it should be. After the eclipse, it's still closer to the sun, but now it's on the other side. On June 4th, every thing is back where it belongs.

Part of the problem in seeing this as a "jump" comes from the fact that the Sun is in the way. We can't see the star have it's apparent shift because it's too close to the Sun. We can't view it from anywhere other than near the Sun, because, well, it's the proximity of the Sun that causes the effect.

As always when I try to give real answers, see below for corrections.

astromark
2009-Apr-28, 08:06 AM
For what its worth (nothing)...No corrections necessary. What does that mean. It means I understood you., and what you have said. I enjoyed your simple approach.
Earlier I had said I found the writings of 'A brief history of time' easy to follow. I now understand that for most, others have said it better. Its a subject I need to read more of before I can comment further. Not having read the works of Timothy Ferris or Paul Davies Rocky Kolb and all...
The original concept of the speed of light making a apparent error of previous predictions not considering the light travel time is interesting when the 16 odd minutes would be disconcerting if not understood.

grant hutchison
2009-Apr-28, 09:35 AM
Okay, what does that actually look like through the eyepiece of a telescope. Does the star jump from one position to another as it's light moves away from the gravitational influence of the sun? Or does it slide across space rapidly for a bit, then come to a relative stop? Is there a video demonstration of this I can see; some recording that someone made through their telescope?No recordings I'm aware of. As hhEb09'1 implies, the practicalities (short eclipse, slow-moving sun) involve simply measuring the position of the stars around the sun, and comparing that to records of their relative position when the sun isn't there (regular night-time observation).
If you could watch it happen (say, with a superdense mass moving quickly), you'd see stars apparently linger close to the margins of the mass: taking extra time to disappear behind it, and hanging around in the vicinity of its trailing rim after they reappeared. This is because stars that "should" be hidden from view behind the mass are actually lifted into view by the deflection of light: we get to see them for longer than straight-line geometry would suggest. In extreme situations, such as exist around a black hole, one might even see the star "reappear" at the trailing side of the mass before it has disappeared at the leading edge: we see a double image of the same star, as its light reaches us via two curved paths.
All of this happens smoothly, since spacetime curvature is smooth and the resulting curvature of the light rays varies smoothly and continuously.

Grant Hutchison

jamesabrown
2009-Apr-28, 02:08 PM
I can't tell what you're asking with these questions. What is the difference between those two?

Maybe use smaller words. :)

Sorry. If I'm looking at a star that's an arc-second away from the edge of the sun, and the sun moves to the left, will the star suddenly jump to, say, two arc-seconds away, or will it visibly move to the new position and then hold steady?

I can see how looking at stars close to the sun would be difficult.


The first time it was done, the stars were photographed very close to the sun--so it had to be done during a solar eclipse. Solar eclipses do not last very long, so the observation of the close-in stars did not last long enough to take a video.

But there's a solar eclipse every couple of years. Hasn't someone taken a video since then?


The change in position is very small, so you wouldn't see large jumps, or rapid movement, anyway. As the image of the star gets nearer to the sun, the effect is stronger.

Okay, but what does that effect look like? I'm not trying to be difficult, so I apologize if I'm coming across that way. I understand the principle; I'm just looking for a visual aid. Even a CGI simulation (based on real-world observations, of course) would be cool.

Although come to think of it, maybe I don't understand the principle. It doesn't make sense to me that a massless photon of light can be gravitationally influenced.

And for that matter, if a star's gravity influences light, does the light influence the star in the same way that a planet and its moon influence each other gravitationally? I'm betting no.

jamesabrown
2009-Apr-28, 02:20 PM
Apparently, he didn't bother to do the calculation, though, if true, is quite suprising. Using their data, it was Huygens that did the first speed of light calculation, but slightly muffed it.

Interesting. Hawking indicated it was Roemer's calculations. (Wiki (http://en.wikipedia.org/wiki/Speed_of_light#Astronomical_techniques)says you're both right: Roemer calculated the ratio between the speed of light and the speed of Earth's orbit. Huygens calculated the absolute speed of light, but based on a misinterpretation of Roemer's figures and thus arrived at a figure too low--although still a mind-blazingly fast 136K miles per second.)


Interestingly, it was Galileo that calculated the ephemerides of his Medician moons and came close to selling these to Spain for navigational purposes. Assuming a navigator could observe the relative positions of these moons, he would know what time it was more accurately than any chronometer known. Spain had recently been burned on another scientific deal, I think, and was dubious it would work. Also, observing moons from a rocking ship wouldn't be a simple task, no doubt.

That's very interesting. It always pleases me to read accounts of theoretical science being used to make scads of money. I like to remind myself of such things when people question the value of theoretical science.

George
2009-Apr-28, 02:52 PM
Interesting. Hawking indicated it was Roemer's calculations. (Wiki (http://en.wikipedia.org/wiki/Speed_of_light#Astronomical_techniques)says you're both right: Roemer calculated the ratio between the speed of light and the speed of Earth's orbit. Huygens calculated the absolute speed of light, but based on a misinterpretation of Roemer's figures and thus arrived at a figure too low--although still a mind-blazingly fast 136K miles per second.) As Grant has appropriately pointed out in the past, Wiki is not always the best source for detail information. [That was the humor behind my "cough", as he knows I know he knows it. :)] It would be interesting to hear the correct version, whatever it may be. Huygens may have had the more correct answer after all, though they were all in the ballpark, excluding those that held to an infinite speed for light (eg. Hooke).


That's very interesting. It always pleases me to read accounts of theoretical science being used to make scads of money. I like to remind myself of such things when people question the value of theoretical science. Galileo was always cognitive of how to capitalize on his knowledge, and he was very skillful in design and, possbily, fabrication. After his father passed-away, he was burdened with a great deal of debt in the form of his sister's sizeable promised dowry, and his brother was of no help. His honor meant a lot to him, apparently, and he seemed to manage to uphold the dowry requirements (though it was a troublesome affair). His marketing of his first (or second) telescope to beat the competition to the City of Florence [Oops, Venice, not Florence] is quite a story. This alone made him somewhat famous, but also got him in trouble -- a routine for him for most his life, I think.

grant hutchison
2009-Apr-28, 03:15 PM
As Grant has appropriately pointed out in the past, Wiki is not always the best source for detail information. [That was the humor behind my "cough", as he knows I know he knows it. :)] It would be interesting to hear the correct version, whatever it may be. Huygens may have had the more correct answer after all, though they were all in the ballpark, excluding those that held to an infinite speed for light (eg. Hooke).A useful exploration of the historical documentation is here (http://www.bibli.obspm.fr/Bobis%20and%20Lequeux.pdf) (2.3MB pdf). Unfortunately, the majority of Rømer's notes were lost in the Fire of Copenhagen, so the record for him is patchy and poorly dated.

Grant Hutchison

George
2009-Apr-28, 03:19 PM
A useful exploration of the historical documentation is here (http://www.bibli.obspm.fr/Bobis%20and%20Lequeux.pdf) (2.3MB pdf). Excellent, thanks.


Unfortunately, the majority of Rømer's notes were lost in the Fire of Copenhagen, so the record for him is patchy and poorly dated. Ouch, what a loss. :(

Sam5
2009-Apr-28, 03:51 PM
Sorry. If I'm looking at a star that's an arc-second away from the edge of the sun, and the sun moves to the left, will the star suddenly jump to, say, two arc-seconds away, or will it visibly move to the new position and then hold steady?

No, it wouldn’t suddenly jump. The effect is so slight that I don’t think it can be noticed as any kind of moving event or a change of position event in a video.

This following link shows an illustration of the effect. The star’s position is calculated to be closer to or behind the sun, as seen from our viewing position, but the still photos taken during and eclipse shows it (visually) to be a little further away from the body of the sun than it actually is in space.

http://www.astro.cornell.edu/academics/courses/astro201/g_lens_sun.htm

cjameshuff
2009-Apr-28, 04:16 PM
Sorry. If I'm looking at a star that's an arc-second away from the edge of the sun, and the sun moves to the left, will the star suddenly jump to, say, two arc-seconds away, or will it visibly move to the new position and then hold steady?

You seem to be asking if there are discrete positions that the star holds. No, the star does not move in "steps", its apparent position changes continuously.



Okay, but what does that effect look like? I'm not trying to be difficult, so I apologize if I'm coming across that way. I understand the principle; I'm just looking for a visual aid. Even a CGI simulation (based on real-world observations, of course) would be cool.

Stars are "pushed away" from the center of the sun, bringing stars just behind the edge of the sun into view and making other nearby stars appear further from the sun than would be expected if light traveled in straight lines. Lines of sight become straighter as their closest approach to the sun widens.

jamesabrown
2009-Apr-28, 04:18 PM
No, it wouldn’t suddenly jump. The effect is so slight that I don’t think it can be noticed as any kind of moving event or a change of position event in a video.

This following link shows an illustration of the effect. The star’s position is calculated to be closer to or behind the sun, as seen from our viewing position, but the still photos taken during and eclipse shows it (visually) to be a little further away from the body of the sun than it actually is in space.

http://www.astro.cornell.edu/academics/courses/astro201/g_lens_sun.htm

Thanks, Sam. There's a similar illustration in BHofT that shows the same thing. I realize the illustrations are not to scale, but the way they are shown it would appear to be a noticeable difference. I imagine as the sun moves across a field of background stars, that around the rim of the sun the stars jump and dance (although admittedly this would be difficult to observe in broad daylight.)

What about SOHO? Doesn't it block out the sun so we can study the corona? Can it see the stars behind the sun's rim?

Sam5
2009-Apr-28, 04:30 PM
Thanks, Sam. There's a similar illustration in BHofT that shows the same thing. I realize the illustrations are not to scale, but the way they are shown it would appear to be a noticeable difference. I imagine as the sun moves across a field of background stars, that around the rim of the sun the stars jump and dance (although admittedly this would be difficult to observe in broad daylight.)

What about SOHO? Doesn't it block out the sun so we can study the corona? Can it see the stars behind the sun's rim?

This is supposed to be a copy of one of Eddington’s glass plates of the 1919 eclipse. This is a negative image, not a positive image:

http://upload.wikimedia.org/wikipedia/commons/d/da/1919_eclipse_negative.jpg

If you enlarge the image and look carefully you can see several pairs of double lines drawn on the negative, with a small black dot in the middle of the space between each pair of lines. Those were the stars whose positions were measured. Again, the deflection of their positions was very slight, but it was measurable.

I think that in the Soho pictures, like this one......

http://sohowww.nascom.nasa.gov/pickoftheweek/

.... the mask over the sun is too large for us to be able to see stars that are very close to the sun, so the mask covers up those stars. I think the small circle in the center of the mask represents the size of the sun’s disk.

grant hutchison
2009-Apr-28, 05:16 PM
I realize the illustrations are not to scale, but the way they are shown it would appear to be a noticeable difference. I imagine as the sun moves across a field of background stars, that around the rim of the sun the stars jump and dance (although admittedly this would be difficult to observe in broad daylight.)They would not "jump and dance", I'm afraid. There would be a very slight change in their apparent position, but that would happen smoothly and progressively, as I tried to describe in an earlier post (http://www.bautforum.com/1478666-post26.html).
The predicted change in position for starlight just grazing the limb of the sun is 1.75 seconds of arc, which is about a thousandth of the apparent diameter of the sun: not something you'd notice with the naked eye, even if the sun were a smooth black sphere.

Grant Hutchison

jamesabrown
2009-May-06, 03:50 PM
I'm pretty sure this chapter is going to be slow-going for me. Fortunately, I have you fine intelligent folks to hold my hand through the scary parts.


The doctrine of scientific determinism was strongly resisted by many people, who felt that it infringed God's freedom to intervene in the world, but it remained the standard assumption of science until the early years of this century. One of the first indications that this belief would have to be abandoned came when calculations by the British scientists Lord Rayleigh and Sir James Jeans suggested that a hot object, or body, such as a star, must radiate energy at an infinite rate. According to the laws we believed at the time, a hot body ought to give off electromagnetic waves (such as radio waves, visible light, or X-rays) equally at all frequencies. For example, a hot body should radiate the same amount of energy in waves with frequencies between one and two million million waves per second as in waves with frequencies between two and three million million waves per second. Now since the number of waves a second is unlimited, this would mean that the total energy radiated would be infinite.

Okay, so I see from glancing ahead that this is "an obviously ridiculous result." So I understand that this is one of those "we used to think X; isn't that silly?" statements akin to the world is flat and orbited by the sun. Looking back at erroneous beliefs shows us how far we've come, and that's a good thing.

What I don't understand is where this belief came from in the first place, the idea that stars radiate in all frequencies equally? What made anyone conclude this? Was this a philosophical conclusion like Aristotle's notion that everything in space is spherical because spheres are perfect and so is God's heaven? Or was this a conclusion of inaccurate observations?

And what does Hawking mean by "according to the laws we believed"? Can something properly be called a law if it's also a belief? Do we currently believe in the laws of gravity but may one day look back and say, "Isn't that silly?"

Nick Theodorakis
2009-May-06, 05:09 PM
I'm pretty sure this chapter is going to be slow-going for me. Fortunately, I have you fine intelligent folks to hold my hand through the scary parts.



Okay, so I see from glancing ahead that this is "an obviously ridiculous result." So I understand that this is one of those "we used to think X; isn't that silly?" statements akin to the world is flat and orbited by the sun. Looking back at erroneous beliefs shows us how far we've come, and that's a good thing.

What I don't understand is where this belief came from in the first place, the idea that stars radiate in all frequencies equally? What made anyone conclude this? Was this a philosophical conclusion like Aristotle's notion that everything in space is spherical because spheres are perfect and so is God's heaven? Or was this a conclusion of inaccurate observations?

And what does Hawking mean by "according to the laws we believed"? Can something properly be called a law if it's also a belief? Do we currently believe in the laws of gravity but may one day look back and say, "Isn't that silly?"

What was missing was the attempt to formulate blackbody radiation predictions according to classical mechanics (the Rayleigh-Jeans Law (http://en.wikipedia.org/wiki/Rayleigh%E2%80%93Jeans_law)) did not take into account that light was quantized (which was not known at the time). Without this assumption, the prediction suffers from what is called the ultraviolet catastrophe (http://en.wikipedia.org/wiki/Ultraviolet_catastrophe), in which energy form shorter wavelengths contribute an increasingly larger amount of energy, resulting in an infinite amount of energy emitted. Since this is manifestly opposed to observation, obviously something was missing, although the Rayleigh-Jeans Law fit for lower frequencies. In contrast, Wien's Law (http://en.wikipedia.org/wiki/Wien_approximation) fit for high frequencies but not for low ones.

Planck was able to derive a relationship (now called Planck's Law (http://en.wikipedia.org/wiki/Planck%27s_law)) that fit the real world data very accurately, by assuming that the energy released at each wavelength was quantized into integral units that were proportional to the wavelength.

For Planck, it was probably more like an inspired guess than a deep insight, but Einstein and others were able to show that Planck's Law worked because light energy was emitted in discrete units now called photons.

Nick

robross
2009-May-06, 05:46 PM
What was missing was the attempt to formulate blackbody radiation predictions according to classical mechanics (the Rayleigh-Jeans Law (http://en.wikipedia.org/wiki/Rayleigh%E2%80%93Jeans_law)) did not take into account that light was quantized (which was not known at the time). Without this assumption, the prediction suffers from what is called the ultraviolet catastrophe (http://en.wikipedia.org/wiki/Ultraviolet_catastrophe), in which energy form shorter wavelengths contribute an increasingly larger amount of energy, resulting in an infinite amount of energy emitted. Since this is manifestly opposed to observation, obviously something was missing, although the Rayleigh-Jeans Law fit for lower frequencies. In contrast, Wien's Law (http://en.wikipedia.org/wiki/Wien_approximation) fit for high frequencies but not for low ones.

Planck was able to derive a relationship (now called Planck's Law (http://en.wikipedia.org/wiki/Planck%27s_law)) that fit the real world data very accurately, by assuming that the energy released at each wavelength was quantized into integral units that were proportional to the wavelength.

For Planck, it was probably more like an inspired guess than a deep insight, but Einstein and others were able to show that Planck's Law worked because light energy was emitted in discrete units now called photons.

Nick

This sounds similar to the problem we have with understanding black holes, where density and curvature go to infinity at a singularity. I wonder if GR and QM unification will make those infinities disappear, like they did in the ultraviolet catastrophe when QM was developed?

jamesabrown
2009-May-07, 06:54 PM
So building on the previous replies (Thanks, Nick), we continue to the next paragraph:


In order to avoid this obviously ridiculous result, the German scientist Max Planck suggested in 1900 that light, X-rays, and other waves could not be emitted at an arbitrary rate, but only in certain packets that he called quanta. Moreover, each quantum had a certain amount of energy that was greater the higher the frequency of the waves, so at a high enough frequency the emission of a single quantum would require more energy than was available. Thus the radiation at high frequencies would be reduced, and so the rate at which the body lost energy would be finite.

Okay, for starters, I'm having trouble equating the notion that stars radiate energy "equally at all frequencies" (from the previous paragraph) with "at an arbitrary rate." Those two phrases don't sound synonymous to me.

Next, I'm stumbling on the word 'packets.' I work in IT, so I think of network packets being tiny pieces of data that can be transferred across a network in a random order. Software takes a large file and breaks it down into small packets where they are reassembled elsewhere. A network packet could be as small as a single bit, I suppose, although header information and whatnot would make the packet size itself much larger.

So what is meant by 'packets'? Wikipedia calls a quantum (http://en.wikipedia.org/wiki/Quanta)"an indivisible entity." Since atoms are traditionally called indivisible units of matter (until recently), would a quantum be an atom of energy, aka, a photon?

While I'm asking questions, are quanta discrete in that they can be counted?

Nick Theodorakis
2009-May-07, 07:35 PM
So building on the previous replies (Thanks, Nick), we continue to the next paragraph:



Okay, for starters, I'm having trouble equating the notion that stars radiate energy "equally at all frequencies" (from the previous paragraph) with "at an arbitrary rate." Those two phrases don't sound synonymous to me.


I think that might just be clumsy phrasing. Perhaps he meant "arbitrarily high" rather than "arbitrary."



...
So what is meant by 'packets'? Wikipedia calls a quantum (http://en.wikipedia.org/wiki/Quanta)"an indivisible entity." Since atoms are traditionally called indivisible units of matter (until recently), would a quantum be an atom of energy, aka, a photon?

Yes.


While I'm asking questions, are quanta discrete in that they can be counted?

Yes. A photomultiplier tube can count them, for example.

Nick

Jeff Root
2009-May-07, 08:33 PM
In order to avoid this obviously ridiculous result, the German scientist
Max Planck suggested in 1900 that light, X-rays, and other waves could
not be emitted at an arbitrary rate, but only in certain packets that he
called quanta.
Okay, for starters, I'm having trouble equating the notion that stars
radiate energy "equally at all frequencies" (from the previous paragraph)
with "at an arbitrary rate." Those two phrases don't sound synonymous
to me.
This is standard use of the term "arbitrary" as used in physics, which
as far as I know is not different from its general use.

I can throw baseballs equally far at all frequencies. For example, I
can throw baseballs over the wall at a rate of one every ten seconds,
or one every second, or ten per second... I can throw balls over the
wall at an arbitrary rate. You name it; I can do it.



Next, I'm stumbling on the word 'packets.'
No need to do that-- It's a simple concept. Quantum = packet =
chunk = individual unit = smallest lump of whatever. In this case, the
smallest lump of energy. However, different lumps can be different
sizes. A lump of 3 MHz electromagnetic energy is a larger amount of
energy than a lump of 3 kHz energy. But whatever size lump you
are looking at, one whole lump is the minimum you can see. You
can't see half of a lump, or 9/10 of a lump. It is either one whole
lump, or none.

-- Jeff, in Minneapolis

jamesabrown
2009-May-11, 07:18 PM
From P. 58:

After a brief explanation of the two-slit experiment:


The remarkable thing is that one gets exactly the same kind of fringes if one replaces the source of light by a source of particles such as electrons with a definite speed (this means that the corresponding waves have a definite length.) It seems the more peculiar because if one only has one slit, one does not get any fringes, just a uniform distribution of electrons across the screen. One might therefore think that opening another slit would just increase the number of electrons hitting each point of the screen, but, because of interference, it actually decreases it in places. If electrons are sent through the slits one at a time, one would expect each to pass through one slit or the other, and so behave just as if the slit it passed through were the only one there--giving a uniform distribution on the screen. In reality, however, even when the electrons are sent one at a time, the fringes still appear. Each electron, therefore, must be passing through both slits at the same time!

Okay, so obviously, by the style of writing, this is not the expected effect. But seriously? Both slits at the same time? How is that possible?

Nick Theodorakis
2009-May-11, 07:27 PM
...
Okay, so obviously, by the style of writing, this is not the expected effect. But seriously? Both slits at the same time? How is that possible?

I think it's impossible to say what exactly the electron is doing, because any descriptive analogy that depends on macroscopic behavior is probably not applicable at the quantum level. But simply put, if you shoot electrons (or photons, for that matter) through a 2-slit apparatus, you see them interfere with each other in the manner that waves do, even if the electron flux is low enough such that only one electron is likely to be passing through at a time. So does that mean that the electron travels through both slits at the same time? Mu. All you know is that the electrons are emitted here and detected there, and that macroscopic analogies that attempt to describe what happens in between are inadequate.

Nick

speedfreek
2009-May-11, 07:34 PM
Or to put it inadequately, each electron acts as if it somehow knows it is part of a wave, or acts as if it went through both slits and interfered with itself!

DrRocket
2009-May-11, 08:13 PM
I think it's impossible to say what exactly the electron is doing, because any descriptive analogy that depends on macroscopic behavior is probably not applicable at the quantum level. But simply put, if you shoot electrons (or photons, for that matter) through a 2-slit apparatus, you see them interfere with each other in the manner that waves do, even if the electron flux is low enough such that only one electron is likely to be passing through at a time. So does that mean that the electron travels through both slits at the same time? Mu. All you know is that the electrons are emitted here and detected there, and that macroscopic analogies that attempt to describe what happens in between are inadequate.

Nick

What you are discussing is what are often called "interpretations of quantum mechanics." The interpretations recognize that the mathematics that describes quantum phenomena seems to be correct, but is not explainable in classical terms. They tend to try to describe processes that are consistent with the mathematics and that use only "everyday language". That results in some fairly strange verbiage.

There are photos of slit experiments, using electrons rather than photons, that demonstrate the development of the "wavelike" interference patterns, one particle at a time. The particles seem to be, well particles. The dots on the screen are discrete dots, with nary a hint of a wave at each point of impact. Only in the aggregate is there "wavelike" behavior. Here is a picture from Wiki http://en.wikipedia.org/wiki/Double-slit_experiment
http://upload.wikimedia.org/wikipedia/commons/thumb/7/7e/Double-slit_experiment_results_Tanamura_2.jpg/200px-Double-slit_experiment_results_Tanamura_2.jpg (http://www.bautforum.com/wiki/File:Double-slit_experiment_results_Tanamura_2.jpg) http://www.bautforum.com/skins-1.5/common/images/magnify-clip.png (http://www.bautforum.com/wiki/File:Double-slit_experiment_results_Tanamura_2.jpg)
Electron buildup over time


You can find similar photos in the book More Than One Mystery by Silverman.


As you say, the macroscopic analogies are inadequate, at best. At worst, they get people arguing about the interpretations, which have NO bearing on the predictions.

A classic example is the "many worlds" interpretation of Hugh Everett. That was good work, but the discussions that one often finds of that work are out in left field. While the interpretation is interesting, it provides nothing more and nothing less than an alternate way of looking at quantum mechanics that provides precisely the same predictions as the usual interpretations.

tdvance
2009-May-11, 09:44 PM
From P. 58:

After a brief explanation of the two-slit experiment:



Okay, so obviously, by the style of writing, this is not the expected effect. But seriously? Both slits at the same time? How is that possible?

Now you get to the place where Quantum Physics is so weird that even Quantum Physicists sometimes just say, "just use the equations, what they mean makes no sense". General Relativity seems funny, but Quantum Mechanics is so far removed from everyday experience (things apparently in two places at once, things moving from A to B without touching anything in between, particles that seem to predict the future, etc.) that the only reason it's accepted is that--the mathematics (appear to be) consistent, and it fits observations to many, many decimal places.

DrRocket
2009-May-12, 03:39 AM
Now you get to the place where Quantum Physics is so weird that even Quantum Physicists sometimes just say, "just use the equations, what they mean makes no sense". General Relativity seems funny, but Quantum Mechanics is so far removed from everyday experience (things apparently in two places at once, things moving from A to B without touching anything in between, particles that seem to predict the future, etc.) that the only reason it's accepted is that--the mathematics (appear to be) consistent, and it fits observations to many, many decimal places.




"There was a time when the newspapers said that only twelve men understood the theory of relativity. I do not believe that there ever was such a time. There might have been a time when only one man did, because he was the only guy who caught on, before he wrote his paper. But after people read the paper, a lot of people understood the theory of relativity in some way or other, certainly more than twelve. On the other hand, I can safely say that nobody understands quantum mechanics." – Richard P. Feynman in The Character of Physical Law

loglo
2009-May-12, 10:35 AM
David Deutsch " Physics isn't hard to understand, it's just weird."

Cougar
2009-May-12, 02:11 PM
"Atoms are not things." -- Heisenberg

jamesabrown
2009-Jun-15, 06:42 PM
Moving on to Chapter 5: Elementary Particles and the Forces of Nature.

P. 66:


Using the wave/particle duality discussed in the last chapter, everything in the universe, including light and gravity, can be described in terms of particles.

Seriously? Have we established that gravity is particles?


These particles have a property called spin. One way of thinking of spin is to imagine the particles as little tops spinning about an axis. However, this can be misleading, because quantum mechanics tells us that the particles do not have any well-defined axis. What the spin of a particle really tells us is what the particle looks like from different directions. A particle of spin 0 is like a dot; it looks the same from any direction. On the other hand, a particle of spin 1 is like an arrow; it looks different from different directions. Only if one turns it round a complete revolution (360 degrees) does the particle look the same. A particle of spin 2 is like a double-headed arrow; it looks the same if one turns it round half a revolution (180 degrees). Similarly, high spin particles look the same if one turns them through smaller fractions of a complete revolution. All this seems fairly straightforward, but the remarkable fact is that there are particles that do not look the same if one turns them through just one revolution: you have to turn them through two complete revolutions! Such particles are said to have spin 1/2.


I've learned some reliable land markers in this book. When Hawking uses an exclamation point, that's where I will stop and say, "Huh?" Then I'll post my question here, and you kind folks will repeat what he said in your own words (meaning, you'll post more exclamation points.) Then I'll swallow hard and press on.

So first he says particles spin. Then he says, Not really--they don't have an axis; spin is just a figure of speech. Then, to describe this non-spin, he uses illustrations of things spinning. Then, just to keep me off-balance, he uses an illustration of an impossible thing spinning.

Just more of that wacky quantum mechanics, I suppose.

Tucson_Tim
2009-Jun-15, 06:49 PM
And I thought I was the only person who had trouble reading A Brief History of Time. I was lost by the 2nd or 3rd chapter.

jete
2009-Jun-18, 03:34 AM
The thread on “Brief History of Time” is a very interesting thread, raises a few questions for me.


This following link shows an illustration of the effect. The star’s position is calculated to be closer to or behind the sun, as seen from our viewing position, but the still photos taken during and eclipse shows it (visually) to be a little further away from the body of the sun than it actually is in space.

If the angle of deflection of light from a star “hidden” behind the sun is 7/4 seconds of arc relative to “actual light path” (i.e. Cornell.edu diagram)
1. Is there a similar, but opposite (directionally), angle of deflection for a star that has a actual position along a line of sight that is close to but not hidden behind the sun? In other words if the star were say along a line of sight that was less than 7/4 seconds of relative arc from the disc of the sun, would it appear visually closer than that due to the same effect?
2. Is there a similar angle of deflection for a star, or planet for that matter, that is “hidden” behind the moon? (I realize that sun has a mass of about 1.989 x 10^30 kg and the moon has a mass of about 7.347 × 10^22 kg which is some 2.707 x10^7 times smaller than the sun) I would calculate then that the angle of deflection would be in the magnitude of about 10^7 times smaller, perhaps too small to detect, but does it occur is what I wonder (and suspect).

Cougar
2009-Jun-18, 02:10 PM
"Using the wave/particle duality discussed in the last chapter, everything in the universe, including light and gravity, can be described in terms of particles."
Seriously? Have we established that gravity is particles?
Well, he said it can be described in terms of particles. He didn't say it is particles. In QM, this difference seems to play larger than 'normal'.

cfgauss
2009-Jun-18, 02:26 PM
Moving on to Chapter 5: Elementary Particles and the Forces of Nature.

P. 66:



Seriously? Have we established that gravity is particles?



I've learned some reliable land markers in this book. When Hawking uses an exclamation point, that's where I will stop and say, "Huh?" Then I'll post my question here, and you kind folks will repeat what he said in your own words (meaning, you'll post more exclamation points.) Then I'll swallow hard and press on.

So first he says particles spin. Then he says, Not really--they don't have an axis; spin is just a figure of speech. Then, to describe this non-spin, he uses illustrations of things spinning. Then, just to keep me off-balance, he uses an illustration of an impossible thing spinning.

Just more of that wacky quantum mechanics, I suppose.

First, when physicists use the word "particles" we don't mean particle in the sense of Newtonian mechanics. Now-a-days, when we say "particle" we mean "thing that satisfies these equations" (well, technically, the parts of the equations that have specific group transformation properties). It seemed stupid for us to make up a new name, so we just kept calling things particles because it doesn't really matter since we all know what we're doing (hopefully).

The spin thing confuses a lot of people. The thing is, spin really is angular momentum in every way except that it isn't angular momentum. It satisfies all of the same relationships and equations as angular momentum, except it does not correspond to motions in "external" space, but in some "internal" configuration space.

Hornblower
2009-Jun-18, 03:43 PM
The thread on “Brief History of Time” is a very interesting thread, raises a few questions for me.



If the angle of deflection of light from a star “hidden” behind the sun is 7/4 seconds of arc relative to “actual light path” (i.e. Cornell.edu diagram)
1. Is there a similar, but opposite (directionally), angle of deflection for a star that has a actual position along a line of sight that is close to but not hidden behind the sun? In other words if the star were say along a line of sight that was less than 7/4 seconds of relative arc from the disc of the sun, would it appear visually closer than that due to the same effect?

No, the deflection will be in the same direction, but by a smaller amount, as the line of sight is moved farther from the Sun.


2. Is there a similar angle of deflection for a star, or planet for that matter, that is “hidden” behind the moon? (I realize that sun has a mass of about 1.989 x 10^30 kg and the moon has a mass of about 7.347 × 10^22 kg which is some 2.707 x10^7 times smaller than the sun) I would calculate then that the angle of deflection would be in the magnitude of about 10^7 times smaller, perhaps too small to detect, but does it occur is what I wonder (and suspect).It would not be that small. If Wiki is correct the angle of deflection of a grazing ray is proportional to the mass of the object and inversely proportional to the radius. The deflection by the Moon would be on the order of a few times 10^-5 arcsecond. That still is very slight and virtually unobservable by simple optical means. Perhaps a superduper interferometer could detect it.

jete
2009-Jun-19, 03:58 AM
I want to thank Hornblower for replying to my post. I do not want to hi-jack this thread so I’ll check to see if this discussion has already been addressed, and resurrect that thread or start a new one.

WayneFrancis
2009-Jun-19, 06:16 AM
Okay, let me repeat your answers back to you and see if I understand it right, because I think I'm missing something. So Roemer has a chart that predicts that on, say, January 10, 16xx, Ganymede will wink out of sight at 10:10 pm. Roemer watches, and it actually eclipses at 10:12 pm. Now since Earth is at the same point in space as the last January tenth, that shouldn't matter, but because Jupiter takes over eleven years to orbit the sun, the giant planet's going to be in a much different position on the same date year to year.

So if Kepler's prediction is for a close Earth-to-Jupiter distance, and Roemer's observation is for a distant Earth-to-Jupiter distance, then that would be enough for him to figure out that light is taking time to travel the extra bit (rather than traveling instantaneously), and calculate the speed.

Is that right? If yes, then that makes perfect sense, and I can move on.

If no, then use Smaller Words.

To jamesabrown, your description of your understanding sounds good to me and I see you have moved on.

To cjameshuff, isn't the time delay more then the variation 16m38s due to the orbit of the Earth about the sun? Should it not take into account the orbit of Jupiter? Meaning that ... wait never mind I almost did what I complain that tommac never does ... after doing the maths it basically is only a 16m38 deviation on average, when using the semi-major axis for orbits.

For those kiddies out there...do the math and you might just answer your own question...here I had a picture in my head that when done out on paper was wrong wrong wrong wrong wrong :)

WayneFrancis
2009-Jun-19, 07:45 AM
Next question, page 31:



Okay, what does that actually look like through the eyepiece of a telescope. Does the star jump from one position to another as it's light moves away from the gravitational influence of the sun? Or does it slide across space rapidly for a bit, then come to a relative stop? Is there a video demonstration of this I can see; some recording that someone made through their telescope?

don't have a video but I do have a picture I whipped up for you
http://users.on.net/~waynefrancis/LightBending.PNG

Obviously not to scale

Bottom green dot = an observer
Yellow dot = Sun
red dots = a single distant star

You can see with the red line what a photons path from the red line
You can see the an actual photon path that makes it to the earth in purple
You can see with the aqua line where we would perceive the stars location as.

As the observer orbits the sun in a counter clockwise direction the distant star would move from the right to left, fast at first then slowing to almost a stop as the photons that reach you are no longer traveling as deep into the gravity well and thus not bending as much.

the deflection of light is not that big either. The effect if our sun was a 1 solar mass white dwarf would be much more apparent as photons could get deeper into the gravity well without actually coming into contact with the sun.

Hope this helps.

WayneFrancis
2009-Jun-19, 07:53 AM
I'm pretty sure this chapter is going to be slow-going for me. Fortunately, I have you fine intelligent folks to hold my hand through the scary parts.



Okay, so I see from glancing ahead that this is "an obviously ridiculous result." So I understand that this is one of those "we used to think X; isn't that silly?" statements akin to the world is flat and orbited by the sun. Looking back at erroneous beliefs shows us how far we've come, and that's a good thing.

What I don't understand is where this belief came from in the first place, the idea that stars radiate in all frequencies equally? What made anyone conclude this? Was this a philosophical conclusion like Aristotle's notion that everything in space is spherical because spheres are perfect and so is God's heaven? Or was this a conclusion of inaccurate observations?

And what does Hawking mean by "according to the laws we believed"? Can something properly be called a law if it's also a belief? Do we currently believe in the laws of gravity but may one day look back and say, "Isn't that silly?"


I'm not sure about the former .... but will we look back at GR and say "Isn't that silly?" I'm not sure. Even if we show GR is wrong I doubt we'd call it silly at this point. Just like we don't call Newtonian mechanics silly. There are many old beliefs that where held without any real proof...that was silly. Just like early astronomers measurements being off wasn't really silly. They atleast used the scientific method and gave answers in a way that could be either confirmed or disproved.

Jeff Root
2009-Jun-20, 01:25 PM
Wayne,

That's a very nice diagram, despite its tiny size!

To answer the question James asked really wants an animation. I'd make
one, but it would be a LOT of work and I think James has probably got the
idea just fine anyhow. If there isn't a good animation showing how stars
appear to move away from the Sun as the Sun goes in front of them,
maybe I'll make one after I've got my new computer set up.

-- Jeff, in Minneapolis

WayneFrancis
2009-Jun-22, 02:28 AM
Wayne,

That's a very nice diagram, despite its tiny size!

To answer the question James asked really wants an animation. I'd make
one, but it would be a LOT of work and I think James has probably got the
idea just fine anyhow. If there isn't a good animation showing how stars
appear to move away from the Sun as the Sun goes in front of them,
maybe I'll make one after I've got my new computer set up.

-- Jeff, in Minneapolis

Thanks for the compliment. I know some people get annoyed with images that are to big. I probably could have gone slightly large though.

I was thinking of making an MPEG using POVRay with a camera view and top down view but the amount of time I'd spend on it wouldn't be worth it. If I was a science teacher and would get more use out of it maybe but I'm not :)

Perikles
2009-Jul-13, 04:27 PM
If anybody has read this recently, could they comment on this statement by an very well-known Colombian author Gabriel Garcia Marquez? His book Noticia de un secuestro is an account of hostage-taking in the 1990s in Colombia, and he reports that a priest is reading Hawking's Brief History, describing it as
a fashionable book which tries to demonstrate by mathematical calculation that God does not existI read the book decades ago, and was underwhelmed by it, so I can't remember whether the above assessment is complete nonsense or not. I suspect it must be, but Marquez is a highly respected author and it would surprise me if he got it competely wrong.

jamesabrown
2009-Jul-13, 08:41 PM
If anybody has read this recently, could they comment on this statement by an very well-known Colombian author Gabriel Garcia Marquez? His book Noticia de un secuestro is an account of hostage-taking in the 1990s in Colombia, and he reports that a priest is reading Hawking's Brief History, describing it as I read the book decades ago, and was underwhelmed by it, so I can't remember whether the above assessment is complete nonsense or not. I suspect it must be, but Marquez is a highly respected author and it would surprise me if he got it competely wrong.

From Chapter 8: The Origin and Fate of the Universe:


The idea that space and time may form a closed surface without boundary also has profound implications for the role of God in the affairs of the universe. With the success of scientific theories in describing events, most people have come to believe that God allows the universe to evolve according to a set of laws and does not intervene in the universe to break the laws. However, the laws do not tell us what the universe should have looked like when it started--it would still be up to God to wind up the clockwork and choose how to start it off. So long as the universe had a beginning, we could suppose it had a creator. But if the universe is really completely self-contained, having no boundary or edge, it would have neither a beginning nor end: it would simply be. What place, then, for a creator?
(p. 140-141)

Perikles
2009-Jul-14, 08:06 AM
From Chapter 8: The Origin and Fate of the Universe:Many thanks for that. :) From this quotation, it would apprear that Hawking is just posing the question of the existence of god, which is a long way from the claim made by Marquez.