Get a Straight Answer

Please note!

This is just a selection--

either

or else

To save space, this list starts from http://www.phy6.org/stargaze/StarFAQ17.htm
A full list is found at http://www.phy6.org/StarFAQsA.htm
and links arranged by subject are at http://www.phy6.org/stargaze/StarFSubj.htm.

Angle between ecliptic and Milky Way

(Continuation)--About the year 2012

396A Posssibility of Asteroid Hitting Earth (1)
396B Posssibility of Asteroid Hitting Earth (2)

Reply

Gravity of course pulls the glider down, but as it begins falling, it acquires some speed, and that speed creates lift on its wings, which slows down the downward motion. As explained in
http://www.phy6.org/stargaze/Sflight.htm
both lift and air resistance ("drag") are approximately proportional to the velocity squared, which means they should be proportional to each other.

When the two forces are in equilibrium with gravity, the glider slowly descends--say, 1 foot for every 19 feet moving forward. The lift of the wing balances 19/20 of the weight of the glider, so only 1/20 of the gravitational potential energy is released each second, and is used up to overcome drag. In fact the motion is very much like sliding down a 1:19 slope.

Soaring birds and experienced pilots know that air often rises faster than that--air rising from a sun-heated parking lot, or from a ridge hit by a steady breeze. By maneuvering again and again into the rising stream they can actually gain altitude. The source of energy is then heat--of sunlight on asphalt, or of the distant weather system which created the wind. See also
http://www.soaringmuseum.org

350. UFOs

A most intriguing question is conspicuous by its absence in your discussions of space. Please allow me to pose it here:

Is the Government of the United States, or any of its agents, contractors, assignees, etc. in possession of any empirical evidence of any kind, which would serve to substantiate/prove the existence of intelligent extra-terrestrial life forms?

Personally, I have had two (visual) encounters with objects which - to me and those with me at those times - definitely did not appear to be of this world. The first sighting was in the middle of the night while traveling on an interstate in Alabama, my traveling companion actually pulled over to the side of the road so that we could get out and observe. The second sighting was, incredibly, right in my old neighborhood in Bayside, Queens.

Notwithstanding my BA in English Literature, I identify far more with the scientific community than with the groupie/fringe community of self-proclaimed UFOlogy experts. That's why I don't believe that I've been abducted, or that an alien object is implanted under my skin somewhere... even though I've been experiencing this awful pain just above my left wrist!

Reply

I cannot speak for the US government or anyone else in the country. But as scientist I can only say that if such evidence existed, it would create tremendous interest and could not be kept secret. In fact, there would be no reason to conceal it, on the contrary--more people are probably worried that we may be alone in the universe than that we are not, and there have existed scientific searches for such life--maybe some still continue.

I don't know what you and your companion saw--especially at night, lots of things can fool the eye and the mind. But the fact is, no reliable sign of alien intelligence has ever been identified. There used to be a big USAF project, and you may read about it in
http://en.wikipedia.org/wiki/J._Allen_Hynek
and in links from there. As far as I know, while life (intelligent or not) in the distant universe is still an interesting target, our government has given up on finding any alien UFOs here.

351. Maximum speed for propeller-driven airplane?

I am curious as to whether or not there is an optimum speed for a FIXED pitch propellor (airplane/submarine/fan, et al) beyond which no further gain in speed is possible. Better said--is there a speed beyond which a prop "can do no more"?

If so what happens to the "vehicle" being driven? Does it just stay at that speed or does the inefficiency now a cause a reduction in speed?
In this situation (if it exists where the prop can do no more) does the now flailing prop develop a heat problem?
Do engine makers and prop makers create governing processes to preclude this occurrence and what happens if a prop designed for 400 MPH is driven at 550 MPH (or equivalent rpms)?

Reply

There definitely exists a maximum speed for propeller-driven airplanes, now quoted as 528.33 mph and held by a converted WW-2 fighter:
http://en.wikipedia.org/wiki/F8F_Bearcat (see at the end there)
As explained on my web site (stargaze/Sflight.htm), as airplane speed increases, the angle of the blade relative to the airstream becomes increasingly inefficient, and while blade tips may go supersonic (very noisy!) it still does not help. Whether the pitch is variable is not important--a variable pitch helps the airplane get to its top speed, but it is the final pitch setting that counts.

The prop does not flail, and certainly does not overheat (air flowing by cools it!), but the thrust it gives levels off. In any airplane, thrust levels off--if the designed cruising speed is 400 mph, the pilot can probably fly a little faster, but will burn a lot of fuel and perhaps overstress the airframe.

The earlier record, about 100 mph less, was set by a German Luftwaffe pilot in 1939, and he was quoted saying "I could have gone faster, but the propeller would not let me." Marine props have a different problem--cavitation, bubbles which limit operation.

352. The speed at which gravity spreads

Enjoyed your website, though a latecomer. We know the EM wave travels at the speed of light. But how about gravity? If this is a valid question to ask--how fast does a "gravity field" travel?

For example, if the Sun were to disappear suddenly, will we fly away in darkness (as would happen if the gravity spread faster than the light, or instantly)? I happened recently to read something about a "torsion field" that, according to the writer, travels at the 10⁹c. I am not sure that is at all true science... but it started me thinking as to whether there is such a thing as the speed of gravity.

Reply

General relativity (another name for Einstein's extension of Newton's theory of gravitation) is not my field, but I am pretty sure that gravity (like electromagnetic and other fields) spreads at the velocity of light. The Sun will not suddenly disappear (mass-energy is conserved). However, some cataclysmic event (perhaps a big supernova collapse or the merging of black holes) may occur and generate gravitational waves, and these apparently travel at the speed of light. It is a tiny effect, but sensitive instruments are already in place to detect such waves, if their source is close enough. As of today, none was confirmed.

But consider a simpler example (maybe too simple--general relativity may have something to say here too). Earth orbits the Sun in a near-circular path--let us simplify the picture and assume it is an exact circle. The Earth is attracted by the Sun's gravity, which provides the force to maintain the curvature of the orbital circle, or to balance the centrifugal force, whichever way you want to put it.

However, what IS THE EXACT DIRECTION of that attraction? If gravity spreads with the speed of light, its pull is parallel to sunlight--directed to there we SEE the Sun and thus perpendicular to the orbit.

However, that same sunlight took 8 minutes to reach us, and meanwhile Earth advanced a fraction of a degree in its orbit. The "real" position of the Sun in the sky should therefore be a small distance AWAY from where we see it, along the ecliptic and towards Zodiac constellations where the Sun had been earlier in the year. If gravity spreads INSTANTLY, its pull should be towards that "real" position.

It is ALMOST the same direction, but not quite: the force will have a small vector component (see http://www.phy6.org/stargaze/Svector.htm) OPPOSING the motion of the Earth, and diminishing its energy, causing it to spiral towards the Sun (faster and faster, by the way). The fact you and I exist suggests this does NOT happen, and that gravity does not spread instantly. In fact, any velocity other than that of light would cause the Earth's motion to lose or gain energy.

353. Layers of the Earth

Hi
My name is Joe, I am in tenth grade in New York. Lately I was wondering, when people discuss layers of the Earth, how do they even know about them, if they can not even go below the crust?
Also, if you go deep enough in the water, would you be able to touch the mantle or whatever is on the bottom, under the crust? Please unconfuse me...
I have asked my teachers, family... no one knows the answer, please let me know!!!!! I am dying to know!!!!!
thank you

Reply

Dear Joe
Most of our information about layers of the Earth comes from the study of earthquake waves (other sources also exist, especially from the chemistry of minerals). The outer layer on which you stand IS the crust, below it is the rocky mantle (with inner and outer mantle), then halfway to the center begins the core, much denser, liquid and probably mostly iron. Inside this is a solid inner core--believed to have solidified from the liquid, because the iron (at its high pressure, from so much weight on top) is not too far from its melting point.

You can read about it on a web page, part of a new set on the solar system
http://www.phy6.org/stargaze/Searth.htm

The crust however is far from even, and in particular, it (luckily!) contains large lighter slabs, the continents, floating on top of denser rock which forms the sea bottom. The slabs of the crust slowly shift position ("plate tectonics"). If you want to pursue the evidence about this, you need to read sections on magnetism in "The Great Magnet, the Earth"
http://www.phy6.org/earthmag/demagint.htm
especially #15 and maybe also #12 and #13, and perhaps others.

Now a request. By the end of 10th grade, students should have covered a lot of that, especially if they had a course on Earth science. If it was not covered, please show this letter to your teacher, perhaps these web sites can help shape future curriculum. Also, tell your friends in school--they can learn a lot from this web material, even on their own.

354. Why doesn't the sky fall on us?

Hi, Dr Stern!
I'm 9 and and at school, my friends asked me a strange question: 'why doesn't the sky fall on the surface of earth ?'.
I know sky may not fall on the earth, but I'm not able to explain why. Can you explain that to me, please? thank you!!!

Reply

Hi, there
What is "the sky", anyway? All there is above you is just air, held by gravity and compressed by its own weight.

Where the jet planes fly, most of the air is below them, so there is less weight compressing the air and it is only about a quarter as dense (which is why airliner cabins are sealed and maintain pressure). Still higher there is even less air, and only a trace remains at, say, 60 miles (about 100 kilometers). We are like fish at the bottom of an ocean of air, except that water has a top surface where it ends, while air decreases gradually.

Above that, there is nothing--just empty space, with Sun, Moon, planets and distant stars, which are really far-away suns. A few atoms and electrons fly around there, but otherwise, NOTHING.

So what is "the sky"? In the daytime you see it blue, because air scatters sunlight, especially the blue part of sunlight. Instead of the blue coming directly from the Sun, some of it comes from all directions (and with less blue, the Sun looks more yellow than it would look, say, from a spacecraft above the air). But there is nothing there except a layer of air.

On a clear dark night you can really see how empty "the sky" is. Air is transparent, so you see the stars in all their glory, and there is hardly anything between you and them.

355. Imagine a non-rotating Earth

Dear Dr. Stern,
My name is Luke and I was wondering if there is any way you could stop Earth's rotation and create a perpetual desert? What I mean, is it theoretically possible to have one half of the earth perpetually in darkness and one half perpetually in light from the Sun. If this were possible, would this create a desert on one side of the world and freeze the other side?

I've been wondering this for quite awhile and when I found your website, "From Stargazers to Starships", I thought I'd send you an email and ask you. Oh and when I say "stop," I don't mean stop abruptly, I mean slowly decelerate until it stops rotating. I hope you will answer my question even if it sounds bizarre or absurd, because its been bugging me for awhile.

Reply

Dear Luke
The Earth's rotation can only be changed by a force coming from outside it. Tides raised by the Sun and Moon do that, but it is an extremely slow process, probably taking billions of years.

It would still be interesting to simulate such a state on a weather-modeling computer, and I would not be surprised if someone had already done so. I gather you mean here an Earth undergoing one rotation per year and so presenting the same face to the Sun at all times. If ALL rotation stopped, sunlight would slowly circle the Earth.

The problem is complicated by the atmosphere. If Earth's atmosphere were rarefied, all water on the sunward side would evaporate and condense again as an ice-cap on the dark side, while the day side would indeed be a hot desert. On the boundary between the two air would circulate vigorously, transporting heat from day to night.

If the Earth's atmosphere were very dense, we would have something like Venus, whose temperature is more or less uniform (and hot) even though it rotates very slowly. Heat there is evenly distributed by winds, which have much more mass than those on Earth, and by the "greenhouse effect" in which molecules in the atmosphere transport heat by absorbing it and then re-radiating it in a random new direction. Which of these situations would resemble a non-rotating Earth I cannot even guess.

356. Flying east with a 1° error

Suppose an airplane attempted to circumnavigate the earth at the equator, flying east and using a magnetic compass. If that compass had a 1 degree error, instead of flying 90 degrees east it would actually fly 89 degrees east. Would it then end up exactly where it started because its path would be a "great circle." or would its flight path look like a corkscrew and it would end up north of where it started?

Reply

The path would be some spiral. All paths making a constant angle with lines of latitude--that is, with constant bearing--are straight on a map drawn in a Mercator projection, and spiral on the surface of the globe. See

http://en.wikipedia.org/wiki/Mercator_projection
http://en.wikipedia.org/wiki/Loxodrome

Of course, if the pilot followed a steady setting of a MAGNETIC compass, the path would be rather irregular, because magnetic lines of latitude deviate very much from circles. Just look up a world magnetic map and see the shape of the magnetic equator! But with a one degree offset, the airplane would not stay on that line, either.

357. US Flag on the Moon

I was recently going through my history book, reading about Neil Armstrong's first step on the moon. I got to thinking about it and was wondering how they got the flag to actually stay on the moon where there is no gravity...have you ever gotten this question before?

Reply

There is no air on the Moon, therefore no wind can blow, and a normal flag would hang limply down (the pressure of the solar wind is w-a-a-a-y too weak).

Unless, of course, it had a sleeve sewn into its top and a rigid cross-bar threading it and connected to the flagpole. Indeed, if you look at pictures of Apollo flags, you will notice how straight their tops are, like the tops of a coffee-shop curtains, and for the same reason.

Clarification I understand how they got the flag to look like it was blowing in the wind, but that's not exactly what I was asking. I wanted to know how they got the flag to stay implanted in the moon. ???
Reply I guess you can stick a flagstaff into the the dry "regolith" (=ground-up debris) covering the Moon, just as you would stick one into beach sand. No wind will blow it down!

358. Rope stretched across a long lake...

I am a pensionaire from Norway, on Grand Canary Island. I read your section on the distance of the horizon and have a similar question about a rope stretched across a long lake.
Mjøsa, a Norwegian lake, has the length 117 km (or say, about 120 km). According to the curve of the earth, how deep beneath the surface would the rope be in the middle of lake?

Reply

Say the lake in Norway is 120 km long. One may ask, "If we have two points at the same elevation but 120 km apart, and draw a straight line between them, how deep is the deepest part of the line?"

The deepest point is in the middle, 60 km from either end. Suppose its depth there is D, while R is the radius of the Earth. You draw your diagram and use the theorem of Pythagoras :

R²= 60² + (R – D²)
= 60² + R² – (2R – D)D
giving approximately
2RD = 60² = 3600
D ~ 3600/2R = 3600/12740
or about 283 meters.

However, a ROPE through the lake will never be straight! Its weight will pull it down in the middle, probably all the way to the bottom, even if the lake is deep.

I am sure you have seen electric trains whose power is taken from an overhead cable. The electric cable must be absolutely level, otherwise the frame connecting to it jumps up and down as the train moves. One cannot stretch the cable so tight that it will be absolutely straight, so (at least in this country) there are always TWO cables, one above the other.

The top cable is steel (probably steel that does not change much in heat and cold) and it curves from the weight it supports. The bottom cable is copper to carry the electricity, and it hangs from the steel by short wires. Those wires get a little shorter in the middle between the towers that hold the steel cable, and are so adjusted that the second cable is straight, even if its supports are not.

359. About studying electronics in the USA

(Message from India)
I am really very satisfied with your answers to my queries. I am also very much satisfied with the outstanding contents of your site.
I have already appeared for my 12th [grade] science exams and they were good and now I want to apply for further studies at California university.

I am going to stay there with my aunt and so I will not be paying my accommodation fees and hope to pay my university fees through part time jobs. I want to study electronics and communications there. Is the future for this field going to be good? Please also suggest me some good and reasonable universities for this course. I could not contact you for the last year as I was busy with my 12th grade studies.
Last time you advised me to improve my English. Is it ok now, or do I need to still improve it?

Reply

I am not in a good position to advise you on a university in California--it depends among other things on what part of California you will be in. Please realize, first, that university can be expensive, California and other states have special fees for students from that state, but all others pay more, and the best universities are private and expensive. In addition, your visa will probably state that you are not to work. Make sure all legal issues are taken care of.

Finally, consider a good university in India, too. It used to be that American universities were automatically considered better, but for many years that is no longer true. There exist some very good universities in your country--in fact, the best ones (I understand) have competitive entrance exams and you need succeed well in those.

Personally, I am about 4000 km from California, and it is hard to recommend. However, you have the internet, and you can collect information from it and find out about locations, about what various universities consider their strong subjects, about fees and entrance requirements, legal requirements for visas and dates for registration. You really should have started your search 1-2 years ago!

Some web sites:
http://www.calstate.edu/
This site is about state universities, which give Californians an advantage.
http://www.calstate.edu/search_find/campus.shtml
http://www.collegebound.net/content/

Most important--ask professionals in India for advice, both those who studied in the USA and those who have studied in India.

360. Publish Stargazers as a book?

Dear Dr. Stern, I'm a father of two 6-graders and have, during the process of learning with them about Newton mechanics, become a great admirer of you and your excellent site. I have just one question: have you ever considered putting it in a book form so one can enjoy reading it while away from his/her computer?
If such a book already exists, please let me know.
Warm regards,

Reply

At one time I tried to publish in print the smallest of my collections ("The Great Magnet, the Earth") and found the effort time-consuming and discouraging. In any case, the future of books probably lies with the computer. Whether future "books" will be "printed to order" as some books are now, or read by compact devices like "Kindle," I do not know. Whatever replaces them should look like a book--not be videos or flashy illustrated stories (too much eye candy distracts), but very much like paper books used now, which is what I try to produce. Perhaps they will allow space to take notes and comments--no need to write them on the pages of a paper book.

As it is, my efforts started in 1995, and the collections are still much in use (about a million pages each month), while most books go out of print much faster. The computer allows extra features, too--internal and external links, optional extensions, glossaries, time-lines, math supplements, links to hundreds of questions-and-answers like this one, translations and greatly expanded material.

All this is very easily downloaded to a CD as "zip-archives," compressed collections which after downloading are split up by the computer into the same files as the ones you find on the web. The central link is
http://www.phy6.org/readfirst.htm
Then go to
http://www.phy6.org/stargaze.zip
http://www.phy6.org/earthmag.zip
http://www.phy6.org/Education.zip

You can make a disk for each of your 6th graders (and also download the archives onto the home computer for off-line use). Let them explore on their own!

361. Charging of Earth by lightning: + or – ?

A question that I can't seem to get clear in my head: does the earth have a positive or negative charge regarding the lightning that strikes--and do you know how the lightning charge builds up in the atmosphere?

Reply

The Earth as a whole (including atmosphere) has zero electric charge. Any charge it acquires--for instance, from positive cosmic ray ions which hit it all the time--is quickly neutralized, by ions and electrons ejected from the top of the atmosphere (positive "polar wind" ions or negative photoelectrons), or else by charges drawn from surrounding space. In either case, the excess electric charge is what creates the attracting or repelling force.

However, there exists a charge separation in the atmosphere itself--high layers have extra positive charge and those near the ground have negative charge, which also determines the rate of voltage change near the ground. The separation is due to the process responsible for lightning, and is therefore greatest in thunderstorms and near them. Under quiet condition this voltage also spreads quite far horizontally, although far from its source it cannot drive any appreciable current, because air is such a good insulator. That makes such voltages hard to measure! The mechanism itself is described in
http://www.phy6.org/stargaze/Svandgrf.htm

362. If no stars were seen--could Earth's orbital motion be discovered?

(abbreviated correspondence)
First of all my congratulations for your excellent web pages: they are a reference point for everyone of us who wants to understand with few logical passages what is behind a physical phenomenon.

My question: we are able to demonstrate that the Earth rotates because there is the Coriolis force that accounts for the swirling water or the deviation to east of falling bodies.

Is there any equivalent proof by which we could tell the Earth orbits the Sun, without considering the seasons and the position of the stars? The only non inertial force that I can see here is the centrifugal force, but since it is perfectly balanced by the gravity force that pulls the Earth to the Sun I wonder how we can devise an experiment to prove that the Earth is orbiting around our star.

Reply

Your question reminds me of a very early science-fiction story by Isaac Asimov, "Nightfall." It is set in a civilization like that of early Mesopotamia, except that the planet is in constant sunlight by two separate suns. When by a rare chance both suns are eclipsed and the stars (a very bright cluster) are first revealed, mass hysteria descends.

Of course, motion with two centers of attraction would not be stable enough. But suppose Earth were like Venus covered by dense clouds limiting our vision. Could we tell it orbited the Sun--short of sending a rocket above the clouds?

In a non-inertial frame, a non-moving compact object is in apparent equilibrium--only its own motion reveals any non-inertial character of its surroundings, by the Coriolis force. The human body is not sensitive enough to sense tiny forces, so it may fail to detect any difference even if a moderate amount of motion exists. A blindfolded astronaut in a space station will just feel "weightless," and a human on Earth won't sense any motion either. If you looked at the example of a draining bathroom sink (below the picture of the hurricane) in
http://www.phy6.org/stargaze/Srotfram.htm
you will realize that on the scale of the human body, the effect is negligibly small, even for the rotation of the Earth.

However, sensitive instruments are much better in telling if a system is inertial or not. A freely suspended spinning gyroscope points in a fixed direction, so if one is available, that is like having a fixed star in view. On a space station its axis (if in the orbital plane) should rotate 360 degrees every orbit, about every 90 minutes. On Earth it should move around a cone of directions in about 24 hours, as if it pointed at some star.

Suppose Earth was permanently under cloud cover, allowing one to see variations of light between day and night, but no more, and therefore guess at the direction of the Sun. The axis of a freely suspended gyroscope pointing at the Sun today should rotate relative to it in a single year. Since the year is quite long, one must be sure the suspension is free enough to isolate the axis from motions of its surroundings, and to eliminate other possible sources of such rotation. That can make a challenging technical problem (and possibly, a cute science fiction story!).

363. Local Solar Time in Iceland

I am trying to derive the actual solar hour of a place. Some websites state that you need to calculate magnetic declination of the place first. Is that true?
In my case, the location is Iceland, relatively close to the North Pole--65° north and 16-21° west. Iceland is 16-21° from the Greenwich longitudes, but its time zone is that of Greenwich, which seems wrong. Its magnetic declination is very high, so I need to know if that should be taken into account when finding the local solar time. Can you assist me with your knowledge on astronomy?
Is actual solar time only measured by longitude, so that to get the solar time, for each degree of longitude difference from 0° +/– one must add 4 minutes to Greenwich time (or subtract from it)?

I found this calculator here and wanted to ask you if it is accurate and if magnetic declination would be needed to find actual solar time:
http://www.jgiesen.de/SiderealTimeClock/index.html

Reply

Solar time depends on the location of the Sun in the sky and has nothing to do with magnetism of the Earth. As indicated on the web site you gave, solar noon is when the Sun "passes the meridian"--when it is exactly south, and is highest above the horizon (for that day).

It only depends on longitude, since it really measures the rotation of Earth around its axis and indeed shifts by 4 minue for each one-degree shift of longitude. Your latitude determines where the Sun actually is in the sky (it could even be night with the Sun below the horizon!). If the Sun is above the horizon, a sundial (http://www.phy6.org/stargaze/Sundial.htm) should indicate solar time, except for a small correction "the equation of time" included on your web site, which equals the difference (some minutes) between actual "solar noon" and "mean solar noon." Mean solar noon assumes all solar days are equal to 24 hours: actually, small differences exist, because of facts like the Earth's elliptical orbit.

Noon by the clock is averaged over large strips of latitude, typically 15 degrees wide, which is the angle the Earth rotates in one hour. When traveling across the sea of the land you therefore need to adjust your clock only when you pass from one "time" zone" to another, usually by one hour. See http://www.phy6.org/stargaze/Slatlong.htm.

About Iceland... I do not know. The web site you cited gives the local time zone for Reykjavik an hour behind Greenwich, as it should be for locations 16 to 21 degrees west of Greenwich. You wrote that actually Greenwich time is used, but maybe that is done out of convenience, people actually use the west European time zone to fit with local time in Scandinavia, Britain and other European neighbors. After all, time zones can adjusted for the convenience of users: all China has the same time zone, even though the country covers several zones, and the time zone of India is 5.5 hours ahead of Greenwich, since a standard time zone boundary would cut the country in half.

364. Is orbital motion same as free fall?

While Sun, Moon, and the Earth are moving in their orbits, are they floating (like men in space), or 'swimming' through space, or in free fall?

Reply

Your question has more to do with use of language than with science. A swimmer exerts a force on the surrounding material, which the Moon etc. do not; so "swimming" is not appropriate. "Floating" was originally applied to light objects on top of a fluid, like a cork on water and in this sense, astronauts in space do not float.

People however also use this word for a state of being suspended without having to apply any force, just as the weight of the cork is balanced by the pressure of the water. In this sense, astronauts FEEL as if they were floating.

"Free fall" suggests motion subject to no force except gravity, and in that sense, the Moon is in free fall around the Earth. However, free fall is not always straight down. That is only true for objects starting with no velocity of their own. If you give an object some velocity (say, throw a ball) its path is curved, and with enough velocity--like that of an artificial satellite, or the Moon--the path is curved enough to wrap around the Earth.

365. Build a straight tower in warped space?

I was taken to one of your pages from a Google search to answer "if we build a straight structure, will it circle the globe?"
My question has to do with the curvature of spacetime, the shape of the earth, and the notion of "straightness." I'm submitting it here because I'm not sure where else I could possibly get an answer. I looked up "Spacetime" in "Wikipedia" and found the statement "In general relativity, it is assumed that spacetime is curved by the presence of matter (energy)" That seems a tough pill to swallow, after being raised on Newton's explanation of gravity being just an attractive force.

I therefore ask:

If we were able to build an ideal structure of unlimited length that was perfectly straight when measured with some theoretical ideal device, would it wrap around the earth and join with itself, or would it extend out into space like a tangent to the earth's surface (ruling out the need to support its mass)? Basic spatial reasoning and the first 12 years of my public school education tells me, "of course it would extend up into space," but my (extremely limited) understanding of relativity seems to suggest, counter-intuitively, that an object considered straight in one context could be curved in another, thus allowing this "straight" structure to "curve around" the Earth.
This also brings up other questions: what exactly is "straight"? Is it too relative? Can "straight" even exist absolutely in a relative universe? My first thought would be to use a laser (or some other) beam as a reference, but that too would likely curve from the same effects... would it still be considered straight?
It seems to me that the Earth is (or at least could be) both flat and spherical simultaneously, which would be an absolute nightmare for history book publishers to get right! "First flat, then round, and now both!?" Am I totally missing something here?

Reply

I am largely ignorant of general relativity, and therefore some of the things below may be wrong. But let me try.
I suspect that you indeed put your finger on the core question, when you wondered about the definition of "straight." Euclid defined a straight line as the shortest distance D between two points, and distance D could be defined by the theorem of Pythagoras

D²= x² + y² + z²

When you deal with cosmic distances, however, time creeps into the definition too. You look at a galaxy a billion light years away, but what you actually see is where it was a billion years ago. You have no way of measuring the path to it instantly. This and other things led Einstein to modify the prescription for distance ("metric tensor" or "metric" for short) to involve time as well, and make "space-time" separation rather than just space distance the foundation of physics. Actually, time is a different kind of dimension--a "time-like" dimension--since all its applications involve the square root of (–1), and that requires using a wider definition of numbers. It. That was the special theory of relativity.

General relativity concluded that the presence of mass warped the metric (which is here a property of actual space--not just a mathematical artifact), causing (for instance) the path of light to curve and such effects as gravitational lensing. The strange arcs seen by telescopes suggest that even though light reaches us by the shortest route, that route is not the same as it would be in the absence of gravity. It is indeed the path a laser beam would take, and is as straight as anything can make it. However, you need extremely intense gravity to make a noticeable difference in the metric: the effect of the Sun's pull during a total eclipse in 1919 was barely noticeable. You need come close to a black hole to make space-time curve significantly, even bend a ray path onto itself.

Let me stop here. You may ask someone more closely familiar with general relativity for a clearer view, but I am not sure it can be done without math. The late John Wheeler wrote "Spacetime Physics" which gives the nitty-gritty, but I'm not sure you are ready for it.

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Author and Curator: Dr. David P. Stern
Mail to Dr.Stern: stargaze("at" symbol)phy6.org .

Last updated 5-14-2008 Edited 2 November 2016

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