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Introduction to the Theory of Relativity Part I: History

By epepke in Science
Fri Jun 13, 2003 at 03:15:23 PM EST
Tags: Science (all tags)
Science

This is the first of a series of elementary, informal, and almost equation-free articles descibing the Theory of Relativity in physics. The series will have four installments:

  1. Part I: History
    This describes the history of ideas in the development of relativity.
  2. Part II: Special Relativity
    This will describe Einstein's Special Theory of Relativity.
  3. Part III: General Relativity
    This will give at least a taste of Einstein's General Theory of Relativity, which extends the Special Theory to cases involving acceleration and gravity.
  4. Part IV: Implications, Controversies, and Miscellany
    This will address implications of the Theory of Relativity, controversies both old modern, and anything else that isn't covered in the first three installments.


As long as there have been people, we have tried to understand the world in which we live. It's been a rocky road, and there has been much in the way of pitfalls, blind alleys, and backtracking. Many different cultures have approached this understanding in many ways, with ideas over time weaving and separating like the threads of a tapesty. The threads are at times tangled, at times cleanly woven. Some threads are cut, new threads are introduced, and colors sometimes disappear only to appear later. Parts of the tapestry have led to modern physics, with many ideas that seem strange at first, including the Theory of Relativity.

In the view of Aristotle, the world was very much an absolute place. You could easily tell whether you were moving or stopped. Rocks fell in "natural motion" toward the Earth, and smoke rose into the air, but eventually, even they stopped. The sun, moon, stars, and planets appeared to move and never stopped, but they were embedded in crystalline spheres that turned.

Aristotle's views weren't the only ones to be developed in ancient Greece. Heraclitus held that all things were in motion, or a contant state of flux though possibly not visibly so, a surprisingly modern view. However, Aristotle's ideas prevailed and held sway in European culture for millennia.

Around the time of the Renaissance, many people noticed that some of Aristotle's ideas weren't good enough and set out to improve them. Some people, such as Tycho Brahe, became interested in making more and more accurate measurements of the motions of the planets and the stars. His technology was simple, but it seems that he looked harder and more carefully than anyone had before. This led Johannes Kepler to come up with his three laws of planetary motion, including the idea that the planets moved in ellipses (so much for crystalline spheres). Later, Galileo made some significant advances in astronomy, developed five laws of motion, and came up with the first known modern statement of the principle of relativity, This played an important role in the long-standing question of whether the earth was stationary or moved.

Isaac Newton developed three laws of motion that relied on Galileo's principle of relativity. Relativity also enabled him to produce a theory of gravitation with only an attractive force, improving on Kepler's work. Yet if Galileo came up with relativity, and Newton embraced it, why all the fuss about relativity over the past century?

One important puzzle that has fascinated people is the nature of light. Newton thought that light was "corpuscular," that it came in chunks. As it turned out, he was right, though his reasons for thinking it were wrong. The idea of light as a particle, however, didn't seem to explain how light worked, so most gradually came to think of light as a wave. In the middle of the 20th century, quantum electrodynamics re-established light as a particle, but at the time relativity was being developed, the wave theory was very much in vogue.

The wave theory of light has a problem: all known waves, such as sound and water waves, move through a medium. It was well known that the stiffer the medium, the faster the waves. Sound traveled much faster though an iron bar than through air. Light traveled so fast that it was generally assumed to be instantaneous. In the 19th century, people started to measure the speed and found that, while it was not infininte, it was still really fast, fast enough to be able to circle the Earth seven times a second. This medium seemed to be the luminiferous ether, an old idea of Aristotle. It had to be incredibly stiff for light to go so fast in it, but at the same time incredibly soft and insubstantial. After all, people could walk through it easily. In fact, it was so insubstantial that nobody had ever detected it.

The luminiferous ether seemed to reintroduce a bit of the Aristotelian absolute to the world. Whatever the ether was, it was obviously important enough to be considered, in some sense, an absolute. So, the old relativity of Galileo was called into question. In the middle of the 19th century, James Clerk Maxwell came up with the Maxwell's equations. They unified the phenomena of electrical charge and magnetism. They predicted that, when there was a change in an electric field, a disturbance would travel out from it at the speed of light. This was identified as light and later also as radio. The equations didn't seem to depend on the speed of the source of the light. This was unlike, say, throwing a ball out of a moving car, but it was just like what you'd expect for light in the luminiferous ether. Aha! people thought. Now we have a way of measuring the speed of the Earth through the ether! We just have to set up a light source and a meter stick and see the difference when we point it in the direction the Earth is going compared to some other direction. The speed of the light doesn't depend on how fast the light source is moving, just like the speed of a boat doesn't change the speed of the waves in water. But surely it must depend on how fast the observer is moving through the medium. Sailors can tell their speed by dropping things into the water and watching how the water carries them along, so let's drop some light and watch the ether carry it along.

The most famous attempt was the Michelson-Morley experiment, and it showed no significant difference. It was controversial for many years. The experiment was hard to perform with the existing technology, and people came up with a lot of other reasons to explain away the null result. (Nowadays, cheap lasers, good metallurgy, and precise machining make it easy to do the experiment using high-school quality equipment, and it comes out the same as Michelson-Morley.) Eventually, a consensus emerged that the null results were real, and the idea of the ether mostly faded from popularity.

At first many people thought that maybe Maxwell's equations were wrong. Since they were newer, it seemed more plausible for them to be wrong than what had been believed for hundreds of years. Some tried changing Maxwell's equations to have terms for the speed of the observer, but this seemed to predict other effects that were not confirmed by experiment. After a while, a consensus emerged that Maxwell's equations were also probably correct, or at least correct enough that the solution to the puzzle must lie elsewhere.

Hendrik Lorenz tinkered with the numbers and came up with the idea that the Michelson-Morley experiment could be explained if you assumed that objects shortened in the direction of travel by a certain amount. The equations turned out to be mostly correct, and we still refer to most of the math in the Special Theory of Relativity as the Lorenz transformations. They are improvements over the Galilean transformations, the common ideas of speeds adding up that are still good enough for most everyday purposes.

Henri Poincaré  suggested that the old assumptions were wrong, that no matter how counterintuitive it sounded, there should be no way at all to tell whether you were moving or at rest or how fast you were moving except relative to something else, and so resurrected the principle of relativity.

This meant that either the speed of something was affected both by the speed of the source and the speed of the observer (like a ball thrown out of a car), or it was affected by neither. If the speed were ever affected by one but not the other, then all we'd have to do is make sure that the source and the observer were stationary relative to each other and detect a variation in speed from what we would expect. Poincaré  presumed this was impossible.

To see this more clearly, consider that only Maxwell's equations or only the null result of the Michelson-Morley experiment, taken separately, don't pose much of a problem. The two, taken together, lead to the problem. Consider the four possibilities:

  1. The speed depends on the speed of the source and the speed of the observer.
    This works fine for rocks, baseballs, rockets, etc. but is inconsistent with Maxwell's equations when applied to light
  2. The speed depends on the speed of the source but not the speed of the observer.
    This is inconsistent with Maxwell's equations for light and doesn't work for rocks, either.
  3. The speed depends on the speed of the observer but not the speed of the source.
    This is inconsistent with the null results of the Michelson-Morley experiment and still doesn't work for rocks.
  4. The speed depends neither on the speed of the source nor on the speed of the observer.
    This is consistent with both Maxwell's equations and the null results of the Michelson-Morley experiment for light. It doesn't work for rocks.

Therefore, to have ideas consistent with what had been observed and with the equations that nobody had been able to break, it became clear that the speed of light had to be completely independent of both the speed of the source and the speed of the observer. While ordinary matter works like case 1, light works like case 4. This basic idea is the starting point for the Theory of Relativity. In Galilean relativity, all speeds were relative both to the speed of the source and the speed of the observer. To have a special kind of thing, light, with a special speed relative to neither required a lot of rethinking and led to some conclusions that seem very strange indeed. It was ironic that the notion that the speed of light was relative had to be abandoned to save relativity, but that's the way it was.

As can be seen, the ideas of relativity were developed by many people. The basic principle was from Galileo, embraced by Newton, restated and refined by Poincaré . The mathematics was already pretty much figured out by Lorenz and Minkowsky. The experiments were provided by Michelson and Morley and others later. Innumerable others made theoretical contributions as well. In many cases, several people came up with the same ideas independently (such as Lorentz and FitzGerald). All these threads, however, still looked like a big tangle.

In 1905, Albert Einstein added a few of his own threads and weaved the whole into the Special Theory of Relativity, at once a rigorous scientific theory making predictions of its own and beautiful story that made all these weird observations and theories fit together. That is the subject of the next installment.

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o Aristotle
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o Galileo
o principle of relativity,
o Isaac Newton
o luminifero us ether
o James Clerk Maxwell
o Maxwell's equations
o Michelson- Morley
o Hendrik Lorenz
o Henri Poincaré 
o Minkowsky
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o Albert Einstein
o Also by epepke


Display: Sort:
Introduction to the Theory of Relativity Part I: History | 194 comments (134 topical, 60 editorial, 0 hidden)
i'm voting for you but (2.66 / 9) (#11)
by auraslip on Fri Jun 13, 2003 at 08:06:59 AM EST

you better fuckin follow through with the rest.
124
yeah... (none / 0) (#76)
by dipierro on Fri Jun 13, 2003 at 04:43:39 PM EST

this one is kind of useless on its own

[ Parent ]
Mistake! (3.66 / 3) (#15)
by StormShadow on Fri Jun 13, 2003 at 08:26:41 AM EST

Quantum Electrodynamics (QED) is what you are talking about and not QCD. Please correct and I'll vote +1FP. For a good QED book, check out Peskin and Schroeder which is my favorite.


-----------------
oderint dum metuant - Cicero
We aren't killing enough of our [America's] enemies. Re-elect Bush in 2004 - Me
12/2003: This account is now closed. Password scrambled. Its been a pleasure.


QED? (none / 0) (#27)
by TurboThy on Fri Jun 13, 2003 at 09:53:11 AM EST

You are wrong, that's for maths.
__
'Someone will sig this comment. They will. I know it.' [Egil Skallagrimson]
[ Parent ]
I really hope you are joking [nt] (5.00 / 1) (#28)
by StormShadow on Fri Jun 13, 2003 at 09:57:16 AM EST



-----------------
oderint dum metuant - Cicero
We aren't killing enough of our [America's] enemies. Re-elect Bush in 2004 - Me
12/2003: This account is now closed. Password scrambled. Its been a pleasure.


[ Parent ]
Quod Erat Demonstrandum [n/t] (none / 0) (#32)
by TurboThy on Fri Jun 13, 2003 at 10:25:02 AM EST


__
'Someone will sig this comment. They will. I know it.' [Egil Skallagrimson]
[ Parent ]
I think you misunderstand (5.00 / 3) (#33)
by StormShadow on Fri Jun 13, 2003 at 10:28:55 AM EST

I know what QED stands for in mathematics but I was referring to the implication of your comment. QuantumElectroDynamcs is always abbreviated QED while QuantumChromoDynamics is abbreviated QCD.


-----------------
oderint dum metuant - Cicero
We aren't killing enough of our [America's] enemies. Re-elect Bush in 2004 - Me
12/2003: This account is now closed. Password scrambled. Its been a pleasure.


[ Parent ]
Also (none / 0) (#114)
by by on on Sat Jun 14, 2003 at 02:05:38 AM EST

Nobody in math actually uses `QED' anymore. They use a little black square instead.

[ Parent ]
I've always seen it as a little triangle. [nt] (none / 0) (#131)
by heng on Sat Jun 14, 2003 at 02:40:12 PM EST



[ Parent ]
Three dots? (nt) (5.00 / 1) (#157)
by DrH0ffm4n on Mon Jun 16, 2003 at 08:16:33 AM EST



---
The face of a child can say it all, especially the mouth part of the face.

[ Parent ]
black square... (none / 0) (#146)
by debillitatus on Sun Jun 15, 2003 at 03:48:44 PM EST

True, except for two weeks a year, I have "throwback week", and I use Q.E.D. in all of my classes. (Just like the NFL)

I've also been known to bust out the slide rule at these times.

Damn you and your daily doubles, you brigand!
[ Parent ]

THERE'S NO POINT TO THIS. IT'S COMMON SENSE FOR US (1.04 / 21) (#29)
by A Proud American on Fri Jun 13, 2003 at 09:58:46 AM EST

 

____________________________
The weak are killed and eaten...


For who? (none / 0) (#137)
by Torka on Sat Jun 14, 2003 at 09:51:55 PM EST

nt

[ Parent ]
-1, too complex (1.00 / 8) (#43)
by United Fools on Fri Jun 13, 2003 at 11:24:48 AM EST

Why can't it be simpler?
We are united, we are fools, and we are America!
Because... (5.00 / 2) (#61)
by GavalinB on Fri Jun 13, 2003 at 01:14:25 PM EST

It's the theory of relativity, which is rather complex by its very nature. The article itself does a good job of exploring the topic. If you want the USA Today version of the theory of relativity, read the following: If your Ford SUV can go light speed and you turn on the headlights, you won't see the road in front of you when you're going full speed. (Add handy and informative graphic showing a truck, headlights, and a road of stars)
---
The Future is Prologue: Join Our Sagas Today!
[ Parent ]
SUV's at light speed (5.00 / 3) (#69)
by The Writer on Fri Jun 13, 2003 at 03:10:58 PM EST

If your SUV could travel at light speed, you'd be at your destination right after you start the engine. Relative to other people, of course, you'd still take non-zero time to get there; but in your reference frame, distance collapses into 0. Which means, actually, that not only you're at your destination, but you're also at every point along the journey simultaneously.

[ Parent ]

Or more simply (5.00 / 2) (#71)
by niom on Fri Jun 13, 2003 at 04:19:40 PM EST

If you travel at the speed of light, time does not pass for you, even though it does for the rest of the universe. Therefore you can be everywhere at the same time (again for you, not for the rest of the universe). Of course, this does not make a lot of sense when applied to people, but it does not matter because only particles with null stationary mass can travel at the speed of light.

[ Parent ]

Null stationary mass (5.00 / 1) (#72)
by The Writer on Fri Jun 13, 2003 at 04:23:30 PM EST

Yep. The beauty of it all is that only light can have null stationary mass. (I.e., if a particle has zero rest mass, it must be travelling at light speed.) I believe only photons meet this requirement, though I could be wrong.

[ Parent ]

Gravitons would too, if they exist [n/t] (5.00 / 2) (#75)
by awgsilyari on Fri Jun 13, 2003 at 04:43:24 PM EST



--------
Please direct SPAM to john@neuralnw.com
[ Parent ]
Zero rest mass (5.00 / 2) (#82)
by niom on Fri Jun 13, 2003 at 05:53:31 PM EST

if a particle has zero rest mass, it must be travelling at light speed

And the reason is very simple: if a particle with zero rest mass does not travel at light speed, it has no energy, so it cannot interact with anything -- which is pretty much the very definition of not existing.

[ Parent ]

Neutrinos? (4.00 / 1) (#110)
by jmv on Sat Jun 14, 2003 at 01:26:29 AM EST

I'm not sure it is known whether neutrinos have a rest mass or not (which also means whether they travel at exactly c or not).

[ Parent ]
All signs say yes (5.00 / 2) (#116)
by Joh3n on Sat Jun 14, 2003 at 02:36:06 AM EST

The recent measurements by Super Kamiokande and SNO (Sudbury Neutrino Observatory) show that although we cannot explicitly say what the mass of the neutrinos are, we can say that there is a difference in mass between neutrino species.
---------------------------------
You can learn a lot about someone by popping in their un-rewound pr0n tape and seeing where exactly they came.
-terpy
[ Parent ]
Don't forget gluons (5.00 / 1) (#115)
by dipierro on Sat Jun 14, 2003 at 02:06:19 AM EST

which do exist

[ Parent ]
Or even more simply... (none / 0) (#79)
by dipierro on Fri Jun 13, 2003 at 05:03:05 PM EST

Moving clocks tick more slowly. Moving rulers get longer. And forces move at the speed of light, not instantaneously.

[ Parent ]
Unless (5.00 / 1) (#179)
by awgsilyari on Wed Jun 18, 2003 at 07:36:29 PM EST

And forces move at the speed of light, not instantaneously.

Unless their gauge particles have mass, in which case the force propagates slower than light speed. If I remember, the weak interaction is carried by the W particle which is massive.

--------
Please direct SPAM to john@neuralnw.com
[ Parent ]

SUV collisions (none / 0) (#106)
by jmv on Sat Jun 14, 2003 at 12:29:26 AM EST

If SUV's could travel at the speed of light, then sone head-on collitions could create SUV/anti-SUV pairs, with the anti-SUV subsequently meeting a nearby SUV and disappearing in a (big!) flash of light.

[ Parent ]
We need more anti-SUVs (4.00 / 1) (#125)
by flo on Sat Jun 14, 2003 at 11:44:47 AM EST

that might solve some environmental problems... on the other hand, the resulting gamma radiation would probabaly kill all the whales :)
---------
"Look upon my works, ye mighty, and despair!"
[ Parent ]
I hate it when those headlights turn blue [n/t] (5.00 / 2) (#70)
by epepke on Fri Jun 13, 2003 at 03:16:51 PM EST


The truth may be out there, but lies are inside your head.--Terry Pratchett


[ Parent ]
Here's a simple version of special relativity (5.00 / 1) (#73)
by The Writer on Fri Jun 13, 2003 at 04:28:14 PM EST

Quoted from Einstein himself: "Sit on a hot stove for a minute and it feels like an hour. Sit with a pretty girl for an hour and it feels like a minute. That's relativity."

[ Parent ]

Why?? Why?? (5.00 / 4) (#85)
by ulrich on Fri Jun 13, 2003 at 06:34:58 PM EST

How, how, how can so many people believe that Einstein said this??

This is a quote that incorporates a mixup common for people who have no clue what relativity means confusing relativism and relativity, a 'punch line' and general style of phrasing totally different from anything Einstein ever said ('THATS relativity', come on), and again _explains relativity to be something which has nothing at all to do with relativity_.

All in all, the quote is obviously totally made up, surely by an American devil.



[ Parent ]
re: Why?? Why?? (none / 0) (#192)
by amRadioHed on Sat Aug 09, 2003 at 01:37:23 PM EST

He did say it. That is the only reason I know of why so many people think he said it.

The humor columnist for Scientifc America, Steve Mirsky printed the short paper Einstein wrote that the quote comes from. Scientic America's web site is down at the moment, but the entire contents of the article is posted here.

Granted it is possible that the entire paper was made up by Mirsky, but I really don't think so. Einstein did have an excellent sense of humor.


We hope your rules and wisdom choke you / Now we are one in everlasting peace -- Radiohead


[ Parent ]
It could... (4.66 / 3) (#78)
by dipierro on Fri Jun 13, 2003 at 04:59:11 PM EST

Why can't it be simpler?

It could, but it would have to be taught at a much younger age. Imagine explaining negative numbers to someone who lived 20+ years of their lives without ever hearing about them.



[ Parent ]
how about this: (5.00 / 2) (#113)
by by on on Sat Jun 14, 2003 at 02:04:18 AM EST

The speed of light is observed to be the same for everyone.

That is the main thing about SR. Everything else in SR can be derived from what we see, and the above sentence.

[ Parent ]

Maxwell's Equations in their modern form (3.50 / 2) (#56)
by curien on Fri Jun 13, 2003 at 12:26:11 PM EST

http://rd11.web.cern.ch/RD11/rkb/PH14pp/node108.html

No, I don't understand all that stuff. I learned them in their "simplified" form, where there's no medium to worry about.

--
All doctors do is support weak genes. Might as well be communists. -- sigwinch

And if you want to know what those triangles mean (none / 0) (#60)
by curien on Fri Jun 13, 2003 at 12:35:16 PM EST

Here's a lesson in vector differential calculus. http://www.uic.edu/classes/eecs/eecs520/textbook/node15.html

--
All doctors do is support weak genes. Might as well be communists. -- sigwinch
[ Parent ]
And, if you want the really snappy form; (none / 0) (#83)
by Zealot on Fri Jun 13, 2003 at 06:03:53 PM EST

See equation 52;

http://www.pact.cpes.sussex.ac.uk/users/markh/RQF1/node16.html
Tthis makes use of the 4-vector form of the vector differential operator, and has an accompanying 4x4 tensor, in eqn 48.

This formulation seems to me nicer than the 4 separate equations, and it incorporates 4-vectors directly.

[ Parent ]

Or even snappier (none / 0) (#86)
by a humble lich on Fri Jun 13, 2003 at 06:42:03 PM EST

Your version assumes a flat space time. If you want to include curvature you can make the derivatives covarient and write

F i j; j = 4 pi ji /c

F i k;l + F l i ;k + F k l; i = 0

[ Parent ]

Maxwell's Equations expained (5.00 / 3) (#105)
by jmv on Sat Jun 14, 2003 at 12:21:54 AM EST

This is what the 4 equations basically mean:

1) Divergence of magnetic field (B) is zero. This mean you can't have a "magnetic charge", or monopole.

2) Rotational of electric field (E) equals minus time derivative of magnetic field. This means that a change in magentic fiels will create a "rotating" electric field. That's why electrical generators work.

3) Divergence of electric flux (D, proportional to electric field) is p. This means an electrical charge creates an electric field "radiating" from it.

4) Rotational of magnetic flux (H, proportional to to magnetic field) equals the current density (J) plus the time variation of the electric field. This means that a current or a change in electric field) creates a magnetic field "rotating" around it. This is what makes solenoids and electrical motors work.

Another interesting thing to note is that Maxwell's equations have a symetry between magnetic and electrical fields. Actually, if a magnetic monopole were to be discovered, the symetry would be perfect.

[ Parent ]

What is speed? (3.00 / 3) (#77)
by dipierro on Fri Jun 13, 2003 at 04:55:05 PM EST

Therefore, to have ideas consistent with what had been observed and with the equations that nobody had been able to break, it became clear that the speed of light had to be completely independent of both the speed of the source and the speed of the observer.

I've never heard it explained quite that way before. I wonder, why can't Maxwell's equations just be modified to fix that problem? Or is that what Einstein did?



"Fixing" Maxwell's equations (none / 0) (#81)
by The Writer on Fri Jun 13, 2003 at 05:30:37 PM EST

It's not so simple as "fixing" the equations so that there is a speed built into it. Maxwell's equations describe the interactions between electricity and magnetism, and his equations express this interaction in a way that is completely borne out by experiment. You can't just add speed to it and still be consistent with experimental results.

That's the problem this article is underlining: you can't add speed to Maxwell's equations, but at the same time, you also need to have a speed for light, since experiment has shown that light speed is not infinite.

[ Parent ]

not necessarily (5.00 / 1) (#97)
by dipierro on Fri Jun 13, 2003 at 11:09:45 PM EST

Maxwell's equations describe the interactions between electricity and magnetism, and his equations express this interaction in a way that is completely borne out by experiment.

Obviously not if Maxwell's equations conflicted with the Michelson-Morley experiment.

That's the problem this article is underlining: you can't add speed to Maxwell's equations, but at the same time, you also need to have a speed for light, since experiment has shown that light speed is not infinite.

If you can't add speed to Maxwell's equations, and experiment has shown that light speed is not infinite, then experiment has shown that Maxwell's equations are wrong.



[ Parent ]
conflict (5.00 / 1) (#99)
by adiffer on Fri Jun 13, 2003 at 11:24:18 PM EST

If you look hard at Maxwell's equations, they conflict with Galilean relativity.  The Michelson-Morley experiment showed light did not obey Galilean relativity even though people expected it to do so, so Maxwell's equations were good.
--BE The Alien!
[ Parent ]
Umm (4.00 / 1) (#103)
by dipierro on Fri Jun 13, 2003 at 11:54:21 PM EST

I thought Galilean relativity said that "one cannot use any mechanical experiment to determine absolute constant uniform velocity." That does not conflict with the Michelson-Morley experiment.



[ Parent ]
Galilean relativity (3.00 / 2) (#107)
by jmv on Sat Jun 14, 2003 at 12:35:08 AM EST

Actually, Galilean relativity also includes equations that look like the Lorentz transformations but without the square root of 1-v2/c2. These equations aren't consistent with the speed of light being constant (Michelson-Morley experiment)

[ Parent ]
Galilean transformations... (5.00 / 1) (#108)
by dipierro on Sat Jun 14, 2003 at 12:54:35 AM EST

Yes, the Galilean transformations don't hold. But that was solved by the Lorentz transformations. And it isn't really a problem with it disagreeing with the Maxwell Equations, so much as a problem with it disagreeing with the Michelson-Morley experiment.

So, yes, you're correct, as are parts of all of the above explanations, but no one seemed to have answered my original question. Really it's only epepke who could answer it anyway, since my question is regarding his phrasing. I suspect there's some hand-waving going on somewhere, and it probably has to do with his use of the word "speed" without giving a definition. Of course, defining speed is a large part of what special relativity is about, so maybe this is coming in the next section. If so, I'd certainly like a preview.



[ Parent ]
Speed (5.00 / 1) (#109)
by jmv on Sat Jun 14, 2003 at 01:18:26 AM EST

I don't think special relativity defines speed in a really different way. The only thing it says is that the speed of light is constant no matter what your frame of reference is. That assumption leads to special relativity and turns the Galilean transformations into the Lorentz transformations. (BTW, the principles of Galilean relativity don't conflict with the Michelson-Morley experiment, the the actual Galilean transformations do)

[ Parent ]
speed=distance/time... what's distance?whats time (none / 0) (#111)
by dipierro on Sat Jun 14, 2003 at 02:00:24 AM EST

Well, I didn't say that special relativity defines speed in a really different way. It does of course define time rather differently, which does therefore affect notions of speed, though. I'll let Einstein do the talking:

In order to have a complete description of the motion, we must specify how the body alters its position with time; i.e. for every point on the trajectory it must be stated at what time the body is situated there. These data must be supplemented by such a definition of time that, in virtue of this definition, these time-values can be regarded essentially as magnitudes (results of measurements) capable of observation. If we take our stand on the ground of classical mechanics, we can satisfy this requirement for our illustration in the following manner. We imagine two clocks of identical construction; the man at the railway-carriage window is holding one of them, and the man on the footpath the other. Each of the observers determines the position on his own reference-body occupied by the stone at each tick of the clock he is holding in his hand. In this connection we have not taken account of the inaccuracy involved by the finiteness of the velocity of propagation of light. With this and with a second difficulty prevailing here we shall have to deal in detail later.

Of course, Einstein delves into this much more deeply, but I'd have to quote pages and pages to get it all, so I just threw out that one paragraph to jog your memory. As you see, time is defined with respect to clocks and rigid bodies. But problems come up, such as the fact that you can't accurately measure when something reaches a faraway point without knowing the speed of light (assuming it is finite). You can only measure round-trip times.



[ Parent ]
oops, small correction (none / 0) (#112)
by dipierro on Sat Jun 14, 2003 at 02:02:58 AM EST

As you see, time is defined with respect to clocks and rigid bodies.

That should say speed is defined with respect to clocks and rigid bodies, of course.



[ Parent ]
You're confusing speeds (5.00 / 1) (#124)
by flo on Sat Jun 14, 2003 at 11:37:41 AM EST

That's the problem this article is underlining: you can't add speed to Maxwell's equations, but at the same time, you also need to have a speed for light, since experiment has shown that light speed is not infinite.
Maxwell's equations do include the (finite) speed of light. That's one of their remarkable aspects. From them one can derive a wave equation for light, and one of the constants in any wave equation is the speed of the wave. From Maxwell's equations one can derive the speed of light as an expression in terms of other physical constants (the fundamental charge and magnetic permeability, I think) - and if you plug these constants into the equations (which no doubt Maxwell did) you actually get the measured speed of light as a result. I can just imagine Maxwell working out this value for the wave-speed (assuming he already had good values for the other constants) and suddenly realizing "Holy cow! This number is familiar... it's the speed of light!"

No, the real point about Maxwell's equations, and more specifically this wave equation, is that the speed is just a constant, a number. Nothing about these equations says anything about a possible medium, or about the speed of the light source.

More ominously, Maxwell's equations are not invariant under a Galilean transformation. This means the following. Suppose we have two different coordinate systems ("inertial reference frames"), x and x', neither of which is under acceleration (hence "intertial"), but which are in uniform motion relative to each other, so that x' = x0 + x + vt. This equation means that our two systems are moving at a velocity v relative to each other, and that at time t=0, the difference x'-x was a value x0. (I'm only working with one coordinate here, so we may choose x0 = 0 if we suppose t=0 at the moment both systems were in the same location. If you use all three coordinates x,y,z, then you can no longer assume that both systems were in the same place at some point in time, hence the need for constants x0,y0,z0).

Now, it seemed obvious that Maxwell's equations should hold true in both reference frames - i.e. if you set up an experiment to test them in each of two spaceships, then the outcomes of these experiments should be the same in each spaceship, even if these spaceships are moving (uniformly) relative to each other. Mathematically, this means that if you plug x+x0+vt into the equation instead of x, the equations should still be the same. Notice that t is another variable appearing in the equation, so this is not trivial. As it turns out, however, you do not get the same results for x and x+x0+vt!

This seemed to be a major problem some 100 years back! That's also where the Lorentz transformation comes in: if instead of x'=x0+x+vt you use a different expression (don't remember it off-hand - it's called the Lorentz transformation) for x', then everything works out fine again. I don't know how Lorentz discovered his transformation - it may well have been through (educated) trial and error.

So what does this transformation mean?... I'm sure the author will explain all this and more in his next installment, I don't want to spoil it for him :)
---------
"Look upon my works, ye mighty, and despair!"
[ Parent ]
permittivity and permeability (none / 0) (#133)
by dipierro on Sat Jun 14, 2003 at 05:10:59 PM EST

From Maxwell's equations one can derive the speed of light as an expression in terms of other physical constants (the fundamental charge and magnetic permeability, I think) - and if you plug these constants into the equations (which no doubt Maxwell did) you actually get the measured speed of light as a result.

The speed of light can be derived from permittivity and permeability, and permeability can be calculated from pi (it's really just an arbitrary unit setting constant, like the number of miles in a kilometer). But how can we measure permittivity without using the speed of light?

Nothing about these equations says anything about a possible medium

I thought you were supposed to use the permittivity/permeability of the medium, which would therefore affect the speed of light (and it does).



[ Parent ]
As it says in the article... (none / 0) (#84)
by Zealot on Fri Jun 13, 2003 at 06:13:26 PM EST

...this was attempted, but it predicted various physical effects that were not borne out by experiments.


[ Parent ]
huh? (none / 0) (#96)
by dipierro on Fri Jun 13, 2003 at 11:01:57 PM EST

...this was attempted, but it predicted various physical effects that were not borne out by experiments.

Umm, so did Maxwell's equations!



[ Parent ]
That movie with the bus. (nt) (3.50 / 2) (#94)
by mmsmatt on Fri Jun 13, 2003 at 10:13:56 PM EST



[ Parent ]
SR and GR fixed the problems (none / 0) (#95)
by modmans2ndcoming on Fri Jun 13, 2003 at 10:41:45 PM EST

so yeah, that is what Einstein was all about.

[ Parent ]
*Relativity is dying (1.84 / 26) (#80)
by rmg on Fri Jun 13, 2003 at 05:23:12 PM EST

It is official; A recent Nature poll confirms:  *Relativity is dying

One more crippling bombshell hit the already beleaguered relativity community when APS confirmed that *relativity's market share has dropped yet again, now down to less than a fraction of 1 percent of all active research. Coming on the heels of a recent Nature survey which plainly states that *relativity has lost more market share, this news serves to reinforce what we've known all along. *relativity is collapsing in complete disarray, as fittingly exemplified by failing dead last in the recent Physics Researchers comprehensive usefulness test.

 You don't need to be a Feynmann to predict *relativity's future. The hand writing is on the wall: *relativity faces a bleak future. In fact there won't be any future at all for *relativity because *relativity is dying. Things are looking very bad for *relativity. As many of us are already aware, *relativity continues to lose market share. Red ink flows like a river of blood.

 General relativity is the most endangered of them all, having lost 93% of its core researchers. The sudden and unpleasant departures of long time General Relativity researchers Steven Hawking and Albert Einstein only serve to underscore the point more clearly. There can no longer be any doubt: General Relativity is dying.

Let's keep to the facts and look at the numbers.

Of the Nobel Prizes awarded in physics in the past 10 years, none have been awarded for work in general relativity. New York Times best sellers in the areas of Chaos Theory (Gleick, Chaos) and String/M-Theory (Greene, The Elegant Universe) underscore the public disinterest in General Relativity. With the demise of cosmology writer and General Relativity evangelist Carl Sagan and subsequently author of A Brief History of Time Steven Hawking, this trend is only likely to continue.

Due to troubles with locality, abysmal book sales and so on, General Relativity was abandoned and was taken over by Quantum Field Theory (QFT) which proposes another troubled program to explain gravitation. Now QFT is also dead, its corpse turned over to yet another dubious theory.

All major surveys show that *relativity has steadily declined in market share. *relativity is very sick and its long term survival prospects are very dim. If *relativity is to survive at all it will be among physics dilettante dabblers and readers of popular science. *relativity continues to decay. Nothing short of a miracle could save it at this point in time. For all practical purposes, *relativity is dead.

Fact: *relativity is dying.

_____ intellectual tiddlywinks

Maxwell's equations are dead, too (n/t) (none / 0) (#118)
by tetsuwan on Sat Jun 14, 2003 at 02:56:33 AM EST


Njal's Saga: Just like Romeo & Juliet without the romance
[ Parent ]

Fact: The Heisenberg Picture is dying. [nt] (none / 0) (#123)
by rmg on Sat Jun 14, 2003 at 11:01:22 AM EST



_____ intellectual tiddlywinks
[ Parent ]

Fact: The Hamiltonian is dead (n/t) (none / 0) (#145)
by tetsuwan on Sun Jun 15, 2003 at 02:01:41 PM EST


Njal's Saga: Just like Romeo & Juliet without the romance
[ Parent ]

Lack of research does not mean "dying" (5.00 / 1) (#129)
by Chemisor on Sat Jun 14, 2003 at 02:21:37 PM EST

Every scientific subject eventually reaches a point when no further study can be conducted on it because everything is already known. Theory of relativity is by itself not a very complex subject. It can be, and probably has already been, studied exhaustively. Unless someone comes up with some new ideas, new questions, or new data, nobody will bother doing any more studies on it. Just like nobody does arithmetic research any more.

[ Parent ]
Ok. Who let in the /. Troll! (1.00 / 1) (#134)
by Cheerio Boy on Sat Jun 14, 2003 at 05:35:46 PM EST

Next time keep the gates closed!

"Relativity is dying" == "BSD is dying".

And remember to use your anti-troll flamethrower...



[ Parent ]
Look, this might be true... (3.00 / 2) (#135)
by rmg on Sat Jun 14, 2003 at 08:48:25 PM EST

but can you really say that the rest of the drivel passing as discussion here is more intelligent? I mean, read the comments. It's not good. We have people taking quotes from popular science books like A Brief History of Time, people making arguments that rely on their ability to "question logic" (as though they have unique and unusual capacities in this area), all sorts of hand-waving and lame philosophizing, etc. etc. This may be a troll, but at least I chuckled to myself over it. Maybe someone else did. Compare to the other posts. Most of them just depressed me. So please don't use your flamethrower on me. If you did, you would be no better than a certain dictator who gassed his own people.

_____ intellectual tiddlywinks
[ Parent ]

Charnel House! (none / 0) (#176)
by ethereal on Wed Jun 18, 2003 at 01:01:29 PM EST

Sadly, you were so close, yet so far.

--

Stand up for your right to not believe: Americans United for Separation of Church and State
[ Parent ]

A Question (3.00 / 1) (#87)
by machiavellieins on Fri Jun 13, 2003 at 07:42:26 PM EST

I pose a question to those more relativity-savvy than myself: You have two masses held stationary a certain distance from each other, and let them go. They accelerate towards each other due to the force of gravity and eventually collide. If you place the same objects a little further apart and let them go, they will again accelerate and collide, yet the velocity just before collision will be larger as they have had a greater distance and thus greater time to gain speed over. You keep increasing the initial separation distance until this precollision velocity is that of light. 'Aha!' say you; the objects get more massive as they accelerate meaning that as they approach light speed their mass will be so great no further acceleration is possible. Yet the force that causes this acceleration, gravity, is directly related to the mass of the objects it comes from. Thus though the objects gain mass as they go faster, any resistance to acceleration will be countered by an increased force of gravity. I think to myself that this idea is false somehow, but I can't explain why.

Gravitational potential, dude. (3.33 / 3) (#88)
by Apuleius on Fri Jun 13, 2003 at 08:13:47 PM EST

It comes in finite quantities. If you separate two objects by an infinite distance (now the mathematicians and physicists gather to fillet me), the potential energy stored up by this is finite. And never sufficient to get lightspeed.


There is a time and a place for everything, and it's called college. (The South Park chef)
[ Parent ]
Gravitational potential, dude. (5.00 / 3) (#90)
by nine4mortal on Fri Jun 13, 2003 at 09:21:52 PM EST

Actually, separating objects an infinite distance leads to a very finite amount of stored energy.  Classically, gravitational potential energy is

- G m1 m2
-----------
    r

G is the gravitational constant.
m1 and m2 are the masses of the two objects.
r is the distance between their centers of mass.

As long as the objects have finite size (i.e. They are not points), the difference in potential energy between r=infinity and when they collide will be finite.  (You will get infinity out of this equation only if one of the objects has zero radius but finite mass.)

The neat thing here is that what is important to the original question is not how far apart you start the objects but how dense the objects are.

For most objects, they will never get anywhere near the speed of light because of gravitational acceleration; they will collide first.

Of course if you make the objects dense enough at some point you are going to have to stop using classical mechanics and start using general relativity to solve this problem.

"Nine for Mortal Men doomed to die..."
[ Parent ]

Acceleration (none / 0) (#91)
by EminenceGrise on Fri Jun 13, 2003 at 09:53:00 PM EST

One thing you should note is that the acceleration (caused by one of the objects by the other one) varies with the square of distance, like so:

a=(GM)/r^2

where G is the Universal Gravitational Constant, M is the mass of one of the objects (say it's the "big" one, e.g. of a tennis ball and the Earth, it's the Earth), and r is the separation between the centers of mass of the objects.

The basic consequence of this is that you will have much better luck with your "experiment" if you make one of the objects extremely massive (such that a~=c).  Of course to get something big (and dense) enough, you'll need something like a neutron star or black hole (minimum).  An interesting approach to the problem night be to consider things in terms of the escape velocity.  However....

You've hit on the reason why we need things like Special (and General) Relativity in the first place - things behave much differently at or near the speed of light.  To even do the problem, you have to consider all kinds of things like Lorentz transformations and such that make even the simple equation above much more complicated.  In short, "near-luminal" problems like this don't behave intuitively (unless you are extremely familiar with General Relativity, and even then, you'd be hard pressed to find someone who is this familiar with the theory to say it was intuitive).  That's why you find yourself saying "I think there's something wrong with this", and why Relativity is extremely bad ass (IMHO).

[ Parent ]

That's kind of interesting (none / 0) (#92)
by epepke on Fri Jun 13, 2003 at 09:57:15 PM EST

20 years or so ago, Martin Gardner wrote an article in Scientific American about an idealized, completely smooth, gravitational world. It turns out that in such a world, it's possible to set up a system of masses such that part of it can be accelerated to infinity in a finite amount of time. This seems awfully weird, and I wish I still had the article, because I can't remember exactly how it worked.

You keep increasing the initial separation distance until this precollision velocity is that of light. 'Aha!' say you; the objects get more massive as they accelerate meaning that as they approach light speed their mass will be so great no further acceleration is possible.

You will get into trouble by mixing special relativistic ideas with Newtonian ideas, especially at the limit. Gravity is what General Relativity is for. Unfortunately, I think that a lot of bad cosmology is based on such mixing, but I digress.

But even we pretend that it's OK to think in terms of Newtonian gravity, modified slightly with the idea that gravitational attraction travels at the speed of light, you can see in a qualitative way why this can't happen. The equivalence of the inertial and the gravitational mass is the basic justification for the Principle of Equivalence in GR. However, in a modified Newtonian system, though the gravitational mass may be the same as the inertial mass, the gravitational force takes some time to get from one mass to the other. Thus, for the purposes of gravitation, a mass will "see" the other mass not as it is "now" but rather as it "was" a moment when the gravitational force "left" it. So, if the relativistic mass of one increases, it will take the other mass some time to "see" this increase.

Of course, concepts like "now" don't have much meaning in terms of relativity.


The truth may be out there, but lies are inside your head.--Terry Pratchett


[ Parent ]
Finite-time singularities (none / 0) (#147)
by debillitatus on Sun Jun 15, 2003 at 04:00:42 PM EST

I'm not sure about this Gardner article you refer to, but what you said reminds me of a phenomenon which happens in the (more than) 3-body problem. It was shown (by Saari, I think) that if you have three bodies using standard gravitation, there are "near-triple-collision" solutions which have one body moving out with arbitrarily high speeds. I guess the other two have to pass really close to each other to store up the potential energy for transfer, I'm not sure.

Anyway, this sort of scenario was exploited by Xia in a 5-body problem, where you have two pairs of closely orbiting bodies, and one which shuttles between them. Anyway, through some complicated machinations, the pairs continue to exchange the lone body and accelerate it each time. In short, some sum doesn't converge and you get to infinite velocity in finite time.

Of course, this is using the idealization of Newtonian mechanics and point-masses, which is of course completely unrealistic. This example is well-known not because it's practically applicable, but because it was a good application of certain techniques in dynamical systems theory. Also, celestial mechanics guys tend to use Newtonian mechanics because their regimes are typically at very low speeds, so there is no relativistic correction.

The real reason something so unintuitive can happen is that the "energy surfaces", i.e. the surface of constant energy in phase space, is unbounded in classical celestial mechanics. As far as I know, whether these surfaces are bounded or unbounded is an open question for relativistic mechanics (lot harder question because the phase-space is now infinite-dimensional).

Damn you and your daily doubles, you brigand!
[ Parent ]

That sounds like it (none / 0) (#158)
by epepke on Mon Jun 16, 2003 at 08:30:52 AM EST

As I remember, Gardner used a 5-body problem as the basic example. I think there was also an 8-body problem that was easier to understand.


The truth may be out there, but lies are inside your head.--Terry Pratchett


[ Parent ]
I'll try to answer (none / 0) (#101)
by Angelic Upstart on Fri Jun 13, 2003 at 11:45:03 PM EST

tho I'm not the smartest guy out there and I'm most likely wrong. First the force of gravity is goverened by the inverse square law, that is the farther from the source the less the effects of gravity is so I don't think you could keep placing them farther apart because the force of gravity would keep getting weaker and weaker. but say that what you say could happen. Gravity like all electromagnetic force travels at the speed of light. so I would believe it would be the same old story of a person standing in a space ship traveling near the speed of light and turns on a flash light pointed forward, would the light from the flash light travel faster than the speed of light? nope it would be going the speed of light reletive to the observer! or something like that. I'm sure this makes no sense and doesn't help anyone and I'm dumb. so no flaming me please.

[ Parent ]
Two Things (none / 0) (#126)
by machiavellieins on Sat Jun 14, 2003 at 12:35:21 PM EST

First, gravitational potential energy is equal to the integral of the function of the force of gravity over some interval of distance. Thus GPE= -(GM1M2)/(R) from a to b. Say you have two massive stationary objects, each 10^40 kilograms in mass and 25 miles (about 40,000 meters) across. You let one go a distance of a 10^25 meters from the other. The work done by gravity until collision is equal to ((6.67 x 10^-11) x (10^40) x (10^40))/(4 x 10^4) minus ((6.67 x 10^-11) x (10^40) x (10^40))/(10^25), which is 1.67 x 10^65 Joules. The kinetic energy of one of these objects at light speed is (.5) x (10^40) x (c squared), which is 4.48 x 10^56 Joules. Thus, in terms of classical mechanics, these objects, whatever their composition, would theoretically have the capacity in terms of potential energy to reach light speed. Second, I view the idea presented that the force of gravity would be warped at relativistic velocities as the likely answer to this query. But how would one describe that in terms of equations and numbers? In other words, what final function can be derived to describe the motion of two masses accelerating towards each other taking Einstein's ideas into account?

[ Parent ]
Answer (5.00 / 2) (#138)
by alexppii on Sat Jun 14, 2003 at 10:46:40 PM EST

You're basically right, except for one thing: the equation

Kinetic Energy = 1/2 * m v^2

is an approximation, valid only when v << c. The relevant equation here is: <p>E = (gamma) mc^2

where

(gamma) = (1 - v^2/c^2)^(-1/2) (An easier to read version can be found here).

You might notice that when v<<c (classical approximation) this equation reduces to <p>E = mc^2 + (1/2) mv^2, or Total internal energy = Rest energy + kinetic energy.

In any case, to find the final velocity v:

with M=10^40 kg, W=1.67*10^65 J/2,

E(final) = Mc^2 + W = (gamma)Mc^2 and (some algebra later)

v = c * sqr(1 - (Mc^2/(Mc^2+W))^2) = c * (1 - 5.79 * 10^-17) = c * 0.9999999999999999421

which is not quite light speed (but pretty close).

--Alexei

[ Parent ]

Some <p>s didn't work-- ignore them [n/t] (none / 0) (#139)
by alexppii on Sat Jun 14, 2003 at 10:49:42 PM EST



[ Parent ]
The real answer... (4.66 / 3) (#143)
by statusbar on Sun Jun 15, 2003 at 08:52:19 AM EST

Is that the 'gravitational force' (or your space-bending equivalent) of an object is related to its 'Rest Mass' - It is not related to the relativistic mass at all.

In fact, the relativistic mass itself is kind of like a slight of hand to make the normal concepts of momentum and inertia and their calculations work out - such that the object's 'resistance to acceleration' increases as the object goes closer to the speed of light.

The object does not get heavier, it just gets harder to push it even faster. Eventually as v approaches c, this resistance to acceleration approaches infinity.

I am not a physicist but I had asked a phd physics professor this exact question before.

Gravitation is related to the rest mass.  Resistance to acceleration is related to the relativistic mass.

--jeff++

[ Parent ]

That still isn't quite it, I'm afraid (none / 0) (#170)
by epepke on Tue Jun 17, 2003 at 09:53:57 PM EST

Is that the 'gravitational force' (or your space-bending equivalent) of an object is related to its 'Rest Mass' - It is not related to the relativistic mass at all.

I'm afraid that this still isn't quite right. The thing is that the spacetime-bending is definitely not at all the same as force. In GR, gravitation is not a force: it's the absence of a force. Someone moving past the Earth very fast, watching the moon go around, would see the resistance to acceleration for both the Earth and the Moon go up. If they had the (fictitous, according to GR) idea that gravitation was a force and worked according to F=dp/dt, then they would have to see the gravitational effects of the masses increased as well. They would have to, because they have to see the same path (corrected for Lorentz contraction and all that). One way of stating the basic principle of GR, the principle of equivalence, is that the inertial mass is always the same as the gravitational mass.

We can calculate the spacetime curvature resulting from something like the Earth (using the Schwarzchild solution). When we do so, we only use the rest mass. We can be confident that our results hold, at least in terms of the geodesics, because they have to hold for all observers. Otherwise, relativity would be broken. However, that's a very different thing from saying that there's something special and absolute about the rest mass. It's conceivably possible to work out the equations of GR in other, weird frames of reference, but in practice, it's terribly hard. Even the Schwarzchild simplified solution is pretty impressive.

So, in one sense, you can say that the distortion of spacetime around a mass only depends on the rest mass. In another sense, you can say that it depends on the relativistic mass, but so does everything else, and it all comes out in the wash.

There are two things about relativity that are quite difficult to get across, even though I'm going to try to do it anyway. One is that it's really relative. I mean it. Seriously. People don't generally like this; they want to say "OK, so it's relative, but c'mon, tell me what's the distance or the mass really." But the whole point of relativity is that you can only tell what's happening relative to you. There usually isn't a a nice, pat answer. The other thing is that most of that stuff we are used to dealing with, including time and space and energy and momentum, consist of shadows (in the case of Minkowsi space, quite literally) of a more basic way of looking at the universe based on the speed of light and the gravitational constant, and there's even hope that we might be able to derive one from the other.

You're welcome and invited to print this out and show it to any PhD physicist of your choosing to see if I'm lying or full of shit.


The truth may be out there, but lies are inside your head.--Terry Pratchett


[ Parent ]
Interesting (5.00 / 1) (#172)
by statusbar on Wed Jun 18, 2003 at 04:58:00 AM EST

Thanks for the clarification... But... can you clarify a little bit further for me?

The moon causes spacetime to bend in its vicinity because of the moon's mass.  If I fly past the moon at 0.9c, would the spacetime bend around the moon 'appear' larger? ie is spacetime curved differently for different observers? If I flew past a star at 0.9c would my path depend on the relativistic mass of the star?

I would think it wouldn't.  Is that a correct assumption?

If my assumption is incorrect, wouldn't it mean that light itself would observe the star's relativistic mass to be infinite and therefore equivalent to a black hole?

(thanks, it's been a while since i've thought about this stuff)
--jeff++

[ Parent ]

Yes in the sense of no (none / 0) (#173)
by epepke on Wed Jun 18, 2003 at 08:58:49 AM EST

The moon causes spacetime to bend in its vicinity because of the moon's mass. If I fly past the moon at 0.9c, would the spacetime bend around the moon 'appear' larger? ie is spacetime curved differently for different observers? If I flew past a star at 0.9c would my path depend on the relativistic mass of the star?

Again, this is one of the trickinesses of talking about relativity. Most of the time, when people talk about relativity, they lie a bit to make things simple. I'm trying very hard not to lie. Many people get the idea that relativity is strange or counterintuitive and doesn't work with common sense. I have a different idea: I think that you have to use your common sense in an unusual way, but if you do, it's just fine.

One of the things about GR that makes it hard is that, while it's fairly easy to calculate the net distortion of a spacetime, it's very difficult to calculate how this works out in different directions.

If you were going past the moon at 0.9c, you would measure a lot of things that seem strange. For one thing, you would see the moon as contracted in the direction of your (or its) travel (although I'm probably getting ahead of myself here). It'd look something like a blancmange or a flabby soccer ball. At 0.95c it would be more like a custard pie, and 0.99c, it would look more like a New York pizza. You'd also see some time effects. You would also have to see the geodesics (the "straight lines" in spacetime of falling bodies, like orbits) contracted by the same amount. So, you would see the orbits as skinny ellipses, with part very flat but part very curved. If you calculated the net curvature of spacetime of the (to you) fast moon in your frame of reference, you would get a number that is consitent with the (to you) relativistic mass of the moon.

Or you could save yourself a lot of pain and suffering and just calculate it in the frame of reference of the moon using only the moon's rest mass. Because it's relative, it has to work out the same.

In my opinion and to my way of thinking, the best way of thinking about relativity is not to argue what is the real, true mass or the real, true distance or time, because there are different ways of solving the equations, and we have some freedom in what we pick as seeming constant or obvious. Solving GR in such a way that the curvature only depends on the rest mass is popular because it's comparatively easy. Similarly, particle physicists prefer to solve the equations of SR in such a way that m is always the rest mass, and the idea of relativistic mass isn't used at all. (They prefer to talk about relativistic energy.)

Rather, the best way is to trust that no matter how we solve the equations, as long as we keep in mind every effect, it's all going to be consistent. That is in my opinion the deep meaning of relativity. It's bad news for people who are uncomfortable if they don't have absolutes (there are absolutes in relativity, such as the speed of light, but people don't seem to like them as much: the speed of light just doesn't somehow seem as solid as a bowling ball). On the other hand, it's also good news, because it means that we have some freedom to pick the solutions of the equations that are easiest to solve and have most relevance to the problem at hand, confident from the principle of relativity that it would work out the same if we did it a harder way.


The truth may be out there, but lies are inside your head.--Terry Pratchett


[ Parent ]
Wow! (none / 0) (#178)
by statusbar on Wed Jun 18, 2003 at 03:14:10 PM EST

Excellent, thank you for your response!

--jeff++

[ Parent ]

want some cool info for Reletivity stuff + beyond (4.33 / 3) (#89)
by modmans2ndcoming on Fri Jun 13, 2003 at 09:20:54 PM EST

for the novice that is(these books got me into physics in highschool)

Michio kaku:
Hyperspace

Michio Kaku & Jennifer Thomson:
Beyond Einstein

Kip S. Thorne:
Black Holes & Time Warps

and the grand daddy of em all......

Stephen Hawking:
A Brief History of Time (illustrated or not illustrated)

those were my favorites but there are a lot more I enjoyed reading rather than listen in my classes :-)

best book, free book, my book (none / 0) (#169)
by bcrowell on Tue Jun 17, 2003 at 08:56:51 PM EST

The all-time greatest nonmathematical book on relativity is Relativity Simply Explained, by Martin Gardner ($12 paperback).

Einstein's own popular-level book is available on Project Gutenberg.

Feel free to check out my own humble offering (see ch. 6).

For the mathematically adept, I'd suggest Taylor and Wheeler's Spacetime Physics as a second go-around.

The Assayer - book reviews for the free-information renaissance
[ Parent ]

The link seems to be broken [n/t] (none / 0) (#174)
by epepke on Wed Jun 18, 2003 at 09:11:11 AM EST


The truth may be out there, but lies are inside your head.--Terry Pratchett


[ Parent ]
You forgot the best parts (4.66 / 6) (#93)
by EminenceGrise on Fri Jun 13, 2003 at 10:10:54 PM EST

Those being:

Tycho Brahe died from a perforated bladder after he spent too long at the dinner table with some nobleman (it was considered bad manners to leave the table before someone of higher stature (condensed version)).  Also interesting is that it was only after Brahe's death that Kepler was able to get full access to Brahe's data and "prove" his theory (Brahe was a bit, well, paranoid about other's stealing his work, and had only let Kepler see bits and pieces of his work).

Of the Michelson-Morley duo, one of them (I think it was Morley, but I can't remember for sure now) spent the rest of his life re-running the experiment because he didn't believe the results.  He essentially went to his grave not believing the results of his own experiment.

Yes, these are only side notes as far as Relativity goes, but they're cool side notes.
 

Yep (none / 0) (#117)
by tetsuwan on Sat Jun 14, 2003 at 02:51:17 AM EST

Kepler actually stole the charts from Brahe's family.

Njal's Saga: Just like Romeo & Juliet without the romance
[ Parent ]

I didn't mention Brahe's gold nose, either [n/t] (none / 0) (#120)
by epepke on Sat Jun 14, 2003 at 07:23:43 AM EST


The truth may be out there, but lies are inside your head.--Terry Pratchett


[ Parent ]
Another aside (5.00 / 2) (#122)
by flo on Sat Jun 14, 2003 at 11:00:36 AM EST

Poincare never accepted Einstein's special theory of relativity. Neither did Lorentz, IIRC. This is quite ironic, given their contributions to the theory. (Further aside: Planck didn't believe his own theory - quantum theory - for more than a decade).
---------
"Look upon my works, ye mighty, and despair!"
[ Parent ]
yes (5.00 / 2) (#130)
by heng on Sat Jun 14, 2003 at 02:33:08 PM EST

much like Einstein never accepted quantum mechanics. "God doesn't play dice".

[ Parent ]
anecdote continues (none / 0) (#161)
by Toshio on Mon Jun 16, 2003 at 12:22:51 PM EST

Presumably this was written in a letter to Niels Bohr, and in the following letter he got his answer, that included something in effect of "Albert, please don't tell god what it can or can not do".

--- To boldly invent more hot water ---
[ Parent ]
Probably an easy question.. (4.25 / 4) (#100)
by nightfire on Fri Jun 13, 2003 at 11:32:36 PM EST

.. but one no one's ever given me a satisfying answer to.

Imagine I'm at a midpoint A (say, a planet), and I have two objects approaching me, from opposite directions, at the 75% the speed of light. I know they're travelling this fast, because according to calculations, they should both arrive in about an hour (and they started ~1.3 light-hours away from me).

If someone were to ask me what their speeds are, relative to each other, I'd have to say 1.5x the speed of light, wouldn't I?

You could... (none / 0) (#102)
by dipierro on Fri Jun 13, 2003 at 11:52:15 PM EST

If someone were to ask me what their speeds are, relative to each other, I'd have to say 1.5x the speed of light, wouldn't I?

You could say that. But if you did, they wouldn't agree with you.

Alternatively, you could say the speed they think they are travelling relative to one another, which is 0.96c.



[ Parent ]
Yes (3.50 / 2) (#104)
by jmv on Sat Jun 14, 2003 at 12:02:53 AM EST

From your point of view, they are moving at 1.5x the speed of light, but it's no problem. Relativity just says that an object can't go faster than the speed of light from your point of view. In this case, the two objects would measure that their speed relative to each other is something like 85% (didn't make the exact calculation) of the speed of light.

[ Parent ]
"Speed Relative to each other" (4.50 / 2) (#121)
by Transfer Error on Sat Jun 14, 2003 at 10:05:28 AM EST

Important thing is: the relative velocity of two objects is not invariant (as it is in classical mechanics). Different observers will measure different velocities.

Everything depends on how you define the term "speed relative to each other". Usually you mean the speed one observer in rest measures for another object. In this case: an observer in one spaceship (that is in rest in her point of view and everything else is moving) would measure the speed of the other spaceship. And for sure she will mesure something smaller than the speed of light.

[ Parent ]

Lorentz transform (5.00 / 4) (#127)
by Nafai on Sat Jun 14, 2003 at 12:39:17 PM EST

From your perspective they are both going .75c, but from the spective of each other, the ships are not. The mathematics behind this are more complex than simply Speed(Ship1) + Speed(Ship2), and actually ends up looking something like:

(.75+.75)/(1+.75*.75)
or
(speed1 + speed2) / (1 + speed1 + speed2)
which = 1.5/1.5625 = 0.96

Google for "Lorentz transforms" or check out a beginner's book on relativity. Of course, you could probably also wait for epepke's next submission, as I'm sure he will discuss this in depth in his coming articles.

[ Parent ]

Nope. (5.00 / 2) (#136)
by mindstrm on Sat Jun 14, 2003 at 09:17:00 PM EST

Because it's relative to the observer. What you see is two ships approaching you at .75c

Your calculations from your point of view are correct, and they will both arrive in about an hour, of your subjective time.

What you must remember is there is no such thing as absolute speed, or absolute time.  From the viewpoint of one of the approaching craft, they see:   You standing on your ship, approaching them at .75c, and another ship, approaching from further away at .96c (their relative speed according to each other,I'm relying on other posts calculations).  They will probably agree that everyone is going to smack into the same point coincidentally.. but that's about it.

[ Parent ]

How about distance (5.00 / 1) (#148)
by daby on Mon Jun 16, 2003 at 12:57:44 AM EST

The measured speed by the "ships" will be different than the one measured by the observer (man in the middle). Since this is the case then what is the distance between the ships in the frame of reference of the "ships"? How long before they all meet from the point of view of the Approaching ships? Since the Approaching ships are moving 0.75C in relation to the observer wouldn't they measure less time until meeting each other, compared to the observer, and hence reckon that the distance is less than 1.5 C hours? Adding a third observer, another frame of reference, always puts a dent into my general confusion. :) Regards.

[ Parent ]
it's magic :) (1.50 / 2) (#181)
by dipierro on Wed Jun 18, 2003 at 09:22:13 PM EST

Well, there are several problems with this. First of all, there is no way for the ships and the observers to agree on simultanaeity. So while the observer might start the timer at one point, the observer might start at a different point. Secondly, you have to remember that each observer thinks that the length measuring devices of all the other observers are shortened.

As for a more specific answer, it all depends on what method you use to determine the distance and time. You can send light beams, you can use geometry, you can do any type of experiment you want, and it's all going to work out almost magically in the end. It's not really magic, though, the Lorentz transformations were specifically designed to work that way.



[ Parent ]
No, they will agree on simultaneity... (none / 0) (#183)
by mindstrm on Wed Jun 18, 2003 at 10:50:38 PM EST

if that's even a real word, because they are all going to arrive at the same point in spacetime. Any observer from any location will have to agree they will all arrive at the same time, because that part is absolute.

IF we have A -> C <- B, where A & B are approaching C on opposite vectors at .75c, and if we assume the transformation means A & B see each other as .96c as someone said (I haven't verified) then :

C looking at A or B sees the same thing as A or B looking at C: same distance, same time to contact.. because they are approaching each other in spacetime.

A & B, however, will see each other goign at .96c,  and as they all agree on the time they will intersect, the distance from C to B from A's point of view (or the opposite) will appear to be shortened, compared to what C sees.

[ Parent ]

Err, I'm wrong... (none / 0) (#184)
by mindstrm on Wed Jun 18, 2003 at 10:55:28 PM EST

It should be longer... the distance between C & B would seem stretched from A's point of view... not shortened. As the apparent speed is higher, and the amount of time until intercept is the same, the distance would have to appear larger.

[ Parent ]
yes, on the arrival times... (3.00 / 2) (#186)
by dipierro on Thu Jun 19, 2003 at 12:02:09 AM EST

But they don't have to agree on the start times.

[ Parent ]
you're all so pathetic. (1.72 / 11) (#119)
by lester on Sat Jun 14, 2003 at 05:14:59 AM EST

you'll vote up anything you don't understand as long as it is "science"

Maxwell's Quaternions (4.50 / 2) (#128)
by Baldrson on Sat Jun 14, 2003 at 01:00:12 PM EST

Maxwell expressed his equations in quaternion form and set the stage for what might have been a much shorter route to general relativity.  It is interesting to think about the path not taken in intellectual development as much as the path taken when the path not taken would have been shorter.

-------- Empty the Cities --------


I bet you're right (none / 0) (#166)
by epepke on Tue Jun 17, 2003 at 03:43:52 PM EST

Quaternions are excellent; I'm going to mention them in Part II, if I ever get the damn ASCII diagrams straightened out. I find them much more intuitive than pseudo-4-vectors with weird operators or rotations in Minkowski space. Unfortunately, they never really caught on, except in computer graphics and some particle physics.


The truth may be out there, but lies are inside your head.--Terry Pratchett


[ Parent ]
biquaternions (none / 0) (#191)
by adiffer on Tue Jun 24, 2003 at 10:09:18 AM EST

The path toward GR leads through biquaternions and tensor products of two of those spaces.  It's neat stuff.  Some of us are playing with those options.
--BE The Alien!
[ Parent ]
Good book on the topic... (5.00 / 1) (#132)
by clearbreach on Sat Jun 14, 2003 at 03:05:44 PM EST

"Einstein's Theory of Relativity" by Max Born Loaded with lots of diagrams and equations, and all that sort of fun stuff that people like me clearly won't ever understand. Nonetheless, much fun to read if you've got a lot of free time.


----------
[01:52:06] <mikepence> only in computer science do men tease one another claiming that theirs is smaller
Mr Tompkins in Paperback (none / 0) (#155)
by c4miles on Mon Jun 16, 2003 at 07:58:36 AM EST

From Cambridge University Press. Excellent layman's introduction, suitable for kids and adults alike, by a Nobel Prize-winning physicist. For the less demanding reader who still wants to know the interesting stuff. Not a lot of hard science but a lot of stuff paving the way for a younger (or less mathematical) person to work their way onto the hard science - "firm" science, if you will.
--
For the Snark was a Boojum, you see.
[ Parent ]
Discoveries made 'at the same time' (4.50 / 2) (#140)
by ebatsky on Sun Jun 15, 2003 at 04:11:31 AM EST

I've thought about this before but I can't really come up with a good solution... Maybe somebody can help me.

I'm curious about how often when there is a scientific breakthrough of some kind, there are usually at least one other person that comes up with the exact same thing and often at the exact same time (often in the same day) as the person credited with the invention. Granted, I haven't really put much thought into it, but it just came back to me when this article mentioned Lorentz and FitzGerald coming up with the same idea independently. How does this happen?

Here's a couple of solutions I can think off the top of my head (and also counter arguments to them):

  1. All information to create the specific invention/discovery has been made available at one time and so more than one person is able to improve on it and come up with the same result.

    The problem with that is how is it possible for people who've worked at some problem for many years to come up with the exact same solution in practically the same day? Also, these are people who are mostly unrelated to each other, living in different countries, etc., so sharing their findings is often unplausible as well, especially in earlier times before Internet, big universities, multilanguage scientific journals, etc.

  2. People steal each other's work and then present it as their own at the same time as the original creator.

    Firstly, this has happened too often to be able to attribute it all to stealing. Secondly, the point above about being unrelated and unable to share information also applies.

  3. The only other thing I've been able to come up with is too mystical and I would have a hard time believing it myself. Basically it goes something like, at a certain time we're meant to discover something and therefore more than one person makes that discovery in case one of them fails due to accident, death, etc.

So, any other ideas?

There is nothing like "at the same time" (none / 0) (#142)
by Transfer Error on Sun Jun 15, 2003 at 08:42:09 AM EST

Different observers will measure differnt time intervalls. It's relativity! :)

[ Parent ]
True, but (5.00 / 1) (#167)
by epepke on Tue Jun 17, 2003 at 04:06:52 PM EST

I think that most of the discoveries involved in relativity were separated by timelike intervals.


The truth may be out there, but lies are inside your head.--Terry Pratchett


[ Parent ]
here here (none / 0) (#149)
by relief on Mon Jun 16, 2003 at 02:15:51 AM EST

its probably a combination of the first two.

its also probably that both parties come up with near finished solutions, but the slower party rushes to present his solution, or at least tries to get some credit for the work he's done.

i would imagine that progress of such magnitude would be quite slow, and this is what makes such "coincidences" possible.

if you weigh the amount of "coincidences" and the amount of "non coincidences", the number of coincidences isn't all that significant. its like asking "how come EARTH is populated with life, and not the other planets?"... well duh. =)

----------------------------
If you're afraid of eating chicken wings with my dick cheese as a condiment, you're a wuss.
[ Parent ]

I think you are basically right (none / 0) (#152)
by Confusion on Mon Jun 16, 2003 at 03:55:10 AM EST

Number one sounds like a valid option. For some experimental evidence: the art of printing books was invented three seperate times, during a relatively short time period, in Germany, the Netherlands and England. The times between the inventions were so short, that the news could have travelled, but not the technical details.

On a similar note, agriculture has definitely been invented more than one time. On a more philosophical note: religion has been invented more than one time, though not entirely seperate from each other.

Lorentz didn't recognize his math for what it was, but obviously the knowledge and the ideas were already there. It was just lacking someone to recognize its power.
--
Any resemblance between the above and reality is purely coincidental.
[ Parent ]
another option (5.00 / 1) (#162)
by adiffer on Mon Jun 16, 2003 at 06:19:47 PM EST

Some of us talk to each other and share ideas directly.  Very often, we walk away from these conversations thinking the other person said one thing when they said another.  If the conversation was on something close to the subjects both reaserchers are working on, though, the shared information may morph into a shared idea without either one realizing the other person helped make it happen.

I've seen this happen and been involved in one such exchange.  It is due to the inefficiency of communication.
--BE The Alien!
[ Parent ]

Discoveries announced 'at the same time' (5.00 / 1) (#163)
by gks on Tue Jun 17, 2003 at 03:48:49 AM EST

These people often work on their invention/discovery for many years before they present their information, it is possible that one hears the news of the other and iimmediately publishes their work, hoping to get credit.

[ Parent ]
Lorentz, not Lorenz (5.00 / 1) (#141)
by Confusion on Sun Jun 15, 2003 at 07:44:42 AM EST

You've spelled the name of Lorentz as Lorenz on several occasions. That wouldn't be all that bad, if it weren't for the fact that Lorenz was also a physicist of the last century that attached his name to some well-known (at least to physicists) phenomena. Lorentz was a Dutchman, Lorenz was a Dane.
--
Any resemblance between the above and reality is purely coincidental.
<p>You're right, and thanks.</p> (none / 0) (#144)
by epepke on Sun Jun 15, 2003 at 10:31:36 AM EST

I also misspelled Minkowski.


The truth may be out there, but lies are inside your head.--Terry Pratchett


[ Parent ]
Twin paradox (5.00 / 1) (#150)
by Dievs on Mon Jun 16, 2003 at 03:16:44 AM EST

  The change in subjective time is often explained by a story, where there are two twins, one stays on Earth, and other goes in a rocket at near-c speed away and back to earth.
  They would be of different ages then, because in the rocket at the very high speed time would pass slower.

But, if all the objects are relative, then we cannot say that 'rocket is moving faster than the earth', because there is no absolute speed.

Can someone explain what is the difference between the rocket and the earth - looking from earth, rocket accelerates and returns, and would experience slower time. But, looking from the rocket, the Earth accelerates and comes back, and thus those on the Earth would experience slower time !

I sort-of understand relativity, and QM and physics in general, but this twin paradox has always baffled me.

Acceleration is the key (5.00 / 2) (#151)
by Confusion on Mon Jun 16, 2003 at 03:48:20 AM EST

In contrast to velocity, which is relative, acceleration is an absolute. The twin that remains on earth, doesn't change from inertial system. The twin that moves in the rocket and accelerates with the rocket, is the one that ages more slowly. The problem isn't symmetric, because only one twin undergoes acceleration. Perhaps this link (and sublinks) wil explain more clearly.
--
Any resemblance between the above and reality is purely coincidental.
[ Parent ]
General relativity (5.00 / 1) (#153)
by Cameleon on Mon Jun 16, 2003 at 06:11:05 AM EST

Also, this is general relativity, while this article only talks about special relativity, which is much easier, both in concepts and in mathematics.

[ Parent ]
No need for GR (5.00 / 1) (#160)
by Confusion on Mon Jun 16, 2003 at 09:12:02 AM EST

The twin-paradox can be explained in Special Relativity.
At least, it was in my book on special relativity ;)
--
Any resemblance between the above and reality is purely coincidental.
[ Parent ]
I remember seeing something like that (none / 0) (#171)
by epepke on Tue Jun 17, 2003 at 09:55:28 PM EST

Unfortunately, I can't remember what the explanation was. Do you have a reference or more details?


The truth may be out there, but lies are inside your head.--Terry Pratchett


[ Parent ]
Doppler shift (none / 0) (#175)
by abdousi on Wed Jun 18, 2003 at 12:57:18 PM EST

The twin paradox was best explained to me using the Doppler shift. There is a lot of information on that on the web.

[ Parent ]
Here's one... (1.00 / 1) (#180)
by dipierro on Wed Jun 18, 2003 at 09:08:38 PM EST

You have to keep one inertial frame and stick with it. The easiest one of course is to pick the Earth as an inertial frame. Then, of course, the rocket ship is the one doing the moving. But say you have the earth doing the moving, and the rocket ship staying still. That's all fine and good on the first half of the trip, but on the second half of the trip, in order to get back, the rocket ship would have to travel even faster than the earth. So while the earth's clock was going slow for both halves of the trip, and the rocket's clock was going normal speed for the first half of the trip, in order for the rocket ship to get back to earth it would have to travel at such a high speed for so long that its clock would actually be behind the earth's clock.

I suggest that anyone who wants to truly grasp relativity do the calculations some time. It's quite insightful when you wind up with the exact same results no matter what you choose to be the inertial frame.



[ Parent ]
That's a good idea (none / 0) (#187)
by epepke on Thu Jun 19, 2003 at 07:50:42 AM EST

For completeness' sake, we could do it in three frames of reference: one stationary to the Earth, one stationary to the rocket going out, and one stationary to the rocket coming back. It has to come out the same in all three frames of reference.


The truth may be out there, but lies are inside your head.--Terry Pratchett


[ Parent ]
See the next installment (5.00 / 1) (#154)
by epepke on Mon Jun 16, 2003 at 07:57:18 AM EST

I have the first draft about 80% done. It's getting a bit long, so I won't actually put the twin paradox in the body but rather present it as a question to discuss.


The truth may be out there, but lies are inside your head.--Terry Pratchett


[ Parent ]
How do clocks work? (5.00 / 1) (#156)
by thogard on Mon Jun 16, 2003 at 08:04:17 AM EST

One of the keys to any relativity expierment is that you must have a very good clock. I'm not sure these exist. Current GPS clocks and atomic clocks are showing odd behavor that isn't quite right according to the equations. There are a few other oddities as well involving deep space probes slowing down more than they should.

If we go back to the dawn of decent clocks (H1->H4 currently in Greenwich), we can see that the physical world has effects on how precise a clock can be. In the early days it was things like bearing friction, spring consistency, pendulum length. Now its ability to measure things down to a precision of 15 to 18 digits. One very interesting thing is if you run the time dialation forumlas on the parts of a pendulum clock at orbital velocities, it shows the clock will preform as predicted. All mechanical clocks have problems at orbital speeds (limited to our ability to measure them) and atomic and electrical clocks show similar properties.

Next parts (5.00 / 2) (#159)
by epepke on Mon Jun 16, 2003 at 08:33:06 AM EST

Part II will discuss an idealized clock. Part IV will talk about, amongst other things, the GPS discrepancies.


The truth may be out there, but lies are inside your head.--Terry Pratchett


[ Parent ]
good stuff! (none / 0) (#164)
by gr00vey on Tue Jun 17, 2003 at 06:07:18 AM EST

Good article and interesting posts!

[ Parent ]
Blast, damn, and every other word I know! (none / 0) (#165)
by epepke on Tue Jun 17, 2003 at 03:32:54 PM EST

So I get Part II to the point where I'm ready to submit it for editing, and what happens? When I submit it to k5, the strings of   in my ASCII diagrams get shredded to hell. Does anybody know of a workaround for this?


The truth may be out there, but lies are inside your head.--Terry Pratchett


don't use contiguous strings of nbsp (none / 0) (#168)
by celeriac on Tue Jun 17, 2003 at 07:58:22 PM EST

alternate your nbsp's with regular spaces.

[ Parent ]
Thanks; that seemed to work. [n/t] (none / 0) (#177)
by epepke on Wed Jun 18, 2003 at 03:03:56 PM EST


The truth may be out there, but lies are inside your head.--Terry Pratchett


[ Parent ]
Newbie on this subject...but (none / 0) (#182)
by stylesgalore on Wed Jun 18, 2003 at 10:41:10 PM EST

Is it possible that we are already moving at the speed of light on a big picture without knowing yet? I have no clue, but it could happen.

Define movement? (none / 0) (#185)
by mindstrm on Wed Jun 18, 2003 at 11:07:38 PM EST

Movement requries something to compare against. Is it possible we are moving faster than the speed of light relative to something? Not within the current physics. IT's not as simple as saying "We just can't go that fast".. it's more like saying "speeds higher than that do not exist, it's nonsense to talk about them"

[ Parent ]
Good question... (none / 0) (#188)
by slipkid on Thu Jun 19, 2003 at 02:04:38 PM EST

There is thought that everything moves through space-time at the speed of light (also, presumably, the speed of gravity). This means that your net speed of motion in each dimension, and your movement in time, would come to equal the speed of light. This means that if you moved really really really fast (like faster than current technology allows), time would slow down noticeably for you, since your speed through time must be reduced to compensate for your extremely fast motion through space.

[ Parent ]
Excellent (none / 0) (#189)
by epepke on Thu Jun 19, 2003 at 05:02:39 PM EST

Once again, I am delighted by the perspicacity of people's intuition. I suggest that you read the second installment, especially the bit about spacetime intervals. And don't ever feel bad about being a newbie. Einstein was a newbie when he published the Special Theory, OK?

The following musings should best be considered part of another universe, not the one in which I'm trying to explain relativity. Just pretend I'm really drunk. I'm not, but thinking about this stuff kind of makes me want to get really drunk.

Relativity is a theory, and one way to look at a theory is sort of as a process to explain things in terms of things we already think we know, because if it isn't in those terms, what the hell does it mean?

On the other hand, there are many ways of thinking about problems. Perhaps with the constant speed of light Nature is trying to tell us (so I'm anthropomorphizing already--these are musings) that it's something basic about the structure of the universe. I've always had a problem with the speed of light being an actual speed. After all, the photon doesn't see any time change, so from the photon's perspective, its speed is infinite. If its speed is infinite, then in some sense it's everywhere along its path at once. We see the photon leaving a place and arriving at another one, but maybe that isn't real speed--maybe it's a kind of illusion based on how we are moving, what our world paths are through a lattice consisting of all possible zero interval spacetime paths. Maybe that can be seen as the basic structure of the universe, and whether we consider it "fixed" or not, it is the thing that we measure our motions within.

After all, there's some weirdness going on with photons at the quantum level. We have the idea that photons mediate the electrical force. When a proton repels another proton, we say that they have exchanged photons. These are called virtual photons because they can't be detected, but this isn't magic about the photons--if we detected them, then they wouldn't work on repulsion. We can sort of detect them by putting up a piece of metal and measuring current to ground, in which case, of course, the repulsion stops. It makes sense with repulsion: throw a photon on something and it will bounce away. But how do we explain the attraction of an electron to a photon? There are a number of ways of looking at the problem, but one way seems to be that at the QM level, it's very difficult to tell what is going forward or backward in time.

Also, even Maxwell's equations are problematic, because they seem to be symmetrical in time. Why don't we then detect radio from the future? Feynman's explanation was that, backward in time, a photon would eventually hit something and send a photon forward in time that just compensated for the earlier photon. This makes sense, because if you go back far enough in the Big Bang theory, there's a point where the entire universe was opaque to photons. This might mean a deep relationship between the idea of the universe as having started from a big bang but not contracting again; if if did, photons sent into the future would eventually hit something and a photon sent back through time to compensate. So radio wouldn't work if the universe eventually collapsed.

But still, if we can't really tell the difference between forward and backward in time, and if the photon doesn't notice any time, then maybe the notion of light speed as a speed in a conventional sense is an illusion based on our relationship to a lattice of light speed.

I don't know the answers, but it certainly makes my brain hurt. It's a good kind of pain, though.


The truth may be out there, but lies are inside your head.--Terry Pratchett


[ Parent ]
I disagree. (none / 0) (#193)
by losang on Sat Nov 08, 2003 at 10:09:26 PM EST

First off I have a bachelors in physics and a masters in applied math so I understand all the technical stuff you can throw at me. Secondly, you should stop hiding your ignorance behind big words. Third, for the most part 20th century physics is wrong. Relativity being one of them.

How can the speed of light be measured the same for all observers? No physicist has ever given me an answer as to why this is so.

Seconly, space is not curved. This is such a stupid idea that I can refute easily.

QFT is another one. There is no such thing as point particles. It amazes me how educated people can make such a blunder. How can things with no size collide with other particles in experiments?

A last but not least string theory. 11 dimentions, please. And the reasoning they give for why they have 11 dimentions. It is funny how scientists criticize religion but accept parallel universes and 11 dimentions.

The problem is that a good part of education goes towards removing any remnants of common sense and replacing it with accepted dogma.

I will give you a clue as to where you went astray. The day you abandoned logic for mathematics is the day you decided to give up the search for reality.

I got one word for you think.

your turn to think (none / 0) (#194)
by fleece on Sat Dec 13, 2003 at 07:00:28 AM EST

First off I have a bachelors in physics and a masters in applied math so I understand all the technical stuff you can throw at me.

Then you'll understand me when I say that technically, you have a chronically undersized penis.

No physicist has ever given me an answer as to why this is so.

I heard it's because they can't stand talking to you on account of the fact that you're an arsehole.

A last but not least string theory. 11 dimentions, please. And the reasoning they give for why they have 11 dimentions. It is funny how scientists criticize religion but accept parallel universes and 11 dimentions.

You have a bachelor's in physics an you still can't spell dimension?



The problem is that a good part of education goes towards removing any remnants of common sense and replacing it with accepted dogma.

Where did you get your bachelor of education again?

I will give you a clue as to where you went astray. The day you abandoned logic for mathematics is the day you decided to give up the search for reality. .

I'm not going to give you a clue where you went astray. You're challenge is to figure it out. (hint: you're a fuckwit)

I got one word for you think.

I got one word for you: tossbag (or is that two words?)



I feel like some drunken crazed lunatic trying to outguess a cat ~ Louis Winthorpe III
[ Parent ]
Introduction to the Theory of Relativity Part I: History | 194 comments (134 topical, 60 editorial, 0 hidden)
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