Speed of light..

[Seb]

This is probably basic physics, but...

I'm a little confused about the speed of light. From what I'm understanding, c is pretty much constant, no matter what speed the source of the light is already moving at. Is this still seen to be correct today?

If it is, then would it not be possible to calculate the speed of the earth moving through space? (which would include the sum of our solar system around the galaxy as well as the earth around the sun.)

[selden]

Seb,

This is usually discussed in first-year college physics courses, which often include introductions to Special Relativity, a related topic. Some high school physics courses touch on it briefly, but without as rigorous a mathematical description.

It's not just that the speed of light is constant, the problem is that the speed of light is always measured to be the same no matter what the velocity of the viewer is. (I'm using the word "velocity" as used in physics: it is a value which includes both speed and direction.) This was determined in a famous experiment by two people named Michelson and Morley. One description of their experiment is at http://galileo.phys.virginia.edu/classes/109N/lectures/michelson.html. As technology improves, newer, ever more senstive versions of their experiment continue to give the same result.

For more information, you might want to locate a textbook for a first-year college phisics course. They usually include an introduction to special relativity. A book on the history of science should be another useful resource.

So, by itself, the speed of light doesn't tell us anything. However, one can measure one's velocity relative to the 3 degree cosmic background microwave radiation! One discussionof this can be found at http://zebu.uoregon.edu/~js/glossary/cosmic_microwave_background.html

[Seb]

Thanks selden, have answered perfectly..

Just seems from the information I've been reading, physicists were still uncertain.

[selden]

Seb,

Sadly, you have to be very careful when reading criticisms of relativity. There are many, umm, uninformed people who pretend to be experts but who have not studied either physics or its history and actually are writing about their own imaginary extrapolations of poorly written "popular" articles.

[Cham]

Yes, this is sadly true.

The "democracy" of the internet brings a lot of crackpots and confused people talking on things they don't know well. There are lots of web pages out there on which some "illuminated" guy pretend to have found a proof that relativity theory is false. I wonder why relativity theory is such a victim, and not quantum theory. Maybe because relativity is almost understandable for the masses, and not quantum theory which is mathematically much more sophisticated than relativity.

Anyway, we must be VERY carefull when dealing with relativity theory on the net.

[Evil Dr Ganymede]

The thing I didn't quite grok about the speed of light is this - isn't it an assumption that the speed of light is constant for all observers? Maybe it was just the way the texts were phrased, but it seemed to me that Einstein simply assumed that nothing could travel faster than light and based everything around that.

I presume there's experimental data to support this assumption, but then one wonders why the speed of light is the fastest that anything can go.

[Cham]

I must admit that, sometimes, crackpots may be fun. They can also be very usefull on an pedagogical way. If you really go into the trouble to understand their arguments, you can learn a lot of things on the real physics. John D. Barrow have wrote a nice book called "impossibilities". According to this physicist, the impossible things can teach us a lots on the real universe in which we are living.

A rapid search on the net with Google gave me those funny web pages :

http://www.sciforums.com/showthread.php ... adid=17506

http://www.ilja-schmelzer.de/ether/crank.html

http://www.crank.net/relativity.html

[Cham]

The thing I didn't quite grok about the speed of light is this - isn't it an assumption that the speed of light is constant for all observers? Maybe it was just the way the texts were phrased, but it seemed to me that Einstein simply assumed that nothing could travel faster than light and based everything around that.

I presume there's experimental data to support this assumption, but then one wonders why the speed of light is the fastest that anything can go.

There are several ways to state the foundations of Special Relativity theory. The must well known formulation can be resumed like this. You have two postulates (you can call them "hypothesis", if you whish, but I call them "axioms", like in maths).

1- The relativity principle. A given law of nature keep the same mathematical form in all inertial reference frames. It is independant of the state of movement of the inertial observer.

This postulate was well known before Einstein, and must apply to ALL fundamental laws of physics. Galileo and Descartes were the first guys to talk about the relativity principle. This postulate can be interpreted as this :

1b- An inertial observer can't learn his absolute state of movement by doing any experiment in a closed laboratory (without looking outside").

The scond postulate can be formulated like this :

2- The speed of light IN VACUO is the same relative to any inertial observer. It is independant of the state of movement of the source and of the observer.

This principle was formulated by Einstein himself. This is the one which is hard to swallow, the first time we learn relativity. It appears contrary to common sense.

There's another way to formulate relativity WITHOUT using the second postulate, but it's a bit more abstract and I wont resume it here.

[Cham]

Evil Dr Ganymede (by the way, your name made my girlfriend laugh yesterday!) :

The speed of light limit may be understood in this way :

The constant "c" isn't really about light. It's the universal limit on information exchange. It is rooted in the universe "fabric" (the vaccum, really). Information of any kind just can't travel faster. It's a caracteristic of our universe. In the Newton theory of mechanics, the limit is simply c -> infinity. But then, if this must be a true caracteristic of the universe, and to be consistent with the first principle (relativity principle, above), it must be independant of any kind of sources and is independant of the observer.

And it appears that light, which is just a special phenomenon like any other one, travel with this maximum speed limit ! A trully modern formulation of relativity doesn't talk about "light". The second postulate should be formulated like this :

2b - There's a maximum information exchange speed ; c, which is the same for all inertial observers.

[wcomer]

I just read an interesting paper titled "The Classical Electron Problem" by Tepper L. Gill, W. W. Zachary, and J.Lindesay.

The paper is found at:
http://arxiv.org/abs/physics/0405131

The relevence to this discussion is two-fold. Firstly, in this reformulation of Maxwell theory, light may travel faster or slower than c due to a change in the definition of time. Secondly, the first few pages have a good narrative background on many of the ideas already brought up in this thread.

Abstract:
In this paper, we construct a parallel image of the conventional Maxwell theory by replacing the observer-time by the proper-time of the source. This formulation is mathematically, but not physically, equivalent to the conventional form. The change induces a new symmetry group which is distinct from, but closely related to the Lorentz group, and fixes the clock of the source for all observers. The new wave equation contains an additional term (dissipative), which arises instantaneously with acceleration. This shows that the origin of radiation reaction is not the action of a "charge" on itself but arises from inertial resistance to changes in motion. This dissipative term is equivalent to an effective mass so that classical radiation has both a massless and a massive part. Hence, at the local level the theory is one of particles and fields but there is no self-energy divergence (nor any of the other problems). We also show that, for any closed system of particles, there is a global inertial frame and unique (invariant) global proper-time (for each observer) from which to observe the system. This global clock is intrinsically related to the proper clocks of the individual particles and provides a unique definition of simultaneity for all events associated with the system. We suggest that this clock is the historical clock of Horwitz, Piron, and Fanchi. At this level, the theory is of the action-at-a-distance type and the absorption hypothesis of Wheeler and Feynman follows from global conservation of energy.

[t00fri]

I just read an interesting paper titled "The Classical Electron Problem" by Tepper L. Gill, W. W. Zachary, and J.Lindesay.

The paper is found at:
http://arxiv.org/abs/physics/0405131

The relevence to this discussion is two-fold. Firstly, in this reformulation of Maxwell theory, light may travel faster or slower than c due to a change in the definition of time. Secondly, the first few pages have a good narrative background on many of the ideas already brought up in this thread.

Abstract:
In this paper, we construct a parallel image of the conventional Maxwell theory by replacing the observer-time by the proper-time of the source. This formulation is mathematically, but not physically, equivalent to the conventional form. The change induces a new symmetry group which is distinct from, but closely related to the Lorentz group, and fixes the clock of the source for all observers. The new wave equation contains an additional term (dissipative), which arises instantaneously with acceleration. This shows that the origin of radiation reaction is not the action of a "charge" on itself but arises from inertial resistance to changes in motion. This dissipative term is equivalent to an effective mass so that classical radiation has both a massless and a massive part. Hence, at the local level the theory is one of particles and fields but there is no self-energy divergence (nor any of the other problems). We also show that, for any closed system of particles, there is a global inertial frame and unique (invariant) global proper-time (for each observer) from which to observe the system. This global clock is intrinsically related to the proper clocks of the individual particles and provides a unique definition of simultaneity for all events associated with the system. We suggest that this clock is the historical clock of Horwitz, Piron, and Fanchi. At this level, the theory is of the action-at-a-distance type and the absorption hypothesis of Wheeler and Feynman follows from global conservation of energy.

Walton and "mathematics-fan" Evil Dr. Ganymede,

the symmetry group of conventional Maxwell theory is actually much larger than the Lorentz group: It's the full conformal group that includes Poincar? (=inhomogeneous Lorentz group), dilatations and space-time inversion. The conformal group has 15 generators altogether.

Did that paper above make reference to the conformal symmetry?

Bye Fridger

[wcomer]

the symmetry group of conventional Maxwell theory is actually much larger than the Lorentz group: It's the full conformal group that includes Poincar? (=inhomogeneous Lorentz group), dilatations and space-time inversion. The conformal group has 15 generators altogether.

Hi Fridger,

That is quite interesting. I had not thought of the Lorentz group transformations as conformal transformations. Although it is clear that they are. The four special conformal transformations were a surprise for me. Do they have a deeper physical interpretation or is their importance purely mathematical?

To answer your question: no, the authors do not discuss any implications of expressing Maxwell's equations under 'source-time' on the full conformal group.