PDA

View Full Version : First glimmerings of relativity?



peteshimmon
2005-Oct-06, 03:34 PM
I believe I have a reasonable grasp of relativity such that I can understand
the twin paradox at least. But I was given to wondering how the first ideas
there was a problem at ultra high speeds came about. To this end I tried
a thought experiment that may have been tried in the mid nineteeth
century. Two railway station are one light hour apart on a straight track.
There are super telescopes that allow them to see each other and their
clocks which are set so they see each others set an hour behind. A
locomotive can travel at half lightspeed. It has a clock mounted on top.
It leaves station A at 12oclock and take two hours to get to B arriving at
2oclock on the clock at B. The driver saw three hours go by on the clock at
B. Looking behind he saw one hour pass on the clock at A. At station A
they saw the loco take 3 hours to reach B. At B they saw the loco take
one hour to come. No problem so far! But the rate of each clock was
different from the viewpoint of the driver and stations. B saw one two hours
on the loco clock take one hour whilw the driver saw three hours on the
station B clock take two hours. Similar problem looking to and from station
A. Of course now we accept the loco clock would show something like
one hour fortysix minutes elapsed for the journey. All rates are then equal!
I wonder if some bright spark thought like this and confused hell out of
his teachers 150 years ago? And got lines or the birch:)

Tim Thompson
2005-Oct-06, 04:09 PM
The problem that eventually led to the formulation of special relativity was somewhat different. Newton's physics implies that there is no such thing as an "absolute" velocity, i.e., all velocities depend on the relative motion of observers. Maxwell's electromagnetism, however, implies that the speed of light is absolute, a constant for all observers. In the late 1800's it was commnly accepted that both Newton & Maxwell were unquestionably correct. It was also commonly accepted that it was impossible for them both to be simultaneously correct. Obviously, this is something of a problem.

Many people worked on trying to remove the paradox, but it was Einstein (http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Einstein.html) who decided to take the drastic step of concluding the Newton (http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Newton.html) was wrong (gasp), and Maxwell (http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Maxwell.html) was right. So special relativity (http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Special_relativity.html) is really nothing more than the application of the relativity principle of Maxwell's electromagnetism to Newton's mechanics, throwing out Galileo's principle of relativity (http://phyun5.ucr.edu/~wudka/Physics7/Notes_www/node47.html), which Newton had adopted.

That explains why the title of Einstein's 1905 paper was On the Electrodynamics of Moving Bodies (http://www.fourmilab.ch/etexts/einstein/specrel/www/).

hhEb09'1
2005-Oct-06, 06:11 PM
throwing out Galileo's principle of relativity (http://phyun5.ucr.edu/~wudka/Physics7/Notes_www/node47.html), which Newton had adopted.I was following you OK until there, Tim. Why "throwing out"? Even your link says "This fact, formulated in the 1600's remains very true today and is one of the cornerstones of Einstein's theories of relativity."

Sigma_Orionis
2005-Oct-06, 06:56 PM
Maybe "Throwing out" was too drastic a term. I see it like this: Galileo's Principle of Relativity works perfectly till the bodies in question have speeds that approach that of light, Special Relativity has a more general way to describe mechanics. If you take a look at the Lorentz Transformations (http://musr.physics.ubc.ca/~jess/hr/skept/STR/node2.html) they can be translated in plain english as follows:

- For velocities that are quite lower than the speed of light everything works as Galileo described it in the 17th century

- If the velocity starts aproaching the speed of light, Galileo's Relativity starts failing, and the motion of the objects in question is described correctly by Special Relativity (of course, Special Relativity works for the first case too, but the differences with Galileo's model are negligible).

- If the velocity reaches the speed of light call Arthur Dent ;)

hhEb09'1
2005-Oct-06, 07:07 PM
- For velocities that are quite lower than the speed of light everything works as Galileo described it in the 17th century

- If the velocity starts aproaching the speed of light, Galileo's Relativity starts failing, and the motion of the objects in question is described correctly by Special Relativity (of course, Special Relativity works for the first case too, but the differences with Galileo's model are negligible).Wouldn't that be Newton, not Galileo?

Sam5
2005-Oct-07, 03:07 AM
I believe I have a reasonable grasp of relativity such that I can understand
the twin paradox at least. But I was given to wondering how the first ideas
there was a problem at ultra high speeds came about..... :)

Hi, the first modern relativity theory was published in 1895 by H.A. Lorentz, in the book “Versuch Einer Theorie Der Elektrischen Und Optischen Erscheinungen In Bewegten Körpern”, Leiden, 1895. Lorentz did not call it a “relativity” theory, he called it an “electrodynamics” theory. An English translation of the title is: “Attempt at a theory of electric and optical phenomena in moving bodies.” Einstein took this basic theory and modified it for his 1905 Special Theory of Relativity, which he titled (English translation): “On the Electrodynamics of Moving Bodies.” Einstein carried Lorentz’s ideas much further and he later went on to develop the General Theory of Relativity.

Here are some photos of pages from the Lorentz book and a page from a 1907 paper in which Einstein gave credit to Lorentz for his 1895 book and theory:

Photos of book pages. Click on enlarge button if necessary:

Lorentz 1895 Book Title:

http://tinypic.com/eanjq0.jpg

First version of the Lorentz Transformation Pg. 37:

http://tinypic.com/eank1w.jpg

The old German letter “p” = the body velocity “v” of today’s equations.

The old German letter “V” = the speed of light.

Lorentz’s first use of his term “Transformation”, in relation to his equations relative to two relatively moving systems, System 1 and System 2, Pg. 38:

http://tinypic.com/eanltw.jpg

Here’s Lorentz’s famous Transformation Ratio, Pg. 125:

http://tinypic.com/eanmki.jpg

Here is Lorentz’s Transformation Ratio as used in Einstein’s “On the Electrodynamics of Moving Bodies”, located about in the middle of Section 4:

http://www.fourmilab.ch/etexts/einstein/specrel/www/figures/img59.gif

English translation of full paper:

http://www.fourmilab.ch/etexts/einstein/specrel/www/

Einstein’s 1907 credit to the 1895 Lorentz book and Lorentz’s “electrodynamics of moving bodies” theory:

http://tinypic.com/eanng7.jpg

A copy of Lorentz's book is available here:

http://www.elibron.com/english/other/item_detail.phtml?msg_id=10017783

:)

peteshimmon
2005-Oct-07, 05:31 PM
Thanks for the responces! My own reading over
the years gave the experiments of Michelson and
Morley on the non-existance of an ether, work
on the behavior of electrons in cathode ray
tubes, the work of Lorentz, Poincare and
Fitzgerald. But my little story can be so
easily stated and I suspect there were many
thoughts on the subject beforehand.

Sigma_Orionis
2005-Oct-08, 02:35 PM
Wouldn't that be Newton, not Galileo?
Yep, you are right, Newton using Galileo's Relativity.....

Thanks for pointing it out....

trinitree88
2005-Oct-14, 12:04 AM
To: PeteShimmon.......
--------------------------------------------------------------------------------

Thanks for the responces! My own reading over
the years gave the experiments of Michelson and
Morley on the non-existance of an ether, work
on the behavior of electrons in cathode ray
tubes, the work of Lorentz, Poincare and
Fitzgerald. But my little story can be so
easily stated and I suspect there were many
thoughts on the subject beforehand.

An interesting point...one of Asimov's texts...I believe it was called "On Physics"...hardbound, blue cover...circa 1978??....Asimov gives the four correct physical interpretations of the negative result of the Michelson-Morley experiment.....only one of the four concluded that the ether did not exist...the others attributed properties to it such that the results were what they were...but did not in and of themselves discount it as a physical reality.....interestingly, only the non-existent ether interpretation gained much footing in the physics community for the last hundred years. :think: Ciao. Pete

Sam5
2005-Oct-14, 01:11 AM
To: PeteShimmon.......
--------------------------------------------------------------------------------

Thanks for the responces! My own reading over
the years gave the experiments of Michelson and
Morley on the non-existance of an ether, work
on the behavior of electrons in cathode ray
tubes, the work of Lorentz, Poincare and
Fitzgerald. But my little story can be so
easily stated and I suspect there were many
thoughts on the subject beforehand.

An interesting point...one of Asimov's texts...I believe it was called "On Physics"...hardbound, blue cover...circa 1978??....Asimov gives the four correct physical interpretations of the negative result of the Michelson-Morley experiment.....only one of the four concluded that the ether did not exist...the others attributed properties to it such that the results were what they were...but did not in and of themselves discount it as a physical reality.....interestingly, only the non-existent ether interpretation gained much footing in the physics community for the last hundred years. :think: Ciao. Pete

It is actually a common myth that the MM experiment "proved" there was no "ether" or light-speed-regulating medium in space. Michelson and Morley believed that their apparatus could not detect an "ether wind" near the sea-level surface of the earth, since the ether could be moving through space with the earth, near the surface of the earth. They suggested that experiments should be conducted well above the sea-level surface of the earth.

Ken G
2005-Oct-14, 05:59 AM
Interesting point trinitree, I did not know that. They must have regretted that suggestion!

About the original thread, I think peteshimmon's thought experiment is an excellent way to calculate the Lorentz factor. The sole requirement is you have to make the answer not depend on whether it is the train that's moving, or the station. That's the key symmetry of relativity. It's actually pretty close to the standard way of deriving the Lorentz factor that I've seen, but has a little less of the flavor of using a Doppler shift in frequency, and more just the flavor of watching a clock. I like the use of a clock instead of, say, regular pulses of light, which is pretty much the same thing but a clock seems so much more concrete. I think I'll use this example to explain the Lorentz factor from now on!

peteshimmon
2005-Oct-15, 10:34 PM
Glad you like the story. Actually I checked the
maths the other night and need to correct the
loco time. As the rates must be equal its just
a matter of equating the two fractions
representing the observed times taken on the
station clock with the shortened loco time as
the unknown. So multiply 60 minutes by 180
minutes and take the square root. Works out
as 103.923 minutes on the loco clock. Easiest
time dilation calculation I have done:) Works
the same for a quarter light speed but I have
not got out a general expression yet.

Ken G
2005-Oct-15, 10:40 PM
Yes, it shows that the "Lorentz factor" is really just shorthand for what can also be found from an intuitive calculation, if set up elegantly as this one is.