PH509003@BROWNVM.BITNET (Jon Kjoll) (01/31/89)
I would like to add my contribution (378 lines!) to the ongoing discussion
on relativity , speed of light , twin paradox and relevance to space.
In an attempt to keep the volume down ( I failed ) I'm a little short .
I apologize for all referneces to Dan Quayle and any HE/SHE
inconsistencies. Those who cannot imagine a speed of v = c
take v = c - epsilon , and let epsilon be *very* small .
** HISTORY ( Simplified ) :
NEWTON assumed absolute time and space . In his picture there
is only one time, independent of speed of travel or
point of observation . His theory of gravitation united terrestrial and
extra terrestrial mechanics. In Newton's picture observed physics
are dependent on the motion of the observer. Nothing forbids travel
at speeds faster than light .
MAXWELL found the laws of eletromagnetism (EM). Maxwells equations has a
free wave soulution , this solution contains a constant - c ,
the speed of light. There is no reference to an "inertial frame" in
Maxwells equations , which means that all observers would measure
the same speed of light , c . An experiment by Michelson and Morley
showed that c is independent of the reference frame . It is the same
in all reference frames .
LORENTZ introduced the Lorentz contraction and a "local time" to
restore Newtons picture . He's goal was to unite the new theory
of light with good old Newtons theroy . He managed to do so ,almost .
The error was of the order (v/c) squared. He then got a law for the
speed of light in ref frame 1 relative to an inertial (r) frame of
observation :
V = speed of frame one relative to frame the reference .
c = c +/- V*(V/c)
1 r
EINSTEIN took the opposite approach. The speed of light must be the same
in all reference frames, because Nature canno't be dependent on the
frame of the observer . Thus the laws of Nature must be the same in
all reference frames . But that implies that Newton's laws are NOT
true laws of nature !!. They can only be approximations .
Maxwell's equations are true laws of nature . They have the same form
in all reference frames .
** SPECIAL RELATIVITY (SR)
A gedanken ( thought) experiment :
Assume you stand at an interstellar traffic light . A space ship with
Dan Quayle on board comes driving down the space road at a speed of c .
As he passes the traffic light , the light turns green .
You will observe that Dan's hair (slightly distored ok ) and the green
light travels down the road parallell to each other . They have the same
speed. Dan ALSO will see the light travel at the speed of light .
Now how is this possible ? Only if Dans time (as observed in your frame)
stands still !!. In his frame everything is ok , because his frame
follows the laws of physics !! Then you ask , How can he *drive* down
the road if his watch doesn't move ?? . The answer has to be that
he doent's measure any traveled distance at all !! . He just passed a
sheat of material that sent out some green light . He observes this
"green" light at another frequency . These are just IMPLICATIONS of
Einsteins revolutionary concept of equality between frames .
The invariant equation valid in any frame of reference
(c - speed of light , tau - INVARIANT eigentime, t - local time and
r the distance , **2 means square ) :
(c*tau)**2 =(c*t)**2 - r**2 (1)
Short example ( R_distance_to_Dan = V_Dan's_speed times time t ) :
(c*tau)**2 = (c*t)**2 - (V*t)**2 = (c*t)**2 - (c*t)**2 = 0
so tau = 0 . In Dans system ( where R is zero as he sits in the
center) , 0 = (c*t')**2 with only solution t' is zero , i.e Dan's
time is zero !!.
The slowing of clocks and the lenght contraction are REAL !!!
** SR and OBSERVED MASS :
Now Dan activates his ion brakes . He spits out ions .
To us nothing happens . His watch doesn't move . His ions stand still .
But if he told us in advance that he would operate the brakes when
he passed us, we can only conclude that his mass went to infinity .
The only quantity the two observers would agree upon is the *rest mass*
, the mass measured in a frame were the car is at rest. (**2 = Square())
A better way of stating this is that to change an objects momentum
you need to apply a force for some finite time t , at
v = c , from Dan's point of view, Dan passes us in no time i.e
the force doesn't work for any amount of time. Also, as Force*Distance
equals energy, we can also accept this equation ( **2 means square() )
Mrest**2 = ENERGYtotal**2 - Pmomentum**2 (2)
( I left out a few c's , if p = 0 , this is mc**2 = E )
This equation says that if you add momentum to a particle , you also
give it energy at a corresponding rate . And note this is the only
meaningful equation to express mass ,energy and momentum in .
Dan would conclude that he drove through a thin sheet .
To him it was the universe that traveled towards him at c,
and he would maybe speculate what laws of physics we would have .
** SR, GRAVITATION, MASS and GRAVITATIONAL INTERACTION :
Now let Dan be weightless and pass the sun at a speed of v = c .
Let us observe Dan from a radially freefalling elevator in the suns
gravitatonal field . Let us have an open elevator and let Dan pass
right through it . As no external forces act on Dan he will travel
in a STRAIGH LINE observed by us inside the falling elevator !! For
an observer fixed at a certain height above the sun he enters the
elevator on one side and FALLS with the elevator and emerges on the
other side !!. Even if he has no mass he falls in the suns gravitational
field . This argument can be repeated for Dan if he carries mass .
The result is the same . Graviational interaction is NOT a
mass mass effect but a CURVED SPACE effect . Gravitational interaction
does not follow a Msun * Mdan's_relativistic_mass law except as a
low speed first approximation .
** GENERAL RELATIVITY (GR) :
When travelling relative to a mass there might be corrections to the
Newtonian gravitational force . Much like a magnetic field is produced
by a travelling electrically charged particle . Einstein showed that
to make a theory that treats time on a equal footing with space ,
makes the theory of gravitation a theory of geometry . GR states that
frames of reference in curved SpaceTime are equally good !! . There is
no absolute frame . The physical invariants , quantities that are
agreed upon by all observers independent of their frame of reference,
becomes slightly more complicated . The wave solution to GR is called
a graviton and sadly for all "above c entusiast" , Nature fine tuned
the speed of the graviton to c ( NO PROVE EXIST YET !! )
The use of GR is to establish a relation between accelerated
frames . SR is more than adequate to describe gravitation in ONE
frame . Its just that Dan and I would not agree upon the valid laws .
As a test of GR I would like to add is the difference in clock rates
between identical clocks in Denver, CO (5000 feet above sea level)
and Greenwhich , England (80 feet above sea level) . Just as GR
predicts .( My altitudes might be off , I have long forgot where
I read this.)
** LIMITS OF SPECIAL RELATIVITY :
SR applies to all problems were gravity is to weak
to warp SpaceTime or cause disturbances like Mercury's presession .
All rests on the equality of refence frames in "flat" 4 dimensional
space . A strong gravitational field slows down time
( atomic clocks tick slower ) and this must be put in in addition in
SR or use GR .
You don't have to resort to GR to explain acceleration in flat space .
GR only is needed when our 4 dimensional space becomes curved and we
want to compare observations .
The geometry of ants living on an orange has the GR features .
Locally flat but still curved . Better be careful if you add the
angles of a large triangle on an orange's surface , 180' is the flat
space result .
** TEST OF SR: ( In addition to previous Space List Communications ):
SR sais that physical quantities must be expressed as 4-vectors in order
to qualify as a description of nature and observed phenomena .
SR ( equation 2 ) is essential to Quantum Electro Dynamics and the
electrons g factor is measured to about 10 digits of the theory .
Take a bunch of electrons travelling down a accelerator . Due to
electrostatic repulsion the beam separates . Strangely enough
the effect is smaller the faster they travel. The reason is that
their time slows down .
Blueshift of photons as they fall in a GR field .
This experiment was done in a 70 feet tower at Harvard U .
The observed lifetime of particles travelling at high speeds becomes
longer because their 'internal' clock slows down as seen by us .
Some cosmic protons have gamma's close to 10 . They'r lifetime and
mass is as predicted by SR . Try to stop they , they appear heavy .
At CERN no corrections to SR were needed to explain observations
at accelerations as high as 10**18 (m/s^2) !!
** THE TWIN PARADOX:
Take a flashlight with you outside a clear night . Direct it towards
the moon and "flash" . When the light hits the moon you are a second
older . When you SEE the light hit the moon you are two seconds older .
This because the light ray has to return for you to see the "hit" .
Previously we stated that for frames at the speed of light time stands
still . So the clock of the photon stands still .
If you have twins send one with the light flash .
What does the travelling twin see ??. On his way to the moon he
sees your watch stand still . The reason is that to him the distance
to the moon is zilch due to contraction . So he turns around imediately
and again has no distance to travel . You on the other hand
see him travel outwards for two seconds !!!! and then as soon
as he hits the moon he is back !!
Thus complete agreement by all observers .
I hope this solves the paradox for all of us ;-) .
** COMMENTS to SPACE QUESTIONS :
> all experiments done to date have involved particles that were
> accelerated by external fields, generally electromagnetic. Thus there
> is really no way to tell whether the mass is actually increasing
> or the particle simply acquires more resistance to being accelerated
> _by an external field_. To check this beyond any doubt, you need
> an object that that can accelerate itself by dumping reaction mass out
> the back.
Not so . After having accelerated the charged particle in an EM field,
nothing prevents you from letting it leave the field an do whatever
measurements you want . Use cosmic rays to do your experiments .
> (2) At the quantum level, a reaction drive is still
> pushing reaction mass out the back by the use of electric fields, i.e.
> electron repulsion, just like any other "macroscopic" force between
> touching objects.
You don't have to resort to Quantum Mech to explain electron repulsion .
And yes you are right, EM forces are responsible for a lot .
> The accelerated particles will not only
> show more inertia, they will also increase the strength of their own
> gravitational fields, thus affecting objects around them. Would this
> be measurable?
By construction SR and GR are "conservation laws" . Forces differ
between frames of refence . Try to stand on a 33rpm turntable and explain
linear motion to your kid . ( If you smile , think again - the turntable
is a perfectly valid frame .) The observed gravitational force has
to be such that the equations of GR are invariant . Then observer A and
B can compare their equations of physics and conclude Nature is
consistent .
** BREAKDOWN of SR ( A fragment of an unlikely scenario.)
If the basic assumption , that all frames are equally good breaks
down, SR breaks down . We can imagine f.ex that space will undergo
a phase transition , freeze somehow and thus change character
completely . What EM and SR tells us is that there is no medium
(Ether) out there in which EMwaves (light) travel. Light travels
through empty space , all alone , unguided. If SR breaks down
the laws of physics might be frame dependent .
There will be different physics in all SpaceTime points !!
Pretty hard to travel under such conditions . Even hard to
be at rest because the laws *might* change with time.
The real implication is that our laws of conservation might be in
danger upon which we have to find new ones or enter the land of
confusion . I remind the audience that one of Einsteins criterias
for a law of nature was simplicity . GR is a theory containing
the second derivatives of the curvature ( bending of a nail put on
the outside of an orange ) . Second derivatives are needed but not
higher derivatives . Of "other" attempts to "relativize"
Newtons V(r) = 1/r law , they all fail the simplicity criteria and
the experimental tests . As Einstein said :" I hope God
didn't make a fool of himself. " ( or words to that effect ) .
> Newton couldn't measure the properties of anything moving at a
> Substantial fraction of C, and we can't measure the properties of a
> macroscopic object moving at a sizable fraction of C. You never know.
and
> Also, consider that relativity is a THEORY, there may be a lot of
> things wrong with it, after all it is possible that at some velocity
> the tendency for mass to increase/time to slow, my stop, thus
> allowing velocities of C or even greater without infinate energy. Of
> course it's kind of hard to run experiments (anyone have a space ship
> and a REALLY great drive system?)
Hmm . Let me suggest a few nebulas for space ships and the best propel
ever - Big Bang. I think that there are observations of nebulas out
there , headed away from us at a speed of more than 99% of c .
We can observe these nebulas and conclude that SR is fine .
We can project ourselves on to a planet in one nebula and
look back at earth ,look beyond earth , at a nebula headed in the
opposite direction at a speed v > 99% c . Continue the process .
The relative speed you ask . Speeds add like TANH .
SR is verified to a very small experimantal error .
Mark R. Kaufmann writes :
> but that we will find some area in which relativity is incomplete. Any
> new theory will have in encompass relativity just like relativity
> encompasses Newtonian mechanics. Don't ask me where relativity is
> incomplete.
I think the difficulties are up a magnitude . We now have a theory of
the force carrier that satisfy some very deep principles . Not just a
phenomenological theory based on a bunch of observations .
I do think Nature has a few surprises for us , but I'm not so sure
SR will be proven wrong when applied to interstellar travel and
the physics of space . It has proven itself successful far into the
relativistic elementary particle regime and to interstellar
high speed physics .
** Travel ABOVE the SPEED OF LIGHT:
Above the speed of light , there is no way atoms can hang together .
Particles communicate with the speed of light so they would no longer
hang together , seen from ANY frame of reference .
As physics has (??) united the weak, strong and the electro-
mechanical force , we really don't have much hope , given that
gravity really is described by Einstein's GR . Experiments verify
Einsteins predictions to within experimental error .
Conseptually there is nothing that prevents travel at speed v >> c.
Take your 33rpm turntable outside a dark clear night , step up on
it and scan the bondary of the universe in 2 sec !! .
** RELEVANCE FOR SPACE :
For the sake of effect lets say we can get the ship up to *almost* c .
The lifetime of the ship increases seen from earth !!
Reliability is no problem.
Aging of the astronauts are no problem .
Communication might be difficult due to the strong shift in frequencies
(Doppler).
The frequencies received will be shifted strongly down .
Also inside the spaceship , not much will take place as you are at
your destination in zero time .
Particles colliding with the ship might easily be fatal .
The really dangerous particles , the ones comming towards us at speeds
close to c are heavy to distract. And we have to detect them far away !
They come towards us at about the same speed as the reflected
radar(?) signal the ship sends out .
Also they are heavy to distract or push out of our way .
To travel at v=c you'll have to be a package of photons .
Careful, charged particles might scatter you off your course .
Parking : At v=c your space ship has no lenght so a parking garage
for your space ship can be arbitrarily short .
Watches and pumps and all moving parts can be left on the drawing table.
** SF (Sience Fiction :-) :
Beyond the speed of c you'd better be careful .
First you'd have to map the universe using this new media of travel.
If not you are prone to hit other objects at v > c .
If you don't interact with them there are no problems . But if no
interaction excists between objects at v > c , how are your
propulsion system buildt ??
Also , you might happen to fall in love upon return with one of
your grandparents , thus preventing your own birth .
** TACHYONS :
Space List continues to introduce concepts so how can a time dilated
grad student keep up ?? .
Tachyons are possible objects that do not contradict equation (1) and
(2) above .
Equation (1) and (2) IS NOT equations for describing possible objects .
They relate observations done between observer A and B and thats all they
do . MAXWELL's equations and DIRAC's equation describe physical
entities that we can observe. Before looking for imaginary objects
I would look for negative mass objects. ( Newton's laws doesn't
forbid them ! . If you find a -190lbs one send it to me ;-) )
** A few FINAL COMMENTS :
Strings and Black Holes are mentioned . Strings depend on SR
( equation 1 and 2 ).
The infinities in QM and Quantum Electro Dynamics stem from the
product of "distributions" ( commutators ) .
Black Holes are stationary solutions of the GR equations .
Black Holes also have the amazing feature that time slows down and
finally stops as an object fall towards and reaches the "horizon" of
the black hole .
"How come c is the upper limit ??"
Because it is the upper speed by which information is carried in
ANY frame of reference , accelerated , rotatating , falling .
C emerges from Maxwells equations and c also enters Einsteins
GR wave equation as it is also the speed of the classical gravitywave.
( Classical as no consistent quantum gravity is found yet . )
The rest is just consequences .
I hope this lengthy contribution clears the clouds ,
And I hope I didn't overlook spelling and logical errors .
Jon Kjoll
Physics Dept
Brown University .
pH509003@BROWNVM.BITNET
Claimer : Dan is the ultimate experimental object .
( To those who say : " Dan at v = c is not possible", please go out
and measure the mass of a neutrino before grilling me . )