misc Special Relativity
(very rough; various quotes on SR)
see
astro_links.html
see
link_farm.html#spacecraft
From: 100130.3306@compuserve.com (Eric Baird)
Newsgroups: sci.physics
Subject: Re: ONW-WAY MEASUREMENT OF THE SPEED OF LIGHT
Date: Fri, 17 Nov 1995 04:18:12 GMT
...
dmeans@ix.netcom.com (Dale Means) wrote:
>Ken,
-
>I missed the first part of this thread. I have had a long term
>interest in the one-way measurement of the velocity of light and I
>have been geniunely puzzled by the opposition to even trying.
-
>Would you please forward me details of your proposed experiment. If it
>is better than mine (which, natrually, is unlikely:-)) I will get
>behind your proposal. I would just like to see a decisive esperiment
>performed.
-
All that goes for me, too.
Actual velocity measurements can be tricky to interpret, but if your
competing theory has a different open-path velocity/shift law to SR
(like mine has), then it's probably easier to forget about measuring
the velocities and concentrate on measuring the shifts. That way,
there's less room for dispute.
-
======================================
THE THREE-BEAM INTERFEROMETER TEST
======================================
-
->
A======(x)======B
| |
| |
\=======Y=======/
|
O
'
A test object (x) travels along the line A_B at constant (unspecified)
velocity.
A light-source O produces a beam which is split and directed at the
object via fixed mirrors at A and B, which also serve to collect the
"return" signals reflected off the object, and to bring them back to
the vicinity of O, where all three signals can then be compared.
'
The "A" signal undergoes two redshifts as it moves from A>x>A, and the
"B" signal undergoes two blueshifts as it moves B>x>B.
'
For any given velocity, the special frequency (fA times fB) will have
the same value, =fO*(1-(v/c)^2), whether the component shifts follow
the SR shift formula or just the plain old Doppler moving-observer
shift formula.
-
However, the three-way ratio fA:fO:fB has a signiture that depends on
the particular formula in operation. Once you know fA:fO, you should
be able to use each formula in turn to calculate the supposed velocity
of the object, and from, this, to predict the ratio fO:fB.
-
Since the apparatus also gives us the _real_ ratio fO:fB, we can use
this to see whether special relativity is more correct or less correct
than the eDoppler formula for calculating motion shifts, without
taking any direct measurements of the object's actual speed, without
measuring or interpreting any of the distances or times involved, and
without having to bother with clock synchronisation theories.
You don't even have to know what the three frequencies actually are,
all you need is the ratios between them.
The (unspecified) velocity of the object can be kept constant by using
one of the frequency ratio measurements within a control loop.
-
Comments, anyone?
-
=Erk=
Date: Wed, 08 Apr 1998 08:03:15 +1200
From: "M.Twain" <muse@ethos.co.nz>
Organization: League of the Last Days
MIME-Version: 1.0
To: Global <muse@ethos.co.nz>
Subject: Superluminal Robert L. Carroll
RLC is (was) one of hundreds in the global dissident physics community
that have spoken to and discarded the fraud of special relativity. We
shared our works and thoughts for five years, before his 'final'
retirement. I met him at the Dissident Physics conference at San
Francisco State University, in June of 1994. He has been featured in
Electric Spacecraft Journal [muse/esj.html], which I highly recommend.
He was unique in that he thought out and discussed the logistics of
superluminal (interstellar) space transportation -- and identified many
of its aspects. He was ridiculed by the establishment, as exampled by
NASA's wannabee conference last year on superluminal physics theory.
That institutional (covert physics) gathering deliberately excluded
theoretical superluminal physics and it's four known pioneers: myself,
Carroll, Alexis Guy Obolensky (New York), and Thomas G. Barnes of Texas.
[I don't claim that there may be no others, obscured in some corner of
the world, who have seen through to the foundations of superluminal
nature. They simply have not been brought into the light yet.]
You can get a Web overview of Carroll's work at [muse/carroll.html] at
either of the two World AntiPhysics Mirrors:
[http://www.ptw.com/~deagle/muse]
[http://galeb.etf.bg.ac.yu/~malovic/muse]
Also, Barnes and Obolensky too, are clickable [muse/barnes.html,
muse/obolensky.html] at either of those sites. Full references (books
and papers) are listed at both sites, and can be made available by me
[see RAPRs below]. RLC references are also available from Mark Goldes
at Magnetic Power, California [try mjs@ap.net]. Barne's books are
distributed by CRS books, and (as of last year) by the aging Barnes.
Copies (some loaners) of all Barnes' works also reside in my library.
Obolensky's works are available through him or me.
To get up to speed on the new (dissident) physics -- see the several
hundred references I have posted on the four issues of the RAPR at:
[http://erg.ucd.ie/arupa/ratbag_antiphysics_rag94.html]
[http://erg.ucd.ie/arupa/ratbag_antiphysics_rag95.html]
[http://erg.ucd.ie/arupa/ratbag_antiphysics_rag96.html]
[http://erg.ucd.ie/arupa/ratbag_antiphysics_rag97.html]
The superluminal foundation of nature is best revealed in the
superluminal aether velocity structures of the proton. Once the aether
and velocity foundations are understood, the observed phenomena --
superluminal quasars and jets, superluminally-expanding supernovae,
superluminal tunnelling in the solid state, superluminal electromagnetic
transmission and signalling in air and transmission lines, etc. -- are
all painfully trivial to explain and quantify. My several papers (The
Undiscovered Physics) on these foundations are available for cost of
printing and postage, from my new residence in New Zealand.
May you fare well on the (oft' superluminal) aether sea,
Millennium Twain
PO Box 21-972,
Henderson, West Auckland,
New Zealand
Date: Wed, 25 Feb 1998 00:16:41 +0000
From: Damien Broderick <damien@ariel.ucs.unimelb.edu.au>
Subject: >H Dr Randell Mills, Blacklight, paradigm challenge
X-Sender: damien@ariel.its.unimelb.edu.au
To: extropians@lucifer.com, transhuman@logrus.org
Reply-To: transhuman@logrus.org
Transhuman Mailing List
I've been noodling around in an extremely strange but just barely possibly
epoch-making revolutionary former Oz inventor/GUT theorist named Dr Randell
Mills, of Blacklight Power, Inc, whose url is
http://www.blacklightpower.com/
and who claims to have constructed a classical replacement for QT that as a
side-effect yields a strange new power source from hydrogen that he's
patented in Oz and is building gadgets from in the States. Almost
certainly a crackpot or scamster but one never knows - he seems to have an
impressive track record. A garbled but interesting interview with him
appeared in the Dec 97/ Jan 98 ish of that odd/loony magazine *Infinite
Energy*, edited by cold fusion guru (sigh) Dr Eugene Mallove. If some of
the physicists here have a gander at Mills's site, it might be nice to hear
an informed assessment.
Damien Broderick
***************************************************************************
Date: Wed, 25 Feb 1998 00:42:29 +0000
From: Damien Broderick <damien@ariel.ucs.unimelb.edu.au>
Subject: >H Dr Randell Mills, Blacklight, paradigm challenge (2)
X-Sender: damien@ariel.its.unimelb.edu.au
To: extropians@lucifer.com, transhuman@logrus.org
Reply-To: transhuman@logrus.org
Transhuman Mailing List
The rambling & embarrassing interview with Mills is on the web at
http://x9.dejanews.com/getdoc.xp?AN=321715515&CONTEXT=888327925.1111031900&h
itnum=1
Dr Mills comes out of it rather better than his hapless interviewer, with
the odd nice facetious jab...
Damien Broderick
***************************************************************************
http://www.blacklightpower.com/
http://x9.dejanews.com/getdoc.xp?AN=321715515&CONTEXT=888327925.1111031900&hitnum=1
Path: hermes.rdrop.com!user
From: d.cary@ieee.org (David A. Cary)
Newsgroups: sci.physics.relativity
Subject: Re: Light's absolute speed?
Date: Sun, 12 Jan 1997 00:30:37 -0700
Organization: rarely.
Lines: 108
NNTP-Posting-Host: ppp-dc.rdrop.com
Summary: If bjon or someone else can answer my questions about absolute
position (which would, of course, revolutionize cartology), then it will be
almost trivial for me to answer all these objections to relativity.
In article <59eds7$aeh@dfw-ixnews9.ix.netcom.com>,
bjon@ix.netcom.com (Brian D. Jones) wrote:
...
+>>If two observers partake in "relative" motion (and no one has defined
+>>such motion), then one of them must be absolutely moving, but not
+>>both.
Well, since no one else has defined it, allow me to define it.
Let us say I have a rod made of aluminum. I attach one end of the rod to
one object A, and always make sure it is free from any acceleration or
other stress that might change its length. At some time t=t1 I make a
scratch in the rod where it touches the other object B. At some later time
t=t2 (while the rod is still attached to A) I make another scratch in the
rod where it touches the other object B.
If the 2 scratches are in different places (rather than one deep scratch),
then object B is, by this definition, "relatively" moving with respect to
A. The velocity of B relative to A can be found by measuring the distance
between scratches (possibly by counting aluminum atoms) and dividing by the
time between when the scratches were made.
There are of course flaws in this definition -- for one thing, it can't be
used if A is accelerating, because of the need to keep the rod free from
stresses. It also requires the B either be moving directly toward or away
from A, since rotations around A cause the rod to "accelerate" (if I
understand mechanics properly). Also, it's a little vague when "time" is
mentioned. I would appreciate someone informing me of better definitions.
Is this adequate for now, bjon ?
+>>That means that in some cases "relative" motion is not really
+>>motion at all, but only apparent motion.
...
+you cannot choose a frame in which both are at rest.
+(Which says that there's absolute motion in there somewhere).
+
+It seems to me that if ALL motion is purely relative, then you should
+be able to eliminate all of it in some way.
+
+And another sign that an observer has absolute motion at all times is
+the simple fact that when he changes this motion, a real effect (or an
+absolute effect) is registered by his own on-board instruments.
Yes, this seems to make sense. However, the integrated argument below also
seems to make sense, and it raises more questions I am unable to answer.
Would you mind helping me revolutionize cartography ?
Permit me to perform the mathematical operation called integration on your
argument and my definition, to see if this newly-generated argument and
definition make sense.
Let us say I have a rod made of aluminum. I attach one end of the rod to
one object A, and always make sure it is free from any acceleration or
stress that might change its length. At some time t=t1 I make a scratch in
the rod where it is attached to A. At some later time t=t2 (while the rod
is still attached to A) I make another scratch in the rod where it touches
the other object B.
If the 2 scratches are in different places, then object B is, by this
definition, "relatively positioned" with respect to A.
->>That means that in some cases "relative" position is not really
->>motion at all, but only apparent position.
...
-you cannot choose a frame in which both are at the same position.
-(Which says that there's absolute position in there somewhere).
-
-It seems to me that if ALL position is purely relative, then you should
-be able to eliminate all of it in some way.
It would seem so, but I haven't been able to do so.
Is there a way to eliminate all of it ?
If there is not way to eliminate all of it, does this mean that there
exists some absolute position ?
Which object is at the absolute origin position ?
How can I build an instrument to measure my distance from the origin
(0,0,0,0) ?
-And another sign that an observer has absolute position at all times is
-the simple fact that when he changes this position, a real effect (or an
-absolute effect) is registered by his own on-board instruments.
Unfortunately, the analogy breaks down here -- as far as I know, a change
in position is completely undetectable by on-board instruments.
+If light has only relative motion, then it should be entirely possible
+to find a frame in which light is at rest.
+ **Jones, B**
+bjon@ix.netcom.com
Hum ? But I *have* found a frame in which the distance a particular photon
travels during its lifetime is zero meters. (I assume that that is what you
mean by "a frame in which light is at rest").
[posted to sci.physics.relativity and complementary copy mailed to bjon]
Please email me a copy of any response you post (my newsfeed is unreliable).
Anyone want a summary of the email response I get ?
--
David Cary
Future Technology, PCMCIA FAQ.
Path: hermes.rdrop.com!user
From: d.cary@ieee.org (David A. Cary)
Newsgroups: sci.physics.relativity
Subject: Re: another puzzle: "massless?"
Date: Fri, 31 Jan 1997 15:28:18 -0700
Organization: rarely.
Lines: 277
In article <01bc05f5$a36b83f0$4e0597cb@JX>,
"John DeHaven" <johnd@mozart.inet.co.th.remove> wrote:
...
+(Hmmmm. This raises a question. Can there even _be_ "observers" moving at
+c? Time would not pass for such an "observer" so how could "observations"
+be done? More generally, is there any meaning to the idea of an "inertial
+frame" at c, or is this just a meaningless noise too?)
I'm pretty sure that yes, I can build a "inertial frame" around a
particular photon such that that photon is "at rest" in this frame. The
math appears to work out -- there are a few things that go to 0/0, but
using limit theory I can get consistent results.
In that frame, (by the definition of the frame) the photon travels a
distance of zero. However, zero time passes. Interesting. In that frame,
the entire rest of the universe appears squashed by length contraction into
a zero-thickness disk.
But that appears to be the limit -- a "inertial frame" that would appear to
be traveling faster than 'c' gets strange and "imaginary" numbers.
+It's "the literature" that imputes, unnecessarily and confusingly, new
+meanings to old words. "Rest" of luxons for an excellent example. Worse,
it
+far too often fails to explain these new meanings to the poor layperson
+struggling to understand. "The literature" is, I contend, inexcusably
+careless and this isn't the only example.
Yes, I find unnecessarily confusing "explainations" annoying.
+In the spirit of showing how easy it is, I'll try to use this new term in
+the rest of this post. You can translate "intrinsic mass" into "rest mass"
+wherever you see it, if it confuses you. I just CANNOT bring myself to
+write it that way about luxons, because it makes zero logical or physical
+sense, "literature" notwithstanding! (Though I more than likely will in
+other communications where this isn't the issue.)
What ? You're going to try to make physics easy for me to understand ?
Is that legal ? :-)
+> mass), and relativistic mass, u, is just another name for energy, E (u
==
+> E/c^2), and thus is not of much use to physicists.
+
+NOT??? I understand it must be taken into account whenever anything is
done
+involving high speeds. For example no particle accelerator can function if
+its behavior is not programmed to compensate for the increased
relativistic
+mass of very high-speed (high-energy) particles.
Yes, he's right. The so-called "relativistic mass" is an obsolete term,
there is absolutely *no* reason to use such a confusing thing.
According to the sci.physics FAQ,
E^2 = m^2 c^4 + p^2 c^2
where
m = mass of an object (what you call the "intrinsic mass").
E = total energy of an object in a particular inertial frame, which *used*
to be called the "relativistic mass", but everyone now calls it Energy.
p = the momentum of an object in (the same) particular inertial frame.
+> By confusing (rest) mass and relativistic mass, you are committing one
of
+> the most common and frustrating mistakes in students of relativity.
+
+Indeed? This is news to me. You are saying there _are_ two kinds of mass
+and that sometimes mass != mass? If the "mistake" of confusing this causes
+people to make further mistakes, please give me an example of the kind of
+mistake it might cause people to make. I'd tend rather to think that _not_
+assuming that mass==mass would cause more mistakes, like building
defective
+accelerators, but I'm here to learn. (And not to imply that I make no
+mistakes, either! ;-)
Yes, there is only one kind of mass, "intrinsic mass".
There are lots of different things that people *used* to *call* mass, but
they are not the same as "intrinsic mass". It would be better all around if
people used some other terms for these other things, like, perhaps,
"Energy".
Occasionally (and this causes no end of confusion), people would convert
some of these other things into "kilograms" or some other unit of mass.
This is just as confusing as saying that I can push my car with a force of
20 "kilograms". The car doesn't mass 20 Kg, I don't mass 20 Kg, this mass
of 20 Kg is so *mysterious* -- where is it, where did it come from, where
does it go when I stop pushing ?
+> I
+> blame it on old and undergraduate textbooks, which introduce the idea of
+> relativistic mass as if it has some use. It doesn't.
+
+I don't believe this, sorry. I know it's hard to prove a negative, but try
+to convice me.
"relativistic mass" is absolutely useless. Where ever a "old-style"
textbook used that in a equation, all "new-style" textbooks substitute the
exact equivalent "gamma*mass" or "gamma*(intrinsic mass)". It's much less
confusing.
+Lurkers: I appeal to you for more evidence to the contrary (the _positive_
+assertion that relativistic mass has "some use") because the only example
I
+can think of right now is of building accelerators.
I refuse to use "relativistic mass". However, whenever I am doing some
calculation, sometimes a number appears on the screen of my calculator that
happens to be exactly the same number as the "relativistic mass" quantity
someone trained in the old, confusing methodology would calculate. We both
get the same results in our calculations. He calls that intermediate number
the "relativistic mass", I don't give it a name -- to me it is the
intermediate result from "gamma*(intrinsic mass)" or "Energy/c^2". It's the
same way that I don't give a name to most of the other intermediate numbers
that show up on my screen during the calculation, in the same way I have no
name for the quantity "(1-v^2/c^2)".
You could claim that it *is* useful, in the sense that I *need* that
intermediate number before I can generate the final result. I claim that
giving that intermediate number a name doesn't help any, and giving that
number a *confusing* name is counterproductive.
+> > Q3: Does this not contradict the physics dogma that photons "don't
+> > interact
+> > with each other?" This would be interaction, however slight, due to
+> > gravitation, due to mass-equivalence of their energy. Or if not, what?
+>
+> They don't interact electromagnetically or quantum mechanically, but
+nobody
+> said anything about gravitationally.
+
+Again, physics-talk, ubiquitous in "the literature," fails! They say, over
+and over, without qualification, "do not interact." The innocent reader
+presumes, reasonably I think, that they mean by this "in no way interact."
+The PROBLEM, just as you point out without meaning it that way, is EXACTLY
+that "nobody said anything about [gravitational interaction]!" Show me a
+statement from "the literature" that is that careful. For every one you
+find, I bet I can find ten that do not qualify the assertion. Science
+writing, even for laymen, should be _careful_ writing, and should not say
+"never" when they mean "almost never" or "only slightly" and so on.
+
+Of course, you may want to exclude science writing for laymen from "the
+literature." If you do, it is hard to see how laymen might come to
+participate, even passively, in physics, and how they might advance beyond
+lay status, or even come to enjoy it. (There are no persons less "lay"
than
+beginning students who know nothing yet at all about some subject.) I
think
+such careless assertions are one reason for the unfortunate tendency of
+many intelligent people to shy away from science.
Yes, this is unfortunate. My understanding is that high concentrations of
photons *do* exert gravitational force on other objects, even though there
is no intrinsic mass present.
However, I've been told that Einstein's Theory of General Relativity (GR)
is "real hard, so we won't get into that.". So all I know is Einstein's
Theory of Special Relativity (SR), where it is specifically assumed that
the force of gravity is so small as to be negligible. This is adequate for
all of my hobbies so far :-).
...
+Well, um, everything I have read about neutrino flux, which is not to say
I
+have read everything about it. Lemmie see. OK here's an example that falls
+readily to hand. From "Superforce" by Paul Davies, page 83:
What ? an actual quote, with page numbers and everything ? Rather than some
unsubstantiated claim ?
+He does _not_ mention how much gravitational contribution they would make
+if they do not have any intrinsic mass, as most people suspect, but only a
+relativistic mass. (Would this make them members of the luxon family?) It
+seems to me that if their intrinsic mass is so tiny, their relativistic
+mass would be a more important component of their net mass.
Translated into less confusing terms,
"It seems to me that if their intrinsic mass (m) is so tiny, their momentum
(p) would be the dominant compontent in their total energy (E)", where
E^2 = m^2 c^4 + p^2 c^2
+ Enough to
+matter with real neutrino flux? I wish he (or somebody!) _had_ mentioned
+this.
Yes, that would be interesting to know.
...
+ There is a neutrino cosmic background just like there's
+> an electromagnetic cosmic background, but as its name suggests it has
+very
+> low energy, just like the electromagnetic cosmic background.
+
+Not obviously suggested to me, if it is true that they are the predominant
+objects in the cosmos! And the examples of neutrinos commonly discussed,
+such as those generated by the sun, and every other neutrino-generating
+activity, are very energetic. But I don't know if they are typical of the
+neutrino background. Some appropriate numbers would settle the matter.
+Lurkers? Can you help out here?
I wish I knew.
....
+johnd@mozart.inet.co.th
+Newsgroups: sci.physics.relativity
+From: mmcirvin@world.std.com (Matt McIrvin)
+Subject: Re: another puzzle: "massless?"
+Date: Fri, 17 Jan 1997 22:33:47 GMT
...
+In article <browe-ya02408000R1601972101190001@10.0.2.4>, browe@netcom.com
+(Bill Rowe) wrote:
+
+> The concept of rest mass was primarily to make a clear contrast to
+> relativistic mass. In modern usage, mass means rest mass, the frame
+> invariant mass component. Relativistic mass, an archaic term, is simply
+> energy. It is much less confusing to use energy and mass rather than
+> relativistic mass and rest mass.
+
+On the other hand, there are a few situations, such as when talking about
+the angular momentum of a rapidly rotating object, in which it's somewhat
+useful to think of the "relativistic mass" as a mass. Sure, it's just the
+energy, but it behaves like a Newtonian mass in some (not all) ways.
Sure, *you* could think of it that way: "In these equations that Newton
gave us, we must replace the mass 'm' with the relativistic mass u", and
you would even get the right answers to your calculations. But I think it
is less confusing to think of it this way: "In these equations that Newton
gave us, we must multiply this term 'm' by a Einstein's favorite fudge
factor 'gamma', resulting in gamma*m."
+A while ago I proposed that the thing that was causing conceptual trouble
+was not the definition of this as a kind of mass, so much as the word
+"relativistic," which falsely implied that the other kind was not
+relativistic. Instead, why not call it "energetic mass"? That implies
+correctly that it's just energy/c^2, and preserves the identification of
it
+as a mass for people who want to deal with it that way.
Why not call it "Energy" ?
+Of course, the "rest mass" is a problematic term too, for precisely the
+reason that you've been discussing in this thread: it applies to things
+that aren't at rest, and it sounds ridiculous to say that an object that
is
+never at rest "has a rest mass of zero." For people who want to be more
+precise than the simple word "mass" about what kind of mass it is, there
+are other terms in use: "invariant mass" and "proper mass" are
unambiguous.
+The latter is particularly nice because of the analogy with "proper time."
+I think the standard term in French is "masse propre."
+
+--
+Matt McIrvin
Yes, this 'rest' term can also be confusing.
Here's yet another synonym: "inertia". Perhaps it would be less confusing
if we claimed that photons have zero "inertia"; in other words, that
applying any sort of force F on a photon has absolutely no effect on its
velocity v -- or, in equations,
F = m * (dv/dt) (Newtonian definition of inertia m)
where, for photons, m=0.
"intrinsic mass"="proper mass"="invariant mass"="inertia"
[copy posted to sci.physics.relativity]
Please email me a copy of any response you post (my newsfeed is unreliable).
Anyone want a summary of the email response I get ?
--
David Cary "mailto:d.cary@ieee.org" "http://www.rdrop.com/~cary"
Future Tech, quantum computing, digital hologram, PCMCIA FAQ, <*> O-
DAV:
Rather than have a actual physical object move FTL, let's imagine a long line of firecrackers.
I can set them off at any time or in any order I like.
I choose to set them off sequentially (in the rest frame of my lawn chair).
At "slow" speeds, it looks like someone is jogging from one end of the firecrackers to the other, setting them off one by one.
At "fast" speeds, it looks (to me in my lawn chair) like someone is jogging faster than light, setting them off one by one.
(At the "fastest" speed, they all go boom simultaneously in the rest frame of my lawn chair).
+From: penkethman@aol.com
+Newsgroups: sci.physics.relativity
+Subject: Re: Time Or Clocks, Space Or Rulers?
+Date: 24 Mar 1997 18:19:54 GMT
...
+In article <857664234.24233@dejanews.com>, nerad@biomed.cas.cz writes:
+
+>
...
+I think time and space have essentially been redefined to be relationships
+between
+events that can be observed. Thus time does not *flow*, etc. By insisting that
+
+these concepts be used in the sense they were designed for, you leave yourself
+behind in the progress of physics.
+
+>What we should care for in the first place
+>is that the description of reality is logically consistent and
+>understandable to a human mind.
+
+Not at all. That reality is logically consistent and explainable in terms of
+rational
+and self-consistent theories is a hypothesis which is testable, not a given.
+That the results must be understandable to the human mind is not guaranteed.
+There is nothing about the human mind that would lead us to speculate that all
+things must be understandable. Insisting that reality must be immediately
+understandable will get us only false and trivial theories.
+
+
+--- Jack Penkethman
DAV:
In my hands I have _Physics of the Atom: 4th ed_ by Wehr, Richards, Adair (not a particularly wonderful book, but it's what I have available). On p. 202 there's a really nice graph (I wish I could find more information about it) labeled
"Figure 5.16 Excess delay time for radar signals from Haystack Astronomical Laboratory in Massachusetts and Arecibo Laboratory in Puerto Rico to Venus and back. Data courtesy of Irwin I. Shapiro of Massachusetts Institute of Technology."
The scale of the graphs plots "Excess" delay (0 to 200 usec) vs. Time (-300 to +300 days).
It seems to be saying that we have measured that a light path (almost) directly into the sun will *decrease* the speed of the photons (relative to a light path that stays much further away from the sun, but travels practically the same distance). (Yes, this contradicts Special Relativity).
Is there any on-line information about this experiment ?
I don't understand General Relativity, but I've been told that it makes a similar prediction about what happens when ordinary objects (toothbrushes, old tennis shoes, etc.) are dropped into a black hole. Although they will (at first) accelerate towards it, just like they do when dropped onto Earth, soon they will *decrease* their speed and eventually come to a complete stop right at the "event horizon". (Normal Newtonian physics would predict that these objects would just accelerate faster and faster, smashing right through the "event horizon" and soon colliding with the singularity).
Shapiro, I. I., "Radar Observations of the Planets," _Scientific American_ 28 (July 1968).
Shapiro, I. I., et al., "Fourth Test of General Relativity: New Radar Result," _Phys. Rev. Lett. 26, 1132 (1971).
From: skaip@tnis.net (Sherwood Kaip)
Newsgroups: sci.physics.relativity
Subject: Really UNDERSTANDING Special Relativity
Date: Sat, 01 Mar 1997 16:03:27 -0600
To really understand SR, you must understand the significance of the
INTERVAL in SR (defined below and by Taylor and Wheeler, "Spacetime
Physics") and what 'time' means in SR, as compared to what you ordinarily
think of as time. Below I explain, demonstrate (prove), and expand on
this a little bit.
(I have not covered the situation where two events occur a distance apart
simultaneously in *some* reference frame--and therefore by SR are not
simultaneous in any other frame moving with respect to the first. I could
cover the situation in a similar manner but the article would be longer.)
Special Relativity, Simplest SR Overview
Copyright Jan, 1997 by Sherwood Kaip
Let us consider a non-moving point x of reference frame F moving
through reference frame G, or, what is the same thing, reference frame G
moving past a point x of reference frame F that is not moving with respect
to reference frame F. A clock located at x in reference frame F ticks off
1.0 second between two light flashes occurring at x. This represents two
"events", flash1 and flash2, wherever they occur in other reference frames
moving past. Observers in reference frame G measure a distance between
the two events. (They check the distance between the burn marks caused by
the flashes occurring at two different points in the G frame due to the
relative motion.) According to Special Relativity (SR), the INTERVAL
between two events which in some reference frame occur at one point at
different times is always a 'time' interval, in this case 1.0 seconds,
because, according to SR (Taylor and Wheeler, "Spacetime Physics"):
(INTERVAL)^2 = (time*c)^2 - (distance)^2
in *all* reference frames (for any two events) where (time) is the time
difference, (distance) is the distance difference in that reference frame,
and c is the speed of light. Since the distance difference is zero in
reference frame F, the INTERVAL between the events equals the time
difference in reference frame F. Since the INTERVAL between two events is
the same in all reference frames, in reference frame G the time difference
is (by rearranging the above equation)
Gtime = (1/c)*((INTERVAL)^2 + (Gdistance)^2)^0.5
The relative velocity between reference frames is the distance any
point of one referece frame travels through a second reference frame,
divided by the time of that travel in the second reference frame (in SR,
since time is not invariant in all reference frames in SR). One cannot
determine the relative velocity between reference frames F & G from the
time and distance of reference frame F, because we do not know the
distance any one point of reference frame G traveled through frame F.
However, we do know the time and distance traveled by the point x of
reference frame F through frame G because we were able to determine the
time in reference frame G by using the invariance of the INTERVAL
determined in frame F. So the relativistic relative velocity between
reference frames is the distance traveled divided by the time *in that
reference frame*, or relativistic relative velocity
u = (distance/time) =
distance*c / ((INTERVAL)^2 + (distance)^2) ^0.5
where the INTERVAL is derived from the time difference in the F frame. It
is obvious from this equation that u<1.0c in *all* cases.
Since we now know u, and we know the time difference in the F reference
frame, then the distance (in the opposite direction) traveled by a point
of the G reference frame through the F frame must be the negative of u
multiplied by the F frame time or
Fdistance = (-)u*(Ftime) = (-)(Ftime) * u =
(-)(Ftime) * (Gdistance*c) / ((INTERVAL)^2 + (Gdistance)^2)^0.5
and since in this case (Ftime) equals the INTERVAL/c,
Fdistance =
(-)(Gdistance)*(c*Ftime) / ((c*Ftime)^2 + (Gdistance)^2)^0.5
From this equation, it can readily be seen that in SR when a clock is at
rest in a reference frame (F in this case), no matter how small the
distance moved through the other (G) frame, the distance any single point
in the G frame moves through the F frame during that clock's time (F time,
INTERVAL/c) is *always* a little less. Also, no matter how far the clock
at rest (point x in the F frame) moves through the other (G) frame, the
distance a point of the G frame will travel through the F frame will
*always* be less than c*(Ftime).
This has all been according to SR. In SR, when speaking about a point
of one reference frame moving through another reference frame (and vice
versa--the F and G can be substituted for each other), neither time nor
distance between the two events are invariant. In Newtonian Mechanics
(NM), when speaking about a point of one reference frame moving through
another reference frame (and vice versa), the distance between the two
events is not invariant because it depends on how your reference frame is
moving relative to the reference frame where the two events are occurring
at the same place. However, in NM the *time* is invariant between these
two events in all reference frames. Now notice this: In the SR example
above, the INTERVAL was invariant, and the INTERVAL is the ***same*** as
the *time* difference, multiplied by c, of the clock where the two events
occurred at the same place!!! Thus,
The SR invariant INTERVAL/c is the *same* as the invariant time of
Newtonian Mechanics.
Therefore, the velocity between reference frames of NM (I use v
rather than u to differentiate it from the velocity, u, of SR) is the
distance between events in a particular reference frame divided by the
INTERVAL/c of SR, i.e.,
distance/(INTERVAL/c) or distance*c/INTERVAL
Using this velocity of NM and the INTERVAL/c of SR as the time,
the distance a point of either reference frame travels through the other
frame is the same in NM.
The so-called time of SR is simply
(SR time * c)^2 = (INTERVAL)^2 + (distance)^2 or
SR time = ((NM time)^2 + (distance/c)^2)^0.5
The velocity of SR (I call it u to differentiate it from the v that I use
for NM) is
u =
(distance/SR time) = distance/((NM time)^2 + (distance/c)^2)^0.5
In other postings on the net I have shown that v=gamma*u (or written v=gu)
where gamma = g = (1-(u^2/c^2))^(-)0.5 = (1+(v^2/c^2))^0.5 (check it out
algebraically).
I have shown in this posting in a largely qualitative way that SR and
NM are actually one to one mathematical transformations of each other.
Therefore, it is not a question of which one is "correct", not at *any*
speed. Either can be used. However, it should be obvious that since they
are transforms of each other, it makes much more sense to use the simpler
system, Newtonian Mechanics. Recognize that the SR INTERVAL/c is the time
of NM (also known as the 'proper' time of SR) and you get rid of 'dilated'
time and 'contracted' distances. You also understand that the meaning
(definition) of 'time' is not the same in SR and NM, nor is the meaning
(definition) of velocity between reference frames.
While this posting is largely qualitative (although totally accurate
quantitatively as far as it goes, barring any typos by me), I have also
demonstrated these concepts in a detailed quantitative manner in many ways
in previous postings available from me by email. (Does anyone wish to
offer some space where these can be put out to be FTP'd or found on the
WWW?)
In the next day or so I expect to post material showing these concepts
directly carried into General Relativity! It should be reasonably easy to
understand because I will be using the somewhat qualitative, but
quantitatively accurate, General Relativity concepts from Dr. Robert
Geroch's book "General Relativity from A to B" (University of Chicago
Press, 1983?).
--
Dr. Sherwood Kaip Home:584-0620
1204 Turnberry (U. S. of America) FAX (915) 833-6264
El Paso, TX 79912 email (latest): skaip@tnis.net
John 20,30-31 followed by Luke 7 (1st half) or John 11
From: skaip@tnis.net (Sherwood Kaip)
Newsgroups: sci.physics.relativity
Subject: 'UNDERSTANDING' applied to General Relativity
Date: Mon, 03 Mar 1997 00:45:33 -0600
This is the material I mentioned in my posting "Really UNDERSTANDING
Special Relativity" as it applies to General Relativity.
General Relativity, A New Overview
Copyright Feb, 1997 by Sherwood Kaip
Use a monospaced font.
This is the followup posting applying what I described for Special
Relativity recently to General Relativity.
The following diagrams and quotes are from Dr. Robert Geroch's book
"General Relativity from A to B" (University of Chicago Press, 1983?)
a
| | a
__ . s | a
|\ __ . s a
| \ |\ a
| \ | q a
t1 | \ ./ __ a
| \ | r a
| \ q | a
| / t1 | a
__ .p / | t2 a
| / | a
t2 | / | a
| / __ .p __ a
__ ./ | a
| r | a
| | a
| | a
| | a
a
clock world line, general [t2 is negative] a
clock world line a
with timelike interval a
FIGURE: a's on right have no significance except to aid in creating the
drawing. Time is vertical traveling upward. Space is horizontal.
Although the world-lines in the book show some horizontal movement
(curvature), there is nothing wrong with an observer holding onto his
clock considering himself not moving (hence, the straight vertical line)
and everything else as moving.
Quoting from Dr. Robert Geroch's book (p. 81) (Brackets [] are my
condensation to shorten the quotation.)
*quote*
We send one of our standard clocks through event p. We send a
light-pulse from the world-line of that clock (say, emitted at event r) to
event q. A second light-pulse is to be emitted from event q so as to
again reach the world-line of the clock (say, arriving at event s). The
point is that we (who travel with the clock, and who experience event p)
cannot thereby experience event q. We therefore allow the light-pulses to
experiencve q, and we record the events of emission and reception of the
light. The two events r and s ( on our world-line) represent "information
about q as carried back to us by light." Now the purpose of the clock was
to make information numerical. What numbers are available to us from this
arrangement?. . .[The clock assigns numbers (times) to the three points s,
p, and r. The time intervals t1=(s minus p) and t2=(p minus r), as shown
above, result.] These numbers in some sense or other describe a
relationship between the two events. . .[A person who knows nothing of
space-time or relativity might say] ". . .since p occurred right here by
me, the spatial distance from p to q must be
(1/2)*c*(t1+t2). . ." (p.83)
*endquote*
[Such a person might answer the question, "What was the elapsed time
between p and q?" by saying that q occurred halfway between r and s or
(1/2)(t1+t2) and p occurred t2 after r. The time difference between q and
p is therefore (1/2)t1+(1/2)t2-t2 or the elapsed time between p and q is
(1/2)(t1-t2)]
and this is what is shown in the book (p. 84).
Thereafter, Dr. Geroch shows the importance of t1*t2:
*quote*
. . .It is the product, t1*t2, which is to be intrinsic [to
space-time]. . .This product, t1*t2 is called the interval between p and
q. . .no matter what clock world-line is chosen, no matter whether it
passes through p or through q, and so on, we shall . . .always obtain the
same interval, t1*t2, between p and q. (p. 91)
*endquote*
He then goes on to show that if our non-relativist's ideas of apparent
distance separations and time intervals are called x and t [this t equals
(1/2)(t1-t2)] respectively, then
GEROCHinterval=t1*t2=(x^2/c^2)-t^2 (p.96)
I call this the GEROCHinterval to differentiate it from the INTERVAL I
have used in other postings (and as found in Taylor and Wheeler,
"Spacetime Physics")
INTERVAL = ((ct)^2 - x^2)^(0.5)
The concept of both is the same and they differ only by the fact that one
is the square of the other when divided by a constant and the sign is
reversed.
Dr. Geroch then differentiates five qualitatively different
situations. r always occurs before s (in time on a world line). However,
p can occur before r, at r, between r and s, at s, or after s. This gives
rise to five different light cone diagrams (p. 89, Fig. 43) and the
descriptions: timelike q future, lightlike q future, spacelike, lightlike
q past, and timelike q past. The diagram on the left above (similar to p.
81, Fig. 38) indicates a spacelike interval, which means that there is
some reference frame moving at such a speed that the two events p and q
are occurring simultaneously (some distance apart) in that frame (and not
simultaneously in any other frame moving with respect to that one,
according to Relativity).
Let's consider two events p and q where r is between p and s (p before
r, i.e., timelike q future). This is illustrated in the right hand
diagram above. This makes t2 negative and therefore this is a timelike q
future GEROCHinterval which is negative and where the ABSOLUTE magnitude
of t1 is greater than t2. (This is because r can never occur after s.)
Specifically, consider the viewpoint with r after p as r approaches s.
When s coincides with r, t1=-t2 and the world line is experiencing *both*
events p and q with p occurring before q. In fact, the clock (which we
are holding) is simply measuring the time between the events p and q
occurring at our location. All other reference frames moving with respect
to ours have different world lines with the absolute value of t1 greater
than the absolute value of t2. (again, because r can never occur after
s.) t2 is still negative, and t1*t2, the GEROCHinterval, is always the
same for the events p and q. The square root of the absolute value of the
GEROCHinterval is, of course, simply the time between the events p and q
occurring where we are located.
As was stated before, the GEROCHinterval=t1*t2=(x^2/c^2)-t^2 and is
negative in this situation. The Taylor and Wheeler INTERVAL is
INTERVAL^2 = (ct)^2 - x^2
and this square of the INTERVAL is positive. Both 'intervals' are called
'timelike'. Since the light did not have to travel any distance to q and
back to our world-line (our world-line coincided with both events p and
q), the value of x is zero and therefore the INTERVAL is *identical* with
the Relativistic time t. (This is the same as the 'Proper' time of
Special Relativity.)
The INTERVAL is invariant between p and q. Other reference frames
moving by (rapidly or slowly) will observe p and q to occur at different
locations in their reference frames (not on their world lines, although q
will always be above, i.e., later than, p. Therefore ct will always be
greater than for "us" on whose world line both events occurred. Notice
that this time multiplied by c equals
ct = (INTERVAL^2 + x^2)^0.5
Note also that in order to determine the time interval between two
events we must know the distance between them. Of course, no timepiece
can determine such a time for no timepiece would "know" what distance to
use!!! In view of this, we should now be ready to admit that a 'timelike'
INTERVAL/c is really time (which it certainly is in the reference frame
where the timepiece is not moving, even in Relativity, as in the current
case) and that the t in ct, unless it equals the INTERVAL/c, is not time
as determined by any clock. As shown by the preceeding equation, t is a
calculated function of a clock reading and a distance.
Observers at p in the other reference frame can indeed send a light out
to where event q occurred in their frame and back and determine distance.
If they are told the timelike INTERVAL for the two events, then they can
calculate the t of ct, even though no instrument can measure that 'time',
t, (for the reason given in the preceeding paragraph). Having been told
the timelike INTERVAL, how do they determine the INTERVAL/c in their own
frame? Easy. They look at their own non-moving (in their reference
frame) clock and tick off an amount of time equal to the INTERVAL/c. I
have shown elsewhere that the INTERVAL/c is simply the reading on a
non-moving clock (in Relativity) and is the same in all reference frames.
I will not carry this discussion further here. My purpose was simply
to show that what I had found in Special Relativity also applies to
General Relativity. I am thankful that Dr. Geroch's book was both
accurate, and yet simple enough that I could accomplish this.
The timelike INTERVAL is the physical quantity which is invariant in
all reference frames and is measured by a physical timepiece. So-called
relativistic 'time' is a calculated function of this INTERVAL and a
distance (except when the distance interval is zero). Recognizing this,
it is quite reasonable to describe the relative velocity between reference
frames as the distance divided by the INTERVAL/c, and this velocity, which
can have any value including greater than c, turns out to be the same as
the velocity of Newtonian mechanics, v=gu, where v and u are the relative
velocities between reference frames according to Newtonian mechanics and
Relativistic mechanics, respectively; and g ("gamma") equals both
(1-(u^2/c^2))^(-0.5) and (1+(v^2/c^2))^(0.5).
This makes Newtonian Mechanics and Relativity one to one mathematical
transformations of each other. The numbers used in the two systems to
describe *a single physical situation* are different. The relative
velocities in the two systems are related by v=gu. The 'Proper' distance
of Relativity and the distance of NM are the same. The timelike INTERVAL
and 'Proper' time of Relativity are the same as the time of NM. The
spacelike INTERVAL of Relativity is the same as distance between
simultaneous events of NM.
Both Newtonian Mechanics and Relativity can describe a physical
situation accurately. After all, they are simply 1:1 mathematical
transforms of each other. It's just that the meaning of time, distance,
and velocity differs qualitatively as well as quantitatively in the two
systems.
--
Dr. Sherwood Kaip Home:584-0620
1204 Turnberry (U. S. of America) FAX (915) 833-6264
El Paso, TX 79912 email (latest): skaip@tnis.net
John 20,30-31 followed by Luke 7 (1st half) or John 11
From: Daryl McCullough <daryl@cogentex.com>
Newsgroups: sci.physics.relativity
Subject: Re: The Basis of Special Relativity
Date: Mon, 03 Mar 1997 11:37:25 -0500
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Xref: hermes.rdrop.com sci.physics.relativity:5377
...
> You admit that Einstein defined them
> relatively. So I ask, how does that which is defined relatively
> become non-relative or objective?
Answer the same question for the geometry of the Earth. Given
a line segment on the surface of the Earth, the description of
that segment in terms of the x-extent and y-extent is relative
to a coordinate system. However, the length of the segment,
(X^2 + Y^2) is independent of any coordinate system.
> If you say that one clock took a longer path through spacetime than
> the other, you obviously are not using purely relative motion anymore
> since the clocks have equal mirror image paths in each other's
> coordinate systems.
No they don't. There is an intrinsic difference between the motions
of the two clocks: one clock follows a geodesic (straight line), and
one doesn't. This will be true in any coordinate system whatsoever.
> So I ask, how are the 4-vectors defined? Are they attached to any
> randomly chosen observer?
Not at all. Vectors have nothing to do with observers. You are
confusing vectors with particular coordinate *descriptions* of
a vector. Once again, let's look at the analogy with ordinary
planar geometry. You take a straight-edge, and draw a line on
the ground. This line is a vector; it has a magnitude and a
direction. It isn't defined relative to any observer or relative
to any coordinate system.
...
> We use the observer's motion relative to mass to
> decide whether SR rules will work for him or not.
No, we don't. SR rules *always* work in a sufficiently small
region of spacetime, just as planar geometry works in a small
enough region on the surface of the Earth. For phenomena
that take place on a much larger area, we have to account
for the fact that spacetime is curved, just as we have to
account for the fact that the surface of the Earth is curved.
> We use mass to define how light will be bent as it grazes its
> surface. We use mass, in some way, to define the spacetime
> in which one twin moves and the other doesn't.
No, that's not right. It is true that the presence of mass
affects the calculation of elapsed time. However, the twin
paradox of SR goes through almost unchanged in GR, provided
that the two twins stay far from any mass. It is definitely
*not* true that the twin that travels the fastest relative
to the closest mass ages the least.
...
Daryl McCullough
CoGenTex, Inc.
Ithaca, NY
physics_is ...
From: Patrick Reany <reany@extremezone.com>
Newsgroups: sci.physics.relativity,sci.physics
Subject: We're all relativists!
Date: Thu, 27 Feb 1997 07:13:29 -0800
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>From 1975 to 1985 I was in doubt of so-called "relativity." I blame
my textbooks for this on two counts.
1) The concept of physics presented to me was that
of the search for truth about "reality" on the
physical level.
2) The concept that "relativity" was invented by Einstein.
Both of these were stumbling blocks to me.
However, physics is NOT about the search for truth about "reality."
Instead, it's about finding good theories to correlate, predict,
and explain phenomena. Physics is about what calibrated clocks and
semi-rigid rods and many other measuring devices have to say about
events in our phenomenal spacetime (not any so-called absolute or
"real" spacetime, whatever that would be). And physics will never
be about Truth until it is proved that our anthropomorphic variables
have any relation to Truth. Up to now we've just assume some
connection and hoped for the best. We once assumed that Truth was
necessary to get consistent results from the scientific method, but
the situation is more subtle than that, and the solution is obvious:
Just make consistency the goal, not the means!
The concept of "relativity" is invented by each of us at an early
age. And this is the way it's been from the beginning of human
existence.
I remember an event in my life at a very early age: I was sitting
in the back seat of my Dad's car waiting for my Dad to start the
car and leave the parking lot. For some reason I didn't notice
that my Dad had started the car moving, and all of a sudden I
noticed in my peripheral vision that the "world outside the car
was moving." Of course, in a split second my "rational" facilities
told me to reinterpret the phenomena as the car moving, not the
world moving and the car "fixed."
With common sense applied, my universe was once again saved from the
appearance of chaos. But common sense is not a basis for good
scientific theories, even though the two do overlap occasionally.
Scientific theories cannot be based on common sense for many reasons
--not the least of which is that phenomena that scientists deal with
is often way outside the experience of direct human perception.
Nevertheless, at the basic level of life we all use relativistic
concepts of space and time. How? Because we all use measuring rods
to measure the lengths of objects, and those measurements are
relative, not absolute which would require taking the differences
of the coordinates of points in absolute space. Even if we could
find a nonarbitrary origin for the cosmos, we would certainly NOT
want to use it for practical measurements. The same goes for
measuring time intervals.
Ultimately, we use relative coordinates, velocities, and accelerations
in physics not because absolutes one aren't available, but because
relative ones are available and every bit as good theoretically,
and much better practically.
This naturally brings us to consider another profound source of
confusion and resistance to so-called relativity--the confusion
between scientific and philosophical absolutism. It has only been
in the last couple decades that physicists could openly speak in
a philosophical manner. Unfortunately this trend seems not to
apply to presentations of relativity (unless you read from Einstein's
own published works).
Regardless of Einstein's personal philosophical views regarding
absolute space and time, his professional view was that notions of
absolute space and time were simply not NEEDED to do kinematics!
At least the kinematics of motion in weak gravitational fields, which
gives us SR.
Relativity was formally started by Galileo and then bolstered by
Newton. Newton founded his inertial-frame independent notion of
force based on the Galilean relativistic transformation equations.
This is classical relativity, and it has its own very "real" form
of "relativistic effects" as seen in the so-called inertial forces.
Since the time that Newton explained the motions of earthly and
celestial projectiles on the basis of a single unifying force
concept, the program was on to attempt to cover evermore
phenonena under fewer and fewer theories. Originally this program
was under the umbrella of the Mechanical view. When electromagnetic
phenomena was revealed, all attempts to subsume it under the
Mechanical program were tried and retried, but to no avail.
Einstein knew that physics did not need to concern itself with the
"truth" of the Mechanical program, only with finding a workable
theory. This he did in SR by postulating:
1) That the MEASURED speed of light in a vacuum is a constant c
when made by any inertial reference observer.
2) The laws of physics (in weak gravitational fields) must have
the same form for all inertial reference systems.
Principle 1) must be correctly understood: Don't think of light as
traveling through space. This is a serious stumbling block. What
Einstein had done was to subtly generalize the notion of what
speed "is," while leaving unchanged the notion of how to measure
speed. This is perfectly alright because science is NOT about
what things "really" are, but only about HOW to measure things
that are "measurable."
By why, you might ask, can't we think of light as traveling through
space? Simple, as Einstein pointed out, space is an unobservable,
a ghost. Unobservables have no rigorous meaning in a scientific
theory because they carry no non-arbitrary constraints on the theory!
Thus, for strictly scientific reasoning the concept of an absolute space
(or any other notion of space) is forbidden until such time as it has
direct observable consequences. However, for heuristic purposes
you can imagine anything you want about space and time. Just don't
claim that such concepts can be reified without providing an empirical
foundation.
Now SR went far to unify space and time in a way that Newton didn't,
though even Newton had a concept of Spacetime. Both Newtonian/Galilean
and Special relativity treated all velocities as relative, but also
treated all accelerations as "absolute." This aspect of SR leaving
the unobservable space as "absolute" was totally repugnant to Einstein,
who saw it as trampling the very notion of an empirically based
epistemology of science. If let stand, then he saw himself as not
following the very rules of how to do science, which seems to be
a point lost on most physicists.
Einstein was not going to let it stand, so he set about to undermine
the concept of absolute space in which accelerations live. This brings
us to ask, as I'm sure Einstein did also, what really do we mean by
an absolute anything in physics. Let me propose this definition: An
absolute concept in physics is a concept which permits exactly one
interpretation in physical terms. Thus Einstein could undermine the
absolute status of space as the fixed home of accelerations if he
could offer any alternative interpretation of accelerational
phenomena in terms of physical processes. And this is exactly what he
accomplished in his Principle of Equivalence of gravity and
acceleration,
at least in this respect: Any experiment performed in an unaccelerated
reference frame itself in a uniform gravitational field can be analyzed
as if the reference frame was in a zero-gravity field but accelerated
at a constant acceleration with respect to the fixed stars, and vice
versa.
This principle has two profound consequences. The first is that
"accelerational effects"--that is, phenomena that can be interpreted
as acceleration--now have more than one physical interpretation that can
be given to them, and thus they are no longer "absolute" in any theory
that includes the Principle of Equivalence.
The other consequence is practical: Any experiment involving
either "fixed" reference frames in uniform gravitational field
or constantly accelerated reference frames in a uniform gravitational
field can be analyzed two ways, allowing us to choose the simpler
method if we so desire. For instance, consider the following thought
problem:
A helium-filled balloon is fixed by a light string to a horizontal
bar in an air-tight bus initially at rest. If the bus then accelerates
forward in a straight line and at a constant rate, after all transient
effects are gone, does the balloon's string tilt toward the direction
of motion of the bus or opposite to it? Using the Principle of
Equivalence we can analyze this as follows: From our experience
we know that the helium-filled balloon on a tied string will (in still
air) "point" opposite to the direction of the local gravitation field
direction (down). So by analogy, the balloon in the bus will point
opposite to its local gravitational field. So if we consider the bus
as fixed, we account for the "accelerational effects" by positing a
gravitational field component pointing to the back of the bus. Thus
the balloon will point in the direction of the acceleration of the bus.
One last confusion to get to: There are many complaints that Einstein
contradicted himself when going from SR to GR. For instance, that the
speed of light is no longer a universal constant as given in SR. Well,
this is no problem at all, because all it means is that SR can be
counted on the give the results it predicts when it is used under
appropriate conditions. The strictest use would be to relegate SR
only to local use, but more generally valid use of SR is possible if
one can find large regions of space in which gravity is zero
(or near zero).
Anyone who believes that SR or GR aren't good scientific theories just
because "they can't possibly be True" doesn't understand the first thing
about a scientific theory. Good scientific theories have no requirement
to prove that they are True!
cheers,
Patrick
[email Kaip and everyone on that page about my SR page.]
Date: Fri, 20 Jun 1997 15:02:17 -0500
To: cary@agora.rdrop.com (David Cary)
From: skaip@tnis.net (Sherwood Kaip)
Subject: Request feedback on email
Status: U
I hope you have read my email to you "SR derived from two movng
objects". I would appreciate your feedback. It's really quite simple, as
described casually below. Are you still will to post the "SR derived from
two moving objects" on your Web pages?
According to ordinary NM, if SOMETHING moves at speed c (ANY
constant speed) in a reference frame perpendicular to the x direction, then
there is no movement in the x direction in that frame. In a 2nd frame
moving in the x direction, the distance the SOMETHING moves will be greater
because the y & z components will be the same but the x component will not
be zero. It could be said mathematically as
10. [(x^2 + y^2 + z^2)^0.5]/T does NOT equal [(x'^2 + y'^2 + z'^2)^0.5]/T
since T (time), y & y', z & z' are equal but x and x' are not. In other
words, obviously NOTHING can go the same speed in two reference frames
moving with respect to each other--EXCEPT....
*****If we use the distance the SOMETHING traveled divided by the
constant speed c as the definition of the time in EACH reference frame,
then we can write:*****
20. [(x^2 + y^2 + z^2)^0.5]/t = c = [(x'^2 + y'^2 + z'^2)^0.5]/t'
and it follows algebraically directly from this for relative motion in the
x direction that
30. (ct)^2 - x^2 = (ct')^2 - x'^2 = y^2 + z^2 = y'^2 + z'^2
which also equals the relativistic INTERVAL^2 (in the form used by Taylor
and Wheeler in "Spacetime Physics"). Now, ANYTHING can travel at the same
constant arbitrary speed (c is as good a variable name as any) in ALL
reference frames. The change from the non-equality Eq. #10 to the equality
Eq. #20 was made possible by the change in viewpoint expressed in the
sentence enclosed in "*****". The Eq. #20 is the general mathematical
expression (c can be any value whatever) that SOMETHINGs can travel the
same constant speed in all reference frames. This is the generalized form
of Einstein's 2nd postulate. From Eq. 20 I derived the equations of SR
using only simple high school algebra. "SR derived from two movng objects"
gives the details.
A casual look at how I got from the non-equality Eq. #10 to the
equality Eq. #20 shows that this change is not physical but mathematical.
The "SR derived from two movng objects" paper shows how the same physical
situation is described equally accurately but with different numbers in SR
and NM. While these numbers are very nearly the same in magnitude at low
relative speeds, they are QUALITATIVELY TOTALLY DIFFERENT at ALL speeds.
Please read the "SR derived from two movng objects" paper and email
me your comments. Thanks.
=====================================================================
Dr. Sherwood Kaip Office:(915)833-2929; Home:584-0620
1204 Turnberry (U. S. of America) FAX (915) 833-6264
El Paso, TX 79912 email (latest): skaip@tnis.net
John 20:30-31 followed by Luke 7 (1st half) or John 11
=====================================================================
From: mikko.levanto@vtt.fi
Newsgroups: sci.physics,sci.skeptic,sci.astro,alt.sci.time-travel
Subject: Re: 'Twin paradox' paradox
Date: 30 Nov 1995 18:06:56 GMT
throopw%sheol.uucp@dg-rtp.dg.com (Wayne Throop) wrote:
> The reason space and time in SR are related by
> t' = (t-ux)/sqrt(1-u^2)
> x' = (x-ut)/sqrt(1-u^2)
> and (mod sign) time along a worldline is
> ds^2 = (dt^2 - dx^2)
> is the same reason that in analytic geometry
> without SR, x and y are related by
> x' = cos(a)x+sin(a)y
> y' = cos(a)y+sin(a)x
^ (one of these should be -, I think)
> and the distance along a line is
> ds^2 = (dx^2 + dy^2)
When I learned this analogy, things became clearer to me.
I think it would be even more clear if you put the equations
in as similar format as possible, e.g,
t' = cosh(a)t + sinh(a)x
x' = cosh(a)x + sinh(a)t
where a is the rapidity, the SR equivalent of angle.
Or, one could use the geometric equivalent of
velocity (what is its English name?)
u = tanh(a) (SR)
u = tan(a) (geometry)
-----------------------------------------------------------------
Mikko Levanto Tel. +358 81 551 2448
VTT Electronics Fax +358 81 551 2320
P.O.Box 1100 Internet: Mikko.Levanto@vtt.fi
FIN-90571 Oulu, Finland
--------------- VTT - Technical Research Centre of Finland ------
From: weemba@sagi.wistar.upenn.edu (Matthew P Wiener)
Newsgroups: sci.physics,sci.skeptic,sci.astro,alt.sci.time-travel
Subject: Re: 'Twin paradox' paradox
Followup-To: sci.physics
Date: 1 Dec 1995 14:11:55 GMT
In article <49krs0$if9@lilja.vtt.fi>, mikko.levanto@vtt writes:
>throopw%sheol.uucp@dg-rtp.dg.com (Wayne Throop) wrote:
>> The reason space and time in SR are related by
>> t' = (t-ux)/sqrt(1-u^2)
>> x' = (x-ut)/sqrt(1-u^2)
>> and (mod sign) time along a worldline is
>> ds^2 = (dt^2 - dx^2)
>> is the same reason that in analytic geometry
>> without SR, x and y are related by
>> x' = cos(a)x+sin(a)y
>> y' = cos(a)y-sin(a)x
>> and the distance along a line is
>> ds^2 = (dx^2 + dy^2)
>When I learned this analogy, things became clearer to me.
>I think it would be even more clear if you put the equations
>in as similar format as possible, e.g,
> t' = cosh(a)t + sinh(a)x
> x' = cosh(a)x + sinh(a)t
>where a is the rapidity, the SR equivalent of angle.
>Or, one could use the geometric equivalent of
>velocity (what is its English name?)
> u = tanh(a) (SR)
> u = tan(a) (geometry)
The English name is "slope". Let m=y/x=tan(a) (vaguely velocity looking),
then the rotation coefficients become
cos(a)=1/sqrt(1+m^2)
and sin(a)=m/sqrt(1+m^2).
--
-Matthew P Wiener (weemba@sagi.wistar.upenn.edu)
From: vergon@cinenet.net (Vertner Vergon)
Newsgroups: sci.physics
Subject: Re: Twin Paradox - new and improved!
Date: 27 Nov 1995 20:08:48 GMT
...
ABERRATION - DOPPLER EFFECT - TIME DILATION
(twin paradox)
Consider the following hypothetical set of circumstances:
(as proposed by Einstein in his paper on special relativity)
(1) Observer O observes a distant star S to which he considers himself
at rest. That is to say the relative motion of O to S is of such
a low order of magnitude relative to c that it is negligible.
(2) O then accelerates to a high order of magnitude of c orthogonal to
the rays of light from S.
(3) O will then observe the phenomenon of aberration; however,
*his_velocity_direction_remains_orthogonal_to_the_rays_in_system_S*.
The equation given by Einstein (Sec.7 of his theory) for the
observed frequency nu' , under these circumstances is:
1 - cos phi * v/c
nu' = --------------------- nu
R
where
phi is the angle of the direction of velocity to the O-S axis in the
system S.
R = the Lorentz transformation
nu = emitted frequency
v = velocity of O
(4) When, as in the case of transverse velocity, phi = 90 deg
then cos phi = 0 , and
nu
nu' = ----
R
This does not square with the result of the Ives and Stillwell experiment
[J. Opt. Soc. Am., 31, 369 (1941) -- Transverse Doppler effect] which
yields
nu' = R nu .
The apparent difference in the two experiences is that in the hypothetical
case it is the observer that is in motion (orthogonally to the O-S axis)
and in the experiment it is the emission source that is in motion (also
orthogonally to the O-S axis).
The principle of relativity requires these conditions be interchangeable,
i,e, identical in results. Thus it is unnecessary to specify whether a
velocity is of the source or observer.
The empirical result of the Ives and Stillwell experiment must be accepted:
When *motion* is orthogonal to the wave normal (O-S axis) a frequency
less than the emitted frequency is observed.
It therefore becomes immediately apparent that the Einstein equation
expressing the Doppler principle is incorrect because when reflecting the
conditions prescribed by the experiment (velocity orthogonal to the wave
normal) it does not give the same result:
Ives & Stillwell give nu' = R nu
nu
Einstein gives nu' = ---- .
R
A SEPARATE TEST OF THE EQUATION.
Assume the following conditions: 90 > phi > 0 and is invariable. Thus
the velocity of S is in a recessional mode and direction does not change.
(0 degrees is directly *away* from the source.)
As v --> c, the equation shows the progressive decrease in frequency to
reverse (when v/c = cos phi) eventually resulting in a frequency greater
than that emitted. There is no known empirical verification of this
contradictory phenomena.
TRANSVERSE DOPPLER EFFECT AND TIME DILATION
Subsequent theorists have attempted to compensate for the above
insufficiency by first considering the direction of the incoming aberrated
light rays from which they then calculated the velocity direction in
system S. Whereas this *angle of observation*, when orthogonal to the
O-S axis, yields nu' = R nu, it does so only when the velocity is *not*
orthogonal to the O-S axis. But orthogonal velocity is exactly what is
required by the Ives & Stillwell experiment.
Thus Einstein's equation *can* yield nu'= R nu but in that case the
velocity is not orthogonal to the light rays; which means there *is* a
component of velocity along the O-S axis; which in turn means the
equation is incompatible with experiment (in which there is no velocity
component).
It's customarily held that in the transverse Doppler situation there is no
component of velocity between observer and source, consequently observed
frequency should equal emitted frequency. The fact that the observed
frequency is reduced by R when it should be equal to the emitted frequency
is generally taken as direct observational evidence of time dilation.
Vital to this deduction is that the component of velocity is zero, but
we see Einstein's equation *has* a component radial velocity when the
condition of nu'= R nu exists and thus does not accurately reflect
empiricism.
If Einstein's equation is inaccurate in the empirical transverse Doppler
instance where it is assumed time dilation is isolated, then the accuracy
of the time dilation concept itself is brought into question.
There exists here an irony. For many years the Ives & Stillwell experiment
has been held forward as "direct verification" of Einstein's time dilation.
As it turns, the experiment rather than being the buttress of that thesis,
is indirectly the instrument of its demise.
We must yield to experiment. Therefore, it follows that the relativistic
expression for the Doppler principle needs revision. When this is done we
will have an equation that will show nu' = R nu when the *velocity*
(not the aberrated ray) is orthogonal to the O-S axis. But it does not end
there. We must also consider time dilation.
An underlying fact (heretofore substantially ignored ) is that known
constant frequencies and time rate are inextricable. This has been
recognized recently in that the new standard of measurement for the second
of time is a known unvarying frequency of the excited cesium atom.
*The_emitted_frequency_is_an_absolute_marking_of_the_passage_of_time.*
Therefore, what has heretofore been implied must now be emphasized: To
observe a known constant frequency is to *observe directly* a clock.
Velocity in relation to the light rays of clocks will alter the
time/frequency observed. *The alteration of frequency and the alteration
of time are one and the same.* The Doppler principle is simply the key
to the mechanics; and a proper equation expressing it will be consistent
for all velocities.
It is unnecessary -- and no longer correct -- to consider a Doppler effect
separate from, then modified by, time dilation. The transverse Doppler
effect is merely a particular case of a continuous time/frequency range
which is a function of velocity.
In regard to time dilation of the special theory of relativity, there
exists an anomaly that of itself invites critical inspection:
(1) Mass increase (or whatever you choose to replace it with) is a
function of velocity -- a vector.
(2) Space contraction is likewise a function of velocity and takes
place along the axis of motion.
(3) However, time dilation is given as a function of speed only;
direction is disregarded as a function. This is strange when one considers
the following:
To look outward in space is to look backward in time (a well accepted
concept in cosmology). This can be written as (-t). Therefore, an
observer may consider that his immediate locale or position represents
present time with negative time extending in all directions.
Thus an observed coordinate system moving radially in space is also
moving "back" or into negative time. This manifests as a slowing
(dilation) of relative time.
A reversal of time is not possible for the following reason: A system
receding at c (the ultimate velocity) would be observed to have a
relative time rate of zero (actually there would be no observation as
the frequency of the signal light would be zero). Therefore, commencing
from the point of observation, when at any position n light-years away
the time observed by the inertial system would be -n years, the
condition we actually perceive in all systems.
What heretofore has not been considered is the converse of the above.
When a system is approaching the observer, it is proceeding from negative
time toward the present, i.e., is traveling forward in the positive
direction of time. This manifests as an observed relative time rate
greater than normal (greater than proper time).
It is no coincidence that this description of time rate as a function of
velocity is the same as the description of frequency variation due to the
Doppler principle. The mechanics involved is one and the same for both.
TIME/FREQUENCY CALIBRATION
As was stated above, it is desirable to establish an equation that
expresses the Doppler principle in such a manner that it is consistent
with the Ives & Stillwell experiment. This equation must show the relation
nu' = R nu when *motion* is orthogonal to the O-S axis (wave normal). The
equation given by Einstein does not accomplish this. The following
equation does:
1 Where V = v/c
nu' = ------------------------- nu
omega_0 + cos phi * V_0
R = (1-V^2)^1/2
V/R = V_0
(1 + V_0^2)^1/2 = omega_0
phi = angle of the line of
motion with the O-S axis
0 deg is away from the light
source S
When phi = 90, cos phi = 0 and
1
nu' = --------- nu
omega_0
1
If the expression --------- is simplified it yields sqrt/(1 - V^2) or R.
omega_0
The equation is then nu' = R nu .
It will be found that when the velocity is in any direction given by phi,
nu' will be the observed frequency. To be more exact, it will be the
time/frequency, viz., nu' = alpha nu represents the observed frequency in
relation to the emitted frequency and t'= alpha t represents the
observed time in relation to proper time.
1
( where alpha = ------------------------- )
omega_0 + cos phi * V_0
At phi = 90, alpha = R .
The following is an example of the universality and application of the
time/frequency concept:
EXAMINATION OF THE TIME ("TWINS") PARADOX
There are difficulties experienced by the special theory of relativity in
respect to time dilation when both positive and negative velocities are
involved.
Utilizing the time-frequency concept (t-f) developed in the Dual Velocity
Theory of Relativity ((( Relativity Beyond Einstein, Exeter Publishing,
1976))) we see the proper results unfold *with no inconsistencies and no
need for further modification or explanation*
THE FINAL SOLUTION TO THE TWINS PARADOX
TIME VARIATION
If one looks out into space, they look backward in time.
If we observe a star 100 light years away we observe it as it was 100
years ago.
If a space traveler were to travel from here to there, when he arrived
he would be 100 years in our past.
So, in essence, he has traveled backward in time.
*During* the trip this would manifest (observed from earth) as a dilation
or retardation of time. (Naturally, the trip would have to take longer
than 100 years -- earth time).
Now what about the return trip? He obviously comes from the past -- into
the present. Ergo, he must travel *forward* in time. This would manifest
(observed from earth) as a compression of time, i.e., time would
speed up.
In substantiation of this, a *constant* frequency is a clock (e.g., the
cesium clock). When one observes such a frequency, one observes a clock.
So, what does the doppler effect tell us?
When an emitting object recedes, the frequency slows -- and so the clock
slows.
When an emitting object approaches, the frequency increases -- and so the
clock speeds up (both observations from earth).
Upon contemplation consider the following: Time rate variation is based
on -- caused by -- *velocity*. Velocity is a *vector* which means the
result is dependent on *direction*. Negative direction: negative time
flow. Positive direction: positive time flow. "Negative" means 'away'
and 'slower'. "Positive" means 'approaching' and 'faster'.
* * * * * *
All this not only means Einstein erred in his calculations by the omission
of compressed time but in consequence his time dilation is quantitatively
off.
For example at .75^1/2 c the time dilation according to SR is .5 when
in actuality it is .268 (by doppler).
We will call this the 'time-frequency' rate, t/f, for one is the same
as the other.
Note, if one were to calculate a round trip based on the doppler rates
for this speed, they would find that the *net* time disparity is .5 --
but this is not what is observed during flight (which is .268 and 3.73).
* * * * * * *
Perhaps an example will clarify.
We will use for a velocity .75^1/2 c.
A, the astronaught, will make the round trip without pause at the terminal.
The distance, D, between earth and the turn around point (TAP) is 3^1/2
light years.
TAP ________
/|\ : Note, this observation is of the
| D accelerated observer. Thus to him
| : the distance E-TAP is reduced by the
| 1.732 LY Lorentz transformation which for this
| : velocity is .5.
| :
| : Therefore, the transit time is
| : .866 LY/.866 c = 1 year
[E] ___:_____
The return trip is the same, 1 year.
Thus, to A the total round trip occupies 2 years.
Therefore, A's observation of E are
1 year outbound * t/f = .268 year
1 year inbound * t/f = 3.732 years
-------------
total 4.000 years
outbound t/f = gamma(1 - v/c)
inbound t/f = gamma(1 + v/c)
Now we consider the same voyage from the viewpoint of E.
We note that the distance E-TAP is in the earth's inertial frame and
therefore the distance is 1.732 LY.
There are three phases to a round trip:
The second phase has two parts.
Phase I
^^^^^^^
Voyage earth-TAP (turn around point). TAP
/|\
|
|
1.732 LY |
-------- = 2 years |
.866 c |
|
|
[E]
Phase II
Light heralding arrival at TAP TAP ______
returns to earth. (II-A) / | > /|\
d | < |
*Simultaneously*, ship travels \ | > ---- (II-A) |
toward E. (II-B) | <
| > D
(II-B) ---- \|/<
> |
< \|/
[E] -----
D
d (distance of (IIB) = --- v/c
c
d
------- = 1.732 years
.866 c
Therefore, E observes t for the outward voyage as
Phase 1 + Phase II = 3.732 years
And T (total transit time E observes as having transpired on A) is
T = t gamma(1 - v/c) = 1 year.
Phase III
(return leg)
Arrival-and-start-of- TAP
-return becomes visible to E \ :
\ :
\ :
\ :
\ :
\__ : _____
| /|\ D-d
Completes return in time t. \|/ _\|/_ ----- = t
[E] v/c
and t * t/f = T (total transit time observed expired on A)
or T = t * gamma (1 + v/c) = 1 year
For better visualization we chart the complete voyage:
=========================================================================
A is observer | Elapsed time on E
^^^^^^^^^^^^^^^ unit time in A x t/f = observed by A
-------------------------------------------------------------------------
/|\
out | 1 t x .268 = .268
back |
\|/ 1 t x 3.732 = 3.732
-------- ----------
total 2 t 4.000 t
=========================================================================
E is observer | Elapsed time on A
^^^^^^^^^^^^^^^ unit time in E t/f observed by E
-------------------------------------------------------------------------
/|\
| 3.732 t x .268 = 1
|
\|/ .268 x 3.732 = 1
--------- ------
total 4.000 t 2 t
**************************************************************************
**************************************************************************
Note that both A and E observe of each other the same t/f rate outbound
and the same rate inbound. However, they observe them for differing periods
of time thus creating a disparity of total time. Note also that the TOTAL
TIME DIFFERENTIAL IS EQUAL TO THE LORENTZ FACTOR.
It is this time *differential* that Einstein gives in his original paper
as being the result of a clock displacement away and back from an inertial
clock.
This is also the essence of the Hafele-Keating cesium clock experiment.
We also see that the time one does the observing is equal to the time
he is observed.
All the parity requirements of Special relativity are met and the time
disparity preserved.
However, the interpretation of time dilation is corrected.
There is no paradox.
V.V.
Newsgroups: sci.physics
From: bhv@areaplg2.corp.mot.com (Bronis Vidugiris)
Subject: Re: Twin Paradox - new and improved!
Organization: What - me organized?
Date: Fri, 1 Dec 1995 19:11:27 GMT
In article <49kkkt$buj@marina.cinenet.net>,
Vertner Vergon <vergon@cinenet.net> wrote:
)["Verton" did not make a mistake. (I *never* make mistakes.)] :-)
)
)
)"Both observers" agree.
)
)Observer 1 is Einstein as *he* set up the conditions.
)
)The other "observer" is Ives & Stillwell. Their experiment was designed
)specifically to give the results of frequency (emitted by moving atoms)
)when viewed from a position orthogonal to their path.
)
)So, you can throw your non sequitur argument below to them.
)Frankly, I cannot even tell what it is.
)
)But one thing is sure, both observations are at right angles.
)
)Now why don't you get on to the meat of the presentation?
)
): Since the definition of a right angle depends on the observer
): (it's not lorentz invariant, as can easily be seen by imagining
): that one side of the right angle undergoes lorentz contraction in
): the direction of motion), one does not expect the cases to be
): interchangable!
I have to go by my interpretation of your description of what
Ives and Stillwell did, because I don't have the original.
My impression is that what they did was calculate the doppler
situation for the following situation:
moving observer
x-----> (motion vector).
^
|
|L
|
|
o-----> X-axis
source
The thing to realize is that the light ray labelled L in the above diagram
is at right angles to moving observer in the lab frame, but it
is not the same light ray that that would be at right angles.
in the observer's frame!
To calculate the above example, let us use a frame of reference
fixed on the source above with the x-axis as shown.
Let the time at which the light ray hits the moving observer
as shown be t=0 to fix the time co-ordinate of this frame.
Let the time of emission be at t= -L/c the light ray arrives
at the observer at time t'=0, at a position of x'=0 and y'=L.
Let's confirm that the lorentz interval along the light ray is zero:
c^2(-L/c)^2 - 0 - L^2 = 0
Now let us consider another emission
at a time -L/c+dt which also hits the observer.
This occurs at time dt, at a position of x=v*dt, y=L. We can confirm
this by checking again that the two ends of the light ray have a
Lorentz interval of zero. The interval between (-L/c+dt,0,0) and
(dt,v*dt,L) is
c^2(-L/c)^2 - (v*dt)^2 - L^2
which is zero (of order dt^2) as desired.
Now, what is the proper time interval measured by the receiver?
Well, the lorentz interval dT in the frame of the observer must
be lorentz invaraint, and this inteval is of the form (a,0,0), (a+dT,0,0)
where T is the proper time in the observer frame, thus the
Lorentz interaval is always c^2*dT^2
This means that c^2*dT^2 is always the lorentz interval, which is frame
independent.
The Lorentz interval between (0,0,L) and (dt,v*dt,L) is
c^2dt^2 - v^2dt^2, thus
c^2*dT^2 = c^2dt^2 - v^2dt^2 and
dT = sqrt(1-v^2/c^2)dt
So we have dT/dt = sqrt(1-v^2/c^2) as desired.
The important thing to note, as I mentioned before, is that the light
ray L which appears to strike the observer squre in the laboratory
frame here, is *not* the same light ray which strikes the observer
at 90 degrees in the *observer* frame. The observer places this
light ray as coming from behind him - it was some light ray at an
earlier time that he judges as coming in at a 90 degree angle.
end
special_relativity_misc.html