harrow@exodus.DEC (Jeff Harrow NCSE TWO/E92 DTN=247-3134) (05/08/85)
There's something I've never quite understood: Consider the following setup: \-------/ (Ship #2 going at .9C) (Laser, at 1.0C) (Ship #1 at 0.1C) | | >--> ------------------------ >--> | Earth |---------------------------------------------------- >--> | | (Laser, going at 1.0C) /-------\ Now, for simplicity we assume that the Earth has zero velocity (I don't think this will mess us up): A laser is fired from Earth which propagates out at 1.0C (relative to Earth!). Ship #1 took off first, a LONG time ago, going in the same direction at 0.1C (relative to Earth!). Ship #2 now takes off going at .9C (relative to Earth!) and fires a SECOND laser in the same direction, said second laser traveling at 1.0C (relative to Ship #2, NOT to Earth!!). Hence, BOTH lasers are going at 1.0C, but RELATIVE TO DIFFERENT BASES. When both lasers get to Ship #1, won't the laser from Earth have an apparent speed of .9C (C minus the speed of Ship #1 (.1C)), and won't the laser from Ship #2 have an apparent speed of 1.8C (.9C Ship #2 velocity plus 1.0C speed of laser minus 0.1C velocity of Ship #1)? Now I KNOW that I'm missing some basic concept here because it would seem that in the first case the ship was GOING FASTER THAN LIGHT, RELATIVE TO EARTH, and that in the second case the speed of the laser from Ship #2 was FASTER THAN C (as perceived on Ship #1). If C IS relative (perhaps a poor word (or the operative problem?) to be using here) to a base, then it would seem that MANY thing could go "faster than light", but if it's NOT relative to a base, "how can that be"? Any good ideas to explain this to a layman? Jeff Work address: ARPAnet: HARROW%EXODUS.DEC@decwrl.ARPA Usenet: {allegra,Shasta,decvax}!decwrl!dec-rhea!dec-exodus!harrow Easynet: EXODUS::HARROW Telephone: (617)858-3134 USPS: Digital Equipment Corp. Mail stop: TWO/E92 1925 Andover St. Tewksbury, MA 01876
freeman@spar.UUCP (Jay Freeman) (05/08/85)
/* libation to line-eater */ In article <2073@decwrl.UUCP> harrow@exodus.DE (Jeff Harrow NCSE TWO/E92 DTN=247-3134) writes: >There's something I've never quite understood: > >Consider the following setup: > >\-------/ (Ship #2 going at .9C) (Laser, at 1.0C) (Ship #1 at 0.1C) | | >--> ------------------------ >| Earth |---------------------------------------------------- >--> >| | (Laser, going at 1.0C) >/-------\ > > > ... Theory and experiment indicate that both laser beams will be perceived as moving at 1.0 C both by observers on Earth and on by observers on each space ship. Note that the original conclusion, that one observer will see light moving at 1.8 C and another at 0.1 C, stems from the implicit assumption that the "right way" to compare speeds is by simple addition and subtraction: But this amounts to making an hypothesis about the physical world, which can be tested by experiment, and so forth. And the experiments and reasoning associated with the development of the special theory of relativity have indicated that mere addition and subtraction are NOT the "right way" to compare speeds. The rule is more complicated, and it leads to the conclusion that all light beams moving in vacuum have the same speed as seen by all observers. When relative speeds are very small, the rule suggested by relativity reduces to simple addition and subtraction, so that our common-sense notions are vindicated. However, common sense is derived from common experience, and there is no reason to assume that it should apply to situations and conditions far beyond the everyday. Flamers will note that there is a lot more that one could say about these matters :-) ... -- -- Jay Reynolds Freeman (Schlumberger Palo Alto Research)
mercury@ut-ngp.UUCP (Larry E. Baker) (05/09/85)
[] > Hence, BOTH lasers are going at 1.0C, but RELATIVE TO DIFFERENT BASES. > When both lasers get to Ship #1, won't the laser from Earth have an > apparent speed of .9C (C minus the speed of Ship #1 (.1C)), and won't > the laser from Ship #2 have an apparent speed of 1.8C (.9C Ship #2 > velocity plus 1.0C speed of laser minus 0.1C velocity of Ship #1)? The light from ship 2 will simply shift to a higher frequency. This is known as the Doppler effect. You can see the same thing happen with cars and trains -- when a car drives by at 60 miles per hour blowing its horn, the tone changes as it pass you. This is due to the compression of the sound waves as the car is approaching, and the expansion of the waves as the car departs. The same is true for light. Were you a stationary observer in front (hopefully not directly in front) of ship 2, then you would see laser light of a much higher frequency as the ship is nearing you, and after it passed (assuming you're still alive), were it to shine the laser BACKWARDS, you would see laser light of a much lower frequency. If the light were 'white' light, then, as the ship approaches, it would shift to the blue end of the spectrum. (ultraviolet shifting out of the visible spectrum, most of the other colors also, and infrared shifting down into the visible spectrum). As the ship departs, you would see 'red' light as the infrared shifts DOWN out of the visible spectrum and ultraviolet shifts down into blue. This rather shakey explination probably has holes big enough to peg rocks through, as it is based on Physics that I learned long ago, but I hope it helps. -- - Larry Baker @ The University of Texas at Austin - ... {seismo!ut-sally | decvax!allegra | tektronix!ihnp4}!ut-ngp!mercury - ... mercury@ut-ngp.ARPA
brown@nic_vax.UUCP (05/09/85)
> There's something I've never quite understood: > > Consider the following setup: > > \-------/ (Ship #2 going at .9C) (Laser, at 1.0C) (Ship #1 at 0.1C) > | | >--> ------------------------ >--> > | Earth |---------------------------------------------------- >--> > | | (Laser, going at 1.0C) > /-------\ > [] Help me net, but light can't go faster than light. If a laser is fire from a moving ship, that laser's speed will be 1.0C relative to EARTH. If, and mean a big IF, a ship could travel at say, 1.5C, then a laser that was fired would end up being passed by the ship as it fired it. The laser probably couldn't even get started as the ship was going faster than the light it was trying to create. Another good point, how can anyone see anything inside of a ship that was going the speed of light or faster? The whole spectrum would be shifted so that we couldn't see anything. -- |------------| | |-------| o| JVC HRD725U Mr. Video | | | o| |--------------| | | | | | |----| o o o | | |-------| O| |--------------| |------------| VHS Hi-Fi (the only way to go) (!ihnp4!uwvax!astroatc!nic_vax!brown)
@S1-A.ARPA:host.MIT-MC.ARPA (05/09/85)
From: Rick McGeer (on an aaa-60-s) <mcgeer%ucbkim@Berkeley> Many, many, many physics undergraduates have thought of the same thought experiment, having fallen in to the same trap you did; namely, light travels at only one velocity (c) and two observers in different inertial reference frames will measure the same velocity. Or, to put it better: Two ships, A and B, are launched from earth, A travelling at .1 c and B travelling at .2 c. A laser on earth is then fired after the ships. Observers in A report that the beam appeared to travel at c (not .9c) and observers in B report that the beam appeared to travel at c (not .8c). Ah, you say, but A and B are travelling at different velocities wrt the light source. Surely this velocity difference, which is real enough (that is, observers in all three frames would agree with it) must manifest itself somehow in their observation of the laser beam, and you are correct. An observer on earth would report that the beam had a wavelength w, an observer on A would say w + w0 (w0 > 0), and and observer on B would say w + w0 + w1 (w1 > 0). Rick.
ables@mcc-db.UUCP (King Ables) (05/09/85)
The thing you're missing here is that as you begin dealing with speeds
which are significant next to the speed of light, you can't add
them linearly (actually, you can't *really* add ANY velocities linearly).
If you throw a ball ahead of you at 10 mph from a car going 30 mph, we
say the ball has a velocity of 40mph relative to the stop sign you
just ran ( :-) ). However, that's not *exactly* true. It's VERY nearly
40mph, but speeds do not add linearly. It's just that when you're
this far from the speed of light, they add extremely close to linearly.
As you get up to .5C, you begin to see things like (this is an
approximation) .5C +.5C = .75C. There is a formula (which I cannot
remember right now, unfortunately) which shows how to calculate
vt = v1 + v2 and it has v/C worked into it somewhere. For velocities near
0.0, v/C is so small that it isn't significant, but as v gets significant
next to C, the v/C value begins to have an effect on vt.
If I can find the formula at home, I'll post it tomorrow, otherwise, I'm
sure someone else knows it and will post it (they may beat me to it, anyway).
Hope this helps.
-King
ARPA: ables@mcc
UUCP: {ihnp4,seismo,ctvax}!ut-sally!mcc-db!ablesjcp@brl-tgr.ARPA (Joe Pistritto <jcp>) (05/09/85)
The effect your forgetting in the two lasers in space problem is known as the Lorentz transformation. Basically, the velocities don't add linearly because TIME is lengthened by an amount which is related to one over the square root of the quantity (1 - v/c). You will note that as v (velocity) approaches c (the speed of light), the quantity approaches zero, so the fraction approaches infinity. This gives the effective slowing of time as c is approached. This also has the effect of reducing velocity (velocity is defined as distance over time...). Since the fraction is asymptotic as v approaches c, you are guaranteed never to exceed c. (The physics types call this 'an important theoretical result', meaning if you prove it wrong, you get a Nobel Prize, no questions asked!) -JCP- PS: Lorentz already got his prize, but they don't take them back if your theory is proved wrong, so don't let that hold you back...
ables@mcc-db.UUCP (King Ables) (05/10/85)
[Aha! I knew I kept those notes from Physics for something!]
The formula for adding velocity vectors (assuming you accept Einstein's
Special Theory of Relativity rather than Newtonian physics) is:
v1 + v2
V = ------------
total (v1)(v2)
1+ --------
2
C
As v1 and v2 tend to "small", the denominator tends to "insignificantly
larger than 1", so the whole fraction tends to (v1+v2)/1 which is what
we normally think of. If we're adding .5c and .5c, we get a more
complicated answer. The denominator is significantly larger than 1, so
the total is significantly < v1+v2.
-King
ARPA: ables@mcc
UUCP: {ihnp4,seismo,ctvax}!ut-sally!mcc-db!ables@S1-A.ARPA:host.MIT-MC.ARPA (05/10/85)
From: crash!bnw@SDCSVAX.ARPA
I've seen this kind of problem before. It stems, in part, from the
problem of mounting a machine gun on a jet that flies faster than the muzzle
velocity of the gun.
The simplest way to explain this is that the speed of light (C) is an
absolute constant that is relative to the universe itself and not conditioned
by the contents of the universe. The universe has rules, and you can't break
the rules by going faster.
/Bruce N. Wheelock/
arpanet: crash!bnw@ucsd
uucp: {ihnp4, cbosgd, sdcsvax, noscvax}!crash!bnwdtuttle@uw-june (David C. Tuttle) (05/10/85)
Well, there's nothing like a layman that can (try to) explain things to another layman, so concerning the Speed of Light problem, I'll give it a shot (trying to remember my sophomore-level physics from 6 years ago): > \-------/ (Ship #2 going at .9C) (Laser, at 1.0C) (Ship #1 at 0.1C) > | | >--> ------------------------ >--> > | Earth|---------------------------------------------------- >--> > | | (Laser, going at 1.0C) > /-------\ > Ship #1 took off first, a LONG time ago, going in the same direction at > 0.1C (relative to Earth!). > Ship #2 now takes off going at .9C (relative to Earth!) and fires a > SECOND laser in the same direction, said second laser traveling at 1.0C > (relative to Ship #2, NOT to Earth!!). > Hence, BOTH lasers are going at 1.0C, but RELATIVE TO DIFFERENT BASES. > When both lasers get to Ship #1, won't the laser from Earth have an > apparent speed of .9C (C minus the speed of Ship #1 (.1C)), and won't > the laser from Ship #2 have an apparent speed of 1.8C (.9C Ship #2 > velocity plus 1.0C speed of laser minus 0.1C velocity of Ship #1)? The problem here is thinking of relativistic speeds as being LINEAR. In fact, they are NOT (0.9c + 0.9c does NOT equal 1.8c). Instead, the speed of light is ASYMPTOTIC. A ship traveling at 0.9c would view a laser overtaking it at 1.0c as going by at 1.0c, not 0.1c (although it might be severely blueshifted (?))! So, when you say the second laser travels at 1.0c relative to Ship #2, but not to Earth, that is wrong. It is 1.0c relative to ALL frames of reference. In fact, "relativity" is a misnomer in that sense, because the speed of light comes out as absolute as ever! The only difference in the lasers will be that of the Doppler effect (redshift and blueshift). So, any ship approaching 1.0c can still be passed by light at 1.0c, thus the ship can never bridge that gap and travel at lightspeed... True physicists are now free to punch holes in this layman's arguments. ============================================================================ "No matter where you go, there you are..." David C. Tuttle -- Buckaroo Banzai Computer Sci. Dept. U. of Washington
miles@vax135.UUCP (Miles Murdocca) (05/10/85)
>> ... An introductory dialogue to a scenario of spacehsips and lasers >> to ask the question: > If C IS relative (perhaps a poor word (or the operative problem?) to be > using here) to a base, then it would seem that MANY things could go > "faster than light", but if it's NOT relative to a base, "how can that > be"? The key to all of this relativity stuff is who the observer is. You mentioned that the lasers and ships were going at velocities relative to some other objects (like Earth, or the ships) so you are halfway there. Now, let yourself be the observer (in the ship farthest away as you had suggested). The ship with the laser will appear to be moving through a much shorter distance than it actually is (space shrinks for a moving body), and the observed speed of light will remain the same. I am not a physicist, but I am told by a physicist friend that it is not known whether or not it is possible to go faster than the speed of light. But if a body moves faster than the speed of light, then it can't move slower than the speed of light. The transition can't be made. Miles Murdocca, 4B-525, AT&T Bell Laboratories, Crawfords Corner Rd, Holmdel, NJ, 07733, (201) 949-2504, ...{ihnp4}!vax135!miles
@S1-A.ARPA:host.MIT-MC.ARPA (05/10/85)
From: rachiele@NADC
The basis of the theory of relitivity is that the speed of light is
Always the same, regardless of your velocity. Think of the speed of light
as the limit of all velocity, and light particles having infinate speed (but
limited by C). Thus, light moves at C, even if you are going at .99C relitive
to some other object.
Jim Rachiele
(rachiele@nadc.arpa)@S1-A.ARPA:host.MIT-MC.ARPA (05/10/85)
From: Slocum@HI-MULTICS.ARPA Organization: Honeywell Computer Sciences Center, Bloomington MN The speed of light is one of those things that always gets people mixed up. The speed of light is constant in all frames of reference. In the example you described, the two light beams would both be going at C, but their wavelengths would appear different to the observer in Ship1. The beam from ship2 would be blue-shifted. You would have to do some reading to get a better explanation. Asimov probably has something that explains this well. I woudl suggest Asimov's three part physics book. I don't remember the title, but it is excellent. It also goes through most of modern physics in a very reasonable understandable way. Brett Slocum (ARPA: Slocum@HI-MULTICS) (UUCP: ...ihnp4!umn-cs!hi-csc!slocum)
sean@ukma.UUCP (Sean Casey) (05/11/85)
My example is something that has been bothering me for years.
Ship A (v = .6c) Ship B (v = .6c)
------------------------------>
<------------------------------
Consider yourself to be aboard ship A. Assume there are no stars, no points
of reference except ship B. To you, your ship appears to be standing still.
According to relativity, when ship B flys by, it is approaching you at no more
than c.
How can this be? Time dilation? How can time dilation be a function of speed,
when speed is a meaningless concept without references?
--
- Sean Casey
-
- UUCP: {hasmed,cbosgd}!ukma!sean or ucbvax!anlams!ukma!sean
- ARPA: ukma!sean<@ANL-MCS> or sean%ukma.uucp@anl-mcs.arpa
-
- "We're all bozos on this bus."edward@ukma.UUCP (Edward C. Bennett) (05/11/85)
[ Eat at Joe's ]
You're misinterpreting your own diagram. Light always travels
a c. The speed of it's source is irrelevant. Ship B (the one @ 0.1c)
will observe the two laser beams to be identical. They'll be red-shifted
due to B's motion, but identical.
I think.
--
edward
{ucbvax,unmvax,boulder,research}!anlams! -|
{mcvax!qtlon,vax135,mddc}!qusavx! -|--> ukma!edward
|
{decvax,ihnp4,mhuxt,seismo}! -+-> cbosgd! -|
{clyde,osu-eddie,ulysses}! ---|
"Well, what's on the television then?"
"Looks like a penguin."
()
|
|-- Support barrier free design
/|---
| \ _
\___/ \=eder@ssc-vax.UUCP (Dani Eder) (05/11/85)
> > My example is something that has been bothering me for years. > > Ship A (v = .6c) Ship B (v = .6c) > ------------------------------> > <------------------------------ > > Consider yourself to be aboard ship A. Assume there are no stars, no points > of reference except ship B. To you, your ship appears to be standing still. > According to relativity, when ship B flys by, it is approaching you at no more > than c. > > How can this be? Time dilation? How can time dilation be a function of speed, You have contradicted yourself. If there are no external reference points, then there is no way to measure Ship A as moving at 0.6c to the right. It moving to the right implies to the right WITH RESPECT TO THE CRT SCREEN, ie an external reference. Ship B will appear to be moving towards you at .882c. You will appear to yourself to be moving at v=0. The relative velocity will be less than c. Dani Eder / Boeing Company / ssc-vax!eder
@S1-A.ARPA:host.MIT-MC.ARPA (05/13/85)
From: Rick McGeer <mcgeer%ucbkim@Berkeley> Well, in fact you are observing the objects A and B from a third reference frame with observer, C, and we presume that observers in A, B, and C all have meter sticks, clocks and what have you. From the question we say that in C's reference frame, both A and B are moving in one dimension on opposite vectors with velocity .6 c. The question is, in A's reference frame, what is B's velocity? From Tipler, pg 680, we obtain: u(x') = (u(x) - v)/(1 - v u(x) / c^2) where v is the velocity of A in the frame of C, u(x) is the velocity of B in the frame of C, and u(x') is the velocity of B in the frame of A. Solving for u(x) = -v = -.6c, we get: u(x') = -1.2c/1.36 or almost exactly -.97c. Rick. ps -- the formula I gave above can be obtained by differentiating the Lorentz Transform: x' = gamma (x - vt) where v is the velocity of the frame S' in terms of the frame S. R.
@S1-A.ARPA,@MIT-MC:lucas@CMU-PSY-A (05/14/85)
From: lucas@cmu-psy-a (pete lucas)
If you'd really like to get a handle on this relativity stuff relatively
painlessly, let me suggest that you go to the horse's mouth: There is a
marvelous little book called "Relativity: The Special and General Theory, A
Popular Exposition" by one A. Einstein. Let me quote from the author's
Preface:
The present book is intended, as far as possible, to give an exact
insight into the theory of Relativity to those readers who, for a
general scientific and philosophical point of view, are interested
in the theory, but who are not conversant with the mathematical
apparatus of theoretical physics. The work presumes a standard
of education corresponding to that of a university matriculation
examination, and, despite the shortness of the book, a fair amount
of patience and force of will on the part of the reader....
The book was written in 1916, but the reference for my copy is New York:
Crown Publishers, 1961.
-Pete Lucas, CMUschrei@faust.UUCP (05/14/85)
Jeff,
You ask good questions. What you are struggling with is the
fundamental observable paradox that led Albert Einstein to the Theory
of Relativity. The speed of light (or any electromagnetic wave)
*in a vacuum* is never relative. It is always absolute -- a constant --
and is independent of the motion of the observer. Now wavelength, i.e.
color in the case of light, is something else.swift@reed.UUCP (Theodore Swift) (05/15/85)
In article <52@uw-june> dtuttle@uw-june (David C. Tuttle) writes: >So, any ship approaching 1.0c can still be passed by light at 1.0c, thus >the ship can never bridge that gap and travel at lightspeed... > >True physicists are now free to punch holes in this layman's arguments. Rather than punch holes in it, maybe we can do some tailoring to a suit with potential, but doesn't quite fit yet. The reason anything with mass can't go the speed of light (e.g., spaceships) has to do with the not-to-easy-to-grasp idea that as your velocity approaches v=c, your _relativistic_ mass increases according to Mmotion=Mrest/sqrt(1-(v*v)/(c*c)). The mess in the denominator is called the "gamma function" (dunno why). If you consider the case where v is approaching c (from below!! we don't wanna mess with the case v>c,though one of the seniors did his thesis on just that idea) you should be able to convince yourself that the sqrt(1-(v*v)/(c*c)) term goes to zero, so the relativistic mass, Mmotion, goes to infinity. To get something going fast (or faster), you need to accelerate it. You apply a force to the mass to accelerate it. (Newton said it best: F=ma). Now, near c, your relativistic mass gets to be huge, so the amount of force necessary to get you going any faster (closer to c) also gets huge. You just can't carry enough fuel to generate "huge enough" forces. The gamma function also works on time. This is the basic idea behind the "twin paradox" (available in any good intro physics text) where the twin in a spaceship going at some relativistic speed ages "slower" than his sibling on the ground (or at rest- he can be suffocating in space for all we care, as long as his Timex keeps on ticking). The neet idea this brings up is that interstellar colonists won't have to go through *as many* generations before planetfall because, if they get truckin', they will age "slower" relative to the Infinite Cosmos (sorry, Carl...). One problem: you gotta slow down, to, unless you just want to leave E. coli on your target planet. Enough mister science for now. I'm going to sleep.
@S1-A.ARPA,@MIT-MC:cef@cmu-cs-spice.arpa (05/16/85)
From: Charles.Fineman@CMU-CS-SPICE Slocum@HI-MULTICS metioned the Asimov books. They are called Understanding Physics (Bantam?) and I found them very infomative on a wide range of topics including a chapter devoted to the development of the relatavistic theory. ~Charlie Fineman (ARPA: Fineman@cmu-cs-spice)