CALVIN@JHUIGF.BITNET ("That's not lake Minnetonka...") (01/24/89)
Hello, all.
I'll be the very first to admit that I'm not a physicist, and know precious
little about relativity, although I am a pure mathematician. This is why I've
decided to ask this question of this newsgroup - I'm confident that it will
be given better answers than I've recieved in the past from physicist-friends.
Anyway, here goes. It seems to me that the argument for the impossibility of
attaining speeds faster than c is flawed. Logically, an argument is invalid
if it, at some point, assumes that which it attempts to prove.
The argument (again, these are in simplistic terms, and I guess I should
apologize.. 8^) ), unless I'm wrong, goes something like this:
An object becomes more massive the faster it travels.
Since F=ma (Newton), an accelerating body requires more and more
force to keep accelerating it
At (near?) c, this force would become infinite, and thus, acceleration
past c is impossible
THEREFORE, c is the highest attainable speed by an accelerating body.
Ok. One thing screams out to me, though. c is a finite number, being 3x10^8 m/s
which all of you know. Then, why would the force required to accelerate a
body past c be infinite if c isn't infinite? How can it be assumed that a
body will become infinitely massive at c if c itself is not infinite, UNLESS
one assumes, subtlely, that c already is the fastest attainable speed (that
is, c is in effect, infinite).
Is my question clear? I know that not only has relativity been around for a
long time (allowing this question to come up by now, I'm sure), but many
quite intelligent and educated people buy into this. My conclusion: I'm
missing something. What is it, or (quite less likely) have I found a glitch
in the "c is the fastest attainable speed" argument? I mean, I could see
the force required being VERY large, but infinite..?
Thanks for your time, and again, I apologize if this question is either very
simple, or has been beat to death in the past. I'ma new subscriber to this
list.
Damian Hammontree
System Programmer
Johns Hopkins School of Medicine, Baltimore, MD (301) 327-2959
DAMIAN@JHUIGF.BITNET
CALVIN@JHUIGF.BITNETjim@nih-csl.UUCP (jim sullivan) (01/26/89)
In article <Added.0Xr94Sy00Ui3IFME9H@andrew.cmu.edu> CALVIN@JHUIGF.BITNET ("That's not lake Minnetonka...") writes: >The argument (again, these are in simplistic terms, and I guess I should >apologize.. 8^) ), unless I'm wrong, goes something like this: > An object becomes more massive the faster it travels. > Since F=ma (Newton), an accelerating body requires more and more > force to keep accelerating it > At (near?) c, this force would become infinite, and thus, acceleration > past c is impossible > THEREFORE, c is the highest attainable speed by an accelerating body. > >Ok. One thing screams out to me, though. c is a finite number, being 3x10^8 m/s >which all of you know. Then, why would the force required to accelerate a >body past c be infinite if c isn't infinite? How can it be assumed that a >body will become infinitely massive at c if c itself is not infinite, UNLESS >one assumes, subtlely, that c already is the fastest attainable speed (that >is, c is in effect, infinite). Being a mathametician you must know that there are many conditions where a limit exists which is never attained. I remember many equations where the curve gets closer and closer to some value but never attains it. Also, relativity means that all things are relative to an observer. An observer on a ship traveling at near c can accelerate and surpass c from his point of view. He will however notice that his destination is now further away than he thought so to get say 5 light-years away, it will still take 5 years even though he continues to accelerate. Also note that relativity allows for matter to travel faster than c. You just cannot accelerate from below c to faster than c. I remember a theory back in the seventies which proposed the existance of "tachyons" (FTL particles). Don't hear much about them anymore. Jim
rodman@mfci.UUCP (Paul Rodman) (01/26/89)
In article <Added.0Xr94Sy00Ui3IFME9H@andrew.cmu.edu> CALVIN@JHUIGF.BITNET ("That's not lake Minnetonka...") writes: > > >The argument (again, these are in simplistic terms, and I guess I should >apologize.. 8^) ), unless I'm wrong, goes something like this: > An object becomes more massive the faster it travels. > Since F=ma (Newton), an accelerating body requires more and more > force to keep accelerating it > At (near?) c, this force would become infinite, and thus, acceleration > past c is impossible And even attainment of c is impossible! > THEREFORE, c is the highest attainable speed by an accelerating body. No, c is NOT attainable > >Ok. One thing screams out to me, though. c is a finite number, being 3x10^8 m/s >which all of you know. Then, why would the force required to accelerate a >body past c be infinite if c isn't infinite? How can it be assumed that a >body will become infinitely massive at c if c itself is not infinite, UNLESS >one assumes, subtlely, that c already is the fastest attainable speed (that >is, c is in effect, infinite). The equation for mass is something like: m(moving) = m(rest) / (1-(v**2/c**2))**.5 clearly this will approach infinity as there is a v/c in it. So, whats the problem with mass => infinity as vel => c? Actually, you CAN go faster than light IF you can conjure up a particle with an IMAGINARY mass (i.e. a mass times (-1)**.5). Nobody is sure what this means, but solutions to the equations with an imaginary mass are possible, if meaningless in nature. Such posulated particles are call tachyons, and have been searched for by several experiments , all with negative results. Paul Rodman rodman@mfci.uucp
tm2b+@andrew.cmu.edu (Todd L. Masco) (01/27/89)
CALVIN@JHUIGF.BITNET ("That's not lake Minnetonka...") writes: > Anyway, here goes. It seems to me that the argument for the impossibility of > attaining speeds faster than c is flawed. Logically, an argument is invalid > if it, at some point, assumes that which it attempts to prove. ... > Damian Hammontree > System Programmer Okay, he's your basic problem. You're looking at the problem as though relativity was attemptig to argue through logic; It isn't _exactly_ trying to do that; rather, it's trying to provide a model that expresses what happens in "reality" (quotes for the enjoyment of you quantum people). The following gives a fairly reasonable explanation for you, as a mathematics person: Picture a typical graph of a hyperbole, say (x-c)(y-m) = (C). [First c = c, second C = some constant, m=rest mass of object]. Now, imagine that, instead of moving along the x axis (which we will now reveal to be 'velocity') when kinetic energy is added, imagine that it moves along the line of the _graph_. Close enough to x=0, the graph seems to be a straight line. No problem. Newtonian mechanics works fine. Once we get past, say x=c/10, we being to notice some amount of discrepency; We're not quite going as fast as we should, time's getting a wee bit altered, and some of our kinetic energy seems to have, strangely enough, gone to our mass instead of our velocity. Undaunted, we continue to accelerate the object, thinking, "hurm. What a wonderful toy the universe is." As we approach c, the graph has begun to approach the vertical asymptote. More and more, our Kinetic energy (remember, KE=(mv^2)/2) is increasing the mass, rather than the velocity. We can add KE to our heart's content; The universe won't care, we'll continue to travel along that hyperbolic line, approaching v=c, but never quit obtaining it. The above isn't exactly what happens. But it's close enough to show the concept involved. Note that the structure does NOT prohibit something moving faster than v=c; It only states that at v=c we have a discontinuity, and anything travelling along one line can't reach the other by conventional means (hedge, hedge). Is it clearer? [I used to be a math major -- I got better] /----------------------------------------------------------------------------\ |Todd L. Masco | ...and the dead are, but for a moment, motionless... | |tm2b+@andrew.cmu.edu ------------------------------------------------------ | |r746tm2b@cmccvb |"The memories of a man in his old age | |...!harvard!andrew.cmu.edu!tm2b | are the deeds of a man in his prime."-PF | \----------------------------------------------------------------------------/
throopw@xyzzy.UUCP (Wayne A. Throop) (01/28/89)
> CALVIN@JHUIGF.BITNET ("That's not lake Minnetonka...") > [...] know precious > little about relativity, although I am a pure mathematician. > At (near?) c, this force would become infinite, and thus, acceleration > past c is impossible > THEREFORE, c is the highest attainable speed by an accelerating body. > [...but...] c is a finite number, being 3x10^8 m/s > Then, why would the force required to accelerate a > body past c be infinite if c isn't infinite? Why is this surprising? Especially to a "pure mathematician"? Take the function (1/abs(x)). The limit is infinity as x->0. So how can a function "become infinite" when the domain is zero? How do you get infinity from nothing at all? The real question is why anybody finds this surprising. Not "surprising that reality is modeled by such a function"... that *is* perhaps surprising. I mean "surprising that a finite domain value can 'map to' infinity" (very, very loosely speaking). > How can it be assumed that a > body will become infinitely massive at c if c itself is not infinite, UNLESS > one assumes, subtlely, that c already is the fastest attainable speed (that > is, c is in effect, infinite). No, the assumption that is made in SR is that everybody "sees" light travel at the same speed, regardless of the speed of the emitter or observer. (This "assumption" is pretty safe, since it is actually what seems to happen with real light in the real world.) From there, Einstein used simple algebra to work out the consequences of this. One of the consequences is that as v->c, force required to increase v increases without bounds. -- You run and you run to catch up with the sun, but it's sinking, racing around to come up behind you again. The sun is the same in a relative way, but you're older, shorter of breath, and one day closer to death. --- Pink Floyd -- Wayne Throop <the-known-world>!mcnc!rti!xyzzy!throopw
holroyd@dinl.uucp (kevin w. holroyd) (01/31/89)
In article <3092@xyzzy.UUCP> throopw@xyzzy.UUCP (Wayne A. Throop) writes: > >Why is this surprising? Especially to a "pure mathematician"? Take >the function (1/abs(x)). The limit is infinity as x->0. So how can a >function "become infinite" when the domain is zero? How do you get >infinity from nothing at all? > stuff deleted > >No, the assumption that is made in SR is that everybody "sees" light >travel at the same speed, regardless of the speed of the emitter or >observer. (This "assumption" is pretty safe, since it is actually >what seems to happen with real light in the real world.) From there, >Einstein used simple algebra to work out the consequences of this. >One of the consequences is that as v->c, force required to increase v >increases without bounds. > Just one note of skepticism here... Back in the 1940's when we were attempting to break the sound barrier, the aerodynamic equations seemed to indicate the the air loads (the force on the wings) would go infinite at Mach speed. Half the aerospace engineers seemed to think it was not possible to accomplish. Good thing Chuck Yeager wasn't real strong in Math. "I know this is against the law of gravity, but then, I never studied law". Bugs Bunny -- ******************************************************************************** Kevin W. Holroyd * CFI Aspen Flying Club * Denver CO. *
gd@geovision.uucp (Gord Deinstadt) (02/02/89)
In article <894@nih-csl.UUCP> jim@nih-csl.UUCP (jim sullivan) writes: > ...Also, relativity > means that all things are relative to an observer. An observer > on a ship traveling at near c can accelerate and surpass c > from his point of view. He will however notice that his > destination is now further away than he thought so to get > say 5 light-years away, it will still take 5 years even though > he continues to accelerate. Actually, it's the other way around. The observer on the ship finds, as he keeps throwing exhaust out the back, that his speed doesn't seem to be increasing much, but instead the distance to his destination keeps decreasing. From his frame of reference, the whole galaxy becomes shorter and shorter in the direction of flight, so naturally it takes less time for him to cross it. From the galaxy's frame of reference, HE is getting squished-up, but from his frame of reference, THE GALAXY is the one getting ever flatter. And they both see the other guy's clocks running slower. Bizarre, but that's relativity. Incidentally, I had assumed that it all balanced out, so that if you put a particular amount of energy into accelerating the ship, you arrived in the same *subjective* length of time, as you would if Newton ruled the universe. However, I plugged in a few numbers, and this is what I got: Vr 0.10000000 Vn 0.100377 ke 0.00504 gamma 0.994987 Tr/Tn 0.998743 Vr 0.20000000 Vn 0.203080 ke 0.02062 gamma 0.979796 Tr/Tn 0.994884 Vr 0.30000000 Vn 0.310757 ke 0.04829 gamma 0.953939 Tr/Tn 0.988143 Vr 0.40000000 Vn 0.426824 ke 0.09109 gamma 0.916515 Tr/Tn 0.977977 Vr 0.50000000 Vn 0.556238 ke 0.15470 gamma 0.866025 Tr/Tn 0.963433 Vr 0.60000000 Vn 0.707107 ke 0.25000 gamma 0.800000 Tr/Tn 0.942809 Vr 0.70000000 Vn 0.894740 ke 0.40028 gamma 0.714143 Tr/Tn 0.912818 Vr 0.80000000 Vn 1.154701 ke 0.66667 gamma 0.600000 Tr/Tn 0.866025 Vr 0.90000000 Vn 1.608824 ke 1.29416 gamma 0.435890 Tr/Tn 0.779189 Vr 0.99000000 Vn 3.489645 ke 6.08881 gamma 0.141067 Tr/Tn 0.497248 Vr 0.99900000 Vn 6.537013 ke 21.36627 gamma 0.044710 Tr/Tn 0.292564 Vr 0.99990000 Vn 11.807832 ke 69.71245 gamma 0.014142 Tr/Tn 0.167000 Vr 0.99999000 Vn 21.100112 ke 222.60736 gamma 0.004472 Tr/Tn 0.094363 Vr 0.99999900 Vn 37.579435 ke 706.10696 gamma 0.001414 Tr/Tn 0.053145 Vr 0.99999990 Vn 66.859076 ke 2235.06803 gamma 0.000447 Tr/Tn 0.029900 Vr 0.99999999 Vn 118.912302 ke 7070.06781 gamma 0.000141 Tr/Tn 0.016817 where Vr is the real (relativistic) speed as a fraction of C, gamma is the resulting Lorentz contraction factor, ke is the kinetic energy of a unit mass travelling at that speed (measured in mass units), and Vn is the speed that would require the same kinetic enery in the absence of relativity. The remarkable thing is the ratio of Tr/Tn, that is, the subjective time to go a given distance, with relativity and without. You actually get there FASTER, in your frame of reference, than you would without relativity. Or, conversely, you can get someplace in the same length of time at a lower cost in hard-earned energy. Of course, everybody else, staying at home, still sees you taking 100,000 years or so to cross the galaxy, but who cares about them? Just be sure to empty the refrigerator before you leave for your weekend jaunt. 8^) Disclaimer: Shucks, ma'm, 'tweren't nothin' -- Gord Deinstat gd@geovision.uucp
sukenick@ccnysci.UUCP (SYG) (02/04/89)
> As we approach c, the graph has begun to approach the vertical > asymptote. More and more, our Kinetic energy (remember, KE=(mv^2)/2) > is increasing the mass, rather than the velocity. We can add KE to > our heart's content; The universe won't care, we'll continue to > travel along that hyperbolic line, approaching v=c, but never quit > obtaining it. You're mixing frames. If you're the thing which is accelerating, everything is wonderful, as long as you have the reaction mass, you'll continue to accelerate to your heart's content. Your mass will measure the same (to you), it's just as easy to accelerate now as it did when your journey started, assuming :-) no particles in your path and the speed of light police don't get you :-). If you're accelerating something, then you will see that it takes more and more energy to get the thing to go faster, kinetic energy goes up, but some of the energy goes into mass. The velocity of that object will travel along that hyperbolic line.
rae@geaclib.UUCP (Reid Ellis) (02/11/89)
sukenick@ccnysci.UUCP (SYG) writes: |If you're the thing which is accelerating, everything is |wonderful, as long as you have the reaction mass, you'll |continue to accelerate. Indeed, if you set out for a star say 15 light years away, and apply a large amount of acceleration, you could get there in much less than 15 years, .. subjectively. So if you don't care about the rest of the universe, you could say that the speed of light is no barrier at all. To state it a different way from that of relativity, there is no limit to the speed with which one can travel. However, as a side effect, the faster one goes, the faster one travels through time as well as space. So there you go: FTL. Wheee. Reid "We've no intention of having any innocent bystanders killed this time, so just come along quietly, all right?" -- Reid Ellis, geaclib!rae@geac.uucp, rae@geaclib.uucp [if you're lucky]