faster then light

8/6/2019 Faster Then Light

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FASTER THEN LIGHT (FTL)

(how to break the speed of light without breaking the law)________________________________________________________________________________

Lightspeed barrier: SR, intro

Just about everyone who's studied the subject knows that special relativityforbids the acceleration of a particle up to and beyond lightspeed relative toan observer. This is supposed to be because the inertial mass of the particle

increases with speed, with the increase becoming significant as the speedbecomes "relativistic". As the object's speed approaches c (says the argument),the mass of the object tends to infinity, so it would take an infinite amount ofenergy to take a particle all the way up to lightspeed. Actually, when you lookat the initial postulates of SR, they pretty much presuppose that FTL traveldoesn't happen.

That's the argument, anyway.

But because SR introduces so many redefinitions, it is actually possible tobreak the famous "lightspeed barrier" in Newtonian terms without explicitlybreaking any SR laws, and to invoke gravitational or acceleration "distortion"effects as an explanation of how a hypothetical FTL object needn't overtake itsown wavefront.________________________________________________________________________________

EASY STUFF:

(1): Playing galactic hopscotch, and travelling between multiple inertial framesprovides a way of achieving (Newtonian) FTL with respect to your startpoint.When multiple intermediate frames are involved, SR helpfully responds byreinterpreting (Newtonian) FTL speeds as being subluminal. To generate thoseintermediate frames, all you have to do is accelerate (the SR derivation didn'tclaim validity for accelerating frames, remember?).

(2): "Newtonian" FTL ... - if we didn't know any better, and just slammed ourfoot down on the accelerator and broke lightspeed, would the folks back homeever know about it? Apparently not, because the "naughty bit" of our journeywould again be obscured behind an event horizon. So does (observerspace) SR justdescribe a lightspeed barrier to observability, rather than what really happens?Is the lightspeed barrier purely an "observerspace" thing? Of course, under GR,acceleration is equivalent to the effect of a gravitational field ...

(3): Gravitational freefall into a black hole - is an example of "legal" FTLtravel. However, (a) SR ignores gravity, and (b) the FTL part of a particle'sfall allegedly can't be seen by a distant observer anyway. So there's still nodirect SR contradiction.

(4): Particle accelerators (on the other hand) are a perfect example of the sortof closed-path observerspace situation that the SR lightspeed limit is likely tobe valid for - our last hypothetical example could probably not be brought aboutusing a solar sail and a home-based particle beam. But it's hardly surprisingthat "dumb" particles never achieve FTL with respect to the coils that areaccelerating them, because at recessional lightspeed, you wouldn't necessarilyexpect the accelerating signal to be able to catch up with the particle to makeit go any faster (think about it).

(5): Propulsion systems - some types are definitely subject to an SR-type upperlimit. Others may not be.________________________________________________________________________________

MORE ADVANCED STUFF:

(6): Time-dilation factors and length-contractions further complicate FTLproblems under SR. It seems that some SR effects aren't testable, as a matter ofprinciple, unless you introduce those illegal accelerations again.


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(7): Spectral shift arguments under SR predict an infinite forward blueshift foran object travelling at lightspeed, which seems to rule out any higher relativespeeds. However, because SR contracts distances (at lightspeed) to zero, thismaximum displacement per unit time, when calculated using non-contracteddistances, actually corresponds to an infinite speed in Newtonian terms. End ofproblem - it seems that "speed" under SR isn't necessarily the same as "speed"under Newtonian mechanics.

(8): Probe chain theory - is the logical consequence of any theory that includesvelocity addition formulae. The formula says that it's possible to view anobject receding with any speed whatsoever, as long as the light passes throughenough intermediate inertial frames for the recession velocity between pairs ofadjacent frames to be less than c. That means that FTL signaling (in one sense)ought to be possible, because the probe chain provides an accelerating path forthe signal. Most physicists won't like this, but it appears to be an inescapableconsequence of the SR math - so hey, don't blame me, guys, this is a side effectof your theory. I'm just the bearer of bad news - this situation ought to havebeen sorted out decades ago. See also the "magic window" problem. * 9: Who saidspace has to be flat? - As the SR flat-space assumption fails for accelerationand gravitation, and also seems to fail in multi-body inertial systems, and intwo-body inertial systems when you consider the gravitational effects of kineticenergy at high speeds, then why should we believe that it holds for anysituation where v>0?

Conclusions

The SR lightspeed barrier limits the recession speed that an observer candirectly induce in a particle, and it limits the speeds achievable in a singlesimple explosion, but it doesn't seem to limit the speeds that a particle canaccelerate to, provided that the particle itself is providing the energy. FTLmight still not be practical - if you get hit in the eye by a bit of grittravelling at 300,000 km/s, it could ruin your whole day - but the currentarguments against it seem to evaporate when you stick them under a microscope.________________________________________________________________________________

What was all the fuss about? Summing up

So, we find that the SR lightspeed barrier, in the sense that it is usuallyportrayed, might not really exist other than in an observerspace projection. Itmight just be an arbitrary "mapping" artifact with no physical existence beyondan individual observer's situation, like the Earth's horizon.

The "infinite mass" argument is an observer-effect, particle acceleratorarguments don't necessarily apply to situations where objects have their ownpropulsion systems, the SR description is compatible with "deduced" FTLrecession hidden behind an event horizon, and the sort of behavior this gives is

already accepted by mainstream physics, as happening when something falls into ablack hole, and FTL Newtonian approach velocities also seem to map to subluminalvelocities under SR, there's no contradiction there, either.

Gravitational and acceleration arguments seem to say that FTL is legal, but areoutside SR's jurisdiction, and SR ignores gravitational effects that occur underGR, despite the fact that GR is supposed to reduce to SR for constant-velocitymotion. Given that kinetic energy (under GR) has gravitational effects, there'sno way you can guarantee that any GR inertial system can be described in a flat-space theory. Reinterpreting Lorentz shift as gravitational destroys the SRpropagation model, and means that there are lightspeed gradients betweencomponents of inertial systems.

It only appears impossible for a particle to be emitted at >c, because thecoupling-efficiency of applied radiation drops to zero for c-receding objects. Aconventional rocket can't expel gases at FTL speeds (relative to itself), butthat doesn't necessarily mean that by continuing to expel gases at subluminalspeeds (relative to itself), it can't eventually achieve a speed relative to its


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start-point that is significantly higher than the speed of the expelledpropellant.

In short, the SR lightspeed barrier is based on a flat propagation model thathas no convincing evidence in its favor, that fails in almost every situationthat it is applied to, and which (if we accept the equivalence principles of GR)can't be correct, anyway.

That's not to say that there might not be other factors that would make faster-

than-light travel impractical, but you won't find those other factors bystudying SR

So, we might not be able to achieve useful FTL travel after all, but if we domanage it, at least we'll be able to use a probe chain get a message back to thefolks at home.

Black hole bungee - jumping, anyone?

'Treason never prospers'; And, aye, there's a reason For if it doth prosper,none dare call it treason ...

old English proverb, Anon________________________________________________________________________________

Notes

Some of the terms used have slightly different meanings on different pages. Thelanguage of physics is still quite crude in a number of ways, and doesn't alwayshave different words for similar things (for instance, most physicists are happyto talk about "the Doppler formula", but don't have words to distinguish betweenthe different variants, which is why I had to make up the eDoppler/oDopplerterminology). I once sat down and tried to see how many definitions there werefor "mass", and ended up with about fifty, some of which normally coincided,some of which didn't.

"Lightspeed" is another extremely slippery word.

In these pages, "faster than light" or "FTL" is used in the sense that it ususually used in "spaceship" questions, where what you actually want to know ishow quickly one can travel between two agreed coordinates (such as two cities,or planets). In this context, expressing the velocity in terms of a redefineddistance isn't particularly helpful, and neither is redefining speeds in termsof the deduced local value of c in the moving observer's frame. I'm notsuggesting that a spaceship can overtake its own lightsignal, because I'm notaccepting the (unverified) SR assumption that lightspeed is anything other thanlocally constant.


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(1): Galactic Hopscotch

(island - hopping taken to extremes)________________________________________________________________________________

Playing galactic hopscotch

Let's suppose that a galaxy is receding from you at 0.6 lightspeed, and a secondgalaxy is receding from you at 0.6c in the opposite direction. The combined

(Newtonian) recession velocity is 1.2c. Can a spaceship leave one galaxy andreach the other?

Let's try it. A spaceship leaves galaxy A at 0.9c and heads blindly in thedirection of the other. After a lot of time, it decelerates a bit, and findsitself at the mid-point of the two galaxies, with each receding at the samespeed of 0.6c. With the engines off, it is now sitting "stationary", with thetwo galaxies A and B each receding at 0.6c in opposite directions, just like wewere in the first paragraph. So far it hasn't broken lightspeed, and everythingis legal.

Now comes the fun bit.

Since it has managed to get to its present position from its home galaxy (A), itmust be able to get back again - after all, this only requires it to travel fora long enough time at less than lightspeed.No problem.

However, there is no real difference between firing up the engines to go home,and expending the same amount of fuel to go on to galaxy B. A and B are nowequally reachable. In fact, if the ship's crew spin the ship around enoughtimes, while they try to make up their minds, and forgot to make adequate noteson their outward journey, they might lose track of which galaxy, A or B, theyactually came from!

So, let's suppose that by accident or design, the crew end up heading for B.Eventually, they get there. They have now managed to accelerate (in two stages)up to a Newtonian speed of 1.2c with respect to their home planet, again,without breaking any SR laws.

How did they do that?

Well, basically, the problem is one of definitions.

If an object is receding at a certain Newtonian speed, then the (directly -observed) recession speed under SR has a particular value. However, the momentthat light from a receding object is passed via a third intermediate frame, SRchooses to reinterpret the total velocity as being less than the sum of the two

halves - the "supposed" velocity of the object actually depends on thecharacteristics of the light-path (see SR velocity-addition formula, magicwindow problem).

So - an object (or inertial frame) can be receding at up to 2c, and you canstill reach it, simply by going via a third intermediate object (or inertialframe), which is used as a sort of staging post. In fact, the test particle canhave any recession velocity whatsoever, provided that it uses enoughintermediate frames. There's actually no upper limit at all. Any combination ofvelocities that are each less than c add together (under SR) to a total velocitythat is also less than c, so with enough intermediate frames, SR can take anyrecession velocity whatsoever and redefine it as being conveniently less thanlightspeed.

So - what constitutes an intermediate frame?

Well, if you want to send a light-signal, it could be a physical object (seeprobe chains), but if you were sending a physical object, the intermediate


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inertial frames could be supplied by the object itself, simply by turning theengine on and off to create inertial "coasting phases" between bursts ofacceleration.

The next logical step is to conclude that even the coasting phases areunnecessary - all the ship would have to do is leave the engines on.________________________________________________________________________________

How the heck can this possibly make sense?

Special relativity is based on the assumption of flat space and observedreality. Any object receding at greater than c can't be directly observed withinflat space, and therefore can't (normally) exist within the theory. Ahypothetical object receding at greater than c couldn't be hit by a ballisticobject launched by the observer at less than lightspeed, so (since an objectcan't be accelerated by the observer to greater than c), the logical assumptionis that speeds >c aren't achievable.

The critical weaknesses in this argument concerns acceleration. Einstein's SR ispurely "ballistic", and deals with constant velocity intervals between pairs ofinertial frames. It Doesn't Do Acceleration (remember this, it's critical).

If you wanted to be shot out of the mouth of a Jules Verne -type cannon at >cthen you'd probably be disappointed, but if you were launched in a rocket atless than c, and kept accelerating then special relativity would obligingly keepreinterpreting your final velocity as being less than c, whatever its value inNewtonian terms.

The velocity-addition formula is SR's greatest get-out clause.

Just put your foot on the accelerator and keep it there.________________________________________________________________________________

Notes: the SR lightspeed limit does not hold across multiple frames.

"Ballistic" arguments have traditionally been a weak point for physics theories.The aeronautical equivalent would be saying that it is impossible to construct asimple craft capable of flying from London to New York, because in order tocomplete the journey, the initial speed of the craft (when launched from a gun)would have to be so fast that it would burn up in the atmosphere. You can getaround the argument by deciding to continually apply thrust, instead ofexpending all your energy in one initial blast.

Another ballistic argument once "proved" that it was impossible to launch apayload into space with a liquid-fuelled rocket, because the fuel tanks, etc.,would always be too heavy to get the rocket all the way up. That line ofreasoning evaporated when someone thought of launching rockets from the top of

other rockets (multi-stage launchers like the Saturn V).


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(2):What happens if you try it?(in which a craft breaks the lightspeed barrier,

and the folks back home are none the wiser)________________________________________________________________________________

What the heck, full speed ahead?

The last section showed how the SR velocity-addition formula allows an object to

achieve a Newtonian recession speed greater than c relative to its startposition, provided that it undergoes acceleration and that the accelerativeforce doesn't originate from its startpoint.

How is this explained? Quite simply. According to SR, you can't just add twovelocities together using standard addition, you have to use a special velocityaddition formula. When an object recedes at 0.5c, SR says that its directly -observed frequency is multiplied by a factor of 0.577... If it recedes atlightspeed, the frequency drops to zero. But if a signal is fed through twostages, each with a recession velocity of 0.5c, then the observed frequency ofthe furthest object (receding at lightspeed) only drops to (0.577..), or0.3333', rather than zero (which you'd normally expect for lightspeed recessionunder SR). The standard SR rules simply don't work the same way whenintermediate frames are concerned - an object with a particular supposedrecession speed could be "legal" or "illegal", simply depending on whether ornot you looked at it through a moving sheet of glass (the "magic window"argument). That's difficult to reconcile with SR's model of simple flat spacewhose light-carrying properties are unaffected by the presence of objects withconstant relative motion - it implies that there is a much more subtle set ofeffects in action than the simple SR lightspeed limit would have us believe.

The SR velocity-addition formula simply takes the way that composite shiftsdeviate from the SR shift law, and works backwards to generate a new velocityvalue that would generate the same result, were the object being directlyobserved, instead. When you multiply two f'/f shifts that are each greater thanzero, the result is (obviously) still greater than zero. So, under SR, when youmultiply to shifts each caused by a recession velocity less than c, the combinedf'/f shift also never reaches zero (as it would be expected to at recessionallightspeed), and the resulting SR velocity is therefore deemed to be less thanlightspeed as a matter of principle. Where the SR velocity/shift law fails forcomposite shifts, SR simply redefines the velocity from the shift value so thatit doesn't fail.

This remapping is, of course, totally arbitrary, and lets us bring anysuperluminal velocity down to less than c without changing what the object isreally doing. It's a way of imposing a lightspeed barrier on paper by redefiningany composite shift to be less than c, provided that a signal can cross theintervening distance, courtesy of an intervening "carrier frame" (see probe

chains). So although SR says that nothing can travel faster than lightspeed, italso says that every velocity greater than c can be re-interpreted as being lessthan c, provided that there is are enough intermediate frames for a signal topass through.

That's why that galaxy-hopping example worked. We know that the total velocityis 1.2c, but SR decides to call it 0.88..c instead, so that it doesn't break thenotional SR lightspeed limit when the ship crosses from frame A to frame B. Theship's own 2-stage acceleration provides the intermediate frame necessary tojustify the application of the velocity-addition formula. (NB: this value wascalculated under SR from two instantaneous velocity-changes each of 0.6c, thetotal figure reduces further when more intermediate frames are involved)

So, is the SR c-barrier a pointless fiction?

Not quite. To understand what's going on, you have to remember that SR is atheory that describes observerspace, that is, it describes phenomena as theyappear to happen. The addition of the extra frames does make the object seem to


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be receding at a slower speed, if speed is judged from the SR shift formula, sounder SR, that speed reduction is deemed to be genuine. Now, if we suppose thatthe spaceship in our last example accelerates smoothly up to 1.2c without takinga mid-flight break, then what would the back-home observer see? Let's try analternative interpretation of the observed phenomena:

- They see the ship to be progressively time-dilated as it approached recessionlightspeed, and as the ship is seen to approach the point in space at which c-recession would actually be achieved (the "c-point"), the ship's clock appears

to be ticking so slowly that it effectively seems to stop. In our hypotheticalsituation, the ship would actually whizz pass this space-coordinate at midnight,ship-time, an indicator light would come on in the ship's cabin, and the crewwould have a bloody good party to celebrate. Back home, though, the ship wouldnever be seen to pass the c-point coordinate, and would eventually seem to behanging in space, ridiculously redshifted, always gaining on the coordinate butnever quite reaching it, the hands on the clock never quite reaching the twelveo'clock position. The party would never be seen to happen, and the homeastronomers might sorrowfully conclude that the unfortunate travelers fate wasto be frozen there until the end of time.

Nothing that happened to the ship after it crossed the-point would ever be seento happen, back home.

"See?", one of the astronomers might shout angrily at the others, "I told youthat FTL travel was impossible!"________________________________________________________________________________

Conclusions:

Because SR is an observerspace theory, what it actually says is that lightspeedrecession can never be observed to happen, i.e., that this phenomenon can neverhappen within observerspace. Our example described the ship happily acceleratingbeyond c, but everything that happened after the ship reached c-recession wasshielded from the home observer by an event horizon, so the home astronomers sawexactly the same things that they expected under SR, even though something elsewas "really" happening. The fact that SR forbids FTL recession isn'tautomatically evidence that such behavior can't happen. The observed classes ofeffects are the same, either way.

This talk of event horizons may have raised some eyebrows. Aren't event horizonsstrictly a "black hole" thing, i.e. a gravitational effect?

Yes and no. Read on ...________________________________________________________________________________

Notes: the SR lightspeed barrier fails for situations involving accelerations.

The observed-clock-stopping of the ship assumes, of course, that the ship isn'tbeing observed through any intermediate frames. If the ship's crew threw aseries of champagne-glasses out of the window as it accelerated, then if youlooked at the ship through this expanding trail of garbage (or through theship's exhaust plume), then the same SR velocity-addition law that made ussuspect that this hypothetical FTL behavior was possible in the first placewould also conspire to make the ship visible beyond the c-point, and to redefinethis "visible" velocity to less than c. Which would mean that the ship'sbehavior wasn't illegal after all (!).

It turns out that the ship's recession velocity is only illegal if you can't seeit, and if you can't see it, then it isn't dealt with by SR. It seems thatwhenever you try to break the SR law, SR either ignores your existence or

forgives you completely.


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(3): Using gravitational gradients to break lightspeed(in which a ship's crew decides to jump into a black hole, just for fun)

________________________________________________________________________________

Using existing gravitational gradients.

In the last section, we described the observed effects of a hypothetical objectsmoothly accelerating up to a speed greater than c, and appearing (to the home

observers) never to actually reach lightspeed. Although we showed that this sortof acceleration could be consistent with the observed effects predicted by SR,we didn't make any attempt to explain how the acceleration was achieved. Itcertainly couldn't be achieved by the use of a solar sail and a home-basedlaser, because this acceleration would still suffer a decrease in efficiency atrelativistically - significant velocities.

So - is there any known force that might be capable of generating this sort ofacceleration?

Yup. It's called gravity.

Let's repeat the last hypothetical experiment, but this time, the ship isn'tpowered by some "magical" engine, but is simply falling directly away from theobservers, into a black hole.

As the ship drifts towards the hole, it picks up speed, slowly at first, andthen as it comes more under the influence of the hole's gravitational field,more and more quickly. The ship undergoes a smooth acceleration away from theobserver, as before, and once again, the home observers see the ship to beprogressively more time-dilated as it accelerates (and falls into the hole'sgravitational well).

Again, the ship's journey has been calculated so that the recession velocityought to hit lightspeed at exactly midnight (ship's time), and the relevantspace-coordinate where this is expected to happen has been marked out on themap. This c-point is the point at which the escape velocity of the gravitationalfield equals that of light - in other words, it lies at a distance from thecentre of the hole corresponding to the hole's Schwarzchild radius - the c-pointis at the hole's event horizon.

Again, the (not terribly bright) crew celebrate the chiming of midnight on theship's chronometer with the popping of champagne corks, and a radio messagebroadcast back home, "We did it!".

Again, the home-based astronomers monitor the ship approaching the c-point, andsee the ship's clock grinding to a halt as its hands approach the twelve o'clockposition. Again, they never see the wild party, they never get the jubilant

message, and they never see the craft ever reaching the coordinates that signalits achievement of recessional lightspeed. The craft appears frozen in time andspace, hovering impossibly at the event horizon, with its signal (correspondingto the last few seconds before midnight), stretched out to infinity.

In both the "gravitational" and "powered acceleration" cases, the ship is neverseen to reach lightspeed. However, in the "gravitational" case, this observedeffect (of the ship hanging forever at the edge of the black hole event horizon)is considered to be an artificial illusion. Nobody (says the current prevailingwisdom) would actually be dumb enough to believe that the craft is really stuckat the event horizon, would they? Surely anyone with a brain would realize thatthere's no reason for the craft not to continue its fall, and that the stoppedclock is simply an observer-related effect caused by the properties of signals

leaving the craft?

Perhaps. However, the treatment of the observed clock-stopping as "real" in away that goes beyond the observerspace definition of the word, is exactly howmost SR people treat the first example.


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________________________________________________________________________________

Conclusions:

The first "fantasy" example of a ship accelerating up to and beyond lightspeedhas a near equivalent in the behavior of an object free falling into a blackhole. In both cases, an event horizon prevents the observer from seeing anyhypothetical FTL behavior that would be expected to occur beyond the c-point.

In the case of a black hole, the unseen FTL behavior is considered to be agenuine effect, and the lightspeed barrier is considered to be an illusory by-product of the event horizon (the mathematical surface around a black hole atwhich infalling matter is expected to achieve lightspeed relative to a distantoutside universe).

In the case of "powered acceleration", the same behavior is interpreteddifferently, the clock-stopping is considered to be "real", and the accelerationto superluminal velocities is therefore deemed "really" not to happen. However,there seems to be no real reason why the same "black hole" logic can't also beapplied to the SR lightspeed barrier.

But surely we know that the lightspeed barrier is genuine where gravity is not afactor? Don't particle accelerator experiments show this?

This is dealt with in the next section ...________________________________________________________________________________

Notes: The SR lightspeed barrier doesn't apply when gravitation (warpage ofspace) is a factor.

1. The black hole example is an obvious case of objects having FTL velocities inmodern cosmology. Another is the case of Hubble recession, where the"natural" recession speed of objects increases with distance, and has noupper limit other than the extent of the universe (this is the reason why thetwo galaxies in the "galaxy-hopping" example were allowed to have FTLrecession velocities in the first place). Both examples involve thedistortion of space, either through explicit gravitation (black hole) orlarge-scale curvature (Hubble recession&shift), so the SR "flat-space" modelis incapable of dealing with them, just as it wasn't able to properly copewith the acceleration example (acceleration warps space, too). According tothe (non-standard) DMS model, even constant-velocity motion warps space, withthe Lorentz correction under SR producing an approximation of the effect. Andsince SR predicts the kinetic energy of an object becoming significant atrelativistic speeds, then according to GR, this energy has a gravitationaleffect. If the effect is the Lorentz effect, then the SR flatspace model iswrong, and there's velocity-dependent curvature (gravitational effects). Ifit isn't the Lorentz effect, then the SR shift formula just isn't accurate at

speeds approaching c. It's a good rule of thumb that whenever you come acrossan example where you'd expect FTL behavior to occur, SR has a good excuse tostop working.

2. Under gravitational freefall, the ship can achieve FTL with respect to anexternal observer, but it doesn't overtake its own lightsignal.


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(4): Particle accelerator behavior

(if something runs away faster than a speeding bullet,you can't shoot it)

________________________________________________________________________________

Particle accelerators

The SR argument for mass-dilation in particle accelerators seems to go something

like this:

1. In the frame of the particle accelerator, the accelerating signal travels atc, so it can't catch up with a particle that is already receding atlightspeed. If the particle's resistance to the force of the beam is taken asa measure of its inertial mass, then the fact that the particle is unaffectedby the beam would tend to lead to the conclusion that the particle hasinfinite mass.

2. In the frame of the particle, the beam is also supposed to travel at c, so itdoes catch up with the particle (under SR, the beam is always supposed totravel with fixed speed relative to any given observer). This apparently-paradoxical result actually generates the same final result, because theparticle (under SR) will see the accelerator coils to be receding atlightspeed, and therefore to be "clock stopped" (through inertial massdilation), so the particle again has zero interaction with the beam, but thistime the zero energy of interaction is reasoned to be caused by the "zero"frequency of the current in the coil, rather than because of propagationfactors.

So, under SR, the deduced behavior of the beam is different for differentobservers, but the final observed effects are consistent in each case. Thissleight-of-hand is both a weakness and a strength of SR - it provides a way ofallowing any observer to reason that lightspeed is everywhere constant withreference to their own frame, at the expense of postulating an additional shiftmechanism that is supposed to be separate from propagation factors as a matterof principle, but whose separate existence is (by the same principle) alwaysgoing to be experimentally unverifiable if the theory is correct.

As the accelerator result can be arrived at by either a Lorentz shift or by apurely propagation effect, or indeed by a range of intermediate solutions, or bya propagation effect that includes the Lorentz shift as a gravitationaldistortion effect, this behavior can't be taken as ironclad evidence that SR'spredictions in other related areas are necessarily going to be correct whentaken out of their (flat-space, observerspace) context. The DMS model discussedelsewhere on this site (for instance) also generates a similar effect inparticle accelerators, but doesn't preclude FTL travel in the wider sense of theword. A similar situation occurs with a range of gravitational theories.

In other words, SR supports one unverifiable assumption (global lightspeedconstancy for all observers) by introducing a second (separation of motionshifts into propagation and Lorentz components), and then hedges thoseassumptions with a range of other techniques (like clock synchronizationmethods) whose purpose is to make sure that certain other interlinked propertiesof the theory are also unverifiable.________________________________________________________________________________

Conclusions

Particle accelerators do provide a special case situation where the "infiniteinertial mass at recessional lightspeed" argument appears to hold. However, this

effect can be calculated from straightforward propagation arguments, i.e. youwouldn't necessarily expect an EM pulse to be able to transfer energy to aparticle that it wasn't supposed to be able to catch up with, so the observedmass of the particle when receding at lightspeed would normally be expected toappear to be infinite in this class of test, in a wide range of models, simply


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because of propagation issues. In the case of force applied by the observer,you'd expect observerspace arguments to hold.

In other cases, the effect is less clear-cut. You can't just extrapolate theparticle accelerator results to different classes of experiment, and assume thatyou'll get the same behavior.

Those particle accelerator tests don't tell us whether this upper limit alsoapplies to situations where it isn't the observer that is supplying the

accelerating force, e.g. particle anchored to distant object by long rubberband, particle fitted with own propulsion unit, particle attracted to distantgravitational body. In the last of these cases (gravitational acceleration), wedon't believe that the SR limit holds, and GR's equivalence principle betweengravitational and non-gravitational acceleration effects rather implies thatthis breakdown may bleed through to the other "acceleration" cases, too (theremay be other complicating factors).

We have little evidence that the c-limit is a practical upper bound in anythingother than purely observerspace situations (force applied from observer'sframe), and we still don't know whether the lightspeed upper limit applies tocraft with simple rocket motors._________________________________________________________________

Notes: The SR lightspeed barrier might not apply outside particle-accelerator-type situations.

In order to evaluate whether the inertial mass is increasing in a wider sense,resistance to applied acceleration isn't terribly useful. Resistance to appliedrelative deceleration (i.e. electromagnetic braking efficiency) might be a moremeaningful test. I haven't heard of anyone carrying out this sort of test, but Ihaven't (yet) looked terribly hard. Rumblings from particle accelerator peoplethat SR mass-dilation is an "old-fashioned" idea are interesting - it impliesthat there may be classes of particle accelerator tests that produce non-SRresults in this area. Could this data deal with blueshift/deceleration stuff,the region where SR and Doppler diverge? Will try to get someone to talk ...


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(5): Propulsion systems

Hypothetical "inertial drives" (aka "gravity drives"), which work by generatinga gravitational gradient in a particular direction, and allowing the craft to"free-fall" in that direction, are allegedly not subject to a lightspeed limitunder GR. Unfortunately, most of them depend on "exotic matter", which we haveno reason to believe exists. Inertial drives based on DST's may also bepossible, but are probably subject to the same high-speed efficiency drop thataffects particle accelerators. Conventional propulsion units don't seem to be

affected.a) "Exotic matter" inertial drives:

"Exotic matter" drives are dealt with rather well in "The Renaissance of GeneralRelativity" by Clifford M.Will (Published in "The New Physics", ed. PaulDavies). Exotic matter is a purely-hypothetical form of matter with negativegravity (there are reasons to suppose that it doesn't exist). What isinteresting about the subject (in this context) is that a hypothetical gravitydrive constructed from a combination of "exotic" and "normal" matter would(allegedly, under GR) not be affected by the lightspeed limit (M. Alcubierrepublished another variation on the ematter drive a couple of years ago). I'mreally not convinced about this "exotic matter" stuff, but there are otherpossible ways of constructing inertial drives, and if GR officially puts noupper limit on the speeds attainable by an ematter drive, there's a faint chancethat this might also apply to the other categories.

b) DST inertial drives:

DST's will be dealt with in a future document.

However, on a brief examination it seems that although DST's do seem to have alot of nice properties, I'd guess that an ability to avoid "particleaccelerator" syndrome isn't likely to be one of them. I doubt that ahypothetical DST engine would be capable of taking you past (or even up to)environmental lightspeed, although it might be useful for braking. I might wellbe wrong on this one, though.

c) Remote-powered drives

One of the smart ideas that has become popular recently is the idea of buildinga very small, very low-mass probe, fitting it with a lightweight "solar sail",and then accelerating it up to god-knows-what speed by beaming energy at thesail from a remote site. The BIG advantage of this method is that youeffectively leave your engine at home - a probe weighing a few pounds (plussail) would then be able to get the full benefit of a particle-beam/laser/whatever apparatus weighing possibly several hundred tons, withhaving to bring it along. Not only is (almost) all the utilizable power goinginto accelerating the payload (plus sail), but you get to keep the engine! Thus

a single "driver" could be situated at a handy site, close to its fuel supply,and reused over and over again on a succession of lightweight probes.

Unfortunately, this (or any other remote-powered drive system) would seem to belimited by the lightspeed barrier. ...unless you stacked achain of them, and powered the whole chain by a single "fixed" driver? Hmmm...

For the purpose of this exercise, Im not classing "nuclear bomb" drives (whereyou throw a nuclear device out of the back of the craft, and ride the shockwave,then repeat the exercise indefinitely) as "remote powered", but as"conventional" (technically, the initial blast is "remote", the rest aren't).

d) Conventional propulsion systems

This one is the big surprise.

It seems that your common-or-garden sacrificial-propellant rocket motor mightnot necessarily be governed by the SR lightspeed limit.


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Let's suppose that you take a lump of matter, divide it into two halves, and setoff a nuclear explosion (or something), causing the two halves to fly away fromeach other at 0.5c. Then you take one of the two pieces (travelling at 0.25c wrtthe immediate environment), and repeat the exercise, blowing it apart so thatthe two pieces (quarters) again recede at 0.5c to each other. One piece is nowstationary wrt the immediate environs, the other (according to Newtonianmechanics) is travelling at half lightspeed. Now keep repeating the exercisewith the "fast" piece. Under Newtonian laws, this (terribly inefficient) method

of propulsion would end up accelerating a tiny part of the total mass up to andbeyond lightspeed.

Interestingly, this Newtonian simplification doesn't seem to be quite illegal -the fact that we aren't trying to achieve lightspeed in a single step means thatthe usual SR prohibition of FTL behavior doesn't hold - all those intermediatesteps mean that the final (deduced, superluminal) velocity is helpfullyreinterpreted by the SR velocity-addition law as being less than c, providedthat the separation velocity of each division is also less than c (which it is).A signal could still be passed along the expanding chain of "propellant" pieces,from end to end, even if the two ends had a Newtonian recession velocity greaterthan c, so in that sense, the speed of light hasn't been exceeded, and thesituation appears SR-legal.

SR prohibits the separation-velocity caused by any single explosion beinggreater than lightspeed and it appears to predict a loss in propulsiveefficiency per explosion, compared to the Newtonian model. It also prohibits thehome-based observer from being able to directly observe the lightspeed barrierbeing broken - to them, each explosion would have a progressively smallerresult, until, close to lightspeed, the observed effect of each explosion wouldbe minimal, and the interval between explosion would eventually become so long,that the explosion that would be expected to take the payload past lightspeedwould never be seen to happen. But we've already shown that this sort ofobserved behavior doesn't necessarily mean that the payload wouldn't be happilyaccelerating past recession lightspeed, unobserved - it could be reinterpretedas the effect of a non-SR light-propagation model on an accelerating object (seeblack hole example). We just don't know. A second observer, in front of theaccelerating payload might see a rather different result. *note

Unlike inertial drives, the characteristics of two pieces immediately prior toan explosion, measured within their initial frame, are supposedly independent ofthe motion of the background (frame-invariance), and the acceleration forces oneach half, and the final speeds ought therefore to be symmetrical about theinitial center of the piece. According to current theory, both the payload andthe propellant pieces would be similarly mass-dilated before an explosion, whichleads us to expect that both pieces would fly off at identical speeds relativeto the "rest frame" that they had just before to the explosion. There are someproblems with this, because the two pieces would be expected to have different

amounts of mass-dilation after the explosion, depending on their relativevelocities to the environment, but accepting this seems to lead to a breaking ofthe principle of the equivalence of inertial frames, so the effect _might_ beanother observer-specific thang.

Under Einstein's definitions, the SR model fails when applied to smoothacceleration (except as a rule-of-thumb approximation where the amount ofacceleration is minimal), and when the acceleration is taken in a series ofquantified steps (e.g. explosions), the SR velocity-addition formula cuts in tomake sure that any Newtonian superluminal velocity that _might_ be presumed tooccur is quickly redefined away as being subluminal, as a matter of principle.Either way, Newtonian FTL does not seem to be prohibited, except as the resultof a _single_ explosion, whose separation speed would then be limited by the

speed of radiation in that frame (c).________________________________________________________________________________


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Notes: While an SR-type lightspeed barrier might affect some types ofpropulsion, others might be immune.

For an explanation of indirect viewing and the significance of the SR velocity-addition formula's reduction of summed velocities that would normally equal >cto less than that of light, see the section on probe chains.


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(6): Time-dilation issues

(in which special relativity manages to predict exactly the same sort ofobserved t-d effects as Newtonian FTL, but with a different interpretation)

________________________________________________________________________________

Time-dilation

Let's try describing the event horizon argument of section 2 in another way.

A manned spaceship equipped with a rocket pack theoretically capable of takingit up to superluminal speeds according to Newtonian mechanics is launched, andthe stay-at-home observer sees the object ageing more and more slowly, andfinally grinding almost to a halt at the c-point. How do we tell if the clockslowing is just an illusion?

Lets consider the situation from the pilot's viewpoint.

The "naive" Newtonian prediction: The ship leaves earth and fires up itsengines, expending so much energy that it reaches a superluminal speed. It thencrosses a distance of one lightyear in less than a year. This is verified by theship's log, and observations made en-route.

The "modern" SR prediction: The ship leaves earth and fires up its engines,expending enough energy to bring it up to superluminal speeds in a Newtonianmodel. However, we "know" that mass-dilation becomes significant at high speeds,so we can deduce that the speed never actually reaches c, and the journeytherefore takes more than a year. However, the mass-dilation effect also slowsthe ship's chronometers (and all biological processes) by the same amount, withthe result that the journey appears to take less than a year, ship-time.However, the uncomfortable fact is that while SR is supposed to make FTL travelimpossible, the pilot onboard the ship simply doesn't see the c-limit operating,and the ship's crew think that they've traveled to their destination at an FTLvelocity, as planned.

In the second example, how do we persuade the crew that they are wrong?

This is where SR pulls another trick. Because the shipboard observers see theirjourney to take so little time that it must have taken place at FTL speeds, andbecause their own time-dilation can't be considered to be real in their frame,SR alters the only remaining parameter. It alters the length of the journey."There!", says the onboard theoretician to a skeptical crew, "The journey didn'ttake less than a year due to our travelling at FTL speeds, or to time-dilation -it took less than a year because the entire outside universe contracted alongour direction of motion. So when we passed all those marker beacons at 1000kmintervals, they weren't really 1000km apart - they were closer together. Andwhen we saw the entire outside universe -- stars, planets, etc -- whizzing pastat more than 300,000 km/s, those weren't _real_ km, because they were moving!

It's just that the entire outside universe sneakily conspired to make it look asif we were travelling at more than c - we weren't really. It was all anillusion!"

At this point, the theorist would probably be thrown out of the airlock withouta suit.

As the theoretician is bundled into the airlock, he makes one last plea forunderstanding.

"I can prove it!" If we turn the ship around and head back for home, the factthat we've been moving relative to our environment will mean that ourchronometers will show less time to have elapsed than the ones back on earth.

The captain thinks. "But shouldn't _we_ see _their_ chronometers to be slow?"

"No - because they weren't really moving - we were!" *


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"Look, ok, I know that that contradicts SR, but the difference is because ofenvironmental factors - we are interacting differently with our environment"

"You mean, gravitationally? Because I thought gravitation or privileged framesinvalidated SR..."

"No - wait! It's possible to set up a symmetrical experiment with two ships, sothat the environmental factors cancel out!"

"And then, does one clock end up slower than the other?"

"Actually no, there's an extra 'relative acceleration' blueshift that cancelsout the timelag when the two ships turn round. In a symmetrical test, both setsof clocks agree at the end of the experiment." **

"And I suppose that extra blueshift isn't compatible with the SR model, but it'sdeduced to happen every time we accelerate towards something? And there's no waywe can head home to check out your claim without accelerating towards it andinvalidating SR anyway? So we just have to take your word that this SR effectexists, because you say there's no real way to verify it without violating theSR rules? And the human race abandoned the idea of FTL travel for a century,because people _believed_ this stuff?"

"Er..."

________________________________________________________________________________

Notes

a) Not a particularly credible argument under SR, which denies the existence ofabsolute motion. Still, it crops up in at least one textbook on SR.

Apparently, this "extra SR" acceleration blueshift formula is given in MTW's"Gravitation", even though it's incompatible with the basic SR model. I haven'tbeen able to check this, though, because nobody in the UK has the book in stock- it's currently between reprintings (23-03-96).


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(7) Spectral shifts

(redshifts aren't a problem,blueshifts require a bit more head-scratching)

________________________________________________________________________________

Redshifts

As we've seen clock-stopping at recessional lightspeed is a feature of a rangeof propagation models, some of which seem to allow FTL behavior. It's not unique

to flat-space SR (see event horizons). Irrespective of how much redshift you seein a receding object, SR will always deem the velocity to be less than c.________________________________________________________________________________

Blueshifts

It is natural to assume that an object approaching at lightspeed rides its ownwavefront, and therefore appears to have an infinitely short wavelength. This isa feature of the SR propagation model, and seems at first sight to be anunavoidable consequence of the theory. A further increase in speed wouldtherefore be expected to result in the object overtaking its own light, with thecorresponding "tachyonic" difficulties.

However, let's now go back to that last "spaceship" example, where a shipmanaged to cross a one light-year distance in less than a year of ship's time,without violating SR (although it appeared to the "ignorant" ship's crew thatthey'd broken the lightspeed barrier). That example was justified (under SR) bya contraction of the spaceship's path, and a redefinition of the ship's speed toless than c. Wouldn't this "Newtonian" FTL lead to the object overtaking its ownwavefront, and wouldn't the fact that the ship is approaching its destination atgreater than Newtonian c, ship-time, lead to the light that's coming from thedestination and hitting the front of the ship being blueshifted to infinity?

Weirdly enough, it doesn't. Although the ship crosses the set distance in lessthan a year, ship-time, the blueshift of the oncoming radiation isn't infinite,because it is now predicted from the deduced SR distance traversed per unittime, which is, of course less than c due to the notional path-contraction. If"speed" is defined using the ship's time and the environment's rulers, then theobject's destination can approach at any speed whatsoever, and (under SR) theblueshift will always be finite. The "SR speed" of the object is alwayshelpfully redefined as being less than lightspeed.

How about the way that the destination sees the approaching ship?

If the above effect is symmetrical (which it should be under SR), then theblueshift seen on the approaching ship again doesn't reach infinity until theship is again travelling at an "infinite speed", with distance instead measuredby the ship's rulers, and time measured in the background frame.

The notion that "moving rulers contract along their direction of motion" wouldhave you believe that the approaching ship's rulers are shorter when it's speedis greater, and that this new notional "infinite speed" therefore occurs whenthe ship is travelling at Newtonian lightspeed, and that Newtonian lightspeed istherefore the limit at which an approaching ship has an infinite blueshift.Unfortunately for this idea, SR rulers don't just contract along their lengthwhen they move, they also contract or lengthen according to whether they areapproaching or receding from an observer, by an amount inversely proportional tothe Doppler shift on the object (NB: not a lot of people know this).

note 1:

The fact that the usual SR descriptions deal only with the special-casetransverse behavior of rulers ought now to be making your stomach curl up into alittle knot, because the Doppler effect is stronger than the Lorentz one, andalthough the Lorentz formula predicts that an approaching end-on ruler iscontracted to zero length, this infinite contraction is calculated after the


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Doppler length-effect. And guess what? The SR "Doppler length" of a rulerapproaching at lightspeed (before you apply the Lorentz contraction), isinfinite.

note 2:

After applying the Lorentz contraction to this infinite length, it's merelyalmost infinite , so again, because the infinite blueshift doesn't happenuntil the ship speed is infinite using the ship's approaching rulers to measure

distance, the SR "lightspeed" is (yet again) equivalent to infinite speedmeasured with Newtonian distances. This is as it should be, because if NewtonianFTL approach velocities are legal for one observer, they should be legal forboth.

Just as in the earlier "redshift" examples, any degree of observed blueshift isalways interpreted by the special theory as evidence of motion at less thanlightspeed.________________________________________________________________________________

Conclusions

One reason why SR is so successful in asserting that objects never travel fasterthan light is that no matter what amount of shift an approaching or recedingobject has, whether the observed frequency of radiation is shifted to ~zero or~infinity, in fact, no matter what data you collect, SR usually has a way ofinterpreting that data as proof that a velocity is subluminal. There simplyisn't any shift value that SR wouldn't map to a velocity less than lightspeed.That makes the idea of a lightspeed limit slightly difficult to disprove

Under SR, there is no lower limit to the amount of time needed to cross agiven Newtonian distance. Any object seen to cross a particular region ofspace in a finite time is automatically assigned a speed less than c, nomatter how short the time-value.

Under SR, there is no amount of observed shift in an object that isn't mappedto a velocity less than c.

Under SR, there is no amount of kinetic energy for an object that isn'tmapped to a velocity less than c.

Under SR, objects can recede with any velocity without generating evidencethat they are receding at >c, because a recession redshift can't make theobserved frequency drop below zero.

Under SR, objects can approach with any Newtonian velocity, and their shiftis still finite, and their velocity is mapped to less than c.

So although SR places a notional upper limit of c on an object's journey throughits environment, in terms of contracted distances, when you re-express this interms of conventional distances, the upper limit comes out not as c, but asinfinity.

Confused yet?

The problem is that SR has been so busy reinterpreting speeds, lengths,distances, times and masses, that there's nothing left for us to look at to seewhether the SR "velocity" parameter actually corresponds to anything in reallife.

Ironically for a theory that's founded on the principle of pure observation,"relative velocity", the one parameter that's agreed on for all observers underSR, ceases to have any physically-observable meaning, because the hypotheticalruler-contraction effect means that you can no longer use "known distance /measured time" as an agreed definition, even when you cancel out any expected

timelag effects. In order to find that original velocity, you are supposed totake the SR redefinitions on trust.

Just think - for decades, people have been reciting that "you can't go fasterthan lightspeed" argument, thinking that it actually means something deep and


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meaningful, when it actually translates (in agreed-distance terms), to: "Youcan't travel faster than infinity".

Kick back your chair, put you feet up, look out of the window and savor thetruth of that second statement for a few minutes. It's a beautiful, world, isn'tit?________________________________________________________________________________

Notes

a) You may find it difficult to find a mention of the Doppler ruler-effectoutside these pages. It does show up in the occasional mainstream paper.There's a brief mention of it in "Invisibility of the Lorentz contraction"(can't remember the author or date right now). There's another run-through onthe relevant DMS page, but using a different Doppler formula and propagationmodel.

b) b) The Doppler ruler-effect is a sadly neglected topic, not because it'sdifficult, or unconventional, but simply because most SR discussions arenormally limited to the effects of purely transverse motion, where (under theSR model), the Doppler length-changes don't apply. As a result, mostphysicists seem not to know anything about it.

Here's how it works - suppose that a train of length l is receding from you, andyou see the rear of the train to be at position x. The equivalent position ofthe front of the train is going to be x+l, but the light from it won't havereached you yet. Because the light from the front of the train has an additionaltime-lag, its viewed position is always slightly more out-of-date than that ofthe back of the train, and because the train is moving away from you, this extraout-of-dateness (differential timelag) makes the front of the train appear to becloser than x+1, and the train appears contracted as a result. If the train isapproaching, then the rear of the train would be showing an older position thanthe front, and would appear to be further back along the track than you wouldtherwise expect. As a result, the approaching train appears lengthened.

For an extreme example, consider a 1m long ruler approaching the observer, end-on, from a marker point 1 light-year distant, according to special relativity(which uses the Doppler version of the formula). If the ruler is travelling at(illegal) lightspeed, then SR models the ruler as riding its own wavefront. Inthis case, a point at the front of the ruler appears to the observer to passfrom a distant marker-beacon to the observer's position in zero time, because itwill arrive at the same moment that it is seen to leave (the events of itpassing the startpoint and reaching the finish-point appear to be simultaneous)

However, because the ruler is travelling at finite speed, the front and rear ofthe ruler don't appear to pass the start-point at the same moment - the rearpasses slightly later. As a result, the observer sees the front of the rulerreaching them before the end of the ruler is seen to pass the start-point, and

the ruler therefore appears to cover the entire one-lightyear distance. For aruler approaching at lightspeed, end-on, it's observed length (before you invokeLorentz contraction) is effectively infinite.

Easy stuff, but not often taught.


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(8): "Probe Chain" theory

(the SR flat-space model can fail in an inertial systemcomprising of more than two objects)

(and not a lot of people know that, either)________________________________________________________________________________

Probe chain: Physical interpretation of the SR velocity-addition formula

If an object accelerated to an "illegal" recession velocity, you wouldn't

normally be able to see the c-breaking event happen if you observed the objectdirectly, and yet under SR, the ship's acceleration through a series ofintermediate frames means that the ship's recession speed is supposed to besubluminal, and the ship therefore _ought_ to be visible at it's higher(Newtonian) velocity.

Can any events that occur beyond the c-point be observed by a home-basedobserver or not? How can the ship have two velocities? What is really going on?

The answer comes when we decide how the ship is to be observed. If we choose toview it directly through the vacuum of space, then (under SR), the notionally-FTL portion of the ship's journey ought to be hidden by an event horizon. But ifwe choose to view the ship through the haze of its own exhaust fumes, then wesee something different. The ship now really does appear to be travelling atless than c, in the sense that the event horizon isn't there any more. Light(under simple SR) somehow finds it easier to travel along the expanding exhausttrail than it does across empty space.

Now the signal isn't attempting to leave the ship and cross over to an observerleaving at lightspeed - it's instead travelling through the expanding gas, whichproduces a near-continuum of intermediate inertial frames between the recedingship and observer.

If the exhaust plume is dense enough for any ray of light to be able to crossthe distance by "leapfrogging" between particles that are always receding fromeach other at less than lightspeed, then the shift incurred by each individualframe transition will always be too weak to bring the frequency quite to zero.Therefore, if the ship is viewed through a series of intermediate frames wherethe individual frame transitions are all less than c, then the signal willalways be able to get through, and the result is what you would have expected ifthe recession shift had been less than c.

That's the effect that the SR velocity addition formula documents - theexistence of intermediate inertial frames removes the original quantifiedvelocity "step" assumed by SR, and replaces it with two or more steps that don'tlie on a straight line. By adding the intermediate frames, we are taking avelocity differential and replacing it with a series of consecutive velocitydifferentials that mark out an approximation of an acceleration curve. A signal

sent through these intermediate frames therefore passes through an approximationof an acceleration curve, which, of course, represents a warping of theproperties of space under GR.

relative velocity along the path of a light-beam

[missing diagram]

So we can have a completely inertial system, with a number of relay probestravelling at fixed (intermediate) speeds to one another, and the compositesignal path isn't flat, but travels along the approximation of a curve,generated by all of the individual nominally-flat frame transitions. Most peopledon't realize that the SR flat-space postulate can fail in inertial systems

comprising of more than two objects, but there it is - add enough straight linestogether, and you've got an approximation of a curve.________________________________________________________________________________


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Probe chains: simple velocity differentials

Let's suppose that the spaceship in the section 2 example accelerates up to andbeyond "Newtonian c", so that it would be expected to be hidden by an eventhorizon. How would the crew ever get a message back home to say that they'dbroken the Newtonian lightspeed barrier?

The solution should now be fairly obvious.

The captain of the ship ensures that when the ship sets out, it is stocked-upwith a supply of numbered communication satellites, each programmed to receiveinformation received from one of its immediate neighbors, and pass it along tothe other, so that the string of satellites forms a chain along which data canbe sent, in either direction.

As the ship accelerates, the crew carefully drops the sequence of satellites outof the back of the craft, one by one (being careful not to damage them with theship's engines), so that the satellites chain marks out a sequence of inertialframes that each have a recession velocity to one another. The key feature ofthis chain is that although a signal sent along the chain is going to beredshifted, the redshift never reaches infinity, and a signal can therefore bepassed along the chain in either direction, even when the two ends of the chainhave a Newtonian recession velocity greater than lightspeed. The ship andhomebase can therefore still stay in contact, although they would still hear thesignals coming from each other to be extremely s.. l.. o.. w.. As the individualprobes are separating in space at constant velocity, and feel no accelerationforces, a signal effectively has the same properties as it passes along thechain as if it was passing along a gravitational gradient, causing the probeseparation. The remaining recession redshift would therefore appear similar to agravitational redshift.

Actually, since the shift is "red", the effect is more like a Hubble shift.Anyhow, probe chains seem to give a legal way of sending signals between objectswith FTL separation velocities, and therefore also seem to provide a way ofsending nominally-FTL signals across any region of space. You just piggyback thelight signal through a messenger-object that's going in the right direction, andit gets there faster. I actually thought that the final probe-chain principlewould turn out to be a lot more complicated than that, but there you go.


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SR Problems: the "Magic Window" problem

(velocity-addition formula, non-flatness of space)________________________________________________________________________________

The "Magic Window"

Intro:

SR's claim to validity is based on the assumption that space is uniformly flat

and that signal propagation times are wholly unaffected by relative motion. Inorder to generate the right results from this propagation model, SR uses anadditional Lorentz redshift to pull the "propagation" shift figures into line.Under SR, the Lorentz shift is deduced to occur at the affected object, and isnot supposed to be a signal-propagation effect.

The "window" problem below shows that an object with a fixed recession velocitycan have its SR redshift reduced simply by being observed through an interveningsheet of glass with an intermediate velocity. SR's workaround to this situationis to say that the object's deduced recession velocity is partly dependent onthe motion of the intervening glass, according to a special "velocity additionformula" that is used for calculating composite shifts. The new (hypothetical)velocity value is then supposed to be used with the normal SR shift formula.

This workaround (in its current form) is not compatible with the SR propagationmodel.

Example:

A directly observed object recedes from the observer at 0.8c. It's observedshift is therefore, under SR,

f'/f = root( (1- 0.8) / (1+ 0.8) )

= root( 0.2/1.8 )

= root(0.11111')

= 0.33333'

Now, this time we are going to look at the object again, but through a thin paneof glass, our "magic window". This "window" is between the observer and theobject, and creates an intermediate frame between the other them. The observerand the object are effectively both receding from the window at 0.4c.

We can now combine the two shifts that a light signal picks up travelling fromthe object to the window, and then from the window to the observer. Each ofthese redshifts is given by the formula:

f'/f = root( (1- 0.4) / (1+ 0.4) )

= root( 0.6/1.4 )

= root(0.42857...)

= 0.65465...

Once the signal has picked up two of these shifts and reached the finalobserver, the total shift on the observed signal is:

f'/f = 0.65465... * 0.65465...

= 0.42857...

In other words, there is less of a redshift when the signal travels via a thirdintermediate frame, than when there is a direct path.


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Possible SR interpretations:1. The speed and energy of of the signal is somehow "stepped up" by its passage

through the intermediate physical frame provided by the "moving" pane ofglass. This sounds promising, but such a mechanism is illegal under SR, whichassumes that propagation times are unaffected by relative motion.

2. The amount of Lorentz shift on the observed object is being changed by thealtered topology of the experiment. This is difficult to reconcile with the

idea of the Lorentz shifts being purely a product of relative velocity, asthe path taken by the signal would also be a factor. The observer can still"peek" around the edge of the glass pane and see the original amount of shiftin the object, and if a lightbeam is split, with one half sent through thewindow and one sent directly, both signals would have different Lorentzshifts. This difference would mean that Lorentz shifts are partly path-dependent, so that Lorentz shift couldn't be totally separated frompropagation effects.

3. Motion in the glass reducing both the Lorentz shift and the propagation shifton the object.

By choosing to deliberately reinterpret the deduced recession velocity of theobject to a different value when it is indirectly observed, special relativityplumps for option (3).

This workaround reduces both the predicted propagation shift and Lorentz shiftof the receding object in the above example. For the "propagation" shift of anobject viewed along a straight-line signal path to be reduced when the glass ismoving, the motion of the glass must (by definition) be affecting the propertiesof that signal path, contra SR.

The SR velocity-addition formula is therefore not compatible with the SRpropagation model, even though it is used to calculate composite shifts underthe theory. For SR to be self-consistent, the velocity-addition formula wouldhave to be replaced with a different formula that preserved the SR propagationshift component, and instead affected only the Lorentz component of anindirectly observed object.

This mistake isn't necessarily fatal to SR, as an alternative correction formulabased around "option 2" is probably possible. However, since the inconsistencyis fairly obvious, you'd expect an amended correction to already be in place.

The fact that it isn't raises questions as to how accurately SR has beenassessed to date.________________________________________________________________________________

Notes:

1. DMS produces the same class of effect. However, DMS uses interpretation [1],and so, doesn't have a problem with the result. Under DMS, the step-up inenergy of the light-signal is caused by the "moving" window "dragging" thesignal along in its direction of motion, as an inertial/gravitationaldistortion effect. A similar mechanism probably exists under GR

2. The SR velocity-addition law for composite shifts is vtotal = (v1+v2) / (1+(v1*v2)/c^2). This formula is supposed to provide the user with an"equivalent" velocity of an indirectly-observed object.

3. Under the SR velocity addition law, the sum of two recession velocities of0.4c is not 0.8c, but 0.689655...c. This new pseudo-velocity can then be"plugged into" the standard SR shift formula to give exactly the same final(less redshifted) shift result that we calculated above from using the twosmaller velocities. That's its purpose. The existence of this formula

documents the existence of the "window" effect in SR. It's given on page 39of Einstein's 'Relativity' book.4. While two two arguments above produce the same numerical results when two

equal velocities are summed, they don't when the two velocities are unequaland neither velocity is c, so unless I'm mistaken, the standard SR addition


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formula has some terms missing. Most examples only use equally matchedvelocities, so the issue doesn't normally come up.

5. The arguments given on this page can be used as a foundation for "probechain" arguments. These lead to a reinterpretation of the nature of the SRlightspeed barrier.

faster then light

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