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Space Science

Near Light Speed Travel Possible After All? 539

Posted by Zonk
from the best-part-about-space-travel-is-you-can-leave dept.
DrStrabismus writes "PhysOrg has a story about research that may indicate that close to light speed travel is possible. From the article: 'New antigravity solution will enable space travel near speed of light by the end of this century, he predicts. On Tuesday, Feb. 14, noted physicist Dr. Franklin Felber will present his new exact solution of Einstein's 90-year-old gravitational field equation to the Space Technology and Applications International Forum (STAIF) in Albuquerque. The solution is the first that accounts for masses moving near the speed of light.'"
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Near Light Speed Travel Possible After All?

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  • by LiquidCoooled (634315) on Saturday February 11, 2006 @05:50PM (#14696047) Homepage Journal
    Theres no point in travelling at close to light speed if your have no way of stopping.

    Mind that planet!

    What planet?

    SPLAT
    • by Dogers (446369) on Saturday February 11, 2006 @05:52PM (#14696059)
      Weapons don't need to stop..
    • by eclectro (227083) on Saturday February 11, 2006 @06:15PM (#14696215)
      Theres no point in travelling at close to light speed if your have no way of stopping....SPLAT

      Well, considering that the nearest star systems are greater than 4.3 light years away [ucsd.edu], you do not have to worry about it, as you would be dead from starvation.

      It's the same reason that Nuclear subs are not limited by how much time they can stay underwater, but how much food they can carry. The need for food makes such long distances impractical, if not intolerable. "Growing" food along the way would mean a very limited diet for eight years (assuming you want to come home), something else that is intolerable.

      The first use of this could be unmanned probes - but a four year wait time for signals to travel means that it would be impossible controlling it, and would have to have it's own artificial inteligence.

      Of course, if you just wanted to visit the Mars and breath its clean fresh air and gaze upon its deep green pastures then this...oh wait...Mars doesn't have that.

      I think the best way to travel long distances is by using a stargate. Mondays on the sci-fi channel.
      • by franl (50139) on Saturday February 11, 2006 @06:32PM (#14696307)
        Well, considering that the nearest star systems are greater than 4.3 light years away, you do not have to worry about it, as you would be dead from starvation.
        If the vehicle travels close enough to the speed of light, the trip will take just months, weeks, or even days for those onboard. Near light-speed travel is a great way to conserve life-support resources for long trips.
        • Personally, I think you need to re-evaluate [wikipedia.org] that comment.

          Stargates are still the only way to go :D
          • by Arctic Fox (105204) on Saturday February 11, 2006 @06:47PM (#14696386) Homepage Journal
            I think you need to reevaluate that.

            For a traveller on the ship it would only seem like months. For the people left behind it would be years.

            Look here. http://members.tripod.com/wmhxbigguy/Theory/time.h tml [tripod.com]
          • by Plunky (929104) on Saturday February 11, 2006 @06:51PM (#14696407)
            Surely time dilation [wikipedia.org] effects would significantly lessen the amount of air and food that needs to be carried?
            • Surely time dilation effects would significantly lessen the amount of air and food that needs to be carried?

              Yes, that was exactly my point. There's another odd effect caused by near light-speed travel: If you fly straight at an observer at near light-speed, the observer sees you approaching faster than the speed of light. This is, of course, an illusion, but an illusion that affects all measuring devices (e.g., radar, eyes, telescopes, etc.). This happens because your ship is following very closely

              • by thesandtiger (819476) on Saturday February 11, 2006 @08:42PM (#14696984)
                No. No, no, no, no, no, no.

                If you were headed right at someone at the speed of light, you would just seem INCREDIBLY blue-shifted (more energetic). You would not, ever, at any time, seem to be moving faster than light.

                If a person is travelling at substantial portions of light speed they will experience time dilation. People moving at near the speed of light would experience, say, a 4.3 LY trip at high speed as, perhaps, several months, but an outside observer would, from whatever position they were standing, see the trip as taking at a minimum 4.3 years + whatever extra time was needed because the ship was slower than light.

                You seem to be confusing time dilation (an effect on those moving at high speed) with ... well, actually, nothing - you just seem to think it applies to all parties, which is not the case.
          • by SEE (7681) on Saturday February 11, 2006 @11:05PM (#14697679) Homepage
            Whatever you may personally think, he doesn't.

            To an observer, the minimum time for another object to move from a point to another a light-year away is one year, yes; that's what makes c invariant. However, for the object moving, experinced time goes down asympotically as the speed of light is approached. If you were moving at c, you would experience literally no passage of time on the trip to Alpha Centauri from Earth, even though it would take you 4.3 years to an observer on Earth.

            Another way to state it is that from the perspective of someone moving near the speed of light, the distance from Earth to Alpha Centauri shrinks; with the distance shorter, of course it takes less time to travel. However, the distance is still the same to the observer on Earth, and so the time for the trip as viewed by the observer is much longer.

            (By the way, this is part of the reason why nothing can go faster than the speed of light; the distance between two points can't shrink to less than zero.)

            This difference in space-or-time from different perspectives is why the theory is called relativity; space and time are not absolute constants for everyone evverywhere, but always exist relative to your reference frame.
      • Exactly. Looks like the Solar System could, barring a most unexpected surprise, finally be achievable. The stars? Not on the basis of this discovery.
      • Time Dilation doesn't actually help much here. You have to accelerate to high speed and deccelerate at the end of the journey. Human beans can handle high accelerations for brief times with few ill affects, but we're talking months here. I suppose if you remain strapped into a squishy chair without having to move around too much then two or three g's might be more reasonable, but I'm pretty sure noone's done the studies.

        Anyhoo, I typed "relativistic acceleration" into google, and two clicks later I was h [ucr.edu]
        • I've read somewhere that if you could maintain 1G of acceleration - speeding up for half the trip and then turning around and decelerating at 1G for the other half - you could basically reach anywhere in the universe within a normal human lifetime because of time dilation effects.
      • as you would be dead from starvation

        This problem is handily defeated by human hibernation technology.

        And I think we are closer [scienceblog.com] to realizing that technology than near-light-speed spacecraft.

    • by Anonymous Coward
      Actually the probability of hitting a star, much less a planet, is pretty low since space is pretty empty. However, what's much more troublesome are huge gas clouds or just the plain intergalactic medium since travelling near the speed of light means that those particles will hit your spaceship at relativistic speeds which is not very healthy to humans or electronics. Even worse, all light gets blue-shifted a LOT. Harmless visible light gets shifted into the x-ray spectrum and x-rays get shifted into really
  • Can (Score:4, Funny)

    by Anonymous Coward on Saturday February 11, 2006 @05:51PM (#14696054)
    Can't

    Can

    Can't

    Can

    Can't

    Wake me when someone actually accomplishes something. I'm sick and tired or the back and forth debate over ethereal concepts that can neither be proven or disproven in our lifetime.
  • WTF? (Score:5, Insightful)

    by at_18 (224304) on Saturday February 11, 2006 @05:53PM (#14696067) Journal
    What was making impossible near-lightspeed travel? Only FTL was prohibited. Problems like engines, fuel, shielding etc. are only technological problems.
    • Re:WTF? (Score:2, Insightful)

      by teslar (706653)

      What was making impossible near-lightspeed travel?

      The forces reducing a human travelling near the speed of light to a greasy patch on the back of the spacecraft. From TFA:

      Felber's antigravity discovery solves the two greatest engineering challenges to space travel near the speed of light: identifying an energy source capable of producing the acceleration; and limiting stresses on humans and equipment during rapid acceleration.

      • Again, that's simply an engineering problem... acellerating at 1 G will still get you there.
        • acellerating at 1 G will still get you there.
          Not exactly rapid acceleration though, is it?
          • Re:WTF? (Score:5, Interesting)

            by imsabbel (611519) on Saturday February 11, 2006 @06:38PM (#14696338)
            Well, we have no problem running around in 1G for our whole live...
            So weeks or months of acceleration wont hurt at all... in fact they would act as a convinient way of creating "artificial gravity" on the ship.

            And even 1G adds up after a few days, and in a matter of a few months you are _highly_ relativistic.

            • According to linear calculations of what it takes to get relativistic, it will take about 2 years under 1 G acceleration to reach the speed of light.

              However, this is actually an underestimate since relativistic effects make it harder to get that close to the speed of light, the closer you get. If you could achieve a constant 1G, that is how long it would take, but this is physically impossible since effective mass increases with velocity.

              I calculated it on Google calculator with the following formula (just
    • by jfengel (409917)
      Light-speed travel is impossible, but near-light-speed travel is wildly impractical, because of the mass you gain. This guy seems to be saying that if you have an anti-gravity machine, you could counteract that. You couldn't get to FTL, but you could go a lot faster than without it. Heck, there's all KINDS of nifty things you could do with an anti-gravity machine.

      And if my grandmother had wheels, she'd be a wagon.

      I think that this guy has been pushing his anti-gravity solution of general relativity for a
      • by barawn (25691) on Saturday February 11, 2006 @06:33PM (#14696314) Homepage
        This guy seems to be saying that if you have an anti-gravity machine, you could counteract that.

        Nonono: he's saying that a mass travelling near the speed of light creates an "antigravity beam" in front of it. This sounds hokey, but it's not unprecedented - frame dragging is a similar situation where general relativity basically says that a moving body can "push" others nearby. So in this case the near-light-speed object is "dragging" its frame forward. Calling it an "antigravity beam" sounds wacko, but it's probably quite straightforward. It's almost like the objects would be riding the "wake" of the NLS object, caused by the fact that the object is moving faster than space can respond.

        He's essentially saying that you can pretty much effortlessly accelerate something to really high velocities with little effort by hitching a ride on a bigger object.

        (Where to find a star moving at greater than .577c is another question.)
  • Where do I invest my Money?
  • Now, if health care will just advance enough to let me live that long, this will actually be useful info.

    2 cents,

    Queen B
  • Actual papers... (Score:5, Informative)

    by QuantumFTL (197300) * <`moc.liamg' `ta' `kciw.nitsuj'> on Saturday February 11, 2006 @05:56PM (#14696092)
    For more information, see Dr. Felber's recent works on arXiv.org:

    Weak 'Antigravity' Fields in General Relativity [arxiv.org]
    Exact Relativistic 'Antigravity' Propulsion [arxiv.org]

    Personally I'm a bit skeptical about his claims, however energy appears to be conserved. This method uses gravitationally-mediated kinetic energy exchange - this is the same principle that allows gravitational slingshot [wikipedia.org] to work.
    • by Dr_LHA (30754) on Saturday February 11, 2006 @07:19PM (#14696558) Homepage
      I think you have good reason to be skeptical, I'm not convinced this guy isn't a crank. Anybody can post a paper on a preprint server. Does he have any papers on this subject that have actually made it into a peer reviewed journal?

      Also this story is basically based on a press release from Starmark, the company that this so-called "noted scientist" founded himself, so basically he wrote the press release I'm guessing.

      Also the fact that he's giving a talk at a conference means nothing, I've been to plenty of conferences where they let a few cranks give talks. I sat through a talk on Creation and the Big Bang at a Astrophysics conference once and the guy was a loon.

      That said the biggest proof that this guy could be a crank is the fact that this story got posted on Slashdot, where something like 90% of the science stories are crap.
  • If I am reading this correctly (IIARTC), there is no way to safely stop with any foreseeable technology. If the anti-gravity wave reduces to near nothing, as you approach near nothing speed, than you have to be pretty damned sure that you aren't bumping into the satellite for Alpha Centauri news when you near it. With unchartered space, a collision is bound to happen when you slow down unless your sensors can detect something oh say the size of a buick from 1,000,000 miles ahead when you tap the brakes.
    • Re:Stopping (Score:5, Interesting)

      by Jozer99 (693146) on Saturday February 11, 2006 @06:55PM (#14696434)
      Buick?  You mean the size of a dust mote.  If a dust particle weighs 1/100 of a gram, and you are going roughly the speed of light, the kinetic energy of the dust particle relative to you (assuming that the dust particle is roughtly standing still) is

      .00001kg x (2.998 x 10^8 m/s)^2
      898800400000 Newtons
      9806 or so Newtons Per Ton
      1,000,000 tons per MegaTon
      20 Megatons per Hydrogen bomb

      Thats 4.6 Hydrogen Bombs of energy that the dust particle has relative to you.  Do you want to collide with 4.6 Hydrogen Bombs?  I don't think that NLST is practicle, even if it turns out to be possible.  What we need is a way to simultaniously transport stuff. 
      • Re:Stopping (Score:5, Interesting)

        by mark_osmd (812581) on Saturday February 11, 2006 @08:52PM (#14697030)
        You make the assumption that the dust mote would actually stop, only then would the bulk of the KE go into the target space ship. More likely is that since the KE of each atom in the dust mote is so much larger than the atomic bond energy holding the grain together, the dust mote to the spacecraft really behaves like a very densely packed bundle of cosmic rays. If the spacecraft walls don't stop individual particles of that energy (ie like cosmic ray protons) then it won't stop the dust particle. The atoms would go in one side, out the other radiating a small fraction of their relative energy as gamma rays as cherenkov radiation and compton radiation. The dust would go out the other side as a diverging cone shaped spray of plasma.
  • now (Score:2, Funny)

    by steelmaverick (936668)
    Wait, we can get close to light speed travel, but we cant figure out how to time travel?! This sucks.
    • Re:now (Score:2, Informative)

      by LnxAddct (679316)
      Umm.. everytime you move you are time traveling. When you run, time is moving slower for you, and so on. Take something the mass of Jupiter, cram it into a very thin spherical shell with an 8-foot diameter or so, sit inside it and come out a year later and you'll see time has advanced decades in comparison to your one year. We know how to time travel, but traveling far distances is hardly feasible (and traveling backwards still only works on paper).
      Regards,
      Steve
    • Re:now (Score:2, Funny)

      by zaphod_es (613312)
      What sucks even more is that until we can exceed the speed of light the police speed cameras are still going to catch us :)
  • by ceoyoyo (59147) on Saturday February 11, 2006 @05:57PM (#14696101)
    Um, except I need a star going more than 0.6c, passing close enough for me to whip in front of it... gee I hope this works....
  • Why is an exotic solution involving anti-gravity even necessary, when there's the Bussard ramjet [wikipedia.org]? While certain versions of this concept are infeasible, there's plenty of room for technical improvement. The ramjet has been a mainstay of science fiction for decades such as in Larry Niven's Known Space [amazon.com] universe, precisely because it seems the solution closest to actual development.
    • by imsabbel (611519) on Saturday February 11, 2006 @06:40PM (#14696344)
      Bussard ramjets are just cool and fine, and i liked the idea, too.
      But the physics dont work out.

      You get at most 2% or so of the mass converted into energy by the fusion process, even if you could fuse everything together perfectly efficient. But once your spaceship is moving quite fast (more than 10% or so of the speed of light), you will need to use more energy to move and collect the particles in your flightpath than you could possibly get by fusing them together.

      It just doesnt work out if you look at the big picture.
    • Larry Niven's Known Space has FTL all over the place. No ramjet can do that.
  • by mpn14tech (716482) on Saturday February 11, 2006 @06:00PM (#14696134)
    One thing I have often wondered is if an object moves fast enough, could its relativistic mass become so large that it would look like a black hole relative to a laboratory frame?
  • by Expert Determination (950523) on Saturday February 11, 2006 @06:05PM (#14696157)
    The most obvious giveaway is
    Felber's research shows that any mass moving faster than 57.7 percent of the speed of light will gravitationally repel other masses lying within a narrow 'antigravity beam' in front of it.
    because, of course, no physical phenomenon can operate only for masses travelling above a fixed speed like that because such a phenomenon would violate Lorentz invariance. Therefore he's not actually using Einstein's equations which are fully Lorentz invariant. Note that I'm making weak assumptions here - I'm not even assuming the validity of Einstein's field equations, I'm just saying that this work doesn't follow from the equations he claims it follows from. That means he's made up some new physics, something completely untested, and is therefore a crackpot.
    • Felber's research shows that any mass moving faster than 57.7 percent of the speed of light will gravitationally repel other masses lying within a narrow 'antigravity beam' in front of it.

      because, of course, no physical phenomenon can operate only for masses travelling above a fixed speed like that because such a phenomenon would violate Lorentz invariance.

      Actually I read this to mean that the repulsion effect requires that the relative velocity is greater than .577c. Blockquoth the abstract fo

    • That means he's made up some new physics, something completely untested, and is therefore a crackpot.

      Truly unique concepts are always met with opposition. There is a quote that I love (don't know the source) "Don't worry about having a unique idea stolen, if it's truly unique you will have to beat them over the head with it."

      I'm not saying I support grandparent, I'm just saying that your comment is anti-science. Just because someone has a new idea does in no way make them a crackpot... most (if not
      • You are completely missing the point even though I was at great pains to spell it out. He claims his deductions are from Einstein's equations. This is impossible. Therefore he has made up new physics. Anyone can make up new equations. Absolutely anyone. This isn't new science at all. Look, I can do it. I think I'll say F=ma^1.0002 and show how I can use this to violate conservation of energy and generate free power for all. You can't just make up new equations to solve an engineering problem unless you have
        • "Einstein didn't just make up E=mc^2."

          That's true, he didn't, it came from the formula E=MV^2 that was found by a French woman dropping steel balls into clay, it was a correction to Newtons erroneous E=MV. The C is just a constant V, Einstein got the idea because of experiments around the time had shown the puzzling result that light travels at the same speed in all directions.

          Now when Einstien published his paper he assumed it was all just a mathematical curiosity, he did not think it translated to t
    • by barawn (25691) on Sunday February 12, 2006 @01:21AM (#14698297) Homepage
      because, of course, no physical phenomenon can operate only for masses travelling above a fixed speed like that because such a phenomenon would violate Lorentz invariance.

      No. (For one thing, Cerenkov radiation is a physical phenomenon that operates only for masses travelling above a fixed speed.)

      All this is saying is that if you've got an object (say object A) at rest, and another object (say object B) approaching object A at more than 0.577c in object A's reference frame, object A will be pushed forward (away from object B). Obviously if object A and object B are aligned exactly, they'll collide - but if object A is off-axis from object B, it will be "pushed along" with object B.

      Since the relative velocity is measured in one object's rest frame, it's Lorentz invariant. (Object B sees object A approaching it at 0.577c, and sees object A pushing object B backwards).

      It's very similar to frame dragging, actually. With frame dragging, there is likely a "critical rotational velocity" above which an object near the rotating object will be forced into an orbit. There's probably a "critical rotational velocity" above which an object deflects every incident object away from it.

      And as with frame dragging, it likely exists for lower velocities - but the "push" is probably not along the axis of object A's direction, which means it won't "push" the object along.
      • (As a trained physicist I agree with your analysis, but as a slashdotter, I have to get a +5 funny)

        This means that, all I have to do to get accelerated to a significant proportion of c is to get someone else to sling something at me at over half the speed of light, with a high degree of accuracy.

        Now, who's going to volunteer to test that out?!

        Justin.
  • Since the dawn of special relativity, travelling near light speed has always been possible. Its going beyond the speed of light thats not possible.
  • by RedLaggedTeut (216304) on Saturday February 11, 2006 @06:19PM (#14696236) Homepage Journal
    While antigravity is a cool SciFi story device, it is quite possible that attempting to implement an antigravity device is like pulling yourself out of the swamp by pulling at your own hair like Munchhausen, or like protecting yourself from rain by sitting in an open boat on a lake.

    Now even when Dr. Felbers calculations are true, you'd first have to find a star speeding at a speed of 57%+ of lights speed(or accelerate one yourself :-P), then you'd have to get in front of it, and in order to avoid the star smacking right into your spaceship, you'd have to have a speed of 0.57c already. Moreover(guessing), when you'd accelerate over 0.57c to take advantage of it, as you move away, the antigravity cone probably would loose focus and dispel just like gravity with a spread function of 1/r^2, quickly rendering it useless unless you'd just float along with the star.

    obLinks: Google "pushing gravity" or (http://everything2.com/index.pl?node=pushing%20gr avity [everything2.com]) predicts similar behavior on a small scale and provides a simpler model for working out strange gravity effects.
    • it is quite possible that attempting to implement an antigravity device

      You're not building an antigravity device. The star acts as an 'antigravity' device, which is a crappy name for it anyway. Just think of it as "forward frame dragging". If a massive object travelling close to c moves close to you, it drags your frame of reference violently along with it. You're "riding its wake."

      Now even when Dr. Felbers calculations are true, you'd first have to find a star speeding at a speed of 57%+ of lights speed(or
  • Put some money in a stock index fund then climb aboard your spaceship. Accelerate to near-light speed and take a cruise of some nearby solar systems for a few hundred years. Come back, having aged little, and collect your fortune.
  • noted physicist Dr. Franklin Felber will present

    "Franklin Felber" [google.dk] has less than 40 hits on google. For that reason I very much doubt he is a noted physicist. By association, I am not going to take his claims seriously...
    • by shaitand (626655)
      One of the fundemental principles of logic is that you can not reduce the credibility of an argument by reducing the credibility of the one posing it.

      In other words, 2+2 is not any more valid when posed by the pope than by Hitler. Or to go less concrete, Relativity would have been no more or less likely if Hitler has proposed it rather than Einstein.

      Judge the good doctors ideas on their merits rather than on his merits.
  • by sdo1 (213835) on Saturday February 11, 2006 @07:15PM (#14696536) Journal
    I'll believe it when I see it.

    Er, or maybe when I don't see it.

    -S
  • by InterGuru (50986) <[jhd] [at] [interguru.com]> on Saturday February 11, 2006 @07:22PM (#14696574) Homepage

    The density of interstellar space is about one atom per cubic centimeter [hypertextbook.com]. If the spaceship were going near the speed of light (3 x 10^10 cm/sec), it would be hit by 3 x 10^10 relativistic particles per cm^2/sec. This is about the equivalent of one Curie [wikipedia.org] per cm^2, which would kill a human and cripple any electronics on board

    A very heavy magnet could deflect the protons, but the neutral atoms would be unaffected by the magnetic field.

  • Huh? (Score:5, Interesting)

    by Phanatic1a (413374) on Saturday February 11, 2006 @07:45PM (#14696707)
    This makes no sense.

    Felber's research shows that any mass moving faster than 57.7 percent of the speed of light will gravitationally repel other masses lying within a narrow 'antigravity beam' in front of it. The closer a mass gets to the speed of light, the stronger its 'antigravity beam' becomes.


    Moving faster than 57.7% of c? Relative to what?

    Right now, the earth is moving through space at a speed greater than 57.7% relative to something. No, I don't know what, or where, but rest assured there's some body out there somewhere in whose frame of reference the Earth is moving at greater than 57.7% of c. And there's some other body in whose frame of reference the Earth is moving at greater than 10% of c, and another body where Earth is moving at 95% of c, and another body where Earth isn't moving at all (Hey, like me!).

    So why isn't the Earth emitting such an antigravity beam, repelling masses in its path? Rest assured that if it were, we'd be seeing its effect, like ferinstance as it played havoc with GPS satellites.

    Or, heck, there are cosmic rays which occasionally smack into the Earth's atmosphere at a speed that's only infinitesimally smaller than c in Earth's FOR. They should *definitely* be emitting some sort of antigravity, if this guy's correct. Should be trivial to observe, but we haven't seen it.

    This smells like bullshit.
  • by Anonymous Coward on Saturday February 11, 2006 @08:00PM (#14696767)
    Ok, I've worked in gravity for a while, but unfortunately I haven't time right now to go through this guy's paper [arxiv.org]. Several things are setting off my B.S. detector, though.

    First, this guy is not a "noted" physicist, let alone a noted gravitational physicist, as far as I can tell. He published some papers [stanford.edu] in accelerator physics while affiliated with the Naval Research Lab. He has no publications, or as far as I can tell, training in general relativity. He's now affiliated with some company ("Starmark, Inc.") in San Diego. Furthermore, gravitational physicists generally give talks at gravity conferences (or at least physics conferences), not space engineering conferences (which have drastically lower standards when it comes to gravity, since the organizers of the conference typically have no GR background).

    Second, I skimmed the preprint of his (unpublished) "antigravity" paper. He claims that a distant observer watching a particle fall into a black hole, in the (initial, local) rest frame of the particle, will see the black hole to approach the particle, and then cause the particle to accelerate away from the black hole. This is not in any weird "warp drive" spacetime, but in ordinary Schwarzschild spacetime — such as the spacetime outside of a star or a planet (!). Yes, you read that right, according to him, even planets create antigravity (if you're traveling fast enough). This bears no relation to anything I know about orbits of particles in Schwarzschild spacetime.

    Then he mentions performing a Lorentz transformation of a particle trajectory into the frame of a distant observer. This is impossible. You can only apply a global Lorentz transformation to a flat (Minkowski) spacetime, not a curved spacetime (such as Schwarzschild). Well, you can apply a transformation to a flat tangent space at a point in a curved spacetime, but you can only transform a vector in the tangent space at that point, not an entire trajectory that spans a continuum of points. It is true that Schwarzschild geometry is asymptotically flat for "distant" observers, and he's speaking of transforming into the frame of a distant observer, but the fact remains that you cannot Lorentz transform a worldline that is not entirely within an approximately flat region of spacetime (and his trajectories definitely aren't always far from the gravitating body).

    Now, you're free not to buy my suspicions, because as I said I haven't the time to go through all his calculations and see what's up (general relativity calculations are a pain in the ass). My bet, however, is that he's simply misinterpreting a coordinate quantity as having physical meaning. This is a common error for GR beginners (and you can see a prime example of it in the crackpot A. Mitra, who claims that black holes contradict the Einstein field equations based on his misinterpretation of coordinate derivatives in Schwarzschild spacetime). The thing about GR is that you can write solutions in any coordinate system you want, and you have to make sure that the quantities you're calculating are physically meaningful, and not just an artifact of whatever coordinates you happened to choose. Anyway, that's my guess based on what this guy has written so far and the kind of errors I see people make when making "wild" claims in GR. But it's also possible he simply made a math error. I am not betting, however, that he has suddenly discovered antigravity lurking within the ordinary Schwarzschild metric.

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