Swimming Through Empty Space
    By Johannes Koelman | July 25th 2009 09:30 AM | 26 comments | Print | E-mail | Track Comments
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    I am a Dutchman, currently living in India. Following a PhD in theoretical physics (spin-polarized quantum systems*) I entered a Global Fortune


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    An article in the latest (August 2009) edition of Scientific American describes an astronaut floating motionless with respect to his distant spaceship. He is not tethered to the spaceship and has no objects available that can be hurled away or can in some other way create a thrust.

    How is he ever going to make it back to his spaceship?

    His situation seems hopeless. However, he remembers the lessons he received as rookie astronaut on swimming in empty space. By applying a weird degenerative form of breaststroke the astronaut slowly moves toward the spaceship and makes it safely back before he runs out of oxygen.
    Swimming in Space

    What to think of this? Repetitive flexing of his muscles causing an astronaut to move through empty space? Swimming without pushing against anything or being pushed by anything? Sounds unbelievable? Literal bootstrapping in a mediocre science fiction scenario? Surely since Newton we know that neither Baron Von Munchausen nor anyone else can pull himself up by his own bootstraps!

    Well, think again. MIT professor Jack Wisdom did demonstrate in a paper published in 2003 in Science that it is possible to translate a deformable body solely by applying internal forces.

    So you ask: if that is so, why can't we lift ourselves up and breaststroke through the sky? Well, the issue is that professor Wisdom's 'breaststroke' is not particularly effective to overcome earth's gravity, as it relies on the local curvature of spacetime. This curvature is very small, and its effects are hardly noticable in everyday life and over small distances. Yet, since Einstein we know that spacetime is curved due to the presence of mass in the universe.

    Distant stars and planets bend spacetime and create a non-Euclidean geometry. Would one measure the sum of the angles of a giant triangle formed in space, these angles would not add up to 180 degress as Euclidean geometry stipulates. It is precisely this deviation from the flat Euclidean geometry that enables swimming through a vacuum.

    So how does it work?

    It is easy to see that in the case of a universe that is curved back onto itself, one can apply an extreme form of spacetime swimming by applying a giant 'crawl' embracing the whole universe. This can be achieved simply by repetitively throwing away an object and catching this object again as it returns from the reverse direction once it has completed its trip through the universe. Referring to this repetitive process as 'swimming' seems cheeting.

    Yet the classification 'swimming' is appropriate once one accepts that 'swimstrokes' can be identified for disconnected systems such as – in this case – the system of thrower plus object. Obviously, the result of each stroke is that this system start and end in the same situation (with the thrower holding the object in his hands), whilst having moved through space due to the backreaction exerted by the throwing of the object.

    As Wisdom demonstrated, in a curved universe less extreme swimming strokes can be defined that do not encompass the whole universe, but that consist of moves within a local region of space. These are true strokes without involving cheats such as disconnected objects. The Scientific American paper describes a simple analogy to our astronaut swimmer in four dimensional spacetime that involves fewer dimensions and can easily be visualized. Imagine a two-dimensional three-legged creature moving frictionlessly over the surface of a sphere.

    Let's say this creature is positioned at the equator with one leg pointing east and two legs pointing along the lines of longitude towards the north and south poles. The swim stroke consists of four moves. First the tripodal creature extends its two longitudinal legs, and subsequently it extends the eastern leg. To complete the stroke, it retracts the longitudinal legs and finaly retracts the eastern leg. As a result of each such 'swimstroke' the creature moves a wee bit westward.

    Why is this?

    Key is that when the eastern leg extends, the longitudinal legs are extended away from the equator, whilst when the eastern leg retracts, the they are closer to the equator. If the creature keeps its longitudinal legs all the time oriented along the sphere's lines of longitude, the backreaction to the eastern leg extending translates into a smaller movement at the tip of the longitudinal legs, and a larger movement at the base of the longitudinal legs located at the equator.

    The reverse is true for the backreaction to the eastern leg retracting. As a result, the westward movement of the base of the longitudinal legs along the equator is larger than its eastward movement.

    A video of the movements will makes all of this hopefully clearer:

    As elaborated in the Scientific American article, key to this swimming in empty space is the fact that the concept of center-of-mass is ill-defined in non-Euclidean space. Non-Euclidean space swimming is geometric in nature and entirely determined by the sequence of shapes assumed. In several ways this swimming is similar to the mechanism by which a cat falling upside-down rotates itself during free fall. Physicists refer to geometric phases to describe these effects.

    Einstein's theory on spacetime curvature is now almost a century old. Only since a few years are we aware that his theory allows for spacetime swimming. The fact that this possibility remained unnoticed for such a long period makes us realize that we are still wrestling to understand all the consequences of Einstein's rich theories, and that we better be ready for a few more surprises at the horizon.


    This gets a thumb up from me because it has a Baron Munchausen reference and it gives kudos to the many nuances still remaining in all the things that came from Einstein's brain.
    Wouldn't this give us the makings of a reactionless drive? Wikipedia says that's impossible.

    It sounds like a pretty major breakthrough if we could scale it up. How does this not violate conservation of momentum though?

    It doesn't violate conservation of momentum because momentum is never actually created (or destroyed)... this technique allows you to change your location, but not to generate momentum - that is, in order to traverse a significant distance it is necessary to perform the sequence of operations over and over... no matter how hard you try, you can't build up any momentum and "coast" until you get to where you want to be...

    Reactionless drives exist and serve well. Wikipedia articles are often written by reactionary trolls, who are following mainstream paradigms only...

    Johannes Koelman
    "How does this not violate conservation of momentum though?"

    Excellent question that gets us to the heart of the matter. Momentum is conserved in spacetime swimming. This is no different from angular momentum being conserved despite cats being able to change their orientation whilst falling.

    Whist momentum is a conserved quantity, in curved space this in general can not be translated into statements about the center-of-mass motion. In fact, center-of-mass is a rather ambiguous notion in non-Euclidean spaces. The SciAm article illustrates this in a very clear way utilising an example of three masses located on the surface of a sphere.

    A detailed (rather theoretical) paper on why straightforward high-school physics fails when considering motion in non-Euclidean spaces can be found here.
    But perhaps unnecessary.  And I'm not specifically referring to the gravity of the spacecraft and the astronout , which should attract each other.  It would work faster than the object would return from it's trip round the universe, though probably still not before he'd run out of air.

    But we really should be able to swim in the Dirac Sea.

    Or indeed the Quantum Field, Higgs Field, New Luminiferous Ether, or whatever else we may end up calling it.

    Even if he's not allowed to 'push' particles back with the action of swimming, just clapping his hands should create enough disturbance to propogate particles from the energy field, which would have gravity to draw him forward.  A very tiny amount perhaps, but if he clapped hard enough.

    OK it may be crazy, ..but when you're facing certain death!
    Connor Davidson
    WOW, that's clever.

    Well, the conservation of momentum law seems to have no objections.
    Alright, I have two questions after spending about half an hour fully comprehending this...

    The first (which is likely the most basic) is what would happen if the arms are extended to the poles? Would that not create an infinitesimal distance, therefore allowing extreme movements? I assume I'm missing something as it looks like in your 3D model that the sphere may be a donut.

    The second is could it not be possible that the arms, when extended, would gain weight relative to the weight at the equator? I just got out of high school, so while I have an alright understanding of special relativity, my understanding of general relativity is vague. My thought is that due to special relativity, an object can weigh more or have a greater length than that of another (relatively) depending on its velocity. In this scenario I assume that one of these factors is different at the end of the 'arms' reaching towards the poles than at the 'tail' at the equator. Momentum would still be conserved, albeit without being able to swim in space. This would also explain why a different center of gravity can be achieved with different methods in a non-euclidean space as it is comparing relative weights to each other (and this is speculation on top of speculation, but might as well).

    To note, I don't think I'm right at all, I just want to hear why I'm wrong. I'm sure it's a case of bad logic due to ignorance, but it is what makes the most sense to me at the moment. Things like this always pique my interest in physics again though. Always a battle between which science I want to major in.

    Johannes Koelman

    Troy - you are asking the right questions!

    1) Yes, your inituition is correct. The effect increases when the arms and their movements increase in size. I have to check the exact calculations, but it is indeed likely that the distance moved per stroke would be maximized with the arms making moves reaching antipodal positions.

    2) The 2D sphere surface model is no more than an analogy to the effect in curved 4D spacetime. It seems that your scenario 'relates to tidal effects rather than spacetime swimming'.

    Of practical interest (and I want no MIBs to visit me...for now):
    (...Now, as a long-retired [and, therefore, quite obsolete] engineer And machine designer I have created a preliminary design [using CAD] of a mechanical device that mimics/emulates the "swimmer" mentioned in the linked article. The difference is that the motorized "motions" are extremely rapid. This creates a "thrust" that might be considered an antigravity device, at least in microgravity, that would achieve a very high V before relativistic effects become pronounced. Once I build the device and test it on a sensitive scale in a local vacuum, I will post the results here and elsewhere.... 'Nuf said. Carry on, folks.) [See you on Mars as soon as I cobble up a space suit, laser for commo, and some Mars bars..........]
    (I invite other engineers to dupe my dupes of the motions with an appropriate device design and then em me at If the theory is correct or partially correct, it is easily done by manipulation of CG very rapidly [TBD])

    Additional: The CG manipulation and "swimmer" motion mimicry would/might occur in cycles like this: very slow (say 2 ms), then very fast (say 0.1 ms) -- all To Be Determined via experiment. . . . . ?

    PS. I am in ill health so it would behoove others to follow my lead as basically described above -- hang in there, All.

    PPS. In the event I am wrong: ;#)

    (Hmm, an alternate design might be penguinish. . . the device is totally emmersed, in effect, of course. . . .)

    Related to my last post above, I posted this update at Analog:
    Update -- Ref. to my post 222 above about "swimming:" I've ordered the appropriate off-the-shelf motors, solenoids, and a cam for my design. The device, using these, will cycle its streamlined limbs forward in about 2 ms. , unfold the 'streamlining' to form 'cupped fins' and then cycle backward for about 0.1 ms. Trials on the scale will indicate cycle adjustments (and stroke distance per arm strength) that might be needed. Keep in mind that this device is merely a crude prototype. Heh, who knows, the final device, as I mentioned above, might be penguin-ish since (effectively) total 'emmersion' cannot be avoided. . . . . .
    Also, since I am quite old, I suggest that others (engineers?) follow my lead to duplicate the device(s) in their own way. (Heh, I might not survive the 'takeoff.')

    Carry on, All.

    I think you are getting a little ahead of yourself with this. I don't see any reason to believe that this method of travel is efficient in any way. It's more reasonable to assume that it would only be useful in an environment where energy is abundant and matter to eject scarce (somewhere in space, and even then....). You also have no idea how space is curved locally, so you couldn't really create a device to swim in it. I would also say the device would have to be enormous to increase the difference in space.

    I don't really understand the phenomenon entirely so I'm not going to say it's straight up impossible, it just seems highly unlikely that what you are trying to do is going to work. Do you understand the math behind this swimming deal and have you read the original MIT paper (I do not and have not)?

    Yes, I read the original. Keep in mind that any experiment is a success whether it fails or succeeds. Incidently the size of the device is a bit bigger than an average person.

    Additional: Naturally a very large device/structure is possible -- even on a low 'DARPA-equivalent' budget -- and might reveal more on a sensitive scale in an 'average' vacuum. The point is -- wouldn't you want to know one way or another?. . .

    And I'm not specifically referring to the gravity of the spacecraft and the astronout , which should attract each other. It would work faster than the object would return from it's trip round the universe, though probably still not before he'd run out of air.

    I guess the key to understanding space swimming is to recognize the swimmer as a distributed mass of which the different parts are extending into energy gradients of the curved vacuum.

    Curved space means that there is a gravitational field. Then part of the distributed mass is feeling stronger gravity that other parts.

    Center of gravity is important in the concept of getting the swimmer back to the vehicle, but not a major feature in the mechanism to achieve differential motion.

    If the arms and legs get long enough and the motions are rapid enough in one particular direction then there is energy leaving the swimmer in the form of gravitational waves from a moving mass. In that case the space curvature is not really necessary. So the two methods are really using different technology.

    In the first sky lab from several decades ago, a discovery was made of the tendency to tumble backward because of the rather long shape of the lab. One of the gyroscopic stabilizers burned out trying to prevent the backward rotation. The lab was responding to the small curvature of the Earth’s gravity field.

    During the following years there was speculation about how that tendency to tumble could be turned into a propulsion system. One of the designs looked like two pairs of heavy weights like dumbbells connected to opposite ends of a space lab type vehicle. The claim was made that if electric power was applied to force the dumbbells into a slow forward tumbling motion then the natural tendency to tumble backwards would result in a forward thrust of the vehicle, as long as one weight on each dumbbell was always closer to the Earth than the other weight.

    From that work came the concept of two or more rotation centers separated by a distance converting moments and torques into linear motion by interaction with a curved space gravity gradient.

    Then the key to understanding is that the mass is distributed among several rotation centers in different gravity fields.

    That was about 30 years ago.

    I differ from the main stream of science in the geometric treatment of space, taking the view of Galileo over that of Copernicus.

    “Non-Euclidean space swimming is geometric in nature and entirely determined by the sequence of shapes assumed”

    While the statement is true within the context where it is used, it represents and old fashioned view of cosmology based on the technology of 1920.

    Einstein treated space as the abstraction of geometry, because he didn’t have enough data about the properties of space to describe it any other way.

    In the same way the classical cosmology was described in abstract geometrical terms (incorrectly) between the time of Ptolemy and Copernicus.

    Einstein admitted in a speech that space would need to have some physical property to change in a gravitational field to support the abstract idea of curvature. The necessary physical data was not available until 1935, and even then the scientific community did not modernize the theories.

    The main problem was that there were very few people who understood Einstein’s work well enough to change it. Dirac and Eddington were two exceptions. They attempted to describe the vacuum in physical terms, but got diverted with the large number concept, a type of numerology.

    Planck units were developed for describing cosmology. They aren’t practical for much else.

    Within the Planck units, general relativity, and the quantum mechanical concepts of zero point and quantum oscillators, there is enough scientific knowledge now to move forward with a new type of field equation, that describes how the measurable physical properties of space change under stress of gravity and electromagnetic energy.

    Then instead of describing space as an abstract mathematics, it can be described as a physical science that can be measured and tested.

    People who lead the way will undergo the Scientific Inquisition every bit as powerful as the opposition to Galileo.

    So we know what the penalty will be. It is early retirement, home confinement , and a book deal in a foreign country (probably Elsevier in The Netherlands).

    The benefit will be a sudden release of creative discoveries in science.

    Curvature can occur from electromagnetic energy as well as gravitational energy, according to Bergman and solutions to the Einstein field equations from about 1919.

    Field effect is the name that has been given to electromagnetic curvature and the machines that produce it.

    The stress energy tensor of Einstein’s field equations contains an electromagnetic term that takes care of reverse curvature, and has done so since 1920.

    Electromagnetic curvature takes a lot of power and is in the opposite direction to gravitational curvature.. Masses repel each other. Both time g(44) and space g(rs) are curved. So it is a bit risky on the first attempt, even more so for the really advanced group from 1935 who learned how to create the field effect from vacuum energy.

    Space swimming takes on a new meaning when the astronaut carries a field effect generator, well designed to point away from the destination vehicle.

    Curvature is created when needed., and by published technology of the 1920’s and 1930’s.

    Momentum action and reaction apply to the vacuum energy as well as to mass and observable energy.

    Exploring space in the next steps requires new technology to replace the chemical rockets of antiquity. An assumption is that 3500 years qualifies as antiquity.

    NASA has a poorly funded office of Break Through Propulsion (BTP). Other agencies and private groups support the same type of thinking.

    Budget cutting at NASA looks to some people like the need to save money. Other people feel that the budget was cut because it had accomplished its purpose.

    In public information beginning in 1935 there is enough technology from the main stream of science to design field effect gravity engines that are powered by vacuum energy. It is the non random feature in Schrödinger’s third law of thermodynamics. There is a big risk in operating this technology, because it removes the power from space that enforces all of the natural laws, including the stability of time and space. Also there is a risk of accidents producing black holes dropped on the ground, neutrons, and bursts of gamma rays. All of these things have been discussed by the leading scientists. So you need a permit and a good safety program with a research grant.

    You cannot do this at home in your garage.

    On the other hand it is the only published technology with a chance of taking us to the stars. Arrival time is a bit uncertain, because this type of device converts time into distance. Field effect means either curved space or worm holes occur depending on whether or not the vacuum gravity term is less than one half or less than zero.

    A gravity engine means that the travelers do not feel any acceleration, that would otherwise crush them with a different technology. Also the vehicles can start and stop abruptly, turn quickly at right angles, climb straight up, sit stationary in the air or travel in space for long distances at high speed.

    The gravity engine means that the vehicle can reach light speed or even change the speed of light, because the relativistic increase of apparent mass is more of a benefit than an obstacle under induced gravity.

    Why are no machines in Popular Science after 70 years?

    Kaiser William, Adolph Hither, and many others both supported development programs and fully expected to receive that type of power.

    I don’t know if their scientists succeeded or not, but from a long life time of reading thick books of difficult mathematics, I would guess that they did.

    The answer appears to be that anyone who acquires that type of power doesn’t need to work for tyrants, ask for investment money, write books, give lectures, or attend conventions. The other explanation would be that the early models were operated without radiation shielding and other safety devices, leading to the demise of the researchers and their machines.

    Swimming in space is not a difficult new idea. It isn’t even new.


    If zero point vacuum energy is the greatest discovery since top soil, why are there no machines using it after 150 years of research?

    Science was receptive to vacuum energy projects in the 19th century, so the status quo can't be blamed for the failure of ZPE in public life. ZPE came later.

    More than 1000 projects have been funded by public and private sources, but not one investor got a profit or a refund. On the other hand there are about 500 inventors who claim technical success and financial failure. Many have patents in a variety of machines.

    A close inspection is not needed to get an opinion that much of the published information is nonsense and fraudulent, but not all of it is.

    After about 50 years of reading nonsense and fraud, the scientific community rejected the entire topic on the conclusions of Michelson and Morley about ether and light speed.

    Michelson and Morley assumed that any ether in space would have mass and move much slower than light speed. They proved rather well that there is no such ether.

    Slowly over a long time the scientific community recreated the theories of vacuum energy into zero point oscillators, moving at light speed in every direction, with no mass.

    Michelson and Morley experiments can not handle energy moving at light speed. in all directions. The equations produce infinities in three places. So it is clear the Michelson and Morley type experiments were never intended to measure the vacuum zero point.

    Scientific resistance to vacuum energy was very strong until 1993 when photon entanglement was proven conclusively in Geneva. Many younger scientists realized that they had been cheated with bad science that had dominated academic studies for many decades.

    Wait a minute?

    How is vacuum energy related to wave form entanglement?

    I confess! They are not closely related.

    When credibility was shattered on entanglement, the shock waves went everywhere making cracks in the armor plate of scientific achievements.

    Every part of physical science came under question by a younger generation that saw a chance to rewrite the text books.

    The result is that there has been a upswing in the support for vacuum energy research, and the findings are supported by research data that makes a lot of sense.

    So!!! If zero point vacuum energy really is the greatest discovery since top soil, why are there no machines using it after 150 years of research?

    Woops! I forgot to answer the question.

    From the very beginning of vacuum energy research there have been a few successes, and some of the machine design drawings survive in public view, not many. The machines are missing, and much of the discussion about the drawings has no scientific merit, but might be fraudulent and deliberately misleading, although drawings from around 1919 do have merit that is still on the leading edge of scientific research.

    On the edge for 90 years???

    In the field of vacuum energy the scientific community is continually starting over from basic principles, instead of moving forward with construction of machines.

    The best work continually disappears from public view, leaving little evidence of it’s existence. You have to be quick to get a copy. Less valuable work continues for decades on public display. Occasionally an old drawing is found in the Austrian State Achieves, filed under an misspelled name, together with the history of people who were ruined financially by fraud.

    So if you find this message less than perfect, please remember that a better piece of work would disappear.

    When a discovery is the greatest thing since top soil, it isn’t going to be left lying around.

    I remember reading a children's space story back in the 60's where the characters actually did this--swam in space to reach floating debris or something like that. They then used whatever it was they found and made a bubble with rubber in the bottom and a makeshift parachute and somehow landed on Mercury. I don't remember the title of the story. I remember enjoying it very much as a kid.

    I Disgagree.