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Mass of fuel would ALSO increase as spaceship comes near the speed of light!

  1. Mar 24, 2009 #1
    Hi everyone,

    Today a strange thought came into my mind. We know that the mass of an object increases as it gets closer to the speed of light so it is often stated we would require more and more fuel to accelrate it further. However the mass of the fuel would also increase. What could be done now is you say build a nanospaceship filled with fuel, accelerate it so close to the speed of light so that it it's mass would be say ten times the original mass, with repect to the external environemnt, and so would be the fuel now. So now the remaining fuel is providing TEN times as much as kinetic energy to the nanoship AGAIN with repect to the external environemnt. By us whor out of the spaceship letting it get bombarded now we could derive appx ten times the energy which we originally provided by the fuel. by reconverting that energy into another fuel and repeating this process over and over one could then require infinite energy. But doesnt this violate the law of conservation of energy. Can somebody explain this?
    Last edited: Mar 24, 2009
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  3. Mar 24, 2009 #2

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    You're doing two things wrong here, jonny. You are mixing frames and are assuming that the increase in relativistic mass equates to a real change in the quantity (number of molecules) of fuel. From the perspective of the spacecraft, the fuel's mass hasn't changed one iota. The quantity of fuel does not change, from the perspective of any observer.
  4. Mar 24, 2009 #3
    Hi there "DH",

    JK- But thats exactly why the spaceship would keep accelrating and exponetially gain in KE as it approaches the speed of light. Say it has accelerated at g and is now at 299,999 km/s. the fuel consumption inside the apcecraft will not suddenly increase because as the mass of the spaceship increases and it requires more force to keep up the same acc. the fuel which is now also more massive, both spaceship and fuel with repect to external environment, will continue to provide it in a simlar way. But now at g theres only abt 1 m/s left be4 LS. Also objects inside the spacecraft will not suddenly experience less acelaration. tht will be as always inside the spaceship too for them. So every so minisculke amount of time tht passes from this pt will cause 1) exponential time dilation 2) exponentinal spaceship dimensional decrement 3) exponential increase in mass and thus KE WITH REPECT TO THE EXTERNAL ENVIRONMENT. so now if tht spaceship is brought back by the ppl external of it it cld provide them, THE OUTSIDERS, with enormous amounts of energy or no?
    Last edited: Mar 24, 2009
  5. Mar 24, 2009 #4
    Hi again "DH",
    Regarding the number of particles/molecules ofcourse they remain same because the mass increment as LS approaches does not depend on number of elementary particles AS IT IS THE MASS OF THE VERY ELEMENTARY PARTICLES ITSELF WHICH INCREASES. And thus it would follow that theyd become more and more energized too becase mass is just another form of energy.
    Last edited: Mar 24, 2009
  6. Mar 24, 2009 #5
    Relitavistic mass, which you are using, is just a fancy way of saying the energy increases. The invariant mass(rest mass) of the objects never changes. If your reasoning was correct any alien flying by earth near the speed of light would observe(per your reasoning as far as I gather) the mass(relative) of the fuel in our nuclear is greater so the energy they release is far greater. so the power output would be far greater. This is not the case. The power output of our power plants doesn't change because someone flies by really fast.

    Long story short, when you go faster you increase the energy of a system relative to another observer. To my knowledge you do not change the energy in any of the bonds or any of the rest masses. relitavistic mass is not interchangeable with invariant mass
  7. Mar 24, 2009 #6


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    The use of capital letters does not make your statements true. You unfortunately have many grave misunderstandings of special relativity.

    To the captain of the spaceship, neither the mass of the spaceship nor the fuel appears to change. The captain can accelerate at g for eternity and will never notice anything "relativistic" happening. He will continue to consume fuel at the usual rate, and will measure his progress through the universe as ever more rapid, taking less and less time to cross a given distance, forever. If he had infinite time, he could accelerate until, according to his watch, it takes zero time to go anywhere in the universe. He will therefore consider his own speed to be approaching infinity. This is all very ordinary and Newtonian -- and it better be, since only one frame of reference is involved, his own. No relativity is necessary to understand the captain's perspective of his own ship.

    To another observer outside the spaceship, the story is quite different. The mass of the spaceship will appear to increase with its speed, its acceleration will appear ever slower, and its speed will grow closer and closer to c. In the limit of infinite time, the spaceship will be seen as moving at c, and all of the physical processes inside the ship (heart beats, etc.) will appear to have stopped.

    The nature of the fuel is actually completely irrelevant to the discussion. If the spaceship is able to accelerate at g, according to its captain, then the discussion is over. It doesn't matter how that acceleration is accomplished.

    - Warren
  8. Mar 24, 2009 #7
    Hi "jefswat",

    JK- But this is exactly my point i.e. "the faster one is more energetic wrt the ones not so fast and as the faster approaches light it becomes expoentially more fast wrt slower or non accelarating object". so say we equip a non manned spacecraft with fuel and allow it to go to 99.9% speed of light which shld take about three months accelerating it at g. From then on with eve small time that passes it would become much more energized wrt us. then we bring it back and collect it's KE.
    Last edited: Mar 24, 2009
  9. Mar 24, 2009 #8
    Hi "chroot"

    JK- You misunderstood. My use of capital letters is not to enforce the truth of my statements but to make my main points stand out. Im actually not sure of this and i want to know your views.

    JK- EXACTLY i agree and I've stated this, However there is no captain becauser the spaceship is controlled FROM EARTH BY US. We just wanna accelrate it to 99.9% because once there every second or so that we continue to allow it to accelrate it's KE shld exponentially increase wrt US. Then we turn the spaceship and collect it.

    JK- Thats the point now.

    JK- Agree but will the accelration start to decrease continually or just as it's about at 99.99% of light? In other words how long would it take for an external observer to experience spaceship at 99.9% of LS, using g acceleration inside of the spaceship without any devices inside ever varying it? And if there was a manned spaceship how long would it take the insiders before theyd experience their spaceship at 99.9% also accelrating at g without ever varying their fuel consumtion?

    JK- But i was talking with repect to the external observers. wouldnt the same fuel now be much more enrgetic for them? thus can the outsiders whor controlling the spaceship now not get back more energy than they cld otherwise get from the fuel at rest?
  10. Mar 24, 2009 #9


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    There's nothing special about 99.9% or 99.99% the speed of light. No relativistic effects "begin" at those velocities. Relativistic phenomena even exist between people walking on sidewalks, but they're so incredibly tiny that we ignore them and use Newtonian physics instead. Your definition of "significant" may be different than mine, however.

    To calculate the amount of time the external (at rest) observer will measure for the spaceship to accelerate to 0.999 c, you should look at the standard relativistic rocket equations (but don't take them on faith -- derive them yourself, too!).


    You want the equation:

    [itex]\Delta v = \frac {a \cdot t'} {\sqrt{1 + \frac{(a \cdot t')^2}{c^2}}}[/itex]

    where [itex]\Delta v = 0.999 c[/itex], [itex]a = g[/itex]. Solve for [itex]t'[/itex].

    The outsiders would seem to have a hard time using the fuel for their own purposes, since it's on a spaceship moving away from them at 99.9% c...

    - Warren
  11. Mar 24, 2009 #10
    I think that main source of misunderstandings like this is in notion of "relativistic mass" that "increases" when you speed-up. Mass of a particle is relativistic invariant and does not change with velocity. Increase of momentum of relativistic particle does not translates to linear increase of velocity, but I think you will do yourself a favour not to relate this phenomenon to mass change. As of your question, you should have a look at

    http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html [Broken]

    and model your situation : you will find that energy is conserved.
    Last edited by a moderator: May 4, 2017
  12. Mar 24, 2009 #11


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    This is well understood. Check the links that have been provided. The bottom line is that energy is conserved but frame dependent.
  13. Mar 24, 2009 #12


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    By the way - the "energy" in the fuel is chemical energy. It doesn't have anything to do with the relativistic kinetic energy of the fuel - it is proportional to the number of molecules, period.

    Also, since you're not doing any calculations here, you are not seeing another obvious flaw beyond even the effect of relativity: since the mass of the ship and mass of the fuel would both be increasing if you were correct, even if there were an associated increase in thrust, there still would be no increase in acceleration. Ie, if you double the mass of the spaceship and fuel and double the "energy" of the fuel, by f=ma, you'd end up with the same "a".

    Errors on sooooo many levels.
  14. Mar 24, 2009 #13
    H "chroot",

    JK- Thankyou for stating the equation involving acceleration. So this means even the ones inside the rocket would experience ever less accelration looking at outside objects? They wouldnt just within secs see it go from 99%-99.9999999% c and in yet anohter sec 99.99999999999999999% c? Ive heard the claim being made somewhere that we can actually reach galaxies whor millions of light years away still being alive, accelrating at g and travelling only a couple of years because of the time dilation factor. ofcourse on the outside millions of years wouldve passed. BUT this must mean that as we get closer to c the time needed to increase the time dilation factor between external world and inside the rocket decreases exponentially. HOWEVER the fuel consumption wrt the insiders SHLD REAMIN CONSTANT for the same accelration.

    JK- What if the outsiders are actually in control of the rocket and they turn it so it travels back towards them at 99.9% c?
    Last edited: Mar 24, 2009
  15. Mar 24, 2009 #14


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    You do understand that "turning" the space ship is not free?
  16. Mar 24, 2009 #15
    Hi "xlines",

    JK- Thankyou very much for that link. However it shows that fuel consumption for continuous travel is exponentially increasing for the ones inside the spaceship as it approaches c. From the site itd be:
    4.3 ly travelled in 3.6 years
    27 ly trvalled in 6.6 years
    30,000 ly travelled in 20 years for the ones inside the rocket
    However what is the cosnumption of fuel here:
    4.3 ly 10 kg fuel in the first 3.6 years of travel
    27 ly 57 kg here we have 5.7 times the original fuel consumed in only 3 years more inside the spaceship.
    30,000 ly 62 tonnes so here we have 6200 times the original fuel consumption in only 13.4 more internal yrs. but earlier it was stated that nothing changes for the ones inside the rocket accelerating at g. how can the fuel consumption suddenly change for the ones inside the rocket? the fuel consumption ought to remain constant for the same accelration for the insiders of the spaceship i.e. in this case 10kg/3.6 insider yrs NOT 10kg/4.3 external lyrs travel BECAUSE REMEMBER THE FUEL IS ALSO GAINING THE SMAE SPEED AS THE ROCKET, thus it's mass increasing proportionally to the rocket and thus proportionally the same amount of fuel per INSIDE unit TIME would be required to keep the rocket accelrating at g. This was exactly part of the problem i had. What is the answer to this?
    Last edited by a moderator: May 4, 2017
  17. Mar 24, 2009 #16
    Hi "russ_waters",

    JK- BUT russ, i never said that the acceleration would change for the insiders. I know it wouldnt but argued that the KE of both fuel and spaceship should increase expoentially wrt outsiders as it gets close to LS, KE being .5*M*v^2, where v is almost constant now and M is increasing relative to the outsiders. The consumptiom of fuel should remain contant for the same acelration relative to the insider, and according to the time calculations on the site provided here by "xlines", after a couple of years the fuel, which itself is speeding up, shldve been converted into huge amounts of KE together with the ship relative to the outsiders. In other words by outsiders using fuel to speed up the object it is contained in and itself, the outsiders can ultimately, as it approaches the speed of light, derive enormous amount of more energy from it then one could ever by just burning the fuel whilst at rest or low speeds considerbsaly lower than c.
    Last edited: Mar 24, 2009
  18. Mar 24, 2009 #17
    Thats because if you want to go 27 light years you need more fuel. This extra fuel is more mass that needs to be accelerated so more energy is going to be needed to move that mass from point a to point b thus more fuel is used.
  19. Mar 25, 2009 #18
    Hi "darkhorror",

    JK- Fuel consumption inside the spaceship has to depend on internal time passage and not on external distance covered due to the time dilation factor. Thus according to the page "xlines" provided if you have fuel onboard which can accelrate the rocket at g for 20 years, you should be able to cover a distance of 300K lyrs externally coz of time dilation. Fuel consumption inside the spaceship will not increase because rlative to the insider neither fuel nor rcket become more massive and even if both did equally thered be no net effect
  20. Mar 25, 2009 #19
    Hi again all,
    Let me make my point even more clear. I know according to special reltivity the force applied to an object of a certain rest mass will be ever increasing as it approaches the speed of light to keep up the aceleration. HOWEVER this is so for the forces acting on the spaceship FROM THE EXTERIOR. What is forgotten here that the fuel is inside the rocket and is also changing in mass BY THE SAME FACTOR as the entire rocket. Thus if originally (elementary particles making up 1mg fuel) / s provided a force of 1M N wrt the outsider, as soon as the time dilatio factor equals 2, mass increment is also by 2 and since the mass of fuel has also increased now the (same no of elementary particles makin up fuel / s) can provide a force of 2 M N wrt to the external world and so on.
    So where always this sudden increase in fuel wrt insiders as theyr getting close to LS beats me.
    Last edited: Mar 25, 2009
  21. Mar 25, 2009 #20
    Let me give you yet another example which involves a spaceship running on hyrogen and oxygen as fuel. NOW say we have onboard 50T of H2 and O2. The spaceship is unmanned and is controlled from earth. For simplicity assume now it starts off in a frictionless environment and with negligible gravity resisting it. As the rocket accelerates the fuel also becomes more massive and thus more energetic wrt the outsiders. Lets say theres a space station preparted to catch the KE of the rocket, convert it into electrical energy and that elecrtical energy would ultimately convert the water there back to H2 and O2 via electrolysis. Assuming now all conversion is 100% efficient one should end up getting more than 50T O2 and H2 on the space station from the KE of the rocket being brought to rest. This is because the fuel energized itself wrt the external environment as it increased in speed by taking relativistic mass into conideration.
    If relativistic mass increases, relativistic energy should also increase. But this would then violate the conservation of energy.
  22. Mar 25, 2009 #21
    It should most certantly not! Yet again, I'd like to suggest that you should throw away notion that mass is increasing with velocity. It does not. Physicist tend to be sloppy with their language and that leads to confusion.

    Two most important thing that you fail to recognize for the problem at hand is that you are applying classical resoning to relativistic problem , that is, you think that for constant acceleration you need constant fuel consumption and you assume that potential of fuel to give thrust to rocket will somehow increase with speed.

    For the later issue, at John Baez site , under "How much fuel is needed?" you will find how much momentum ( not velocity !!! ) can you get out of perfect engine that transforms mass into kinetic energy.

    At wikipedia link, you will find relation between velocity and time for constant acceleration - another sloppy use of language. Even travelers will expirience "inertial forces" of constant acceleration, in reference frame rocket will not accelerate constantly : it's acceleration will drop to zero as rocket approaches c. Furthermore, should you insert that equation into total energy equation for the rocket, you will see that energy consumption rises without limit which contradicts your opinion on fuel consumption.

    I'm sorry I can not elaborate on the subject with more details, but I would suggest that you return to the basics of SR to understand difference between relativistic momentum and velocity and don't think of mass as of something that changes with velocity.

  23. Mar 25, 2009 #22
    Hi "xlines",

    JK- Then why is it that the article youve posted shows that in the first 3.6 yrs of travel the fuel consumption is 10 kg and in the following 3 years it is 50 kg to keep the same accelrating effect? This cannot be for the one inside the spaceship can it? He/shed not suddenly have to increase the fuel supply in order to experience the same g effect would he/she?

    JK- YES that is exactly what i was assuming and if it's not so i need to know the exact reasons why this is not so. If time dilates according to the forumula and that causes real age differences btw outside and inside worlds even after the spaceship comes to rest again then why aint the mass effect real too this increasing potential energy of any fuels on board wrt the outsiders? Are you saying that whilst an atronaut accelerating with g in a rocket and watching the fuel consumption wld after a certain time see significantly more fuel being consumed in order to experience the same accelration?

    JK- Accelreation will only drop to zero FOR AN EXTERNAL OBSERVER or are you saying that the astronaut inside the rocket would suddenly experience significantly less acceleration if he doesnt change the fuel input to the engines?

    JK- Again time changes with velocity are real so why wouldnt the mass effects be which have simlar equaltions? thnx
  24. Mar 25, 2009 #23
    Hi again everyone,
    Can we have it both ways? That is can we have the time effects due to dilation being real causing real differences of age between on board travellers and observers at rest even after the rocket slows down again but at the same time mass and thus monetum and energy effects not being real?
  25. Mar 25, 2009 #24
    Hi again "xlines",
    There are actually two types of accelrations for the ones inside the spaceship 1) experienced acceration on their body 2) visual accelration as the insiders watch the outside objects flying by fater and faster. i can understand that obviously no. 2 would drop to zero as c approaches and would require ever increasing fuel consumption to keep up BUT 1 should remain constant with constnat fuel consumption.
  26. Mar 25, 2009 #25

    Imagine, a particle flying at some relativistic velocity v. If it hits something and comes to a full stop, it will transfer much more momentum than Newton said it would ( m * v ). You can see that if you let your target be so massive that it's recoil velocity is nonrelativistic. What you get is "failure" of momentum conservation law e.g. m*v < (M+m)*v' .

    In physics, there are really good resons to retain MCL instead preconceptions we draw from expiriencing reallity from human scale .

    One way to think of it is to say that it's mass depends on velocity ( as m(v) = m*[tex]\gamma[/tex] ), so you can still use Newton's formula. BUT ... there are some things in relativity called fourvectors . Scalar product of 4vector do not change when you change inertial frames. Momentum and energy give you valid 4vector and it's scalar product with itself is MASS2 - so mass doesn't change when you enter any other frame of reference. Corect thing to do is abandon Newton's formula that p = m*v in a sense that momentum is just speed "masked" with mass, although some people have hard time doing just that. True link between those quantaties is p = m v [tex]\gamma[/tex] and that is why so many concepts from classical mechanics we are used to use fail at large velocity - spending constant amount of energy to gain constant amount of velocity beeing one of them. What you get from constant amount of energy ( or fuel ) is constant amount of momentum! True origin of factor [tex]\gamma[/tex] is the change in geometry of spacetime.

    Acceleration drops to zero in reference system or external observer, as you choose to call it. I belive astronauts expirience constant acceleration. Their fuel consumption rate goes high without bound to maintain that constant acceleration.

    Well, to put it real simple : mass is quite a different concept than time =)
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