Q: If time slows down when you travel at high speeds, then couldn’t you travel across the galaxy within your lifetime by just accelerating continuously?

Physicist: Yup!  But sadly, this will never happen.

This is a good news / really bad news situation.  On the one hand, it is true (for all intents and purposes) that if you travel fast enough, time will slow down and you’ll get to your destination is surprisingly little time.  The far side of the galaxy is about 100,000 lightyears away, so it will always take at least 100,000 years to get there.  However, the on-board clocks run slower (from the perspective of anyone “sitting still” in the galaxy) so the ship and everything on it may experience far less than 100,000 years.

First, when you read about traveling to far-off stars you’ll often hear about “constant acceleration drives”, which are rockets capable of accelerating at a comfortable 1g for years at a time (“1g” means that people on the rocket would feel an acceleration equivalent to the force of Earth’s gravity).  However!  Leaving a rocket on until it’s moving near the speed of light is totally infeasible.  A rocket capable of 1g of acceleration for years is a rocket that can hover just above the ground for years.  While this is definitely possible for a few seconds or minutes (“retro rockets“), you’ll never see people building bridges on rockets, or hanging out and having a picnic for an afternoon or three on a hovering rocket.  Spacecraft in general coast ballistically except for the very beginning and very end of their trip (excluding small corrections).  For example, the shuttle (before the program was shut down) could spend weeks coasting along in orbit, but the main rockets only fire for the first 8 minutes or so.  And those 8 minutes are why the shuttle weighs more than 20 times as much on the launch pad than when it weighs when it lands.

The big exception is ion drives, but a fart produces more thrust than an ion drive (seriously) so… meh.

Rockets: in a hurry for a little while and then not for a long while.

Rockets: in a hurry for a little while and then not for a long while.

In order to move faster, a rocket needs to carry more fuel, so it’s heavier, so it needs more fuel, etc.  The math isn’t difficult, but it is disheartening.  Even with antimatter fuel (the best possible source by weight) and a photon drive (exhaust velocity doesn’t get better than light speed), your ship would need to be 13 parts fuel to one part everything else, in order to get to 99% of light speed.

That said, if somehow you could accelerate at a comfortable 1g forever, you could cross our galaxy (accelerating halfway, then decelerating halfway) in a mere 20-25 years of on-board time.  According to every one else in the galaxy, you’d have been cruising at nearly light speed for the full 100,000 years.  By the way, this trip (across the Milky Way, accelerate halfway, decelerate halfway, anti-matter fuel, photon drives) would require a fuel-to-ship ratio of about 10,500,000,000 : 1.  Won’t happen.

The speed of light is still a fundamental limit, so if you were on the ship you’ll still never see stars whipping by faster than the speed of light (which you might expect would be necessary to cross 100,000 light years in only 25 years).  But relativity is a slick science; length contraction and time dilation are two sides of the same coin.  While everyone else in the galaxy explains the remarkably short travel time in terms of the people on the ship moving slower through time, the people on the ship attribute it to the distance being shorter.  The stars pass by slower than light speed, but they’re closer together (in the direction of travel).  “Which explanation is right?” isn’t a useful question; if every party does their math right, they’ll come to the same conclusions.

Answer Gravy: Figuring out how severe relativistic effects are often comes down to calculating \gamma = \frac{1}{\sqrt{1-\left(\frac{v}{c}\right)^2}}, which is the factor which describes how many times slower time passes and how many times shorter distances contract (for outside observers only, since you will always see yourself as stationary).  Photon ships make the calculation surprisingly simple.  Here’s a back-of-the-envelope trick:

If your fuel is antimatter and matter, then the energy released is E=Mc2 (it’s actually useful sometimes!).  If the exhaust is light, then the momentum it carries is P=E/c.  Finally, the energy of a moving object is γMc2 and the momentum is γMv.  It’s not obvious, but for values of v much smaller than c, this is very nearly the same as Newton’s equations.

For a fuel mass of f, a rocket mass of m, and a beam of exhaust light with energy E, lining up the energy and momentum before and after yields:

\begin{array}{ll}\left\{\begin{array}{ll}(m+f)c^2 = \gamma mc^2+E\\0=\gamma mv - \frac{E}{c}\end{array}\right.\\\Rightarrow (m+f)c^2=\gamma mc^2+\gamma mcv=\gamma mc(v+c)\\\Rightarrow \gamma = \frac{c}{v+c}\left(1+\frac{f}{m}\right)\end{array}

So, when v ≈ c (when the ship is traveling near light speed), \gamma \approx \frac{1}{2}\left(1+\frac{f}{m}\right) \approx \frac{f}{2m}.  That means that if, for example, you want to travel so fast that your trip is ten times slower than it “should” be, then you need to have around 20 times more fuel than ship.  Even worse, if you want to stop when you get where you’re going, you’ll need to square that ratio (the fuel needed to stop is included as part of the ship’s mass when speeding up).

More tricky to derive and/or use is the math behind constant acceleration.  If a ship is accelerating at a rate “a”, the on-board clock reads “τ”, and the position and time of the ship according to everyone who’s “stationary” are “x” and “t”, then

x(\tau) = \frac{c^2}{a}Cosh\left(\frac{a}{c}\tau\right)-\frac{c^2}{a} \approx \frac{c^2}{2a}e^{\frac{a}{c}\tau} t(\tau) = \frac{c}{a}Sinh\left(\frac{a}{c}\tau\right)

this is lined up so that x(0) = t(0) = 0 (which means that everyone’s clocks are synced when the engines are first turned on).

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33 Responses to Q: If time slows down when you travel at high speeds, then couldn’t you travel across the galaxy within your lifetime by just accelerating continuously?

  1. Buck Rogers says:

    In theory (not necessarily a fact) according to Albert Einstein we cannot travel faster than the speed of light. In the eras before us, our earlier scientist believed it impossible for man to fly or to travel faster than the speed of sound; however, with imagination, discovery, and with persistence… those beliefs were eventually proven wrong.

    In fact the laws of physics are not actually absolute laws at all, but are only “laws of theory”. What we know for fact is what we know by proof; to dismiss the premise that we could possibly travel faster than the speed of light is to dismiss our ability to discover new types of propulsion or to time travel.

    We in this day think we know it all, as did our predecessors, but we don’t know diddly; it’s called egotism; our whole university system revolves around it. Perhaps in the future to travel across the galaxy one might not need a rocket ship at all. The only thing limiting mankind, is his belief that we already know everything; that’s called narrow mindedness.

    It wasn’t that long ago man thought the earth was flat, and any thought otherwise was either considered by the experts to be heresy or lunacy.

    We should know by now to say something is impossible, is to say we’re just too ignorant to imagine it. Even Albert Einstein said “imagination is much greater than education”. Luckily we still have dreamers, discoverers, and visionaries; sadly our hindrance is from the naysayers who we call experts.

  2. Jordan says:

    Well, totally true. But why shell we move across space, using Newton’s third law (actio, reactio) pulling out behind us “something material” and move forward, instead wrapping the space in front the rocket and expanding behind us. Yes, right – this is the Star Treck Warp-drive conception. Only concluded, but never done before. Noone can say, if it is possible, but some physical phenomena show, that it might be a completely possible. The basic effect, used as prove such thoughts is the Casimir Effect. which is proven more accurate in the past few years. At this point, we cannot talk any more of Newton’s low of motion, but referring to the QFT (quantum field theory) and vacuum fluctuations. It is now the question – how to transform a vibration into a controlled motion. To all skeptics I’d like to give a link to an article “Light created from a vacuum” : http://www.sciencedaily.com/releases/2011/11/111118133050.htm which I personally consider as a binding part between material and non material world. So, finally, it is a question of a engineering construction, which combines the known Phenomena. The mile stone to all above is to start thinking, that more than 3 dimensions exist. Please, comment further.

  3. Nikos D says:

    Warp theory is all well and fine…apart from a tiny little hitch – exotic matter – and the fact that nothing close to it has ever been observed. In fact, my guess (and Mr. Physicist, correct me if I’m wrong), is that most respectable physicists have no reason to think such matter could exist.

    As for rocket ships and galaxy-traveling…everything we know about physics indicates that we could never develop interstellar space travel. We probably won’t even make it to Alpha Centuri – EVER. We could (and will), send machines to various places one day, but it’s a relatively safe bet that the only space exploration any intelligent being will do, will be with tiny drones.

    Getting intelligent life anywhere is highly unlikely…actually, just a plank’s length from impossible. I mean, you could, in theory, sufficiently genetically modify humans (and we’re talking mass modifications), to get them to survive being put in stasis, (or whatever’s needed to get them there alive)…but we’re talking tens of thousands of years to get to the closest star system (thousands of years in the best case scenario). Not that we’d want to send life there…it *seems* there’s nothing there for life to colonise anyway (but until we get our trusty Virgin drones there, we can’t know for sure).

    I wish I were wrong – but even if we’re missing some really important puzzles pieces that would permit interstellar travel for an intelligent life form, you’d think if it were possible, you’d have a few civilisations around the galaxy, sending off billions of drones to scout each habitable star system, and at least one of them would have set up shop here.

  4. MatthewC says:

    @Buck Rogers: Special Relativity is a fairly accurate description of reality, proven time (hehe) and time again. If you don’t believe me turn on a GPS. We aren’t saying S.R. (or G.R.) prohibits anything and everything from ever travelling FTL from any perspective, just that you can’t do it through regular space. When we discover new things we don’t discard the old stuff, we augment it. G.R. augmented Universal Gravitation, it didn’t get rid of it. S.R. will always tell us that under conditions we can currently produce, massive objects cannot reach c. Nobody actually thought that we couldn’t break the sound barrier!!!! Whips have been doing it for thousands of years, we knew this. I don’t know why people keep repeating this silly notion.

    In this day we think we know it all? Alright physicists! Pack up, go home. We got it all figured out! Nopers, ain’t nobody today doing any research because we got it ALL figured out. Zero unanswered questions. How absurd. Physicists and their ilk are very likely the first to say we don’t know, but here is what we do know. Perhaps we might travel the galaxy without a rocket. But we almost certainly won’t travel FTL WITH a rocket.

    We knew the Earth was round some three hundred years B.C.E. Or maybe it was C.E. I forget. Not important, the point is, science is new and shiny and spectacular and has brought us from peasantry to a quality of life greater than that of kings in a relatively short time. That same science tells us that a massive object cannot travel through normal space faster than a beam of light in a vacuum.

    We have plenty of visionaries, they are in labs shooting lasers at stuff and doing supremely complicated math and being incredibly frustrated that this stupid machine won’t work and why won’t the University get new equipment and what is that smell? But I digress. No okay. Seriously, why does the physics lounge always smell like that?

    We are due for another scientific revolution any time now with consequences we can’t yet imagine opening doors to machines we literally cannot yet conceive of. Our hindrance? These hindrances, are going to be the people who make the discoveries that make possible FTL travel if it ever is possible. Hindrances. The author of this column must be aghast at what he/she reads in these comment sections. Especially given the next comment.

    @Jordan: Yay warp drives! Theoretically possible, theoretically impractical. The amount of energy needed to adequately warp space to do anything would require, even with White’s design improvement that I in no way understand at all, is about the mass of Jupiter. I like looking at Jupiter sometimes and would be put off if someone used it to gas up their space car.

    The Casimir Effect has absolutely nothing to do with the curving of space. That is General Relativity, the C.E. come from some part of quantum mechanics I don’t yet understand, I think, maybe it comes from something completely different. But I do know it doesn’t have anything to do with G.R. I also know that since the plates return to their original position the net work done is zero. since there is zero net work there is zero net energy as energy is defined as something’s ability to do work.

    We always have to talk about Newton’s laws of motion, even if it is a conversation of how to get around them.

  5. John David Dunson says:

    @Buck Rogers:
    if there is a human alive that thinks they know everything, i’ve yet to meet or even hear of him. nobody thinks we know everything. especially not the experts. we’re not in the dark ages anymore.

  6. Nikki Ty says:

    Interesting link from Jordan. Now maybe we’re all too concerned with mass and transporting mass across the galaxy. I’d be more able to believe its a question of alternating between mass and energy. But then I’m not a physicist … I’m a mystic who believes my soul is energy and has created and is in the process of creating what seems to me to be my physical reality. Just for entertainment … as Bentov suggests.

    Hoiking space vehicles across the cosmos seems pretty primitive to me. I’ll save my energy to get things up and running once I reach destination.

    On the other hand there are those worm holes. Which are an intriguing possibility.

  7. MatthewC says:

    @Nikki Ty:
    E = m * c^2 and some other less poetically small and catchy stuff. Point is, energy and mass do the same thing, namely warp spacetime. Energy cannot travel faster than the speed of light conventionally either. My physical reality seems pretty similar to yours, at least we are both reading the same article on the same internet created by your soul, so thanks! But in all seriousness, if reality is just created by individual souls then the entire scientific enterprise would fail as any two individuals would need to create the exact same reality to get the exact same result from the equipment malfunction. And trust me, a Ph.D. candidate’s reality is far different than his/her advisor’s, yet they both conclude the machine’s malfunction is due to the crack in the 30 year old vacuum tube. So it seems an improbable conclusion, even though to you this seems like just a paragraph or two (or three, who knows, haven’t gotten that far yet) popping up on your screen in the comments section of an intriguing article about Special Relativity, I laughed, sent a humorous text to my lovely girlfriend, and considered lowering the temperature on the thermostat while typing this. I didn’t by the way. Open windows are good enough. I don’t feel like something created for your entertainment. Been wrong before though, well, at least didn’t give the answer the professor wanted, but he never said it WASN’T a photon and that made finding the mass much easier lol!

    But yeah! Wormholes are very neat! I know very nearly next to nothing about them, can’t do the math yet, but how cool is the idea of bending spacetime to bring two points together?! I can finally tell my college freshman self to not bother with boring old Engineering and just go into physics straight off and save yourself two years of misery! But I didn’t get a visit from me, so I doubt we will have access to them in our lifetime, however long that may be yay medicine and the other icky sciences!

  8. Jordan says:

    @MatthewC – Casimir effect and the Energy Integral (your net work example) does not have anything common indeed. And they should not have, because they are two different things. When we speak about energy conserving low, we consider it within a closed system (i.e. thermodynamics). When we speak of vacuum fluctuations measured by Casimir effect, we do not measure any Energy. We think, we believe actually, that we measure a property of the space. If you want to apply a conserving low, which shell involve an mathematical integration and also a relation between Integrals, such like = or (comparing numbers), then by Casimir’s effect you probably have to integrate ofer the Planc’s measures between the plates and outside them. The simple calculation, without adding any numbers show, that space between the plates has less atomic bits, where matter can be, than outside. It is described by a simple relation, like INSIDE < OUTSIDE. Replace both with Integral values and the relationship still keeps. anyway. The mentioned effect do only prove one thing – a vacuum fluctuations, where by we consider the vacuum not as empty space (empty from matter, atoms, molecules, no light, no sub particles etc), but as a super fluid. major property of such fluid is to be everywhere it is possible to be in a closed system. So further – we do not wrap any space by such kind of fluctuations. We only see, that a Matter (plates) do attract themselves when space between them get less. No wrapping, once again. If we do not wrap, we do not need energy, regarding the GR. Please, keep comment. Good ideas may be born 🙂

  9. The Cool Dude says:

    Mathimatically, an infinite number of dimensions (known in math as variables) could exist. Einstein disproved Newton’s equations by vamping one single variable up to a ridiculous value, and created a new limit to what the universe, and intelligent life like ourselves, are capable of. Some brilliant scientist of the future may very well come along, vamp up (or down!) some other variable, and fix Einsteins equations like he did Newton’s. Because we haven’t done it yet, only time will tell. There are so many variables to test, but there is so much time for people to do it in.

    Fun, mostly unrelated fact:
    Most notable particles in the universe emit a force on all objects, inward or outward, the strength of which is inversely proportional to the square of distance of the object it’s acting on. In that way, the force is greater on the inside than on the outside. If there were to be a particle which produced force which was directly proportional to distance, greater force on the outside than on the inside, it would expand the entire universe dramatically at higher distances. Furthermore, if it could break the laws of special relativity, it would not matter one bit where the particle was actually located. It would produce an effect on the universe exactly identical to the spacial expansion already in place.

  10. MatthewC says:


    I understand that there is some pressure exerted on the outside of the plates from virtual particles, whether this has to do with their de Broglie or something else I do not know. The reason I do not think it could ever be used to produce any usable energy is due to the fact that a non isentropic process will be necessary to pull them apart again. That said, I know only the general idea of the Casimir effect and none of the real physics going into it.

  11. Greg says:

    @Buck Rogers, you should read this excellent essay by Isaac Asimov

  12. exstud says:

    Maybe far fetched, but couldn’t we use gravitational forces of stars and planets to keep the acceleration going?

  13. Jordan says:


    If your spaceship was so big to experience the attraction of a Planet/Sun – yes, perhaps it would be a possible way to save some fuel. The idia of using gravity acceleration is used by spacecrafts, which have only a mission to accomplish, but not saving a life time of a crew members. What I say – saving fuel based on gravity, spend a time of the travel, which is not good for the crew.

    What my point of for all comments posted by myself above, was to move the mind flow of any participant in this discussion to a rails, which does not include mathematical limitations. Because…… the Maths is always a foot step behind the physics. Why? Because Math does a model of a Nature Phenomena, based (mostly) of using real (not always) numbers 1,2,3,4,13.3, Pi, Phi etc. Describing a physical law of any mechanical (newton) motion, we model the dependency between any route for any given time and so we define the law of motion, the law of acceleration. And any physical test proves our calculations. Thus all calculation and models on a piece of paper are worthless if they are not covered by a real test scenarios. Anyway. The point is – we have to start to think different and apply a new concepts into the Math’s tools and get a different results. The idea for space travel, not using 3rd Newton’s Law, but wrapping the space seems to much people impossible. And yes, it is impossible, if you think for the motion in sense of Newton. If you think for any motion in sense of Einstein, and specifically in the sense of Quantum Theory – wow, we have a totally different picture of moving particles which does not cover the motion of a train. The point is – Newtons motion is a special case of moving a big set of small particles (we call them atoms and molecules). Particles do move in the space, but their movement is more likely propagating an information of their properties, from one point to other. We can detect particles behavior by measurement of physicals properties but we insert also distortion. So what we measure is not reliable, because of our measure instruments. So the concept to work with particles is wrong, if we accept them as a smaller part of the matter we know already (atoms and molecules). If we consider that the real nature is the nature of elementary particles, and all other (the matter we know and also not know – dark matter) is a special case of combined particles and it defines it rough laws of newtons motion and their mathematical form s=v.t etc, why instead of thinking how to move in the space with rocket fuel, we start to think how to convert a human body into elementary particles and after that combine them to the same shape as initial?! Does anyone of you ever heard of photon, frozen at one point in the space? Nooo. But no one ask the question, why a photon always moves in a direction. Does it uses a chemical fuel? Noooo. If we convert a matter to a particle, there will be no one scientist who will ask the question how to move a photons from a matter. Photons just move.

    Guys, no matter how many words we spent to describe our ideas and thoughts. This idea exchange is very helpful if it has a result. And my point shortly is – let us change the concept of thinking. Let us find out how to propagate the information for a chunk of matter with photons and condense it to its initial form, we will no more need the idea of acceleration or chemical fuel. Because light moves with the speed of light and is slow down only by the medium it moves through.

    You see, if you change the concept, the problems we face are no more how much Oxygen we need for fuel for our space shuttle, but how to get previous shape we used to be. Sounds phantastic right?! Yes, it is. Sounds absurd. Sure. We never did it before, so we can freely reject it. We have no experience with such technology – so we can reject the possibility of such existence of such technology.

    I am having very bored business call – so I used the time during the session to write my thoughts. Wish you all good luck of generating Ideas. This is what we really need now – new ideas, no matter how silly they may look. The only difference whether an idea is genius or ridiculous is defined by our view point and estimation.

  14. e c peters says:

    as far as space travel goes , two points of thought, one is velocity, the other being time. But the goal is distance. Our only hope at present is that intelligent life will discover us and recognize us for more than just a curiosity.
    Theory. Time dilation is the key to space travel.

  15. Houdini says:

    “That said, if somehow you could accelerate at a comfortable 1g forever, you could cross our galaxy (accelerating halfway, then decelerating halfway) in a mere 20-25 years of on-board time. According to every one else in the galaxy, you’d have been cruising at nearly light speed for the full 100,000 years. By the way, this trip (across the Milky Way, accelerate halfway, decelerate halfway, anti-matter fuel, photon drives) would require a fuel-to-ship ratio of about 10,500,000,000 : 1. Won’t happen.”

    You’d also be encountering whatever interstellar dust you hit at a speed differential of almost c. And the starlight from the direction you are travelling towards would be profoundly blue-shifted. So your ship is going to need some crazy shielding.

  16. Alan Christ says:

    I think you all have not considered , If a clock on earth said 12:00 and a clock at the other side of the Universe said 12:00
    and it took five minutes to get to clock1 [earth] to clock 2 [end of universe] both clocks will read 12:05..
    It dose not matter if you were travaeling 1 mph or faster than the speed of light.. clocks do not change time just becouse you traveled super fast to get somewhere..and the clocks would say the same time with or without light in the universe, I would like to no how this could not be correct?

  17. Not a physicist says:

    @alan Christ .. I think you are not understanding the theory of special relativity correctly. Keplar-186f. You are thinking of time as a clock, ticking once every second, when in reality, time is effected by numerous other forces in the universe. It is more accurately describe as spacetime, as time can be effected by not only speed, but gravity as well. So in your example, let’s say we have 1 person standing with a stop watch on earth and 1 person standing on Kepler-186f (earth sized planet recently discovered in the habitable zone of the Cygnus constellation about 500 light years away). For arguments sake, gravity, orbit speed, and Galaxy speed are identical for both planets, so the 2 stop watches would be identical as well. You also have a stop watch around your neck. The person on earth yells “ready, set, go!” (Loud enough for the person on Kepler-186f to hear!) and everyone starts their watch and you take off from earth for your 5 minute trip to Kepler-186f at 99.999% the speed of light. When you get there and compare the watches, the watches on earth and Kepler-186f say 5 minutes exactly. So your example above would be correct (only bc earth and Kepler-186f had identical forces acting upon them). Then, you look at the watch around your neck and it says 4 minutes and 10 seconds. But how can that be? That is because time is relative to the forces that are acting on an object. A larger scale, and more accurate example- you fly a round trip to Kepler-186f at the speed of light, which is 500 light years away. When you get back to earth, 1,000 years have passed, but you have only aged 10 years (I know the math is not right. Just an example). That is because of the connection between space and time.

  18. Wes Tausend says:

    Thanks, Physicist, for another of your great explanations. I sincerely do enjoy your take on science. 🙂
    The best laid plans of mice and men. If only our entire physical being wasn’t so obviously contained within the claustrophobic confinements of E=mc²…

  19. N J Holtzman says:

    If Traveling many light years from distant galaxy’s at incredible speeds, could it be that we have no true concept of high speeds. We assume we can bend space so that we can bend time and speed. I am confused.

  20. Greg says:

    So we can! travel faster than light.
    It depends ONLY on which point of view you take.
    Viewing from Earth we will never see our astronaut go faster than light.
    But our astronaut WILL.

    Before he leaves earth he MEASURES the distance to his target. Say it’s 100,000 light years. He also checks his calendar watch.

    Then he accelerates, at say, 1G till he reaches the midpoint, reverses and decelerates at that speed.

    When he arrives he makes the same two observations.
    Using Newton he compute his speed as distance over time.
    And sure enough it declares he went MUCH faster than the speed of light.

    The only thing I don’t understand is why physics teachers (and practically everyone else) keeps assuming one point of view without ever pointing out that there are an infinite set of POVs and that he’s selected Earth because he was in a mood to do so. Or because he’s vain, but mostly just because s/he too is egocentric.

    Einstein’s theory simply doesn’t say what people say it says. (Try reading it).
    It says that we, here on earth, will never OBSERVE any mass-bearing object accelerate to and beyond C. It doesn’t even say you can’t go faster than light (tackyons) . It’s only about limits on acceleration observed by a second observer (us, here).

    I spell it tacky in the spirit of humour.

  21. Zant Burdine says:

    Oddly enough, Im writing a short story about 3 guys working from their garage, trying to build a better speaker, and inadvertently instead build a working Quantum Door. This tied in with software from a cell phone, they slowly expand their business to completrly change the direction of everything American, refill all the lakes, get people into space on a large scale, Help move human populations to the moon, venus, mars, and beyond. No Humans would be Piloting the Hundreds of Saturn 5 or Space Oddesssy vehilces or silent running vehicles. People would use Quantum doors to Travel vast Distances, with little power use, Vehicles would be Designed with a fill cap, and Doors mounted to the outside of the ships. when they run out of fuel. a Service tech would connect the hoses with a Hydrogen station located near Saturn/Jupiter to take advantage of the gas giants free atmosphere. Mankind would Conquer Space itself, and we can skip arguing over all this Math. Time would not be a factor at all. People would go back to enjoying Life. One of the biggest hinderances to Human development of space at the moment is the abilty to get out there and experiance it. if every school kid could go to the moon on a daily basis, we would see a explosion of growth unlike any seen since the 1920s industrial revolution.

  22. Wes says:

    I mostly agree with Greg. I think his response is quite well written.

    “Greg says:
    February 20, 2016 at 5:06 pm

    So we can! travel faster than light.
    It depends ONLY on which point of view you take.
    Viewing from Earth we will never see our astronaut go faster than light.
    But our astronaut WILL. …..”

    What Greg has said demonstrates the essence of relativity, aka the Principle of relativity ( https://en.wikipedia.org/wiki/Principle_of_relativity ):
    “In physics, the principle of relativity is the requirement that the equations describing the laws of physics have the same form in all admissible frames of reference. For example, in the framework of special relativity the Maxwell equations have the same form in all inertial frames of reference.” No frame of reference is more valid than another.

    In a way, the light speed limit seems in the eye of the beholder.

    In a peculiar twist, the astronaut should also see the clocks in his home base slow down as the universe speeds by him ever faster. When he (or she) gets home, the ride will still have been faster than the speed of light, even by the clocks on the walls of home. One other easy way to look at it is that on the way out, the distance got shorter for everybody. And on the way back too.

    The one minor flaw… is the ship cannot contain enough fuel to overcome the relativistic increase in it’s mass towards infinity. This is true whether one wants to consider the point of view of the ship propelling forward, or the rest of the universe propelling backwards… in which case the inertial mass of the universe becomes infinite instead of the ship doing so. More and more ship fuel will only add “starting” mass which will become even heavier relativistically, in addition to the original mass gain of the lesser fuel. At anything less than lightspeed, time passes rapidly. Fail.

    Only if the ship were to be converted entirely to photons by totally disassembling ALL the atoms, would the mass problem disappear. And photons travel at the speed of light only, not faster… well because they are light. All energy comes from disassembling atoms, no matter how crude the fire. The mass of all the exhaust (smoke) plus the leftover fuel “weighs” just a bit less than what the ship (or campfire) started with.


  23. Greg says:

    A footnote. Einstein did not like the use of the word “relativity” to describe his theories. He preferred “invariance” theory. The opposite of the way it is almost universally thought of today. He was fascinated by quantities that DIDN’T change for any observers regardless of their state of motion. And his work was about observations, not realities.

    His response to the jab “everything is relative” would likely be something like “NO!”, not everything is. I search for those things that re NOT relative.

    So his theory says: no observer will ever perceive an object with mass reach the speed of light. He didn’t say you can’t go AT the speed of light nor FASTER than the speed of light. He only spoke of what an observer can, and never can, see.

    More great trivia about relativity at: http://discovermagazine.com/2008/mar/20-things-you-didnt-know-about-relativity

  24. John David Dunson says:

    it doesn’t matter what he said. his published works speak for themselves. and they tell us all about how things are relative and how light is the ultimate speed limit.

  25. Wes says:

    QUOTE Greg says:
    June 30, 2016 at 10:46 am
    “.. A footnote. Einstein did not like the use of the word “relativity” to describe his theories. He preferred “invariance” theory. The opposite of the way it is almost universally thought of today. He was fascinated by quantities that DIDN’T change for any observers regardless of their state of motion. And his work was about observations, not realities.
    ..His response to the jab “everything is relative” would likely be something like “NO!”, not everything is. I search for those things that re NOT relative.
    ..So his theory says: no observer will ever perceive an object with mass reach the speed of light. He didn’t say you can’t go AT the speed of light nor FASTER than the speed of light. He only spoke of what an observer can, and never can, see….”

    I appreciate the link. I agree that is precisely correct, Greg.

    Invariance theory is nowadays more of an abstract algebraic expression, but Einstein fortunately thought in terms of the invariance of some logical geometry like Galileo, allowing himself to recognize the full significance of an otherwise ordinary formula like E=mc². Max Planck was the first to use the popular term Special Relativity (in a lecture, I believe), and Einstein acquiesced later.

    In deference to thinking like Galileo, it is not possible to determine fundamental qualities using equations alone, something that seems lost on modern science in a seeming modern disdain for the sweeter fruit of pure philosophy. As an example, though a master mathematician, the sweet philosophy of Heliocentricity would never have popped out of Ptolemy’s numbers by itself. And though Ptolemy’s lesser Geocentric coordinate system remains still technically valid and useful today, in terms of intellectual satisfaction, it is fortunate the philosophy of more simple geometry prevailed.

    Since Einstein’s family was involved in electrodynamics (they built motors, generators), he developed quite an early personal interest and was later intrigued by Maxwell’s equations which derived an invariant speed limit for magnetic, i.e. electrodynamic, waves. A subsequent discovery that light was a magnetic wave, and the combination of Michelson–Morley’s search for Absolute Rest (using light), also implied that the measurement of light therefore had an invariant speed limit. Einstein ingeniously put two & two together and came up with another new coordinate system that is again mathematically valid and at least works a little bit better for now. “At least”, I say, until the conflict between Quantum Dynamics and General Relativity is publically resolved.

    So now we have two theoretical limits of motion for all observers, the speed of light which is measurable, and the root of Absolute Rest, a suitable light-speed substitute the measurement of which continues to appear elusive. Or so it seems.

    QUOTE John David Dunson says:
    June 30, 2016 at 3:57 pm
    “..it doesn’t matter what he said. his published works speak for themselves. and they tell us all about how things are relative and how light is the ultimate speed limit..”

    Let no footnote go unanswered…

    Since observations in Cosmology imply inordinately higher-than-light-speeds exist (summarily excused with ad hoc explanations), and quantum entanglement peeks out at us and grins like a cat, it might not be so prudent to say, “they tell us… how light is the ultimate speed limit”.

    Rather light-speed appears more the ultimate speed limit of wavicles conceivably measured by precise standard rulers made of platinum and/or peak-to-peak magnetic wavelengths. In the end, our objects and speeds are proudly measured by objects and speeds that are but made of themselves. They sure look constant. Or so it seems.


  26. Greg says:

    Does anyone remember Larry Niven’s use of a “Bussard Ramjet” to overcome the infinite fuel requirement/argument? Essentially the ramjet collects hydrogen as it moves forward, ignites it to fusion, and never really runs out of gas.

    I don’t know the physics well enough to testify as to the plausibility of this method.

    – Greg

    PS: more at https://en.wikipedia.org/wiki/Bussard_ramjet

  27. Angel says:


    Albert Einstein never stated the speed of light to be a limit, but you can conclude directly from his special relativity equation that it is not possible for a massive object to ever accelerate to the speed of light. The behavior is asymptotically in the sense that as we approach light speed, the relativistic mass and hence the energy of the object approaches infinity. You will need infinite energy, which implies infinite fuel, or infinite mass, and both require infinite amount of acceleration time to achieve the speed of light. However, the issue of having to travel eternally with infinite mass is problematic at best. Assuming these conditions were even possible, we are only achieving catching up to light, but we cannot travel faster than light because if traveling at light speed requires infinite time and infinite relativistic mass, ergo infinite momentum, then accelerating even more to travel faster than light requires greater-than-infinity time and greater-than-infinity energy or mass. That is unless we propose the existence of tachyons, wavicles which always travel faster than light, but they have an opposite yet equal limitation to us: tachyons can never decelerate to travel at only light speed, they must always travel faster for similar reasons than us. The difference between a standard wavicle and a tachyon is that a tachyon has imaginary mass. However, the mathematics work the same.


    You err. Science was never meant to be able to express and explain fundamental qualities with equations alone. Science serves itself with mathematics, but science is not identical with mathematics. Saying that modern science relies on philosophy is at best an insult. Every scientist knows numbers by themselves in a vacuum are meaningless. They need a conceptual context in order to be meaningful. Saying 3 + 5 = 8 is not science because it is meaningless on its own, it tells you absolutely nothing about the nature of the universe. If you say 3 m of vector A + 5 meters of vector B = 8 meters of vector C, now we are taking science, because it now has a context and the numbers mean something. But this context is conceptual science: it pre-requires knowledge of vectors. So of course numbers by themselves will not tell you anything about the geometry of orbits or the dynamics of it.

    You also err terribly by trying to counter an argument about relativity theory using quantum theory. It is beyond obvious that quantum theory is incompatible with relativity theory. Quantum entanglement is irrelevant to this discussion. The question we are discussing now is whether relativity theory does indeed imply that speed of light is the limit for measurable movement or not, quantum theory has nothing to do with it.

  28. Angel says:


    The theoretical ramjet presents many problems and it cannot be possible.

    1. For the ramjet to travel at the speed of light, it must use infinite fuel for infinite time. The problem is that the ramjet method you are proposing does not provide a supply of infinite fuel, given that there is a finite amount of hydrogen available in the observable universe, and perhaps in the universe as a whole.

    2. The ramjet could not travel for infinite time since the universe itself at some point is expected to end, and the ramjet will end with it.

    3. There is not enough hydrogen within the interstellar vacuum to propulse the ramjet at such a high speed. Tons of it are required, but the amount that can be found amounts to micro quantities.

    4. The electromagnetic field itself is problematic: because of the size it covers, it is of the magnitude of a planet. A planetary magnetic field traveling at such a high speed will cause too much cosmic chaos, and it is more likely than not an accident will occur.

    The ramjet method is not really plausible. How does one achieve infinite fuel? How does one achieve travel during infinite time? You need to travel an infinite amount of time before achieving light speed, but you are traveling during infinite time, then there will never be a point at which you reach light speed, because at the moment you do, the traveling time is no longer infinite, this breaking the equation.

  29. Greg says:

    @Angel: Albert Einstein never stated the speed of light to be a limit, but you can conclude directly from his special relativity equation that it is not possible for a massive object to ever accelerate to the speed of light. ”

    That is almost exactly what I’ve been saying. And, you’re still misstating. All we can say is that we, here, on earth will never OBSERVE the phenomena you described. But we CAN see objects with a relative speed greater than zero. However, we will provide an earth-centric explanation. But FTL is NOT prescribed by SR.

    Also, if you READ the article in Wiki that I sited you’ll see that no one is yet certain about the feasibility of the Ramjet. There are numerous complications and the jury is still out. You will not find the word “cannot” in the article, though you present it as a fait acompli.

    Nearly everything you are saying is egocentric. You’re describing what we see here on earth. Other observers have very different observations.

  30. Angel says:


    Wrong. Special relativity states clearly that in no inertial frame of reference you can observe such phenomena. It is not just applicable to Earth, but to the entire universe. No situation in which a combination of two frameworks of observer-observed will experience the phenomenon of either body traveling or accelerating to light speed or faster will ever occur. Not egocentric at all.

    The Wiki article never says “cannot” because Wiki never gives conclusions, only data. The conclusions are made by the reader.

  31. Wes says:

    I don’t suppose The Physicist minds a little friendly debate as long as we are civil.

    Angel says:
    You err. Science was never meant to be able to express and explain fundamental qualities with equations alone. Science serves itself with mathematics, but science is not identical with mathematics. Saying that modern science relies on philosophy is at best an insult.”

    I mostly agree with you Angel. There is sometimes a popular modern opinion that everything is mathematical. But my objection is that mathematics is a (very useful!) subcategory of Philosophy which really totally encompasses that which science relies on.

    Actually I think mathematics is a sub-subcategory of geometry which is a higher direct subcategory of Philosophy. Although I admit today math is often used as a term to denote both arithmetic and geometry. In some ancient circles, mathematicians were commonly known as Geometres. So I think saying modern science relies on philosophy is not an insult at all, but rather a fundamental truth.

    For the differences of geometry vs math, it might pay to consider the anthropology of which likely came first. Humans are fairly unique in that, as a tree-dwelling primate that leapt branch to branch, the visual spacial ability of instinctive geometry became a carefully honed survival skill. One must after all, be able to picture and calculate in ones mind, the correct parabolic curve of each leap, or risk falling.

    This “geometry/gravity” skill in turn became the basis for a tree-dweller being able to throw a weapon in a parabolic curve, leading the target, being more concerned with the study of geometry and gravity in general and finally paved the way to shoot well-aimed arrows at Mars, all further enhancing survival, we hope. Only the gods can build a tree, but only a tree could build us.

    Looking back again, the deft pictoral geometry eventually became a hand-smitten symbol representing 3D geometric objects on cave walls, sound and finally arithmetic symbols which appeared eons later. Following geometry, arithmetic lastly became the perhaps evil skills of counting goats, the size of geometric pastures and the spare arrowheads to protect them with, a warlike thing not required when goats were free before the advent of early capitalistic private ownership. This marked the subsequent semi-decline of hunting and gathering though it is ever in our blood. Merely domesticating plants and animals is secondary to retaining possession, lest the hunters amongst yet gather your stuff, a problem that since continues to this very day on Wallstreet.

    Philosophically, math has it’s shortcomings in that it often cannot prove which geometry is true, such as heliocentricity versus geocentricity or prove answers to many quadratic equations, only that a seeming useless geometry may seem irrational or even false. We must rely purely on our instinct, our philosophy for our conjectures which form the basis for our number-laden theories. So you see, I haven’t erred. Philosophy is not an insult; a remarkable journey in live science maybe.
    “You also err terribly…”
    On the entanglement problem, I combined quantum with relativistics which allows an ultimate speed faster than light (godspeed?), but I haven’t done it publicly. Greg notes that lightspeed is a MEASURED speed limit and that is the simple key. Except for entangled particles, ordinary particles still require considerable acceleration. However to my credit, I did note above that an evident mass increase alone is sufficient to preclude such a trip. But since I certainly shouldn’t be encouraged to use a non-peer reviewed model on this revered blog, and standard relativity disallows it, I’ll sheepishly give you this one. You are right, Angel.


  32. GREG ROBERT says:

    In the end mathematics is nothing but a system for manipulating meaningless symbols. It is PURELY lexical. It gains no truth, no usability, no meaning until humans assign meanings to the symbols and then make the jump that when the origin symbols are typographically manipulated, under certain lexical rules, that the resulting symbols must be as valid as the original symbols.

    The number 2, for example, means only “two-ness”. When you say “2 apples” it takes on physical meaning.

    Thus mathematics is, in it’s final and purest form, a typographical lexical system.

    – g

  33. RoundEarther says:

    @Buck Rogers

    In answer to your first comment flying and travelling faster than the speed of sound were considered to be engineering problems not fundamentally impossible, the attitude of “we were wrong in the past so we’ll be wrong again” although probably correct is useless, we are closer to being right than we were before and must continue to make progress but unless you have evidence that we can go faster than light go by the overwhelming evidence that we can’t.

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