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Speed limit (of light)

  1. Jan 9, 2004 #1
    I'm not sure I understand the limit on the speed of light correctly. After all, it appears if I accellerate constantly, even mildly, for a long enough time, I should be able to reach any speed at all. I have heard Dr. Hawking say that the reason is that as an object increases in speed it also increases in mass. By the time it reaches the speed of light, it is too massive to accellerate any futher.

    However, I am still wondering about how this would operate on an object whose accelleration was powered by the mass energy equivalence. Wouldn't the energy increase as the mass increased? It seems to me these effects should cancel.

    I am thinking that there must be a relationship between the idea of a speed of light and the idea of an event horizon. It has been noted that an object can pass through an event horizon, only no information about the object can make the return trip. Is it possible that a mass energy drive ship could pass through the speed of light in the same way an object can pass an event horizon?

    Maybe someone here has some illuminating thoughts to share on this question.

    Thanks for being here,

    Richard
     
  2. jcsd
  3. Jan 9, 2004 #2
    You need to remember that the event horizon is caused by the limitation of the speed of light, so if you could pass the speed of light, then you would change the event horizon.

    As for your an object whose accelleration was powered by the mass energy equivalence, as the object accelerates it would need to loose mass to energy, and would burn out before you reached the speed of light. Besides that, you need to remember that newtonian mechanincs doesn't work at high velocities, and you have to use GR which forbids objects to move faster than c.
     
  4. Jan 9, 2004 #3
    Thanks,

    You said:

    "As for your an object whose accelleration was powered by the mass energy equivalence, as the object accelerates it would need to loose mass to energy, and would burn out before you reached the speed of light."

    I was thinking of a scoop drive proposal I read about which runs on fuel it collects as it passes through space, so it wouldn't have to "burn out".

    You said:

    "Besides that, you need to remember that newtonian mechanincs doesn't work at high velocities, and you have to use GR which forbids objects to move faster than c."

    I remember this well, thank you. It is to the root of my question. GR forbids. But surely if there was some forbidding, there must have been some "before" for GR to forbid in. So are you not saying that there was a time before objects were required to move slower than c? A time before GR?

    Thanks,
    Richard
     
  5. Jan 9, 2004 #4
    ?a better question?

    On second reading, this caught my attention. No matter how fast your speed, your local physics remains the same. If you were traveling at near light speed, which is permissable in relativity, you would still measure light as traveling at c. There would be nothing to notice at the "Event Horizon," because the EH is a creature of the "stationary" observer. A Stationary Observer has to be assumed in the definition of an event horison. Perhaps if you were on board tracking the origin of your trip, exchanging messages with the stay at home twin, as you passed the EH you would recieve no further messages from your twin.

    This is to say, in more formal terms, that the assumption of a speed of light in itself assumes a preferred frame of reference, which is that of the observer. Perhaps this brings us closer to the right question. There is a symetry involved which goes something like this: If I travel there, can I ever come back here again? Note that it is a symetry expressed in time, since the symetric sections are offset from each other in time as well as space.

    Thanks for being,

    Richard
     
  6. Jan 10, 2004 #5
    No there wasn't any limit on c before GR, and you can't use part of GR for the event horizon and not the speed limit.
     
  7. Jan 10, 2004 #6

    selfAdjoint

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    Richard is right. In the first place yuou don't just "travel fast", you travel fast with respect to some other frame of reference, say a planet or a mother ship. There is no absolute frame in which you travel fast wrt all observers. In particular, when you are not accelerating you are an inertial observer yourself, and you are obviously at rest with respect to yourself. This is Einstein's first postulate (in his final formulation). Te laws of physics are the same for all inertial pnservers.

    Einstein's second postulate is that all inertial observers measure the same velocity of light c.

    So if you were traveling at 99.9% of c relative to your mother ship, and not accelerating, then if you did an experiment to measure the speed of light relative to you, what you would get is c, not .0001c.

    So now suppose you accelerate away from your mother ship at some rate and you just keep on accelerating at that rate. Will you eventually reach "any speed"? No. As the mother ship observes you it will see your lengths getting shorter and your time passing more slowly. So it will see your acceleration dwindle as you get closer to c (relative to it, of course). Your speed curve (relative to the m.s.) from your constant acceleration, instead of being a straight line as in Newtonian physics, will be a flattening curve, with an asymptote at c. Your speed always approaches c, from below, but never reaches it.
     
  8. Jan 11, 2004 #7

    HallsofIvy

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    Actually, your original statement:
    is correct. The problem is "accelerate constantly". Since F= ma,
    a= F/m. Yes, it is true that, as velocity, increases, so does mass: it is given by m= m0/√(1- v2/c2). That means that, in order to maintain constant acceleration, you would have to be constantly increasing the force. Since mass increases without bound as v approaches c, your force would have to increase without bound.

    Surely that's not true (I assume you mean "limit of c on v" rather than some "limit on c"). In special relativity, the length contraction was given by x= x0&radic(1- v2/c2) which approaches 0 as v approaches c. The "speed limit" was already there in SR.
     
  9. Jan 11, 2004 #8
    HallsofIvy you are correct, SR came before GR, so there was a limit on c before GR, but I think that rtharbaugh1 was asking about a rule in Newtonian Mechanics, which does not limit v or c, in fact c was believed to be infinite or atleast unmeasurable at the time of Newton.
     
  10. Jan 12, 2004 #9

    chroot

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    A captain on a starship can fire his thrusters at the same rate forever, and the accelerometers on his ship will always record the same acceleration. All the pendulums and clocks and experiments on the ship will continue working just as they always did, at any other speed. He can accelerate indefinitely. He will measure the time taken in travelling between two points as constantly getting smaller as he accelerates. He can accelerate to a velocity such that distant galaxies are only minutes, or seconds, or fractions of a second apart. According to him, he is accelerating smoothly toward an "infinite" velocity, at which it will take zero time to fly anywhere in the universe. Of course, he cannot accelerate to infinite speed in finite time, but he can get asymptotically close. To him, aboard his starship, everything behaves just as Newton and Galileo said it would. There is no way for the the captain to deduce his "velocity" without looking out the window.

    The difficulty is in determining what an outside observer would see. His friends back on Earth would not see him reaching an infinite velocity. His friends would see him asymptotically approaching the speed of light. As he gets closer and closer to c, it will appear to his friends as if his clocks are running slower and slower. His heartrate will appear very slow, as will his speech and his oxygen consumption and his sleeping schedule.

    As you can see, the question "is there a speed limit?" is a complicated one. Its answer depends upon who is observing whom. The captain does not notice a speed limit according to his own watch, but those watching him do (according to theirs).

    - Warren
     
  11. Jan 12, 2004 #10

    russ_watters

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    I thought that as he accelerates he observes the distance between points in space decreasing? So while it may take less time to get to Alpha Centuari, he doesn't see himself moving FTL because the distance he thinks he's traveling is smaller. So he never calculates his own speed to be above C. Is that wrong?
     
  12. Jan 12, 2004 #11

    chroot

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    That's true. If he's using his own ruler and his own watch, he'll never go faster than c.

    If he's using his own watch and using the distances as measured by earthlings, however, he'll think he's going faster than c.

    Subtle point, but thanks for bringing it up!

    - Warren
     
  13. Jan 12, 2004 #12
    approaching the quasar

    This brings the question of what the captain sees of what the earthlings see. The earthlings might observe a quasar at the end of spacetime, and send the captain on an infinite drive ship to try to reach the quasar. Of course none of them would live long enough to see the captain reach the quasar. But what might their far descendants see of the captain? They might see that the goes slower and slower as it goes farther away, and eventually, it would approach what might appear to them to be a full stop. Generation after generation could pass while his aorta flapped shut. He would be frozen in spacetime like Orion the hunter.

    But what would the captain see as he approached the quasar? He looks at the quasar and it literally changes, evolves as he watches it. This evolution is a matter of scale. Or, as above, a matter of shifting the event horizon. The event horizon includes both the Planck and Schwartzchilde limits.

    But the captain can never reach his own S limit or P limit, because as he accellerates, his limit shifts along with him. He does not sense his S and P limits changeing as he accellerates at all.

    Now what happens as he approaches the quasar at the earthly limits of accelleration? The earth first becomes very far away, then approaches the limits of observable smallness, then passes that limit and eventually comes to the limit of smallness itself, which is the Planck limit. It also evolves to the end of its time line.

    I think a quasar will look quite different if sufficiently blue shifted. Temperatures and forces that seem enormous to us here would no longer be so drastic. Time would change, and temperatures rely on time for their measure. Time much longer would experience the temperatures much lower. Same with tidal forces.

    Thanks for being here,

    Richard
     
  14. Jan 13, 2004 #13
    And so, what happens if the captain decides to accelerate "forever"? He would find c speed limit (in his own reference frame) anyway, wouldn´t he?
    As long as his mass is constantly increasing due to the approach to c, he would notice that his acceleration (keeping the same engine thrust all time) would slow down more and more infinitely, then never achieving c. His watch would run perfectly, tho. Please correct me, if needed, in this reasoning.


    And what happens if I measure speed of light while hard acceleration?
     
  15. Jan 13, 2004 #14

    chroot

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    Yes, in the limit.
    No. His engines would work the same way the whole time. His accelerometers would always measure the same acceleration. If he doesn't look out the window, he will have no idea how fast he is going with respect to any other object. Keep in mind the mass increase is seen by other observing watching HIM; he doesn't feel anything different in his own spaceship.

    - Warren
     
  16. Jan 14, 2004 #15
    Being a physics newbie, I find hard to swallow (i.e understand) some concepts. The more I learn, the more respect Mr Einstein deserves for me.

    Sorry for my stupidity but, if "His accelerometers would always measure the same acceleration", how can that ship accelerate forever if c is the actual speed limit in any reference frame?
    Thank you all for help me understanding relativity (and for your patience).
     
  17. Jan 14, 2004 #16

    chroot

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    Keep in mind that his definition of "time" is constantly changing as he accelerates, as well. From an earthling's perspective, his clock will run slower and slower and slower as he accelerates. They'll also notice him accelerating less and less briskly as he gets closer to the speed of light. He, aboard the spaceship, is subject to that time dilation, though he won't feel anything different. The earthlings measure a slowing acceleration and a slowing passage of time, and the two go hand in hand to make the captain's measurement of his acceleration constant, for all time.

    - Warren
     
  18. Jan 14, 2004 #17
    The price of immortality is eternal exhile.

    So the captain goes on and on, and what do the far descendents of the earthling see? Does he still go on and on, even until the earth reaches the end of time? And is there any reason why the captain's time should end just because the time of the earth has ended?

    And my questions, and speculations, have to do with what the captain sees when he looks out his window. What does the universe look like to him, when he goes on beyond the end of earth time? I will repeat my question. The captain has gone off, accellerating toward the speed of light. Earthlings see her hanging out there toward the end of the universe forever. So what happens after twenty billion years? Earth Sun has burned out, the earth and everything nearby is entering entropy death, and our captain is still going. What does she see when she looks out her window? Does she still see the universe she has always known? Or does it all dissolve around her like a bad holodeck?

    Enjoy. Thanks for being here.

    Richard
     
  19. Jan 14, 2004 #18

    chroot

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    Re: The price of immortality is eternal exhile.

    He can go on and on until he pressed the 'stop thrusters' button. Earth's "time" has nothing to do with it.
    Time does not end, as far as we know, except in a Big Crunch. Why do you think the captain and the Earth have anything to do with each other?
    His "going on beyond the end of earth time" is wholly irrelevant. He will see the entire universe as being foreshortened until it seems like everything is in virtually the same place. Galaxies would seem only inches apart, and it would only take tiny fractions of a second (on his watch) to move from one to the other. Furthermore, he will see the universe as running very slowly. Nothing will ever seem to happen to the universe around him as he zips from place to place. The universe appears dilated in time to him (just as he appears dilated in time to others in the universe). In the limit as he reaches the speed of light, it would look to him like nothing ever happens in the universe at all. In the limit as he reaches c, the universe is all in one point, and the notion of time no longer exists. "Time stops," if you'll accept the sloppiness of that phrase.
    It'll look to her like Earth has scarcely changed at all. For her, the Earth is severely time dilated, and changes very very slowly. In the limit as she reaches c, the Earth will appear to her to never change at all.

    If this seems confusing to you, think about it this way: the light from the Earth travels at c, and it is the light from Earth which she uses to see what's happening on Earth. The information about the state of the Earth propagates at c. Let's say someone is flashing a laser at her every second, and she uses the period of the flashes to determine how things are going at home.

    If she is moving very quickly, a significant fraction of c with respect to the Earth, that information will appear "stretched out" to her, because each pulse has to travel much further than the last to reach her. The pulses will not arrive once every second; they will arrive only once every month, or year, or decade. In the limit as she reaches c, she is travelling as fast as the laser light is travelling. The laser light never catches up to her, and so she never sees any pulses ever again. It appears to her that Earth time has stopped completely.

    - Warren
     
  20. Jan 14, 2004 #19
    G this is fun but got to go. Be back in a few hours to feed the fires. Richard.
     
  21. Jan 16, 2004 #20
    One flash or two?

    I wrote:
    Does he still go on and on, even until the earth reaches the end of time?

    You said:"He can go on and on until he pressed the 'stop thrusters' button. Earth's "time" has nothing to do with it."

    Yes, the stop button is an interesting feature. But do we agree that as the captain approaches the speed of light relitive to Earth, the Earth twin sees the captain reach a state of near stasis in which the captain does not seem to move or age at all? The Earth twin might be able to calculate the distance to the captain at any time, but the spatial measurable will be the arc position of the captian in relation to the twin's sky. Just as the stars appear to us as fixed objects as we linger to look upon them in the night sky, the captain also will have an increasingly "fixed" direction from the earth. He might, for the sake of conversation, take off in the direction of the Orion's belt Nebula, and pass in a more or less straight line from here toward there. To the earth twin's view, the captain will always be "over there," and the twin could at any time point to the place where the captain is, along the line to Orion's navel.




    I wrote:

    "And is there any reason why the captain's time should end just because the time of the earth has ended? "


    You said:

    "Time does not end, as far as we know, except in a Big Crunch. Why do you think the captain and the Earth have anything to do with each other?"


    I am not speaking of Time here, but of the time of the earth. I think we all agree that the earth is not eternal, and will one day come to some sort of end. The Universe may go on, but earth will meet the fate of all objects, be it heat death in eternal expansion or tidal collapse in some sort of big crunch. I would not mention this except to establish agreement on basic principles.

    Of course the captain and the earth have to do with each other. They are definately connected in this story by birth, by the twin principle. However I do think it interesting, altho not established yet in this thread, that even the conception and development that lead to the twins as a reasonable device comes into question when we start to look closely at the concept of sequence of events. I believe I have read somewhere about a speed of light train on which some strobes are arranged and then it is shown that the sequence of flashes of the strobes will be seen as different, even reversed, by different observers.

    What does this mean to the twins? Is there a spatial displacement (such as accelleration into another frame of reference) which would result in the birth order being opposite? Is there a spatial displacement (to the frame of another observer, you see, where the time sequence is different) where the two are not twins, but sibs? Or to where they are only one being, undifferentiated?

    I wish to look very closely at this question.




    I wrote:

    And my questions, and speculations, have to do with what the captain sees when he looks out his window. What does the universe look like to him, when he goes on beyond the end of earth time?

    You said: "He will see the entire universe as being foreshortened until it seems like everything is in virtually the same place. Galaxies would seem only inches apart, and it would only take tiny fractions of a second (on his watch) to move from one to the other. Furthermore, he will see the universe as running very slowly."

    Then you said: "Nothing will ever seem to happen to the universe around him as he zips from place to place. The universe appears dilated in time to him (just as he appears dilated in time to others in the universe). In the limit as he reaches the speed of light, it would look to him like nothing ever happens in the universe at all. In the limit as he reaches c, the universe is all in one point, and the notion of time no longer exists. "Time stops," if you'll accept the sloppiness of that phrase."

    I think we need to seperate some referents here. Surely the universe he sees as foreshortened and slow or even stopped is not the same universe he sees as going on normally all around him. Remember that he measures the speed of light just as he always has, just as he did back on earth before he left his twin. His clock and his measuring stick seem perfectly normal to him.

    Of course, our ship is not just ballistic, it has windows. Captain can look at the stars, even the same stars he saw before leaving his twin on earth. He can watch the stars change as he moves toward them. When he passes nearby stars, he will see them shift in their arc positions in his sky. He will leave our sun and planets behind, eventually he will leave the belt nebula behind. To him, the universe seems to continue to change and go on in a perfectly normal manner, regardless how long, ships time, he continues to accellerate.





    I wrote:

    I will repeat my question. The captain has gone off, accellerating toward the speed of light. Earthlings see her hanging out there toward the end of the universe forever. So what happens after twenty billion years? Earth Sun has burned out, the earth and everything nearby is entering entropy death, and our captain is still going. What does she see when she looks out her window?

    You said: "It'll look to her like Earth has scarcely changed at all. For her, the Earth is severely time dilated, and changes very very slowly. In the limit as she reaches c, the Earth will appear to her to never change at all.

    If this seems confusing to you, think about it this way: the light from the Earth travels at c, and it is the light from Earth which she uses to see what's happening on Earth. The information about the state of the Earth propagates at c. Let's say someone is flashing a laser at her every second, and she uses the period of the flashes to determine how things are going at home.

    If she is moving very quickly, a significant fraction of c with respect to the Earth, that information will appear "stretched out" to her, because each pulse has to travel much further than the last to reach her. The pulses will not arrive once every second; they will arrive only once every month, or year, or decade. In the limit as she reaches c, she is travelling as fast as the laser light is travelling. The laser light never catches up to her, and so she never sees any pulses ever again. It appears to her that Earth time has stopped completely.

    - Warren


    So it seems to me that we have the universe in two observed conditions: it has changed, it hasn't changed. It collapses into a single point, or it goes on forever more or less as we see it today, or it dilates into the cold scattered dust of heat death.

    THis whole thing is very interesting to me, and I think we may be able to come to a language which has meaning if we pursue this discussion. As usual, I am neglecting chores and must rush off to do what needs to be done. My coffee is cold, and the wash water on the stove sounds like it has begun to boil.

    THanks for being here,

    Richard
     
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