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Did I understand this correctly - time slowes down due to acceleration?

  1. Oct 9, 2011 #1
    Did I understand this correctly - time slows down due to acceleration?

    Well I need to know if I understood the textbook correctly: Times goes slower in a gravitational field, but according to the equivalence principle you can't distinguish between a system being accelerated by a gravitational field with an acceleration g or the entire system being accelerated in the opposite direction by an acceleration g-.

    OK, so this means that a basketball being accelerated in empty space - time slows down for it in comparison with an observer who stands still, because it doesn't matter if the acceleration comes from rockets or from black holes as long as the directions are opposite and the absolute value equal?

    Another question:

    you guys know the twins-paradox? The explanation of why it isn't a paradox has to do with one of the twins being accelerated and the other not. I would like some explanation behind this because I'm a bit fuzzy. And try to keep it simple, please!
     
    Last edited: Oct 9, 2011
  2. jcsd
  3. Oct 9, 2011 #2
    Btw do they teach this relativity-theory and the like to engineering students? I mean it's kind of a waste of time teaching this, if we take into account the already huge workload.
     
  4. Oct 9, 2011 #3
    also excuse me if this is stupid but since the mass of an object increases if we increase its velocity, is the reason that time goes slower around a very fast-moving object simply because the gravitational field around it increases (due to the increased mass) in intensity? so basically time dilation is solely a consequence of acceleration? am I just talking ******** here or..?
     
  5. Oct 9, 2011 #4

    phinds

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    Time dilation can happen purely due to relative speed. Here's a full explanation:

    http://www.phinds.com/time%20dilation/ [Broken]
     
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  6. Oct 10, 2011 #5
    Nice explanation phinds. And yes, the twin experiment is not so weird. If you looked at Phinds explanation you saw that it used the fact that light is a invariant, a 'constant' 'c'.

    Now stop thinking of that as a speed, think of it as a beat instead. The invariant beat of a universe. Then think of a 'light clock' consisting of a rod with two mirrors at it endpoints. |----| then let a 'light corn' bounce |<---->| in-between them, making it into a metronome, keeping 'time' for you.

    Now send it out in space at some relativistic speed. What path will that light-corn have to take according to you on Earth, a straight one or a angled path, remember that your light-clock goes very fast now, covering a lot of space between each 'beat' of that light-corn between the mirrors. A angular one right?

    Will that make it take a longer time according to you?

    What would you see if you were sitting on that light clock, 'at rest' with it, would the light-corns path be angular then too? or would it now be the same straight path, as it was before you accelerating it?

    Then there is one last thing.

    It's not a optical illusion, we have one invariant clock in SpaceTime. Radiation, and if you watch that 'slow down' relative you, then 'time' is the participant to blame, not lights speed in a vacuum. And it fits as hand in a glove with the fact that there is no way you locally ever will get another 'speed' from light than 'c'. Also it explains why you can't live longer by 'speeding up' or staying at neutron star, you only have a defined amounts of 'beats' locally, and they will be the same where ever you go, no matter how fast.

    That you will find other frames of reference 'Speed up & contract' while sitting on that 'light clock' has no influence on your 'local time frame'. And that's why the traveling twin will be younger when coming back.
    ==

    The same light clock can also be used to show why a Lorentz contraction is real, not a illusion, you just need to make a system of two light clocks for that, formed as a 'L' , you will find that the vertical 'light clock' must become Lorentz contracted to keep 'c' a constant.

    And it all builds on one principle Lights invariant constant speed in a vacuum.
     
    Last edited: Oct 10, 2011
  7. Oct 10, 2011 #6
    There is a recent thread asking if a "light spot" made on the surface of the Moon from the Earth using a laser could move across the face of the Moon "faster than light".

    The relativistic ship with the two mirrors and the light bouncing between them, as viewed from THE SIDE of the apparatus by the stationary observer, seems to be uncomfortably close to the misapprehension that the distant light spot's motion should not translate faster than c...

    What justification does the observer use to believe he is actually seeing the angled path of light vs. a visual artifact (maybe actually a conceptual artifact, since he does not really in a position to receive the actual light in question)?
     
  8. Oct 10, 2011 #7
    In the example you give it is the relation between the guy turning his flash light and the apparent 'motion' of its laser beam. That laser has only one speed 'c', at all times. In the examples here, nobody is turning anything.
     
    Last edited: Oct 10, 2011
  9. Oct 11, 2011 #8
    Right, what I'm wondering about is the similarity between the moving light spot and the moving "image" of the light path between the mirrors...

    The moving light spot is not a "thing" so to speak, it is a visual inference. The eye treats the apparent translational motion of a visual entity as a real thing in motion - the mind realizes what it really is and knows better.

    When one is looking at the ship with the mirrors and bouncing light path inside as it passes by, to what degree is the observer's inference that the light takes angled paths a similar inference? In this case, it is the mind that assumes the geometric answer first and requires angled paths because the eye cannot actually see the light path itself.

    I'm wondering if the light clock thought experiment may not be the best way to demonstrate time dilation.
     
  10. Oct 11, 2011 #9
    allright, thanks I understand. But what about the questions in post #1? Namely the twin paradox & the equivalence principle?
     
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  11. Oct 11, 2011 #10

    phinds

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    The twin paradox is fully explained by youron's post #5

    I think, but don't know for sure, that the occurance of time dilation in a deep gravity well can only be explained properly with mathematics and I can't help you with that one. My non-accelerating example doesn't require math beyond the very simple d=rt.

    bahamagreen, your analogy isn't an analogy, it is unrelated and your logic is totally incorrect. This is because in your example nothing is moving. That is, the photons coming out of the flashlight are moving but the sweep of their incidence across the face of the moon is NOT something moving at all and has no relation to the discussion at hand.
     
  12. Oct 11, 2011 #11
    phinds,

    Read it again; I'm agreeing with you that the moving light spot is "...the sweep of their incidence across..."

    I'll try to be more clear about my question: Isn't the assumption or interpretation by the stationary observer that the light path between the mirrors of the ship is angled based on the same "...the sweep of their incidence across..."?

    Consider postulate #2: the observed relative motion of the passing ship should have no bearing on the speed or direction of the light path.
     
  13. Oct 11, 2011 #12
    Bahama, I agree in that it becomes a very weird universe. Almost as if what we call our three dimensions, (let's ignore time for this) when compared to some other frame of reference gets replaced by ? a flat surface ? When reading about it. And that hurts my head too. But there is a clear relation between what you see, if one now ever could 'see' a photon propagating, and the 'time', as well as 'distances' measured.

    So there you have a connection, when it comes to the example you use I call that a illusion. That is your eye relative the cosmos, every time you look up at the sky and turn your head around you might as easily say that your eye do FTL.

    The sad thing is that I had better and clearer definitions for how this worked mathematically. "In special relativity, the speed of light is constant when measured in any inertial frame. In general relativity, the appropriate generalization is that the speed of light is constant in any freely falling reference frame (in a region small enough that tidal effects can be neglected." And easiest to define it for me is to talk about its 'speed' as a local measurement, relative myself/the detector.

    That way there should be no misunderstandings, hopefully. And that way is the way you relate to the universe too, you can't do it other than 'locally'. All other definitions are conceptual, coming from comparing 'frames of reference', as I see it. I had a beautiful example of the relation of 'lightclocks', relative observers, and I probably still have, somewhere? Ahh found it :)

    This one is a pleasure to read. http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/Special_relativity_basics/index.html [Broken] At least it was for me.

    Something more.
     
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  14. Oct 11, 2011 #13

    phinds

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    No, you're not understanding the situation at all. In my drawing, the thing that is being observed by both observers is a SINGLE PHOTON that moves from the photon gun to the mirror and back, and the perception of the two observers is exactly what I have drawn. You can find similar drawings on numerous web sites that explain this.

    There is just no relationship between what my drawing depicts and the "sweep of incidence" in your example which is a totally unrelated phenomenon and is in fact absolutely no different that you moving your eye from one star in the night sky to another and thinking that something moved between them faster than light. You can look at the two spots on the moon WITHOUT the flashlight beam moving on the surface at all --- it the same thing.
     
  15. Oct 11, 2011 #14
    Read this example to see what gravity can do to a 'clock' relative your 'frame of reference' observing. NIST. It's so simple, and so beautiful.

    Now I'm sure you wonder what a 'frame of reference' is. Well, to me a frame of reference is a conceptual construct defining what you find to be a 'systems' time locally. If we take the description of two light clocks sharing the same 'frame of reference' by getting synchronized by a light beam, sent from the exact middle of some place of a defined 'gravity' and compensated for those influences then yeah, maybe?

    But a better definition is to admit to all clocks in SpaceTime being slightly different, as seen from any local measurement, and that a same 'frame of reference' shouldn't be taken as a absolute definition. It's a conceptual, and also one that we use due to our inability to experience those incredibly small scales those atomic clocks work on, well, as I see it. To me the only same 'frame of reference' is the one where we have superimposed bosons. And we're not bosons. But you can argue about it and use some scale that, to you, define a 'smallest bit', for example, the Planck scale. And that one is also about if there should be a 'flow' or 'bits' defining SpaceTime at its smallest scales.

    So this is more of a assumption from my side than a proven fact. Another question that comes to mind is then what makes our 'time, or frame of reference' possible to define/deduct. And there I would point to radiations invariance locally. It's the finest 'clock' I know of.
     
  16. Oct 11, 2011 #15
    phinds,

    I am not likely to believe that both observers see the same photon...

    I'm just curious about a very simple question...

    Let's take postulate #2 to be true...

    Second postulate (invariance of c)
    As measured in any inertial frame of reference, light is always propagated in empty space with a definite velocity c that is independent of the state of motion of the emitting body.


    The part that specifies "...a definite velocity c that is independent of the state of motion of the emitting body" is the foundation for my curiosity, here.

    A definite velocity means a definite direction and a definite speed - it is a vector.

    If the ship was not yet in relative motion, which velocity (particularly, which direction) would the stationary observer assume or infer to be the light path? He would assume a perpendicular path to the direction in which the ship is not yet moving.

    Why would the stationary observer assume or infer that the light path would be an angle (different velocity) for a ship in relative motion when postulate #2 forbids the light path's velocity (including it's direction) to be contingent on the state of motion of the ship?

    Basically, if the light's velocity by postulate #2 requires it be independent of the ship's relative motion, where is the "angle" (change in velocity) in the light clock thought experiment coming from when the ship is in relative motion?
     
  17. Oct 11, 2011 #16
    Nikitin, I’ll try to answer ALL of your original questions.
    You have that right. And nicely done I might add. To help you think about this, GPS satellites have to account for both SR and GR. From our point of view on the ground, SR makes those clocks tick slower and GR makes them tick a little faster. But SR has a much bigger effect. So in total, the clicks have to be sped up a tiny bit.
    You’re right that it all happens when the traveler turns around. But the deceleration and acceleration are not needed to explain it. For instance, you could have 2 travelers heading in opposite directions, #1 away from earth and #2 toward earth. As they pass each other, #2 sets his clock to match the clock that #1 has. When the second clock gets back to earth, the time dilation is just what’s predicted by SR. And it all happens without any acceleration.

    I think the best explanation is the Wikipedia page. The bouncing light inside the ship business is great for understanding SR but it’s complicated for understanding the twin paradox. I think the key is understanding simultaneity. When the travelling twin turns the ship around, simultaneity jumps forward quite a bit along the earth bound twin’s timeline. Look for that in the Wikipedia page. I can explain more if you want.
    http://en.wikipedia.org/wiki/Twin_paradox#Resolution_of_the_paradox_in_special_relativity
    I don’t know but I don’t think so.
    Wow! You're really thinking about this. I’d say no. Here’s why. A photon has no mass yet the time dilation due to speed means that it does not experience time. Here’s a better one. Neutrinos! (They’ve been in the news recently.) Physicists know how long it takes for one neutrino to turn into another. But when they travel from the sun to the earth, that change takes longer. That’s due to time dilation. Yet the increase in mass still leaves the neutrino very light. It would need a mass much larger than the sun to explain the time dilation through gravity.

    How'd I do?
     
  18. Oct 11, 2011 #17
    "As measured in any inertial frame of reference, light is always propagated in empty space with a definite velocity c that is independent of the state of motion of the emitting body."


    To me that one just says that you 'locally', no matter wherefrom you measure that 'photons' speed, never will find it to have another speed than 'c'.

    If you can prove that statement to be wrong, you will be far on your way to invalidate most of modern physics, as I see it. There are those saying that it won't matter if a 'photon' has a slight mass, I don't agree to that idea myself. There are a lot of ideas that build on no mass, check up Bose for example.
     
  19. Oct 11, 2011 #18
    To me, it implies that to the stationary observer, the direction of the light clock light path must be perpendicular to the long axis of the ship independent of whether the ship is in relative motion or not.

    Thus, my curiosity about the assumption that he would see the light clock light paths take angled bounces when the ship is in motion... how is that assumption not a violation of postulate #2?

    Seems like postulate #2 would mean that the stationary observer should anticipate that the light path in the moving ship would miss the mirror because motion of the ship can't alter or compensate the velocity (direction) of the emmision... in the way that a boy on a bicycle bouncing a basketball can...
     
  20. Oct 11, 2011 #19
    Einsteins definitions is about the geometry of SpaceTime, the way 'space' can compress and stretch, the way 'time' can do the same, relative the observer that is. And if you go from SR then that is a direct consequence of light always having the same invariant speed locally, as measured by you.

    So to connect the geometry to lights invariant speed makes a lot of sense, although it wrecks havoc with how we normally perceive the room, when nothing is moving relativistically relative us. Maybe you are trying to define a absolute 'space'? Where something that makes sense from one frame, should be expected to be the same when observed from some other 'frame of reference'? As I see it there are no 'same frames', they seem all observer dependent to me.
     
    Last edited: Oct 11, 2011
  21. Oct 11, 2011 #20

    phinds

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    My explanation was simple and has the added advantage of being correct. I do agree w/ you about the singe photon --- it's more of a thought experiment. I am at a loss as to how to be any further assistance in your willful refusal to believe it. I suggest that you check for various explanations of time dilation. You will see that many of them use a quite similar explanation as I have. Now, we COULD all be wrong, but it's really a lot more likely that you just haven't gotten your head around it yet. Good luck with that.
     
  22. Oct 11, 2011 #21
    "I am at a loss as to how to be any further assistance in your willful refusal to believe it."

    I don't disbelieve it, I just don't understand it enough to answer my question.

    Maybe someone else can help me understand how the velocity of the light clock light path as viewed by the stationary observer is apparently dependent on the motion of the ship when the second postulate clearly states that "As measured in any inertial frame of reference, light is always propagated in empty space with a definite velocity c that is independent of the state of motion of the emitting body".

    "As measured in any inertial frame of reference" certainly includes the stationary observer's frame of reference and his measurements.

    "always" means always, including the stationary observer's measurement of the moving ship's light clock light path .

    "With a definite velocity c" means in a particular direction and with speed c.

    "Independent of the state of motion of the emitting body" means that same above particular direction and speed whether the ship is in relative motion to the stationary observer or not.

    What am I misunderstanding in the second postulate that allows the light clock light path to take a different velocity (angled bounces) dependent upon the ship's motion? How is this not a violation of the second postulate?

    Is it assumed that the light paths are angled because the photons are comoving with the ship at the moment of their emission? If so, this makes the velocity of the light path dependent on the state of motion of the emitting body wouldn't it, contrary to postulate #2?
     
  23. Oct 11, 2011 #22

    PAllen

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    The speed of light being the same for all observers in no way implies the angle is the same for all observer. Using the single photon thought experiment others have suggested, consider:

    1) Observer at rest (O1) with respect source at x=0,y=0 and target at y=1. They see light move 1 unit in y, in time 1/c. Speed 1/(1/c)=c.

    2) observer moving at .6c in negative x direction relative to O1. They see O1's clock slow, thus light takes 1.25/c seconds to go from (0,0) to (.75,1). The .75 comes from (.6c * 1.25/c seconds). This becomes distance traveled 1.25 (pythagorus) / (1.25/c) = c.


    At this point you need to think, and read rather than reject reality.
     
  24. Oct 11, 2011 #23
    Please, no more accusations of willful disbelief or rejecting reality; I'm only not understanding something, happens to all of us. Let's work on that.

    PAllen,

    It seems that my misunderstanding is coming from trying to reconcile statements like yours

    "The speed of light being the same for all observers in no way implies the angle is the same for all observer."

    with the second postulate's phrase "with a definite velocity c..." which I read to mean in a definite direction. And in the context of the whole postulate, in a definite and like direction for all inertial observers. And thus so, independent of the relative motion.

    I have reread the postulate (came from Wiki) a dozen times.

    Maybe it would help if someone parsed the phrases and specified precisely what each means as I did, or look at mine and identify the incorrect assumption. Then I might find the discrepancy and at least know what particular part of the concept I need to look at more closely?
     
  25. Oct 11, 2011 #24
    That's the danger with words Bahama.
    And why mathematicians would prefer us all to to use symbols and numbers.

    All velocities define, as you say, some value and a direction. A speed only defines a value. When we define 'c' we speak of the 'speed of light in a vacuum' not the 'velocity'. Which means that the speed of something bouncing between mirrors can be constant while its velocity only can be the distance of one bounce, with the next bounce defining a new velocity, even if it is the exact same (speed).

    There is one more reason for using the word speed as I see it. We can only measure light as it annihilate, as far as I know. That means that we cannot assume that it 'move' in the same way we can describe a car to 'move' and so have a velocity. That we find a source and a sink connect that 'photon' doesn't, to me that is, prove its existence at all those other points of its presumed 'propagation'.

    But there you will find a lot of people disagreeing with me :)

    The guy that wrote "As measured in any inertial frame of reference, light is always propagated in empty space with a definite velocity c that is independent of the state of motion of the emitting body." was, as I think, of the distinct opinion that light 'propagates', and that you therefore can assign it a velocity, indicating a direction as well as a speed inside our 'room time'

    And it's also a function of gravity, gravity defines SpaceTimes 'straight lines', just as Earths 'roundness' defines the shortest line for you walking between two points. But gravity is trickier as it is in three dimensions, whilst the surface of our Earth could be described as being in only two as I think of it, like a bent paper.
    ==

    "As measured in any inertial frame of reference" is not necessary as I see it, 'locally' (your frame of reference, as your retina) I know no way you ever can measure 'c' as being of another speed than 'c', be it in a acceleration or in a uniform motion. A inertial frame of reference is one that is 'at rest' aka 'uniformly moving'. A planet may not fit that as it is 'gravitationally accelerating' but we still use Earth as a inertial frame. It's somewhat of a matter of taste that one. But it's tricky, as most definitions in physics.

    =
    Rethinking that one, maybe it's simpler to use a uniformly moving frame as a reference as when we measure a speed always will need a distance, measured in time. So yes, it makes sense as a accelerating frame will have a red/blue shift and a 'gravity' redefining the clocks in your spaceship depending on where they are placed relative the spaceships overall acceleration/direction. But in theory there should be no difference as i think of it. The speed of 'c' is constant in all motion. Maybe someone here knows a better way to define it?
    ==

    "light is always propagated in empty space with a definite velocity c that is independent of the state of motion of the emitting body." is perfectly correct, if we assume a propagation, and remember the fact that motion and gravity distort the geometry that 'photon propagate' in, same as the Earth distort our definition of a shortest line, that as we measure it on a bent surface.

    Relativistic aberration is about how 'things' move, relative motion. The faster you go, the more acute angle of rain. If you bounce a ball on the floor inside a very fast moving railway car (made of glass) it will to you go straight down and up, but according to your friend on the railway-bank describe a 'V' formed motion as it bounce.

    So it is observer dependent, and a function of relative motion, meaning that you can use the same logic for that railway car as we used for the 'light clock', namely that the railway car must present your friend with a 'slower time', relative his clock. According to your friend the ball had 'two directions', not only down but also moving in the direction of the train, and so it also had to take a longer 'time' for it to cover that distance, relative his observation/clock. And you can use a 'light clock' standing vertically to find the same thing happening, the difference being that the light clock uses a 'invariant' bounce, whereas the balls bounce varies with its momentum.
    =

    The strongest objection to this way of looking at it comes from the fact that all uniform motion can be defined as being 'at rest', but the geometry I describe must be true for an accelerated motion too, so to refer it (time dilations and Lorentz contractions) solely to acceleration is not correct, as I see it. To me it is a question of 'energy', and if the universe has a way of defining different energies to different relative motions. And as far as I can see the universe have a definition of that, even though it won't be measurable in a 'black box scenario'.
    ==

    If we think of a and b as some locations on a bent surface, represented by 'O', then you have 'a O b', where the 'shortest line' obviously is a tunnel :) but most often easiest to follow the surface. And that's what that 'photon' seems to think too, mostly that is. As you have 'tunneling' there too. And gravity's 'surface'? That would be something to see, 'gravity unwrapped ' I wonder how, and if, it even would be possible to do that?
     
    Last edited: Oct 12, 2011
  26. Oct 11, 2011 #25

    PAllen

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    Use of velocity for the constancy of c postulate is simply an imprecision. Speed should be used. There is a whole section of Einstein's 1905 paper on 'aberration', wherein he derives formulas for the difference in angle of light between different observers. There is also a classical formula for aberration - Einstein showed how it had to be modified for relativity.
     
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