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Paradoxes in relativity, and an absolute reality

  1. May 8, 2012 #1
    This is my first post, so forgive me if I'm posting in the wrong place or violating a rule.

    I've been doing some reading on relativity, and find myself flummoxed. I understand gravitational time dilation and the principals behind relative velocity time dilation, length contraction, and the relativity of simultaneity.

    What I DON'T understand is how these things are ACTUALLY relative without creating paradoxes.

    The easy way out of this mess for me is to say, "It's only our perception things that is relative, and that's all we can work with because it's all we have as humans and in science," but that's not what I've read either. People insist it's actual, not just perceived, and that when we take into account things like light propagation, the answer that science has arrived at is that it actually IS relative. But science depends on our measurements, which are always from a reference frame and can't access absolute reality.

    I have a feeling the answer coming at me might be something like, "There is no absolute reality! It's all relative, that's the point!" Given that, am I to believe that depending on how many observers there are of a given event, reality actually adapts to accommodate all of them and all of the things they observe (different length contractions, etc...) actually happen, even if they contradict each other and create a paradox. Furthermore, I don't believe the universe will tolerate a paradox because by its very nature a paradox is impossible, and paradoxes abound in relativity. I wish I could include a specific link I found, but it's my first post, so I can't. Just google "why time dilation is impossible" find the one I have in mind.

    Would it be fair to say that all the things discussed above are relative to the best of our knowledge because our measurements depend on a field of reference, but that there might still be an absolute reality (outside of human measurement) that we simply cannot talk about scientifically? Or, is our current understand that stuff really does physically change depending on your perspective?

    As a side note, I've read that the relativity of simultaneity is supposed to solve the clock paradox and the ladder paradox, but I just don't see how it helps things at all. It doesn't explain to me how A can be greater than and less than B at the same time. Maybe that's the crux of my problems, or maybe that's a separate thread.

    As you can see, my brain is kind of whirling, but I've tried to gather my thoughts before posting. Thanks for your help.

    -Aaron
     
    Last edited: May 8, 2012
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  3. May 8, 2012 #2

    phinds

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    A large part of your problem (ALL our problem when we first start getting into this stuff) is that cosmology (the very large) and quantum mechanics (the very small) are TOTALLY outside our natural experience and we have no valid "intuition" about them, we just THINK we do, but we are WAY wrong.

    Some things in cosmology and just about everything in quantum mechanics are COUNTER-intuitive. When I first started getting into each, I spent a fair amount of time jumping up and down and pulling on my hair and screaming obscenities to myself because it JUST COULD NOT BE SO !!!!

    But it is. Get over it.
     
  4. May 8, 2012 #3
    Haha. Fair enough, but are you saying that these paradoxes do exist in nature? I thought even with the counter-intuitiveness of relativity, paradoxes still weren't considered possible, and that they were supposed to be solved with relativity of simultaneity.

    Also, when we've done experiments with time dilation, we come up with non-paradoxical results (e.g. one clock slowing down, the other staying the same). What would a paradoxical result even look like? It would be impossible...
     
  5. May 8, 2012 #4

    phinds

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    I did not say, nor mean to imply, that there are paradoxes, what I'm saying is that physical reality often LOOKS like a paradox. Things like the dual nature of photons, and the 2-slit experiment are the kind of things that made me tear my hair out, but the universe just doesn't CARE what we think.

    Here's another way to think about the stuff you read, and your reaction to it. I often post this when someone posts a particularly inane "fact" that they have just made up (but may well believe, regardless of how silly it is). I am NOT suggesting that you have done that, I'm just offering advice:

    When you come up against something that flies so utterly in the face of established science, it is not a good idea to start off reaching different conclusions and stating them as correct but rather to start off with the assumption that you have made a mistake somewhere and try to find out where it is. If you have NOT made a mistake you will find the flaw in the established science, but that is very unlikely to happen. If you start off thinking that you have overturned established science you are likely to just end up embarrassed.
     
  6. May 8, 2012 #5
    All paradoxes of Special Relativity can be solved in a very easy way.
    You simply need to picture the scenario in a (x,t) diagram.
    You can then add (x',t') axes for another inertial frame on the same diagram.
    You will see the paradox melt like snow in the sun.
    You will even wonder why so much time can be lost on such trivial questions.
    After all, the coordinates do not change the picture.
    This will draw highlight the basic facts of SR, specially regarding simultaneity.
     
  7. May 8, 2012 #6

    Nugatory

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    It's easy to identify genuine paradoxes - for example, if one observer could see two objects collide (they were both in the same place at the same time) and another observer saw them not collide, that would be a genuine paradox. Relativity of simultaneity doesn't allow this to happen, and you could reasonably say that the fact of the collision is an "absolute reality".

    Here's one fairly intuitive way of thinking about what's "real" and what's "relative" in relativity ("real" in quantum mechanics is an altogether different problem)...

    First, draw a space-time diagram of what's going on, showing all your events (explosion here, flash of light there, light meets a human eyeball or photoreceptor here), the worldlines of the various particles. Then ERASE THE COORDINATE AXES from your diagram; when you do, you've just erased all the relativity and what's left is "real". And if you want, you can draw a new and different set of coordinate axes for some new observer in some other frame... but that doesn't change the events in the spacetime diagram.
     
  8. May 8, 2012 #7
    That sounds so lovely. I'll stare at some (x,t) diagrams for a while and meditate upon a world without a coordinate axis and see if it sinks in.

    While I do that, another question:

    From what I understand, all of these dilations and contractions and such happen at "normal" speeds (e.g. walking, driving), but it's just so minute that it's practically undetectable. Does this mean that we (and every object) are moving around shrinking and expanding, slowing down and speeding up, and perceiving things as simultaneous differently than each other, AND changing in mass all the time, but we'd never notice it?

    Again, let me know if such questions should be a separate thread.

    Thanks! This forum has been invaluable already.
     
  9. May 8, 2012 #8

    Erland

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    It is a misunderstanding that Relativity Theory means that everything is relative. Some things are relative (i.e. dependedent of the observer), such as time, lentgh and mass, but some things are NOT relative, such as light speed and, more generally, the four dimensional space-time distance. Actually, Einstein considered naming his theory "Invariance Theory" instead of "Relativity Theory".
     
  10. May 8, 2012 #9

    Saw

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    coktail, when you understand SR a little better, you will realize that there is nothing counter-intuitive in it. It is pure logic. It may clash against the traditional use of words, but not against elementary logical notions.

    As you have been told, events (what happens at a particular point in space and time, like a collision or an explosion) are the same in all reference frames. All observers, no matter their different states of motion, agree that the same things happen or not. A different thing is that in order to reach that conclusion, they must measure, that is to say, they must play with instruments which share the observer's state of motion and hence forcibly measure different values. This was so in Newtonian relativity, if you think of the distance (space) traversed by a projectile in a certain time period. Einstenian relativity only adds to that the simple idea that (for sound physical reasons) the same frame-dependence affects length and time measurements. Fortunately, in spite of this complication, intelligent observers, ala detectives, manage to interpret those clues in a reasonable manner, combine them in crafty equations and reach the same conclusions about whether certain facts happened or not. Thus all observers find the same practical solution to all practical problems, which is what physics is about, after all.

    In more abstract words, this is what you have also been told: space and time (the clues) are variant or relative but the spacetime distance between two events (that is to say, whether one can influence another at all or not) is an invariant or absolute deduction (which you arrive at through interpretation of the variant clues).
     
  11. May 8, 2012 #10

    Nugatory

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    Yes.

    But even that is not as weird as it sounds at first. Suppose I told you that when you climb a flight of stairs, you lose weight? You do, because you're moving away from the center of the earth, and the force of gravity diminishes with distance. In this case, the weight change is on the order of one part in 1E12, meaning that a 100kg man loses far less than the weight of a speck of dust. This is perfectly ordinary standard classical Newtonian physics, no one notices, and no one has any trouble accepting that it's happening all around them even though we don't see it.

    The time dilation and length contraction effects for (for example) an automobile at highway speeds are even smaller.
     
    Last edited: May 8, 2012
  12. May 8, 2012 #11
    I like phinds comments and would also add to his that before studying all this stuff, our perception of 'reality' is quite different from actually exists. "Reality' is not so easy to define. That's because our senses have evolved to protect our lives rather to properly interpret the subtlies of science.

    Niels Bohr said:

    "If quantum mechanics hasn't profoundly shocked you, you haven't understood it yet." Relativity is not so different.



    absolutely NOT...except for the relativity of simultaneity. The reason that piece is correct is that you included 'differently than each other' implying different fames of reference. With YOUR frame of refernce, where you are, NONE of that stuff happens...you experince only proper time and proper distance locally. It is ONLY when different frames of reference are compared that time dilation and length contraction occur.

    In addition, you do not change [rest mass]...but you can change energy or 'relativistic mass' which a perspective that has lost favor over time. In your own frame of reference, your rest mass remains a constant; the coorect definition means that others also will observe your rest mass, but not necessarily your total energy, as a constant.
     
    Last edited: May 8, 2012
  13. May 8, 2012 #12
    It all begins with noticing that when things are far enough away from you or moving fast enough, the observation of distant things (the data from afar) does not match your expectation of comparable observations of local things (data from right in front of you).

    The classic examples are thought experiments (and equivalent real experiments) where these things measured locally don't measure the same when far away or moving fast. Since an observer in the distant fast moving situation will measure his rods and clocks to be the same as you will measure your own local rods and clocks, this raises the fundamental question, "what is the real situation?"

    The mainstream way physicists look at Relativity is that it is an existential theory - that the message of the peculiar data is true for that observing frame of reference - and has to be, in spite of other reference frames having different measures. Then the nature of the transforms that relate these measures is examined to figure out what that means about the underlying existential nature of spacetime geometry.

    Some others, rarely physicists, may take the position that it seems apparent that the data changes while in transit. The actual local data measured by the distant fast mover is the same to him as your local data measured at rest, so something has happened to change the data. Then transforms are used to put it back straight so the rods and clocks may be comparable. In this case Relativity is not so much an existential theory as it is a theory about data, a theory of measurement and how to adjust or correct altered data from distant fast moving sources, a method for relating comparable data from fast far sources with local sources at rest. This position retains a little of the comfort of an absolute system in that it implies both local and distant measures are "correct" and it is only the effects of distance and speed that "corrupt" the data in transit.

    And maybe these two perspectives are not really different if "what happens to the data in transit" is really the same as "the underlying existential nature of spacetime".
     
  14. May 8, 2012 #13

    ghwellsjr

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    I noticed you didn't say anything about the Lorentz Transformation or Reference Frames. These are really key to putting everything else in place. If you haven't learned about how to transform the co-ordinates of events from one Reference Frame to another one moving with respect to the first one, you haven't grasped what Special Relativity is all about.
    Virtually all so-called paradoxes in Special Relativity come about by mixing the co-ordinates from two different Frames of Reference. If you define a scenario in one Frame and then transform all the significant events to another Frame, you'll never have any problem with paradoxes. This is essentially what lalbatros was saying in post #5.
    A Reference Frame doesn't come for free. You need to understand how it is constructed and how you define events within it. Until you do, you cannot even have meaningful measurements. This doesn't conflict with an absolute reality, it merely provides a meaningful way to address reality.
    You have it the other way around, reality doesn't adapt to different observers, different observers adapt differently to reality. There's only one reality, we just define it differently from our different points of view. Nothing changes in reality just because we do a mathematical transformation on the co-ordinates for the events in one frame to see what the corresponding co-ordinates for the same event look like in a different frame.
    There are no paradoxes in relativity.
    Now if you google that expression, you get your first post so you need to change the word "is" to "must be", correct? But that link is full of misconceptions. I'm tempted to critique them all as anyone with an understanding of Special Relativity could easily do. You should be aware that all of his complaints about Special Relativity are pointless.
    Yes, that is fair.
    No, that isn't right, nothing physically changes because of your perspective. You need to learn what a Frame of Reference is and how you transform it into another one (which is what I think you mean by "perspective").
    It's no more complicated than saying that A sees himself at rest with B traveling while B sees himself at rest with A traveling, is it?
    Glad to help. Please learn how a Frame of Reference is constructed.
     
  15. May 9, 2012 #14
    Welcome then! :smile:
    From the title, your topic seems to be at the boundary of physics and philosophy.
    That certainly is an easy way out. If you have not read that, then it's simply because you did not read (or dig) enough. :smile:
    Here's one paper that is often cited in the QM forum (because of another much more mind-boggling issue!):
    http://cdsweb.cern.ch/record/142461?ln=en
    See p.16; option 3 implies something that you might call "an absolute reality".
    Some people say this, and other people say that. The hard and simple fact is that we can only disprove ideas by experiment (except if they are inconsistent). And the "no reality" idea corresponds somewhat to option 4 in that paper. :tongue2:
    The first time that the clock "paradox" issue was brought up by discussing two differing perspectives - but without presenting it as a paradox - was likely this paper, starting from p.50 but relating to p.47:
    https://en.wikisource.org/wiki/The_Evolution_of_Space_and_Time
    You may be surprised to see the explanation by one of the main relativists of the time.

    In summary, there is no need to try to accept an interpretation that doesn't make sense to you; different people interpret the observations differently.
     
    Last edited: May 9, 2012
  16. May 9, 2012 #15
    Wow. I cannot thank you all enough for the time and thought you've put into your replies. This is truly a wonderful resource.

    From this thread, I interpret that the relativity of time, length, and mass (not resting mass) is no different than the relativity of speed as measured in Newtonian physics. An absolute speed doesn't exist because by its very nature it depends on the reference frame (and relative motion) of the observer. If I'm right about that, this is starting to click. It will still take some work to wrap my head around, and I do have some learning to go through about reference frames. And of course I have more questions.

    One piece I'm still really struggling with is how some of these relativistic effects remain once brought back into the observer's reference frame, but others seem not to. For example, in the Hafele and Keating experiments the clocks stayed dilated once the planes landed and were back in the hands of the observers on the ground. We notice this with satellites brought back to Earth as well, I'd presume.

    However, if an object was to move past you at the speed of light, it would appear contracted in length in the direction of its motion, but if it were then to stop and you were to walk up to it, it would no longer appear contracted. Is there a fundamental difference between time dilation and length contraction in this way?

    If I was somehow able to reach out and touch someone as they passed me at near light speed, they feel thin (stretched vertically), and would I simultaneously feel thin to them?

    If a clock is moving at 98% the speed of light relative to one observer, but 99% the speed of light relative to another observer, does it dilate to varying degrees depending on the reference point? And what if you were to then slow it down and bring it to both of the observers' reference frames, would it read different times for both of them, even if they were to move together into the same reference frame?

    It's this sort of question I'm still hung up on. Maybe it's all due to my lack of understanding of reference frames.

    I've never been a person of faith, and I find myself having to put some faith in the science that other people have done and which I cannot do (because I suuuuuuuuuck at math and have no training in it), so this is a real exercise for me, and I appreciate your guidance. Baby steps.
     
  17. May 9, 2012 #16
    That is spot on - except for the mistaken positivism that is contrary to Newtonian physics. It is a logical error (or a religious claim) to pretend that we must be able to observe everything that exists, but we can say what we can't observe. :wink:
    Yes, the fundamental difference in that way, is due to the fact that clock time accumulates while an object's length doesn't. You can make the comparison equal, by for example looking at clock frequency and object length. Clock frequency (or time period) is just like object length, it has no memory. :smile:
     
    Last edited: May 9, 2012
  18. May 9, 2012 #17

    ghwellsjr

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    It would be more correct to say that an absolute speed doesn't exist because we cannot measure and identify any such absolute speed. This is independent of any theory that we use to explain the facts of nature since it is one of the facts of nature that any theory must comport with.
    Think about the speedometer in your car and the odometer. When you take a drive, the speedometer goes up but when you return to your starting point it goes back down to zero. However, your odometer just keeps going up and has a different reading at the start of your trip and at the end. This is just a crude analogy to a ruler that contracts while traveling but goes back to its original length when you stop.

    Now compare this to a metronome and a clock. If time was slowing down for you while you were traveling, the metronome would register that change (although you wouldn't notice it) and when you got back to your starting point it would be ticking away at the same rate as a similar metronome left behind. However, the clock would accumulate time at the same rate that the metronome was and would accumulate less time than a similar clock left behind.
    Yes, although you probably wouldn't make this determination by touching but rather by timing how long it took for them to pass you and based on the speed you could calculate how thick they were. They could do the same thing for you and both of you would determine that the other one was length contracted by the same percentage.
    In order to not get mixed up and create a paradox, you need to define everything in terms of one reference frame, it doesn't matter which one. So you could say the master clock was stationary in your given reference frame and two observers (with their own clocks if you want to consider that) start out at rest with the respect to the master clock. Then one of them accelerates instantly to 0.98c while the other one does the same thing to 0.99c in the same or the opposite direction (your choice). Then we can talk about the tick rate of each clock according to the chosen reference frame (the one traveling faster will tick slower than the other one, both ticking slower than the master clock). Then after awhile, they both instantly turn around and return to the master clock arriving at the same time. Now the faster clock will have the least amount of accumulated time compared to the master clock with the slower clock being somewhere in between.

    Now you can imagine different scenarios such that the master clock is the one that instantly accelerates but you will have to be precise in exactly what you mean concerning the two observers traveling at different speeds because it is not possible for all three to start out together and end up together unless at least one of the observers accelerates. It is a requirement that clocks must be physically located together at the beginning of the scenario and at the end of the scenario in order to compare accumulated times in a meaningful way. (The starting location and ending location do not have to be the same and they don't even have to be at rest in the same frame.) But any scenario that you can imagine can be analyzed in any frame and you will always get the same answer for clocks that meet the requirement that I just stated.
    The math of reference frames and the Lorentz Transform can probably be done on any calculator that you have (as long as it can do square roots). It's really easy so don't be afraid. The derivation of the Lorentz Transform is more complicated but that's where you can exercise faith and just believe that other people have done it correctly. You can easily demonstrate that they did do it correctly even if you don't understand how they did it. It's kind of like before we had square root buttons on our calculators, it may be very difficult to find the square root of a number but once someone tells you the answer, you can trivially multiply the number by itself on your old four-function calculator to verify that the answer is correct.
     
  19. May 9, 2012 #18

    phinds

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    Seems to me he has it right and you have it backwards. It doesn't exist for the reason he stated, NOT because we can't measure it.
     
  20. May 9, 2012 #19
    Here is an example that might help illustrate that time dilation and length contraction are more similar than you might initially think. Let's say we have a 1 light year long railway line (in the Earth rest frame) with gear teeth in the track that engage with gear teeth in the wheels of the train to prevent slipping similar to some tracks you might find in steep mountain regions. On this train is a device that records rotations of the wheel to measure accumulated distance (basically an odometer as fitted to most cars) and another device that records accumulated time (basically a chronometer or clock). If we reset the devices and make the train travel very slowly so that the chronometer reads 1000 years when the journey is completed, then the odometer will record the accumulated distance as 1 light year as near as dammit. At the end of the journey we stop the measuring devices and leave them at the end of the track. Now we repeat the experiment with a new chronometer and odometer, but this time the train is travelling at 0.8c relative to the track and clocks at rest with respect to (wrt) the track record the journey time as 1/0.8 = 1.25 years. The chronometer on the train records the accumulated journey time as 0.75 years and the odometer on the train records the accumulated journey distance as 0.6 light years. At the end of the journey we compare the chronometer and odometer measurements with the measurements recorded on the devices we removed at the end of the first experiment. Now it can be seen that accumulated time and accumulated distance are both contracted in accordance with time dilation and length contraction in a way that can be recorded on devices that can be compared side by side after the experiment. According to the train driver the speed of the train was distance/time = 0.6/0.75 = 0.8c which is in agreement with the speed measured by observers at rest wrt the track.
    This one is difficult, because in order to feel the width of a moving object without altering the speed of the moving object you would have to match your hand speed to the speed of the object and no length contraction would be measured. We can only measure the length of a moving object (without altering its speed) by making measurements at either end at synchronised times. This means that length contraction is intimately intertwined with time measurements and how we define simultaneity, so more often than not time and distance cannot be considered completely independent entities. Hence we have the concept of spacetime.
    Let's go back to the train example I gave earlier with the train travelling at 0.8c relative to the track. The time measured by the clock on the train is 0.75 years. Adam is at rest with the track and says the train journey time was 1.25 years. According to Adam the time dilation factor is 1.25/0.75 = 1.6666 or equivalently the train clock is ticking approx 1.6666 times slower than his own clocks. Lets say another observer (Ben) was travelling in the opposite direction to the train and according to Ben the train was travelling at 0.99c relative to himself. Ben measures the time the train took to travel the length of the track as 5.317 years. According to Ben the time dilation factor is 5.317/0.75 = 7.01 and so he reckons the train clock is ticking approximately 7 times slower than his own clocks. Note that both Adam and Ben agree that the time that elapsed on the train clock is 0.75 years, even though they disagree on the journey times measured by their own clocks and the speed of the train relative to themselves.

    Hopefully you can now see that the answer to your question "would it read different times for both of them, even if they were to move together into the same reference frame?" is no. All observers agree that the elapsed or accumulated time recorded on a single clock between any two events is the same. Such a time measurement by a single clock present at both events is called a proper time interval and this is invariant.
     
  21. May 9, 2012 #20

    ghwellsjr

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    He stated:
    What is the nature of something that doesn't exist?

    This issue came up recently in the thread The terms "absolute" and "relative" and it was pretty much agreed that sticking the word "absolute" in front of something that was thought to exist in the past (prior to Einstein) but for which there is no evidence does not imply that it is related to any relative reference frame. If evidence had been found for an absolute speed, it presumably would not be related to relative frames but would be related to an absolute rest frame and we would have a whole different kind of physics not related to relativity or the relative motion of any observer.

    So I don't understand why you think I have it backwards.
     
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