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How is C speed invariance - hows it suppose to work mechanically?

  1. Mar 19, 2013 #1
    Are photons partially non-local? Warping time-space to acheive this? Seems a bit confusing.

    I get that c is always supposed to be the same for all observers according to special relativity, but i am trying to picture what actually is supposedly happening there?

    Forgive me if interpretation of the math/idea is either not possible, or beyond the scope of this forum. I thought there might be some kind of explaination, even if it has some math or logic component to it I dont mind...
     
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  3. Mar 19, 2013 #2

    ghwellsjr

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    Your questions are confusing but I think the answers are no and no.
    The easiest way to understand Special Relativity is to learn what an Inertial Reference Frame (IRF) is and how you can specify events in it at various locations and times and then use the Lorentz Transformation to see how the coordinates of those events change in a new IRF moving with respect to the original one. It's especially helpful to draw the events on several spacetime diagrams, one for each IRF. I have made many such diagrams to explain various scenarios. If you do a search on "diagram" with my user name, you can find lots of examples. You don't need any math to appreciate these diagrams but even then, the math is very simple.
     
  4. Mar 19, 2013 #3
    Ill look at both those things tommorow. Thanks for your answer :)

    Do you think that will help me a little, or a lot, to understand how photons are invariant, in a conceptual way?

    (Where I can imagine in my mind what is happening with the observer and the photon in real life to create this invariance)
     
  5. Mar 19, 2013 #4

    ghwellsjr

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    It helped me a lot. To think that you can draw a diagram depicting what various observers see in a scenario and how light travels at c (along 45-degree diagonals) and then transform to another IRF and even though the speeds of the various observers are different and their locations are different at different times, yet the same visual information is carried between them at the same speed c along 45-degree diagonals but of different lengths than originally. I think it's awesome and amazing and yet so simple.
     
  6. Mar 19, 2013 #5

    timmdeeg

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    The constancy of the lightspeed is a postulate, http://www.gsjournal.net/old/files/4281_anderton104.pdf [Broken]. As various predictions of Special Relativity have been verified experimentally with high accuracy, this postulate is accepted. If light wouldn't propagate with c, we had no explanations regarding these measurabe effects.
     
    Last edited by a moderator: May 6, 2017
  7. Mar 19, 2013 #6
    I am not denying it, trying to understand it mentally, how to visualise or understand how it occurs.

    Although I am not one for accepting every single assumption simply because the math works out (there could theoretically be equivilant or even superior maths - if a GUT exists especially)--->this particular prediction/feature of SR, has been experimentally verified through the measurement of light hitting the earth regarding its motion, and from moving distant objects, as I understand it. A number of times. Assuming they worked outside of a margin of error (at minimum at the types of speeds involved), I have real no reason to doubt, C is invariant.

    Seems to be a given.

    But personally agreeing with it, hasn't yet made it make mental sense for me. Hopefully it will when I look up these diagrams and such tomorrow.
     
    Last edited by a moderator: May 6, 2017
  8. Mar 19, 2013 #7

    Dale

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    I agree with ghwellsjr. For me personally, I struggled with SR off and on for about seven years. I knew the basic equations, but they all seemed disjointed and confusing. I didn't "get it" until I stumbled on spacetime diagrams and four-vectors. Then everything "clicked", almost immediately.
     
  9. Mar 19, 2013 #8
    Imagine simply that photons (and all things moving at c) are not travelling through space but that they (their momentum) are “jumping” space in a sort of teleportation (proper time=0, proper length of travel distance=0).

    With this picture in mind it seems logic that in all reference frames the same speed (c) is measured.
    By the way, this picture harmonizes with maths and other principles of special relativity; perhaps it is not the final truth, but it helps very much to understand special relativity.
     
  10. Mar 19, 2013 #9
    You'll end up having to understand how we measure times and distances, and how we decide that distant events are simultaneous with events at our own location. When I say that I measure light to be moving at c, this means I have one event A - light is emitted , let's say. Then I have another event B - light shows up on a screen. I have a framework in which I give particular time coordinates and particular space coordinates to those 2 events. I divide the space-difference by the time-difference and that gives me c. Let's take someone who leaves A and goes to B at .5c by my reckoning. Classically we would imagine that they would find light to be moving at .5c. The reason that they measure the speed of the light from A to B that they are following to be c as well rather than .5c relates to them having a different calculation regarding which events are simultaneous. For instance to that moving person, if I hold up both arms simultaneously (for me) and snap my fingers, they would carefully assign a time and space coordinates to both of those events and find that my fingers snapped at slightly different times. This relativity of simultaneity is how c can end up having the same speed to all observers. http://en.wikipedia.org/wiki/Relativity_of_simultaneity
     
  11. Mar 19, 2013 #10

    Dale

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    I don't think that is legitimate. A timelike interval is the proper time or the time read on a clock at rest wrt the object, and a spacelike interval is a proper distance or the distance in a frame where the two events are simultaneous. I don't think that it is reasonable to interpret a null interval as either a 0 proper time or a 0 proper length since there is no frame where a clock is at rest wrt the object and there is no frame where the two events are simultaneous. I.e. a null interval is neither a timelike interval nor a spacelike interval, it is not both.
     
  12. Mar 19, 2013 #11
    You may call my picture not reasonable, but the problem is: what else can you propose? Several important physics phenomena have become very inaccessible in the past 100 years, and I wonder if this is really unavoidable.

    Sorry, but your answer:
    for me personally, does not seem very helpful.
     
  13. Mar 19, 2013 #12

    ghwellsjr

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    If I do what Einstein said to do in his 1905 paper introducing Special Relativity I need to set up a mirror some measured distance away and measure who long a flash of light takes to go from me to the mirror and back to me. If I'm supposed to imagine that the photons "jump" the space between me and the mirror in zero time, how do I calculate the speed of light? Do they take a long time getting back?
    I guess you could postulate the same speed is measured, but how do you know it's c?
    Sorry, but your answer, for me personally, does not seem very helpful.
     
  14. Mar 19, 2013 #13
    Different scientists mean different things by "how". Some scientists like to here an explanation in terms of conservation laws, some by symmetry principles and some by forces. I am a "force" person, myself. I am satisfied by explanations in which all the forces contributing to a certain phenomena are explained. This includes the internal forces that hold the measuring instruments together. As long as the explanation has a complete inventory of the forces involved in the phenomena, I am satisfied.

    There are other ways to explain "how" that are mathematically equivalent to explanations that involve force. Some scientists like explanations that involve a concept called space-time continuum. I applaud those people who can follow a theorem involving the warping of space and time. I recently tried to teach myself that type of mathematics. Although it is difficult in some ways, it has a certain charm to it. However, I feel dissatisfied with such an explanation until somebody tells me what it means in terms of forces.

    When I see a theorem involving space-time, I generally do little side calculations to figure out how the forces are effected. You may not like forces in your calculations. When I give an explanation in terms of forces, you may want to rethink it in terms of space-time.

    Explanations that involve forces are often self consistent in only one inertial frame. The magnitude and direction of a force may vary with the inertial frame. The timing of a specific event may vary with the inertial frame. However, the explanation is considered valid as long as it is self consistent to any one inertial frame. There could be more than one explanation that is valid, but each has to be self consistent in one inertial frame.

    Thus, I am happy with an explanation as long as it provides an inventory of forces and events that is self consistent within one inertial frame. It doesn't bother me if there is a "contradiction" in explanations given by observers in different inertial frames. It doesn't matter to me if there is "contradiction" in an explanation given by an observer who changes inertial frames in the course of the experiment. As long as I have a sequence of events and an inventory of forces that is self consistent within one inertial frame, I say it is consistent with special relativity.

    A measurement of the speed of light often involves devices for measuring length, which I will refer to as rulers, and devices for measuring time, which I will call clocks. Rulers are a fixed length because the internal forces hold the atoms of the ruler together in at fixed distances. Clocks have oscillations of fixed time duration because the internal forces that make the clock works go oscillate in a certain way. In order to measure the speed of light, certain events have to be synchronized. It makes no sense to measure a distance of travel with a ruler if you don't know when the end of the ruler passes a fixed marking on the ruler. Again, synchronization usually involves some forces acting between objects. Usually, the force is electromagnetic. It could be light, radio waves, or near field electromagnetic interactions. Sometimes, the interaction can be gravitational as when one looks at the moons of Jupiter. All these ways to synchronize involve forces with a delay.

    Consider an inertial frame that I will refer to as S. A ruler that is standing still in the inertial frame S has a fixed length. However, the these forces vary with the velocity of the ruler relative to the origin of S. If you accelerate the ruler to a certain velocity, the forces that hold the ruler together will get stronger in the direction of motion so that the ruler gets shorter in the direction of motion as seen by an observer in S. Similarly, a clock standing still relative to the origin sees the clock oscillate at a certain rate. If the clock is forced to move, the forces that hold the clock together change and slow the clock down. As seen by an observer in S, there are delays in the forces used to synchronize the events. All these changes in forces are self consistent to any observer restricted to inertial frame S.

    Consider an inertial frame, S', that is moving relative to S. There is a ruler that is moving as seen in S. However, it is stationary with respect to S'. The internal forces that keep the ruler together as seen in S' are not the same internal forces that keep the ruler together in S. S' sees a longer ruler than S, but he sees forces consistent with this difference in length. A similar argument applies to the clocks. And to the synchronizing signals.

    Thus, S and S' see a different inventory of forces. The "inconsistencies" come about only when an observer changes inertial frames. An observer can always tell when he is switching inertial frames by an "accelerometer" of some type. As long as the observer doesn't accelerate in any way, the forces that he measures will be consistent with the lengths and the time units that he measures.

    Anyway, I always try to translate special relativity problems into an inventory of forces. That approach always makes sense to me. The mathematical results coming out of that result are equivalent to the results found using other starting points. So I can't claim my approach is any more "correct" than any other approach you may have. In fact, some people tell me one could have done it easier without calculating forces. That is probably true. However, if the calculated results are the same then the experimental predictions are the same. Therefore, the theory is the same. A theory is defined by its experimental predictions, not its approach.

    A difference that makes no difference is no difference.
     
  15. Mar 19, 2013 #14

    timmdeeg

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    But this is no surprise, as in order to calculate the speed of the photon its proper time is of no interest. You talk about coordinate time, the time the photon moves from a to b in your frame.
     
  16. Mar 19, 2013 #15

    Dale

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    Any correct statement is better than any incorrect statement, even if the correct statement is "inaccessible" and the incorrect one is not.

    I have no problem with using the spacetime interval and pointing out that it is null for light. But it is incorrect to call that either a proper time or a proper distance.
     
  17. Mar 19, 2013 #16
    ghwellsjr, could you post a link to one of these diagrams?

    I tried doing a search, and I did find some diagrams, but I am not sure they were helpful in terms of conceiving how this mechnically/pratically works in everyday life, or if indeed they were the ones you were talking about.

    Thanks :)
     
  18. Mar 19, 2013 #17

    ghwellsjr

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    Here's one, currently right below your thread:

    https://www.physicsforums.com/showthread.php?t=669629

    Go down to post #8.
     
  19. Mar 19, 2013 #18

    Nugatory

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    Are you thinking of photons as particles that travel at the speed of light, and thinking of particles as things like grains of sand except even smaller? That feels like a natural starting point (what else could a "particle" be?) but is misleading in a number of ways - and you've just found one of these ways.

    It's really hard to form a mental model of constant speed of light if you're thinking in terms of tiny little photon-lumps of light moving past you.

    Instead, try the alternate picture of light as an electromagnetic wave traveling through a vacuum. There's a time-varying electrical field, there's a time-varying magnetic field, the behavior of two are connected by Maxwell's laws of electrodynamics (and it is not a coincidence that Einstein introduced special relativity in a paper entitled "On the electrodynamics of moving bodies"). These laws say that as the electrical field changes it will change the magnetic field nearby, the changing magnetic field will in turn change the electric field nearby... and there we have an electromagnetic wave, aka light.

    WARNING: What follows is hand-waving. If it helps you form an intuitive picture of how the speed of light could be the same for all observers, good. But don't treat it as any more than an rough hand-wavy description, and don't push it any further...

    Electrical and magnetic fields look different to observers moving relative to one another; we could say that there is really one electromagnetic field that looks like a different mix of electrical and magnetic fields depending on the observer's motion. So if two observers moving relative to each other look at the exact same oscillating electromagnetic field, they will see different oscillating electrical and magnetic fields, and the differences are just enough to compensate for the differences in the observers' speeds, so they both end up with an electromagnetic wave (aka light) spreading at the same speed relative to them.

    Two cautions here:
    1) Did I mention that this is all handwaving? Unfortunately, I don' think it can be fixed without some serious quality time with a college-level E&M text - I like Purcell for its good connection to relativity.
    2) It is also dangerously circular. The transformations of the electrical and magnetic fields depend on the Lorentz transforms. But the Lorentz transforms were derived from an assumption of constant speed of light - so OF COURSE it the electrical and magnetic field transformations had to come out the way they did.

    However, it is a reasonable line of thinking for getting you past your question of what's so special about light ("Are photons partially non-local? Warping time-space to achieve this?")... Nothing is special, we're just subjecting electricity and magnetism to the same rules that we're subjecting everything else to.
     
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