Space-time curvature is incorrect

Discussion in 'Physics & Math' started by Frencheneesz, Aug 26, 2002.

  1. Frencheneesz Amazing Member Registered Senior Member

    Messages:
    739
    Chroot:

    "who don't actually even understand the theory, are so content to call it wrong. "

    Im beggining to think you know very little about this subject as well. You seem only to insult people, instead of actually DISCUSSING the material. If we don't understand it, why don't you explain it them.

    "That's not a very fundamental definition"

    You seem to think in absolutes. That may not be YOUR definition, BUT it WAS how i WAS using the word. If I used the word carrot to mean gravity, you should be able to understand it after i give you MY definition for it.

    "all derivatives of position are important, if you insist on looking at things that way. "

    I understand the mathmatic theorys are considerably accurate. Is there a mathmatical calculation to find a sum of infinte derivatives?

    "If you move further away from the sun, the light will take longer to get to you, since it has further to go and it must go the greater distance at the same speed. "

    I love how you treat me like I am mentally slow. I DO think that is how things work, but I was under the asumption that relativity thought differently.

    If light always travels at the same speed for all frames of reference, then consider this example:

    Two observers are both 100 light-seconds away from a light source. The light source pulses. At 50 seconds after the light left the source, observer MOVE starts moving away from the source at .01 c, while the other observer, STAY, stays in place.

    You said "the light will take longer to get to you, since it has further to go", therfore the moving observer should see the light after the stationary observer.

    LS = Light-second
    D([bserver]= distance of observer from light pulse
    SC([observer]) = Speed of light (derived) relative to observer

    at time 0 s - D(STAY) = 100 LS D(MOVE) = 100 LS
    at time 50 s - D(STAY) = 50 LS D(MOVE) = 100 LS
    at time 70 s - D(STAY) = 30 LS D(MOVE) = 30 + 20*.01c = 100.2 LS
    at time 100 s - D(STAY) = 0 LS D(MOVE) = 0 + 50*.01c = 100.5 LS
    at time 100'000/995 ~ 100.5025 D(MOVE) = 0

    Average Speed = d/t
    SC(STAY) = (100-0)/100 * c = 100/100 * c = 1 * c = c
    SC(MOVE) = (100-0)/(100'000/995) = 995/1000 ~ .995 c

    As you can see, with the asumption that light takes a longer time to travel to an oberver who had started to move away from it, you can not also make the assumption that light has the same speed for all observers. This is because the distance between the light and the observers was ALWAYS less than 100 meaning that the fact that one observer moved makes the light travel slower, not the overall distance increase.


    Rav:

    "In other words, everything is always travelling through space-time at the speed of light. "

    Ok, that is actually a very intuitive way to put it, thanks.

    Prosoothus: "relativists also believe that the time dilation a moving observer experiences is dependent on the direction the particles of light are moving relative to the observer. "

    I haven't heard that particular hypothesis before. How would this work, do you know?
     
    Last edited: Oct 5, 2002
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  3. chroot Crackpot killer Registered Senior Member

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    "Im beggining to think you know very little about this subject as well. You seem only to insult people, instead of actually DISCUSSING the material. If we don't understand it, why don't you explain it them. "

    The irony. People try to explain things to you. As has already been pointed out, you cling to your own stupid explanations and refuse to listen.

    "You seem to think in absolutes. That may not be YOUR definition, BUT it WAS how i WAS using the word. If I used the word carrot to mean gravity, you should be able to understand it after i give you MY definition for it. "

    Welcome to Step 7.

    "I love how you treat me like I am mentally slow. I DO think that is how things work, but I was under the asumption that relativity thought differently."

    You are mentally slow.

    "Ok, that is actually a very intuitive way to put it, thanks. "

    Unfortunately, it's wrong.

    - Warren
     
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  5. Frencheneesz Amazing Member Registered Senior Member

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    "You are mentally slow."

    Hey, I thought you were a college graduate. Unless you are some kind of super geneious that graduated college at age 11, i think your remarks are a tad immature.
     
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  7. James R Just this guy, you know? Staff Member

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    <b>Rav</b>:

    <i>It is. There is one fixed constant speed at which everything travels through space-time. You can't go any slower, and you can't go any faster.</i>

    I'm afraid that's not true.

    <i>It will help if you assume that the train is travelling at a significant percentage of the speed of light relative to the embankment, since things don't become plainly obvious otherwise.</i>

    The speed of the train is irrelevant. It could be moving at 1 km/hr and the result is the same.

    <i>I'm still struggling with certain aspects of Einsteins theories myself because human intuition dies hard.</i>

    Yes, it seems you are.


    <b>Tom</b>:

    <i>Relativity ASSUMES that length contracts and time dilates for a moving observer so that the speed of light is always c in the observer's frame of reference.</i>

    That's not an assumption - it is a derived result, confirmed by experiment.

    <i>If that's not illogical enough, relativists also believe that the time dilation a moving observer experiences is dependent on the direction the particles of light are moving relative to the observer.</i>

    Please don't tell lies.

    <i>Personally, I believe that Einstein's imagination overpowered his reasoning abilities.</i>

    Personally I believe that you don't even want to try to understand relativity.


    <b>Frencheneesz</b>:

    <i>I understand the mathmatic theorys are considerably accurate. Is there a mathmatical calculation to find a sum of infinte derivatives?</i>

    How is that relevant?

    <i>I DO think that is how things work, but I was under the asumption that relativity thought differently.</i>

    Well, now you know it doesn't.

    Let's look at your example:

    <i>Two observers are both 100 light-seconds away from a light source. The light source pulses. At 50 seconds after the light left the source, observer MOVE starts moving away from the source at .01 c, while the other observer, STAY, stays in place.</i>

    So, taking the position of the light source as zero, and measuring distances in light seconds and speeds in light seconds per second, the positions of the light and observers at time t are given by:

    light(t) = t
    STAY(t) = 100
    MOVE(t) = 0.01 (t - 50) + 100 for t>50 s, and 100 for t<50 s

    Now, let's look at your calculations:

    <i>LS = Light-second
    D([bserver]= distance of observer from light pulse
    SC([observer]) = Speed of light (derived) relative to observer

    at time 0 s - D(STAY) = 100 LS D(MOVE) = 100 LS
    at time 50 s - D(STAY) = 50 LS D(MOVE) = 100 LS
    at time 100 s - D(STAY) = 0 LS D(MOVE) = 0 + 50*.01c = 100.5 LS
    at time 100'000/995 ~ 100.5025 D(MOVE) = 0</i>

    From my equations, I get:

    at time t=0, STAY = 100, MOVE = 100, light = 0
    at time t=50, STAY = 100, MOVE = 100, light = 50
    at time t=100, STAY = 100, MOVE = 100.5, light = 100
    at time t=100000, STAY=100, MOVE = 1099.5, light = 100000

    The distances between the observers and the light pulse are:

    at time t=0, STAY = 100, MOVE = 100
    at time t=50, STAY = 50, MOVE = 50
    at time t=100, STAY = 0, MOVE = 0.5
    at time t=100000, STAY=99900, MOVE = 98900.5

    In all cases, the speed of light relative to either observer is the distance the light has travelled divided by the time. In all cases, this comes out to be 1 light second per second.

    Let's work out when the light catches up with each observer. The light catches up with STAY when STAY = light. From above:

    light(t) = t
    STAY(t) = 100
    so t = 100 seconds

    i.e. the light takes 100 seconds to reach STAY. No surprises there.

    light(t) = t
    MOVE(t) = 0.01 (t - 50) + 100 for t>50 s
    so t = 0.01t - 0.5 + 100
    0.99t = 99.5
    t = 100.505 seconds

    i.e. light reaches MOVE 0.505 seconds after it reaches STAY, because MOVE is moving away.

    What's the problem?
     
  8. Frencheneesz Amazing Member Registered Senior Member

    Messages:
    739
    "taking the position of the light source as zero, and measuring distances in light seconds and speeds in light seconds per second"

    I was not taking the position of the light source as zero. I was taking the position of the observer as zero.

    The light source became old history after the light left it.

    "MOVE(t) = 0.01 (t - 50) + 100 for t>50 s, and 100 for t<50 s "

    This is the equation for the observer MOVE's position relative to the light source. I think you will find that my equations show the observers position from the actual light pulse.
     
  9. James R Just this guy, you know? Staff Member

    Messages:
    30,360
    Frencheneesz,

    It makes no difference (and in any case I already calculated that too). My equations for the distance of the observers from the light pulses at time t are:

    STAY(t) = |t - 100|
    MOVE(t) = |0.99t - 99.5| for t>50 s, and |t - 100| for t<50 s

    At time t=0, STAY = 100, MOVE = 100
    At time t=100, STAY = 0, MOVE = 0.5
    At time t=100000, STAY = 99900, MOVE = 98900.5

    Notice, for example, that at t=100, the light pulse has not yet reached MOVE, because MOVE is moving away from the source.

    So?
     
  10. Frencheneesz Amazing Member Registered Senior Member

    Messages:
    739
    Well, as luck will have it, I can prove my point with your equations.

    "MOVE(t) = |0.99t - 99.5| for t>50 s, and |t - 100| for t<50 s "

    I'm just wondering where the .99t and the 99.5 come from. Where do they come from?

    "At time t=0, STAY = 100, MOVE = 100
    At time t=100, STAY = 0, MOVE = 0.5 "

    Velcity = Distance/Time

    Velocity(Stay) = (100-0)/100 = 1

    Velocity(Move) = (100-0.05)/100 = .9995

    these are clearly not equal. Therefore proving my point that with the asumption that light takes a longer time to travel to an oberver who had started to move away from it, you can not also make the assumption that light has the same speed for all observers.
     
  11. James R Just this guy, you know? Staff Member

    Messages:
    30,360
    Frencheneesz,

    Step me through your calculations. What are the numbers you are putting into your speed calculations? I can't see where you're getting them from.
     
  12. Rav Valued Senior Member

    Messages:
    2,422
    James R,

    The following passages are from "The Elegant Universe" by Brian Greene. I'm quoting from this particular book since I happen to have it in text format on my PC. In other words, it's convenient.

    "When an object moves through space relative to us, its clock runs slow compared to ours. That is, the speed of its motion through time slows down. Here's the leap: Einstein proclaimed that all objects in the universe are always traveling through spacetime at one fixed speed—that of light."

    Are you suggesting I throw this book away? It's not the only one either written by a very credible physicist that I'd have to discard. This is a core truth, however mind blowing it might be.

    "However, were one to take a trip in a futuristic space vehicle traveling at a substantial fraction of light speed, the effects of relativity would become plainly obvious."

    This is what I was getting at.

    James, when I say I'm struggling with certain aspects of Einteins theories, I'm not saying I can't understand them. What I am saying is that I am endeavouring to gain an "intuitive" understanding of them. There's a big difference as far as I am concerned. What is really going on? How does this shed light on the nature of the universe? I want to "feel it in my bones".

    I'm certainly no mathematician although I've chosen to learn certain things out of neccessity, in order to clarify things for myself. And I'm the kind of person who genuinely seeks truth, which means I apply my common sense, and check out the facts for myself. I read books, I research, and I pretty much don't ever stop. You can never learn too much. That obviously doesn't make me infallible, and if I'm wrong, I want to know about it.

    Can you elaborate on why you think my current understanding is flawed?
     
  13. James R Just this guy, you know? Staff Member

    Messages:
    30,360
    Rav,

    I have Greene's book. Do you have a page reference, or can you give me more of the text, so I can put the piece you quoted in context. As a bald statement, it doesn't make sense.

    <i>Are you suggesting I throw this book away?</i>

    Far from it. It is an excellent book.

    <i>"However, were one to take a trip in a futuristic space vehicle traveling at a substantial fraction of light speed, the effects of relativity would become plainly obvious."</i>

    I agree.

    <i>Can you elaborate on why you think my current understanding is flawed?</i>

    At this stage, I cannot. I need to see the full quote. Perhaps Greene is in fact talking about spacetime intervals rather than speed through 3-d space. I won't know until I see the context.
     
  14. Rav Valued Senior Member

    Messages:
    2,422
    James,

    Unfortunately I can't tell you what page it's on. My beaten up copy is at work right now. But I'll copy and paste some more text which should put it in context for you. The text document I have doesn't include page numbers.

    "Motion through space is a concept we learn about early in life. Although we often don't think of things in such terms, we also learn that we, our friends, our belongings, and so forth all move through time, as well. When we look at a clock or a wristwatch, even while we idly sit and watch TV, the reading on the watch is constantly changing, constantly "moving forward in time." We and everything around us are aging, inevitably passing from one moment in time to the next. In fact, the mathematician Hermann Minkowski, and ultimately Einstein as well, advocated thinking about time as another dimension of the universe—the fourth dimension—in some ways quite similar to the three spatial dimensions in which we find ourselves immersed. Although it sounds abstract, the notion of time as a dimension is actually concrete. When we want to meet someone, we tell them where "in space" we will expect to see them—for instance, the 9th floor of the building on the corner of 53rd Street and 7th Avenue. There are three pieces of information here (9th floor, 53rd Street, 7th Avenue) reflecting a particular location in the three spatial dimensions of the universe. Equally important, however, is our specification of when we expect to meet them—for instance, at 3 P.M. This piece of information tells us where "in time" our meeting will take place. Events are therefore specified by four pieces of information: three in space and one in time. Such data, it is said, specifies the location of the event in space and in time, or in spacetime, for short. In this sense, time is another dimension.

    Since this view proclaims that space and time are simply different examples of dimensions, can we speak of an object's speed through time in a manner resembling the concept of its speed through space? We can.

    A big clue for how to do this comes from a central piece of information we have already encountered. When an object moves through space relative to us, its clock runs slow compared to ours. That is, the speed of its motion through time slows down. Here's the leap: Einstein proclaimed that all objects in the universe are always traveling through spacetime at one fixed speed—that of light. This is a strange idea; we are used to the notion that objects travel at speeds considerably less than that of light. We have repeatedly emphasized this as the reason relativistic effects are so unfamiliar in the everyday world. All of this is true. We are presently talking about an object's combined speed through all four dimensions—three space and one time—and it is the object's speed in this generalized sense that is equal to that of light. To understand this more fully and to reveal its importance, we note that like the impractical single-speed car discussed above, this one fixed speed can be shared between the different dimensions—different space and time dimensions, that is. If an object is sitting still (relative to us) and consequently does not move through space at all, then in analogy to the first runs of the car, all of the object's motion is used to travel through one dimension—in this case, the time dimension. Moreover, all objects that are at rest relative to us and to each other move through time—they age—at exactly the same rate or speed. If an object does move through space, however, this means that some of the previous motion through time must be diverted. Like the car traveling at an angle, this sharing of motion implies that the object will travel more slowly through time than its stationary counterparts, since some of its motion is now being used to move through space. That is, its clock will tick more slowly if it moves through space. This is exactly what we found earlier. We now see that time slows down when an object moves relative to us because this diverts some of its motion through time into motion through space. The speed of an object through space is thus merely a reflection of how much of its motion through time is diverted."


    EDIT: Chapter 2 under the heading "Motion through Spacetime".
     
    Last edited: Oct 5, 2002
  15. Frencheneesz Amazing Member Registered Senior Member

    Messages:
    739
    I think Rav said what I was trying to get across to you before, much better than I did. I understand these concepts, but I lack an intuitive understanding, as he said.

    "I can't see where you're getting them from."

    Likewise with this formula:
    "MOVE(t) = |0.99t - 99.5| for t>50 s, and |t - 100| for t<50 s "

    OK, heres what my numbers came from:

    [Stupid site wouldn't link a picture]

    Velocity(Stay) means The velocity of Stay relative to the light pulse
    Velocity(Move) means the velocity of Move relative to the light pulse.
     
    Last edited: Oct 6, 2002
  16. Prosoothus Registered Senior Member

    Messages:
    1,973
    Q,

    Take a look at the Lorentz's boost transformations. According to the boost transformations, the time a one-way beam of light takes to travel in a moving frame of reference is not only related to the speed of the moving observer, but is related to the direction of the motion of the light relative to the observer. If the direction of the light was not taken into consideration in the boost transformations, the omnidirectional speed of light would not be c in the moving observer's frame of reference.

    Crisp, James, and I have had a lengthy discussion about this "inconsistancy" before. Weren't you paying attention?

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    Tom
     
    Last edited: Oct 5, 2002
  17. James R Just this guy, you know? Staff Member

    Messages:
    30,360
    <b>Rav</b>:

    It seems Greene is not talking about normal speeds, but some kind of speed in 4 dimensions. That is different from our ordinary idea and definition of speed. I suspect he is using the 4-vector velocity and creating a scalar quantity from it, which turns out to be the same for both light and massive particles in timelike motion. That quantity is probably related to the proper motion through spacetime of whatever the object is. Here's the relevant part of the text:

    "This is a strange idea; we are used to the notion that objects travel at speeds considerably less than that of light. We have repeatedly emphasized this as the reason relativistic effects are so unfamiliar in the everyday world. All of this is true. <b>We are presently talking about an object's combined speed through all four dimensions—three space and one time—and it is the object's speed in this generalized sense that is equal to that of light.</b>"

    His explanation is a bit unclear, so I can see how the confusion arises here.


    <b>Frencheneesz:</b>

    You need to be more careful what you calculate with. You are not calculating the speed of light by taking the distance light travels over time (as you should). Instead, you're plugging in numbers which represent the distance between each observer and the light pulse at some arbitrary time. The speed you calculate that way is not the speed of light, but the (average) speed at which the distance is closing between the light pulse and the observer.

    Notice that the gap is closing slower for the MOVE observer than for the STAY observer - exactly as we would expect.


    <b>Tom:</b>

    <i>Take a look at the Lorentz's boost transformations. According to the boost transformations, the time a one-way beam of light takes to travel in a moving frame of reference is not only related to the speed of the moving observer, but is related to the direction of the motion of the light relative to the observer.</i>

    The time it takes to travel where?

    <i>If the direction of the light was not taken into consideration in the boost transformations, the omnidirectional speed of light would not be c in the moving observer's frame of reference.</i>

    Huh?

    <i>Crisp, James, and I have had a lengthy discussion about this "inconsistancy" before. Weren't you paying attention?</i>

    What inconsistency? I don't remember any inconsistency arising in our previous discussion.
     
  18. Rav Valued Senior Member

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    2,422
    Thanks for the reply James

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    Of course. You have to talk about speed in all 4 dimensions. Space-time is 4 dimensional, so you have to think 4 dimensionally. It's what I've been trying to get across all along. What I don't understand is why both yourself and chroot disagree with the following;

    "Einstein proclaimed that all objects in the universe are always traveling through spacetime at one fixed speed—that of light"

    I think Brian is perfectly clear, and that you are making this far more complicated than it needs to be.

    Lets do it this way, if you don't mind. Can you explain to me why it's wrong to take the above quote from Brians book at face value? It didn't need to be put in context, since the context only reaffirmed what it means when you take it at face value. It doesn't conflict with anything, and it comes from a man who seems to have a very deeply developed understanding. To me, it seems to be an accurate and very enlightening way of looking at things.

    I'll see if I can dig up the other sources I mentioned that have given me every reason to feel confident in my interpretation.

    This makes absolutely perfect sense to me. I also understand that scientifically that is largely irrelevant. I keep an open mind, and in the words of Carl Sagan, I "try not to get overly attached to a hypothesis just because it's [mine]". In this case, not overly attached to an interpretation.

    I invite everyone to take thier very best shot at showing me why this isn't an essential truth. My intention is not to sound arrogant but to get this cleared up. If you don't mind

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    Last edited: Oct 5, 2002
  19. (Q) Encephaloid Martini Valued Senior Member

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    Prosoothus

    Crisp, James, and I have had a lengthy discussion about this "inconsistancy" before. Weren't you paying attention?

    Yes, I was paying attention. And from my point of view, it was quite obvious when and where your misunderstandings of that lengthy discussion took place. Crisp and JamesR however, went to great lengths to point out those misunderstandings, not only on this thread, but several others.

    Good on them, bad on you, for it is you who is not paying attention.
     
  20. (Q) Encephaloid Martini Valued Senior Member

    Messages:
    19,125
    Rav

    I invite everyone to take thier very best shot at showing me why this isn't an essential truth.

    OK, I'll give it a shot, but words cannot explain it as well as math:

    Spacetime position x = (ct, x1, x2, x3)

    Velocity = dx/d{tua} which has magnitude c, here {tau} is the "proper time" defined by:

    d{tau}^2 = dt^2 - c^-2(dx1^2+dx2^2+dx3^2).
     
  21. Rav Valued Senior Member

    Messages:
    2,422
    Q,

    As I mentioned in a previous post, I am no mathematician. No doubt atleast someone here, perhaps you, might think that if I don't understand all of the mathematics involved, I have no business posting in this thread. At present, I am endeavouring to understand things conceptually. Einstein himself didn't think it was a waste of time for people to pursue that course, which is why he wrote a book for them. Perhaps one day, if I am interested enough and have reached an impass, I will take it further. For now it's just an intellectual pursuit stemming from an insatiable curiosity about the nature of the universe.

    If you feel inclined, I'd like it if you could try to communicate your ideas in view of that. If not you, I hope someone else can.

    Here's a quote from "Relativity Visualized".

    "The reason you can't go faster than the speed of light is that you can't go slower. Everything, including you, is always moving at the speed of light. How can you be moving if you are at rest in a chair? You are moving through time.

    Why are clocks moving through space perceived to run slower and slower as they travel faster and faster? Because a clock properly runs throught time, not through space. If you compel it to run through space, it is able to do so only by diverting some of the speed it should use for traveling through time. As it travels through space faster and faster, it diverts more and more speed. How much speed can it possibly divert? The clock can divert ALL its speed. Then it is going through space as fast as it possibly can, but there is nothing left for traveling through time. The clock stops ticking. It stops aging."


    This, I now remember, is where I first encountered the idea. Brian Greene is saying the same thing. And there are other books I've read that I'll quote from when I come across the relevant passages again. I don't understand why any of this is wrong, and I don't understand why several people who are obviously well versed in special and general relativity are disagreeing with the authors of some of the best books out there.
    I am not saying anything that they haven't said already.

    I'd like to resolve this here, because I've been following this thread with interest, and there are some talented people who have a lot to offer, and I'm more than willing to listen.
     
    Last edited: Oct 5, 2002
  22. c'est moi all is energy and entropy Registered Senior Member

    Messages:
    583
    rave,

    the idea is plain stupid (just to name one of my objections: spacetime is ONE according to the theory - you're moving through SPACETIME ... )

    I've never come across it through lectures on relativity
     
  23. c'est moi all is energy and entropy Registered Senior Member

    Messages:
    583
    just one more thing: I wonder what FOR you take to say that you're moving through time
     

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