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Measuring the wavelength of light?

  1. Jul 4, 2003 #1
    If a ray of light was capable of grabbing the end of our tape measure as it passed us, it could prove to the world once and for all that the speed of light is not the same for observers at different velocities. Consider the following:

    Imagine we are observing a ray of light that has a frequency of 10 cycles per second, and a wavelength of 1 foot. We can calculate the speed of light to be 10 feet per second. If the light grabbed the end of our tape measure as it passed, it would pull out 10 feet in one second. What happens if we increase speed towards the source sufficient enough to double the frequency? Textbooks will tell you that as you increase speed towards the source, the frequency will increase and the wavelength will decrease. So at our new speed, how far do you think the light (in 1 second) will pull out our tape measure? Textbooks will say 10 feet, since you now have a frequency of 20 cycles per second and a wavelength of 6 inches.

    At our new speed, the tape measure would actually be pulled out 20 feet in 1 second. This is because it is impossible to change the distance light has to travel through space from the source to complete one cycle by simply observing it at different speeds. The number of cycles we see in a second (frequency) is completely related to our speed relative to the source. The distance the light has to travel from the source to complete one cycle (wavelength) is always the same. You cannot change the distance a ray of light has to travel from the source to complete a cycle by running into the next cycle.

    To plot our ray of light that has a frequency of 10 cycles per second, and a wavelength of 1 foot, we can draw a 10-inch line that represents 1 second. On that line will be 10 dots representing each completed cycle, they will be spaced 1-inch apart. If we increase speed until the frequency is doubled and then plot the new ray of light, we will now have 20 dots spaced a half an inch apart. Calculating the speed we will find that the light is still traveling towards us at 10 feet per second. Our flaw comes from not adjusting the length of our line. The length of the line does not just represent 1 second; it represents the amount of distance traveled in 1 second. So as we increase speed towards the source, we must also increase the length of our line. This will cause an increase in frequency, the wavelength stays the same, and the speed increases.

    At our increased speed, interferometers and oscilloscopes will both squeeze the 20 cycles on our 10-inch line. This will indicate that the speed of light does not change as we travel at increasing speed towards it. If we believe this, then we must believe that by changing our speed towards the source, we can control the distance the wave must travel from the source in order to complete 1 cycle.

    Try to imagine a source of light that instead of shooting out a beam of light, it shot out 1-foot rulers, one after the other in a straight line. If you increase speed towards the source you can increase the amount of rulers you pass in a second, but you cannot change the length of the rulers. Don’t let perception distort reality.
     
    Last edited: Jul 5, 2003
  2. jcsd
  3. Jul 4, 2003 #2
    That is such a long post, I don't even wanna read it. Yeesh. Put some paragraph marks in!
     
  4. Jul 4, 2003 #3
    Maybe that's why

    light doesn't go around grabbing the ends of tape measures?

    If you want to learn something about Relativity get "Spacetime Physics" by Taylor and Wheeler. It's a very intuitive presentation which only requires moderate math skills, but is rigorous nontheless.

    Special Relativity is a very self consistent formal structure based on the Poincare group of transformations. So self consistent that it is hard to combine it with other theories, which greatly limits the possible ways the world can be described. So you need to be very carefull when you propose another theory that it conforms to Poincare invariance.
     
  5. Jul 5, 2003 #4
    You missed a point somewhere..
     
  6. Jul 5, 2003 #5

    drag

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    Greetings !

    That is indeed quite a long post. One thing it is important
    for you to realize is that wavelenght * frequency = c .
    If the wavelenght contracts then the frequency increases
    and the opposite. I advise that you read about SR.
    This book can help:
    http://www.bartleby.com/173/

    If you have more specific questions (shorter ones ) on
    this subject I'll be glad to help. :smile:

    Live long and prosper.
     
  7. Jul 5, 2003 #6
    I understand and am not questioning the fact that frequency times wavelength equals the speed. I am questioning if what we calculate and what we believe to measure is in reality the true wavelength. With all memorized facts put aside, try to picture what really happens as you approach the light. The beam of light is out in space, it is exactly the same whether we are there or not.

    A beam of light has to travel a specific amount of distance from the source to complete one cycle. This distance cannot be changed by our perception. What I wish to discuss is our methods of measuring wavelength. Oscilloscopes, interferometers, and even plotting on paper all assume one thing. They all create a line with a specific length, and give it a value, such as “1 second time period”. Then they plot each new cycle on the line at the time it occurred. If they accelerate towards the source, they again plot the new cycles, but they use the same line with the same length. Doing this, the frequency will always increase and the wavelength will decrease.

    What I think is flawed is that this line is not just a “1 second time period”, it is “the distance traveled in one second”. The length of this line needs to be extended (or rescaled) if we increase speed towards the source. If not we are saying that the distance light travels from the source to complete a cycle gets smaller because we are approaching it.

    Picture yourself driving down a road with telephone poles installed every 200 feet. Draw a 1-foot line and plot out the poles on the line at the corresponding time you passed it. If you increase speed and again plot the poles on the same line, you will see more dots that are all closer together. Frequency goes up because you pass more poles, but can you really believe the distance between them have changed?
     
  8. Jul 5, 2003 #7

    drag

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    Greetings grounded !
    What you have to understand is that measures of time, distance
    and even energy are all relative according to the theory of
    relativity.

    The Special theory of Relativity is the result of two basic assumptions:
    1. The laws of physics are the same for all observers.
    2. A law of physics: the speed of light = c.

    What does that mean ?

    Imagine a train and a passenger inside it. Imagine another person
    outside the train. If the person outside observes a light
    beam travelling along the tracks he'll observe it's velocity as c.
    The person in the train travelling at speed v will also observe
    the light beam at speed c, NOT v + c.

    What happens with the wavelenght and freq. ?

    They change accordingly while maintaining the ratio
    according to the formula I told you about, because the speed
    of light is still c. Now imagine that you look at an object -
    see the light that it reflects. The wavelenght changes, so
    the dimensions you see also change. Thus, like Einstein said,
    everything is relative (there is no "true" wavelenght).
    The speed is the same - c - speed of light, but the
    distance and time - wavelenght, are relative.
    Of course, because if you go fast enough (close to c) the
    distance contracts significantly. Why ? Because distance and
    time are relative. If you say that the distance is 200 feet
    then you have to specify the rest frame in which it is so. In
    a rest frame relative to which the poles travel at 1/2 c the
    distance is just about 174 feet.

    I really advise you to read Einstein's book to which I provided
    a link. It's very simple and basic level for the popular
    reader and as far as Special Relativity goes - you'll understand
    this whole thing after just about the first 20 pages.

    Hope this helps. :smile:

    Live long and prosper.
     
  9. Jul 5, 2003 #8
    Drag..thanx 4 reply

    I totally understand Einstein’s Special Theory of Relativity. I am not here to argue his theory. What I want is to pick YOUR brain by asking you a question that you should be able to answer on your own. Pretend you never heard of Einstein, my question only involves simple math and obvious deductions.

    Regarding what I originally wrote:

    Picture yourself driving down a road with telephone poles installed every 200 feet. Draw a 1-foot line and plot out the poles on the line at the corresponding time you passed it. If you increase speed and again plot the poles on the same line, you will see more dots that are all closer together. The frequency will go up because you pass more poles.

    Imagine that at first you were driving 55 MPH, then you increased speed to 80 MPH.

    Do you agree with me that in order to plot this on our paper correctly, either the length of the line we mark the cycles on has to be increased, or the scale of the line has to be changed?

    If so, do you see that as speed is increased the frequency will go up but the wavelength cannot be changed? Do you understand my point? What is YOUR opinion? Do you see why the wavelength cannot change no matter what your speed?
     
  10. Jul 5, 2003 #9
    But the lengths and times do change because of your speed, or more exactly, because of your change in velocity. In Einstein's original paper on the subject "The Electrodynamics of Moving Bodies" he described several cases similar to the one you present just to show people that this was the case and was logically consistent.
     
    Last edited: Jul 5, 2003
  11. Jul 5, 2003 #10
    I am not talking about relativistic speeds…

    At a constant velocity of 55MPH, in 1 hour you will pass 1452 poles.
    At a constant velocity of 80MPH, in 1 hour you will pass 2112 poles.

    If we plot both tests on the same line (based on 55MPH and 200' between poles), without changing its length or scale, at 80MPH the distance between the poles will only be 137.5 feet instead of 200 feet.

    Not only that, but our speed will always be calculated to be 55MPH.
     
  12. Jul 5, 2003 #11
    This statement is definitely false. When you increase speed relative to the source you will have first and second order changes in the number of rulers you pass. The second order changes definitely will change the length of the rulers from your viewpoint.
     
  13. Jul 5, 2003 #12

    drag

    User Avatar
    Science Advisor

    Greetings !
    I am not certain what it is that you're trying to do, however,
    if your velocity increases from 55 to 80 then the distance
    you pass will increase not the distance between the poles.
    It's ridiculous to draw your total distance passed on a
    paper as the same each time and thus mistakenly deduce
    that the distance between the poles changed.

    Live long and prosper.
     
  14. Jul 6, 2003 #13
    I agree…the length of the line must be increased in order to show a greater distance traveled in the same amount of time. My question is why do we not lengthen the line when we are measuring light? If we are measuring poles and do not increase the line, our speed will remain the same no matter how fast we travel. As we increase speed, the frequency of the poles will increase but the distance between them, as plotted on paper, will decrease. Doing this, frequency times the wavelength will always equal 55 MPH.

    Is this not the same thing we do with light? We take a line, call it one second, and plot the cycles on it. If we give this line to anyone, traveling at any speed, in any direction, and they plot the cycles without changing the length or scale of this line, everyone will measure the speed to be the same, just as it is for the person plotting the poles.

    If the person plotting the poles increases the length of their line as they increase speed, they will now come up with the correct speed of 80 MPH. The length of the line must be increased because it represents the amount of distance covered in a specific amount of time. The time stays the same but more ground is traveled requiring the amount of distance the line represents to be increased.

    If we used an oscilloscope to measure a beam of light, as we increase speed towards the source, the number of cycles on the screen will be increased and the distance between them will be decreased. Doing the math, we will find that the beam always travels at the speed of light. If we increase the length of the line, since we increased speed and are covering more ground in the same amount of time, we will see that the speed of light is not constant. It is the wavelength that remains the same. The number of cycles we run into, and the speed at which we approach the light, are the only thing capable of change. You cannot change the distance light has to travel from the source to complete one cycle just by traveling towards the source.

    The only way to get a changing wavelength is to NOT adjust the length of the line. If you cover more distance in the same amount of time, do you not have to increase the line that represents the amount of distance covered in an amount of time?
     
  15. Jul 6, 2003 #14

    Janus

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    1 hr as measured by whom? the car or the poles. As measured from the cars, at 55mph you will pass 1452.00000000000188284465020576498
    poles in an hour and they will be 199.999999999999740655006858710394 ft apart.

    At 80, you will pass 2112.00000000000579423868312759586
    poles in an hour and they will be 199.999999999999451303155006857958
    ft apart.
     
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