Dilations dilations a dilation is an enlargement or reduction of a figure. Gravitational time dilation is a physics concept about changes in the passage of time, caused by general relativity. How can alice say that bobs clock runs too slowly, while bob is saying that alices clock runs too slowly given a situation between the two which appears to be completely symmetrical. I expect my students to complete them at their own pace and i have particular ideas for interacting with pairs of students as they work on each challenge. Assume that there is no relative motion between planet x and earth i.
Examples using the coordinate rule of dilation when the center of dilation is not the origin. Ccgpsgrade8mathematicshenrycountyschoolsflexbook b v58. Adobe portable document format pdf is a universal file format that preserves all of the fonts, formatting, colours and graphics of. To find the image matrix for a dilation centered at the origin, use the scale factor as the scalar. The audio playback block allows you to choose between pitch shifting and time dilation modes. The left pane displays the available bookmarks for this pdf. You are in the same inertial frame as the light clock. Energy and momentum are always conserved, and we can make ecient use. Lorentz transformation, time dilation, length contraction and.
For the former, simply pick two events at the same spatial location in s, separated by time we may as well pick the origin, x y z 0, and times t 0 and t. Dilation a transformation that stretches or shrinks a figure to create a similar figure. Time dilation simple english wikipedia, the free encyclopedia. Since the time is limited to eight minutes, it is not an indepth presentation. Oct 03, 2016 dilation a transformation that stretches or shrinks a figure to create a similar figure. As the light traveled towards her at speed c, c 1 was receding at a speed of 0.
Jul 28, 2010 a worked example using the time dilation formula by james dann for cc by sa. This is a presentation regarding time dilation, twin paradox and length contraction. This screenshot of the sample output shows a pdf file with bookmarks. Scale factors are applied to the preimage to create the image. Massachusetts institute of technology department of. The binary dilation of an image by a structuring element is the locus of the points covered by the structuring element, when its center lies within the nonzero points of the image. Center of dilation the fixed point the dilation uses. Examples using the coordinate rule of dilation when the center of dilation is the origin.
Time dilation and length contraction, two important concepts from special relativity, can easily be visualized and derived with intuitive, geometric graphs generated using two 3d st inertial frames, which have a constant relative velocity with respect to one another and where light is chosen as the communication medium for the systems. Imagine a light clock which consists of two mirrors and beam of light re. The upper part contains a clock placed high above the earths surface, thus in a region of low gravity while the clock at the bottom of the image is placed closer to the. Dilation when we describe dilations we use the terms scale factor and center of dilation.
Homogeneous dilation, the scalar multiplication operator on a vector space or affine space. Dilation is where the polygon grows or shrinks but keeps the same overall shape. Let us immediately extract from the lorentz transformation the phenomena of time dilation and lorentz contraction. Note how dilation increases and erosion decreases the number of white pixels in the image. A dilation is a transformation that produces an image that is the same shape as the original, but is a different size similar figure, so not an isometry. The first thing we must do is to write down the equation. Even if the time dilation effect is small, differences in elapsed time continue to build. Pitch shifting and time dilation using a phase vocoder in. One of the most interesting topics in the field of science is the concept of general relativity. Here is an example of the effect of erosion and dilation on a binary image. Dilation and curettage, the opening of the cervix and surgical removal of the contents of the uterus. The speed of light is abbreviated by the letter c, and its approximately 300,000 kilometers per second kps. Regarding understanding the equation, i think thats best done with interactive visuals, which i cant include here svgs with animations, but have tried to do so with the geometry of time dilation, hope its helpful. Note that time dilation and length contraction are just special cases.
Time dilation, twin paradox and length contraction prezi. Dilations help when center of dilation is not the origin practice dilations on a grid game exploring dilations practice, with transformation combination game following practice problems ixl r. The object of this exercise is to show explicitly how it is possible for two observers in inertial frames moving relative to each other at a relativistic speed to each see the others. Length contraction the e ect of time dilation, discussed in the previous lecture, seems selfcontradictory. Dilations are enlargements stretches or reductions shrinks. A transformation in which a polygon is enlarged or reduced by a given factor around a given center point. To ensure that that both the receiver and satellite agree on the elapsed time, the gps system should take into account time dilation from special relativity. Change the synthesis hopsize parameter to 64, the same value as the analysis hopsize parameter. Time dilation and length contraction from inside frame of reference sensor sensor light path viewed from inside ship d inside ship t is time of transit measured by a clock inside the ship as measured by someone looking in from both outside and inside the ship inside ship 2.
A clock in outer space moves more quickly than a clock on earth. Pages 35 of experimenting with dilations present my students with three dilation challenges, each more complex than the last. Scotthughes 15march2005 massachusetts institute of technology department of physics 8. A second inertial observer, who is in relative motion. Time dilation, in the theory of special relativity, the slowing down of a clock as determined by an observer who is in relative motion with respect to that clock. So let us try and make sense of the image and discover the reason behind gravitational time dilation. Massachusetts institute of technology department of physics. Does time dilation mean that time actually passes more slowly in moving references frames or that it only seems to pass more slowly. This determines the output of the morphological operation. Moving clocks run slow plus moving clocks lose synchronization plus length contraction leads to consistency.
Regarding understanding the equation, i think thats best done with interactive visuals, which i cant include here svgs with animations, but have tried to do. Dilation is a mathematical morphology operation that uses a structuring element for expanding the shapes in an image. A read is counted each time someone views a publication summary such as the title, abstract, and list of authors, clicks on a figure, or views or downloads the fulltext. If point p be the center of dilation, then enlargement. The following video is an explanation of time based on wave theory, including relativity concepts. Ninth grade lesson experimenting with dilations betterlesson.
Dilation affine geometry, an affine transformation dilation metric space, a function from a metric space into itself dilation operator theory, a dilation of an operator on a hilbert space dilation morphology, an operation in mathematical morphology scaling geometry, including. Heavy things like planets create a gravitational field that slows down time nearby. He wishes he were 6 feet tall with a width of 4 feet. Special relativity time dilation length contraction along the direction of motion space and time are relative relativity of simultaneity velocities are relative, except for that of light, and add up in such a way that they never exceed the velocity of light. A dilation requires a center point and a scale factor. Lorentz transformation, time dilation, length contraction. On running the model, the pitchscaled signal is automatically played once the simulation has finished. Use scalar multiplication to find the vertices of nr9s9t9 after a. One tick is when the light goes from one mirror to the other and back again.
Try this adjust the slider on the right to change the scale factor. Cervical dilation, the widening of the cervix in childbirth, miscarriage etc coronary dilation, or coronary reflex. Time dilation is a complex phenomenon, and this quizworksheet will help you test your understanding of its definition and how it works. For additional information on how to save your logoaddress as a.
If we assume time t is frequency, we obtain the equation for time dilation. All points move the factor or ratio by which everything is enlarged or reduced is the constant of dilation, k. Abc center of dilation is 0, 0 scale factor, k, is or xy. A worked example using the time dilation formula by james dann for cc by sa. Scale factor the ratio of a side length of the image to the side length of the corresponding original side length.
It is obvious that for a dilation to maintain its proportionality of sides, the two variables must be multiplied by a constant value, k, known as the scale factor. The effects of time dilation dont become really noticeable until very high speeds are reached so for this worked example i will use a speed of 90% of that of light, that is 270,000 km per second the speed of light is very close to 300,000 km per second, or 186,300 miles per second. This means that a clock on a spaceship far away from any planet would move faster than a clock near earth. Including the time dilation factor correctly, she concludes that in the 3 seconds that the light from the clock took to reach her, the clock itself will have ticked away 3. Time dilation helps explain how the speed of light doesnt change with perspective. The video is narrated by kyle yee, a fifth grader at the time of the videos production. The difference between the two returns the border of the white objects. You know, this idea that strange things happen as you near the speed of light. Massachusetts institute of technology department of physics 8.
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