|Jun28-08, 01:21 PM||#1|
Possible Analogy for Objects Moving at C
From my understanding of spacetime, space and time are one; an object cannot be displaced a distance without also being displaced in time. The only way to travel through space without also moving through time is to "curve" spacetime around you. Previously, I have had difficulty understanding exactly what was meant by "curving" spacetime, but I think I might have found an analogy that speaks to how this is done.
Imagine a supercavitating torpedo at rest in an ocean; it uses gases to force water out of its way as it moves beneath the surface. We'll say distance in the ocean is measured according to our normal experience on Earth. However, time is measured by displacement through the water. The only way to travel through space without also moving through the water is to "curve" the water around you
We'll say the supercavitating torpedo is spraying gases a little bit when it is at rest, making an air/water bubble mix in the area immediately around the torpedo. If a rag were to suddenly appear right next to the torpedo, it would become saturated with water slightly after a similar rag simultaneously placed a longer distance away.
Now as the torpedo begins to accelerate, we'll say its gas pressure also increases. The water is being forced out of the way more quickly, but there is also back pressure from the water in front of the torpedo, caused by forward motion. However, we'll say the gas pressure increases slightly faster than does the back pressure from the water in front of the accelerating torpedo. Therefore, time appears to slow down on board the torpedo to a stationary observer, due to an overall decrease in water flux past the torpedo. Eventually, the torpedo reaches a certain velocity where the gas pressure becomes high enough to create a cavity in the water, in which the torpedo travels. Now, there is no water flux past the torpedo, so it ceases to experience time.
Does this analogy illustrate roughly why a hypothetical conscious observer on a beam of light would not experience time? The light travels in a translating cavity wherein the time component of spacetime has been somehow evacuated?
I think the picture in this Wikipedia article illustrates my visualization.
Of course, there are changes to space as well, but I would rather talk about the time component of this subject.
|Jul7-08, 02:20 AM||#2|
Okay, forget about the torpedo analogy.
I still think my question has merit. I have attached a picture which I hope illustrates my thinking more clearly. Pictorially, if the space component of spacetime is blue, and the time component is red, spacetime is purple. An object that is moving at the speed of light does not experience time (from what I have read both here and elsewhere), but is still displaced a distance. In my interpretation of this, such an object is moving through "blue" spacetime (i.e. in the absence of the "red" time component). This assumption creates in my mind the image of the redness splitting away from the blue, curving around the object, and rejoining the blue behind the moving object. From the green ball's perspective, it lies in a coordinate system with only space (distance), and no time component.
I know, of course, that the space component is also affected. I would like to know, however, if this passes muster as a rough analogy of the reason why light-speed objects do not experience time.
edit: graphics rendered in Rhinoceros 4.0
|Jul7-08, 04:06 AM||#3|
it falls to me to tell you that your idea has no merit. Objects never travel faster than light, and any statement about their condition or 'experience' is without meaning.
Spacetime is not like a fluid, as far as we can tell, so the analogy doesn't work.
|Jul7-08, 04:01 PM||#4|
Possible Analogy for Objects Moving at C
As far as the analogy is concerned, I am trying to address what I view as a shortcoming in special and general relativity - the ability to depict phenomena in an easily-digestible and meaningful way. I have seen the familiar worldline diagrams, light clocks, "bedsheet/rubber sheet" gravity models, funnels, warped cylinders and other illustrations, in addition to matrices and equations. To me, and arguably many others, these do very little to explain why a clock orbiting the Earth ticks faster than one on the surface, or how the Twin Paradox works.
To me, one should always be able to create an analog for abstract phenomena, or risk becoming detached from the subject at hand. I witnessed this peril when my college linear algebra instructor showed on an x-y plot the visual analog of a linear transformation - several weeks into the course. Many students (me included), who had been doing matrix operations for over a month, uttered exclamations to the effect of: "So that's what we've been doing." To illustrate, I present this Wikipedia article as an example. Is it useful to students? I argue, mostly, "no."
I would like to be proven wrong, but I suspect that many in the science and math fields do not possess useful analogs for the concepts they deal with on a daily basis, having risen to their level principally due to their skills in mathematics and critical thinking.
Math is ubiquitous in its usefulness, but the story of Newton's Apple shows that inspiration often comes from elsewhere. And even Einstein is known for his thought experiments.
So, as far as spacetime is concerned, I have presented an analogy which I feel attempts to describe motion through spacetime in a relatable way. I sought to explain how I visualize the process by which an object passes between two points without encountering time (light-speed). You have rejected this analogy.
What, then, is an appropriate view of the fabric of spacetime?
|Similar Threads for: Possible Analogy for Objects Moving at C|
|Do Objects Ever Stop Moving?||General Physics||29|
|Objects moving in a plane.||Introductory Physics Homework||12|
|objects moving in 2D||Introductory Physics Homework||9|
|Acceleration and Moving Objects||Introductory Physics Homework||2|
|Moving objects in space||General Physics||2|