moth

the wikipedia page on the Ehrenfest paradox http://en.wikipedia.org/wiki/Ehrenfest_paradox

says Einstien showed that Circumferance = 2 * pi *r* (1−v2)^-1/2.

maybe the disk has become bowl shaped?

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if i was using Lorentz equations on a rotating disk (radius=1 for simplicity) i would center the disk at the origin and look at x=0,y=1(and ignore y=1 since it's not changing much)for my x.

then calculate the velocity of the edge of the disk(pi * diameter * r.p.m.) for v(how do i tell if v is positive or negative?).

what value do i use for t?

other than that, it seems straightforward enough.

ok after looking at the classical equations i see x-vt is the relative motion of the x' origin so if v=(change in x)/time, and the change in x is positive and time is positive v is positive.

also i guess any (small?) value but 0 will work for t(because at t=0 nothing has happened?) and the answer is an offset from t.

am i on the right track here?

according to wikipedia Planck time is about 5.39124 * 10^-44 seconds so 1/Planck time is about 1.8548 * 10^43 cycles per second. 1/(3*Planck time) might be a better estimate of a maximum frame rate so you could get a couple of samples per frame.

according to quantum mechanics Planck time is the smallest unit of time so 1/Planck time would probably be your theoretical maximum frame rate(physical limitations of photodetectors and memory will keep you from getting anywhere close), but as Baby Astronaut pointed out you have to wait for the photons to bounce off something and hit the camera before you see anything.

maybe centrifugal force is warped spacetime pushing us away from the center

thanks for the encouragement swansont and MrSkeptic.

" Keep in mind that it is space itself being bent as well as anything in it."

does that mean pi has a different value on a rotating disk?or does time dilation balance the books here too?

Merged post follows:

if i was using Lorentz equations on a rotating disk (radius=1 for simplicity) i would center the disk at the origin and look at x=0,y=1(and ignore y=1 since it's not changing much)for my x.

then calculate the velocity of the edge of the disk(pi * diameter * r.p.m.) for v(how do i tell if v is positive or negative?).

what value do i use for t?

other than that, it seems straightforward enough.

that makes sense to me now, acceleration is acceleration. gravity only seems special because it's not obvious whats doing the pushing.

in my last post i said the distance from the surface of the earth when i should have said center of the earth but i think you get the idea.

i'm just not sure if it applies when you're underground.it seems like your weight would decrease underground until you reached the center where you would be weightless.

i don't think artificial gravity would cause time dilation but thats just my opinion. there are people here who know.

i guess it's a question of wording. it would be interesting to find out if 1G in a rotating artificial gravity chamber caused the same amount of Lorentz contraction and dilation as 1G on earth, but when i try the math i get confused about that vx/c^2 term in the time part of Lorentz equation.

from the little bit of math i know the force of gravity decreases by the square of the distance so something that weighs 1 pound some distance from the surface of earth,weighs 1/4 pound when it's twice that distance 1/d^2. since 1 divided by a huge number is a tiny little number no matter how huge the big number gets (even 13 billion light years) this means earths gravity(for example) is still a force even at the edges of the observable universe.

i don't know about centrifugal force and time dilation it seems like you would need to be spinning really fast to slow a clock.

thanks for the input npts2020 and klaynos

i understand you couldn't build a physical example i'm just trying to understand where the distance "goes" during lorentz contraction. lacking the math skill to solve the equation i try and model in my head and read wikipedia and of course this forum.

i'm starting to get the idea that time dialation and length contraction balance each other so lightspeed stays constant but it's a journey.

npts2020 "propellers only move at a small fraction of the speed of light, "

it sounds as if you're saying the solution to the Ehrenfest paradox is the train flies off the track.

what if instead of a propeller i used a carbon nanotube spinning in a magnetic field?

it seems like the propeller blades would bend back like boomerangs as the tips slower time passage would begin to affect how much distance they could cover without exceeding lightspeed.

as for the bend in the time direction, we can't see it in our 3-d view of this 4-d bend.

picture a box sitting on a 2-d surface like the floor. the vertical dimension would be the box's height. now try and picture the vertical dimension as the length of time the box sat on that spot on the floor.kind of rotate the familiar height dimension out of view and the time dimension into it's place so you have a 2-d slice of the box (the width and the depth) for every instant the box sat on that spot on the floor in our 3-d picture.now if you could pull on the top of the box (in time) you might expect the width and/or depth to change too, and that change would show up in our everyday 3-d worldview. of course there might also be weird effects at both ends of the duration(the top and bottom of the box in the rotated time view).

thanks for your reply N.T.W.K.

in the Ehrenfest setup the people on the platform see the train cars as contracted, and the people on the train see the platform as being contracted. it just seems natural to think of this as an arc in the time direction with the endpoints of the arc getting closer as the radius of the arc decreases(velocity increases).

So how slow can time go? the answer is here i think http://www.scienceforums.net/forum/showthread.php?t=37601

i'm still checking it out.

may be nobody is interested in this but i am considered a pest by many.

i found this while reading a relativity and g.p.s. link from another thread http://en.wikipedia.org/wiki/Ehrenfest_paradox

this construction seems to leave time out of the picture while implying the distance does not change(or pi is only defined for non-rotating bodies) our rulers get shorter.

a look at wikipedia topic lorentz contraction seems to also "cheat" a bit by saying you make 2 measurements (leading edge of high velocity object and trailing edge) implying two world events seperated by an unspecified amount of time.

is it just unconventional to think of this length contraction as the train cars being bent in time or is there a contradiction somehow?

i'm not an expert but check the documentation for "command line options" or "compiler flags" something like that. you usually have to tell the compiler you want an executable and not something to be linked into a program later or some other kind of file.

the last line in the dos window looks like a prompt from the compiler for more info so you might try /? or /help or something at that point,the compiler may have some help built in.

hope that helps.

keep at it, it does get fun after a while.

hello,

i enjoy reading about physics, special and general relativity have always interested me but they also provide confusing questions.

thank you for providing this generous resource, both of questions already asked and answered, and links to further reading on the web.

my math skills are non-existent so i apologize if this is nonsense.

by bent in time i mean the same thing that happens to space in a high gravity potential.

if you set up a graph with x-axis as the long axis of the propeller with the origin at the hub and y-axis as past and future with now at the origin and then plotted several points along the propeller blade as it spins around would the points with the greatest velocity move off the x-axis forming a curve in the -y direction as time slows down for them?

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thanks N.T.W.K.

the faster i'm wrong,the quicker i can move on.

if you have a propeller spinning fast enough SR says time dilates with velocity so you get a gradient of time(s?) between the hub of the propeller and the tip.

does this mean the propeller is bent in time?

if it is bent, could it somehow be frozen in that bend so it remained curved after it stopped spinning?

would such a thing bend space?