• Quick note - the problem with Youtube videos not embedding on the forum appears to have been fixed, thanks to ZiprHead. If you do still see problems let me know.

Relativity - Oh dear, here we go again!

Gertrude said:
There is no 'absolute' time dilation and it is in this sense that I say time dilation is apparent.
Click to expand...

Time dilation is relative, that's certainly true, but I think the word "apparent" is a poor choice, precisely because the effect is still quite real and definite.

Here's a nice little problem involving time dilation which might help out a bit. We set up a "rest" reference frame, stick an observer at the origin and let him stay there (along with a clock) for the duration of our experiment. Now we take several volunteers with clocks, sync all the clocks together, and have them start moving in circular trajectories which all start at the origin (and hence return there periodically), which they will travel along at constant speed (with respect to our rest frame). Now one of the nice features of using circular orbits is that the acceleration and the speed are now independent parameters. We can have high-speed trajectories with small accelerations by using large circles, we can have small speed trajectories with large accelerations by using small circles, or any other combination. Now we ask, when these traveling clocks swing by the origin, how do their times compare with our stationary clock?

The answer is quite simply that the travelling clocks are slowed down compared to the stationary clock because of time dilation, by a factor given by their speed. Now, just like the twin paradox, there's an asymmetry in the problem because the moving clocks experience acceleration and the stationary clock doesn't. But here's the interesting bit which becomes clear because of the setup of the problem: the acceleration never actually enters into the calculation! Remember, we can make trajectories which have the exact same speed but different accelerations, or different speeds but the exact same acceleration, but the ONLY thing we need to know to figure out how much time dilation a trajectory experiences is the speed. The answer is totally independent of the value of the acceleration, and so acceleration is, in one sense, completely irrelevant to that observed time dilation.
 
Yllanes said:
Incidentally, such a uniformly accelerated observer can outrun a photon, even though his velocity never reaches c.
Click to expand...
Really, then how do his atoms not fall apart because the virtual photons in the atom, as you say, can't keep up?

Paul

:) :) :)
 
boooeee said:
How does the travelling twin use Special Relativity to explain that time is moving faster for his twin?
Click to expand...
In a few words, there is only so much speed to go around for all 3 dimansions. The more you used in one direction and/or dimension the less you have for the other two.

Paul

:) :) :)
 
Paulhoff said:
Really, then how do his atoms not fall apart because the virtual photons in the atom, as you say, can't keep up?
Click to expand...

He didn't make this explicit, but what he's refering to is photons which you have a head start on. In other words, for constant proper acceleration and a sufficient head start, you can stay ahead of a photon forever (but you can't ever stop accelerating). More details here:
http://en.wikipedia.org/wiki/Event_horizon#Event_horizon_of_an_accelerated_particle
 
Ziggurat said:
He didn't make this explicit, but what he's refering to is photons which you have a head start on. In other words, for constant proper acceleration and a sufficient head start, you can stay ahead of a photon forever (but you can't ever stop accelerating).
Click to expand...
This most likely would work a lot easier if space itself is expanding, which looks like it is now happening.

Paul

:) :) :)
 
Yllanes said:
The important thing about four vectors is that their magnitude is the same in all reference frames.
Click to expand...
I think that for clarity's sake, you should write "four-vectors" and "four-velocities".

Gertrude said:
I lost you right there! If the rest frame has the same velocity as the particle, it cannot be inertial since the particle undergoes acceleration!?
Click to expand...
It's like the tangent lines in the derivative. Each point has its own tangent line, so even though each line is straight, the curve is not.

Gertrude said:
I am quite good at expressing things in the most confusing possible manner. I'll give an example that may be clearer. The statement "moving clocks run slower" is confusing because it does imply that time slows down with speed (relative to any observer). The reality is that moving clocks measure events occuring in a slower inertial frame as having longer duration than what a clock at rest relative to said event would measure.
Click to expand...
I think that's still not quite right. Rather, if you have events proceeding, in one reference frame, at the same place, but at different places, then in another reference frame, they will be assigned different spatial corrdinates, and temporal coordinates that increment at a lower rate than those in the other reference frame.

A big problem in understanding relativity is that people don't understand how relative it is. When they're told that moving clocks run slower, they think that there is some absolute "time" through which the clock moves more slowly. Rather, the clock runs at normal speed in its own reference frame. That is, there is a quantity called "time" which increases at a normal rate. In another reference frame, the clock is measured with a different quantity, and found to have less of that quantity. That this other quantity is given the same name as the other one is what causes the confusion.

If we look at a car going down a road, one person might describe it as going 40 miles north in an hour. That is, after an hour, its ditance from the South Pole increases 40 miles. Another person might observe that its distance from the Prime Meridian increases by 50 miles. If the first just says it traveled 40 miles, and the second says that it traveled 50 miles, it may seen that they are contradicting each other. But if we realize that the two instances of the word "mile" refer to different things (North-miles vs. East-miles), there is no contradiction.

One way of thinking about it (which, I suppose, might inspire its own misconceptions) is that each tick of the clock has a certain magnitude, so to speak, and that magnitude stays the same no matter what. A stationary clock has all of that magnitude going into time, so it runs at full speed. For a moving clock, each tick moves through space and time, so some of its magnitude is "used up" by the movement through space, and the amount that it travles through time is less. But the whole issue of whether the stuff it goes through is "space" or "time" is simply a labeling issue; one person calls the stuff its going through "time" and another person calls it "some time and some space".

If A and B are in two different inertial frames, B would see the clock of A running slower because it is moving relative to A and A would see the clock of B running slower because it is moving relative to B.
Click to expand...
It's important to note that they don't just disagree about the results of the measurement of the clocks. They disagree as to what to measure. That's why they're getting different answers. If they both measured the same thing, they would get the same answer. Remember how earlier, I talked about East being the distance to the Prime Meridian? The Prime Meridian is a set of points that is considered to all be “zero East”, and one’s distance East is then measured from the closest one of those points. For A, there is a collection of points which he considers to all be at “time zero”. He measures time as the distance to the closest of those points. When he looks at his own clock, that’s no problem, because the closest is always the same (his starting point). But when he looks at B’s clock, the closest point in the “time zero” set is constantly changing. (For those are getting lost: asking what the “closest point” in A’s “time zero” is the same thing as asking “According to A, where would B have been at the beginning, if he had remained at rest and ended up where he is now?” or “What, according to A, was, at time zero, the same place as B?”) Now, both A and B agree on what the distance to this point is. The trouble is that, according to B, this point that A is measuring from is the wrong point. B doesn’t disagree with the result of A’s measuring, he just says that A is measuring the wrong thing. According to B, he has remained still, so his “closest point” is always the same: where B started from.

So, really, they don’t disagree about the speed of their clocks. They both agree that B’s clock is proceeding through “A time” more slowly than A’s clock. It’s just B says that “A time” isn’t “real” time, it’s a confabulation of time and space.

RussDill said:
Einstein says rubbish. Time and space are inseperable, we live in a 4 dimensional world.
Click to expand...
[Annoying pedant]According to Einstein, time and space are inseparable[/Annoying pedant]

Kinda like if you take slices of a cylinder. The flat slice will show a circle. Other slices will show an ellipse. You are saying that it can't be a circle and an ellipse at the same time. It isn't. Its a cylinder. You just can't visualize the cylinder.
Click to expand...
Actually, the issue of visualization isn’t really the issue. We can visualize two dimensional space just fine, but the same issues come up. The real issue is that we want to deal with real numbers. In other words, we want to decompose space into one-dimensional coordinates. And once we do that, we’re going to get different answers depending on what coordinate system we use.
 
Ziggurat said:
Saying that it's the turnaround that matters is equivalent to saying that (say) a right angle in a Euclidean path is what makes it longer than the straight line. That may be true in one sense, but the extra length in the bent path isn't found in the bend itself. Likewise, the "missing" time isn't subtracted from the turnaround of the twin either. Each leg of the traveling twin's path really is shorter than half the stationary twin's path.
Click to expand...


I think the traveling twin would agree only if he is permitted to include in "half the stationary twin's path" that portion of the path simultaneous, according to himself, with half his period of acceleration. He would not agree that the stationary twin ages more rapidly than he does, during any part of the unaccelerated portion of his trip.
 
Paulhoff said:
It was reworded...... :rolleyes:
Click to expand...

:D

But you still didn't get it right...

1. Now spaceman (1) takes one of the clocks and travels in any direction at 99,9999999% speed of light for one second and stops. Spaceman (1) now is 100 ft away from spaceman (2) and the two clocks remanding clocks.
Click to expand...

If Spaceman (1) travels for one second, he is going to be travelling a WHOLE lot further than 100 ft.
I think you mean "for one second in frame of reference of Spaceman (2)"

;)
 
69dodge said:
I think the traveling twin would agree only if he is permitted to include in "half the stationary twin's path" that portion of the path simultaneous, according to himself, with half his period of acceleration.
Click to expand...

This isn't actually necessary. Pick a frame, any frame, and you can calculate the halfway point of the stationary twin's worldline. Furthermore, every observer, regardless of their frame, will agree on the calculation of the proper time experienced over this half journey. The only reason to sync the halfway point of the traveling twin's acceleration with the halfway point of the stationary twin's path is if we want them to be simultaneous, but there's no reason we need to pick a frame where the two halfway points are simultaneous.

He would not agree that the stationary twin ages more rapidly than he does, during any part of the unaccelerated portion of his trip.
Click to expand...

Well, sure. I thought this was already clear.
 
Can I really be older than my twin....?

Alkatran said:
http://casa.colorado.edu/~ajsh/sr/paradox.html

This website is what I was looking at when I finally understood what special relativity was getting at. Read down the page and think about it for a minute, then go to the next page for Einstein's solution.
Click to expand...

Looked on this link of yours...pretty good...BUT...take this situation here...


Time dilation


But now suppose Cerulean goes off at velocity v relative to Vermilion, in a direction perpendicular to the direction of the mirror.
A far as Cerulean is concerned, his clock tick-tocks at the same rate as before, a tick at the mirror, a tock on return.
But from Vermilion's point of view, although the distance between Cerulean and his mirror at any instant remains the same as before, the light has further to go. And since the speed of light is constant, Vermilion thinks it takes longer for Cerulean's clock to tick-tock than her own. Thus Vermilion thinks Cerulean's clock runs slow relative to her own.


Let's say I am red {stationary} and my twin 'goes for a fast ride'...I want to keep things descriptive rather than mathematical because... as Einstein said to Bohr..."Q.M. just doesn't ''feel'' right"...

By the way...having never really studied GR/SR I got the slopey turning of the cones thing pretty easily... before they told me. So what 'we' want is a physical description... so back to it....

Now my twin, Blue, moves off and I see his clock showing a slower time, but he will see the same 'normal' time on his clock, as I do with my clock... that's what that diagram tells me. It most certainly doesn't imply that Blue's clock is 'actually' slowing down and he is getting younger, or conversely that I myself {Red} am (not) getting older.

"thinks" is the word! Even 'observes'... but not actual time change and so not actual age difference.

What do you guys think... I teach, and I know it's very frustrating 'not to be able to get the point across'... and I'm not blaming your efforts or 'our' ignorance of GR/SR, I'm just asking/learning....

Thanks, Griff....Interesting...spell check can't live with a tock!
 
So Lorentz was nearly there before Mr.E! Well all this comes from some easy 'O' level-GCSE maths.... and just add a 'c' to get (v/c) and Bob's' your uncle...​

12 + (
gamma.gif
v)2 =
gamma.gif
2​



from which it follows that the Lorentz gamma factor
gamma.gif
is related to Cerulean's velocity v by


​
which is Lorentz's famous formula.


"While Vermilion thinks events happen simultaneously along horizontal planes in this diagram, Cerulean thinks events occur simultaneously along skewed planes. Thus Vermilion thinks her clock
verball.gif
ticks when Cerulean is at the point
cerring.gif
, before Cerulean's clock
cerball.gif
ticks. Conversely, Cerulean thinks his clock
cerball.gif
ticks when Vermilion is at the point
verring.gif
, before Vermilion's clock
verball.gif
ticks."

Now this paragraph above, correct me if I'm wrong (asking for it!)... but how can Red or Blue 'see' something that hasn't happened?

Isn't this all just a bunch of 'observed' effects due to the wave properties of light and in no way reflects physical reality?

I can hear clogs turning....

Griff...Please, no maths... not because I'm afraid of it, I nearly chose it for degree, but instead I want true physical explanations....

eg. to explain diffusion I would say the balls wiggle past each other to get 'somewhere' that's no more important than where they are; because there's nothing to stop them.

No maths needed. So come you Physicists...who's up for it? Trust me, if you can make 'us' understand, you'll be doing science a great favour!
 
Last edited:
Sorry but what does x=vt mean?

"Step 3


Draw a rectangle, sides 45o from vertical, with the origin at the centre and Cerulean at one corner. The rectangle represents the path of light rays which Cerulean uses to define a hypersurface of simultaneity, as described on the simultaneity page, Spacetime diagram illustrating simultaneity from Cerulean's point of view. Draw the extra diagonal across this rectangle. The diagonal is a hypersurface (reduced to a line) of simultaneity, a `now' line, for Cerulean. The now line lies along t = vx in Vermilion's frame, and along t´ = 0 in Cerulean's frame. "

Earlier they said "x=vt" which is fine; displacement = vel x time.

But Time = vel x displacement ? I don't get that!
 
polaristutoring@tisc said:
Looked on this link of yours...pretty good...BUT...take this situation here...


Time dilation

[qimg]http://casa.colorado.edu/~ajsh/sr/timev.gif[/qimg]
But now suppose Cerulean goes off at velocity v relative to Vermilion, in a direction perpendicular to the direction of the mirror.
A far as Cerulean is concerned, his clock tick-tocks at the same rate as before, a tick at the mirror, a tock on return.
But from Vermilion's point of view, although the distance between Cerulean and his mirror at any instant remains the same as before, the light has further to go. And since the speed of light is constant, Vermilion thinks it takes longer for Cerulean's clock to tick-tock than her own. Thus Vermilion thinks Cerulean's clock runs slow relative to her own.


Let's say I am red {stationary} and my twin 'goes for a fast ride'...I want to keep things descriptive rather than mathematical because... as Einstein said to Bohr..."Q.M. just doesn't ''feel'' right"...

By the way...having never really studied GR/SR I got the slopey turning of the cones thing pretty easily... before they told me. So what 'we' want is a physical description... so back to it....

Now my twin, Blue, moves off and I see his clock showing a slower time, but he will see the same 'normal' time on his clock, as I do with my clock... that's what that diagram tells me. It most certainly doesn't imply that Blue's clock is 'actually' slowing down and he is getting younger, or conversely that I myself {Red} am (not) getting older.

"thinks" is the word! Even 'observes'... but not actual time change and so not actual age difference.
What do you guys think... I teach, and I know it's very frustrating 'not to be able to get the point across'... and I'm not blaming your efforts or 'our' ignorance of GR/SR, I'm just asking/learning....

Thanks, Griff....Interesting...spell check can't live with a tock!
Click to expand...
Wrongo. Very much a real age difference.
Take a look here for data on an experiment in which this was acutally tested.

Remember, these clocks traveled only at the speed of a normal commercial jet. The difference was present and measurable, and in line with the predictions made by relativity theory.

Here's a more prosaic application of relativity. Your GPS receiver depends on compensation for relatavistic effects for it's accuracy.
 
You must log in or register to reply here.

Back
Top Bottom