Clocks, Time, and Special Relativity

[MolaKule]

Special Relativity

Without having illustrations, this might be more difficult, but here goes.

Reference Frames:

When you pass me going down the highway, my speedometer is showing 70 while yours is showing 75. A person standing by the road is seeing your speed as 75 mph, but your speed relative to mine is 5 mph.

A reference frame is a coordinate system in which experimenters equipped with meter sticks and stopwatches to measure length, time, and velocities.

1. A reference frame extends infinitely in all directions.
2. 2. The experimenters are at rest in the reference frame.
3. The number of experimenters and their equipment are sufficiently accurate to measure positions and velocities.

A reference frame is not the same as “point of view.” All experimenters at rest relative to each other share the same reference frame.

Let’s take another example. A 300 gram ball moving to the right at 2 m/s has an elastic collision with 100 gram ball moving to the left at 4 m/s. What are the direction and speed of each ball after collision (momentum is conserved). The stationary reference S is the frame in which the 300 gram ball is moving, and the reference frame S’ is the reference frame in which the second (100 gram ball) is moving. In the reference frame S’, the balls before collision are moving at 6 m/s and 0 m/s, respectively. After collision, in the reference frame S’, the large ball is moving at 3 m/s to the right and the small one is moving at 9 m/s to the right. In the reference frame S, the large ball is moving to the left at -1 m/s and the smaller ball is moving to the right at 5 m/s.

Time Dilation:

The reason clocks show different elapsed times when moving relative to each other is because of time dilation. Now speed or velocity is = change in distance/change in time, or as we say, v = del x/del t, the ratio of distance traveled to the time interval the test is occurring. Suppose we do a test in which the lamppost on our street is the marker for timing and measuring distance. Your driving by in your car and I’m standing still, and we’re both measuring the velocity of a bicycle. The velocity measured by you and me will be different for the bicycle because your reference frame is different from mine. Your change in distance and my change in distance will be different because we are in two separate reference frames. You will show v’ while mine will show v.

Repeat the measurement with the velocity of light as it travels from the tree to the lamppost. Once again, your change in distance will be x’ while mine will be x. The obvious conclusion is that you will measure v’ for the light and I will measure v, but this conclusion is not correct, because the speed of light u will equal u’, since light travels at speed c = u in ALL reference frames, that is, u’ = u. The only way this can true is that your change in time is NOT the same as my change in time, that is, t does not equal t’. We then have to change our understanding of time. In this case, the speed of light is the same, the measured distance is the same, but the variable that has changed is time. Therefore, in your reference frame, time has shortened. For clocks that travel around the world or at high altitudes, their time has dilated. Your time on the ground has remained constant.

And that’s why when clocks fly, time does not!

 

[wwillson]

MolaKule,

This is a concept that I've struggled for years to understand, but still don't.

"that is, u’ = u. The only way this can true is that your change in time is NOT the same as my change in time, that is, t does not equal t’. We then have to change our understanding of time."

This is the part I just don't understand and can't seem to take for granted. Just absolutely blows my feable mind.

 

[rpn453]

quote:

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Originally posted by wwillson:
This is a concept that I've struggled for years to understand, but still don't.

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It took me a couple reads to catch on back in my first-year modern physics class. The right illustrations are essential!

 

[SteveD2]

That gave me a headache....

 

[MolaKule]

The whole matter hinges on the "invariability" of the speed of light in any reference frame , i.e, the speed of light is the same in any reference frame and that "it is the only thing that does not change."

Since the speed of light does not change, and distance is constant for each experiment, then the only thing that is FORCED to change is time.

 

[wwillson]

quote:

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Originally posted by MolaKule:
The whole matter hinges on the "invariability" of the speed of light in any reference frame , i.e, the speed of light is the same in any reference frame and that "it is the only thing that does not change."

Since the speed of light does not change, and distance is constant for each experiment, then the only thing that is FORCED to change is time.

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Ok - so let's say that I'm a space traveler going near the speed of light. I travel for 100 earth years, but only age say 1 earth year. How can I travel for 100 years in time, but only be 1 year older after my travels. It just can't be! My head hurts and now I'm really tired....

 

[MolaKule]

The time interval between two ticks of a clock in frame S is not the same time interval of two ticks of a clock in frame S'.

It is a consequence of the fact that time flows differently in two reference frames moving RELATIVE to each other.

 

[DavoNF]

Another strange one is that time is dilated in a very strong gravitational field. To a distant observer, clocks on a neutron star would seem to be running 20-30 per cent slow.

Clocks in orbit very close to a spinning black hole could display an arbitrarily large time dilation. Conversely, an observer in such an orbit could observe the universe "speeded up" by a similar factor.

An aircraft flies at about a millionth of the speed of light. You could prolong your life by about a millisecond by spending the whole time flying around the world from west to east.

These things seem paradoxial only because they require conditions vastly remote from our everyday experiences that have moulded our common sense.

Nuff said.

Dave

 

[Pablo]

DaveNF - I was thinking the about the same during my pondering of gravity. It does not seem possible to us mortals in a barely 3 dimensional world using Newtonian physics that gravity would have an effect on time....we can picture gravity having an effect on particles, but even that seems to stay limited by the human mind.

What interests me is the inverse....is the whole expanding universe the inverse or what really is on the "other side" (so to speak) of a black hole?

As far as I'm concerned...we just don't know time.

 

[keith]

quote:

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Originally posted by wwillson:
Ok - so let's say that I'm a space traveler going near the speed of light. I travel for 100 earth years, but only age say 1 earth year. How can I travel for 100 years in time, but only be 1 year older after my travels.

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YOU have been away for 1 year of YOUR time and have only aged one year. Folks left behind on earth have aged by 100 years of THEIR time, and are probably dead of course!

This stuff is difficult to grasp, and yet has a beauty of its own. I recall deriving the time dilation equations in high school on a single sheet of paper, it really is very simple.

Having said that, Einstein (and Lorentz, etc.) were operating on a different mental level than the vast majority and were able to understand the problem before the experimenters could verify their theories.

Keith.

 

[novadude]

To Quote Chicago:

"Does anybody really know what time it is? Does anybody really care...."

LMAO!

 

[MolaKule]

quote:

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Theory of Relativity Evidence Found
Washington Post 10/22/04
author: Guy Gugliotta

Copyright 2004, The Washington Post Co. All Rights Reserved

By measuring variations in satellite orbits, scientists have found the first direct evidence of one of the hallowed tenets of Albert Einstein's theory of general relativity -- that the Earth and other large celestial bodies distort space and time as they rotate.

Researchers reporting yesterday in the journal Nature said improved satellite data had enabled them to show the effect known as "frame-dragging" with a degree of precision never previously possible.

"We improved our accuracy by orders of magnitude," said geodesist Erricos C. Pavlis of NASA's Goddard Space Flight Center in Greenbelt and the University of Maryland at Baltimore. "In a while, we should be able to do even better."

Scientists expect that the results of the experiment, by Pavlis and Ignazio Ciufolini of Italy's University of Lecce, will be reinforced by NASA's ongoing Gravity Probe B, a satellite mission designed to measure frame-dragging and another Einsteinian effect by a different method -- calculating gyroscope deviations over time.

"Gravity Probe B is less systematic, but will provide higher accuracy -- within a margin of error of less than 1 percent," said Michael Salamon, NASA's discipline scientist for fundamental physics. "What this research [yesterday's report] means is that GPB may not in fact provide the first direct evidence of frame-dragging."

In the early 20th century, Einstein theorized that the gravity of large bodies such as the Earth distorts space and time, much the way a bowling ball would stretch a rubber sheet held aloft on all four corners.

Frame-dragging occurs, he said, because the Earth's rotation pulls space-time along with it. Salamon likened the effect to dipping a spoon into a cup of honey and turning it. Close to the spoon the honey twists, but the effect dissipates with distance.

Scientists have wanted to prove Einstein's theory since the dawn of the space age. Gravity Probe B, conceived more than 40 years ago, is measuring frame-dragging from a satellite by focusing a telescope on a distant "guide star" and measuring how the axes of gyroscopes deviate from their original positions pointing directly at the star.

Pavlis and Ciufolini used satellites in a completely different way. They closely tracked the orbits of LAGEOS and LAGEOS2, passive satellites covered with "retroreflectors" that reflect laser beams from ground stations, giving precise measurements of distance from the station to the satellite.

The satellites' orbits are slightly distorted -- not perfectly circular or elliptical -- because irregularities in Earth's surface jog them. But even after subtracting this surface caused "noise," the researchers were still left with orbits that deviated slightly from what they should have been. The difference, they said, reflected frame-dragging.

"The satellite orbits are not perfect because the Earth is not perfect," Salamon said. "So subtract them out, and what you're left with are the effects of space time. The results are better with two satellites, and three would have been even better."

The key to the experiment's success was better data on Earth's gravity field -- a better map of the Earth-induced orbital distortions. This information, collected by another new satellite, enabled Ciufolini and Pavlis to shrink their margin of error dramatically from the 20 percent
they obtained from an earlier attempt.

"There was a tremendous amount of criticism then, and a lot of people said 20 percent was on the edge of being acceptable," Salamon said.
"This result, between five and 10 percent, is a lot cleaner."

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[Tree Hugger]

quote:

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Originally posted by rpn453:

quote:

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Originally posted by wwillson:
This is a concept that I've struggled for years to understand, but still don't.

---

It took me a couple reads to catch on back in my first-year modern physics class. The right illustrations are essential!

---

'Modern Physics'!

Relativity is circa 1900!

 

[moribundman]

Because v’ is not the same as v, I could talk myself out of almost all speeding tickets.

 

[1sttruck]

DavoNF said "An aircraft flies at about a millionth of the speed of light. You could prolong your life by about a millisecond by spending the whole time flying around the world from west to east. "

As I recall this was actually an experiment; atomic clocks were flown around the world at high altitude, and the effect although small, was confirmed.

An analogy of 2 dimensions vs 3 dimensions might help in trying to visualize higher dimensions. A 2d person living in a 2d world would experience a 3d object one 2d slice at a time, as it pased thru his 2d world. A ball would look like a point, grow in size and then shrink, and then go back to a ball again. The 2d person may not suspect the 3d nature of some objects in his world if they're stationary. Now try to consider how we experience things in our '3d' world (which is usually considered to at least be 4d), and how a 4d person in a 4d world would describe our limitations in how we perceive things; one 3d slice at a time :^)

From what I've been able to figure out a photon, obviuously travelling at the speed of light, might be everywhere he has been and everywhere he will be, all at the 'same time'. The photon sees his extension in time the same that we see our 3d extension in 3d space.

The EPR paradox is a bit more bizarre, as so far it seems true that some things are 'connected' in a manner that things happen 'instantly', at faster than the speed of light, and in theory at unlimited distances.

 

[Terry]

quote:

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An aircraft flies at about a millionth of the speed of light. You could prolong your life by about a millisecond by spending the whole time flying around the world from west to east.

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I actually do this and I can tell you that I am still old and fat, and old. But unlike others here I still have good hair.....

 

[oilguy3]

If you all are really interested in this subject but don't really grasp it (not you Mola, physics professor extrodinare) I suggest reading "The Elegant Universe"....one of the best books I have ever read.