Freethought & Rationalism Archive

Ted Hoffman · 09-03-2002, 01:32 AM

I came across the Twin Paradox in Stephen Hawkins' A Brief History of Time, the twin Paradox states that if we have two twins and we sent one off to space, the one who remains on earth will age faster than the one in space because time moves faster closer to the earth.
Can someone please explain to me what that means?

Friar Bellows · 09-03-2002, 03:13 AM

Quote:

Originally posted by Intensity:
Can someone please explain to me what that means?

A good link is the following:

<a href="http://www.math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html" target="_blank">The Twin Paradox</a>

It's from the sci.physics usenet FAQ.

Ted Hoffman · 09-03-2002, 05:28 AM

Friar Bellows,
Thanks for the link. My brain seems incapable of understanding wtf happens, so I will read it tomorrow when I am fresh.
Do you understand the mechanism that the twin paradox operates under?

strubenuff · 09-03-2002, 05:43 AM

What is the paradox? I haven't looked at the site, so forgive me if this is redundant. The best analogy I have seen is the stroy of the race car driver. Imagine a man racing down a flat away one-hundred miles long, at 100 miles an hour. He shows his friend his times at the end of his day, and his friend is disturbed. He sees that he made the first 4 or so in exactly an hour. Howveer, towards the end, their was a significant increase in his times. The driver explained the sun was in his eyes, so he had inadvertantly traveled a little to the right or left, which added time to his runs.
What's this have to do with spacemen? The point is that, even though the driver's speed didn't change, it took him longer to complete the same distance. This is because he entered a different dimension. Instead of traveling in a straight line (1st dimesnion, length), he has also traveled left or right (2nd dimension, width).
This is also true for all matter. You are currently traveling through time (4th dimesnion) at the speed of light. When you travel through space, say by driving your car, you are diverting some of that speed into different dimensions (the first three), so you go slower through time. This doesn't really matter for general purposes, since our speeds through space are so slow. However, when traveling into outer space, our speeds are fast enough (albeit still very slow compared to light) to measure. That's why the twin was some fraction of a second younger after he had traveled to space.

[ September 03, 2002: Message edited by: strubenuff ]

Ernest Sparks · 09-03-2002, 07:32 AM

It can be demonstrated by physical phenomena.

In a nuclear particle accelerator, particles called 'pions' are produced by collisions and circle around the machine. These will have different speeds depending on the energy of the collision that creates them. After a very short time, a free pion decays into other particles. As observed in the machine frame of reference, pions going closer to the speed of light last longer than pions going significantly slower than the first.

Atomic maser clocks of fantastic precision are placed in two airplanes. One airplane flies eastward around the world and the other airplane flies westward. When they re-unite, the eastward flown clock is behind the westward flown clock. Relative to the rotating earth, the eastward airplane travels faster than the westward airplane.

Friar Bellows · 09-03-2002, 09:32 PM

Quote:

Originally posted by Intensity:
Do you understand the mechanism that the twin paradox operates under?

Any description from me will be worse than that link I gave you. My advice is to read that link, and then come back to this thread with any questions you might still have. I can't guarantee that I'll be able to answer those questions, but maybe somebody else will.

LeftCoast · 09-04-2002, 08:49 AM

Intensity,

The mechanism is due to the differing rates at which time passes for each observer(twin) in their respective references frames. This is only a "Paradox" in the sense of "Zeno's Paradox" in that the results seem to defy our logical preconceptions, however, once you understand the physics of what is going on, there is no paradox at all.

The whole effect is the result of the two differing reference frames experienced by each twin. For the twin that remains on earth, time passes at the same rate as for all of us. For the twin that is accelerated to ~c time passes at a much slower rate due to the Lorentz contraction described by the equations of Special Relativity.

The time-dilation factor for the faster twin is:

gamma = 1/sqrt(1 - v**2/c**2)

Where:

T(Earth-Twin) = gamma*T(fast-twin) and
'v' is the relative velocity between the two twins.

Gamma is always greater than 1 so the clock for the faster twin will always register a slower time than the earth-bound twin. However, unless you get to values very close to c, the effect is too small to be detected by any but the most accurate atomic clocks. (e.g. - at 100km/h the effect is only to one part in 10**12 - IOW it would take 31,688 years(~ 1 million-million seconds) for a difference of 1 second to be realized between two clocks moving with a relative velocity difference of 100km/h)

Hope this helps.

Answerer · 09-04-2002, 05:34 PM

The twin paradox in the moving twin case isn't regarded as an inertial reference at all since he do accelerated during his journey. In relativity, when things accelerated, we say that they were under the effects of gravitional frequency shift.
Gravitional frequency shift is the effect that was largely responsible for the asymmetric effects of time on the twins after the journey. I will try to find the link for this effect as I don't think I could explain quite well. So, please wait.

ohwilleke · 09-05-2002, 04:44 PM

The Twin Paradox is a way of forcefully illustrating the implication of the theory of special relativity that time is not a universal thing that passes at the same rate for everyone. Instead, time is something that crudely speaking passes at different rates for each person and thing based on their motion relative to other persons and things. Absolute coordinates of time and space against which everything can be measured don't exist.

Einstein's remarkable insight in relativity is realizing that even though everyone has a different ruler and a different personal clock, the entire system can be consistently in compliance with a set of physical laws that apply to all observers.

[ September 05, 2002: Message edited by: ohwilleke ]

DNAunion · 09-05-2002, 05:20 PM

DNAunion: Here's something I posted just a couple of weeks ago here at Infidels about time dilation and the Twin Paradox (I made a couple other posts on these topics, but won't include them also).

Quote:

DNAunion: Special Relativity
Einstein�s theory of special relativity produces a Universe most of us would find counterintuitive. Loosely speaking, some examples include: it is possible for one identical twin to end up being many years younger than the other; events one observer sees as being simultaneous are not simultaneous for some other observers; velocities do not add together in simple 20mph + 20mph = 40mph fashion; time is divided not only into the present, the past, and the future, but also into something called the elsewhere; observer A�s clock can be running slower than observer B�s clock and at the same time observer B�s clock can be running slower than observer A�s, without there being any contradiction; and so on.

Yet all of the above-mentioned counterintuitive conclusions follow from the simple idea of special relativity...the laws of physics are the same for all (observers in) uniformly moving reference frames. Let�s look briefly at what this tells us about the speed of light and then about measures of time.

Maxwell�s Equations
Magnetism and electricity � which had been thought to be two completely separate phenomena � were unified into electromagnetism by James Clerk Maxwell in the 1800s. One consequence of his unifying equations was that there should be electromagnetic waves and these waves must travel at approximately 186,000 mi/s (or about 300,000 km/s). This result � which matched the already known speed of light, c � fell naturally out of Maxwell�s equations: he did not need to manipulate his work to force this result. No counterintuitive conclusions followed yet because it was thought that while the laws of Newtonian mechanics (i.e., the laws of motion, gravity, etc.) were the same for all observers, the laws governing electromagnetism were not.

Speed of Light is a Constant (c)
But Einstein changed all of that when, in 1905, he published his theory of special relativity. Then all of the laws of physics � including the laws of electromagnetism � were the same for all (observers in) uniformly moving reference frames. Since Maxwell�s equations are among the laws of physics and they mandate that electromagnetic waves travel at approximately 186,000 mi/s (in a vacuum), then all uniformly moving reference frames must measure the same speed of light (and other electromagnetic waves), even reference frames that are moving relative to each other! An example might shed some light on this.
Suppose there are two observers, A and B, in two separate uniformly moving reference frames and a pulse of light, emitted from a star, is traveling towards them. Let us suppose that observer A is at rest here on the Earth. Since scientists have already measured the speed of light from here on Earth to be approximately 186,000 mi/s, we know that A will obtain that result, regardless of how B is moving. Let�s now look at things from B�s perspective (reference frame). First, suppose that B is in his car speeding down the highway into the oncoming light pulse at 100 mph. According to Einstein�s theory of special relativity, B will not measure the speed of that light to be 186,000 mi/s + 100 mi/hr, but rather simply 186,000 mi/s (the same speed as that measured by observer A). Furthermore, if observer B were flying in a jet airplane into the oncoming light pulse at 600 mi/hr then he/she would not measure its speed to be 186,000 mi/s + 600 mi/hr, but rather, again, simply 186,000 mi/s (the same as observer A). In fact, if B were rocketing into the oncoming light pulse at half the speed of light, he/she would still measure the speed of that light to be 186,000 mi/s: and not 1.5 c. And finally, even if observer B were rocketing away from the light pulse at half the speed of light, he/she would still measure its speed to be 186,000 mi/s: and not 0.5 c. Unlike the speed of sound and another wave that is propagated only through a medium, not only is the speed of light independent of the motion of its source, it is also independent of the speed of its observers. Thus the speed of light (in a vacuum) is a constant: the same everywhere and for everyone in uniform motion (this is why it came to be symbolized by c).

Light Clock
So what does this invariance of the speed of light do to time? The best way to describe it is to use a thought experiment involving a �light clock�. What is a light clock? Imagine a clear boxlike device consisting of a light emitter fixed to the inside bottom and a mirror attached to the top directly above the emitter. This hypothetical clock keeps time by firing a photon up to the mirror, which reflects it straight back down; and the exact instant that photon strikes the emitter, another is shot out up towards the mirror. These repeating events occur at regular intervals since each cycle � consisting of one �tick� (photon shot up to mirror) and one �tock� (light reflected to the emitter) - would take exactly the same amount of time.

Now let us again imagine observers A and B in two separate reference frames. A is, once again, at rest (here, with respect to the clock) and B is in motion (relative to the clock). We are interested in the events that comprise a single cycle of the light clock: one firing-reflection-return. Observer A sees the photon shoot directly up, reflect off the mirror, and exactly retrace in the opposite direction its upward path. Therefore, the distance the light travels according to observer A�s perspective is simply twice the height of the box. But observer B is moving, let�s say to the left. So the light clock is in motion to the right relative to him/her so he/she sees something different. The photon that is emitted still hits the mirror dead on (it must, since both observers are examining the exact same set of events), but, since the whole device has shifted to the right between the time that the photon is emitted and the time that it strikes the mirror, the mirror has moved to the right slightly. Consequently, observer B does not see the photon travel directly upwards, but rather upwards at a right slant (needed to hit the repositioned mirror). The photon is then reflected and still hits the emitter square on (again, the two observers are witnessing the exact same set of events so they must agree on this), but the whole device has moved rightward again in the time between the photon�s reflection and its return. Thus observer B sees the downward trajectory also slant off to the right. All of this means that observer A and observer B see two different versions of the same exact set of events due to their motions relative to one another. The length of the path the photon travels from observer A�s perspective is simply twice the height of the box, but for observer B, the total length is twice the height plus some additional distance in the right horizontal direction. Therefore, the photon travels a greater total distance in B�s frame of reference frame than it does in A�s. What does this mean?

If this above light clock thought experiment had been performed before Einstein�s special theory of relativity, the explanation for the two observers measuring different distances would have simply been that they measure different speeds for light (electromagnetic waves). In other words, by definition, speed is equal to the distance traveled divided by the amount of time that elapsed (think what a speed of 50 mi/hr means). Since the time that elapses for the same set of events must be equal, and the distances differ, then the speeds must differ. The explanation would have been that simple.

Time Dilation
But Einstein strictly forbade that, stating that the speed of light is a constant, even for observers in motion relative to one another. Now, if the speed of the light pulse is the same for both observers, yet the distances for each differ, then the amount of time that elapsed for observers A and B, who were both in uniform motion, moving relative to one another, must be different, even though they both witnessed the very same set of events! Yes, despite what our everyday experience tells us, time does not pass at an absolute, fixed rate. Two observers in relative motion to each other will measure different rates of the passage of time: if their relative speed is great enough, one person�s second could be the other person�s minute!

A common cram-it-all-into-one-bite-size-nugget-so-that-it-is-easy-to-remember expression used to convey this complex subject is, �moving clocks run slow�. Though helpful as a memory device, besides other problems, this shorthand version (and the light clock example) implies that this effect is restricted to light clocks and mechanical or digital clocks/watches. But that is not so. This phenomenon of time variance relates to all processes, including physiological (heart beat, metabolism, mental processes, etc.) and physical (decay of radioactive isotopes, etc.). It is time itself that is different for those two observers. Time dilation, as it is called, is not mere fantasy: it has been experimentally verified by multiple experiments.

Time-Traveling Twin Paradox
Time dilation explains why two twins can end up being years apart in age (as alluded to previously). Suppose that while one twin remains here on the Earth, the other rockets off at near the speed of light to a star several light years away, turns around, and then returns home. Since the �moving� twin�s �clock� would have been �running slow�, when the pair meet again after the trip, the space-traveling sibling could be up to many years younger than his/her twin.

[ September 05, 2002: Message edited by: DNAunion ]

09-03-2002, 01:32 AM	#1
Ted Hoffman Veteran Member Join Date: Feb 2001 Location: "" Posts: 3,863	Someone Help with the Twin Paradox I came across the Twin Paradox in Stephen Hawkins' A Brief History of Time, the twin Paradox states that if we have two twins and we sent one off to space, the one who remains on earth will age faster than the one in space because time moves faster closer to the earth. Can someone please explain to me what that means?

09-03-2002, 05:43 AM	#4
strubenuff Junior Member Join Date: Oct 2001 Location: NY Posts: 96	What is the paradox? I haven't looked at the site, so forgive me if this is redundant. The best analogy I have seen is the stroy of the race car driver. Imagine a man racing down a flat away one-hundred miles long, at 100 miles an hour. He shows his friend his times at the end of his day, and his friend is disturbed. He sees that he made the first 4 or so in exactly an hour. Howveer, towards the end, their was a significant increase in his times. The driver explained the sun was in his eyes, so he had inadvertantly traveled a little to the right or left, which added time to his runs. What's this have to do with spacemen? The point is that, even though the driver's speed didn't change, it took him longer to complete the same distance. This is because he entered a different dimension. Instead of traveling in a straight line (1st dimesnion, length), he has also traveled left or right (2nd dimension, width). This is also true for all matter. You are currently traveling through time (4th dimesnion) at the speed of light. When you travel through space, say by driving your car, you are diverting some of that speed into different dimensions (the first three), so you go slower through time. This doesn't really matter for general purposes, since our speeds through space are so slow. However, when traveling into outer space, our speeds are fast enough (albeit still very slow compared to light) to measure. That's why the twin was some fraction of a second younger after he had traveled to space. [ September 03, 2002: Message edited by: strubenuff ]</p>

09-05-2002, 04:44 PM	#9
ohwilleke Veteran Member Join Date: Jun 2000 Location: Denver, Colorado, USA Posts: 4,834	The Twin Paradox is a way of forcefully illustrating the implication of the theory of special relativity that time is not a universal thing that passes at the same rate for everyone. Instead, time is something that crudely speaking passes at different rates for each person and thing based on their motion relative to other persons and things. Absolute coordinates of time and space against which everything can be measured don't exist. Einstein's remarkable insight in relativity is realizing that even though everyone has a different ruler and a different personal clock, the entire system can be consistently in compliance with a set of physical laws that apply to all observers. [ September 05, 2002: Message edited by: ohwilleke ]</p>

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09-03-2002, 05:28 AM	#3
Ted Hoffman Veteran Member Join Date: Feb 2001 Location: "" Posts: 3,863	Friar Bellows, Thanks for the link. My brain seems incapable of understanding wtf happens, so I will read it tomorrow when I am fresh. Do you understand the mechanism that the twin paradox operates under?

09-03-2002, 07:32 AM	#5
Ernest Sparks Veteran Member Join Date: Jun 2000 Location: Portland, OR USA Posts: 1,248	It can be demonstrated by physical phenomena. In a nuclear particle accelerator, particles called 'pions' are produced by collisions and circle around the machine. These will have different speeds depending on the energy of the collision that creates them. After a very short time, a free pion decays into other particles. As observed in the machine frame of reference, pions going closer to the speed of light last longer than pions going significantly slower than the first. Atomic maser clocks of fantastic precision are placed in two airplanes. One airplane flies eastward around the world and the other airplane flies westward. When they re-unite, the eastward flown clock is behind the westward flown clock. Relative to the rotating earth, the eastward airplane travels faster than the westward airplane.

09-04-2002, 08:49 AM	#7
LeftCoast Senior Member Join Date: Aug 2000 Location: San Diego, CA, USA Posts: 913	Intensity, The mechanism is due to the differing rates at which time passes for each observer(twin) in their respective references frames. This is only a "Paradox" in the sense of "Zeno's Paradox" in that the results seem to defy our logical preconceptions, however, once you understand the physics of what is going on, there is no paradox at all. The whole effect is the result of the two differing reference frames experienced by each twin. For the twin that remains on earth, time passes at the same rate as for all of us. For the twin that is accelerated to ~c time passes at a much slower rate due to the Lorentz contraction described by the equations of Special Relativity. The time-dilation factor for the faster twin is: gamma = 1/sqrt(1 - v2/c2) Where: T(Earth-Twin) = gammaT(fast-twin) and 'v' is the relative velocity between the two twins. Gamma is always greater than 1 so the clock for the faster twin will always register a slower time than the earth-bound twin. However, unless you get to values very close to c, the effect is too small to be detected by any but the most accurate atomic clocks. (e.g. - at 100km/h the effect is only to one part in 10*12 - IOW it would take 31,688 years(~ 1 million-million seconds) for a difference of 1 second to be realized between two clocks moving with a relative velocity difference of 100km/h) Hope this helps.

09-04-2002, 05:34 PM	#8
Answerer Veteran Member Join Date: Feb 2002 Location: Singapore Posts: 3,956	The twin paradox in the moving twin case isn't regarded as an inertial reference at all since he do accelerated during his journey. In relativity, when things accelerated, we say that they were under the effects of gravitional frequency shift. Gravitional frequency shift is the effect that was largely responsible for the asymmetric effects of time on the twins after the journey. I will try to find the link for this effect as I don't think I could explain quite well. So, please wait.

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