# How Time Flies: Ultraprecise Clock Rates Vary with Tiny Differences in Speed and Elevation

Newly developed optical clocks are so precise that they register the passage of time differently at elevations of just a few dozen centimeters or velocities of a few meters per second

IT'S ALL RELATIVE: James Chin-wen Chou with one of the aluminum-ion optical clocks at the National Institute of Standards and Technology. Image: J. Burrus/NIST

• ### Neutrino Hunters

If you have ever found yourself cursing a noisy upstairs neighbor, take solace in the fact that he or she is aging faster than you are.

Albert Einstein's theory of general relativity predicts that clocks at different gravitational potentials will tick at different rates—a clock at higher elevation will tick faster than will a clock closer to Earth's center. In other words, time passes more quickly in your neighbor's upstairs apartment than it does in your apartment.

To complicate matters, the theory of special relativity, which preceded general relativity by a decade, predicts a similar effect for clocks in motion—a stationary clock will tick faster than a moving clock. This is the source of the famous twin paradox: Following a round-trip journey on a spaceship traveling at some exceptionally high velocity, a traveler would return to Earth to find that her twin sibling is now older than she is, because time has passed more slowly on the moving ship than on Earth.

Both of these so-called time dilation effects have been verified in a number of experiments throughout the decades, which have traditionally depended on large scales of distance or velocity. In one landmark 1971 test Joseph Hafele of Washington University in Saint Louis and Richard Keating of the U.S. Naval Observatory flew cesium atomic clocks around the world on commercial jet flights, then compared the clocks with reference clocks on the ground to find that they had diverged, as predicted by relativity. But even at the speed and altitude of jet aircraft, the effects of relativistic time dilation are tiny—in the Hafele–Keating experiment the atomic clocks differed after their journeys by just tens to hundreds of nanoseconds.

Thanks to improved timekeeping, similar demonstrations can now take place at more mundane scales in the laboratory. In a series of experiments described in the September 24 issue of Science, researchers at the National Institute of Standards and Technology (NIST) in Boulder, Colo., registered differences in the passage of time between two high-precision optical atomic clocks when one was elevated by just a third of a meter or when one was set in motion at speeds of less than 10 meters per second.

Again, the effects are minuscule: It would take the elevated clock hundreds of millions of years to log one more second than its counterpart, and a clock moving a few meters per second would need to run about as long to lag one second behind its stationary counterpart. But the development of optical clocks based on aluminum ions, which can keep time to within one second in roughly 3.7 billion years, allows researchers to expose those diminutive relativistic effects. "People usually think of it as negligible, but for us it is not," says lead study author James Chin-wen Chou, a postdoctoral research associate at NIST. "We can definitely see it."

The NIST group's optical clocks use lasers to probe the quantum state of aluminum ions held in radio-frequency traps. When the laser's frequency is just right, it resonates with a transition between quantum states in the aluminum ion whose frequency is constant in time. By constantly tuning the laser to drive that aluminum transition, an interaction that only occurs in a tiny window near 1.121 petahertz (1.121 quadrillion cycles per second), the laser's frequency can be stabilized to an exquisitely sensitive degree, allowing it to act as the clock's pendulum. "If we anchor the frequency of the oscillator—in our case, laser light—to the unchanging, stable optical transition in aluminum, the laser oscillation can serve as the tick of the clock," Chou explains.

To put the sensitivity of the optical clocks in perspective, Chou notes that the two timekeepers in the study differed after a height change of a mere step on a staircase—never mind the entire floor separating you from your noisy neighbor—or with just a few meters per second of motion. "If you push your daughter on a swing, it's about that speed," he says.

In the past, such relativistic experiments have involved either massive scales of distance or velocity, or else oscillations so fast that their ticks cannot be reliably counted for timing purposes, says Holger Müller, an atomic physicist at the University of California, Berkeley. "It's an enormous achievement that you can build optical clocks so good that you can now see relativity in the lab," he says.

Müller has used atom interferometry to make precision measurements of relativistic effects, measurements that rely not on counting individual oscillations but on tracking the interference between two waves. (The frequencies of such waves, which oscillate tens of billions of times faster than the petahertz laser in an aluminum clock, are simply too high to monitor and count.) It is a process akin to striking two tuning forks to listen to the pulsations of their interference, without actually measuring how many times each fork vibrates. In that sense atom interferometers are pendulums without clockwork, so although they can make physical measurements with great precision, they cannot be used to keep time.

"The new work operates on familiar scales of distance and velocity, with clocks that can be used for universal timing applications," Müller says. "They see the effects of general and special relativity, and that makes relativity something you can kind of see and touch."

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1. 1. tharriss 05:31 PM 9/23/10

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

Cool stuff! :-)

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2. 2. akmangalick 06:07 PM 9/23/10

Einstein would be proud, I bet.

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3. 3. _GnXd 10:04 PM 9/23/10

For an instance, time existed

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4. 4. jtdwyer 01:41 AM 9/24/10

Very interesting. This will take a while to properly digest (if possible), but to pick on the low hanging fruit, the article states:
"—a stationary clock will tick faster than a moving clock."

As I understand this perpetuates a misconception: there are no stationary clocks. Everything in the universe is in motion: the progression of time is dependent on velocity. The difference in clock progression rates is produced by their differential relative velocities (including the equivalent effect of gravitation). If one could attain the speed of light the progression of time would halt. If we ever truly halt our momentum the progression rate of our watches would reach infinity. At least, that's my guess...

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5. 5. desch 03:25 AM 9/24/10

I wonder what influence gravity has on 'the unchanging, stable optical transition in aluminum'?

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6. 6. Banned Anna in reply to jtdwyer 05:42 AM 9/24/10

Not quite, jt... There's no absolute standard of movement. We can pick one velocity (any velocity) to call zero. Anything moving at this velocity, such as a clock, we say is stationary with respect to that totally arbitrary standard. Anything moving relative to that clock, e.g. another clock, we call moving. All else being equal, the clock we decided to treat as moving runs slow compared to our chosen standard, the clock we we're calling stationary. But we could just as well have taken the other clock's velocity as zero and defined the first clock as the moving one. Measured against this new standard of what it means to be at rest, it's the first clock that runs slow. Of course, that seems like a paradox, but only till you see how it fits together with the relativity of distances and simultaneity. If you're curious, try this: http://www.lightandmatter.com/html_books/0sn/

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7. 7. jtdwyer in reply to Banned Anna 10:20 AM 9/24/10

Thanks - you certainly are correct, in terms of general relativity, which for all practical purposes makes you absolutely correct. I admit to being generally ignorant of specific established laws of physics and have no intention of becoming an accredited lawyer or physicist.

However, if all observers are actually in motion (relative to the rest of the universe) and must therefore be considered to be in motion, is GR universally applicable, or 'merely' a useful method of local approximation for an observer and an object of observation? GR was conceived for use within the known Milky Way 'universe' of the early 1900s - does that restrict its scope?

Like I said, this will take a while for me to properly digest... I certainly don't understand how each of two clocks could be running slower than the other, unless there was some unstated restriction of scope. I'll keep thinking. Thanks also for the link to the instructional textbook.

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8. 8. jtdwyer in reply to Banned Anna 10:42 AM 9/24/10

One more thing...

In the case of these new clocks, I suggest that if the clock is moved to a lower step, it will be the stationary clock that will be running faster.

The kinetic energy expended moving the clock in this experiment is insignificant to the effective velocity of gravitation and/or velocity of Earth's rotation at the higher/lower elevation.

Unless I'm wrong, doesn't this clearly demonstrate that it is the relative velocity of the two clocks that determine which runs faster, and that both clocks are actually in motion?

I'd appreciate your consideration...

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9. 9. jtdwyer in reply to jtdwyer 10:54 AM 9/24/10

Sorry I misstated the proposal - it's so confusing...

I suggest that if one of the new clocks is moved to a lower step, it will be the 'stationary' (unmoved) clock that will be running slower.

The kinetic energy expended moving the clock in this experiment is insignificant to the effective velocity of gravitation and/or velocity of Earth's rotation at the higher/lower elevation.

Unless I'm wrong, doesn't this clearly demonstrate that it is the relative velocity of the two clocks that determine which runs faster, and that both clocks are actually in motion?

I'd appreciate your consideration...

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10. 10. jtdwyer in reply to jtdwyer 11:39 AM 9/24/10

I also failed to mention the orbital velocity of the Earth around the Sun and the Solar system's orbital velocity around the Milky Way, but both of these velocities would be effectively equivalent even for a space traveler headed to the outer Solar system.

It is the relative velocities of the textbook twin paradox that renders the velocity of the 'stationary twin' back on Earth inconsequential in estimating the differential clock progression rates.

I certainly haven't figured everything out, but I do think that the 'twin paradox' problem and solution statements have to be reconsidered in the context of these super-precise clocks. Unless, of course, I'm wrong...

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11. 11. WillHopkins in reply to jtdwyer 02:11 PM 9/24/10

The article does a poor job in describing special and general relativity. Unfortunately this is all too common. It is especially annoying that the assymtery of the twin's paradox is not highlighted.

Special relativity deals with observers who are in motion at constant velocity and are not accelerating. The laws of physics should be the same for each observer and the observers cannot distnguish who is moving and who is stationary.

An accelerating observer can determine that he is accelarating as he feels a force and this is the realm of general relativity which is based on the equivalence principle that says the acceleration due to gravity is equivalent to and indistiguishable from other forms of acceleration.

In the case of the clocks they are experiencing differing accelerations and therefore can distinguish their frames of reference. If the clocks are brought back together the clock at the higher elevation will have measured more elapsed time.

The twin's paradox is likewise poorly described. The situation is not symmetrical as one twin undergoes acceleration during the switch from the outward bound journey to the inward one. When the twins meet up again the twin who has undergone the acceleration will be will be younger than the other.

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12. 12. WillHopkins 02:50 PM 9/24/10

If you are interested in an example calculation of the twin's paradox where the journeying twin accelerates at the rate of earth's gravity for each of four segments of trip (accelerate for time T, then decelerate for the same T then accelerate back towards the other twin for T and then finally decelerate for T to rejoin the other twin) see http://plus.maths.org/latestnews/sep-dec09/timetravel/#seven

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13. 13. jtdwyer in reply to David Cota 04:31 PM 9/24/10

Why on Earth are you arguing my own assertion to me? I was attempting to take exception with the article's statement: "the theory of special relativity, which preceded general relativity by a decade, predicts a similar effect for clocks in motion - a stationary clock will tick faster than a moving clock."

Read the article, and concentrate real hard on the third paragraph.

I've been taken to task for first being incorrect about there being no stationary clocks and now mistakenly by you thinking I was arguing the opposite.

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14. 14. jtdwyer in reply to David Cota 04:33 PM 9/24/10

Very interesting, David. I'm understanding more every turn of the screw.

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15. 15. WillHopkins in reply to jtdwyer 05:44 PM 9/24/10

Um the wording of the article is poor. Rather than "a stationary clock will tick faster than a moving clock." it would have been more correct to say "an observer will find that a clock moving relative to him will tick more slowly than a clock stationary to him". If you have two observers who are moving relative to each other then each will observe the others clock moving more slowly.

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16. 16. Wayne Williamson 08:14 PM 9/24/10

excellent article and i loved the comments....

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17. 17. nathan 12:04 AM 9/25/10

This experiment is bogus. Time rate really doesn't change but when the two clock is separated by a distance, time rate only changes by amount of time it takes to close the distance therefore the clock in a distance must appear to run faster since it has to makeup for the time it takes to close the distance gap. And for gravity it is also an illusion.

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18. 18. carlofab 01:34 AM 9/25/10

Suppose we assume the earth is stationary and the universe geocentric? We could still calculate the apparent motions of starts and planets though it would be a little more complex.

But could modern day physics describe such a universe? Would the world as we know it, especially modern technology, still "work"? What would the "big bang" look like, and would it make gravitational sense?

I don't know the answer, but if it's "no" then you can't pick just anyplace and declare it stationary.

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19. 19. jtdwyer in reply to WillHopkins 03:08 AM 9/25/10

Thanks! That is a bit more easily digestible than the seemingly absolute (either clock will be running slower depending on which is considered to be moving). So, it is only from the observer's seemingly stationary frame of reference that the other clock appears to be running more slowly than the observer's, correct? Sorry I can't do the math, but your previous explanations are also very good - thanks again for the help.

SO, in my previous sample experiment when one of the new clocks is moved to a lower step, I'd expect that the 'stationary' clock would run slower than the moved clock, since it is the stationary clock that is now moving at greater velocity than the moved clock (from GR gravitation, rotation, etc.). I would intuitively expect the clock on the higher step would run slower regardless of the observer's location.

Based on special relativity, is it true that moved clock, now on the lower elevation step, would appear to run slower when viewed from the higher step? (I'm not just trying to be difficult here) - Thanks.

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20. 20. Ralf123 04:25 AM 9/25/10

Time flies like an arrow; fruit flies like a banana.

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21. 21. cook2son 08:27 AM 9/25/10

wow my upstairs friend is now showing a red shift but he's not really moving away from me at all! Is the universe really expanding or are we actually looking at the future? Expanding or the earths rotation slowing down? is time and aging really same thing?Thanks Sa, I'd forgotten how stimulating SA was in my youth! I will resubscribe and catch up with u all.

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22. 22. cook2son 09:00 AM 9/25/10

forget the clocks! doesn't this prove that the fabric of space is moving faster than the heavenly bodies contained within? Is the fabric of space driving the rotation of the masses contained within? could what we consider gravity be the effect of pressure caused by the differences in these speeds?

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23. 23. phasered 04:16 AM 9/26/10

I would like to see what the time difference would be if they put one of the clocks in a stationary (relative to our orbit) location in space. The time could be transmitted to us and the transmission time lag could be compensated for. This would also remove it from the Earth's gravitational field and it would be a great distance from the core of this planet. They could also send one along for the ride to any of the planets we decide to visit...

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24. 24. Largo 03:38 PM 9/27/10

Considering the number of constants that are now being challenged due to identification of variations, what sets these fellows as apart?
Their assurdedness?
All of these ultra-precise exercises are set to fail in some way. We do not know enough to be so blase'. Every value we know of is an approximation. At best, with enough caveats, we come closer to refining those findings.
It's the way of the world...

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25. 25. Joseph C Moore, Cpo USN Ret 05:00 PM 9/28/10

Great! So get up off of your duff and move. You'll live longer.

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26. 26. jtdwyer in reply to David Cota 01:06 AM 9/29/10

Re. the increase in particle mass when accelerated:
Considering particles to be the stationary manifestation of alternating particle/wave state energy, with particle state mass as the centrally directed, self-opposed potential emission energy, the application of external force to objects of mass produces both increased kinetic motion and increased potential energy (mass) proportionate to the probabilistic material state manifestations as particles and waves. This proportional application of force to increase mass as well as impart velocity prevents objects of mass from attaining the speed of light: the force applied partially produces motion as well as partially resists motion.

I think Feynman's comment about antimatter was in reference to it's opposingly directed spin and opposite charge compared to matter. I don't think his antimatter comment had anything to do with FTL acceleration. Do you have some source for the FTL acceleration inversely directed in time? I don't think this has been established, much less any relation to any unspecified communication of events controlling the 'arrow of time'.

I attempt to describe as precisely as I can my ideas about physical processes producing unexplained phenomena. In my experience, the incidence of extremely large volumes of events produces 'fuzzy' effects of seemingly random results without including any 'fuzziness' within the process being described.

In my own opinion, you are also considering things exactly as 'wired' to do. Feel free to continue enjoying my exacting specifications. If you design a device to produce unexpected results, it will not likely produce the results expected of it. Thanks.

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27. 27. bucketofsquid 03:00 PM 9/29/10

Just a couple of thoughts:
1. I have never encountered a definition of time as a set number of physical events. This is why I find talk of time running faster or slower difficult to process. So you change the velocity and/or elevation of an Aluminium ion and events happen to it faster. I don't see that time is occuring any faster. More physical events are occuring in the same span of time but time itself hasn't changed. The passage of time from the perspective of the ion may be greater. This is only a difference in measurement but not in time itself. If the ion was having fun would the number of events increase? After all; "time flies when you are having fun".

I've always felt that we are limited by our narrow perceptions but this seems to be stating that there is no universal law or set of laws of physics. This makes everything completely subjective with no over arching absolute.
The old "mass becomes infinite as you approach the speed of light" is patently silly. The apparent mass due to the transfer of energy to whatever you hit may be infinite but the mass hasn't changed at all. It still contains the same amount of matter. People lose that "apparent" conditional term and convert the phrase into an absolute when it isn't, in fact, absolute at all. It is completely subjective. What are the "situational ethics" of physics?

2. I keep hearing that time runs faster in a gravity well. The same people who say this also say that if there are 2 observers with 1 in the event horizon of a black hole and 1 outside, the person on the outside would view the person on the inside as stationary. Aside from the whole "no light escapes so you wouldn't see anything at all" issue,if time runs faster for the person inside then they would see the person outside as stationary. Conversely, the person outside with time running slower would see the person inside moving insanely fast. By "moving" I mean being crushed into an invisible speck by enormous gravity. Am I missing something vital here or do Hollywood and most other people have it wrong?

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28. 28. jtdwyer in reply to David Cota 06:53 PM 9/29/10

Well, in the only Feynman diagram examples I find for electron-positron annihilation, according to the supplied description following the chart's arrow of time, one electron and one positron collide, producing one or two (gamma-ray) virtual (temporary) photon(s) which may quickly decay, emitting another particle pair, which may radiate another particle such as a gluon. This certainly does not match your description.

I don't have access to the 1949 issues of Physical Review: if you could point me to a web address with an example of what you're referring to I could review it.

Feynman diagrams do have the capability of depicting processes going back in time, but I couldn't find much at all about that.

It's possible that Feynman's (1949) theory theory you're referring to never gained acceptance within the physics community.

Wikipedia's entry on Tachyons sstates:
...in the framework of quantum field theory, tachyons are understood as signifying an instability of the system and treated using tachyon condensation, rather than as real faster-than-light particles, and such instabilities are described by tachyonic fields. Tachyonic fields have appeared theoretically in a variety of contexts, such as the bosonic string theory. According to the contemporary and widely accepted understanding of the concept of a particle, tachyon particles are too unstable to be treated as existent."

While general relativity does not exclude "apparent" or "effective" FTL by 'massive' distortion of spacetime, it certainly hasn't been proved, and, while may be possible in some really extreme conditions, I think is generally disregarded as infeasible.

I also encountered some mention of 'imaginary time' in quantum theory, but that quickly put me to sleep...
I prefer the simplest explanations that can produce the observed validated evidence, at least that's my objective.

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29. 29. Jan Jitso 07:44 AM 9/30/10

Chou's measurements regard phase difference, which is explained by him as confirming the general theory of relativity. However such a phase difference can exist as a surplus or a short. Therefore the theory of Vasily Yanchilin in his book "The quantum Theory of Gravitation" (2003) that time runs faster near mass, so also at lower height on Earth, is not prooved to be wrong by the experiment. In fact the fast speed of happenings at the Big Bang with its big mass contradicts standstill of time at so called black holes due to their enormous masses. Einstein only accepted constancy of the speed of light as a temporary hypothesis; he did not believe that such a physical phenomen could be independent of everything else. Yanchilin argues that near mass time runs faster and at the edge of the universe stops in what is called a chaos situation without determined speed, direction, and so on. Namely mass limits the amount of the Heisenberg uncertainty. He sees the electron as innumerous times appearing and disappearing within a sphere with Heisenberg dimensions. If I call such an appearance an iet and reserve the name electron for the whole thing than iets nearer to an external mass will have less uncertainty and therefore less transitions (reappearances) in the most distant half of the electron than iets originating in that farther half. The result is movement towards the external mass. This is the first really qualitative explanation of gravitation. Newton and Einstein only could describe quantitatively and they are excused not knowing quantum mechanics.
Yanchilin proposes an experiment with two clocks on different heights and says the lower one will be faster. Elsewhere in his book he explains that radio-activity increases when concentration of mass lessen. So if radio-activity plays a key role in the clocks then this factor has to be analyzed carefully.
Meanwhile the special theory of relativity stays valid if understood thus that the speed of light at a certain spot and moment is independent of the motions of observers. Because c depends in the new theory on the potential of the total mass of the universe. Yanchilin broadens the horizon but new questions arise and have to be answered: Building up potential requires energy; how and what? Therefore students should read his book carefully and not act like Wikipedia which boycotts the Russian scientist like in the dark Middle Ages unwelcome books were burnt.

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30. 30. jtdwyer in reply to David Cota 11:34 AM 9/30/10

Thanks very much. Looks very interesting, as I'd expect from Feynman. However, I was hoping to find a Feynman diagram representing the events you'd described. It'll take me a while to get through a couple of dozen pages of Feynman-speak...

Trying to reason through the possibility that antiparticles characteristically travel 'backwards' in time, that would seem to almost preclude the collision of electrons and positrons. A nearly stationary electron residing in the local frame would have to contact a positron appearing precisely in the very near future so that, preceding backwards in time it could meet with the electron.

Moreover, in the Feynman diagrams I've seen, the electron and positron should not be shown moving in the same direction relative to the arrow of time, colliding at same point in space and time.

I'll look through the Feynman lecture if its explained there...

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31. 31. jdennys@yahoo.com 03:40 PM 10/3/10

i jumped ahead so pardon if this has been mentioned...

any measurement taken of one object would only describe the effect on that one relative to the speed and direction of the other, correct? so, in order to find the exact measurement of the effect, one of the clocks would have to be placed at the exact point of absolute zero motion in any direction relative to every other object in the universe - the exact center of the universe. if you find that point, any measurement made relative to it couldn't be wrong.

my apologies if my comment sounds like it came from a completely average intellect... it did, but it just seemed to be a valid question...

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32. 32. jdennys@yahoo.com in reply to jdennys@yahoo.com 03:48 PM 10/3/10

i realized there is a simpler way to put it - the universe literally revolves around this point. find this point, and put the clock there.

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33. 33. jtdwyer in reply to David Cota 12:22 AM 10/8/10

The expanding balloon analogy has always intrigued me. It's often used to illustrate the apparent omnidirectional expansion of spacetime, as galaxies all appear to expand away from each other on the surface of the balloon.

However, the balloon is indeed geometrically expanding radially from a central point. The radial force of expansion produces the apparent omnidirectional expansion as a lateral component motion.

So, in the balloon example, observed galaxies are typically considered to be contemporaneously expanding away from each other on the balloon surface.

However, our observations of galaxies are not contemporaneous. The surface of the balloon is not visible to us because of the speed of light at the scales of intergalactic distances. By the time light from distant galaxies reaches us, we are observing points on the surface of the balloon as it existed long ago, when the balloon was much smaller. The farthest points represent the earliest, smallest balloon.

For this reason, when it was determined that farther galaxies were 'receding away from us' at faster than nearer galaxies, it should not have been concluded that the expansion of the universe is accelerating: those observations were evidence that the universe had been expanding at greater rates in the past and expansion is now decelerating. This is the condition of the universe that is in accordance with the second law of thermodynamics.

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34. 34. mo98 06:49 PM 10/11/10

Intriguing instrumentation. Just read how 1000 dual core processors were used in 24 hours to for an n-body gravity simulation reduced to 75000 dust particles to simulate planet accretion in the early solar solar system. Seems like we are still ages away from postulating anything about gravity dilation or any associated waves with it. Time dilation experiments may be useful in examining propagation differences in light speed through crystals at prime angles to identify imperfections and what could cause water to store information so differently in differing samples near the triple point.

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35. 35. jtdwyer in reply to mo98 09:49 AM 10/17/10

Seems like the mass of 750,000 dust particles would not produce sufficient gravitation to accrete an approximately spherically symmetrical object, unless someone had their thumb on the scale...

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36. 36. eco-steve 05:01 PM 10/25/10

This article does not prove that time varies with speed, only that clocks tick faster. Is this because total energy is related to speed?
And what happens to time when clocks travel at the speed of light?

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37. 37. Ashbert 09:38 AM 12/26/10

Einstein's "length contraction" has never been experimentally tested and "time dilation" has only been tested with atomic (i.e. matter based clocks). There are theoretical suggestions that certain testing by beyond non-atomic clocks may show NO time dilation.

One lone highly-respected physicist broke from the crowd in mid-20th century and suggested that Einstein special relativity equations could be wrong. All others who said this are considered crackpots who don't understand relativity.But this person no one
dares call a crackpot? How come? Details at http://www.physicsnext.org

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38. 38. laurob 01:58 AM 3/27/11

Einstein’s “Law of Relativity”
I am no scientist, just an amateur Physicist, however I truly love physics, and within my understanding of what is defined as E=MC(2)… I have some doubts: There is one basic issue or missing component.
When Einstein made reference of relativity, he spoke about observing a specific event from the point of view (observation made) by an individual sitting at a position where the relativistic event took place. I will call this location A for the purposes of this discussion. Position A is therefore the position of the INITIATOR of a specific relativistic event. From the initiator’s point of view it is clear that the formula E=MC(2) makes sense. The reason for this is that the missing piece in the formula is equivalent to zero, therefore is it logically invisible for the initiator of the event. From an initiator’s point of view, nothing else impacts the relativistic E=MC(2) formula. In this case, all is good, Science remains predictable and Einstein remains correct.
However, he forgot to expand that ‘vision’ from the point of view of ‘external’ observers. To put it more clearly, Einstein is totally correct in defining the ‘local’ impact of relativity from the point of view of where a relativistic event takes place or starts. However, very simply, he forgot to go a bit further. If there was someone else observing the relativistic event (herein called observer B) from a different position (location), I then ask what are the things that would impact what observer B is seeing?
Well. In very simple terms, observer B would need to understand a few things:
1. Mass
2. %Speed of light
3. Energy
4. And something else. He would only be able to calculate an outcome from what he observes if he also takes into account his DISTANCE from the initiator, or distance from the event for which the initiator created.
There is a critical part here, and it still conforms to Einstein’s law of relativity.
There is a missing component missing in the formula to make it truly relative to everything else, not only to the initiator of the event, and this is DISTANCE.
From observer B standpoint, he will observe an event created by observer A, however, from his point of view, he also needs to take into account how far away he is from the event which observer A created so that he can appropriately calculate how the laws of relativity impact him in terms of where he is located. Assuming that observer B can only observe a certain action taking place at the speed of light, it therefore means that the further away he is from the event created by observer A will determine (mathematically) how early or late he will observe the event.
So to make Einstein’s relativity formula complete, you need to add r=distance to it. Here, therefore it now becomes easy to understand the relationship between distance and time : r and t: And it becomes clear that r and t are one and the same, therefore r and t are the same, therefore r=t.

So the actual formula is E=MRC(2)
And by inference, therefore, the definition of Time IS R=MC (2)/E
This also implies that Distance is equivalent to Mass x % Speed of light / Energy, therefore also implies that a spaceship can cross the universe in an instantaneous manner, depending on who is observing the spaceship.
There is a ‘wave type’ duality between distance and time. Here I am not sure how it works, however if you take into account the above formula the human definition of time will be directly related to the definition of distance. So here, time and distance is the same thing.
I have many sketches on this, which, from a visual perspective, simplify what I am discussing here.
In summary, Einstein was totally right. Time, and therefore Distance… is relative however, its relativity depends on distance from the relativistic event.
If you are interested I can forward sketches.
To spice up the subject, observer B would experience something very different if he decided to get closer to the event initiated by observer A. In the first stage, prior to getting close to the relativistic event, he would see TIME dilation relative to the event in front of him, but as soon as he reaches and clearly overtakes the event, if he looks back at the event created by observer A, he would see time compression. At the same time all this is happening, his own reference to his own initial location of observation would be one where his own time has slowed down relative to his initial location.
In other words, this, to me proves a number of things:
1. Distance is indeed a factor which was not taken into account
2. The multiplicity of time (relative to specific events, its creators and observers) and its mutual relationships are complex… therefore it is clear that TIME is something which can be manipulated, dependent on location of observation
3. There are multiple dimensions of observations, and depending on who is observing a specific event, the outcome will be different. It will be different in terms of TIME, and if TIME is equals Distance, it means that there could be a number of places (distances) an event will take place, and if this is so, and although there is one reality and one outcome for a specific observer, there is an infinite number of TIME/DISTANCE outcomes for different observers.
4. And finally, it therefore seems that one can predict a PHYSICAL outcome, but one cannot predict when and where it will happen as this will depend on where the observer is located.
5. However if we were able to build a framework where you can predict a specific event outcome from an infinite number of observer positions, one
6. Would be able to predict a specific location and time for the outcome of an event to everyone observing it.
7. It further implies that the speed of light limit does exist, however it only exists in relation to observer A, not to observer B. And therefore it means that the speed of light restriction is not real, as it is only real to observer A, whilst not for the remainder of INFINITE observers watching the same event from different locations. And therefore, distance from event initiation is FUNDAMENTAL in terms of defining the law of relativity.

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39. 39. Cramer in reply to laurob 06:19 PM 4/6/11

laurob,

Time and distance effects are already accounted for experimentally through r=ct, not r=t. Distance of observation is irrelevant to the theory of relativity, because light travels at the same speed in a vacuum in all inertial reference frames (therefore, it is easy to account for in practice).

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