Showing posts with label Time Dilation. Show all posts
Showing posts with label Time Dilation. Show all posts

Sunday, April 28, 2013

Getting Perspective on Time


Time has no independent existence apart from the order of events by which we measure it.Albert Einstein

Currently with the new book written by Lee Smolin about Time, to me, it is a fundamental question about what arises, and,  on how we use time to measure. Also for me,  to ask what relevance time means,  as an emergent product for any beginning.


LEE SMOLIN- Physicist, Perimeter Institute; Author, The Trouble With Physics

Thinking In Time Versus Thinking Outside Of Time

One very old and pervasive habit of thought is to imagine that the true answer to whatever question we are wondering about lies out there in some eternal domain of "timeless truths." The aim of re-search is then to "discover" the answer or solution in that already existing timeless domain. For example, physicists often speak as if the final theory of everything already exists in a vast timeless Platonic space of mathematical objects. This is thinking outside of time. See: WHAT SCIENTIFIC CONCEPT WOULD IMPROVE EVERYBODY'S COGNITIVE TOOLKIT?
 A "scientific concept" may come from philosophy, logic, economics, jurisprudence, or other analytic enterprises, as long as it is a rigorous conceptual tool that may be summed up succinctly (or "in a phrase") but has broad application to understanding the world.

What ignited this question for me goes to a comment I wrote as to what I saw as a precursor to this question for Lee Smolin and others. Further to this, the lessons and explanation Sean Carroll gave toward how we look at time.

Darwinian evolutionary biology is the prototype for thinking in time because at its heart is the realization that natural processes developing in time can lead to the creation of genuinely novel structures. Even novel laws can emerge when the structures to which they apply come to exist. Evolutionary dynamics has no need of abstract and vast spaces like all the possible viable animals, DNA sequences, sets of proteins, or biological laws. Exaptations are too unpredictable and too dependent on the whole suite of living creatures to be analyzed and coded into properties of DNA sequences. Better, as Stuart Kauffman proposes, to think of evolutionary dynamics as the exploration, in time, by the biosphere, of the adjacent possible. See: Thinking In Time Versus Thinking Outside Of Time
While we then become cognoscente of the rules around which parameters have meaning in relation to Time, it was also important to understand that the idea of cross pollination of the sciences recognizes what is brought to the table.

"It is very good that Stu Kauffman and Lee are making this serious attempt to save a notion of time, since I think the issue of timelessness is central to the unification of general relativity with quantum mechanics. The notion of time capsules is still certainly only a conjecture. However, as Lee admits, it has proven very hard to show that the idea is definitely wrong. Moreover, the history of physics has shown that it is often worth taking disconcerting ideas seriously, and I think timelessness is such a one. At the moment, I do not find Lee and Stu's arguments for time threaten my position too strongly."- Julian Barbour

In regard to The Adjacent Possible I was well aware of the implication and parameters  around such thinking to realize that even while applying the trade,  Stuart, was traveling new ground. His thinking is encouraging the flexibility that I am talking about with regard the restrictions one places on them self. I encourage this kind of thinking so as to bolster the lull in scientific advancement to stimulate and foster the idealization of creativity that I think has become stagnate while  moving from one point in the measure to the next. Why Murray Gell-Mann's  move and his expertise is understood in context of new approaches. Simplicity and complexity.




Setting Time Aright



See Also:

Thursday, June 28, 2012

Intent in the Actualized

 Remembering

Return to Home,
Safety seeking,
In my mind,
Continually speaking

Out of the sky,
Eyes Earthbound,
Stalagmite in open cavern,
Fertile lands all around.

The era of design,
Like a Justice Hall,
Women in bonnets,
Mennonite clothes,

In the Town of Williams,
Some time ago,
In the late eighteen hundreds,
Scenery I know.

by Platohagel




 Before I begin I just wanted to say I am deeply connected to the science today and what I am displaying now may not sit well with scientists.  Those who discount subjectivity as a part of our existence not tried and tested. This subjective existence\experience is real and very individual. How could you discount this from a point of a view of a scientist.  I thought they might say, but yes,  lived with responsibility and in a true validated sense?

So it was in this sense that one could consider the exercise that follows as a science fiction possibility that raises the questions about time and the relationship of the probability distribution of a possible future and the lived past. The present, in becoming, and in this case,  I wanted to look at the past.

The question is that we know that the world of subjective influences and experiences are deeply personal in that they become the life you have live. We work all day and we work all night in the virtual realities.You discover the Intent in the Actualized?

This distinction if not understood within the parameters of the subject entertained it would have lacked the understanding that our virtual reality within the confines of the parameters as being explicit in what we create would have been missed. I can talk about such a park and you might believe the context of such an example if I were to tell you that I was able to remember that at a very young age.

Can an individual experience the actualized past as if viewing a place in our history as part of that history. These questions had crossed my mind over 35 years ago as I explored the dream world. I tried to keep as much of this in poetic form dreaming as I was experiencing it. So I thought it would be nice to write it down in that form.

Now there are many reasons why this area of subjectivity was of interest to me. It was in that what I believed, that not only our footprints left an image in the sand, but our impressions of our life was in the footprints.

Two section variable capacitor, used in superhet receiver
Technically such excursions would have been of interest if I could track the ability by some means. So it was not beyond me to think that a tuning could take place by some individuals in helping to reconstruct the past  by going back in time. Not only by Carbon dating. But possibly by some other technical means as well in terms of a super heterodyne solution.

Now I am sure the idea of a fireman and a radio might be trigger in your mind. Aurora flickering in the sky and a son who goes to work on his Dad's radio?  You will find many references to time travel in this blog because of this idea I have had for a long time about our the ability each of has to visit the historical past as an Intent in the Actualized.

Frequency is a 2000 science-fiction film that contains elements of the time travel, thriller and alternate history film genres.

So the idea for me here was about creating a device that could tune into the past? Why then, is it we are not capable in consciousness as a virtual reality?





The Super Hero Versions

Miracles StudiosThrone Plates
To activate Thorne plates, the distance between each plate must be less than the width of an atom. The resulting wormhole will be equally small, so getting in and out might be difficult. To widen the portal, some scientists suggest using a laser to inject immense amounts of negative energy. In addition, Thorne believes that radiation effects created by gravitons, or particles of gravity, might fry you as you enter the wormhole. According to string theory, however, this probably won't happen, so it's scant reason to cancel your trip.


Miracles StudiosGott Loop
To take you back one year, the string must weigh about half as much as the Milky Way galaxy. You'll need a mighty big spaceship to make that rectangle.

Many scientists believe the big bang that created the universe left behind cosmic strings - thin, infinitely long filaments of compressed matter. In 1991, Princeton physicist J. Richard Gott discovered that two of these structures, arranged in parallel and moving in opposite directions, would warp space-time to allow travel to the past. He later reworked the idea to involve a single cosmic-string loop. A Gott loop can take you back in time but not forward. The guide to building your own:


Miracles StudiosGott Shell
This is a relatively slow method of time travel, and life inside the shell could become tedious.

In essence, a Gott shell is a huge concentration of mass. The shell's sheer density creates a gravitational field that slows down the clock for anyone enclosed within it. Outside, time rolls along at its familiar pace, but inside, it creeps. Thus the Gott shell is useful for travel into the future only. If you're planning a jaunt to the past using a Gott loop, you might want to bring along a Gott shell for the return trip. What to do, step by step:


Miracles StudiosVan Stokum Cylinder
The cylinder must be infinitely long, which could add slightly to its cost.

Mass and energy act on space-time like a rock thrown into a pond: the bigger the rock, the bigger the ripples. Physicist W. J. van Stockum realized in 1937 that an immense cylinder spinning at near-light speed will stir space-time as though it were molasses, pulling it along as the cylinder turns. Although Van Stockum himself didn't recognize it, anyone orbiting such a cylinder in the direction of the spin will be caught in the current and, from the perspective of a distant observer, exceed the speed of light. The result: Time flows backward. Circle the cylinder in the other direction with just the right trajectory, and this machine can take you into the future as well. How it works:


Kerr Ring
The Kerr ring is a one-way ticket. The black hole's gravity is so great that, once you step through it, you won't be able to return.

When Karl Schwarzschild solved Einstein's equations in 1917, he found that stars can collapse into infinitesimally small points in space - what we now call black holes. Four decades later, physicist Roy Kerr discovered that some stars are saved from total collapse and become rotating rings. Kerr didn't regard these rings as time machines. However, because their intense gravity distorts space-time, and because they permit large objects to enter on one side and exit on the other in one piece, Kerr-type black holes can serve as portals to the past or the future. If finding one with the proper dimensions is too much trouble, you can always build one yourself:
See:A User's Guide to Time Travel-Superpower Issue




See Also: Tom Campbell: Calgary Theory only (Sat) 2/3

Wednesday, September 07, 2011

The Synaptic World of Experience and Knowledge



 It is important that people realize that as much as topological seasoning is added to the world by myself,  I see ourselves intrinsically linked to the inductive/deductive process. It is as if the tail of each is linked as a image of a our inner and outer relation with the world continually exchanged. We are the central process in this, as if link the past and the future together, as to the outcome in life. A self eventual recognition of the arche and our place on it as to the decision and acceptance of outcome according to our conclusions?
I think that Fig. 34.1 best expresses my position on this question, where each of three worlds, Platonic-mathematical, physical and mental-has it’s own kind of reality, and where each is (deeply and mysteriously) found in one that precedes it ( the worlds take cyclicly). I like to think that, in a sense the Platonic world may be the most primitive of the three, since mathematics is a kind of necessity, virtually conjuring its very existence through logic alone. Be that as it may, there is a further mystery, or paradox, of the cyclic aspect of these worlds , where each seems to be able to encompass the succeeding one in its entirety, while itself seeming to depend only upon a small part of its predecessor.”(Page 1028-The Road to Reality- Roger Penrose- Borzoi Book, Alfred A. Knoff- 2004)

For me, the visual helps to reinforce some  the understanding that is required of how let's say Sir Roger Penrose may look at the idea of "information transference?" How I may see this in individuals who are interacting with the world. I believe too, that how the universe is formulated into the Cyclical Universe is to direct our attention to the facets of time attached to the ideas of how this is formulated within ourselves as well. This are the same correlations of the past, as well as the future, in our now, in our universe(our neighborhood) as well.

If we can put everything together, we might have a model that reproduces everything we see in our detector."


Plato's problem is the term given by Noam Chomsky to the gap between knowledge and experience. It presents the question of how we account for our knowledge when environmental conditions seem to be an insufficient source of information. It is used in linguistics to refer to the "argument from poverty of the stimulus" (APS). In a more general sense, Plato’s Problem refers to the problem of explaining a "lack of input."
Solving Plato’s Problem involves explaining the gap between what one knows and the apparent lack of substantive input from experience (the environment). Plato's Problem is most clearly illustrated in the Meno dialogue, in which Socrates demonstrates that an uneducated boy nevertheless understands geometric principles.

The understanding here is that all knowledge exists in the universe and that we only have to awaken it within ourselves. This hasn't changed my view on the universal access to information that we can tap into. How is this accomplished.

This view I carry to the world of science and look for correspondences in experimental associations. I believe the answers we are looking for already exist.  It is just a matter of asking the right questions, as well as looking inside as to the truth of what we are looking at,  as a potential in the discourse of our existence as human beings. The role we are playing as components of this reality to better ourselves.

Thursday, September 01, 2011

Setting Time Aright



Time has no independent existence apart from the order of events by which we measure it.Albert Einstein

While Event has since past, I hope the lecture itself will remain in public domain. It helps so as to see the context of the discussion provided by this conference with regard to that subject of time.




Video streaming by Ustream

See:Setting Time Aright

In 1952, in his book Relativity, Einstein writes:

Since there exists in this four dimensional structure [space-time] no longer any sections which represent "now" objectively, the concepts of happening and becoming are indeed not completely suspended, but yet complicated. It appears therefore more natural to think of physical reality as a four dimensional existence, instead of, as hitherto, the evolution of a three dimensional existence
.

Setting Time Aright
View more presentations from Sean Carroll

***

  If man thinks of the totality as constituted of independent fragments, then that is how his mind will tend to operate, but if he can include everything coherently and harmoniously in an overall whole that is undivided, unbroken, and without a border then his mind will tend to move in a similar way, and from this will flow an orderly action within the whole. (David Bohm, Wholeness and the Implicate Order, 1980)


Lee Smolin:
I suspect this reflects the expectation many people have that time is not fundamental, but rather emerges only at a semiclassical approximation in quantum cosmology. If you believe this then you believe that the fundamental quantities a quantum cosmology should compute are timeless. This in turn reflects a very old and ultimately religious prejudice that deeper truths are timeless. This has been traced by scholars to the theology of Newton and contemporaries who saw space as “the sensorium” of an eternal and all seeing god. Perhaps the BB paradox is telling us it is time to give up the search for timeless probability distributions, and recognize that since Darwin the deep truths about nature cannot be divorced from time.

The alternative is to disbelieve the arguments that time is emergent-which were never very convincing- and instead formulate quantum cosmology in such a way that time is always real. I would suggest that the Boltzman Brain’s paradox is the reducto ad absurdum of the notion that time is emergent and that rather than play with little fixes to it we should try to take seriously the opposite idea: that time is real.

***

Bar of Lead Tungstate Source: A Quantum Diaries Survivor-Calorimeters for High Energy Physics experiments - part 1 April 6, 2008
Calorimeters measure the collective behavior of particles traveling along approximately the same path, and are thus naturally suited for the measurement of jets-Dorigo Tommaso


See

Thursday, December 09, 2010

Time Dilation

....... is a phenomenon (or two phenomena, as mentioned below) described by the theory of relativity. It can be illustrated by supposing that two observers are in motion relative to each other, or differently situated with regard to nearby gravitational masses. They each carry a clock of identical construction and function. Then, the point of view of each observer will generally be that the other observer's clock is in error (has changed its rate).

Both causes (distance to gravitational mass and relative speed) can operate together.

Contents

Overview

Time dilation can arise from:
  1. the relative velocity of motion between two observers, or
  2. the difference in their distance from a gravitational mass.

Relative velocity time dilation

When two observers are in relative uniform motion and far away from any gravitational mass, the point of view of each will be that the other's (moving) clock is ticking at a slower rate than the local clock. The faster the relative velocity, the greater the magnitude of time dilation. This case is sometimes called special relativistic time dilation. It is often interpreted as time "slowing down" for the other (moving) clock. But that is only true from the physical point of view of the local observer, and of others at relative rest (i.e. in the local observer's frame of reference). The point of view of the other observer will be that again the local clock (this time the other clock) is correct and it is the distant moving one that is slow. From a local perspective, time registered by clocks that are at rest with respect to the local frame of reference (and far from any gravitational mass) always appears to pass at the same rate.[1]

Gravitational time dilation

There is another case of time dilation, where both observers are differently situated in their distance from a significant gravitational mass, such as (for terrestrial observers) the Earth or the Sun. One may suppose for simplicity that the observers are at relative rest (which is not the case of two observers both rotating with the Earth—an extra factor described below). In the simplified case, the general theory of relativity describes how, for both observers, the clock that is closer to the gravitational mass, i.e. deeper in its "gravity well", appears to go slower than the clock that is more distant from the mass (or higher in altitude away from the center of the gravitational mass). That does not mean that the two observers fully agree: each still makes the local clock to be correct; the observer more distant from the mass (higher in altitude) measures the other clock (closer to the mass, lower in altitude) to be slower than the local correct rate, and the observer situated closer to the mass (lower in altitude) measures the other clock (farther from the mass, higher in altitude) to be faster than the local correct rate. They agree at least that the clock nearer the mass is slower in rate and on the ratio of the difference.

Time dilation: special vs. general theories of relativity

In Albert Einstein's theories of relativity, time dilation in these two circumstances can be summarized:
  • In special relativity (or, hypothetically far from all gravitational mass), clocks that are moving with respect to an inertial system of observation are measured to be running slower. This effect is described precisely by the Lorentz transformation.
Thus, in special relativity, the time dilation effect is reciprocal: as observed from the point of view of either of two clocks which are in motion with respect to each other, it will be the other clock that is time dilated. (This presumes that the relative motion of both parties is uniform; that is, they do not accelerate with respect to one another during the course of the observations.)

In contrast, gravitational time dilation (as treated in general relativity) is not reciprocal: an observer at the top of a tower will observe that clocks at ground level tick slower, and observers on the ground will agree about that, i.e. about the direction and the ratio of the difference. There is not full agreement, all the observers make their own local clocks out to be correct, but the direction and ratio of gravitational time dilation is agreed by all observers, independent of their altitude.

Simple inference of time dilation due to relative velocity


Observer at rest sees time 2L/c.

Observer moving parallel relative to setup, sees longer path, time > 2L/c, same speed c.
Time dilation can be inferred from the observed fact of the constancy of the speed of light in all reference frames. [2] [3] [4] [5]

This constancy of the speed of light means, counter to intuition, that speeds of material objects and light are not additive. It is not possible to make the speed of light appear faster by approaching at speed towards the material source that is emitting light. It is not possible to make the speed of light appear slower by receding from the source at speed. From one point of view, it is the implications of this unexpected constancy that take away from constancies expected elsewhere.

Consider a simple clock consisting of two mirrors A and B, between which a light pulse is bouncing. The separation of the mirrors is L and the clock ticks once each time it hits a given mirror.
In the frame where the clock is at rest (diagram at right), the light pulse traces out a path of length 2L and the period of the clock is 2L divided by the speed of light:
\Delta t = \frac{2 L}{c}.
From the frame of reference of a moving observer traveling at the speed v (diagram at lower right), the light pulse traces out a longer, angled path. The second postulate of special relativity states that the speed of light is constant in all frames, which implies a lengthening of the period of this clock from the moving observer's perspective. That is to say, in a frame moving relative to the clock, the clock appears to be running more slowly. Straightforward application of the Pythagorean theorem leads to the well-known prediction of special relativity:

The total time for the light pulse to trace its path is given by
\Delta t' = \frac{2 D}{c}.
The length of the half path can be calculated as a function of known quantities as
D = \sqrt{\left (\frac{1}{2}v \Delta t'\right )^2+L^2}.
Substituting D from this equation into the previous and solving for Δt' gives:
\Delta t' = \frac{2L/c}{\sqrt{1-v^2/c^2}}
and thus, with the definition of Δt:
\Delta t' = \frac{\Delta t}{\sqrt{1-v^2/c^2}}
which expresses the fact that for the moving observer the period of the clock is longer than in the frame of the clock itself.

Time dilation due to relative velocity symmetric between observers

Common sense would dictate that if time passage has slowed for a moving object, the moving object would observe the external world to be correspondingly "sped up". Counterintuitively, special relativity predicts the opposite.

A similar oddity occurs in everyday life. If Sam sees Abigail at a distance she appears small to him and at the same time Sam appears small to Abigail. Being very familiar with the effects of perspective, we see no mystery or a hint of a paradox in this situation.[6]

One is accustomed to the notion of relativity with respect to distance: the distance from Los Angeles to New York is by convention the same as the distance from New York to Los Angeles. On the other hand, when speeds are considered, one thinks of an object as "actually" moving, overlooking that its motion is always relative to something else — to the stars, the ground or to oneself. If one object is moving with respect to another, the latter is moving with respect to the former and with equal relative speed.

In the special theory of relativity, a moving clock is found to be ticking slowly with respect to the observer's clock. If Sam and Abigail are on different trains in near-lightspeed relative motion, Sam measures (by all methods of measurement) clocks on Abigail's train to be running slowly and similarly, Abigail measures clocks on Sam's train to be running slowly.

Note that in all such attempts to establish "synchronization" within the reference system, the question of whether something happening at one location is in fact happening simultaneously with something happening elsewhere, is of key importance. Calculations are ultimately based on determining which events are simultaneous. Furthermore, establishing simultaneity of events separated in space necessarily requires transmission of information between locations, which by itself is an indication that the speed of light will enter the determination of simultaneity.

It is a natural and legitimate question to ask how, in detail, special relativity can be self-consistent if clock A is time-dilated with respect to clock B and clock B is also time-dilated with respect to clock A. It is by challenging the assumptions built into the common notion of simultaneity that logical consistency can be restored. Simultaneity is a relationship between an observer in a particular frame of reference and a set of events. By analogy, left and right are accepted to vary with the position of the observer, because they apply to a relationship. In a similar vein, Plato explained that up and down describe a relationship to the earth and one would not fall off at the antipodes.

Within the framework of the theory and its terminology there is a relativity of simultaneity that affects how the specified events are aligned with respect to each other by observers in relative motion. Because the pairs of putatively simultaneous moments are identified differently by different observers (as illustrated in the twin paradox article), each can treat the other clock as being the slow one without relativity being self-contradictory. This can be explained in many ways, some of which follow.

Temporal coordinate systems and clock synchronization

In Relativity, temporal coordinate systems are set up using a procedure for synchronizing clocks, discussed by Poincaré (1900) in relation to Lorentz's local time (see relativity of simultaneity). It is now usually called the Einstein synchronization procedure, since it appeared in his 1905 paper.

An observer with a clock sends a light signal out at time t1 according to his clock. At a distant event, that light signal is reflected back to, and arrives back to the observer at time t2 according to his clock. Since the light travels the same path at the same rate going both out and back for the observer in this scenario, the coordinate time of the event of the light signal being reflected for the observer tE is tE = (t1 + t2) / 2. In this way, a single observer's clock can be used to define temporal coordinates which are good anywhere in the universe.

Symmetric time dilation occurs with respect to temporal coordinate systems set up in this manner. It is an effect where another clock is being viewed as running slowly by an observer. Observers do not consider their own clock time to be time-dilated, but may find that it is observed to be time-dilated in another coordinate system.

Overview of formulae

Time dilation due to relative velocity


Lorentz factor as a function of speed (in natural units where c=1). Notice that for small speeds (less than 0.1), γ is approximately 1
The formula for determining time dilation in special relativity is:
 \Delta t' = \gamma \, \Delta t = \frac{\Delta t}{\sqrt{1-v^2/c^2}} \,
where Δt is the time interval between two co-local events (i.e. happening at the same place) for an observer in some inertial frame (e.g. ticks on his clock) – this is known as the proper time, Δt ' is the time interval between those same events, as measured by another observer, inertially moving with velocity v with respect to the former observer, v is the relative velocity between the observer and the moving clock, c is the speed of light, and
 \gamma = \frac{1}{\sqrt{1-v^2/c^2}} \,
is the Lorentz factor. Thus the duration of the clock cycle of a moving clock is found to be increased: it is measured to be "running slow". The range of such variances in ordinary life, where vc, even considering space travel, are not great enough to produce easily detectable time dilation effects and such vanishingly small effects can be safely ignored. It is only when an object approaches speeds on the order of 30,000 km/s (1/10 the speed of light) that time dilation becomes important.

Time dilation by the Lorentz factor was predicted by Joseph Larmor (1897), at least for electrons orbiting a nucleus. Thus "... individual electrons describe corresponding parts of their orbits in times shorter for the [rest] system in the ratio :\scriptstyle \sqrt{1 - v^2/c^2}" (Larmor 1897). Time dilation of magnitude corresponding to this (Lorentz) factor has been experimentally confirmed, as described below.

Time dilation due to gravitation and motion together

Astronomical time scales and the GPS system represent significant practical applications, presenting problems that call for consideration of the combined effects of mass and motion in producing time dilation.
Relativistic time dilation effects, for the solar system and the Earth, have been evaluated from the starting point of an approximation to the Schwarzschild solution to the Einstein field equations. A timelike interval dtE in this metric can be approximated, when expressed in rectangular coordinates and when truncated of higher powers in 1/c2, in the form:[7][8]
 dt_E^2 = \left( 1-\frac{2GM_i}{r_i c^2} \right) dt_c^2 - \frac{dx^2+dy^2+dz^2}{c^2}, \,




(1)
where:
dtE (expressed as a time-like interval) is a small increment forming part of an interval in the proper time tE (an interval that could be recorded on an atomic clock);
dtc is a small increment in the timelike coordinate tc ("coordinate time") of the clock's position in the chosen reference frame;
dx, dy and dz are small increments in three orthogonal space-like coordinates x, y, z of the clock's position in the chosen reference frame; and
GMi/ri represents a sum, to be designated U, of gravitational potentials due to the masses in the neighborhood, based on their distances ri from the clock. This sum of the GMi/ri is evaluated approximately, as a sum of Newtonian gravitational potentials (plus any tidal potentials considered), and is represented below as U (using the positive astronomical sign convention for gravitational potentials). The scope of the approximation may be extended to a case where U further includes effects of external masses other than the Mi, in the form of tidal gravitational potentials that prevail (due to the external masses) in a suitably small region of space around a point of the reference frame located somewhere in a gravity well due to those external masses, where the size of 'suitably small' remains to be investigated.[9]
From this, after putting the velocity of the clock (in the coordinates of the chosen reference frame) as
v^2=\frac{dx^2+dy^2+dz^2}{dt_c^2}, \,




(2)
(then taking the square root and truncating after binomial expansion, neglecting terms beyond the first power in 1/c2), a relation between the rate of the proper time and the rate of the coordinate time can be obtained as the differential equation[10]
\frac{dt_E}{dt_c}= 1-\frac{U}{c^2}-\frac{v^2}{2c^2}. \,




(3)
Equation (3) represents combined time dilations due to mass and motion, approximated to the first order in powers of 1/c2. The approximation can be applied to a number of the weak-field situations found around the Earth and in the solar-system. It can be thought of as relating the rate of proper time tE that can be measured by a clock, with the rate of a coordinate time tc.

In particular, for explanatory purposes, the time-dilation equation (3) provides a way of conceiving coordinate time, by showing that the rate of the clock would be exactly equal to the rate of the coordinate time if this "coordinate clock" could be situated
(a) hypothetically outside all relevant 'gravity wells', e.g. remote from all gravitational masses Mi, (so that U=0), and also
(b) at rest in relation to the chosen system of coordinates (so that v=0).
Equation (3) has been developed and integrated for the case where the reference frame is the solar system barycentric ('ssb') reference frame, to show the (time-varying) time dilation between the ssb coordinate time and local time at the Earth's surface: the main effects found included a mean time dilation of about 0.49 second per year (slower at the Earth's surface than for the ssb coordinate time), plus periodic modulation terms of which the largest has an annual period and an amplitude of about 1.66 millisecond.[11][12]

Equation (3) has also been developed and integrated for the case of clocks at or near the Earth's surface. For clocks fixed to the rotating Earth's surface at mean sea level, regarded as a surface of the geoid, the sum ( U + v2/2 ) is a very nearly constant geopotential, and decreases with increasing height above sea level approximately as the product of the change in height and the gradient of the geopotential. This has been evaluated as a fractional increase in clock rate of about 1.1x10−13 per kilometer of height above sea level due to a decrease in combined rate of time dilation with increasing altitude. The value of dtE/dtc at height falls to be compared with the corresponding value at mean sea level.[13] (Both values are slightly below 1, the value at height being a little larger (closer to 1) than the value at sea level.)

A fuller development of equation (3) for the near-Earth situation has been used to evaluate the combined time dilations relative to the Earth's surface experienced along the trajectories of satellites of the GPS global positioning system. The resulting values (in this case they are relativistic increases in the rate of the satellite-borne clocks, by about 38 microseconds per day) form the basis for adjustments essential for the functioning of the system.[14]

This gravitational time dilation relationship has been used in the synchronization or correlation of atomic clocks used to implement and maintain the atomic time scale TAI, where the different clocks are located at different heights above sea level, and since 1977 have had their frequencies steered to compensate for the differences of rate with height.[15]

In pulsar timing, the advance or retardation of the pulsar phase due to gravitational and motional time dilation is called the "Einstein Delay".

Experimental confirmation

Time dilation has been tested a number of times. The routine work carried on in particle accelerators since the 1950s, such as those at CERN, is a continuously running test of the time dilation of special relativity. The specific experiments include:

Velocity time dilation tests

  • Ives and Stilwell (1938, 1941), "An experimental study of the rate of a moving clock", in two parts. The stated purpose of these experiments was to verify the time dilation effect, predicted by Lamor-Lorentz ether theory, due to motion through the ether using Einstein's suggestion that Doppler effect in canal rays would provide a suitable experiment. These experiments measured the Doppler shift of the radiation emitted from cathode rays, when viewed from directly in front and from directly behind. The high and low frequencies detected were not the classical values predicted.
f_\mathrm{detected} = \frac{f_\mathrm{moving}}{1 - v/c} and \frac{f_\mathrm{moving}}{1+v/c}\,=\, \frac{f_\mathrm{rest}}{1 - v/c} and \frac{f_\mathrm{rest}}{1+v/c}
i.e. for sources with invariant frequencies f_\mathrm{moving}\, = f_\mathrm{rest} The high and low frequencies of the radiation from the moving sources were measured as
f_\mathrm{detected} = f_\mathrm{rest}\sqrt{\left(1 + v/c\right)/\left(1 - v/c\right) } and f_\mathrm{rest}\sqrt{\left(1 - v/c\right)/\left(1 + v/c\right)}
as deduced by Einstein (1905) from the Lorentz transformation, when the source is running slow by the Lorentz factor.
  • Rossi and Hall (1941) compared the population of cosmic-ray-produced muons at the top of a mountain to that observed at sea level. Although the travel time for the muons from the top of the mountain to the base is several muon half-lives, the muon sample at the base was only moderately reduced. This is explained by the time dilation attributed to their high speed relative to the experimenters. That is to say, the muons were decaying about 10 times slower than if they were at rest with respect to the experimenters.
  • Hasselkamp, Mondry, and Scharmann[16] (1979) measured the Doppler shift from a source moving at right angles to the line of sight (the transverse Doppler shift). The most general relationship between frequencies of the radiation from the moving sources is given by:
f_\mathrm{detected} = f_\mathrm{rest}{\left(1 - \frac{v}{c} \cos\phi\right)/\sqrt{1 - {v^2}/{c^2}} }
as deduced by Einstein (1905)[1]. For \phi = 90^\circ (\cos\phi = 0\,) this reduces to fdetected = frestγ. Thus there is no transverse Doppler shift, and the lower frequency of the moving source can be attributed to the time dilation effect alone.
  • In 2010 time dilation was observed at speeds of less than 10 meters per second using optical atomic clocks connected by 75 meters of optical fiber.[17]

Gravitational time dilation tests

  • Pound, Rebka in 1959 measured the very slight gravitational red shift in the frequency of light emitted at a lower height, where Earth's gravitational field is relatively more intense. The results were within 10% of the predictions of general relativity. Later Pound and Snider (in 1964) derived an even closer result of 1%. This effect is as predicted by gravitational time dilation.
  • In 2010 gravitational time dilation was measured at the Earth's surface with a height difference of only one meter, using optical atomic clocks.[17]

Velocity and gravitational time dilation combined-effect tests

  • Hafele and Keating, in 1971, flew caesium atomic clocks east and west around the Earth in commercial airliners, to compare the elapsed time against that of a clock that remained at the US Naval Observatory. Two opposite effects came into play. The clocks were expected to age more quickly (show a larger elapsed time) than the reference clock, since they were in a higher (weaker) gravitational potential for most of the trip (c.f. Pound, Rebka). But also, contrastingly, the moving clocks were expected to age more slowly because of the speed of their travel. The gravitational effect was the larger, and the clocks suffered a net gain in elapsed time. To within experimental error, the net gain was consistent with the difference between the predicted gravitational gain and the predicted velocity time loss. In 2005, the National Physical Laboratory in the United Kingdom reported their limited replication of this experiment.[18] The NPL experiment differed from the original in that the caesium clocks were sent on a shorter trip (London–Washington D.C. return), but the clocks were more accurate. The reported results are within 4% of the predictions of relativity.
  • The Global Positioning System can be considered a continuously operating experiment in both special and general relativity. The in-orbit clocks are corrected for both special and general relativistic time dilation effects as described above, so that (as observed from the Earth's surface) they run at the same rate as clocks on the surface of the Earth. In addition, but not directly time dilation related, general relativistic correction terms are built into the model of motion that the satellites broadcast to receivers — uncorrected, these effects would result in an approximately 7-metre (23 ft) oscillation in the pseudo-ranges measured by a receiver over a cycle of 12 hours.

Muon lifetime

A comparison of muon lifetimes at different speeds is possible. In the laboratory, slow muons are produced, and in the atmosphere very fast moving muons are introduced by cosmic rays. Taking the muon lifetime at rest as the laboratory value of 2.22 μs, the lifetime of a cosmic ray produced muon traveling at 98% of the speed of light is about five times longer, in agreement with observations.[19] In this experiment the "clock" is the time taken by processes leading to muon decay, and these processes take place in the moving muon at its own "clock rate", which is much slower than the laboratory clock.

Time dilation and space flight

Time dilation would make it possible for passengers in a fast-moving vehicle to travel further into the future while aging very little, in that their great speed slows down the rate of passage of on-board time. That is, the ship's clock (and according to relativity, any human travelling with it) shows less elapsed time than the clocks of observers on Earth. For sufficiently high speeds the effect is dramatic. For example, one year of travel might correspond to ten years at home. Indeed, a constant 1 g acceleration would permit humans to travel as far as light has been able to travel since the big bang (some 13.7 billion light years) in one human lifetime. The space travellers could return to Earth billions of years in the future. A scenario based on this idea was presented in the novel Planet of the Apes by Pierre Boulle.

A more likely use of this effect would be to enable humans to travel to nearby stars without spending their entire lives aboard the ship. However, any such application of time dilation during Interstellar travel would require the use of some new, advanced method of propulsion. The Orion Project has been the only major attempt toward this idea.

Current space flight technology has fundamental theoretical limits based on the practical problem that an increasing amount of energy is required for propulsion as a craft approaches the speed of light. The likelihood of collision with small space debris and other particulate material is another practical limitation. At the velocities presently attained, however, time dilation is not a factor in space travel. Travel to regions of space-time where gravitational time dilation is taking place, such as within the gravitational field of a black hole but outside the event horizon (perhaps on a hyperbolic trajectory exiting the field), could also yield results consistent with present theory.

Time dilation at constant acceleration

In special relativity, time dilation is most simply described in circumstances where relative velocity is unchanging. Nevertheless, the Lorentz equations allow one to calculate proper time and movement in space for the simple case of a spaceship whose acceleration, relative to some referent object in uniform (i.e. constant velocity) motion, equals g throughout the period of measurement.

Let t be the time in an inertial frame subsequently called the rest frame. Let x be a spatial coordinate, and let the direction of the constant acceleration as well as the spaceship's velocity (relative to the rest frame) be parallel to the x-axis. Assuming the spaceship's position at time t = 0 being x = 0 and the velocity being v0 and defining the following abbreviation
\gamma_0 := \frac{1}{\sqrt{1-v_0^2/c^2}},
the following formulas hold:[20]
Position:
x(t) = \frac {c^2}{g} \left( \sqrt{1 + \frac{\left(gt + v_0\gamma_0\right)^2}{c^2}} -\gamma_0 \right).
Velocity:
v(t) =\frac{gt + v_0\gamma_0}{\sqrt{1 + \frac{ \left(gt + v_0\gamma_0\right)^2}{c^2}}}.
Proper time:
\tau(t) = \tau_0 + \int_0^t \sqrt{ 1 - \left( \frac{v(t')}{c} \right)^2 } dt'
In the case where v(0) = v0 = 0 and τ(0) = τ0 = 0 the integral can be expressed as a logarithmic function or, equivalently, as an inverse hyperbolic function:
\tau(t) = \frac{c}{g} \ln \left(  \frac{gt}{c} + \sqrt{ 1 + \left( \frac{gt}{c} \right)^2 } \right) = \frac{c}{g} \operatorname {arsinh} \left( \frac{gt}{c} \right) .

Spacetime geometry of velocity time dilation


Time dilation in transverse motion
The green dots and red dots in the animation represent spaceships. The ships of the green fleet have no velocity relative to each other, so for the clocks onboard the individual ships the same amount of time elapses relative to each other, and they can set up a procedure to maintain a synchronized standard fleet time. The ships of the "red fleet" are moving with a velocity of 0.866 of the speed of light with respect to the green fleet.
The blue dots represent pulses of light. One cycle of light-pulses between two green ships takes two seconds of "green time", one second for each leg.

As seen from the perspective of the reds, the transit time of the light pulses they exchange among each other is one second of "red time" for each leg. As seen from the perspective of the greens, the red ships' cycle of exchanging light pulses travels a diagonal path that is two light-seconds long. (As seen from the green perspective the reds travel 1.73 (\sqrt{3}) light-seconds of distance for every two seconds of green time.)
One of the red ships emits a light pulse towards the greens every second of red time. These pulses are received by ships of the green fleet with two-second intervals as measured in green time. Not shown in the animation is that all aspects of physics are proportionally involved. The light pulses that are emitted by the reds at a particular frequency as measured in red time are received at a lower frequency as measured by the detectors of the green fleet that measure against green time, and vice versa.

The animation cycles between the green perspective and the red perspective, to emphasize the symmetry. As there is no such thing as absolute motion in relativity (as is also the case for Newtonian mechanics), both the green and the red fleet are entitled to consider themselves motionless in their own frame of reference.
Again, it is vital to understand that the results of these interactions and calculations reflect the real state of the ships as it emerges from their situation of relative motion. It is not a mere quirk of the method of measurement or communication.

See also

References

  1. ^ For sources on special relativistic time dilation, see Albert Einstein's own popular exposition, published in English translation (1920) as "Relativity: The Special and General Theory", especially at "8: On the Idea of Time in Physics", and in following sections 9–12. See also the articles Special relativity, Lorentz transformation and Relativity of simultaneity.
  2. ^ Cassidy, David C.; Holton, Gerald James; Rutherford, Floyd James (2002), Understanding Physics, Springer-Verlag New York, Inc, ISBN 0-387-98756-8, http://books.google.com/?id=rpQo7f9F1xUC&pg=PA422 , Chapter 9 §9.6, p. 422
  3. ^ Cutner, Mark Leslie (2003), Astronomy, A Physical Perspective, Cambridge University Press, ISBN 0-521-82196-7, http://books.google.com/?id=2QVmiMW0O0MC&pg=PA128 , Chapter 7 §7.2, p. 128
  4. ^ Lerner, Lawrence S. (1996), Physics for Scientists and Engineers, Volume 2, Jones and Bertlett Publishers, Inc, ISBN 0-7637-0460-1, http://books.google.com/?id=B8K_ym9rS6UC&pg=PA1051 , Chapter 38 §38.4, p. 1051,1052
  5. ^ Ellis, George F. R.; Williams, Ruth M. (2000), Flat and Curved Space-times, Second Edition, Oxford University Press Inc, New York, ISBN 0-19-850657-0, http://books.google.com/?id=Hos31wty5WIC&pg=PA28 , Chapter 3 §1.3, p. 28-29
  6. ^ Adams, Steve (1997), Relativity: an introduction to space-time physics, CRC Press, p. 54, ISBN 0-748-40621-2, http://books.google.com/?id=1RV0AysEN4oC , Section 2.5, page 54
  7. ^ See T D Moyer (1981a), "Transformation from proper time on Earth to coordinate time in solar system barycentric space-time frame of reference", Celestial Mechanics 23 (1981) pages 33-56, equations 2 and 3 at pages 35-6 combined here and divided throughout by c2.
  8. ^ A version of the same relationship can also be seen in Neil Ashby (2002), "Relativity and the Global Positioning System", Physics Today (May 2002), at equation (2).
  9. ^ Such tidal effects can also be seen included in some of the relations shown in Neil Ashby (2002), cited above.
  10. ^ (This is equation (6) at page 36 of T D Moyer (1981a), cited above.)
  11. ^ G M Clemence & V Szebehely, "Annual variation of an atomic clock", Astronomical Journal, Vol.72 (1967), p.1324-6.
  12. ^ T D Moyer (1981b), "Transformation from proper time on Earth to coordinate time in solar system barycentric space-time frame of reference" (Part 2), Celestial Mechanics 23 (1981) pages 57-68.
  13. ^ J B Thomas (1975), "Reformulation of the relativistic conversion between coordinate time and atomic time", Astronomical Journal, vol.80, May 1975, p.405-411.
  14. ^ See Neil Ashby (2002), cited above; also in article Global Positioning System the section Special and general relativity and further sources cited there.
  15. ^ B Guinot (2000), "History of the Bureau International de l'Heure", ASP Conference Proceedings vol.208 (2000), pp.175-184, at p.182.
  16. ^ "Journal Article". SpringerLink. http://www.springerlink.com/content/kt5505r2p2r22411/. Retrieved 2009-10-18. 
  17. ^ a b Chou, C. W.; Hume, D. B.; Rosenband, T.; Wineland, D. J. (2010). "Optical Clocks and Relativity". Science 329: 1630. doi:10.1126/science.1192720.  edit
  18. ^ http://www.npl.co.uk/upload/pdf/metromnia_issue18.pdf
  19. ^ JV Stewart (2001), Intermediate electromagnetic theory, Singapore: World Scientific, p. 705, ISBN 9810244703, http://www.google.com/search?ie=UTF-8&hl=nl&rlz=1T4GZAZ_nlBE306BE306&q=relativity%20%22meson%20lifetime%22%202.22&tbo=u&tbs=bks:1&source=og&sa=N&tab=gp 
  20. ^ Iorio, Lorenzo (27-Jun-2004). "An analytical treatment of the Clock Paradox in the framework of the Special and General Theories of Relativity". http://arxiv.org/abs/physics/0405038.  (Equations (3), (4), (6), (9) on pages 5-6)
  • Callender, Craig & Edney, Ralph (2001), Introducing Time, Icon, ISBN 1-84046-592-1 
  • Einstein, A. (1905) "Zur Elektrodynamik bewegter Körper", Annalen der Physik, 17, 891. English translation: On the electrodynamics of moving bodies
  • Einstein, A. (1907) "Über eine Möglichkeit einer Prüfung des Relativitätsprinzips", Annalen der Physik.
  • Hasselkamp, D., Mondry, E. and Scharmann, A. (1979) "Direct Observation of the Transversal Doppler-Shift", Z. Physik A 289, 151–155
  • Ives, H. E. and Stilwell, G. R. (1938), "An experimental study of the rate of a moving clock", J. Opt. Soc. Am, 28, 215–226
  • Ives, H. E. and Stilwell, G. R. (1941), "An experimental study of the rate of a moving clock. II", J. Opt. Soc. Am, 31, 369–374
  • Joos, G. (1959) Lehrbuch der Theoretischen Physik, 11. Auflage, Leipzig; Zweites Buch, Sechstes Kapitel, § 4: Bewegte Bezugssysteme in der Akustik. Der Doppler-Effekt.
  • Larmor, J. (1897) "On a dynamical theory of the electric and luminiferous medium", Phil. Trans. Roy. Soc. 190, 205–300 (third and last in a series of papers with the same name).
  • Poincaré, H. (1900) "La theorie de Lorentz et la Principe de Reaction", Archives Neerlandaies, V, 253–78.
  • Reinhardt et al. Test of relativistic time dilation with fast optical atomic clocks at different velocities (Nature 2007)
  • Rossi, B and Hall, D. B. Phys. Rev., 59, 223 (1941).
  • NIST Two way time transfer for satellites
  • Voigt, W. "Ueber das Doppler'sche princip" Nachrichten von der Königlicher Gesellschaft der Wissenschaften zu Göttingen, 2, 41–51.

External links