It might be better to unravel special relativity first, before going on to tackle general relativity. So let us, for a while, ignore accelerated motions and gravity fields.

Consider a train. Some thing which always has the speed of light is running backwards and forwards through the train. It does not have to be a wave phenomenon, so we do not have to talk about the Doppler Effect.

The Principle of Relativity states that no experiment done within the train can ascertain whether the train is standing still or moving at some constant speed in some arbitrary direction.

That is: any numerical description of whatever is happening inside the train must not change under a Galileo Transformation:

X' = X - Vx * t
Y' = Y - Vy * t
Z' = Z - Vz * t
T' = T

This Principle has long been accepted to hold true, but it seemed to break down for electromagnetic phenomena, because Maxwells Equations do not, when subjected to a Galileo Transformation yield the same equations again.

Lorentz did however discover that these equations do yield themselves when subjected to a different transformation, which is therefore called the Lorentz Transformation.

In this Transformation, there is a constant, C, which has the dimension of speed. The curious thing is, that anything moving with speed C in one frame will still move with speed C in any other frame (though possibly not in the same direction!).

And light itself, an electromagnetic phenomenon, can be shown from Maxwells Equations to have just this speed C.

So if I run back and forth through the train with this speed, and a light wave is running alongside me, we will arrive at the same moment. Actual light is not needed to explore relativistic phenomena.

Back to the train. Say that we see it move in the X-direction. Seen from the platform, the runner will need more time to traverse the train running forward than running backward. But seen from the train, this cannot be the case (because he takes care to run always with speed C).

His speed is of course DX/DT before the transformation and DX'/DT' after the transformation.

Under a Galileo Transformation his speed would become C - Vx when running forward and C + Vx when running backward. But the Lorentz transformation is different:

Instead of X' = X - Vx * T we have X' = (X - Vx * T) / B
And instead of T' = T we have T' = (T - Vx * X / C * C) / B
where B * B = 1 - Vx * Vx / C * C

Now his speed remains the same in both occasions.

If we compute it, we will now see that two clocks situated in the front and the back of the train will both seem slow by a factor B, but the back clock will at any moment give a later time than the front clock. If we combine the readings of the two clocks as they flash past the station, it is now the clock on the platform wich seems slow by a factor B. The paradox disappears.

This must of course be so, because the person running up and down the train can synchronize the two clocks, ensuring that he sees the same difference in time running forward and running backward. If the train stood still, this would mean that both clocks give the same time, but if the train moves forward, the difference in time needed to overtake the front clock and to meet the back clock (as seen from the platform) translates into a difference between the time given by the two clocks (also, as seen from the platform).

We should not, of course, use light to read the clocks, but some infinitely fast signal, because to do otherwise would muddle the issue.

Notice that there is no mention here of motions perpendicular to the train or of triangles. It can all be done, using only one dimension of space.

The general Lorentz Transformation can be found by first applying a rotation, then the transformation given above for motion in the X-direction, and finally the inverse rotation.

And people who do timing professionally, or any other careful person, would compensate for this. i.e you'd adjust the length of the pendulum, or adjust the frequency of the counter you used to count the oscillations. Which is why you can build a clock using any base oscillation frequency - you just have to calibrate it. This is apples and oranges, though. (g/l)^1/2 is a separate effect from relativity.

An atomic clock (on the geoid) at the equator, however, ticks at the same rate as one at the north pole, even though they are sampling slightly different gravitational potentials. As predicted by relativity (i.e. one of the many laws of physics).

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It depends on an observer. An atomic clock oscillate slower for an distant observer when the clock is in a stronger gravitationally field or moves faster relatively to the observer.
An atomic clock "tick" faster on a mountain's top if an observer is at sea level.

No matter how many times you say it, it still won't be true.

By what factor does GR predict an accelerating atomic clock will change its tick rate, Sam?

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It depends on where the clock is, not the observer. You can be anywhere around the earth and receive data from an atomic clock located at sea level and compare that tick rate with your own local atomic clock tick rate where ever you are located, then you can have someone move the atomic clock from sea level up to a mountain top and you will notice that its tick rate speeds up a little when it is on the mountain. This has nothing to do with an observer's position, not in this modern era of radio, television, and computer communications. The old idea that an individual "observer" saw "such and such" when he was in "so and so" place, was a product of an old scientific era before there were radios, television, and the internet.

You need 2 clocks if you want to detect any time dilation.
Observers may be indeed anywhere.

Semantics. In scientific discussion "observer" is generally understood to be what- or whoever is making the measurements, and at the location where the experiment is carried out.

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Right. And the master clock we are using for our time base must remain stationary and not change elevation during the experiment so that we can be sure that it doesn't change rates.

We accept the master clock in our reference frame as stationary and an eventual civilisation circling close around a supermassive Black Hole seems to live very slowly and long relatively to us. This hypothetic civilisation has its own stationary clock and we live very fast and short relatively to them.

Then how do you expain the constancy of the speed of light for all inertial observers? Or do you think that this postulate of SR is wrong?

What has that got to do with SR time dilation? Oh and by the way, people and pendulums are made of atoms too you know.

The amount by which you'd age more rapidly on a mountain top du to gravitational dilation is also very slight, obviously.

True, the actual effect is virtaully undetectable, and humans wouldn't make good measuring devices, but better measuring devices do confirm the prediction. Your argument is akin to saying that length contraction doesn't apply to people because a yard is affected more by the length of one's stride.

But the pendulum's differing rate is predictable by Newtonian physics and therefore has nothing whatsoever to do with actual time dilation.

Again, totally irrelevant to time dilation. You're talking about processes that can be slowed down. Time dilation is not the slowing down of a process, it is the slowing down of time itself and affects all processes equally -- it is therefore not locally observable, you can't watch your own clock slow down due to time dilation.

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If logic doesn't work, then surely it does.

That's a fantasy. Biology doesn't work that way. The biology and time processes of living things are determined more by thermodynamic time factors. You can place an atomic clock in a strong enough gravity field to slow down the clock, but you can't place a human in a strong enough gravity field to slow down the life processes of the human based on a slow-down in the internal harmonic oscillation rates of his atoms, because such a strong field would crush the human to death. You need to read some biology books that discuss thermodynamic time issues and enzyme reaction velocity rates.

Try:

http://72.14.203.104/search?q=cache:...=en&lr=lang_en

http://72.14.203.104/search?q=cache:...=en&lr=lang_en

and:

http://72.14.203.104/search?q=cache:...=en&lr=lang_en

Of course, life can't exist close to supermassive Black Hole like in our Milky Way. But time dilation exists in our Earth"s conditions - it is relation 10-^16 with every 1 m of the heigth on the Earth.

If a man pass an Event Horizon of a small BH he will be rended because an acceleration's difference.

If a man pass an Even Horizon of Supermassive BH (10^12 sol.) the acceleration is compared to our on the Earth. There is problem with radiation and others, of course, but larger BH = less problems.

At lest our Universe with flat geometry has density of Black Hole=Mass(dark+visible)/Radius=cc/G

Sam5, could you cut the nonsense about biological time, freezers, pendulums, variable rate playback devices, and any other process who's varying speed can be understood in purely Newtonian terms and stick to what I believe is the central issue of your gross misunderstanding of relativity. If there is no time dilation in SR due to relative motion then how do you explain the constancy of the speed of light for all intertial observers? Or do you disagree with that postulate of SR? You've had almost a year to think about this since you were threatened with banning from badastronomy.com for refusing to answer the queston.

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If logic doesn't work, then surely it does.

This isn't biology, it's physics.

Hey, by what factor does acceleration cause an atomic clock to change its tick rate in GR?

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This is more of an aside, but I just thought it worth pointing out that in SR there is no problem in a photon possessing different momenta even though it always travels at c.

Human biological processes slowing down is a function of thermodynamic time. That is biology. Consult a biologist. They don’t stop the aging processes of embryos by shooting them off into space at the speed of c. They merely freeze them. Ask any doctor about it.

And nothing to do with SR or GR. (and sorry, I don't understand "thermodynamic" in this context).

Lets get a few things straight:
SR is concerned with observers moving at constant velocity.
GR is concerned with acceleration - both increasing-speed and gravity.

For simplicity, lets keep to SR (ie. ignore tops of mountains, etc).

The twins paradox came with SR, not GR.
That seems pretty clear time dilation to me

Sam5 is under the impression that there are different kinds of time, some of whom change under SR or GR transformations, and some that don't. That this is blatantly counter to the fundamental principles of SR and GR by providing a way to discern "absolute speed" doesn't seem to bother him.

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Well, it still looks like no one has proven Einstein wrong. But, feel free to argue.... Same tired old arguments that have been refuted time and time and.... I find it interesting none of the 'Illuminated Ones' seem able to belly up to the bar and 'show the math'. Although I admit the cute little logical exercises are amusing.

The problem is, Thanatos, that the math can be easily put here on the web, or we can point out to a lot of good books, but several members on this board do not seem to believe in math, so that does not help.

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Time slowing down is a function of SR. That is physics.

Hey, you accept GR, right? By how much does GR predict the tick rate of an accelerating atomic clock will change?

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here's a few more results.

and i think this shows pretty clearly what einstein was modelling his mathematics on.



at left of each animation is a blue light-clock....it represents our observer, and standard time rate.

the red light-clock (the one that will exhibit the time dilation effect) moves perpendicularly to the transmission vector....and the alteration of the position of the receiver causes a transmission delay...simply because the light has further to travel.

the physical length of the light path is the value of the time rate, and the controller of the effect is the velocity.

***************************************

Velocity = 0.2C



Time Dilation = 1.02

***************************************

Velocity = 0.4C



Time Dilation = 1.09

***************************************

Velocity = 0.6C



Time Dilation = 1.25

***************************************

Velocity = 0.8C



Time Dilation = 1.67

***************************************

Velocity = 0.9C



Time Dilation = 2.29

***************************************



not only are the correct results for time dilation displayed, but the parameters are clear as to what form they must take for this exercise to operate.

the light velocity remains constant against absolute space...and this is no different than in a 3d game engine where the space is denoted by a fixed and unmoving 3d axis and numerated coordinates.

just like in a 3d engine, if i give an object a set velocity, it will always remain at that velocity, and this will be a "constant in all frames".

those other frames may move at velocities relative to eg: light (and it's constant speed)..and this is how we get effects like "velocity based doppler shifting"...by intercepting light at different velocities and therefore altering the detection frequency.

if light did not move at a constant velocity, but instead matched it's velocity to the observer (to generate the "constant" effect), we would not be able to achieve that velocity based doppler shifting...since the frequency of detection would never alter.

so constant means it doesn't alter it's own velocity.

but we may alter ours in relation to it, even up to the point of matching or even surpassing it.

************************************************** ******


einstein formulated a method with the deliberate intent of hooking it to physics at the atomic or molecular level and thereby affording it some credibility.

his method does not rely upon observers or reference frames, but is an inherent effect caused solely by velocity...and is seen as an effect upon transmission time for photon-matter exchanges internally.

in the manner in which his experiment is set up, he sought to produce a symmetrical effect...and was successful in both that and modelling it all with a mathematical formula.

but it is limited to operating correctly only when the photon exchanges are aligned perpendicularly to the direction of motion.

and if we were to realistically consider photon-matter exchanges in 2d or 3d?...then we would find that "light-clocks" are oriented fairly randomly.

so only a small percentage would ever be aligned to an arbitrary direction of motion....most would be misaligned...and that would give us asymmetric transmission distances for the bulk of the matter and therefore asymmetric time rates (no smooth "tick-tocking"..and exchange photons are alternately blue and redshifted).


Velocity = 0.5C



Time Dilation 1 (red) = 2
Time Dilation 2 (blue) = 0.68



so actually we can't take einstein's show on the road and have it operate correctly for all photon-matter exchanges (ie: always obtaining symmetrical "tick-tocking").
and it would be stretching things a bit to believe that photon-matter exchanges (light clocks) always instantly align themselves perpendicularly to any arbitrary direction of motion...just so we can have symmetrical exchange times?

it seems the real combined effects would be a jumble of mostly asymmetric exchanges...and he has just made a model for the small fraction that by chance may become aligned perpendicularly to the direction of motion and achieve symmetrical exchanges?

madman:

1) If light maintained a constant velocity relative to "absolute" space and we could adjust our own velocity relative to "absolute" space, we would be able to detect the different velocity of light relative to us through experiments such as Michelson-Morely. Such experiments have shown the opposite.

2) Velocity-based Doppler effects do not require light to maintain a constant velocity relative to an "absolute" space. If transmitter and detector are not moving relative to each other, there is no measured Doppler effect, regardless of their motion relative to their surroundings. If they are moving relative to each other, the measured Doppler effect depends solely on their motion relative to each other, again regardless of their motion relative to their surroundings.

3) Relativity does not depend on the light pulses traveling perpendicular to the direction of movement. In point of fact, the first time Einstein talks about light pulses in his seminal 1905 SR paper, he is discussing pulses travelling parallel to the direction of travel. This leads to the failure of absolute simultaneity, and then to time dilation.

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SeanF

the gifs display the parameters that produce the correct (exact) results.

if the light (and light-clock) do not move relative to an absolute coordinate space in this way...we will not get these results.

Sure we will. However:

Consider what everything looks like from an observer who is moving with the red* clock. To that observer, the red clock is motionless and the blue clock is moving.

In an "absolute space" universe, that observer would measure the blue clock as ticking faster than the red clock is, because that is an "absolute" reality.

In a Relativistic universe, though, that observer would see the blue clock ticking slower than the red clock.

Experiments like Michelson-Morely have demonstrated that we are living in a Relativistic universe, not an "absolute space" universe.

*I'm color-blind. I hope those clocks are red and blue!

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Hi Madman,

First off, I love those gifs. Did you make them yourself, ar off another site?

I'm a bit bemused by the blue "stationary" examples in the gifs. They show a light pulse reaching the other observer, and then coming back. This isn't what time-dilation is about; the light pulse should in all cases just traverse the distance.

I wonder if you can picture this one :
Have a stationary "sender" (I'll call "Alice") at the Bottom-Right.
Have a stationary "receiver" (I'll call "Bob") at Top-Right.
Have a moving receiver (I'll call "Charlie") travelling from Top-Left to Top-Right, arriving at Bob's position at the same time as the light pulse.

Clearly, in Alice's and Bob's frame, the light pule takes unit time.
However, what about in Charlie's frame (which is as valid as Alice's and Bob's)?

Charlies frame of the SAME event could be represented by a gif showing :
- Charlie stationary top-left
- Alice moving from bottom-right (where she fires the light pulse) to bottom-left
- (Bob, if you want him, moving from top-right to top-left).
- The light-pulse always staying above Alice.

Clearly, the light pulse in this picture is travelling further than the light pulse in the first (say 50% longer), and yet :
- as stated, it is the same event with the same light pulse, and
- Alice, Bob and Charlie all measure the light to be travelling at c.

The only way to reconcile these statements is for each individual to see the other's movement in slow-motion - ie. time-dilation.

Hi Madman
I appreciate your graphical demonstration.

1. This problem is like muon observed from outside. The muon has its internal structure and it decays when all needed information reach all points of its space. We observe from distance that if muon moves near speed of light the decay is slower and the shape of this particle become deformed. The bosons move then along a curved line and need longer time to send a proper information.
For an inside observer all information go along straight line and muon looks spherical . For this inner observer the outside processes act and move very fast .

2. We observe a jet ejected from a Quasar and it seems for us to move faster then light. It is because the jet lives slower and in its space the information (light) reaches longer distance then in our reference frame. For an inner observer in this jet he moves normal but the outside Universe moves very fast with z >1.

3. An object moving toward a Black Hole reaches it after an infinite time for an distant observer because it moves slower and slower. An observer on this object will see as he is approaching to the Black Hole with acceleration and the outside Universe moves also faster. The object close to BH send to us a redshifted light and an observer on this object receives from us a blueshifted light.

One problem I see is that the gifs only show half of a tick of the light clock. The light pulse has to return to the origin to be a clock, which is why the horizontal example will also give the same result - it's the round-trip time that matters, not the one-way time.

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swansont

the gamma formula uses a triangle...which equates to one leg of the light-clocks "tick-tocking".

it does not use 2 triangles back to back....and 2*((v*v)/(c*c))

You can use that triangle in the analysis because of the symmetry in that orientation (i.e. all you get is a factor of two that cancels out since it's the ratio of the two that's important), but to compare with another orientation, you cannot actually construct the clock that way. How does the clock indicate when it should send out the next pulse? You have to "close the loop" of timing information, somehow, and that also takes time, which is subject to time dilation. The simplest way is to bounce the light pulse - the "tick" is completed when the photon returns to the bottom. Otherwise it doesn't work, as you point out, but that's because you built a flawed clock and not because of a failure of relativity.

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