[Rog]

From the Wiki I see that flat earth theory accepts gravitational time dilation.

Conventional wisdom is that it is caused by warped spacetime but I'm guessing that's not the flat earth explanation.

If not warped space time, then what is the cause of GTD on a flat earth?.

[Tom Bishop]

Time dilation is not actually caused by warped spacetime in the conventional model. This is a misconception. The explanation they use is that light travels at a set speed and it takes longer for a light ray to travel diagonally in a moving clock than when stationary.

https://www.einstein-online.info/en/spotlight/light-clocks-time-dilation/

How long does it take from my perspective for the light of the moving light clock to run from the upper to the lower mirror and back? In other words: How much time passes from my point of view between two successive ticks of the moving light clock? The answer is given by the following animation, which shows two identical light clocks. Instead of the counter, these light clocks have an indicator lamp that flashes briefly each time the light pulse arrives at the upper mirror. At the top of the picture you can see my own light clock, which is resting relative to me. Below, the moving light clock flies by at about 86.7 percent of the speed of light:



Light clocks, one resting, one moving

Apparently, from my point of view, the moving light clock moves much slower than my own identical light clock: Between two ticks of the light clock (corresponding to the indicator light blinking twice), twice as much time elapses for the moving clock as for my own. In other words: In the period between the first flashing of the indicator lamp of the moving clock (on the left side of the picture) and the second flashing (on the right side of the picture), the resting clock has flashed three times altogether!

Different lengths

What is the reason for this discrepancy? Why does the moving light clock blink more slowly?

The constancy of the speed of light is valid: Light moves with the constant speed of 300,000 kilometers per second. If I divide the distance the light has traveled on its way from the upper to the lower to the upper mirror by this speed value, I get the time the light needed for a round trip.

We have already made this calculation for the light clock at rest. There, from our point of view, the light runs vertically downwards and then vertically upwards:



The time needed for this is therefore twice the mirror distance divided by the speed of light. With the assumed mirror distance of 150,000 kilometers and the value 300,000 km/s for the speed of light, the running time is exactly one second.

The same explanation is used at the University of Pittsburgh:

https://sites.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/Special_relativity_clocks_rods/index.html

Here's an animation that shows a light clock at rest and a second light clock that moves perpendicular to its rod. The light signal in the moving clock chases after the rod. To reach the other end, it covers more distance and, as a result, requires more time.



Here's the same animation in larger size in case you have a big screen.

If you watch the animation carefully, you will see that the moving light clock ticks at exactly half the speed of the resting clock. That is because the light signal of the moving clock has to cover twice the distance to go from one end of the rod to the other.

[sirtomato]

What about the time dilation measured on Earth, ie brining atomic clocks to the tops of mountains. On a flat earth these clocks should be moving at exactly the same speed as the whole earth has the same velocity. Am I wrong?

[Tom Bishop]

The earth isn't moving upwards at a set velocity. It is accelerating. More specifically, the surface of the Earth is accelerating upwards into the things above it.

If you walk off of the edge of a chair and go into freefall it will hurt a lot less than if you walk off the edge of a skyscraper. In the skyscraper situation you are inert in space and the Earth has more time to build up velocity and smash into you.

Therefore, in a situation where the Earth is accelerating upwards if you have a broadcasting photon clock light source at the altitude of a chair and a photon clock at the altitude of a skyscraper, from the perspective of a detector on the floor, those photons would be perceived to be hitting it at different rates of reception. The time for the light source on the skyscraper will appear faster than the light source on the chair.

It is also what would happen between the floor and ceiling inside of a rocket ship accelerating upwards through space.

From p.8 of Cosmological Physics by John A. Peacock, PhD. we read the following:

  “ Many of the important features of general relativity can be obtained via rather simple arguments that use the equivalence principle. The most famous of these is the thought experiment that leads to gravitational time dilation, illustrated in figure 1.1. Consider an accelerating frame. which is conventionally a rocket of height h, with a clock mounted on the roof that regularly disgorges photons towards the floor. If the rocket accelerates upwards at g, the floor acquires a speed v = gh / c in the time taken for a photon to travel from roof to floor. There will thus be a blueshift in the frequency of received photons, given by Δv / v = gh / c^2, and it is easy to see that the rate of reception of photons will increase by the same factor.

Now, since the rocket can be kept accelerating for as long as we like, and since photons cannot be stockpiled anywhere, the conclusion of an observer on the floor of the rocket is that in a real sense the clock on the roof is running fast. When the rocket stops accelerating, the clock on the roof will have gained a time Δt by comparison with an identical clock kept on the floor. Finally, the equivalence principle can be brought in to conclude that gravity must cause the same effect. Noting that ΔΦ = gh is the difference in potential between roof and floor, it is simple to generalize this to Δt / t = ΔΦ / c^2 ”



“ Figure 1.1. Imagine you are in a box in free space far from any source of gravitation. If the box is made to accelerate ‘upwards’ and has a clock that emits a photon every second mounted on its roof, it is easy to see that you will receive photons more rapidly once the box accelerates (imagine yourself running into the line of oncoming photons). Now, according to the equivalence principle, the situation is exactly equivalent to the second picture in which the box sits at rest on the surface of the Earth. Since there is nowhere for the excess photons to accumulate, the conclusion has to be that clocks above us in a gravitational field run fast. ”

See the bolded. If you imagine yourself running into the line of photons it is apparent that the clock above you would run fast, because you are running into them. This is a physical explanation for how this works under the concept of upwards acceleration.

In contrast, the Round Earth Theory adopts a non-physical explanation for this which occurs in a hidden layer of reality, in which space is bending to cause the apparent speedup of time at different altitudes. In my opinion this is completely ad-hoc. Physics behaves as if the surface of the Earth is accelerating upwards, but that can't work in RE, so they created this space-bending explanation in an untestable layer of reality which seeks to emulate the physics of upwards acceleration.

In one situation, with upwards acceleration, we can describe what is happening on a physical level for why the rate of reception speeds up when the photons are coming from higher altitudes. In the case of space bending, we cannot. We just call it "space bending" like a magic wand and say that it's physically equivalent to upwards acceleration to explain the otherwise unexplainable. Clearly, there is a difference between the two views.

Why should this space bending mechanism cause photons to travel faster from higher altitudes rather than slower from higher altitudes or no difference at all? What physical reason is there other than to claim that it must be the case because that is what is experienced? One quickly finds a lack of answers.

[Rog]

Time dilation is not actually caused by warped spacetime in the conventional model. This is a misconception. The explanation they use is that light travels at a set speed and it takes longer for a light ray to travel diagonally in a moving clock than when stationary.

I’m not talking about time dilation due to relative velocity (one moving clock and one stationary). I’m talking about Gravitational Time Dilation (two stationary clocks at different elevations)  Those are two different phenomena.

In physics and relativity, time dilation is the difference in the elapsed time as measured by two clocks. It is either due to a relative velocity between them (special relativistic "kinetic" time dilation) or to a difference in gravitational potential between their locations (general relativistic gravitational time dilation). 

https://en.wikipedia.org/wiki/Time_dilation

“ Many of the important features of general relativity can be obtained via rather simple arguments that use the equivalence principle. The most famous of these is the thought experiment that leads to gravitational time dilation, illustrated in figure 1.1. Consider an accelerating frame. which is conventionally a rocket of height h, with a clock mounted on the roof that regularly disgorges photons towards the floor. If the rocket accelerates upwards at g, the floor acquires a speed v = gh / c in the time taken for a photon to travel from roof to floor. There will thus be a blueshift in the frequency of received photons, given by Δv / v = gh / c^2, and it is easy to see that the rate of reception of photons will increase by the same factor.

Now, since the rocket can be kept accelerating for as long as we like, and since photons cannot be stockpiled anywhere, the conclusion of an observer on the floor of the rocket is that in a real sense the clock on the roof is running fast. When the rocket stops accelerating, the clock on the roof will have gained a time Δt by comparison with an identical clock kept on the floor. Finally, the equivalence principle can be brought in to conclude that gravity must cause the same effect. Noting that ΔΦ = gh is the difference in potential between roof and floor, it is simple to generalize this to Δt / t = ΔΦ / c^2 ”

Note in the wikipedia quote that GTD is caused by a difference in gravitational potential (not relative motion or velocity), that is also the cause noted in your quote that I have bolded.    A clock at the top of rocket and at the bottom aren’t moving relative to one another.  They are effectively stationary.  Just like a clock on the top and bottom of a skyscraper are stationary. Even according to flat earth, they would be accelerating at the same rate with the same velocity. Why would two stationary clocks show different times?

It is an interesting quote, but it refutes the point you are making.  The only reason the Equivalence Principle is true  in the first place is because of warped spacetime.

In an unaccelerated frame of reference, without gravity, an inertial object’s worldline will be straight.  Put that inertial object in an accelerated frame of reference and its worldline curves. Just as if it were accelerated by gravity.  That is the reason you can’t tell the difference between a gravitational field and an accelerated frame of reference.

But it is still inertial, it is still going “straight” and there is no force or gravity to change its path. The only reason that its worldline would deviate from straight to curved is because it is moving through curved spacetime.

Why should this space bending mechanism cause photons to travel faster from higher altitudes rather than slower from higher altitudes or no difference at all? What physical reason is there other than to claim that it must be the case because that is what is experienced? One quickly finds a lack of answers.

It doesn’t cause photons to travel faster in space from higher altitudes.  It causes time to slow down in lower altitudes because the closer to the center of a mass, the more spacetime is warped. The more spacetime is warped, the farther light has to travel.

[Tom Bishop]

Why should this space bending mechanism cause photons to travel faster from higher altitudes rather than slower from higher altitudes or no difference at all? What physical reason is there other than to claim that it must be the case because that is what is experienced? One quickly finds a lack of answers.

It doesn’t cause photons to travel faster in space from higher altitudes.  It causes time to slow down in lower altitudes because the closer to the center of a mass, the more spacetime is warped. The more spacetime is warped, the farther light has to travel.

Really, and why should it cause time to slow down at lower altitudes rather than cause time to speed up at lower altitudes?

We know why one would perceive oncoming photons to approach at a greater rate when you accelerate into them.  There is physical understanding to that. We don't know why this occurs under the "space is bending" explanation on a fundamental level. It just happens to explain observations. There is no physical explanation for it.

On p.116 of The Five Ages of the Universe by Fred C. Adams, PhD and Prof. Greg Laughlin, its authors describe gravitational time dilation by giving an analogy of an upwardly accelerating rocket in space which contains a clock attached to the ceiling and an astronaut sitting on the floor of the rocket with another clock. The astronaut on the floor first observes his own clock, and then observes the ceiling clock:

“however, he observes that the ceiling clock is running faster. The ceiling clock sends a tone (in the form of a radio wave) down to the floor. Because the floor is accelerating upwards, it intercepts the radio wave sooner than if the rocket were merely coasting along. If the acceleration continues, subsequent tones also arrive earlier than expected. In the viewpoint of the astronaut on the floor, the ceiling clock is broadcasting its time intervals at an increased rate, and is running fast compared to the floor clock.

According to the equivalence principle, the phenomenon of mismatched clock rates, which occurs in response to the acceleration of a rocket, also occurs in a uniform gravitational field. The equivalence principle therefore insists on a seemingly bizarre conclusion. Two clocks at different heights above Earth's surface must measure the flow of time at different rates. This strange behavior is an intrinsic feature of gravity. The variation of the flow of time within a gravitational field is entirely independent of the mechanism used to measure time. Atomic clocks, quartz watches, and biological rhythms all experience the passage of time to be dilated or compressed in the same manner.”

The authors explain that time dilation should be a natural consequence in an upwardly accelerating rocket, and acknowledge that its equivalent application to gravity on earth is "strange" and "bizarre".

It's only "strange" if you reject the natural and physically understandable explanation that it is caused by upwards acceleration.

[Rog]

I guess you don’t understand what is meant by spacetime warp.  If you agree that time moves differently at different elevations, you are conceding spacetime warp, whether you realize it or not.  Spacetime warp is about how the relationship between space and time changes.  If time changes due to elevation, then so does space because the two are inextricably linked. Space expands as time contracts and vice versa. If time changes, so does space.  The faster you go in space, the slower you go in time.  Everything moves at c in spacetime.  If velocity is increased in space, then velocity through time has to decrease.

In the diagram below, three objects are moving through space at different elevations.  If space time were flat, space and time would “line up” and you could connect the objects with the straight red lines.  Instead, connecting the objects with the green line shows how the relationship between space and time changes from the higher elevation and the lower.  That relationship is clearly warped. Space expands and time contracts at lower elevations and space contracts and time expands at higher elevations.  If that’s not the definition of warped, I don’t know what is. 


If time moves faster at the top of an accelerating rocket ship it is because the space inside the rocket is warped due to acceleration.  This goes back to the point I made before about the equivalence principle and what happens to the worldline of an inertial object when you accelerate the frame of reference.  It changes from straight to curved. I am sure you have seen or read about how light falls in an accelerating elevator.  If you shine a light across an elevator at rest, the beam will shine straight across.  When you accelerate the elevator upwards, the beam curves down. But there is no reason for it to curve down unless the space in the accelerating elevator is warped.  There is no force on it to change its path through spacetime, so it must be the spacetime itself that is warped. Same concept applies to an accelerating rocket. As it accelerates, the spacetime inside becomes warped, just like the spacetime in the elevator as it accelerates.

Really, and why should it cause time to slow down at lower altitudes rather than cause time to speed up at lower altitudes?

I told you why.  Lower altitude means more curvature.  More curvature means more space and more space means less time.



The speed of light is always constant, and the distance is fixed, so time equals distance divided by speed. Now consider light traveling from point C to point D but in a curved line. The speed is constant, but the distance is longer than before. This means that the numerator is bigger than the previous equation. With a bigger numerator, this means that the time it takes for the light to travel the exact same distance is longer. Therefore time has just been warped.
Here is another way of looking at it.  The lines are traveling at the same speed but the straight line is higher in elevation and not as effected by the warp.  Therefore, it travels farther in the same amount of time.

[Tom Bishop]

You are explaining what it does, not why it should do it. We could also imagine that time moves faster when there is greater gravitational potential, or a scenario where gravitational potential does not affect time. Why should it move slower with greater gravitational potential? Explaining what it does does not demonstrate why it should do so.

If time moves faster at the top of an accelerating rocket ship it is because the space inside the rocket is warped due to acceleration.

What? Please quote a source on that. That is not even the conventional explanation.

We know why time dilates in the upward accelerating rocket scenario, and it has nothing to do with bending space. This has nothing to do with a requirement of bending spacetime to make this happen. The explanation was given in the previous two book quotes I gave. Books which were written by physcists. They do not explain that spacetime bends to make that happen.

You are in a long spacecraft under zero gravity. A line of water droplets is traveling from one end of the spaceship towards you, hitting you at a rate of 1 drop per second:



You then accelerate towards the drops. Will you experience the water droplets hitting you at a rate quicker than 1 drop per second?



This scenario has nothing to do with bending spacetime.

This scenario has nothing to do with Einstein's theories.

This scenario replaces photons with water droplets. Will they hit you at a rate quicker than 1 drop per second when you accelerate into them?

Yes, they will. This is a direct effect of movement and acceleration. This is an explanation which is eminently understandable and a necessary consequence. I can't say that the explanation that spacetime bends in a hidden layer of reality is as solid.

The concept of time dilation due to velocity was derived in Newtonian space by another author before Special Relativity was invented. Einstein merely adopted time dilation due to velocity into his Relativity theory to be more inclusive. It doesn't actually say that spacetime is bending when bodies accelerate. This effect is not exclusive or unique to SR.

[stack]

You are explaining what it does, not why it should do it. We could also imagine that time moves faster when there is greater gravitational potential, or a scenario where gravitational potential does not affect time. Why should it move slower with greater gravitational potential? Explaining what it does does not demonstrate why it should do so.

In the wiki Universal Acceleration it states, "Objects on the earth's surface have weight because all sufficiently massive celestial bodies are accelerating upward at the rate of 9.8 m/s^2 relative to a local observer immediately above said body."

I'm confused as to why should the clock moves slower with UA when closer to the ground? If everything under UA is accelerating at 9.8 m/s^2, why is there a difference between a GPS clock and a ground-based clock, or at the top floor of the Burj Khalifa versus the basement? If everything is accelerating at 9.8 m/s^2 shouldn't the clocks be the same exact time? What is UA doing that causes this time difference?

[Tom Bishop]

What is UA doing that causes this time difference?

Higher clocks appear to run faster than lower clocks because the Earth is accelerating into the photons. See this quote:

If you walk off of the edge of a chair and go into freefall it will hurt a lot less than if you walk off the edge of a skyscraper. In the skyscraper situation you are inert in space and the Earth has more time to build up velocity and smash into you.

The longer you are in freefall, the greater velocity the Earth will smash into you at, since the Earth is accelerating upwards.

An observer on the ground with photon clocks above his head at various elevations will see the clocks at increasing elevations above him run increasingly faster. As the photons are in the air the Earth is accelerating into the photons at increasing velocities, causing the perceived increase in clock rate for the higher clocks. The higher they are, the longer the photons will stay in the air, and the greater velocity the Earth will hit them at. This is why higher clocks run faster than lower clocks.

[Rog]

You are explaining what it does, not why it should do it. We could also imagine that time moves faster when there is greater gravitational potential, or a scenario where gravitational potential does not affect time. Why should it move slower with greater gravitational potential? Explaining what it does does not demonstrate why it should do so.

More warp=slower time because it takes longer to move through a more warped area than one less warped.   Its the same reason it takes longer to drive up a mountain on a curvy, winding road with a lot of switchbacks than it takes to just go straight up. 

The concept of time dilation due to velocity was derived in Newtonian space by another author before Special Relativity was invented. Einstein merely adopted time dilation due to velocity into his Relativity theory to be more inclusive. It doesn't actually say that spacetime is bending when bodies accelerate. This effect is not exclusive or unique to SR

Again, I am not talking about TD due to velocity.  I am asking about, time dilation due to a difference in gravitational potential. Two different things.
Gravitational time dilation is part of general relativity, not special relativity. And both phenomena can happen at the same time.  Clocks on GPS satellites have to account for both.  They run slower because they are in motion relative to clocks on earth, but part of that is made up for because their elevation.

Because an observer on the ground sees the satellites in motion relative to them, Special Relativity predicts that we should see their clocks ticking more slowly (see the Special Relativity lecture). Special Relativity predicts that the on-board atomic clocks on the satellites should fall behind clocks on the ground by about 7 microseconds per day because of the slower ticking rate due to the time dilation effect of their relative motion [2].
Further, the satellites are in orbits high above the Earth, where the curvature of spacetime due to the Earth's mass is less than it is at the Earth's surface. A prediction of General Relativity is that clocks closer to a massive object will seem to tick more slowly than those located further away (see the Black Holes lecture). As such, when viewed from the surface of the Earth, the clocks on the satellites appear to be ticking faster than identical clocks on the ground. A calculation using General Relativity predicts that the clocks in each GPS satellite should get ahead of ground-based clocks by 45 microseconds per day.
dThe combination of these two relativitic effects means that the clocks on-board each satellite should tick faster than identical clocks on the ground by about 38 microseconds per day (45-7=38)

http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps.html
So even assuming that your “accelerating into the photons” is correct, that doesn’t negate the fact that the spacetime inside of an upward accelerating object is warped. The worldline of an inertial object (which would include a beam of light) curves when it is in an accelerating frame of reference. That happens independent of anything related to time dilation due to velocity.

An inertial object, by definition moves in a straight line, at constant velocity and doesn’t deviate from that unless a force is applied.  Why would that inertial object’s path change from straight to curved when it is in an accelerating frame of reference?

EDIT:

An observer on the ground with photon clocks above his head at various elevations will see the clocks at increasing elevations above them run increasingly faster. As the photons are in the air the Earth is accelerating into the photons at increasing velocities, causing the perceived increase in clock rate for the higher clocks. The higher they are, the longer the photons will stay in the air, and the greater velocity the Earth will hit them at. This is why higher clocks run faster than lower clocks.

An observer at lower elevations isn’t accelerating into the photons that the clock is measuring. A photon clock at the top will count time at one rate and another rate at the bottom.  An observer will see the two clocks measuring different rates.  That’s the point.

[stack]

What is UA doing that causes this time difference?

Higher clocks appear to run faster than lower clocks because the Earth is accelerating into the photons. See this quote:

If you walk off of the edge of a chair and go into freefall it will hurt a lot less than if you walk off the edge of a skyscraper. In the skyscraper situation you are inert in space and the Earth has more time to build up velocity and smash into you.

The longer you are in freefall, the greater velocity the Earth will smash into you at, since the Earth is accelerating upwards.

An observer on the ground with photon clocks above his head at various elevations will see the clocks at increasing elevations above him run increasingly faster. As the photons are in the air the Earth is accelerating into the photons at increasing velocities, causing the perceived increase in clock rate for the higher clocks. The higher they are, the longer the photons will stay in the air, and the greater velocity the Earth will hit them at. This is why higher clocks run faster than lower clocks.

A little bit more definition to my example: Nothing is in freefall. I'm standing in the basement of the Burj Khalifa staring at an atomic clock synchronized with the atomic clock you are staring at on the top floor of the Burj Khalifa. After an hour or so, we notice that your clock is running a smidge faster than mine.

If you and I, both atomic clocks, and the Burj Khalifa itself, are all accelerating upwards at the same constant rate of 9.8 m/s^2, I don't quite get why "the greater velocity the Earth will hit them," when the rate of acceleration is constant for all people/things involved. What is this "greater velocity"? Is there some sort of "UA Potential", that the further away you get from the upward accelerating earth time moves faster? Even if your not moving, not in freefall, just standing there way up high. And if so, why? Does the constant rate mentioned in the wiki actually change the higher up you go?

[Rog]

If you and I, both atomic clocks, and the Burj Khalifa itself, are all accelerating upwards at the same constant rate of 9.8 m/s^2, I don't quite get why "the greater velocity the Earth will hit them," when the rate of acceleration is constant for all people/things involved. What is this "greater velocity"? Is there some sort of "UA Potential", that the further away you get from the upward accelerating earth time moves faster? Even if your not moving, not in freefall, just standing there way up high. And if so, why? Does the constant rate mentioned in the wiki actually change the higher up you go?

At least there is one person who gets what I am trying to say 

Bob is observing a  clock at the top of a skyscraper (or accelerating rocket) and Alice is observing one at the bottom  Both Bob and Alice agree that Alice’s clock is running slower.  According to flat earth theory, Bob,  Alice, both clocks, and the building (or rocket) are accelerating at the same rate with the same velocity, so there shouldn’t be any velocity related time dilation.

Even if there was, they wouldn’t agree that Alice’s clock is running slower because velocity time dilation is mutual.  Each observer sees the other’s clock running slower.

Contrarily to velocity time dilation, in which both observers measure the other as aging slower (a reciprocal effect), gravitational time dilation is not reciprocal. This means that with gravitational time dilation both observers agree that the clock nearer the center of the gravitational field is slower in rate, and they agree on the ratio of the difference.

https://en.wikipedia.org/wiki/Time_dilation#Reciprocity

[Tom Bishop]

More warp=slower time because it takes longer to move through a more warped area than one less warped.   Its the same reason it takes longer to drive up a mountain on a curvy, winding road with a lot of switchbacks than it takes to just go straight up.

Yet the animation you just gave showed that time was speeding up and moving faster as it went into the gravity well. We can clearly see it moving faster as it goes into the dip:



According to this time should speed up as light moves towards the surface of the earth, not slow down. Your examples do not make any sense at all.

You also continue to try to explain how it works without showing the necessity of why it should be so.

A little bit more definition to my example: Nothing is in freefall. I'm standing in the basement of the Burj Khalifa staring at an atomic clock synchronized with the atomic clock you are staring at on the top floor of the Burj Khalifa. After an hour or so, we notice that your clock is running a smidge faster than mine.

If you and I, both atomic clocks, and the Burj Khalifa itself, are all accelerating upwards at the same constant rate of 9.8 m/s^2, I don't quite get why "the greater velocity the Earth will hit them," when the rate of acceleration is constant for all people/things involved. What is this "greater velocity"? Is there some sort of "UA Potential", that the further away you get from the upward accelerating earth time moves faster? Even if your not moving, not in freefall, just standing there way up high. And if so, why? Does the constant rate mentioned in the wiki actually change the higher up you go?

Actually in fiberoptic and copper cables the electromagnetic signal is moving separate from the cord surrounding it, so your example would have no difference. A ball moving down a tube is also moving independently of the tube.

[stack]

A little bit more definition to my example: Nothing is in freefall. I'm standing in the basement of the Burj Khalifa staring at an atomic clock synchronized with the atomic clock you are staring at on the top floor of the Burj Khalifa. After an hour or so, we notice that your clock is running a smidge faster than mine.

If you and I, both atomic clocks, and the Burj Khalifa itself, are all accelerating upwards at the same constant rate of 9.8 m/s^2, I don't quite get why "the greater velocity the Earth will hit them," when the rate of acceleration is constant for all people/things involved. What is this "greater velocity"? Is there some sort of "UA Potential", that the further away you get from the upward accelerating earth time moves faster? Even if your not moving, not in freefall, just standing there way up high. And if so, why? Does the constant rate mentioned in the wiki actually change the higher up you go?

Actually in fiberoptic and copper cables the electromagnetic signal is moving separate from the cord surrounding it, so your example would have no difference. A ball moving down a tube is also moving independently of the tube.

I have no idea what you're referring to with fiberoptic and copper cables. Do you?

What do cables and balls have to do with anything?

Again, does the constant rate mentioned in the wiki actually change the higher up you go?

[Tom Bishop]

It has everything to do with it. The Earth will be moving at a different rate to a ball that is released from a higher altitude versus a ball at a lower altitude. They do not experience the same thing.

Please look up the definition of accelerate. It does not mean to travel at a set velocity. Refer yourself to this previous explanation for why time appears to pass quicker for a clock at a higher elevation of an upwardly accelerating rocket:

From p.8 of Cosmological Physics by John A. Peacock, PhD. we read the following:

  “ Many of the important features of general relativity can be obtained via rather simple arguments that use the equivalence principle. The most famous of these is the thought experiment that leads to gravitational time dilation, illustrated in figure 1.1. Consider an accelerating frame. which is conventionally a rocket of height h, with a clock mounted on the roof that regularly disgorges photons towards the floor. If the rocket accelerates upwards at g, the floor acquires a speed v = gh / c in the time taken for a photon to travel from roof to floor. There will thus be a blueshift in the frequency of received photons, given by Δv / v = gh / c^2, and it is easy to see that the rate of reception of photons will increase by the same factor.

Now, since the rocket can be kept accelerating for as long as we like, and since photons cannot be stockpiled anywhere, the conclusion of an observer on the floor of the rocket is that in a real sense the clock on the roof is running fast. When the rocket stops accelerating, the clock on the roof will have gained a time Δt by comparison with an identical clock kept on the floor. Finally, the equivalence principle can be brought in to conclude that gravity must cause the same effect. Noting that ΔΦ = gh is the difference in potential between roof and floor, it is simple to generalize this to Δt / t = ΔΦ / c^2 ”



“ Figure 1.1. Imagine you are in a box in free space far from any source of gravitation. If the box is made to accelerate ‘upwards’ and has a clock that emits a photon every second mounted on its roof, it is easy to see that you will receive photons more rapidly once the box accelerates (imagine yourself running into the line of oncoming photons). Now, according to the equivalence principle, the situation is exactly equivalent to the second picture in which the box sits at rest on the surface of the Earth. Since there is nowhere for the excess photons to accumulate, the conclusion has to be that clocks above us in a gravitational field run fast. ”

If there were another story to the rocket, and the clock were twice as high, the floor of the rocket would be increasing velocity into the photons even faster, and the time for the elevated clock on the ceiling of the second story of the rocket would appear to be moving faster.

The floor of the rocket is accelerating into the line of photons, causing them to intersect with the detector on the floor at an increased pace. The longer the line of photons, the greater rate. A clock at increasingly higher altitudes with appear to tick increasingly faster.

[stack]

It has everything to do with it. The Earth will be moving at a different rate to a ball that is released from a higher altitude versus a ball at a lower altitude. They do not experience the same thing.

No one is releasing a "ball" of anything. I have no idea what you're referring to. Please refer yourself to this previous example - The scenario is: Two people just standing, each staring at a clock - Both clocks sync'd to the same time - observer A is in the basement and observer B is 150 floors above.

Again, does the constant rate mentioned in the wiki actually change the higher up you go? Is observer B's clock running faster than observer A's? And if so, how does UA make that happen?

[Tom Bishop]

It has everything to do with it. The Earth will be moving at a different rate to a ball that is released from a higher altitude versus a ball at a lower altitude. They do not experience the same thing.

No one is releasing a "ball" of anything. I have no idea what you're referring to. Please refer yourself to this previous example - The scenario is: Two people just standing, each staring at a clock - Both clocks sync'd to the same time - observer A is in the basement and observer B is 150 floors above.

Again, does the constant rate mentioned in the wiki actually change the higher up you go? Is observer B's clock running faster than observer A's? And if so, how does UA make that happen?

At some point the photons or signals are moving independently of the clocks, through a medium, to the detector below. The Earth is accelerating into the photons, causing the higher clock to appear to tick faster, and clocks above that to tick even faster. See the previous rocket ship examples from literature and look up what accelerate means.

[stack]

It has everything to do with it. The Earth will be moving at a different rate to a ball that is released from a higher altitude versus a ball at a lower altitude. They do not experience the same thing.

No one is releasing a "ball" of anything. I have no idea what you're referring to. Please refer yourself to this previous example - The scenario is: Two people just standing, each staring at a clock - Both clocks sync'd to the same time - observer A is in the basement and observer B is 150 floors above.

Again, does the constant rate mentioned in the wiki actually change the higher up you go? Is observer B's clock running faster than observer A's? And if so, how does UA make that happen?

At some point the photons or signals are moving independently of the clocks, through a medium, to the detector below. The Earth is accelerating into the photons, causing the higher clock to appear to tick faster. See the previous examples from literature and look up what accelerate means.

How does UA make that time difference happen? According to the wiki, Observer A and his clock is accelerating upward at exactly the same as observer B and his clock along with the building itself. There should be no difference, everyone and everything is moving together at the same rate. How does UA cause photons to move independently of everything else that is moving upward together?

[Tom Bishop]

It has everything to do with it. The Earth will be moving at a different rate to a ball that is released from a higher altitude versus a ball at a lower altitude. They do not experience the same thing.

No one is releasing a "ball" of anything. I have no idea what you're referring to. Please refer yourself to this previous example - The scenario is: Two people just standing, each staring at a clock - Both clocks sync'd to the same time - observer A is in the basement and observer B is 150 floors above.

Again, does the constant rate mentioned in the wiki actually change the higher up you go? Is observer B's clock running faster than observer A's? And if so, how does UA make that happen?

At some point the photons or signals are moving independently of the clocks, through a medium, to the detector below. The Earth is accelerating into the photons, causing the higher clock to appear to tick faster. See the previous examples from literature and look up what accelerate means.

How does UA make that time difference happen? According to the wiki, Observer A and his clock is accelerating upward at exactly the same as observer B and his clock along with the building itself. There should be no difference, everyone and everything is moving together at the same rate. How does UA cause photons to move independently of everything else that is moving upward together?

Look up the difference between linear movement and accelerated movement.





The Earth is accelerating, not moving at a linear rate.

The Earth will, therefore, accelerate into a long line of photons at a greater rate than a shorter line of photons.