"Clete, really! This is appalling ignorance.
You need to sit down with an elementary physics book. People separated in space-time most certainly do NOT experience the same moment. They cannot, as the speed of light gets in the way.
There's a thing called interval you need to study.
Wander away from me a light-second and turn on a lamp. One second later, I'll turn on my own. To me, the two lights will appear simultaneous, even though to you, they are separated by two seconds.
Think about it."
Clete said:
You are introducing irrelevant variables. One must account for the time it takes for the light to travel to me and whatever other variable may change my perception but in the end you turned on your light at a particular moment and at that moment I was doing whatever I was doing and we were both present at that moment in time together.
Excuse me, Clete, I didn't until just now see you had posted this response.
The "variable" I'm introducing is "the existence of separate frames of reference at the heart of both general and special relativity." As such, in a discussion of relativity, it is absolutely relevant, by definition.
At its heart, relativity denies the very concept of simultaneity for "events" separated in space-time. In particular, this includes those events separated exclusively in the spatial dimensions whether the separation is one mile or one light-second, and whether the separation occurs in a "flat" or "curved" region of space-time. It was the similarity between these separations I attempted to introduce in my previous, admittedly impolite, post, and, by extension, the need to consider frames of reference when discussing either special or general relativity.
Again, I apologize for my needless abrasiveness.
Still, I ask you to realize that the "moment in time" we share is an illusion. We are not able to agree even on as simple a thing as what "moment in time" we each turned on our lights. You say it was two seconds ago, I say it was simultaneous. Were time absolute, one of us would have to be wrong! Giving us separate frames of reference has the distinct advantage of not having to fight over who should be called a liar.
:chuckle:
This is why Bob's illustration is so brilliant. You have two people who are on the same planet with one another and yet are supposedly experiencing time dilation effects relative to each other because of the difference in the pull of gravity in one location relative to the other.
I've split your paragraph here in the interest of isolating the position where your argument becomes difficult to follow.
Because special relativity is easier to understand, I expressed my example in terms of events separated in an "uncurved" region of space-time amenable to special relativity. To construct a similar example directly linked to the gravitational effects in Bob's example, one in which his "day" would be comprehensible to an observer limited to experience on the scale of a human lifespan, it would be necessary to move his example to the near vicinity of a black hole, an area where our intuitive grasp of conditions is far less stable, but also an area where the true alien nature of the separate frames of reference becomes noticeable.
Bob's example hides this alien nature by extending a human lifespan across millions of years in order to simulate an intuitive grasp that does not actually exist. Millions of years of personal experience really is as foreign to our understanding as life in a black hole.
It still works because according to Relativity, gravity is nothing more than an acceleration along curves in the "fabric of space-time" thus when you are in a gravitational field, you are, in effect, traveling along that curve and if someone's gravitational pull is different that means their acceleration along that curve is different and so their time dilation is accordingly altered. (Is this elementary enough for you?).
"It still works" uses a preposition without a referent I can follow and thus I'm not able to understand what conclusion you hope to support with this sentence.
Turning to your "because" clause, you say that "gravity ... is an acceleration along curves in the fabric of space-time."
This varies widely from the theory and takes some work to unravel. Gravity is, in general relativity, the cause for curvature in space-time, not an acceleration along curves implying the movement of some object.
'
Given a path in space-time, travel along it cannot properly be described in terms of acceleration. Acceleration is a change in spatial velocity over time, where velocity is a change in spatial position over time. I've drawn out these definitions to focus on the meaning of space-time itself.
Now to unravel the fabric, we need to move slowly.
***
What is the "fabric" of space-time? It is the set of 4-dimensional positions in space-time called "events." Similar to the separation of points in space we call distance, there is a separation of events in space-time called "interval." This interval incorporates distance in space, which I'll call spacedistance to differentiate it from distance in time, which I'll call timedistance. Using nothing more than the standard Pythagorean theorem, interval can now be readily described.
Interval is the squareroot of (squared spacedistance + squared timedistance)
Notice that for contemporary events, interval is just normal distance.
In order to calculate interval it's necessary to match units of time to units of distance. This is done by multiplication of a fundamental constant linking distance and time. This fundamental constant is called "c", the speed of light, and the formula for separation in spacetime reflects this.
Spacedistance is given by "ict", where i is the squareroot of negative one, c is the speed of light and t is the separation of events in time. Note that squared timedistance is negative. Thus, from my frame of reference, lighting your lamp one second ago in time cancels out your one lightsecond of distance, so the interval between where-when I see your lamp and my own is zero.
***
With the above concepts in mind, consider "acceleration in spacetime". Acceleration occurs in space (not space-time) over time. Space-time, as a representation, incorporates time as part of its structure. It simply doesn't make sense to ask how fast we can cover an "interval." Geometrically, one needs to "project" events out of spacetime into space in order to speak of acceleration.
You can "project" your three dimensional self by standing in the sunshine and allowing a shadow to fall onto a two-dimensional sidewalk, thus eliminating your height. Here we come to the nub. Similarly, you can "project" the set of 4-dimensional events in spacetime that form your life by "falling" into a reference frame, thus eliminating your extended existence across time.
***
Thus, acceleration in spacetime is inherently without meaning. Standing on this misperceived foundation, you continue, but I see no reason to follow until you've recovered your footing. With this in mind, perhaps you'd consider attempting to rephrase your "elementary" description of gravity's relationship to the general theory of relativity.
The point here is that we don't have to introduce the complicating factors of having to calculate and account for the time it takes light to travel to the observer because they are on the same planet and that time is negligible.
My point is, that to discuss the consequences of the general theory of relativity, it is necessary to have a basic understanding of the general theory of relativity, an understanding I'm sure lies within your grasp should you decide to make the effort.
In particular, it is necessary to understand how separate frames of reference are fundamental to the theory and how they lead naturally to the definition of space-time itself, created to provide a place for frame-invariant descriptions. In the process, one discovers a previously unlooked for understanding of time, so wonderfully addressed by ThePhy's recent post.
So could we concentrate on the illustration we have been given and stop with all the red herring distraction techniques. You guys are stumped on this one, and I am not going to let you change the subject so as to make yourselves feel better.
Resting in Him,
Clete
Again I urge you to spend a few hours with a standard physics book that covers the theory, do a few of the sample problems and reconsider your positions about both the definition and absolute nature of time. There is a clarifying effect that occurs only when the hand-waving ends and the numbers have to go into the calculator. This, to a scientist, is where the rubber meets the road.
Until you make this effort, unfortunately, you will be "stumping" your readers with an excursion into physical fantasyland.
In peace, Jesse
(I invite Johnny or ThePhy to correct any glaring errors in this presentation. I haven't done any study in this in beaucoup years. I'm basing most of this on the n-space realms with which I'm more familiar.)