Gravity

Originally posted by humy
as I understand it; only if we have relative motion and/or acceleration with each other and/or not using the same frame of reference. If we are using exactly the same frame of reference and you are not moving and/or accelerating relative to me then we should be able to agree with the same time. (please will somebody correct me here if I haven't got that exactly totally right)

What you have said is correct, but the states of motion do not have to be identical. In a gravitational well clocks run slower, and clocks run slower for fast moving objects - so if we have one stationary observer on the surface of a planet and another observer a large distance away, but moving at the right speed then their clocks can run at the same rate.

Originally posted by DeepThought
What you have said is correct, but the states of motion do not have to be identical. In a gravitational well clocks run slower, and clocks run slower for fast moving objects - so if we have one stationary observer on the surface of a planet and another observer a large distance away, but moving at the right speed then their clocks can run at the same rate.

Quantitatively is time not additive? If you and I start clocks simultaneously our paths through space-time will inevitably deviate. If I go take a jog and you stand still our state of agreeable time has been lost. Then I sit still and you take a drive etc... We are all living in different states of time from one another. I might be slightly in the future or past relative to you. Is this correct?

Originally posted by joe shmo
Quantitatively is time not additive? If you and I start clocks simultaneously our paths through space-time will inevitably deviate. If I go take a jog and you stand still our state of agreeable time has been lost. Then I sit still and you take a drive etc... We are all living in different states of time from one another. I might be slightly in the future or past relative to you. Is this correct?

No, I don't stop existing while you are driving around. Assuming we have perfect watches what happens is that while you are driving your watch is running slow compared with mine. Suppose while you are driving along there are some events, equally distant from each of us. We both measure the time that elapses between them. You will claim that they happened say 10 minutes apart, I'll claim it took slightly longer than that.

Also time is a coordinate, not a vector. What you are doing is akin to trying to add two longitudes together, it doesn't make sense. On a plane the tangent space looks identical to the plane so we get the impression that we can talk about distance vectors - in fact this only works on a plane, on a curved space like a sphere it won't. Velocities and accelerations are vectors because they "live in" a flat space tangential to the space the particle they are associated with is moving on. Similarly in Lorentz space (the space time of special relativity) the space is flat so we can play this game of pretending that coordinates are vectors. But in the space-time of general relativity the space-time is curved so we can't and we need a tangent space to put our vectors in. You can't just add times like that.

Originally posted by DeepThought
... In a gravitational well clocks run slower, ....

I know. Gravity is equivalent to acceleration according to general relativity which is why I said "...motion and/or acceleration ..." and not just "...motion..." thus I thought I had in effect included that. I should have said "...motion and/or acceleration and/or gravity..." for better clarity.

Originally posted by humy
I know. Gravity is equivalent to acceleration according to general relativity which is why I said "...motion and/or acceleration ..." and not just "...motion..." thus I thought I had in effect included that. I should have said "...motion and/or acceleration and/or gravity..." for better clarity.

Yes, but we don't have to be in the same frame of reference to agree on timings, we can be in different frames of reference provided clocks run at the same rate in them. Which is the point you seemed to miss in your earlier post.

Originally posted by KazetNagorra
It takes time for communication to travel, and it travels slower than the speed of light - the fastest way we know how to communicate is using light.

What can happen is that when two observers see the same two sources of information from different points in space-time and that they disagree over which message was sent first, the so-called relativity of simultaneity.

So they can perceive things out of order? Is this some semi caveat in what DeepThought said above?

Originally posted by DeepThought
No, I don't stop existing while you are driving around. Assuming we have perfect watches what happens is that while you are driving your watch is running slow compared with mine. Suppose while you are driving along there are some events, equally distant from each of us. We both measure the time that elapses between them. You will claim that they happ ...[text shortened]... we can't and we need a tangent space to put our vectors in. You can't just add times like that.

No, I don't stop existing while you are driving around. Assuming we have perfect watches what happens is that while you are driving your watch is running slow compared with mine. Suppose while you are driving along there are some events, equally distant from each of us. We both measure the time that elapses between them. You will claim that they happened say 10 minutes apart, I'll claim it took slightly longer than that.

Ok,so both of us make the correct measurement in our respective frames. Are we moving through time at all? How do we get from point A in time to point B in time, when we can experience individual and distinctly different changes in time between A and B?

Originally posted by joe shmo
So they can perceive things out of order? Is this some semi caveat in what DeepThought said above?

No, what Kazet is describing is not communication between two entities but something else. Suppose from Earth we see two simultaneous supernovae. The supernovae are far apart from each other and not causally connected, no signal could have got between them. Two observers in spaceships whipping along at a significant fraction of the speed of light relative to us on earth, but in opposite directions, will both think the supernovae happened at different times. However they will disagree about which order the supernovae happened in. This is possible because the supernovae had a spacelike separation and the one could not have caused the other. With my signalling example the sending and receiving of a signal (assuming it's a slower than light signal) are separated by a timelike interval. They are causally related and no observers will disagree about the order they happened in, no matter what frame of reference they are in. If the signal is at the speed of light, for example radio, then again they are causally connected and again no observers will disagree about the ordering. In that case the interval is zero. An extremely fast moving observer will think they happened at almost the same time, but no observer will think the ordering swapped over. You can prove this to yourself using Lorentz Transforms.

Originally posted by DeepThought
Yes, but we don't have to be in the same frame of reference to agree on timings, we can be in different frames of reference provided clocks run at the same rate in them. Which is the point you seemed to miss in your earlier post.

understood.

Originally posted by joe shmo
.... How do we get from point A in time to point B in time, when we can experience individual and distinctly different changes in time between A and B?[/b]

In whos frame of reference? And note that A and B are two different observed events. If I have X frame of reference and you have Y frame of reference and we don't agree with the same interval of time between event A and and event B then from A to B may be 100 seconds in my frame of reference and 99 seconds in your frame of reference. There is no contradiction between the two (the 100 and 99 second intervals) because they are in two different frames of references and so the two time intervals between event A and event B can be different providing they are in the two different frames of references. There cannot somehow be two different ones (interval between A and B) in the same frame of reference because that would be a contradiction, but there isn't so there is no problem here.

You should gain a better understanding of this if you read and understand at least some of:
https://en.wikipedia.org/wiki/Frame_of_reference