[jeffreyH (OP)]

Consider three frames labeled A, B and C containing objects a, b and c respectively. If we set our frame of observation to be A we can then define the motions of B and C. observations from A show that C is moving away with a constant velocity and B is maintaining an equal distance between both in straight line. Now we can determine that time dilation must be greater than that in A for both B and C. However, the inverse must also be considered possible if we take our observation point to be frame C. In both these situations the value of time dilation in A and B cannot be equal. If we now consider B to be our observation frame then the values in A and C MUST be equal. To state that this is because all things are relative misses the point. The absolute values of time dilation may be impossible for us to determine but that doesn't mean they do not exist. Opinions?

[alancalverd]

There is no time dilation within a frame moving at constant velocity.

[jeffreyH (OP)]

You are talking about proper time so of course not. Proper time has a Lorentz factor of 1. That is no time dilation so that every measurement is taken with respect to the proper time in the observer's frame. Yes my language was poor.  Can we discuss the topic now?

[MikeFontenot]

[...]

I don't see what your point or problem is.  There's nothing at all controversial about two or more inertial observers moving with respect to each other, at least once you understand the relativity of simultaneity.

[jeffreyH (OP)]

Well then you are missing the point entirely. The observations of A are different from B which are different again from C. They cannot all be right. The observations of A and C are inverses of each other. B sees no difference between A and C. So you are saying we can ignore this because of the relativity of simultaneity. Someone's clock must be the slowest. They have relative velocity differences.

[jeffreyH (OP)]

BTW This relates to the expansion of the universe.

[saspinski]

If we now consider B to be our observation frame then the values in A and C MUST be equal

 V_A(C) = v and V_C(A) = -v. If only A and C are involved, each one measures the time passing slowly on the other.
If the distance A-B and B-C is kept constant, B has half of C velocity, as measured by A. V_A(B) = v/2
But for C, the velocity of B has to be calculated: V_C(B) = (-v +v/2))/(1+v.v/2) = (v/2) / (1+v²/2) (I take c=1).
And velocity of C measured by B is of course (-v/2) / (1+v²/2), and velocity of A measured by B is -v/2.
So B measures different velocities for A and C, and its calculations for time dilation are not the same.

[evan_au]

They cannot all be right

The shocking thing about Special Relativity (and it's expanded set of examples in General Relativity) is that they are all right/correct.

This is the point of the twin paradox (or at least the non-accelerated variants of it) - different observers don't agree.

[jeffreyH (OP)]

The twins paradox does not require acceleration. That is a fallacy.

Let's take this a step further. Let's have an infinite lattice of frames where the distance between any two of them is constant at any one time. So that they are all expanding away from each other at a constant rate. Which one has the slowest clock now?

[jeffreyH (OP)]

The situation described above is homogeneous and isotropic.

[Janus]

Well then you are missing the point entirely. The observations of A are different from B which are different again from C. They cannot all be right. The observations of A and C are inverses of each other. B sees no difference between A and C. So you are saying we can ignore this because of the relativity of simultaneity. Someone's clock must be the slowest. They have relative velocity differences.

Your belief that one clock must be the slowest in an absolute manner comes from trying to apply a Newtonian notion of time to Relativity.  In Relativity time is an aspect of of 4 dimensional space-time.   The difference between this and the Newtonain notion of time is the in Relativity, the "direction" of time is not fixed, but is frame dependent.
An analogy would be that in Newtonian physics, you could treat time and space like the North-South and East-West directions, in that no matter what direction someone is facing, they would all agree on these directions.  In Relativity, they  behave more like the Left-Right and forward-backward directions which are entirely dependent on the direction you are facing.
Time dilation between relatively moving frames of references in this analogy would be like two people starting at a same point and walking in different directions at an equal pace.   Each person measures forward progress as being in the direction that he is walking, and by this basis, the other person is always falling behind.  There is no absolute meaning as to who is ahead of who, as the answer to this question depends on which way you are facing.
Relativity involves a whole new way of looking at the very nature of time and space.

[jeffreyH (OP)]

The directionality is important. Why does no one else mention it?

[jeffreyH (OP)]

The nub of the issue is exactly the absolute. In the infinite lattice none of the clocks can be the slowest. Otherwise the system cannot be isotropic. Any one position is indistinguishable from any other. That sounds a lot like our universe. Except that the universe does not have a uniform mass distribution. This has to have a bearing on our view of time dilation. If it is simply discarded then you are not missing but ignoring the point.

[Janus]

The directionality is important. Why does no one else mention it?

The "directionality" that I was talking about was in reference to the Space and Time axes in Space-time, and not the relative motion as measured from any given frame.

[jeffreyH (OP)]

Motion perpendicular to the direction of travel is no longer a straight line but must become a diagonal. That is directional bias and preserves time dilation in all three spatial dimensions. In the direction of travel we have blue shift and against it red shift. If this is not directional then what is? To assume that this is limited to the spacetime diagram is again, missing the point. The spacetime diagram simply highlights the effect with non orthogonal axes.

[jeffreyH (OP)]

How would the situation on the following page change within the infinite expanding lattice?
http://galileo.phys.virginia.edu/classes/252/time_dil.html

[jeffreyH (OP)]

For information on the infinite lattice please see:
http://www.scholarpedia.org/article/Special_relativity:_kinematics

[guest4091]

Don't agree with B-C velocity

relative velocities:
A=0, B=v, c=2v, per A

ref   A       B         C
A   0       v         2v
B   -v       0         v/(1-2v2)
C   -2v   -v/(1-2v2)      0

Each pair should experience reciprocity.

Let's take this a step further. Let's have an infinite lattice of frames where the distance between any two of them is constant at any one time. So that they are all expanding away from each other at a constant rate. Which one has the slowest clock now?

If each is separating at a constant speed, the separation will not remain constant!

[jeffreyH (OP)]

I said nothing about speed. Just as you cannot assign a speed to receding galaxies. Since, eventually, you would have to assign a superluminal speed.

[jeffreyH (OP)]

If you take the absolute magnitude of the velocity you can get rid of the opposing signs altogether. Why confuse the issue?