Time Dilation: Variables Beyond Speed & Gravity?

[LightningInAJar]

TL;DR

Time dilation without speed or gravity?

Can time dilation vary without a gravity well or accelerating a viewer towards light speed? Are there other variables that affect the flow of time?

 

[PeterDonis]

Moderator's note: Thread level changed to "I".

 

[PeterDonis]

Can time dilation vary without a gravity well or accelerating a viewer towards light speed?

The two things you refer to are not the same anyway; the common usage of the same term, "time dilation", to refer to both is a source of confusion, not understanding.

The easiest way to see that the two things are not the same is to observe that time dilation due to relative speed is symmetric--each observer calculates the other's clock to be "running slow" (though this calculation is actually a coordinate artifact--see below)--while gravitational time dilation is not symmetric--both observers will agree that the clock of the one who is at a higher altitude in the gravitational field is running faster (but again the usual way of doing that calculation is a coordinate artifact--see below).

Are there other variables that affect the flow of time?

What you are calling "the flow of time" is an artifact of coordinates, not a physical thing. As far as you are concerned, your own time always flows at the same rate--1 second per second. And if you are not co-located with someone else, there is no invariant way for you to specify how their "flow of time" relates to yours.

What is a physical thing is what is properly called "differential aging", such as in the "twin paradox", where two twins separate and then come back together and find that their ages are no longer the same. Unfortunately, there is no single general rule that predicts which one will have aged more, other than the brute force rule of computing the lengths of the two paths through spacetime that the twins follow and comparing them. Nor is there, as noted above, any invariant way of specifying the "rate of time flow" of the two twins while they are separated; the only invariant fact of the matter is their relative ages when they meet up again. Nor is there any short, simple list of things that can cause differential aging; there are an infinite number of possible curved spacetime geometries, and an infinite number of possible paths through spacetime between two points in any given spacetime geometry.

In many cases, claimed comparisons between "rates of time flow" involve particular choices of coordinates, but those choices are left implicit and not acknowledged, which can also cause confusion. For example, in the case of gravitational time dilation between two observers who are at rest at different altitudes in a gravitational field, the comparison of their "rates of time flow" implicitly uses coordinates in which they, and the gravitating mass whose field they are in, are all at rest. Other choices of coordinates could lead to different answers. To really make the comparison properly, one would need to add further invariants to the scenario--for example, the two observers could exchange round-trip light signals and measure the round-trip travel times by each of their clocks; the observer at higher altitude would find the round trip light signals to take more time by his clock, and this is an invariant that does not depend on any coordinate choice. However, this kind of thing only works for observers at rest relative to each other (so that the round trip light travel times don't change); it wouldn't work for observers in relative motion in flat spacetime.

 

[phinds]

Summary:: Time dilation without speed or gravity?

Can time dilation vary without a gravity well or accelerating a viewer towards light speed? Are there other variables that affect the flow of time?

Light speed, or anything close to it, is irrelevant to your question. Velocity time dilation has been measured here on Earth with an airplane and it measured every second of every minute of every day by the GPS system. The magnitude of relative motion determines the AMOUNT of time dilation but not its existence. That is, time dilation due to motion exists for ANY speed (it's just hard/impossible to measure for slow speeds such as human walking).

 

[LightningInAJar]

When near a black hole time runs faster compared to on earth? When traveling half the speed of light time runs slower compared to on earth? I'm asking about other things besides gravity and acceleration that affect relative passage of time?

 

[phinds]

When near a black hole time runs faster compared to on earth?

No. Time runs slower near the BH when viewed from Earth and time on Earth runs faster when viewed from near the BH. Reread post #3 where this was explained.

When traveling half the speed of light time runs slower compared to on earth?

Only from the frame of the Earth. From the frame of the moving object time is slower on the Earth.

I'm asking about other things besides gravity and acceleration that affect relative passage of time?

What did you have in mind? I'm not aware of any such thing.

Clearly you have not understood any of the answers you already got in this thread. You should read them again and think about them.

 

[PeroK]

When near a black hole time runs faster compared to on earth? When traveling half the speed of light time runs slower compared to on earth? I'm asking about other things besides gravity and acceleration that affect relative passage of time?

Suppose two objects start at the same point in spacetime and, after taking different paths, end up at the same point as each other again. Then, the amount of time that has elapsed for each is a function only of their path through spacetime. Nothing else is relevant. Only the description of the relevant portion of spacetime and the two paths (aka worldlines).

 

[Ibix]

When near a black hole time runs faster compared to on earth? When traveling half the speed of light time runs slower compared to on earth?

The point is that "time runs faster" is a bad way to think about this. It's just that the elapsed time along a worldline is the equivalent of distance along a path through space, and some routes from A to B are shorter than others.

Near a black hole spacetime is curved, and you have shorter routes near the black hole in a (loosely...) similar way to the fact that the distance from the Greenwich meridian to 90W is shorter near the pole compared to at the equator. In the "twin paradox" scenario you have flat spacetime and the discovery that a straight line is the longest "distance" between two events in spacetime.

I'm asking about other things besides gravity and acceleration that affect relative passage of time?

Acceleration doesn't really affect anything - it's perfectly possible to construct variants of the twin paradox to demonstrate this. But the key point is that all of the clock effects in relativity boild down to "different routes between the same places may have different lengths". Any time you pop to the shops and your other half stays at home you experience different elapsed times - in fact you really have to plan carefully to have the same elapsed time along two non-identical worldlines.

So it isn't gravity or speed that causes any of this. It's just a non-Euclidean version of the common sense observation that two lines don't necessarily have the same length.