Should I think of gravity/ time dilation as directional?

[QuestionMarks]

Should I think of gravity/"time dilation" as directional?

Imagine this scenario, a photon skirts across the near edge of some highly massive object's gravitational field. If I imagine that field as a sphere, its near edge might be a section defined by height, width, and length, each with unequal magnitudes. If I imagine that gravity as the typical cartoony depression of some bowling-ball like object in a net, I could imagine the depth of the depression in the photon's path still greater in magnitude than the direct length of its path. In this way, I feel myself wanting to think of an object in influence of a gravitational body to be experiencing that differently in all directions (a la, stuff is pulled towards the body after all). This then makes me think that time dilation would be odd and directionally influenced, which confuses me.

For instance, a human body near another massive object. It would seem to me that time would slow far more for any interaction in movement parallel with the direction of force pulling to the massive object. Say if the object was to the person's left, all physical and chemical interactions involving left-right movements would be slowed, whereas primarily up-down movements would be less slowed and more bent.

If anyone could expunge my confusion I would be appreciative. And of course, I imagine my wording somewhat garbled and perhaps need of a rephrase, offered as requested!

 

[PeterDonis]

If I imagine that field as a sphere...If I imagine that gravity as the typical cartoony depression of some bowling-ball like object in a net

Neither of these visualizations are really good ones for gravitational time dilation. The "depression" one is perhaps a bit closer--you can think of gravitational time dilation as depending on how deep you are in the depression. But you still have to be careful; see below.

I feel myself wanting to think of an object in influence of a gravitational body to be experiencing that differently in all directions

Tidal gravity does vary with direction; but tidal gravity is different from gravitational time dilation. Gravitational time dilation depends only on your "altitude" above the gravitating body (more precisely, on your radial coordinate r).

In fact, strictly speaking, "gravitational time dilation" applies to static observers--observers who are maintaining a constant altitude and are at rest relative to the gravitating body. If you are orbiting the body at a constant altitude, you are not at rest relative to it, so there's an additional effect due to your motion. Also, if you are changing altitude, even if you are not changing anything else (i.e., you are moving purely radially), there is an additional effect due to your change of altitude. And of course if you combine these it gets even more complicated.

In many cases, the complications don't matter; you can idealize the objects or observers of interest as being at rest at some constant altitude. Usually, when you see people talking about "gravitational time dilation", they're talking about that kind of special case, where the only difference between two observers is a difference in altitude, which leads to a difference in "rate of time flow" for the two of them. If you're trying to think about how gravitational time dilation works, that's probably the best simple example.

 

[PeterDonis]

It would seem to me that time would slow far more for any interaction in movement parallel with the direction of force pulling to the massive object.

I should also comment on this: "time dilation" of any kind (gravitational or otherwise) is not something you see yourself as having. Your own time always appears to "flow", for you, at its normal rate. "Time dilation" only arises when one observer is compared with another, and in general it depends on how you do the comparison. The particular case I gave for gravitational time dilation, comparing two static observers at different altitudes, is one way of doing the comparison, the one that I think best isolates "gravitational time dilation" from all other effects.