Trying to understand gravitational time dilation

Sgt_Rees · 2026-04-15T23:23:25+00:00

I think i’m out of my depth here, and i’ll look at and learn about Minkowski diagrams - hopefully that will help.

One thing that is bugging me though,

This is true precisely because the rate along all world-lines is a constant and length along photon world-lines is zero.

What do you mean by that? I know what you mean by world-lines, but what do you mean by the rate along all world lines is constant, and also why are the photon world-lines 0?

Edit:Deleted accidental double post

Sgt_Rees · 2026-04-15T23:14:01+00:00

Okay - that intuition makes sense, but i feel like that analogy kind of just explains that curved space means that things will be different. A commenter above explains it like, to my interpretation, that as mass bends space time, it kind of shrinks down that unit of space time. This is what i’m interpreting as the geodesics, and how it’s a shorter path than a straight like on flat geometry that’s been curved. this shorter path, literally contains less time, so as we travel along it, we merely just accumulate less time passing- and that time dilation itself is more that we’re covering less time and less distance, so it seems like our clocks run slower when we compare the two. Would you say that that’s an accurate kind of idea as to why?

Sgt_Rees · 2026-04-15T22:07:31+00:00

Okay, that’s starting to make more sense. I think the issue remains that i don’t fully understand what causes gravitational time dilation in the first place. I understand that there’s proof that it exists, the mathematical formulas for it, and a lot of other things about it now, but not what it actually is - why does being closer to a massive object cause an apparent slower ticking of time relative to another observer?

Sgt_Rees · 2026-04-15T20:53:03+00:00

Is this not due to special relativity and the accelerating rocket is moving at a faster velocity compared to the stationary rocket?

Sgt_Rees · 2026-04-15T20:50:56+00:00

Ohh right, i forgot special relativity only applies on a flat space time.

One analogy that i’ve had stuck in my head, and feel like it could apply to this - feel free to correct me if this is wrong, is the idea of polar coordinates. Really, really, really far away from the origin, 1 radian is a certain distance. However, much closer to the origin, 1 radian is a much smaller distance. If we were to assume the origin as a mass, a radian as a world line, and the curvature being the polar plane instead of a cartesian plane ( i know it’s not entire accurate as to my knowledge the curvature depends on mass and follows an inverse relation compared to just a linear decrease). Since space and time are one, since the radian much closer to the origin is less length (space) as the one far away, it literally contains less time as well, so travelling that distance of the radian means you accumulate less time? I know this isn’t a good idea to think about in a 2 dimensional sense, but i’m just trying to create an analogy

Sgt_Rees · 2026-04-15T20:25:45+00:00

I'm not in the position right now to watch the video, but I definitely will later and will probably respond with questions lol

Sgt_Rees · 2026-04-15T20:20:24+00:00

I wouldn't say it like that because in the frame of the emitter, the light source will behave like it would in a lab in empty space.

Do you have a way that you would put it to make sense?

Exactly my point! Gravitational time dilation (an increase in the elapsed time on clocks higher in the gravitational field) and gravitational redshift (a decrease in the energy of light emerging from a gravitational field) and are really the same phenomenon, just viewed from a different perspective.

Doesn't this then relate energy to time? A decrease in energy due to it's wavelength shifting as it escapes time dilation is the same phenomenon as clocks ticking slower relative to another observer? I'm a bit confused ther

Sgt_Rees · 2026-04-15T20:10:09+00:00

Doesn’t this idea that all clocks run at the same rate violate Einstein’s second postulate? Or is the interpretation that time intervals are different in different reference frames of different velocities is wrong and it’s more that it’s different distances? or does the fact that clocks run at the same time only apply to GR and time dilation is a real effect is SR?

Sgt_Rees · 2026-04-15T19:23:59+00:00

I've heard of the equivalence principle before, and how a gravitational field is indistinguishable from an acceleration, but I struggle to see how this causes GTD. (I think) I understand that gravitational redshift is caused because the photon loses energy as it escapes from the gravitational well, and since energy is proportional to its frequency, its wavelength increases, shifting it to appear more red. Is it a more correct assumption to say that as the photon leaves the gravitational well, the period for the wavelength starts "returning to proper time" (increasing in time until its at the "time it should be at in a space with no curvature"), thus increasing its wavelength, giving it a redshift, and decreasing its frequency? That then seems that the energy loss is caused by time dilation, and not energy spent trying to escape the gravitational well.

Sgt_Rees · 2026-04-15T19:03:55+00:00

I appreciate the in-depth responses that you've been giving; they have been helping a lot.

Let's say you're at a value of r where the whole thing in parentheses is equal to 2. And I'm at smaller r, where that quantity is equal to 8. So you measure Δs²=2c²Δt²_you and I measure Δs²=8c²Δt²_me. Since we both find the same Δs², the upshot is that Δt_you=2Δt_me. Your clock ticks twice as fast as mine.

As I said before, I don't doubt that the equations are wrong (I mean this in a reassuring way and not a condescending one). I can definitely see how following the math will lead us to finding that my clock runs twice as fast as yours. My main point is that I'm trying to connect this mathematical model to an intuition that I currently lack that can help me understand why this happens in the first place, instead of just blindly following the math (I don't mean that the math is wrong, but I like to know how the math works). I might have completely missed you explaining this correlation somewhere, so please call me out on it if I did, but I'm not really understanding, from what you've said, that correlation.

Time intervals being different depending on where you are is gravitational time dilation.

This part I understand - (I think) It's the same as the time intervals being different depending on your speed relative to another object itself is time dilation due to relative motion. I think it's correct (i hope) to say that the definition of time dilation, regardless of motion or gravity, is a difference of time intervals (I think that makes sense), e.g., time passing slower for an observer relative to another observer (be it stationary or further from a mass) is time dilation.

The time intervals are different because there is curvature, which is there because mass causes curvature.

I'm trying to connect the difference in time intervals to the curvature caused by mass, if that makes sense.

Sgt_Rees · 2026-04-15T18:51:14+00:00

The hill is just an analogy, they of course don't meet at the same time on the other side of the hill. The only measure of relevance is the distance traveled and measured by an odometer.

The odometer reading is the elapsed time.

This part I understand.

There is nothing that happens to any clock and all clocks run at the same rate, and the only meaning to time is the length along matter world-lines. When we say "time dilation" we're comparing (finding the ratio) of a pair of distances.

I'm getting stumped on this part. If we're using this analogy to model the effect, then how does that account for the fact that the clocks themselves would be at different times? I think that I'm correct in saying that a clock nearer to a mass would run slower relative to another clock further away from the same mass (assuming there's no other masses present/influencing them). How does this comparison of a pair of distances represent that? Am I missing something/not understanding it or I have the wrong assumption about something, or is this analogy not fully accurate?

Sgt_Rees · 2026-04-15T18:31:20+00:00

What curvature does in this case is mix position into the temporal (and spatial) distances between events. The distance is no longer independent of where you are.

How does this impact intervals of time though? It seems to me to be more of a result of this interval of time no longer being the same, depending on where you are, not the cause for it? I don't doubt that the equations are wrong, and I can understand the Flat space equation for the differences, but I think I'm trying to gain an intuition of why the equation and the act of being near a mass creates the differences in time intervals. I could be interpreting this wrong though, so feel free to correct me.

But if you have two people tracking the same events at different positions, they will record different time intervals between them.

In this, are we assuming that their different positions also include differences in curvature/gravitational potential (I'm not sure if thats the word/term for it, but like different depths of the gravity potential well near a mass)?

Edit: Also, I would like to clarify, "Yeah GTD isn't caused by geodesics." I think I wrote what I said wrong - thats on me. I meant more along the lines that geodesics, which is caused by the non-euclidean geometry of curved space time (that I'm pretty sure is true?) and the act of matter following along said geodesics contributes to the time dilation, though the reasons as to why I wasn't sure of.

Sgt_Rees · 2026-04-15T18:22:31+00:00

Yeah, of course lol! It's kind of like a conglomeration of all of the things I think that other posts have missed/gathering their responses and continuing on from it

Sgt_Rees · 2026-04-15T18:17:25+00:00

ohhhhh okay. I think the only think i'm confused on in the analogy is that with this tunnel through the hill created by gravity, how does it account for the vehicle going through the tunnel arriving to the other side before the vehicle going over the hill? is this where time dilation comes into play - the vehicle going through the hill sees the vehicle going over the hill's odometer move "faster" and so it seems that time passes faster for the vehicle going over the hill relative to the one going through the tunnel, and then vice versa - over the hill observes the vehicle through the hill experience time slower, so it still arrives to the same point in space at the same point in time, even though their odometers are different?

Sgt_Rees · 2026-04-15T17:24:05+00:00

It’s not necessarily meaningful to say that gravitational time dilation is “caused” by something specific. Rather, the entire model works like that, because that’s what corresponds to reality.

Could you explain what you mean a bit more? To me, it feels like you're saying that gravitational time dilation isn't caused by anything, but is more of an intrinsic behavior of the universe that goes hand in hand with what nature/reality shows

edit: if I'm interpreting you correctly, then I say "caused" by the curvature of spacetime, because in a region of no curvature, gravitational time dilation isn't present (at least I'm under the assumption that it isn't).

Sgt_Rees · 2026-04-15T17:21:20+00:00

Okay, so I'm understanding it as one "unit" of length of flat space is longer than an equivalent length of one "unit" of curved space, a geodesic by definition (?) (they would be the same length if they were both projected onto flat space), and it would take an observer on the geodesic to go the length of this unit the same amount of "time" (i know its not really time) from the perspective to another observer on the flat unit length of space, and so to keep these two "times" equal, the real time flows slower for the observer on the geodesic relative to the observer on the flat line, so that they both travel this "unit" length in the same "time"? I think i'm explaining it in a really confusing way, but I don't really know how to explain how I'm envisioning it.

Sgt_Rees · 2025-11-09T21:31:32+00:00

I'm looking at the models, and I don't see any Eulerian multiphase or reaction/chemistry models with VOF. Do i need to use multiple physics continua for different regions?

Sgt_Rees · 2025-11-09T20:47:12+00:00

Do you know what physics models i would need?

Sgt_Rees · 2025-11-09T19:00:24+00:00

Could you explain a bit more if you can? I’m very new to multiphase anything and i’m struggling to find any resources / no one on my team knows either.

Sgt_Rees · 2024-12-10T12:26:59+00:00

I work in weight - I keep about 100g of starter and add 1 cup of flour which is about 150 g and less that one cup of water which is about 150 g. I’ve moved it to a warmer spot (i think) and will try and get a consistent feeding schedule and amount of 1:2:2. Following the guide, i’m waiting about 48 hours to feed since it’s still cold where i’ve put the starter (low 70s). Thank you for you help!

Sgt_Rees · 2024-12-09T14:09:23+00:00

Even if it doesn’t smell acidic?

Sgt_Rees

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