• Aug. 23, 2019, 3:11 p.m.

    Hey, I've been a long time subscriber to the channel and after many of the topics discussed, I wonder most about why gravity has an effect on time. I'm hoping that folks explain or share links that can explain (to a layman) why gravity causes time dilation. It's something that has baffled me to no end and Google searches have only left me more baffled. I do grant that this may just be outside my scope of understanding. Any effort on this request will be appreciated.

  • Aug. 27, 2019, 12:54 p.m.

    I've been wondering about these things myself for a long time too.

    I have only ever read about the gravity-time relationship as a simple assertion, and I suspect that's all anyone else knows about it too. That is, if you had the absolute, true answer to this question you would know something that no other physicist on Earth knows right now. I don't think scientists would be shy in admitting if this is the case.

    That said, I've had some impressions (don't confuse my opinions with facts!):

    Maybe time dilation causes what we see as gravity and not the other way around. This is at least half true. Light bends in a gravitational field in part due to bent space, but also because the speed of light is slower the deeper you are in a gravity well. As a result, light is 'refracted' or bent around objects like the Sun (in part) because the wave front propagates more slowly on one side than the other. Before the 1919 solar eclipse measurements, Einstein got his math wrong by only expecting time dilation to bend the starlight. Later he corrected this by also including space curvature, which as far as I understand doubled the amount of bending expected. So half of the 'falling' of light is really time dilation.

    Anyway if you chose to model all matter as little knots of light, then this same refraction (my term) would cause all matter to drift inward to wherever time is slowest. This does nothing to answer your question, but it does turn it inside out!

    Another, contradictory possibility is that time dilation is caused by space being more timelike and vice versa near a large mass. That is, visualize the classic funnel of curved space we always see in magazines and note that its surface is more and more slanted near the center. If you assume the future is 'up' in this model, then for someone close to the center, their progression in time will be at more acute of an angle to their space, so what would have been time progression instead becomes more spatial acceleration and less time.

    I may be completely wrong but I have been reading and thinking about these same questions for decades and this is the best I can offer.

    BTW FTLdrummer is a great handle. FTLguitar would be thrash?

  • Oct. 27, 2019, 5:16 a.m.

    I do agree that the concepts of special and general relativity are hard to grasp. To answer your question we need to explore:

    • The nature of ‘speed’ (which relates distance with time). It is as simple as it sounds - how fast something goes over time.
    • The nature of 'gravity' - not in that it is a force, but it's effect of accelerating objects together
    • The concept of relativity and how it relates to gravity

    So let's look at the concepts of relativity first. There was substantial confusion century-before-last as to how observational data was not lining up with theories at the time in relation to magnetic fields and classical mechanics. This distilled down essentially to two observable, seemingly (note) contradictory facts:
    - light was measured as being a constant speed no matter where measured, or how fast measurements were 'made'
    - otherwise 'classical' motion is indistinguishable no matter where, or how fast you are. In other words it makes sense doesn't it that a ball thrown while in a rocket is expected to behave predictably the same as if I was on the ground and threw a ball.

    So how can both be true, if the speed of light from a torch on a rocket is measured the same if I am on a rocket, yet when I observe that same light looking at the rocket it should also be the same speed? Previous logic stated that it should be different speeds when measured from different velocities, but they were the same speed. This was the conundrum (simply put - there was a lot of stuff about electric fields and so on, but don't need to get into detail here).

    Einstein reconciled these in special relativity, by saying both are true, because in essence observations were that that they were.
    He simply then started to think: if they were both true, what else would be true? The difference is really in concepts of time, velocity and distance. So if the speed is of light is the same, it follows on that time must change to accommodate this truth. The rocket must be experiencing slower time to ensure that the speed of the light from the torch is the right speed when measured by someone on the ground. Hence, time and distance dilation occurs when objects are accelerating or decelerating.

    Now: general relativity. Einstein had the same truths about gravity. He was likely wondering what gravity is, as concepts of ‘ground’ is also not really defined. Newton said gravity was just a ‘force’ between two masses, however Einstein was dissatisfied with this. If motion and acceleration is relativistic, why not acceleration due to gravity? Surely there shouldn’t be two forms of acceleration out there in the universe…

    Hence two postulates for general relativity:
    - no matter where you are or how fast you are, special relativity holds true
    - including on a planet - where you are experiencing gravity. Ie. there is no difference between gravity and accelerating. Eg. if you are in a rocket, it is the same as if you were on a planet, you are experiencing the same special relativity effects.

    So given these two factors - it holds that when you experience gravity it is the same as if you were in a rocket, you experience time and distance dilation as per the previous explanation of special relativity.

    NOW THE IMPLICATIONS: Space becomes very weird (or rather just more complicated). Time dilation and distance dilation occur in relation to mass, not just if they were accelerating on rockets. This means light speed from a torch on a rocket is the same speed as measured from a stationary space station (meaning the rocket experiences time dilation) is the same effect as a torch on a planet also (meaning the location on the planet is experiencing time dilation).

    This has matched observations, mainly Mercury, which Einstein proved was experiencing slower time close to the sun than when it was further from it, effectively proving the theory of General Relativity.

    There is a lot of maths here that is omitted, and this is ‘thought experiment’ realm only, but is the basic principle - which is acceleration causes time dilation (because light is the same speed no matter where measured from), and gravitational acceleration is the same as normal linear acceleration.

    Now another aspect of your question of 'why' relativity is true is more philosophical - and calls into question 'why' behaviours we observe are like this and hence the investigations of black holes and so on which push this theory to the limit - and there are still many mysteries to be solved...

  • Oct. 27, 2019, 6:07 a.m.

    When you are in a gravity well, you are falling. Suppose get into a balloon, rise to the edge of space, and jump off. You are not in orbit. You are going to fall for all practical purposes straight down. As your speed increases while you plummet to the earth time slows down.

    When you are in orbit around a black hole, your falling down but also moving to the side. To stay in orbit close to a gravity well you have to be moving very fast and time will slow down. Suppose you are not in orbit and just using rocket thrusters to keep from falling into a black hole. Well you might be stationary relative to the singularity. Relative to the space itself that is rushing by you as it falls into the black hole, you are moving quit fast through that space and time will slow down. Think of a speed boat at the edge of a water fall using its motor to keep itself from being carried by the water down the water fall. From the shore the boat may appear stationary, but it is actually moving through water at a very high rate of speed.

    Hope that helps.

  • Nov. 6, 2019, 4:45 p.m.

    Maybe you can clear up something for me too...

    Speed itself causes time dilation, but so does acceleration, which is just the change of speed.

    If you accelerate for a long time and then stop accelerating, you are still coasting at a great speed.

    Then what happens to your time dilation? Does it decrease?

  • Nov. 13, 2019, 12:48 a.m.

    Yes well they are actually related, although in different ways. Special Relativity relates to 'object in comparison to...', whereas General Relativity relates to 'object is not at rest as it is accelerating, when in a gravity field'.

    So imagine a 'photonic clock', ie, 2 mirrors locked in place with a photon bouncing between them. By moving the clock, the photon will need to 'travel' a longer distance and the effect is:
    - Under Special Relativity: if you are inside the clock, you notice no difference. If you are outside the clock moving at a different speed, looking at it, it will tick at a dilated rate because the photon will still travel from your point of view at the same speed, so the 'ticking' will be slower.
    - If it accelerates, Special Relativity still occurs but at the same rate as the new speed. The photon will begin it's journey as normal in the clock from one of the mirrors, but by the time it gets to the other mirror, the clock has accelerated and thus the distance is larger. So, in regards to Special Relativity, there is no difference between velocity and acceleration. In your example above, if you stop accelerating, your dilation will now remain the same from then on, relative to someone else at a different speed.

    Now consider the clock also is affected by General Relativity, if it is in a gravitational field (which all objects in the universe actually is). This is an additional effect, so you could say both forms of time dilation exist at the same time on the clock. But there are some differences:
    - The clock is inside a gravitation field, and time elapses differently in the space around mass. This is not a function of the clock's velocity, but rather its location close to mass. Yes, it is experiencing 'acceleration' if it is close to a mass, however to clarify my simplistic post above it is not actually due to acceleration (the acceleration is the manifestation) but more accurately its 'gravitational potential'. So if the clock is on a planet, it looks like it is at rest, however it has 'gravitational potential' so if a hole suddenly appears under it and it starts to fall, this only manifests as acceleration.
    - It is this 'potential' that causes the time dilation, different to special relativity's 'velocity'.
    - I have omitted the obvious next step here, which is to do with 'spacetime', worthy perhaps of another thread. This explains why dilation would occur in the middle of the planet too, which theoretically there is no 'acceleration' because mass is all around you, yet the dilation would be the strongest here because that is where the field is the strongest.

    SO, there are some key differences between SR and GR dilation:
    - SR dilation is dependant on someone's viewpoint traveling at a different speed to yours.
    - GR dilation is dependant on if someone is closer to mass.
    - The difference means that if we all had clocks, in SR, our clocks would be seen as slower by each other, as we are moving away 'from each other'.
    - Whereas the GR effect (which is in addition to SR), our clocks are moving at different rates by each if we are in different areas of Gravitational Potential (distance from mass) so this means a clock in orbit, as seen by a clock on the planet, could be faster, and a clock on the planet, as seen by a clock out in orbit, would be slower. This is a different result to SR where both would be slower as seen by each other.

  • June 29, 2020, 7:45 p.m.

    Since you're on this forum, I assume you watch Isaac Arthur videos, which also makes me guess you like educational YouTube videos. Thus, I wonder whether you've seen these YouTube series by physicists about relativity:

    Don Lincoln from Fermilab: www.youtube.com/watch?v=BhG_QZl8WVY&list=PLCfRa7MXBEspw_7ZSTVGCXpSswdpegQHX
    PBS Space Time: www.youtube.com/playlist?list=PLsPUh22kYmNAmjsHke4pd8S9z6m_hVRur (also www.youtube.com/watch?v=fHRqibyNMpw&list=PLsPUh22kYmNCLrXgf8e6nC_xEzxdx4nmY&index=4 points out that Hub's photon clock is indeed similar to how the interactions in matter lead to our perception of time.)
    For detailed video explanations of the math, you might check out: www.youtube.com/watch?v=ev9zrt__lec&list=PLkyBCj4JhHt_pz8HUG7rbMeKFsStae10k

    I don't really understand general relativity yet, at least not on a mathematical or deeply conceptual level, but the math for special relativity really isn't that hard. It's mostly algebra, though sometimes people use more advanced types of math with it, as they always do. Play around with the math and Minkowski diagrams for a while (maybe with an online graphing calculator tracking lots of points, like I did). Also, on the subject of math, especially linear algebra, which is useful here because A: the Lorenz transformation is a linear transformation, and B: the equations of General Relativity use tensors, which linear transformations are an example of, I highly recommend 3Blue1Brown videos. Also, my actual introduction into the special relativity and how it actually worked that helped me start to understand it was a 50s or 60s edition of a little book Einstein wrote called "Relativity: The Special and the General Theory" (from "Über die spezielle und die allgemeine Relativitätstheorie") designed to teach the concepts without anything more than high school math, although it does take a lot of thinking, and the way I learned from it is that I read the first half a few times and messed around with the math; and I've read the whole thing once or twice, without really managing to fit it all in my head. My dad was probably right when he said that Einstein's book probably wasn't the best introduction to relativity, although I did like the way it started out explaining basic philosophy of math and physics and then explained the logic that lead to the development of the theory (or at least logic that could lead to it). I've also never seen the discussion of the relativity of rotating objects anywhere else yet, although I know it was a big area of research for relativity physicists in the first half of the twentieth century.

    Firstly, since I like Minkowski diagrams, here are a couple in case you don't know what I'm talking about:

    (The dots on the line in the linked animation are ticks of the object we're following's clock as we move our reference frame along its worldline at one tick per second of our time. You can see how these ticks look farther apart from each other in time when we look at parts of the object's path that are at different velocities from the current velocity. That represents the fact that objects moving on those paths would seem time-dilated to our object if it didn't accelerate to enter those reference frames. The other dots are events that happen at specific times and locations, not physical objects in space, as those would exist across multiple times and thus look like lines. The reason the description says "momentarily co-moving inertial frames" is because our time axis extends straight along the path of a constant-velocity object, when we could have instead used a reference frame where the entire path of the object was a straight line, which would distort everything else so that paths of non-accelerating objects would look like they were accelerating, although I think everything would just move down in straight lines as we scrolled across the worldline after we'd done this, since we'd only have to change our time coordinate as we scrolled rather than our velocity as well. This would be an accelerating reference frame—one with changing acceleration/gravity, in fact. Space-time coordinates in general relativity are based on something called "Gaussian coordinates" rather than Cartesian coordinates like we're used to. I think this ability to make any curve into a straight line if you want is related to the idea I've been told that General Relativity works just as well if you use curved coordinates on flat spacetime as if you use coordinates as straight as possible on fundamentally curved spacetime.)

    Also, I want to point out a couple of things I don't see mentioned much about relativity.

    1) When you see popular explanations of how gravity is really just curved spacetime, they often show planets making a depression in a sheet representing space. First of all, it's important to note that the geometry would work exactly the same if planets created hills rather than depressions, since all that matters is how the curvature affects "straight lines" on the surface; it has absolutely nothing to do with objects falling down the slope created by bending space, which would involve some external force of gravity in some other dimension space was embedded in. Of course, 3D space is embedded in another dimension — time, and I'm told that time curvature is really what causes gravity (though that sounds like a rather imprecise statement), so maybe the popular explanation isn't too far off in that respect. I don't actually understand it properly*, so I won't claim that.

    *It does sort of make sense to me, though, in that time is required for things to fall. Imagine a "Minkowski space-time diagram", where the x-axis is one direction of space is distance along a particular line in space and the y-axis is time. (Usually, either measure the x-distances in light-time units (i.e., divide it by the speed of light) or measure the time in distance units (i.e., multiply it by the speed of light).) In flat spacetime, i.e., no gravity, two objects floating next to each other will look like vertical lines, with position staying the same at every point in time. (If they were moving relative to your coordinate system, but at rest relative to each other, they would look like parallel lines.) However, under if gravity were pulling them together, then their lines would have to cross at some point. General relativity says that rather than the lines of the the objects ("worldlines") curving to meet each other, spacetime curved so that they meet each other, sort of like if you had drawn your Minkowski diagram on the equator of a sphere and the worldlines of the two objects meeting at the pole like longitude lines (although obviously not exactly like that in most cases, since all the latititude lines on a sphere meet at the same time, so that would bring everything in a finite universe together into one point at the same time, like the Big Crunch). What I don't understand is how a massive object like a planet, which would look like a line on a Minkowski diagram, can create curvature that would do this. I strongly suspect that once I do know, then I will also understand why such curvature (gravity) causes time-dilation.

    2) The effect of the Doppler shift looks like time dilation, but is actually a totally different effect on top of time dilation: If a rocket car is driving towards you at half the speed of sound blaring ridiculously loud music, that music will sound to you like it's playing at double speed. Imagine each beat of the song moving away from the car and towards you at the speed of sound for one 4-beat measure before it almost hits you. (What a jerk!) (Just to explain a measure to non-musicians, this should be "1, 2, 3, 4, almost-hit" from the car's perspective). When beat 1 reaches you, the car will already be half-way closer to you, and therefore emitting beat 3. In general, the car will always be half the distance away when you hear a sound as it was when that sound was emitted. The following table will be easier to follow than any explanation I can write of the other beats times:

    ("Passby" would be beat one of the next measure.)
    (If you consider that the car is moving at constant speed, then you can see that the distance the car is at is also a good coordinate for the time events happen at.)
    (Also note that I've defined a unit of distance that has a remarkably convenient length for this problem, no need to calculate what that is, which would depend on the tempo of the song and the speed of sound in the air.)
    (Sure would be nice if there were a way to insert tables and I knew it, but alas no.)

    As you can see, this adds up to the song sounding twice as fast from your perspective, since the beats are all scrunched up in front of the car and hit you in fast succession.
    Afterwards, it will be moving away from you at half the speed of sound, and the effect will be one of making the music sound like 3/4 speed to you (so a measure is 150% as much time):

    *This is what was called "passby" before — beat 1 of the second measure.
    **= of measure 3
    (I'm using negative units just to emphasize that the car is now moving in the opposite direction from the table above.)

    This is because the beats have to travel back towards you at the speed of sound and each beat is emitted from a further distance away. If you imagine where the waves are in space, they are stretched out further apart from each other behind the rocket car, just as they are scrunched up in front of it. (The math is more confusing on this one because the sound-waves are moving back towards you at the speed of sound while the car is only moving away from you at half the speed of sound. If it were moving away at the speed of sound, the tempo would be halved.)

    That's the Doppler effect with sound. It affects tempo of songs just as much as it affects pitch of sound waves. The Doppler effect with light also affects tempo of songs played on radios as much as it does the frequency they are transmitted at, but is different for two reasons. A: Sound moves relative to the air: if you were in the rocket car driving past someone standing still who was playing ridiculously loud music, you would actually get different results (1.5x speed on approach and .5 speed afterwards). This is not true with special relativity, since part of the whole premise of relativity is that all reference frames are equally valid. B: Special Relativity, which is actually based on this principle combined with the principle that light moves at a constant speed relative to everyone, has time-dilation and length-contraction affects that are separate from the affects of classical Doppler shift.

    One interesting effect of this is that, if we ever intercepted a transmission from billions of light years away, in the early universe, everything would be in super slow-motion from the combined effect of the Doppler shift and time dilation, (although these are already combined in the redshift, and what is called "relativistic Doppler shift" includes time dilation.) On the flip side, one might note that time dilation of any kind looks like Doppler shift, so one should also expect redshifting of light coming from incredibly dense objects like neutron stars. I've never heard about this specifically, but I assume it must be something well known to astronomers who study such things.

    3) In special relativity, your local time is simply the time you experience. If you have a clock, the time coordinate for any event you observe can be determined by the reading on your clock. However, if you look at a Minkowski diagram, your reference frame gives time coordinates for places other than your location. This seems like an obvious thing, but it's actually pretty weird if you think about it, and is arguably where all the weirdness of special relativity comes from. The way Einstein defines this time coordinate is rather interesting: If you observe light from an object one light second away, then whatever you see is happening one second in the past. This idea can be extended to all times. Also, it technically isn't talking about observing light, it's talking about any information reaching you at the "speed of light" or maximum speed of information.

    The thing about this definition is that it isn't actually based on assumption about how fast information moves through space; it's more like a semi-arbitrary definition of how to relate time and space, since there isn't any better way to define how time in one location is related to time in another location. This definition is really at the core of special relativity. When people say that observers moving at different velocities disagree about the order of events in distant places, they mean that their time-coordinates, as determined by subtracting the light-time distance as measured by them from the time they observed the signal, do not come in the same order according to different observers. Arguably, our real notion of time comes from the causation, which can only happen when there is enough time for information to pass from one place to another. The above definition of the "time" that events far from the observer happen is convenient because it makes a coordinate system where everything that could have affected an observer is in a hyper cone spreading back in time before the present and everything the observers present could affect in the future is in a hypercone of exactly the same angle in front of the observer.

    On the more practical and less philosophical side, this definition allows you to see how speed affects time and space (under these definitions): For example, if you are floating in space and see two bright lights on either side of you at almost exactly the same time, a person flying past you at a significant fraction of the speed of light, away from one and toward the other, will see the one in front of them significantly before they see the one behind them, and the difference in time compared to the difference in distance will be such that they conclude it happened first. (Put another way, it will have happened "first" in their coordinate system, even though the events happened "at the same time" in your coordinate system, all based on the above definition of times at distant locations being related to distance and the speed of light.) On a Minkowski diagram, you can investigate the times that different observers see things at by drawing 45 degree (i.e., slope 1) lines, which is what things moving at the speed of light looks like to any observer. This will allow you to see things like how how time time dilation is the same both ways (if 2 people are moving at different velocities, each person will judge the other's clock as moving slow). If you draw Minkowski diagrams on curved surfaces (or on "conformal" projections of them) you can even see general relativity effects, although I'll have to get back to you on how well that works for me.