Why does time 'change' when gravity increases? I was doing some research on gravitational time-dilation, my topic for the Breakthrough Junior Challenge (a science video contest where contestants have to explain a hard science/math topic in 3 min video). I haven't actually written down my research/findings or anything - I decided on a topic and I think spacetime dilation is (very) challenging, yet enthralling. So I found this website here that says that time goes faster "the farther away you are from the earth's surface". I read the article but I'm still kind of confused as to why this happens...is it actually due to the difference in gravitational strength and the warping of space-time by large masses? And how would that even alter how time proceeds? Thanks.
 A: A way to understand why that must happen uses the equivalence principle. A free fall observer can be considered as a inertial frame.
If he compares the rate of his clock with another clock fixed somewhere at height $= h_0$, according to the special relativity the fixed clock (that is moving with respect to the free fall observer) shows a smaller tick rate.
When comparing with another clock at a smaller height $= h_1$, when the relative velocity is bigger due to the acceleration of gravity, it will show an even smaller tick rate.
On the other hand if the observer is very far from the gravitational field, where the acceleration is very small, the tick ratio is almost constant between different points.
A: To think about this, first we need to think about what we mean by time passing. A good way is consider some regularly repeating process, such as an object undergoing simple harmonic motion. We count the number of oscillations of the object, between two events nearby that are of interest to us, and this count gives a measure of the amount of time that has passed. In fact the standard of time, based on caesium atomic clocks, uses this principle. The oscillation is the oscillation of the nucleus of a caesium atom relative to the electrons. It oscillates 9192631770 (that's about 9 billion) times per second.
Now let's think about one of the properties of gravity: as things move upwards in a gravitational field, they lose kinetic energy. In the case of light waves this means that a wave emitted with a certain frequency at a low down place will arrive at a high up place with a lower frequency.
Now consider the waves emitted by a caesium atom. We start with a pair of caesium atoms at a high up place. They are emitting microwaves all the time, with the frequency 9 GHz. We leave one of them where it is, and take the other on a journey. The latter one is first lowered down to a low place in a gravitational field and then held there for a while. While it is there it keeps emitting waves. Let's say it makes $4.5$ billion oscillations, emitting that number of oscillations of the electromagnetic field near to it. These waves propagate up to the upper atom, and they arrive there with a lower frequency because of the loss of potential energy. Let's say this frequency change is by a factor 2, just to have a concrete example. It means that the waves arriving at the high up place (after being emitted low down and travelling upwards) have twice the wavelength, when they arrive, of the ones emitted locally by the atom at the high up place. Therefore they also have twice the period. So in the time taken for the $4.5$ billions wavelengths to arrive, the upper atom oscillates $9$ billion times. So a person at the upper atom will consider that 1 second has passed, because that is how long it takes a caesium atom to oscillate $9$ billion times. But, according to what has been observed, the lower atom has only oscillated $4.5$ billion times. How are we to interpret that?
We do another experiment, starting with the same two atoms, and sending one on a journey to the same low-down place as before. Now we let it stay there for longer, say while it oscillates 18 billion times. The waves propagate upwards as before, losing energy as they go and consequently also getting a longer wavelength and a longer period. For the two places we are considering, this change is by a factor 2. It means that the waves arrive at the upper atom with a period twice that of the upper atom, so now the upper atom will oscillate 36 billion times while the waves arrive. That will take 4 seconds. But during those 4 second the lower atom has only oscillated 18 billion times.
I hope you are beginning to get the picture: as far as the upper atom is concerned, what is happening at the lower atom is going more slowly.
But is this a property of just these two atoms? Well according to gravitational physics, the physics at any given place is just the same, so if one atom is going slowly at some location, then so are other atoms, and molecules, and solids, and everything at that location. Relative to other things right at that location, all the processes have their usual rates relative to one another, but relative to processes at another location (one high up in the gravitational field) they are all going slowly.
The example I gave, with a factor 2, is a rather extreme example. You can only get gravitational time dilation as large as that from things like neutron stars and black holes.
The original question was why does this happen. So far in my answer I have simply said that it is connected to another fact: the fact of red-shift as electromagnetic waves (or any waves) climb out of a potential well. I have shown that these two observations are not just mutually consistent, but really two things that go together; they each imply the other. That is all we can ever do in physics: show how phenomena are connected. The ultimate answer to why gravity causes time dilation is to turn the statement around and say that the phenomenon of a spatially-dependent time dilation is the very thing we call gravity. One can support such a statement by adding some further aspects of the physics and mathematics, and especially important is the fact that things move so as to take the most time to get from one event to another. For this reason a spatially-dependent time dilation will cause the trajectories to curve in interesting ways, and this is what we call gravitational acceleration.
In the last paragraph above I have simplified a little, but a more precise statement would need a longer answer and this answer is already long enough!
Added comment on the path of most time
An event is a point in space and time. If we have two fixed events $A$, $B$ then there may be many lines or paths through spacetime from $A$ to $B$. There is a time, called proper time, for an entity following each path. It is the internal time registered by all the dynamic processes of that entity. Among all the paths between $A$ and $B$ there is one where the proper time is the most. An object which only has gravitational forces acting on it, and which is present at $A$ and $B$, will follow that path.
Here is an example. Suppose an ordinary ball is present in my hand at some moment (event $A$), and it is there again in my hand one second later (as indicated by my watch) (event $B$), and in between the only force on the ball was gravity. In this case the path in spacetime where the ball stays permanently in my hand will not have the longest proper time for the ball, because of gravitational time dilation. There are paths where the ball first goes up and then comes down again; some of these paths register more proper time because they access regions higher up where there is less gravitational time dilation. However, the paths which go very high involve fast motion because we are only considering paths which return to my hands quick enough to be present at event $B$. If the motion is fast then there will be less proper time owing to the time-dilation associated with motion, which is a feature of special relativity. The actual path followed by the ball is a parabola in spacetime. This path allows the ball to reach some higher place where its proper time accumulates more quickly, while not introducing too much slow-down by motional time dilation. This is the path of most proper time.
A: Yes, gravitational time dilation is due to the warping of space-time by matter. The pop-science picture of this warping as being like a heavy mass sitting on a rubber sheet is misleading, because that shows only the spatial warping. But in fact in ordinary circumstances by far the largest component of the warping is in the time dimension; that is, while matter warps both space and time, it mostly warps time (strictly speaking mass doesn't warp space at all, but the pressure inside matter does).
An entertaining, if somewhat simplified, view of this is the Science Asylum video at https://www.youtube.com/watch?v=F5PfjsPdBzg
A: You've asked a challenging question that can have several interpretations, but I'll try to give you one that you can understand.  But you should realize that you've set off on a journey that could take you years.
You ask "why does time change when gravity increases?"  This is not a good interpretation. Many scientists believe that the gradient of time dilation IS gravity. That is, things fall because they want to move to where time runs slower.  (There is a famous saying something like "the reason your bum is stuck to your seat is because time runs faster at your head than your feet.")  So it is because time runs slower on the ground than it runs 3 metres above the ground that things fall from the top of a ladder.  Keep in mind that the difference is extremely small.  The difference in the speed of time from sea level to the top of Mount Everest is about 1 second in 30,000 years.
Why do things want to move to where time runs slower?  This would be because everything wants to give up energy, which is the same as increasing entropy.  By moving to a region with slower time, a falling object is giving up energy.
You will read many say that mass warps spacetime. Yes, this is technically correct, but really this is only true near extremely massive objects, like a neutron star or a black hole.  Near the Earth or sun, 99.999% of the curvature is only curvature of time, not space.  It is only near a black hole that the curvature of space reaches 50% of the total.
So now the question becomes, just how does mass curve time?  And here I am going to get speculative so take this with a large grain of salt.  Keep in mind that mass is really only a different word for matter. And what is matter?   Matter is the atoms that make up a planet.  It's interesting that if you were to blow the Earth up to dust that scattered across the solar system, it would have the same total gravity to a far away observer as the Earth does now.  So it is not the total planet that has gravity, but rather each individual atom.  Atoms are made up of protons and neutrons, which in turn are made up of quarks and gluons.
Gluons are massless, but because they have so much energy (they move at the speed of light) they actually make up 80% of the mass of a proton based on mass/energy equivalence.  So you can think of these gluons as spinning around like crazy, just like electrons do.
You know that magnets are magnetic because the electrons are spinning.  Did you know that every atom is itself a tiny magnet?  Magnets have a stronger magnetic field around them, which is essentially an excitation of the magnetic field near the magnet.  There is no reason why gluons would not also cause an excitation of the gluon field surrounding a planet.  The only difference between a gluon in a planet and an electron in a magnet is because all of the electrons in a magnet are polarized to spin in the same direction, while the gluons are spinning in random directions. So it takes all the spinning gluons in the 10^50 atoms in the Earth to generate the excitation of the gluon field surrounding the Earth.
Now I'm going to get even more speculative.   Many scientists are proposing a theory known as loop quantum gravity.  In this theory, space is particulate, made up of very very small particles.  In this gluon field concept, the excitation of the gluon field surrounding a planet leads to a dilation of this particulate space.  The particulate space is fundamental, that is there is nothing smaller.  So a dilation of this space would itself mean a dilation of time, and thus gravity.  Simple, right?
I hope that this gives you something to think about.  Good luck on your journey.
A: The 'why' of things is tricky in physics. Let me give a spin to this question by considering the alternative: why would space and time be completely uncorrelated to whatever happens in time and space?
We would have two metaphysical dimensions in nature: one, similar to a container, the all and ever unchanging space/time background, like a stage where the second dimension, the dynamics of all existing objects and radiations plays out.
Nature would be a collection of objects dancing around within a well defined overencompassing stage. That's a strikingly sharp duality.
Then, why would it be so? This metapicture seems fit for some meta-observer, looking at the play and able to describe what is happening from its vantage point of view. This observer could be identified to science itself, describing the world, or maybe to some divinity, having set the whole thing in motion and enjoying the show.
What I am coming to is that the stage/play duality must somehow imply an implicit third point of view, from which this duality is apparent, and which has a metaphysical standing as profound as both spacetime and all that happens there - that's a pretty mighty third element, not adressed by physics very much by definition.
So by Occam's razor, we might want to get rid of this all-outside quasi-divine observer thing. In Newtonian physics, there is no way to do so. In relativistic physics, it is done automatically: the stage/play duality does not exist. I find this rather satisfying.
A: If the speed of light falling in gravity varies as per Newton, as suggested in the texts below, then there is no gravitational time dilation (general relativity is nonsense):
University of Illinois at Urbana-Champaign: "Consider a falling object. ITS SPEED INCREASES AS IT IS FALLING. Hence, if we were to associate a frequency with that object the frequency should increase accordingly as it falls to earth. Because of the equivalence between gravitational and inertial mass, WE SHOULD OBSERVE THE SAME EFFECT FOR LIGHT. So lets shine a light beam from the top of a very tall building. If we can measure the frequency shift as the light beam descends the building, we should be able to discern how gravity affects a falling light beam. This was done by Pound and Rebka in 1960. They shone a light from the top of the Jefferson tower at Harvard and measured the frequency shift. The frequency shift was tiny but in agreement with the theoretical prediction. Consider a light beam that is travelling away from a gravitational field. Its frequency should shift to lower values. This is known as the gravitational red shift of light." https://courses.physics.illinois.edu/phys419/sp2011/lectures/Lecture13/L13r.html
Albert Einstein Institute: "One of the three classical tests for general relativity is the gravitational redshift of light or other forms of electromagnetic radiation. However, in contrast to the other two tests - the gravitational deflection of light and the relativistic perihelion shift -, you do not need general relativity to derive the correct prediction for the gravitational redshift. A combination of Newtonian gravity, a particle theory of light, and the weak equivalence principle (gravitating mass equals inertial mass) suffices. [...] The gravitational redshift was first measured on earth in 1960-65 by Pound, Rebka, and Snider at Harvard University..." http://www.einstein-online.info/spotlights/redshift_white_dwarfs.html
"To see why a deflection of light would be expected, consider Figure 2-17, which shows a beam of light entering an accelerating compartment. Successive positions of the compartment are shown at equal time intervals. Because the compartment is accelerating, the distance it moves in each time interval increases with time. The path of the beam of light, as observed from inside the compartment, is therefore a parabola. But according to the equivalence principle, there is no way to distinguish between an accelerating compartment and one with uniform velocity in a uniform gravitational field. We conclude, therefore, that A BEAM OF LIGHT WILL ACCELERATE IN A GRAVITATIONAL FIELD AS DO OBJECTS WITH REST MASS. For example, near the surface of Earth light will fall with acceleration 9.8 m/s^2." http://web.pdx.edu/~pmoeck/books/Tipler_Llewellyn.pdf
A: When gravity increases, speed increases more quickly, and time decreases in the same proportion. So when gravity increases, time decreases. That's the change that you'll get - a decrease in time.
A: Fact:
Yes, space is curved around a body. Newtonian gravity takes this into account. The surprise was that time is also curved, and that curve is defined by $\sqrt{1 - R_s / r}$.
Don’t forget that, with all that speed as one falls in, that there is also kinematic time dilation, defined by $\sqrt{1 - v^2/c^2}$. The integration of the precession of the perihelion of Mercury relies on a factor of 3... two parts gravitational time dilation, one part kinematic time dilation... https://farside.ph.utexas.edu/teaching/336k/Newton/node116.html
Speculation:
A test particle is assimilated by the gravitating body as the test particle falls toward it. The process of the interior of the test particle decreases in frequency, and time is dilated. The test particle’s interior process is interrupted, more so as one gets closer and closer to the gravitating body. At the event horizon of a black hole, the particle will have become fully assimilated. The black hole and the test particle are now one process.
