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Mudassir Ali

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In your question, the word ‘actually’, from a relativistic viewpoint, is all about whether or not different observers, with different opinions on what is happening simultaneous in their surroundings, agree with each other. In the case of gravitational time dilation, they all do.

I’ll be taking the more comprehensive, visual approach with my answer. No TL;DR, I’m afraid…

To address your first question about the nature of time, it’s important to let go of any intuitive ideas you might have about time flowing equally in and all around us. Time only exists within matter in the form of rate of change, and it depends very much on its relative motion.

At quantum level, within the matter of, for instance, our bodies, there are fundamental forces interacting, that result in all the possible change at an atomic, molecular and cellular level, and so on. These fundamental forces at quantum level are interacting inside all of matter at the constant speed of light, which is therefore the limit to our observed rate of change.

When we look at an object that’s not in relative motion, we only see the effect of the fundamental forces at light speed inside it, in the form of rate of change, or: time.

So don’t think of a static object being completely still: inside it, it’s interactions are continually communicating at light speed, even for holding status quo. It turns out that the relative rate of change within matter works perfectly synchronous to Einstein’s light clock;

This is a clock that has a certain distance between two mirrors, and it simply counts the received light pulses on top. When we see a clock that’s not moving in respect to us (left image), we see a faster moving clock, than when it moves in respect to us (right image), because for us, these light pulses need to travel a longer distance at its always observed constant speed.

But for the person that’s moving along, together with this clock, it’s not observed going slower at all, since the rate of change within that person’s brains, and all other matter at this velocity, is going exactly in sync with the light clock next to him. For him, the other clock will actually be observed going slower (I’ll get back to that later).

So, the sum of the observed speed of motion, together with the internal speed of the fundamental forces, which cause the observed of rate of change, always adds up to the constant speed of light for all inert observers in flat spacetime.

This is why time is an imaginary (−1−−−√) quantity in physics, when calculating (contracted) proper distance: The Pythagorean spacetime interval constant needs to get a minus sign for the time part: x2+y2+z2−(ct)2−−−−−−−−−−−−−−−−√, or distance is an imaginary quantity, when calculating (dilated) proper time: (ct)2−x2−y2−z2−−−−−−−−−−−−−−−−√. This is because dilated time, or contracted distance can both also be expressed in both time and distance, with light speed as an exchange factor, so we can subtract them Pythagorean. It is Pythagorean, because in the first picture, the observed time dilation is not proportional to the length of the actual travel path of the hypothenuse, but to the ratio of the opposite:hypotenuse. The sum of the total travel path will always be c. It is often described as “moving through time at the speed of light”, when not being in relative motion.

Another important thing to understand, before being able to explain gravitational time dilation, is the relativity of simultaneity, and how this is able to cause two observers measuring each other’s Einstein light clocks, or time, going slower.

Understand how we are able to define what has happened simultaneous within our surroundings, by making use of the constant speed of light, by sending out light pulses to our surroundings: everything that is reflected back at the same time must’ve been happening at the same time, at the same distance. See the below example, where depth and width represent 2 dimensions of space, and height represents time. If a certain distance up represents a second, then the same distance wide and deep represents a light-second, so light is always shown moving at 45° angles;

A’ and A were happening simultaneous, because the first sent pulse was received simultaneous, after being reflected by these two events. Event 0 happened simultaneous to A’ and A, because it was exactly in between the moment of sending and receiving of the initial light pulse.

But when in linear motion, a static observer will ‘see’ light gaining you slower from behind: you have moved a bit during the time that light, at its constant speed, was traveling towards you. This is, for similar reasons, observed reaching you faster for light coming in from the front.

These differences are not observed by the traveler himself, because the rate of change within all matter is observed being asymmetric across its length of motion: an Einsteins light clock on its side will be observed by the static observer with light moving slower from back to the front, and faster from front to the back, in relation to the ship. The traveler, on the other hand, will always observe it at a constant, symmetric rate.

This asymmetry is observed by the static observer to cause the following artifact, when the traveler defines his spatial simultaneity;

The moment we, as static observers, define event 0 (in the middle) to be happening simultaneous to us, with a ‘horizontal’ view on simultaneity, the traveler moving away will define a moment in our past to be happening simultaneous. And the further he travels, the further he ‘looks’ into our past. This looking further and further into the past, while time keeps on passing, will make the traveler observe us as being time dilated as well.

Note that there’s not really a different mechanism behind this symmetrically observed time dilation between the two observers, where one seems to have ‘actual’ time dilation, while the other subjectively looks towards the other’s past. They’re only different views on the exact same phenomenon. Understand there’s no such thing as absolute motion: the traveler can also be seen as static, with the other moving away from him.

Here are two insightful examples of how different opinions on simultaneity will always observe the other being time dilated;

At event 0, the meeting point, they actually agree with each other’s time.

Now, to finally explain gravitational time dilation, you have to know that acceleration behaves, on small scales, in the exact same manner as gravity. It is impossible for someone in an accelerating spaceship to perform an experiment to conclude if he’s experiencing gravity or acceleration (besides looking outside his ship).

This was Einstein’s happiest thought, and is known as the equivalence principle.

Note that when we look at an object in linear motion, with our ‘horizontal’ opinion of simultaneity, we actually see (minus light delay) a later diagonal simultaneity moment at the rear side of the ship, and an earlier simultaneity moment at the front;

This Minkowski space-time diagram works the same as before: time is upward, space is sideways, light travels at a 45° angle. The ‘static’ observer only moves through time: straight up from the origin, at ct, while the traveler follows the ct’ worldline. Some of the ship’s angled simultaneity planes are marked in red. The fat blue arrow shows the length contracted ship, as observed by the traveler: part of its length remains hidden in the time dimension, with always a later moment presented to the observer of its back (when it was already a bit further ahead), and an earlier moment of its front (when it wasn’t that far ahead yet).

Time ticks slower, with the 45° bouncing blue light pulses inside Einstein’s (huge) light clock, throughout the entire ship, compared to the faster time ticks of the static observer on ct, although the traveler observes the same time dilation for the ‘static’ observer, since he’s ‘looking’ back into the static observer’s time, with its diagonal simultaneity lines.

When we’d do the same observations for a uniformly accelerating traveler to ‘simulate’ gravity, its back will continually present a later and later moment of simultaneity of the traveler to the ‘static’ observer, because of its gaining speed. This results in always observing a faster accelerating rear side, compared to its front, even though the traveler himself will continually measure the back remaining at the same distance (so equal acceleration), with its converging simultaneity lines. This faster rear side will be just enough to give the length contraction effect for the horizontal simultaneity of the static observer;

But proper time, on the other hand, flows proportional to the two Einstein’s light clocks in the back and the front (represented by the 45° angle bouncing lights). So you can see that when the front clock reads 4 seconds, its opinion on simultaneity is with the moment when the back clock read 2 seconds. Furthermore the back follows this exact same simultaneity line towards the future, at this particular moment, so the back actually agrees with the front that it is time dilated (although it won’t experience this there, obviously: time inside all matter always flows exactly in sync with the light clock next to him: one second per second, pun intended).

Nearby energy (mostly nuclear: 99% of the energy within mass is the binding energy between the constituent quarks inside the protons and the neutrons) will make light speed behave exactly similar to the accelerating traveler described in the diagram above, with the only difference that these effects are all happening, while remaining at the same relative location. This is known as curved spacetime.

Hope this clarifies a bit.