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Can someone intuitively explain how physically time dilation happens?

Please don't explain about the invariant speed of light and the mathematical background, I am familiar with that. I just can't imagine how this time dilation process is happening physically, and I can't understand how to distort my mind to understand it!!!

Sorry for this question, it probably sounds like, "Why there are positive and negative charges", but I have to ask!

What could make the question clear is the equivalent one: how could be that the two moving observers do not agree on the simultaneity of events and one sees the other in slow motion but he also knows that the other see him in slow motion. How to imagine the reason of this time dilation, probably something similar to banding of space leading to contracting lengths but for the time. It would have been more clear if the time difference was unsymmetrical and if observer A sees me in slow motion then I should see him in faster motion, so ok I agree that my time has being delayed and he agree that too, but this is not the case.

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What do you mean how it physically happens? – Kyle Kanos Feb 21 at 18:48
I mean, what in the world is making this symmetric time difference, for instance length contraction could be due to distortion of space and as far as I know what is space (not that I really know) I can imagine that phenomena, but not and the time! – Pekov Feb 21 at 18:57
There is a great (really) short book that explains relativity thus the difference in time. It's Landau and Romer's What is relativity? book. – YoMismo Feb 22 at 11:35
Why are there positive and negative charges? I have no idea – John Carpenter Feb 23 at 1:47
If we ask why, we might as well ask plenty more "why?"s @JohnCarpenter – Sidarth Feb 24 at 9:53
up vote 36 down vote accepted

One result of special relativity is that the magnitude of all 4-velocity vectors $\vec{u}$ is the speed of light. Written with the (-,+,+,+) signature:

$$\vec{u}\cdot\vec{u} = -c^2$$

One way to think of this is that everything is always moving the speed of light in some direction.

When I stand still, I move the speed of light in the time direction. My clock advances as fast as possible. When I look at other observers in other moving frames their clocks all advance more slowly than mine.

Imagine someone moving close to the speed of light. Their clock seems to hardly advance at all relative to mine.

If I start running, my 4-velocity vector is still the speed of light long. Now it has some non-zero component pointing in the space direction to account for my motion. That means the time component of my 4-velocity must have shrunk. My clock does not advance as fast as it used to, relative to everyone else, who remains standing still.

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This is a bit misleading though. Moving fast in the space direction means you cover a lot of distance every time your clock ticks; moving fast in the time direction means a lot of time passes every time your clock ticks. That is, if you are 'moving quickly through time', your clock appears to tick slower, not faster. This is exactly the opposite of how you've described it. – knzhou Feb 21 at 20:31
This mistake 'cancels out' with the fact that the signature has a minus sign in it to make the result look right, but the reasoning actually doesn't make sense. – knzhou Feb 21 at 20:33
@knzhou Doesn't this sentence contradict itself: "That is, if you are 'moving quickly through time', your clock appears to tick slower, not faster."? 'Moving quickly through time' is meant to mean 'increasing ones time coordinate more than ones space coordinate, relative to another body that is moving in a different manner'. Increasing a time coordinate would be analogous to experiencing clock ticks. Not moving through time at all would be experiencing no clock ticks. – Todd Wilcox Feb 21 at 20:38
Reading these comments, this explanation may not check out according to physics 100% — but this is by far the best explanation I have ever read to explain why speed and time could possibly be correlated like this. – j6m8 Feb 22 at 2:04
@j6m8 It also has issues with math and terminology. For instance a 4-velocity has components and all the words 4-velocity and component have an established mathematical meanings already. And with those meanings it's just wrong to say the time component shrinks, the time component is actually larger for a length $c$ vector with additional spatial components. The part where moving straight gives the most clock ticks is correct, but the rest is an abuse of terminology. And will probably lead to twin paradox type questions too. An explanation that leads to paradoxes later is a band aid at best. – Timaeus Feb 22 at 2:51

Clocks don't measure time and tape measures don't measure distance. They both measure the metric along a curve. Just like how a tape measure depends on the path so does a clock.

Take 4d spacetime, look at the path of the clock in 4d and note that at some of the events, it ticks. So at one point the clock ticks. And how far along the path should the clock go before it ticks again is 100% the entire question.

And it is based on two things. How deep a gravity well it is in, and how much of the curve is there between the two events, the start point and the end point of the curve in 4d.

Now curves are longest when going in straight lines, that's just how geometry dictates lengths in a Lorentzian geometry. So you can break down the curve into pieces and replace each little piece with a straight line and you've over estimated the length (in Euclidean geometry you'd be underestimating the length). So now you just need the length of each piece. You get that from the metric. Why? You can imagine there is some real time and the clocks are mean and just don't tick that way. Instead they tick based on a metric. The metric literally tells them how to tick. They tick because they measure the metric rather than measuring time.

You can imagine that the clock has to go along a 4d path and that the space and time flow through it as it ends up at different events. And for each little bit it computes the metric of that little bit and keeps a running total and when it gets to a certain total it ticks.

All you have to do is accept that clocks literally measure $\mathrm ds=\sqrt{g_{ij}\mathrm dx^i\mathrm dx^j}$ for each little piece and add it to a running total and then tick when that running total crosses the cut off running total.

And everything else too. When something is supposed to happen at a certain rate instead of waiting a certain amount of time, you go along a curve in 4d spacetime, compute $\sqrt{g_{ij}\mathrm dx^i\mathrm dx^j}$ along the curve and instead of doing it y times a unit of time you do y times every unit of $\sqrt{g_{ij}\mathrm dx^i\mathrm dx^j}.$

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Maybe you should clarify in what sense straight lines are the longest. Otherwise this is confusing. – Merlin1896 Feb 24 at 8:51

I think it might be more instrctuive for you to show yourself what is going on. If you work through the following example you'll come out with a decent understanding of the phenomenon. Consider a light clock onboard a ship that is moving at velocity v relative to an observer. Te light clock works by boucing light vertically between two mirrors spaced one light second appart. Given the postulate upon wich all of special relative is based "the speed of light is the same in every inertial frame" You can work out that the stationary observer sees the light in the clock to travel a greater distance tan the one moving with the clock. Therefore because the speed of light has to be the same in both reference frames time must be slower in the movig frame. i.e.

distance = speed x time

distance is less in te moving frame, speed is the same so less time must have passed. Therefore time is moving slower in the moving frame, hence time dialation. If you do the maths for the example you will be able to derive an equation for it.

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I understand that the reason is the invariant speed of light and the mathematical derivation is pretty clear to me for both the time dilation and the length contraction. But my confusion is mainly in the process of time dilation. The length contraction is due to bending of space, something I imagine like bending a sheet of paper that shrinks the lengths for an observer out of the curved surface. But how the time bends is what I can’t imagine. – Pekov Feb 22 at 12:47
@Pekov Please imagine the 4th Euclidean dimension. Imagine that 3d space curves through the 4th Euclidean dimension, which is time. Now imagine the 5th. Imagine that the 4d space-time curves through the 5th dimension. Now imagine that instead of Euclidean dimensions, they are Lorentzian. That is how you could visualise it. But I personally think formula are easier. – wizzwizz4 Feb 22 at 17:18
@wizzwizz4 Ok could you give an example but for a 2D creatures where the time is their third dimension and so on? – Pekov Feb 22 at 17:36
@Pekov Ok... Just be warned that although I think I understand this, I might be completely wrong. The curvature of space-time would be similar to that of placing a 2d object on an infinite rubber sheet. Light travels in straight lines on the sheet, but is curved by the curvature of the rubber sheet. Speed is sort-of logarithmic; momentum has no limit, but the more relative momentum you have, the more slowly you get closer to the speed of light relative to another object. – wizzwizz4 Feb 22 at 17:48
If you look up the concept of rapidity you will notice that Lorentz transformations look suspiciously like rotations of atan(iv/c) 4D space time. Though I don't think anyone is actually proposing that's an underlying physical mechanism. – Duke of Sam Feb 23 at 12:58

Forget everything you know about relativity for a moment. Assume that there is some absolute frame of reference in the universe. That the subatomic particles and waves we are made of are themselves made out of pieces on a 3D chessboard.

Things that keep "absolutely" still stay on the same squares (well, cubes). Things that move will jump from square to square along the chessboard.

This begs the question: does light travel at a constant speed with relation to the chessboard (like sound does, relative to the air it travels in), or with relation to the source that generated it (something like ejected particles)?

The latter can be easily shown to be false by timing how long it takes light to reach you given a moving light source. What about the former? Well, on a fast-moving spaceship, you would expect light to travel much faster going towards the rear of the ship than towards the front. But this isn't the case. No matter how fast you are travelling, light seems to move the same speed no matter who creates it or which direction it is sent in.

How can this be? Most people believe there is no "3D chessboard" and that it is simply a physical law that the speed of light in all directions be the same for all observers. Personally, I believe that the "3D chessboard" does exist in some form (something that admits curvature), but we can't observe any differences in the speed of light, because our clocks and rulers are implicitly calibrated by the very same speed of light! It is like trying to measure inflation by seeing how many \$10 notes it takes to buy a \$50 note.

I will present an oversimplified picture of time dilation to make my point. The physical processes that make a clock tick depend on the speed of light. If light travelled slower, the clock would also tick more slowly, so it would be undetectable! Actually the reality is more complicated, because light would not be uniformly slower but rather slower in certain directions and faster in others, so lengths in various directions get distorted, as well as the time it takes for signals to reach an observer. But everything cancels out in the end, meaning that the observer cannot observe her own speed relative to the "3D chessboard".

If you go down this path it is very important to distinguish between distance and time as measured by us, and "absolute distance" and "absolute time" as measured against the absolute frame of reference. The equations of Relativity deal with distance and time as measured by us. "Absolute distance" and "absolute time" are things we cannot measure and do not have any units for.

Maybe there is no absolute frame of reference (I'm not aware of any evidence supporting it). But even so, I think it's a useful stepping stone to getting your head around Einsteinian Relativity.

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Pekov: Without going into mathematics (which you may know more than I do), this is an as fundamental question as "how mass curves space/time". Because the effect comes out of that curving.

One way is, you can accept curving, and then trust the math.

There is no yet known physically describable mechanism of "how the curving actually takes place". So, we are out of luck here.

However, how I soothe myself is this way - Any object in motion feels some kind of stress due to the speed through space. This stress may arise from the fact that the nature (the object, its fields, space around it etc.), has to know changed position of the object at every moment as it moves. To do that, nature has to continuously do some heavy computations. Due to this stress, all events in the moving system slow down a bit depending upon how fast it is moving.

I can not do better than this - a philosophical answer for a philosophical question.

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Timaeus: I think what is described is its its quantitative analysis. Actual physical mechanism is not defined per my information. You can watch it developing does not mean we know what is actually going on between mass and space. Do we know which one acts first? i.e. "Mass tells space how to curve" first, or "space tells mass how to move" first. I mean, where does the most fundamental cause reside. When we push a car, we know the fundamental (action initiating) cause resides in our muscles, hands, their electrons .... If we do not push, car does not move. – kpv Feb 22 at 1:37
If mass acts first, why/how does mass curves space, what is that property of mass. I am not desputing the mathematics at all. But when we start looking for such answers, then it turns out that gravity is defined in terms of gravity. I think that is why real scientists do not look into these kind of questions and carry on with mathematical theory, and experiments. When we start asking why/how fundamental forces work, the questions become philosophical to some extent. – kpv Feb 22 at 1:43
I respectfully disagree that is a mere quantitative description. And I further disagree that matter tells space how to curve. Einstein's Equation dictates the physical mechanism whereby spacetime curvature evolves just as Maxwell's Equation gives the physical mechanism whereby electromagnetic fields evolve. These are no different than the older cases whereby Newton dictated how momentum changes via the second law. You have a thing, it changes by a physical method, you state that method. It agrees with observations. – Timaeus Feb 22 at 1:44
The questioner has specifically mentioned not to give the mathematical background. That tells me that S/he is not looking for an explanation/description in terms of Einstein's or Maxwell's equations. – kpv Feb 22 at 1:46
The equations never tell anyone how something happens. They only give the quantitative aspect. Well, I am asking you to answer the same question and you are answering it in terms of these equations. – kpv Feb 22 at 1:53

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