# Time dilation. Why? [duplicate]

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We are able to predict, measure and mathematically demonstrate time dilation, but are we able to explain 'why' it happens? what would be that explanation?

Edit1
Think the question backwards:
After some time traveling in space they noticed that the clock that was on the shuttle was always running a few seconds back... they also noticed that the difference was larger when the traveling speed was greater... So why, the faster we travel, "slower" time passes?

Edit2
People keep saying "it is because it is" (or something like that)... so Time Dilation is a Axiom?

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• Time dialation is needed for the speed of light to be the same in any reference frame. – Sheepman May 13 '15 at 13:29
• I don't think any other reason but that is the way the nature works! – Gonenc May 13 '15 at 14:08
• Have you browsed the dozens of other time dilation questions on the site? How are they failing to meet your needs? – dmckee May 13 '15 at 14:48
• How is answering the question "why" different from predicting, measuring and mathematically deriving it? I don't know what your question actually is. – ACuriousMind May 13 '15 at 19:18
• Voted to reopen. The question "Why does time dilation occur?" is clear and asked by everyone that learns special relativity. The answer is "because that is the way nature works." Never the less, it is possible to say something useful about it. – mmesser314 May 15 '15 at 11:21

## 3 Answers

Time dilation is a result of a fundamental symmetry of the universe.

Start with good old Newtonian motion. Suppose I see some object move a distance $(dx, dy, dz)$, then Pythogoras' theorem tells me that the total distance it has moved, $ds$, is given by:

$$ds^2 = dx^2 + dy^2 + dz^2 \tag{1}$$

Now suppose you're using a coordinates rotated relative to mine (maybe we're in cities at different latitudes). The individual values for $dx$, $dy$ and $dz$ that you measure won't be the same as mine. But if you use equation (1) to calculate $ds$ you'll get the same answer as I do. So we have a symmetry that the distance $ds$ is the same for all observers. We say $ds$ is an invariant.

Actually, this should be obvious. The length $ds$ could just be the length of a rod, and the length of rod doesn't change if you rotate it or move it around (well, not in Newtonian physics ...).

What special relativity says is that equation (1) needs to be extended to include movements in time as well, and the new form is:

$$ds^2 = -c^2dt^2 + dx^2 + dy^2 + dz^2 \tag{2}$$

(we multiply the time $dt$ by the velocity $c$ to turn it into a length in light seconds $cdt$ - that way we are adding lengths together). And again special relativity says $ds$ is an invariant and all observers will agree on its value. But note a key difference between equations (1) and (2) - in equation (2) we have a minus sign in front of $c^2dt^2$.

Equation (2) describes a fundamental symmetry of the universe called Lorentz covariance and it's this symmetry that requires time dilation to happen. Why Lorentz covariance should be a fundamental symmetry of the universe I don't know. That's just the way the universe is. To see how time dilation (and length contraction) arise from Lorentz covariance have a look at the question How do I derive the Lorentz contraction from the invariant interval?.

Physics explains how the universe works. It models the behavior of the universe as mathematical laws. The only help it can offer why one law is true is that it can be verified by experiment, or that it can be derived from another law. As in mathematics, this leads back to more fundamental laws until you reach "axioms." At this point, why can only be answered "because that is the way the world is."

But I expect the question isn't really "Why is the universe thus?" It is "Why is the universe different from what everyday experience leads me to expect? Why the apparent contradictions of special relativity? Why is correct physics so counter-intuitive?" This can be at least made more plausible by relating it to familiar situations.

Time is hard to understand because it has some of the same properties as space. We don't notice this because we move so slowly.

The speed of light is about $3 * 10^8 m/s$. We are comfortable at everyday speeds around $3 m/s$.

Consider a world where the fastest things moved at $3 * 10^{-8} m/s$. This works out to about $1 m/year$, the speed of a glacier. It is not much faster than $1 cm/year$, the speed of continental drift. What kind of physics would a glacier world physicist come up with? What would he think of everyday physics?

For one thing, he sees a fundamental difference between time and space. Objects move in time, but are frozen in space. The position of an object is an unchangeable property of the object. The vector distance from one object to another is an unchangeable constant.

In the everyday world, I stand on the side of a road and watch a car drive by. At $t_0$, the car starts at $x_0$. At $t_1$, the car arrives at $x_1$. On the other hand, the driver thinks the car is fixed. At $t_0$, the car seat starts at $x'_0$, right under him. At $t_1$, it arrives at $x'_0$, still right under him.

If two cars drive past me in opposite directions, we might all agree that I start at the same place, $x = 0$. One driver might think I arrive at a position to the south of the start. The other would think I arrive at a northerly position. I think I don't move.

None of us find anything remarkable in these disagreements about whether two events at two different times occur at the same place or not. It is a simple consequence of motion.

A glacial physicist would find these disagreements very confusing. He might accept that I can be in different places at different times. But he might wonder how I can arrive at multiple places at the same time.

The root of all differences between glacial and everyday physics is that time and space are more alike than he expects. You move in both time and space. He does not see that because he moves so slowly.

We have exactly the same problem when we think about relativistic physics. Time and space are more alike than we expect, but we move too slowly to see it. All of the differences between everyday physics and special relativity follow from this.

We see many counter intuitive effects at high speeds. It is customary to start with one, the constant speed of light, and derive all the other effects of special relativity from it. Einstein started this convention because it quickly leads to all the important math with only one new postulate. But it is certainly possible to start somewhere else.

We will start with some observations about cause and effect in classical physics. In quantum mechanics, cause and effect is not so simple. We will ignore quantum mechanics. Gravity also changes things. We will ignore gravity.

Suppose two events occur at the same place, but at different times. The earlier event might be the cause of the later one. Suppose two events occur at the same time, but different places. Neither event can be the cause of the other.

Suppose two events occur at different times and places. We can reduce this to one of the simpler cases above. Suppose somebody can drive at constant velocity from one event to the other. From his point of view, they occur at the same place and different times. This driver has proved that one can be cause and the other effect. Everybody else can rely on his proof.

In the everyday world, we expect time to be universal. We do not expect one observer to see the two events at different times and another to see them at the same time. We see no need to have separate descriptions of time for stationary and moving observers.

Never the less, we can state it this way. If one driver at constant velocity sees that two events at different places occur at the same time, then he has proved for everybody that neither event is the cause of the other.

So what is cause and effect in an everyday, classical world where we ignore gravity and quantum mechanics? For our purposes, pretty much everything can be reduced to one of these cases.

• Cause: particle 1 travels to particle 2 and collides. Effect: particle 2 recoils or something.
• Cause: particle 1 exerts an electrical or magnetic force on particle 2. Effect: particle 2 accelerates.
• Cause: particle 1 exerts a strong or weak force on particle 2. Effect: particle 2 accelerates.

This glosses over a lot. (E.G. Particle 2 explodes or annihilates particle 1.) But we are only interested in one essential feature: For an effect to occur, something must travel from the time and place of the cause to the time and place of the effect.

We won't consider strong or weak forces further. In this particular point, they behave like electromagnetic forces, but the full description quickly gets into quantum mechanics.

Classical electromagnetic forces are described by fields. If you wiggle particle 1, particle 2 doesn't feel the effect until the field travels from 1 to 2. That is, the electromagnetic field is the agent of cause and effect. For this case, cause and effect travel at the speed of the electromagnetic field. Or more famously, at the speed of light.

The situation is similar for particles. Nobody has been able to accelerate any particle with mass up to the speed of light. If we dip into quantum mechanics, photons are massless particles that travel at the speed of light. Cause and effect are again limited by the speed of light.

Hopefully this much makes it clear that the speed of light is more important than you might have expected. Perhaps it is a little bit reasonable that the speed of cause and effect should be the same for everyone, no matter how they move.

The standard derivation of special relativity still leads to the very counter-intuitive result that time is different for a moving observer. A space time diagram is the best way to see this.

It turns out that time and space are more alike than we expect. Every strange new feature of time is just like an everyday feature of space. We are confused by each feature of time in exactly the same way that a glacier world physicist is confused by the corresponding feature of space.

Confusing to a glacier world physicist: I see two events separated by a short distance and long time. A driver can choose a velocity less than the speed of light that changes how he sees positions. He makes the points occur at the same place from his point of view by driving from one to the other. Though I still see them at different places.

Confusing to me: I see two events separated by a long distance and short time. A driver can choose a velocity less than the speed of light that changes how he sees time. He makes the points occur at the same time from his point of view. (He cannot drive through them both.) Though I still see them at different times.

This doesn't make it any more intuitive. But I hope it helps to understand why simply going fast produces counter-intuitive results.

This is still pretty sketchy. Pictures would help. But I have run out of steam for tonight.

I think the answer to your question of are we able to tell why it happens is because we are able to predict, measure and mathematically demostrate time dilation.

• i was hopping for something like "The USA invaded Afghanistan because it was hosting terrorists/oil"... – Leonardo May 13 '15 at 13:27
• @Leonardo Actually, the question you have answered there is can be written imprecisely as "why did the USA invade Afghanistan?" but this is actually a shorthand for "what was the motive for the human decision to invade Afghanistan?". This confusion between "cause" (which physics seeks to explain) and "motive" (which has no place in physics unless you think the Universe is a person with desires and beliefs) is a common reason for people to be dissatisfied with the answers physics can give (i.e. causes) to "why is this true?" questions. – Mark Mitchison May 13 '15 at 15:23
• @MarkMitchison sorry for mis-espressing myself, I'm indeed looking for "cause" and not "motive"... please refer to the edit portion of the question. – Leonardo May 13 '15 at 17:28