# How does velocity cause time dilation?

I've been trying to learn about the speed of light and time dilation, but I'm at an impasse.

The presented facts say that if I travel around the solar system at 50% the speed of light and then come back to earth I will have experienced less local passage of time than them. I will effectively have traveled to their future. I've also read that gravity causes time dilation too.

I understand that space-time is a sort of unified thing and that affecting space affects time. It makes sense then that gravitational forces bending space will also bend time. But velocity? I can't wrap my head around it and I can't find a good explanation for it.

People cite orbiting craft and planes as proof of time dilation, since their clocks will go slower than those in the surface (and vice-versa). This certainly explains gravitational time-dilation, but not necessarily velocity. Can't the change in local time passage be caused solely by the gravitational bending of space-time?

Trying to find an answer, I came to a very recurring and frustrating example in texts that seek to explain time dilation. A man on a moving train throws a ball forward. Since he's moving with the train and the train is his point of reference, the ball to him only moves at the speed he threw it. But to a woman on the station the ball is moving at the speed of the train plus the speed it was thrown with. To some authors, this seems to open the mind to time-dilation understanding. To me it only explains the relative nature of motion. It says nothing of time.

Another example I've found: if person A speeds away from person B very quickly, A's clock will seem to advance slower from B's point of view. How is this time dilation, though? The difference can be explained by the longer time it takes light to get to B, can't it?

I realize I can't be right against the fine physicists out there, so I was hoping someone here could enlighten me. Where does the notion that velocity causes time-dilation come from?

• Another way to intuit it.. superman can fly as fast as a speeding bullet - go superman! If superman flies nearly as fast as the bullet it is moving slowly awa from him. However, if the bullet were moving at the speed of light, he would see it speeding away from him at light speed, even if travelling at .9c. The only way this could be true is if time were slowing down from his reference point. This analogy helped me twig it! – Mark D Jan 7 '16 at 22:01

Special relativity (let's leave aside GR for now) is notoriously unintuitive - generations of physics students have found this to their cost, so you are far from alone. So there is no simple intuitively clear explanation over what is going one. That said, I will attempt a quasi-intuitive explanation.

I think the mistake students make is to take time dilation in isolation. It's easy to think here's a phenomenon called time dilation: what causes it? What actually happens is that different observers will disagree about what constitutes space and what constitutes time and time dilation is just part of a bigger phenomenon.

As I sit here at my keyboard I'm not moving in space, but I am moving in time. So for some activity (e.g. from the start to the end of me typing this sentence) my $\Delta x = 0$ and my $\Delta t = T$ for some time $T$. However the bug eyed alien that has just zoomed past at $0.9c$ disagrees. The alien, seated at their own typewriter, sees me moving at $-0.9c$, so in between starting and finishing my sentence the alien sees that I have moved some distance $\Delta x = d$. But in SR space and time are linked, so if the alien measures a different $\Delta x$ they must also measure a different $\Delta t$. The two are linked by the relationship:

$$c^2 \Delta t^2 - \Delta x^2 = c^2 \Delta t'^2 - \Delta x'^2$$

where the unprimed $t$ and $x$ are what I measure and the primed $t'$ and $x'$ are what the alien measures. Even without doing the maths it should be obvious that because $\Delta x < \Delta x'$ it follows that $\Delta t < \Delta t'$. In other words when the alien times how long it takes me to type the sentence they measure a longer time than I do. For the alien my time has been dilated.

You've probably also heard of length contraction. Well this is the other side of the coin. Time dilation and length contraction always occur together because in effect some of the time is being converted into length and vice versa.

All this follows from a fundamntal symmetry called Lorentz invariance. This states that if we measure a property called the line interval and defined by:

$$ds^2 = -c^2dt^2 + dx^2 + dy^2 + dz^2$$

then the quantity $ds^2$ is an invariant and all observers will measure the same value for it. To get the equation above linking my $(t, x)$ with the alien's $(t', x')$ I just exploited this invariance to require that $ds^2 = ds'^2$.

All very well, but I have really only pushed the non-intuitiveness one stage farther down, since my explanation assumes Lorentz invariance and this in turn is unintuitive. Still, hopefully this allows you to get some handle on what is going on.

First, for observers in uniform relative motion, time dilation is symmetric: A observes B's clock to run slow; B observes A's clock to run slow.

Second, for "twin paradox" type scenarios, the situation is not symmetric. If you travel outward from Earth at 50% of the speed of light and then return, your worldline between the two events (one event is your leaving, the other event is your returning) is a much different path through spacetime than those on Earth.

But, it's an elementary result from SR that the straightest possible path between two events in spacetime has the longest elapsed time. Any other path, has less elapsed time.

I can't find a good explanation for it.

This is a well known, well understood result that (1) has been explained here many times, (2) has been explained in many fine and not so fine textbooks, and (3) has been explained in many ways and many places online.

My question to you is: what specifically, with all these explanations available to you, isn't clear or isn't "good"?

Your 3 points may be right, but whatever explanation I find are insufficient for an ordinary man like me to understand. I was hoping someone here had a better ability to teach.

And teachers often hope (even despair) for students with the desire to learn rather than to be simply taught. A teacher can only guide learning.

Here's a simple animation that shows time dilation due to motion. It's from this online explanation: All that's required to intuitively grasp time dilation due to uniform motion is

(1) by stipulation (postulate), all uniformly moving observers measure the same speed c for light and

(2) the distance light travels for the moving light-clock is longer than the distance light travels for the stationary light-clock.

Do you agree?

• I'm sorry but I can't understand what you said in your 3rd paragraph. I know this is all fact, but I feel as when I was younger and nobody could explain to me what fire was or gave me odd incomplete citations of how mass caused gravity. Your 3 points may be right, but whatever explanation I find are insufficient for an ordinary man like me to understand. I was hoping someone here had a better ability to teach. – user48721 Oct 30 '13 at 2:56
• I know now that fire is a chemical reaction between oxygen and a material that happens when enough heat is achieved. The particles react and form new compounds, changing in density and elevating, while also radiating light and heat. If I visualize space as two-dimensional I can understand the distortions that mass create in what we call gravity. But I don't understand this. It hasn't been explained simply enough, if you will. – user48721 Oct 30 '13 at 3:03
• @user48721, the simplest, most intuitive example to explain time dilation due to motion is the moving mirror light clock. pitt.edu/~jdnorton/teaching/HPS_0410/chapters/… What about that explanation isn't clear? – Alfred Centauri Oct 30 '13 at 10:47
• I know I'm 3 years late, but I have to ask this. In that animation you posted, imagine that the light-clock of the right returns to its initial position. At the end of the trip, the light-clock of the left would have witnessed itself tick 8 times and the light-clock of the right to have ticked 4 times. However, from the light-clock of the right's point of view, the light-clock of the right is the one moving, therefore, at the end of the trip it would have witnessed itself tick 8 times and the light-clock of the left to have ticked 4 times. How do we unravel this contradiction? – AxiomaticNexus Feb 25 '16 at 21:16
• @user21820 This is the answer I always get, "oh, there's acceleration now, so general relativity does not apply", and the response ends there. No one goes on to explain what actually happens to the accelerating light-clock with or without general relativity. So, what happens to it? – AxiomaticNexus Mar 6 '16 at 19:41

An effect related to time dilation is length contraction - objects moving in a certain direction are shortened in the direction of their motion.

The first person to come up with this idea was Fitzgerald, and he did it in 1889 - 16 years before Einstein published on special relativity. At first, they didn't have a good idea of why things should contract. They just noticed that if things contract, it explains some puzzling experimental results about light and interferometers. So people started trying to find the reason things contract - if they're contracting, what's pushing on them? Lorentz, Heaviside, Poincare and probably some others built up a theory based on the idea of the aether - the hypothetical medium through which light travels. They thought that the forces that hold atoms together work in such a way that when you start moving through the aether, everything gets physically crunched down. (I personally don't know the details of this theory; there is no need to learn them, since it is incorrect.)

Einstein's theory showed that nothing of the sort is happening. Things aren't getting crunched down by aether winds at all. In fact, there is no aether, and no such thing as movement in an absolute sense.

Instead, in relativity, different people simply have different frames of reference, and measurements in one frame of reference don't transform naively into another frame of reference.

Taylor and Wheeler's textbook uses the analogy of two surveyors, one who measures land based on magnetic north, and one who uses geographic north. They will tell you different numbers about how far east-west and north-south your land extends because they have different coordinate systems based on their different (rotated) frames of reference. Just so in relativity. In different frames of reference, you will get different numbers for the distance and time between different points in spacetime, just as the surveyors will get different east-west and north-south coordinates. These different space and time coordinates mean that in different reference frames, we observe durations and lengths to be different. But it's not a dynamical effect. There are no velocity gremlins that pop out of the quantum foam and make clock hands start running through molasses. It's purely kinematics.

Okay, but why should observers in different frames have different coordinates for space and time? Why shouldn't everyone say the times are all the same? Well, why should they do the opposite? Why should time be some special, absolute thing that is the same for everyone? The natural thing that most people have in their mind is that time has some sort of default state, so that it goes by at the same rate for everyone, and then if you want to change that, you'd need some special vortex-reality-warping Star Trek effect to come in and slow it down. Learning special relativity is learning to let go of that bias.

What nature does isn't related to satisfying our intuitions. It's just about following rules. The central rule to relativity is the idea that all of physics is the same, no matter your velocity, and further that when you switch between reference frames, all the space and time coordinates transform into each other so that distances and durations change. There's no real justification for this. It's just the rule that we've found nature to follow. It's not happening by some particular mechanism of giant scissors slicing up spacetime and making all the readings come out different. It's just a hypothesis that coordinates transform in this way.

That hypothesis can certainly be stated in many different ways. Most introductory textbooks take it as a hypothesis that the speed of light is constant, and from that fact derive how the transformations have to work. Or, you can take it as a hypothesis that the spacetime interval between events is invariant, and work out the transformation rules from there. (This is what John and Alfred's answers do.) It doesn't really matter, though. At some point you are just taking it as a hypothesis that this is how spacetime works, and we have accepted that there's nothing in physics that matches the anthropocentric idea of "making it happen".

Not sure if you're still looking for an explanation about this since was posted 4 months ago.

The animation posted by Alfred Centauri is a great example. In fact, this is the illustration that Einstein used in his thought experiment. If you look at the light beam, imagine that every time the light beam reaches one side (mirror or origin/flash light), you have one tick on the clock. The speed of light is constant.

The speed of light is the same when going back and forth in the lab. Now, the speed of light is also the same when it's inside the rocket, only here, the speed of the light beam is in the direction of the path drawn in the animation. The light beam is deflected by a certain angle because of the motion of the rocket. Now, the light beam's velocity is being "shared" between a vertical and horizontal motion. Since a portion of the light ray's velocity is being used to travel horizontally, some of that velocity has to be "taken away" from the vertical velocity.

The velocity of the light ray in the rocket has two components now. One component in the horizontal direction and one component in the vertical direction. Since the total velocity has to be "shared" between horizontal and vertical, the vertical component of velocity is smaller now because it needs to be added to the horizontal velocity. The amount of progress that the light ray makes towards traveling towards the mirror is being subtracted, or taken away. Remember, each time the light ray reaches one of the two sides of the lab (or rocket), it's one tick on the clock. The light ray's vertical position along the lab/or rocket is synonymous with the passage of time. So, when you look at the animation, compare the light ray's vertical position in the lab with the light ray's vertical position in the rocket. The ray's vertical position in the lab is always greater than the vertical position of the light ray in the rocket. That means that the time that has passed in the lab is greater than the time that has passed in the rocket. How do we make that conclusion just by looking at the position of the light ray? Well, time $$t=\frac{d}{v}$$ distance divided by speed. This means that time is proportional to the distance the beam has to travel. So, the passage of time in the lab is faster than the passage of time in the rocket. Space and time are very closely related. If you stand still, you are passing through time. But if you want to pass through space, you have to trade that space with time.

This also took me a long time to figure out, here are some things that made the whole idea much simpler. This for a moment discards frames of reference, to bring things into being understandable in Newtonian Physics

Time does not actually slow down. It's only that time in any way we can possibly measure it slows down. Because the 2 ideas are the same for physics we simply call it time slowing down.

So if we stop measuring time by some god method, and start thinking about time as it is perceived, we can think of the fact that we measure time by events. For instance the tick of a clock, or radioactive decay of a particle. So if all events were to slow down we would call it time slowing down.

Now lets imagine something traveling at he speed of light. This means all parts of it are traveling at the speed of light. Now let's think it is a mechanical clock. A mechanical clock has moving parts to keep track of time. The problem is though none of these parts could move. If any of them would, some part of the clock would exceed the speed of light. As this can't happen the clock is perfectly stationary in it's own frame and "time does not pass". Our radioactive particle would be affected the same way.

Getting away from the impossible situation we can go back to the 50%. At this point objects can only dedicate half of their motion to events, and the other half to traveling. This is what creates the perceived slowdown

At very high velocity, time is dilated with respect to an observer. The speed of light remains constant but since the distance that the light must travel increases, the time that it takes for it to travel from say a point A to a point B is longer than if it were stationary relative to the observer.

time delation is very simple phenomenon.Time delation occurs because the speed of light is same for all observer in same media.so the rate of time experienced by the observer changes with respect to object moving near to speed of light because two events in space time having different time origin with respect to each other never coincide with each other.

# 1st Law of Motion

Every object in a state of consistent motion tends to remain in that state of motion unless an external force applied to it.

# 2nd Law of Motion

It is pertaining to the relationship between an object’s mass, its acceleration, and the applied force. In this law, the direction of the force vector is the same as the direction of the acceleration vector.

# 3rd Law of Motion

For every action there is an equal and opposite reaction.

Generally speaking, there are two categories of motion i.e. the constant and the variable motion. When we mention that a rising force of something would generate a new equal opposing force, such as the Newton’s third law of motion, we are actually referring to a process of action and reaction under a circumstance of constant motion (constant opposing forces). In other words, we could mention that the come factor is equal to the become factor: -

Come factor = Become factor

However, under a circumstance of variable motion, the opposing forces would orientate in a unique harmonising mechanism, such as the Newton’s second law of motion, shown as below: -

Scenario 1 - Acceleration

When come factor accelerates, the relative become factor would decelerate: -

Force A come ↑ Force A become

For example, the thought experiment of twin paradox which concerns a twin who flies off in a spaceship traveling near the speed of light and returns to discover that his or her twin sibling has aged much more. This scenario depicts the circumstance of time dilation in Einstein’s special theory of relativity. Literally, the acceleration of spaceship would decelerate the becoming process of the twin who sits inside it. The deceleration of the becoming process would mean the slowing down of the aging process for the same twin. In other words, the mental and the physical progression of the twin who sits inside the spaceship would slow down relatively.

Scenario 2 - Deceleration

When come factor decelerates, the relative become factor would accelerate: -

Force A come ↓ Force A become

For example, if the speed of the car decreases, it is literal to speak of deceleration; mathematically, it is acceleration in the opposite direction to that of motion and vice versa. Besides, this scenario explicates that a physically sick or a mentally stressful individual is advisable to go for a full resting at home or a cool vacation elsewhere for this state of affairs would decelerate the come factors in or around the same individual. Consequently, the process of recuperation on the same individual, both mentally and physically, would speed up.

## protected by Qmechanic♦Sep 20 '14 at 7:13

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