What is the actual cause of time dilation? Does it depend on magnitude of velocity? Or does is also depend on direction?

Question

Hi I was having after thoughts after learning about time dilation in relativity and had some questions. I was initially taught if there were two space ships traveling relative to each other, the time of the clock in spaceship 1 that person in space ship 1 sees will differ from the time of the clock in space ship 1 that a person in the spaceship 2 sees. To me, it sounds like the cause of it is the observer's relative speed to the light that delivers information about clock. So this got me wondering if the time dilation occurs in an isotropic manner or if it only occurs in the direction of travel in space.

Here is an example that relates to my question: I travel down a road towards North from the starting point A, so that there was a time dilation between myself and stationary people along side the road, because of the relative speed of light that reaches from myself to the people and the relative speed of light that reaches from the people to myself. Then if there were bunch of people from somewhere down the road east from the starting point A, so that the light that reflects off them cannot reach me, obstructed by buildings, would there still be time dilation between those people and me? Thanks

Answer 1

"I was initially taught if there were two space ships traveling relative to each other, the time of the clock in spaceship 1 that person in space ship 1 sees will differ from the time of the clock in space ship 1 that a person in the spaceship 2 sees."

This may well be the case, but it's not what time dilation (TD) means. TD is not due to the transit time of light (though arguments that it must take place may involve the transit time of light).

Special Relativity demands inertial reference frames that are supposed to be equipped with (synchronised) clocks at each point in space, so that an event can be assigned a time (from a clock right next to it) as well as well as three spatial co-ordinates.

We can therefore determine the time interval – call it $\Delta t$ – between two events in one frame (S) and in some other frame (S') – call it $\Delta t'$. Fairly obviously the spatial separation of the events will also be different in S and S'.

We can show (at an introductory level using the transverse-rod-and-mirror thought experiment) that the time between the events is the shortest (call it $\Delta \tau$) in the frame in which the events occur in the same place ($\Delta x=0$). The time between the events in any other frame is given by $$\Delta t = \frac{\Delta \tau}{\sqrt{1-\frac{v^2}{c^2}}},$$ in which $v$ is the relative velocity between the frames. This is what is meant by time dilation.

TD is, then, a consequence of the nature of time and space, and not really about light. More could be said about the role of $\Delta \tau$. TD is often summed up as "moving clocks run slow", which is fine if you know what it means! What it doesn't mean is that moving clocks, as read by someone moving relative to them, read slow.

Answer 2

Time dilation is caused by one strange property of the universe: The universe has a maximum speed at which things inside of it can move. No object can move faster than this speed at all. Objects without mass [such as photons, the particle of light] move at this speed, but not faster—we say "the speed of light," but it'd probably be better to say "the maximum speed of the universe," because other things can also move at this speed, not just light.

Speed, we know, is $\text{length-per-time}$. That is, an object's speed can be quantified in units that measure how far it's gone over a certain period of time. (i.e. - $\text{miles per hour}$ or $\text{kilometers per second}$).

So, why does the existence of a maximum speed (let's call it $c$) cause time-dilation? Well, an object's speed is relative. If I'm standing still, and you're moving in a car that goes past me at $60$ m.p.h., then when I clock you with a speedometer, your car is moving at $60$ m.p.h. But, what if you're still driving at $60$ m.p.h., and I'm driving passed you in the opposite direction at $70$ m.p.h.? To me, your car would be moving at $130$ m.p.h. (even though you maintained the same amount of pressure on the gas pedal).

Well, ok. That still doesn't really explain why time dilation occurrs. But think of this: What happens if your driving at $(2/3)c$ (that is, two-thirds of the speed of light) and I'm driving passed you, in the opposite direction, also at $(2/3)c$ ? Then, when I clock you, you should be moving at $(4/3)c$ ... right?

But there's a maximum speed that anything can be moving in any frame of reference. So I can't clock you at $(4/3)c$, because that's faster than the maximum speed. Let's say I'm measuring your speed in $\dfrac{\text{kilometers}}{\text{second}}$. Since I can't measure your speed as $(4/3)c$, it must be that I measure your speed as less than $c$ (since $c$ is the maximum).

How does $\dfrac{\text{kilometers}}{\text{second}}$ suddenly get... smaller?

It gets smaller if the $\text{second}$ in the denominator increases (time dilation) or if the $\text{kilometers}$ in the numerator decreases (length-contraction). That is—in order for this scenario, where we're driving passed one another at $(2/3)c$ to work out while the universe has a maximum speed, your $\text{second}$ must be longer than mine. Thus, time dilation. It is caused by the fact that the universe has maximum speed at which anything can move, in any frame of reference.

Answer 3

Hi I think this is answered in the math surrounding this answer (Relativity tangential light clock, in which I do a basic derivation of Lorentz contraction [lots of ways to do it, btw])

In summary, then, the initial impact of relative velocity is indeed directional. Of course it would be, relative velocity is a vector. Light and therefore the rate of interaction of all things takes longer in that relative direction.

The next step is to consider that time is perceived by us as scalar. I mean, intuitively you just wouldn't build a physics in which the rate time elapsed varied with direction. (Now I'm sure there's a theorist or two out there who's tried it, of course ) In terms of the "equivalence principle", the founding assumption of relativity, we are looking for scalar [directionally homogeneous] time in each equivalent frame. This so that the same physics works in these frames.

Our perception/measurement of the universe has to cope with this? We perceive that, in essence, everything in the direction of travel outside our own frame appears shorter, the famous "length contraction" phenomena. Things are shorter by exactly the right amount to achieve our perception of scalar time in those other frames. Shorter by exactly the right amount to make our laws of physis apply so that frame is equivalent to our own.

Answer 4

First of all, you have to realize that visual observation is not measurement. There is a difference. Visual observation is when the photons , or light rays from some object reach your 'eye'( i.e the measurement device located at some specific point in the co-ordinate system).

Now, imagine you laid your co-ordinate system and placed a clock at every point in space, so that whenever an event happens, the clock at that point records the time. This is measurement.

Time dilation is a real phenomenon and the reason is Relativity of simultaneity. Both of them would say that they are right and the other person is wrong because they would say that the clocks of the other observer is not synchronized and hence, time dilation takes place.

To summarize, It's because of the fact that the speed of light is same in all reference frames because of which simultaneity becomes a relative concept bcz of which the clocks appear unsynchronized and time dilation takes place.