# A question about motion and time dilation

I was thinking that if you are in empty space with another person (with no other objects around), and from a distance you see that the other person is approaching you a constant speed, you wouldn't actually know who is the one moving towards the other, you can assume that you're the one that's moving and he's at rest, or he is the one that is moving and you're at rest, making either assumption is correct, and the other person also has the freedom to make either assumption.

But I'm uncertain how it would be if we imagine the same situation with acceleration instead of a constant velocity, because one of you is experiencing time dilation.. Let's say you're the one accelerating towards the other person who is at rest, so after meeting him you're clocks wouldn't agree because of time dilation, right? So I have a question here:: Will you be able to tell that you were the one who was accelerating and he was the one at rest without having to check your clocks after meeting? (let's say the time dilation is not so huge that one would actually notice difference in age, and assume you can't sense inertia from acceleration, like you're just a camera)

Now I am not sure about that but I think the answer for that question would be: "No"

If the answer is indeed "No", then why does that happen? if you can't tell whether you're the one who is accelerating or the other person is, and either assumption can be correct, then why does only one of you experience time dilation?

Edit: @"because you imposed the artificial condition that you are unable to feel the effects of acceleration even though they would be there." What I meant is that can you tell you have accelerated (in empty space) depending only on observing another object? Or say, you have a camera in space that's filming an object which appears to be getting closer to your camera, can you tell whether your camera was actually pushed by something and the other object is at rest? or the other object is the one that's moving towards the camera?

I'm no expert, so I might not explained it properly, but , as far as I know, time dilation happens so that the speed of light remains constant, it seems to me that it's more valid to talk about observation rather than "sensing" acceleration physically, the light reflected from the object you see is affected by acceleration in some manner that it remains constant I believe, but even though you can't tell which object is accelerating and which is at rest, only one of them will experience time dilation.

• only one experiences time dilation because only one is accelerating. You cannot tell which one was accelerating without looking at clocks because you imposed the artificial condition that you are unable to feel the effects of acceleration even though they would be there. – Jim Apr 9 '14 at 18:33
• The one accelerating can feel the acceleration, or use a spring scale, or any number of other ways to detect a force resulting from the acceleration. This is why the "Twin paradox" is not a paradox. The twin that experiences acceleration is the one whose clock is slow. – C. Towne Springer Apr 10 '14 at 22:50
• @user43783: Congratulations, this is what General Relativity is all about. Begin by remembering that there is no absolute position, and no absolute time. – Phil H Nov 28 '14 at 17:07

Time dilation is linked to motion. Be it from acceleration, or velocity, or both.

It is because the speed of light is invariant for all observers. If this speed is the same, then what changes is 'time.'

As for the who experiences time dilation, the answer is both of you. You both feel time dilation with respect to each other. Time dilation is not 'whoah I'm in slow motion,' in fact you can only notice it when you compare it to something else.

What is stated above works best for constant velocity, but is still valid for acceleration. However acceleration adds additional forces, meaning you can still tell if you are accelerating by throwing a baseball and seeing if it travels in straight lines or not. If it does then you are not accelerating. This does not change time dilation though.

All inertial reference frames are equivalent. This is the most basic assumption of Special Relativity as well as Newtonian Mechanics.

This means that if you are in an inertial reference frame, say, a car moving with constant velocity, you can never tell if the car is moving or not (unless you look out of the window of course).

This is not true for a non-inertial reference frame, which is a frame which is accelerating with respect to an inertial reference frame. Now imagine that the car that you were in suddenly increases its velocity. You are suddenly pushed back because of inertia, ie. you feel a force pushing you back. This force is a clear indication that the car accelerated. You can also see this pseudo force by dropping a ball inside the car.

Coming back to the question, if you are accelerating towards another person, both of you will see each other accelerating towards one another but both of you will be able to check if you are accelerating or not. Your reference frames are not equivalent in this case like they were earlier.

You also added an assumption that you cannot feel inertia from accelerating, in that case, the whole point of a non-intertial reference frame is gone. You might as well consider an inertial reference frame then about which you already know. Only one of you will experience time dilation and you will not be able to tell who that person is without checking the clocks, in that case.

The most helpful path to getting your mind wrapped around physics of your question is to examine how you pose the question itself.

Most importantly, you write: "...with acceleration instead of a constant velocity, because one of you is experiencing time dilation"

This is wrong on a few counts: Time dilation occurs whenever there is relative motion, whether the motion is accelerated or not. Furthermore, you can't say that "just one" observer is time dilated while the other observer is not - each observer's time is dilated relative to the other (you don't need an observer there, or a thing, just lay two coordinate axes at an angle is spacetime and the projections of the spacetime intervals on to each other reveal time dilation).

Let's look at "you wouldn't actually know who is the one moving towards the other, you can assume that you're the one that's moving and he's at rest"

It may be helpful to think of it this way: It's not that we don't know which is actually moving but rather meaningless to ask which is moving - this is a subtle but important difference. For example, take two lines and draw a big "X" and then ask which leg of the "X" is really vertical? You can orient the paper any way you like, it's meaningless to ask. You simply have two lines at an angle. In spacetime, objects in relative motion have worldlines that form an angle. This is also the reasoning why you can't say which traveler is experiencing time dilation, or which is not.

Then there is the issue of acceleration. If you suggest that the acceleration is intrinsically undetectable by an accelerometer then you're operating in a universe with different laws of physics. If you send an accelerated object that simply doesn't record the acceleration then you need to look at the clocks. Assuming the clocks were synchronized at some point, the time for the clock in the free-float frame will be an extremum, and here record the minimum time, i.e., your accelerated clock will read the longer time because it actually traveled a great distance in spacetime.

The difference between unaccelerated (which includes stationary) and accelerated state is that in case of the latter you can actually feel (and measure) the force causing acceleration.

Example: Without looking out the window, you cannot tell whether the train you are in is currently moving or not (relative to Earth) unless there is some acceleration (increase or decrease in speed), which pulls you either back or forward. Yet when acceleration is actually applied, there is always a force that can be felt, or at least measured without any comparison to another body.

Therefore you do not need to compare clocks to tell if it is you accelerating or the other person.

Let's say you're the one accelerating towards the other person who is at rest, so after meeting him you're clocks wouldn't agree because of time dilation, right?

Let's make the thought experiment more precise. In some inertial frame of reference, a moving clock is located at $x = 0$ when both the coordinate time $t$ and the moving clock time $\tau$ are zero.

The clock is decelerating and comes to stop at $x = X$ and $t = T$. In other words, in the inertial frame of reference, the decelerating clock comes to a stop after $T$ seconds have elapsed and after travelling $X$ meters.

What can we say about the elapsed time according to the moving clock? According to special relativity, $\Delta \tau < T$; the moving clock will read less than $T$ when the clock comes to as stop.

Will you be able to tell that you were the one who was accelerating and he was the one at rest without having to check your clocks after meeting?

Of course, the accelerometer attached to the decelerating clock will give a non-zero reading - we say that the deceleration clock has a non-zero proper acceleration which is absolute, i.e., is independent of the reference frame.

Thus, the situation is not symmetric. The clocks in the inertial reference frame are unaccelerated (accelerometers read zero) and the moving clock is accelerated thus we can absolutely say which clock records less elapsed time.