I always find this connection between motion and time quite intriguing. Kant himself reasoned to the existence of time like so: "Changes are real. Changes are only possible in time. Therefore time must be something real." So, again, he based it on changes, on motion.
But that sometimes feels like saying that if we didn't have centimeters, distance wouldn't exist. It feels like time must exist whether or not something is moving or changing. I mean, consider the following: something moves in the universe (so now time exists) and then it stops (so now time doesn't exist). Then, after a while (during which time time didn't exist), something moves again. So, if time doesn't exist unless something moves, it means that there was no pause between the first move and the second move. So, for all we know, what I did a second ago could've happened a billion years ago, because if it did happen a billion years ago, and then everything stopped, and then resumed, time wouldn't exist during those billion years, because there was no motion. So, in a way, it's impossible for motion to stop completely, because we'd have no way of knowing it. Non-motion could only happen in non-time, i.e. never! Hope this thought experiment makes sense!
Your thought experiment is flawed, in that it fails to take into account important factors, such as the observers reference frame, memory and volition - for we the conscious beings/observers, and others. As a matter of fact, your understanding of time is to some extent in line with the kind that was believed in before the advent Einstein's theories of relativity and it was greatly advocated by Isaac Newton. That kind of time is referred to as Newtonian time, where time is considered to be absolute - the same for all observers and independent - it exists without dependency on anything including motion. Although before Newton, Galileo had discovered that time just like motion can be relative - not absolute, his theory is now referred to as Galilean invariance/relativity. Galilean invariance is an extension of Newtonian mechanics without regards to the speed of light in vacuum and Einstein's theories of relativity are extensions of Galilean invariance - taking into account the vacuum speed of light as maximum speed limit.
Now back to your thought experiment.
First of all, this is from the perspective of an observer "outside" the moving object. If the something is moving in uniform motion (technically uniform velocity), an observer "inside" the moving something cannot tell if he's in motion or not, in most cases he says he is not in motion, this is due to Galilean invariance and it's why despite the fact that our planet is in motion we still don't notice it. So therefore, it's only an observer "outside" of the something moving uniformly that can say with certainty that the something is moving. If in our reference (on Earth) we are at rest and time only exist when there's motion, then how do we still observe time ?
It basically has to do with the changes (motion) happening around us, note that we are not inside those things that are changing - we are outside them. With respect to time of the day (the one your wall clock reads), it's because "relatively" our sun is moving around our planet - your wall clocks are basically cliberated based on this motion (sun and Earth). Other types of time we observe are different from the time of the day, they are either called duration or interval and it's because they mostly exist for a limited period, e.g the time it takes when you move from your house to your work place. But that doesn't mean that because we exist inside a moving object we can't tell if it's in motion, we can tell if such object was accelerating - not moving uniformly.
Time doesn't exist to an observer that just came into existence after the motion (when motion stops). Here such observer wasn't aware/lacks memory that there was motion initially, in this state (no motion) he doesn't observe any change and can't tell time exists.
Here, it's still the same observer at first motion, no motion and second motion. For the observer to tell if there's no motion, he originally had knowledge of the first event (first motion) that happened, to tell if changes had occurred there must be something new which are the no motion state and second motion otherwise the observer cannot tell the difference between first motion, no motion and second motion. In this case, the memory of the observer has a role to play, if not for his memory, he can't distinguish between different events. Also there's what is called volition - the belief that whatever you do today affects tomorrow, this volition began a long time ago when man first started keeping track of time, especially time of the day and it has been a belief to this day, remember that the time of the day is on the other hand due to the relative "motion" of our planet and our sun. Memory and volition, especially for "the same" observer have roles to play and that's why there never appears to be a pause between the first motion and second motion in your thought experiment. Your thought experiment seems to be mostly based on your own experience in our universe, it's not really an ideal thought experiment to probe time and motion, plus you seem to be lacking in your knowledge of modern physics, especially relativity .
Yes my thought experiment was like an 'everyman's' thought experiment. Of course I know that in modern physics time and the other 3 dimensions are entangled (space-time), but I still preferred to base my thoughts on 'intuitions'. I also realized that the observer was always presupposed in the thought experiment, and if there's an observer then there necessarily is motion (like his eyes, his brain neurons, etc.), but it's probably impossible to make any thought experiment without an observer!
I think I understand most of your responses, but I don't know if I'm entirely clear on your reply to the 'stop-start universe' let's call it. Let's say that in our universe now, the one you and I inhabit, absolutely everything stopped moving right now. And then, after some 'time', everything started moving again. In fact, let's say that this happens to our universe every single second. For every second of motion, there are 'billions of years' of non-motion. There's no way, it seems to me, for us to know that this is not happening. We could be living in such a universe and not know it. Of course, I can't imagine such a universe without an external observer, because I am that observer! And how do I know those billions of years exist? Because there's motion in my head, I'm thinking consecutive thoughts, I'm maybe restless and jittery because I'm waiting for billions of years for this universe to start again, etc. But I don't know what this means exactly. Does it mean that, if we remove the observer, then those billions of years simply cannot exist, because time cannot exist without motion? On the one hand I can imagine everything just stopping, I don't feel there is anything logically contradictory in everything stopping, and remaining like that for a long 'time', but on the other hand I understand that we, as observers, can't detect time without motion, so if everything stopped, including us, then started again, there would in fact be no pause: if everything stops at the same time, there is no stop. In other words, it is impossible for the whole universe to stop. Things can only stop in relation to something that remains moving, because if nothing remains moving, then time does not exist for something to be stopped during that time. Therefore motion will always exist. There is no time during which there will be no motion anywhere. Therefore, the universe will always exist, and has always existed.
Thank you for your always detailed replies, and awaiting your next one.
I don't quite get the purpose of your thought experiment, is it meant to show that time depends on motion or not?
From what i can observe from your thought experiment and your conclusions, time depends on motion.
If everything stops moving in our universe, nothing would exist including you and I. If the universe comes back into motion and we are to exist again, then the universe would have to start all over from the beginning - big bang, and our memories would be reset. Who then is making the measurement of time throughout the whole event?, Is it an observer outside our universe or we in a reset universe ?
I would assume, the one second observed in our universe is with respect to an observer outside of our universe, the question now is, the billions of years you speak of, is with respect to what observer ?
There would be no pause with respect to the observer outside our universe because of his memory and volition, with those properties, he can combine all the events (before and after reset) and it would appear continuous - no pause. But for we in the universe, there would be pause because our memories have been reset (memory of the first motion is lost) when the universe started again.
The last time I checked, the universe is approximately 13.8 billion years old and it started with the big bang, it indeed had a beginning and it may have an end, it has not always being in existence. Now, you can see that your flawed thought experiment has led to a false conclusion. As at the moments of existence of our universe, motion is very necessary, that is, no motion, no existence (including our time : not including the time of an observer outside of our universe) but that doesn't mean our universe never had a beginning or would never have an end.
Like I said before you seem to be lacking in your knowledge of physics. If you still don't understand everything I've said here, then there's nothing much i can do and as consequence, i may not reply your next comment regarding this same issue - your thought experiment.
The purpose of the thought experiment was for me to try and understand things better, for example by asking whether something strange would follow from assuming that 'time does not exist if there's no motion'. So I asked you, since you seem to know more about this than I do.
Another question that I forgot to ask: why do you say that we would have no memory? If all the neurons etc. are in place, why won't starting them up again revamp all the memories that are encoded in the brain?
My knowledge of physics is indeed very superficial. But, strangely, it often turns out that my superficial knowledge is much deeper than the 'deep knowledge' others have. I'm not saying this is true in this case, just speaking generally.
Also, one doesn't need to know anything about physics to understand time. Once, a mathematician told me that the circle has been squared. I asked for details, and he gave me taxicab geometry. I said that the taxicab geometry 'proof' could just as easily be construed as a proof that something about the definition of 'circle' is lacking. It's a decision, and mathematicians and scientists do it all the time. For example if there are 2 good solutions to a problem, but one solution leads to a dead end, and another solution leads to opening many further research opportunities, mathematicians and scientists will always prefer the latter. No one knows what physicists will think about time in 100 years. But the important thing is that 'circle' is not something that belongs only to mathematicians, they are not the only ones who have the right to define 'circle'. The same is true of time: we all experience it, it belongs to all of us, we can use logic to think about it, we don't need to know anything about physics, just as Darwin didn't need to know anything about genes to know that natural selection was real. I think you will agree with me that the circle definitely has not been squared, nor can it ever be squared, because that would just be ridiculous (illogical). That is true despite the fact that my knowledge of mathematics is very superficial.
To see if I understand your conclusion: are you saying there was a time when the universe didn't exist? And are you saying there will be a time when then universe won't exist?
I appreciate your time and your effort at explaining things to me. It's okay if you don't reply to this.
Maybe another way to phrase my last question is like so:
Does the question "Did the universe exist 14 billion years ago?" have any meaning? Is it possible to answer such a question? Do physicists have an answer to that question?
For now, our universe seems to have no information about it's existence beyond 13.8 billion years ago. So yes, the universe existing 14 billion years ago is meaningless for us inside of it, "for now".
I don't totally blame us for having different perceptions of the same things and still call them facts, after all, why do we have subjective consciousness. Anyways, good luck with your "superficial knowledge", who knows the kind of discoveries you may make.