But in that case time dilation would be dependent on acceleration rather than velocity and the clocks would not have shown a difference .
The time experienced remains different. But there is no displacement.
Your travel around the world relative to someone staying at home is the same as taking one of the two different paths to travel somewhere. Once you come together agin, you are both in exactly the same location in spacetime. Nobody is offset for the other. You prior experiences are different, And if we had the capability, we might be able to detect the result of those differences in experience. But there is no intrinsic offset.
You claimed there would be a distance displacement without qualification. Just as you assert there must be a time displacement. It is exactly the same physics. Once you come back together again you are in the same location in spacetime. There is no displacement, just different experience.
No, and neither will you reset. There’s a fundimental misunderstanding here, The clocks experienced time at different rates to an outside observer, but each clock experienced time at 1 second per second. Just like when you were on the plane you experienced time at 1 second per second and your granddaughter experienced time at 1 second per second, even though to an outside observer they might look different. Once they’re moving in the same frame of reference they track time identically, even if they no longer are in sync.
By definition, you and your grand daughter are in the same place in time (same frame of reference). There’s no residual effect of your previous travel on your current state.
To measure the time dilation an oscilloscope would have to experience the time dilation. It would have had to travel with you, and you would have needed to start a second oscilloscope and leave it at home. You could then measure the difference only when you bring the two oscilloscopes together. You can calculate the time difference any number of ways, but to measure it the instruments must experience it. And that ship has sailed.
Then the clock experiment was faked?
Yeah, I dare you to try it
It’s a thought experiment. Would you prefer the phrasing “Let’s say you travel around the earth at nearly the speed of light”
Of course not. The clocks read different time when brought back together representing the time dilation, but now that they are back together they will keep track of time exactly the same. They will be 2 microseconds off of each other but that difference won’t change.
“There’s no residual effect of your previous travel on your current state.”
How can the two clocks no longer be in sync if there is “no residual effect”?
And that is the point I am making - we are out of sync by 2 microseconds. Can we figure out a way to measure it?
No. The clock experiment is valid and correct. The clocks now have different prior experience. One has seen more time pass than the other. They are now back together in the same location. They are now at the same location in spacetime. There is no contradiction here. Just physics.
The key point is that there is no intrinsic time property that objects carry. Everyone experiences time - proper time - for themselves. If you are co-located with something else, you experience the same proper time. There is no absolute time, and since it doesn’t exist, you can’t be displaced relative to it.
You are simply the result of your past and where you are right now. But I can only tell your past based upon the currently existing state you have. A clock may have seen slightly less time pass, so appears slow to me, or in the case of the twins paradox, one person may be clearly older. But what there isn’t is some displacement against an absolute reference. There isn’t an intrinsic time property that can be measured.
If you reset both of those clocks to the same time they would be indistinguishable. They “lived” different amounts of time but that’s not a property of the object. You as a person have no way to measure time - you lived 1 second per second and always will. Same with the clock. The two clocks just lived different seconds.
That is why the clocks or oscilloscopes have to experience the time dilation so it shows on their readings. You can’t look at a person or object and see how much time they experienced unless they are synced before the experiment and brought back together at the end. They have to be measuring time during the experiment.
But it is in the two clocks. The clocks just have an incidental observable property.
You are not out of sync.
No. The clocks have different experience. What they have experienced is exactly the same as two travellers travelling along different roads. Each counts their paces. They arrive together, and over breakfast compare how many paces they took. They are different. But how can this be? They are in the same place!? There is no intrinsic property in our travellers that we can measure that tells us which took the longer route.
This is exactly what the two clocks experiment is.
The clocks are in the same place but their experience (time) is out of phase. Has to be residual or you could not read it.
I suspect we’re reaching 0.999… =/= 1 territory.
Not at all. 2 microseconds is a world of time in computers.
It is residual in the state of the object. It is not an intrinsic offset against an absolute time. The time offsets are identical to the difference to the number of paces difference in our travellers.
You are not wrong, but you need that wristwatch or else there is nothing to read (pursuing those thoughts to their logical conclusion is how Einstein came up with the whole model in the first place). NB I hope there is no confusion in anyone’s mind between where the clock is now (some place) and it’s entire history.
So PS I cannot think of a way to measure your time dilation displacement. Had you been to Andromeda, you would probably notice your identical twin is a few million years older, but there is still nothing to measure directly.
I was referring to the atomic clocks. I don’t fully understand your traveler analogy.
Had you brought such a clock along with you for your entire life’s high speed travels, and also left one behind sitting at home, the difference would be clear and obvious on the clocks’ faces. They’d be ticking along merrily now at exactly the same rate sitting side by side, but offset 2 us from each other.
The problem is that since you didn’t think to set up those clocks first, there is no tool you can use now to re-create or re-measure retroactively that accumulated difference.
You are certainly free to calculate that your difference has to have been e.g. 2 us, and then adjust one clock to match your calculation, thereby observing the difference in thier readings. But that doesn’t prove anything.
Agreed, and I am looking for a post hoc wrist watch. The scope is an indicator like the read out on the clocks and doesn’t have to experience the travel.
Conceptually it seems like the kid and I could both align a pulse or phase with a reference there would be a 2 microsecond difference in the result. These values are easy to work with so there’s no challenge there. I’m looking for ideas on the method.
Like I said, unless you buy some atomic clocks and put them on planes, there is no reference. Perhaps one could do something with observing GPS satellites?
Or find some Doppler shifts you can measure, could be a fun experiment for a kid.