Moving clock, what exaclty "ticks" slower then the stationar

[revv]

I am wondering when people say moving clocks "ticks" more slowly then the stationary clock what exactly is ticking more slowly?

Is it the mechanism in the clock itself?

Like the actual gears inside the clock?

 

[Dale]

Yes. The actual mechanism ticks slower, regardless of what that mechanism is.

 

[revv]

So the mechanism in the clock "moves or ticks" slower in any direction in the air or space then the stationary one if I understand correctly?

And at the quantum level what exactly happens? Do we know?

 

[rootone]

Even the duration of atomic half lifes change for the moving object.
This is from the point of view of the stationary observer remember.
Nothing changes at all as far as the object moving is itself concerned.

This is a consequence of relativity, There is no reason to suppose quantum effects play any part.

 

[phinds]

Yes. The actual mechanism ticks slower, regardless of what that mechanism is.

Hm ... that doesn't seem to me to be a good way of expressing what happens, since it implies to the beginner that the effect is true locally, which it is not. The clock does not actually tick at a different rate than then other one, but it ticks a different number of times because it is on a different world line. Dale, I know you know this, but I'm questioning why you expressed it the way you did.

 

[UncertaintyAjay]

Hm ... that doesn't seem to me to be a good way of expressing what happens, since it implies to the beginner that the effect is true locally, which it is not. The clock does not actually tick at a different rate than then other one, but it ticks a different number of times because it is on a different world line. Dale, I know you know this, but I'm questioning why you expressed it the way you did.

Could you expand a bit on that for relativity novices? The world line thing?

 

[Nokx]

I believe it goes like this. Spacetime has four dimensions that include time, and when one object is moving at a nonzero speed relative to the observer, then the dimensions get shifted, sort of like turning the axis on a coordinate system, so that time and distance progresses differently for the observer than the object. In this case, the worldline is the path of the object over each instant of time, and the worldline would be difference for the object and the observer in terms of the position of the observer.

 

[phinds]

I believe it goes like this. Spacetime has four dimensions that include time, and when one object is moving at a nonzero speed relative to the observer, then the dimensions get shifted, sort of like turning the axis on a coordinate system, so that time and distance progresses differently for the observer than the object. In this case, the worldline is the path of the object over each instant of time, and the worldline would be difference for the object and the observer in terms of the position of the observer.

That seems to me like a good explanation, and to add a bit to it for the uncertainty man, another way of looking at it (disliked by some) is that everything is always traveling at c relative to you in spacetime but normally things are doing all, or almost all, of their traveling along the time axis so there is little or no disagreement on time. BUT ... when things travel along the distance coordinates relative to you, and at a very high speed, they are using up some of their total travel allotment of space time and thus do not travel as much in time.

SO ... if I travel away from you at a high speed and then come back again, I've traveled more in space and less in time, so we disagree on how much time has passed when we get back together and I will be younger than you even though along the entire space-time paths both your clock and mine ticked at one second per second (mine ticked fewer times). This is known as the "twin paradox" and is explained in approximately 17,000 places on the internet.

 

[UncertaintyAjay]

"Uncertainty -man" I think I like that.
Thanks for the explanation. So basically , the world line thing is saying that you can't really say that the clock ticks slower, only that it appears to tick slower for an external observer because, for the guy traveling at a high speed, the co-ordinates have been transformed. Is that right or have I missed the point?

 

[UncertaintyAjay]

Yeah, Ik about the twin paradox and all that. I read about relativity from the Feynman Lectures Volume 1. I've just never come across mention of the world line. Thanks for the explanation.

 

[Dale]

And at the quantum level what exactly happens? Do we know?

Atomic clocks show the same behavior at the quantum level.

 

[Dale]

Hm ... that doesn't seem to me to be a good way of expressing what happens, since it implies to the beginner that the effect is true locally, which it is not. The clock does not actually tick at a different rate than then other one, but it ticks a different number of times because it is on a different world line. Dale, I know you know this, but I'm questioning why you expressed it the way you did.

Well, any question posed in English requires a bit of translation to get it to something that can be answered. So I assumed that he was asking about $d\tau /dt$ for a clock, which does decrease as a clock moves fast in any given frame. You are saying that $d\tau/d\tau$ is always equal to 1, which is also correct.

 

[phinds]

"Uncertainty -man" I think I like that.
Thanks for the explanation. So basically , the world line thing is saying that you can't really say that the clock ticks slower, only that it appears to tick slower for an external observer because, for the guy traveling at a high speed, the co-ordinates have been transformed. Is that right or have I missed the point?

Yeah, I think you have it

 

[phinds]

Well, any question posed in English requires a bit of translation to get it to something that can be answered. So I assumed that he was asking about $d\tau /dt$ for a clock, which does decrease as a clock moves fast in any given frame. You are saying that $d\tau/d\tau$ is always equal to 1, which is also correct.

Fair enough. thanks.

 

[UncertaintyAjay]

Thanks phinds. If i may ask, What's dτ/dt? Or, basically, what's τ?

 

[Dale]

"Uncertainty -man" I think I like that.
Thanks for the explanation. So basically , the world line thing is saying that you can't really say that the clock ticks slower, only that it appears to tick slower for an external observer because, for the guy traveling at a high speed, the co-ordinates have been transformed. Is that right or have I missed the point?

Yes. Phinds point above is more focused on the worldline. That is the part that is important for the "internal observer" and the actual physics. My point is more focused on the coordinates. That is the part that is usually intended to express an observers "perspective".

 

[Dale]

Thanks phinds. If i may ask, What's dτ/dt? Or, basically, what's τ?

$\tau$ is the time measured locally by a given physical clock, no synchronization involved. In terms of the worldline it is the length of the worldline, or the distance along the worldline between two events.

 

[UncertaintyAjay]

Another question if I may, phinds referred to a travel allotment- what determines how much travel through space time a body is allotted?

 

[phinds]

Another question if I may, phinds referred to a travel allotment- what determines how much travel through space time a body is allotted?

Well, that's a "pop-science" explanation that I happen to like, but I have no math to back it up. Basically the limit is c. If you are traveling very, very close to c relative to me and circle around and come back and we meet up there will be a HUGE discrepancy in our ages (in fact, I'll be long dead and you'll hardly have aged at all), but if you are traveling at a more human speed of essentially zero percent of c then we won't disagree about time or will disagree very little.

The same thing happens in gravity wells. If you go into a gravity well deeper than me and then come back, you will have aged less.

There is an interesting discussion about the GPS system somewhere out there on the internet (sorry I don't have a specific link) that talks about how BOTH of those issues of time dilation (gravitational and due to speed) have to be taken into account in order for the GPS system to not send you off into corn fields and the sides of buildings. The differences due to each are minuscule by human standards (tens of microseconds per day) but significant to the GPS system.

EDIT: here's what I have in my notes (still no link):

GPS satellites need to account for -7 microseconds/day due to SR (motion) and +45 microseconds/day due to GR (gravity)

 

[UncertaintyAjay]

Thanks

 

[pervect]

So the mechanism in the clock "moves or ticks" slower in any direction in the air or space then the stationary one if I understand correctly?

And at the quantum level what exactly happens? Do we know?

You need to consider two issues, one of which is not as trivial as it looks. The first issue and most obvious is what you asked. "What is a clock, and how does it tick". The SI definition of the second is handy, here, as the second is the unit of time in the Scientific Internationale (SI) system of measurement. Thus the definition of the SI second gives us a reference standard or operational definition of the second that we can use to actually measure time (in seconds), in the most accurate manner known to current science, without getting into the question of "what time is".

The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom.

Now, it's clear that the SI standard for the second is based on quantum mechanics, it involves a quantum transition. As far as whether we know "exactly what happens" during a quantum transition, we can say that the mathematics makes predictions which are extrodinarily accurate. Which I hope is satisfactory, because you need to go beyond this, you start moving from the realm of science into the realm of philosophy, and we don't discuss philosophy on Physics Forums anymore.

The second issue is not as obvious, and trickier than it looks. If we have two clocks, as defined above, that are moving relative to another , we need a process of comparison to say which one is ticking faster, and which is slower, or if they are ticking at the same rate. The abstract concept behind this comparision process of comparing clocks is called "simultaneity", we need a concept of simultaneity in order to compare clocks. The "Einstein synchronization method" is a key element of how we do this, but I will defer more details to the existing threads on the topic.

The non-obvious issue with simultaneity in special relativity is that it depends on the observer, it's not universal. See any of the numerous discussions of "Einstein's train" for more on this topic. So according to the simultaneity conventions of one observer, whom we will call Able, who considers himself to be "at rest" in his own frame of reference, the second moving observer's clock(whom we will call Betty) ticks more slowly. When we exchange the two roles, in Betty's frame of reference, Able's clock is the one that ticks more slowly. THis is possible because Able's notion of simultaneity is not the same as Betty's notion of simultaneity.