Understanding Proper Time vs. Layman's Time

[p1l0t]

What is proper time? As opposed to time in the layman's term?

[Mentors' note: This thread was split from another thread, and when it was a stray irrelevant quote was accidentally included. It has been removed, along with two later posts trying to clear up the confusion introduced by the stray quote]

 

[jbriggs444]

What is proper time? As opposed to time in the layman's term?

Proper time along a path is the elapsed time that would be measured by a wristwatch following that path. This is as distinct from "coordinate time". Coordinate time would be measured by looking at a wall clock at the end of your trip and subtracting the reading of a wall clock at the start.

By analogy, proper time is what you measure with your odometer rather than what you measure with a ruler on a particular map.

 

[p1l0t]

Proper time along a path is the elapsed time that would be measured by a wristwatch following that path. This is as distinct from "coordinate time". Coordinate time would be measured by looking at a wall clock at the end of your trip and subtracting the reading of a wall clock at the start.

By analogy, proper time is what you measure with your odometer rather than what you measure with a ruler on a particular map.

So in a way proper time is the layman's time. As opposed to coordinate time. Thanks.

 

[Ibix]

What is proper time? As opposed to time in the layman's term?

Your proper time is the time measured by your wristwatch. My proper time is the time measured by my wristwatch. If we meet up and synchronise our watches, then go our separate ways, then meet up again our watches won't necessarily agree how much time elapsed - this is the heart of the resolution of the twin paradox.

The other kind of time is coordinate time, which is the time shown by a particular family of clocks at rest with respect to each other.

I'm not sure what a layman's idea of time is, really. People seem to have diffetent ideas

 

[p1l0t]

Your proper time is the time measured by your wristwatch. My proper time is the time measured by my wristwatch. If we meet up and synchronise our watches, then go our separate ways, then meet up again our watches won't necessarily agree how much time elapsed - this is the heart of the resolution of the twin paradox.

The other kind of time is coordinate time, which is the time shown by a particular family of clocks at rest with respect to each other.

I'm not sure what a layman's idea of time is, really. People seem to have diffetent ideas

For me it's the wristwatch but I know time is really a whole lot more.

 

[sweet springs]

For me it's the wristwatch but I know time is really a whole lot more.

Wristwatch does not make your time but it measures the common time shared with all the phenomena of you e.g. your hunger, growing or aging.

Note: If you keep turning round and round your arm with extremely high speed, your wristwatch time is delayed than your body time. Your proper time should be separated to your arm time and your body time. Similarly heart is slightly younger than other organs because it keeps beating.

 

[Ibix]

For me it's the wristwatch but I know time is really a whole lot more.

The important thing to realize is that in relativity, time is a "private" quantity (to use Bondi's terminology), like distance travelled, where we can be face-to-face and have different values depending on how we got there. This is different from the "public" quantity that it is in Newtonian physics, where everyone agrees on "the time" once they agree a zero for it.

 

[Herman Trivilino]

For me it's the wristwatch but I know time is really a whole lot more.

If all you care about is your own proper time then there is nothing more to it. But if you were to compare your own proper time to someone else's and found a legitimate discrepancy circumstances might motivate you to provide an explanation. Physicists have anticipated that need and provided the explanation.

 

[p1l0t]

If all you care about is your own proper time then there is nothing more to it. But if you were to compare your own proper time to someone else's and found a legitimate discrepancy circumstances might motivate you to provide an explanation. Physicists have anticipated that need and provided the explanation.

Now now, I didn't say I don't care. Time (not just in the proper sense) is bit of an obsession of mine. My math skills are nowhere near physicist level but I learn what I can. Actually after deriving the time dilation equation from Pythagoras I went down the dark path of trying to understand trancendental numbers. I was able to pull myself back before I went crazy like Georg Cantor but I still revisit it anytime I think I have a new 'angle' on it.

 

[Nugatory]

ime (not just in the proper sense) is bit of an obsession of mine.

You want to get hold of a copy of Taylor and Wheeler's "Spacetime Physics".

 

[p1l0t]

You want to get hold of a copy of Taylor and Wheeler's "Spacetime Physics".

No kindle version... Now I have to wait 2 days.

 

[stevendaryl]

So in a way proper time is the layman's time. As opposed to coordinate time. Thanks.

Yeah, proper time is in a certain sense easier to get a grasp of than coordinate time. You have a watch on your wrist that has an associated number that advances continuously, never halting and never reversing. That watch allows you to describe your history as a function of proper time: At 1:00 according to my watch, I was in Paris, and by 7:00 I was in Brussels.

Coordinate time requires certain assumptions beyond the existence of proper time. What Newtonian physics assumes is that if you and I have identical wrist watches, and we meet up in Paris and note that our watches are synchronized, and then depart to go by different routes to Brussels, when we meet up in Brussels, our watches will show the same times. That's an assumption of Newtonian physics, but is not true for Special Relativity.

 

[p1l0t]

Yeah, proper time is in a certain sense easier to get a grasp of than coordinate time. You have a watch on your wrist that has an associated number that advances continuously, never halting and never reversing. That watch allows you to describe your history as a function of proper time: At 1:00 according to my watch, I was in Paris, and by 7:00 I was in Brussels.

Coordinate time requires certain assumptions beyond the existence of proper time. What Newtonian physics assumes is that if you and I have identical wrist watches, and we meet up in Paris and note that our watches are synchronized, and then depart to go by different routes to Brussels, when we meet up in Brussels, our watches will show the same times. That's an assumption of Newtonian physics, but is not true for Special Relativity.

I assume Newton wasn't assuming you'd be traveling at near the speed of light...

 

[Nugatory]

I assume Newton wasn't assuming you'd be traveling at near the speed of light...

No, but he also wasn't assuming that it would make a difference. Newtonian physics uses Galilean relativity, in which the speed of light is just another speed - faster than we're accustomed to, but then again if snails were physicists they would say the same thing about the speed of galloping horses. In his time and most of the next two centuries, there was no reason to doubt this assumption; to this day most laypeople still assume Galilean relativity, and even professionals who know it's not exactly right use it in their daily lives. (Also, the nature of light was less well understood at the time).

If Galilean relativity were correct (and it takes very sensitive experiments to show that it is not, something that didn't happen until well into the 19th century) then there would be no distinction between coordinate time and proper time - the one would always equal to the other under all conditions.

 

[sweet springs]

I assume Newton wasn't assuming you'd be traveling at near the speed of light...

Time is absolute. Space is absolute with only slide by speed. Such is Galilean transformation.
Later when we are getting familiar with speed c then found that a mixture of time and space $c^2\delta t - \delta x^2 - \delta y^2 - \delta z^2 >0$ called (square of ) world interval is absolute, not time $\delta t$ and space $\sqrt{\delta x^2 + \delta y^2 + \delta z^2}$ independently. Proper time $\tau$ is world interval divided by c.
$c^2 \tau^2 = c^2\delta t - \delta x^2 - \delta y^2 - \delta z^2$
It is a t in special IFR where $\delta x^2 + \delta y^2 + \delta z^2 =0$, meaning that the particle is staying still during the events.
In particle's own IFR, it stays still during the events. In another words it is the time of running particle from start to goal.

Similar to proper time, proper length is introduced in case (world interval)^2= $c^2\delta t - \delta x^2 - \delta y^2 - \delta z^2 <0$. It is a distance in a special IFR where the two events are simultaneous or $\delta t=0$.

 

[p1l0t]

Time is absolute. Space is absolute with only slide by speed. Such is Galilean transformation.
Later when we are getting familiar with speed c then found that a mixture of time and space $c^2\delta t - \delta x^2 - \delta y^2 - \delta z^2 >0$ called (square of ) world interval is absolute, not time $\delta t$ and space $\sqrt{\delta x^2 + \delta y^2 + \delta z^2}$ independently. Proper time $\tau$ is world interval divided by c.
$c^2 \tau^2 = c^2\delta t - \delta x^2 - \delta y^2 - \delta z^2$
It is a t in special IFR where $\delta x^2 + \delta y^2 + \delta z^2 =0$, meaning that the particle is staying still during the events.
In particle's own IFR, it stays still during the events. In another words it is the time of running particle from start to goal.

Similar to proper time, proper length is introduced in case (world interval)^2= $c^2\delta t - \delta x^2 - \delta y^2 - \delta z^2 <0$. It is a distance in a special IFR where the two events are simultaneous or $\delta t=0$.

So
c = lightspeed
tau = Circumference/Radius
xyz = vectors or vector velocities?
and
delta is what, a derivative or some constant?

Thanks for making my own thread out of this by the way whoever did that. I guess I asked a good question. I did get my book by Taylor/Wheeler but I'm day 5 of 9 in a row #pilotLife (well I volunteered 2 extra days in the beginning I'm usually 7 on 5 off). After that though I have a vacation coming up so I'll have some time to really read it and work through some of the equations. My alegbra is pretty solid, calc I know there are derivitives (rates of change) and integrals (the area under a curve or something a big total) that's about it, trig I know there's Pythagoras, angles, cos/sin/tan etc... Most of my math/physics background is just recreational reading but I will work like I'm writing a proper paper if I want to know something and this interests me greatly.

 

[sweet springs]

delta is what, a derivative or some constant?

$\delta x = x_2-x_1$, etc. when we denote the two events as $(t_1,x_1,y_1,z_1)$ and $(t_2,x_2,y_2,z_2)$.

First 10-20 pages of the book http://detritus.fundacioace.com/pub/books/Landau%20L.D.%20%26%20Lifschitz%20E.M.-%20Vol.%202%20-%20The%20Classical%20Theory%20of%20Fields.pdf might help you to understand relativity. Be careful it is compact but too dense to understand fully in first tens times readings.

 

[Ibix]

I did get my book by Taylor/Wheeler

Chapter 1 (which I think is available online) covers the interval, which is the quantity sweet springs is referring to - equation 1.5 and 1.6, I think.

 

[p1l0t]

So I just finished reading chapter one. I get the whole spacetime being a thing as a opposed to space and time. What I don't get is what the profound difference is of space separation having a negative value adds. I get that there is a difference but if it was explained why or what that is I missed it.

Referring to:

(interval)^2 = (time speration)^2 - (space separation)^2

 

[PeterDonis]

What I don't get is what the profound difference is of space separation having a negative value adds.

It means that there can be a zero interval between two points without them being the same point.

More generally, it means that, instead of there being just one kind of interval, there are three: timelike, spacelike, and null. Timelike is where the "time" part is larger than the "space" part; spacelike is where the "space" part is larger than the "time" part; null is where they're equal.

 

[Herman Trivilino]

So I just finished reading chapter one. I get the whole spacetime being a thing as a opposed to space and time. What I don't get is what the profound difference is of space separation having a negative value adds. I get that there is a difference but if it was explained why or what that is I missed it.

Referring to:

(interval)^2 = (time speration)^2 - (space separation)^2

First of all understand that the interval is an interval between two events. If the square of the interval, as you've written it, is negative it means that it's not possible for anything, however fast, to be present at both events. We say that the separation is spacelike. This means that it's not possible to assign an absolute order to the two events! Meaning that to some observers they will occur in an order that's the reverse of what others will observe, depending on their state of motion.

All of this is discussed at length in future chapters, so it's not that you missed it, it's just that they haven't gotten to it yet.

Do you have the 1st or 2nd edition?

 

[p1l0t]

First of all understand that the interval is an interval between two events. If the square of the interval, as you've written it, is negative it means that it's not possible for anything, however fast, to be present at both events. We say that the separation is spacelike. This means that it's not possible to assign an absolute order to the two events! Meaning that to some observers they will occur in an order that's the reverse of what others will observe, depending on their state of motion.

All of this is discussed at length in future chapters, so it's not that you missed it, it's just that they haven't gotten to it yet.

Do you have the 1st or 2nd edition?

2nd

 

[Nugatory]

What I don't get is what the profound difference is of space separation having a negative value adds.

When the squared interval $\Delta{s}^2=-\Delta{t}^2+\Delta{x}^2+\Delta{y}^2+\Delta{z}^2$ between two events is positive, then an observer (and any other object, or message, or other form of communication) would have to move faster than light to be present at both events, which is impossible. In this case, nothing that happens at the first event can have any causal influence over the second event (and this is a good thing because different observers in motion relative to one another will disagree about which event happened first). $\Delta{s}$ is the distance between where the two events happened according to an observer for whom the two events were simultaneous (that is,for whom $\Delta{t}$ is zero).

Conversely when that squared interval is negative, it is possible for an observer (or any other object) to be present at both events. For example, one event might be the firing of a gun and the other the bullet striking its target; the bullet is present at both events. In this case, all observers regardless of their relative motion will agree about the order of the two events - and a good thing too, because we can't have bullets striking the target before they've been fired.