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## Main Question or Discussion Point

What is proper time? How can I solve proper time? "There is only one frame of reference in which clock is at rest, and there are infinitely many in which it is moving." What does it mean?

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- Thread starter Zephaniah
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What is proper time? How can I solve proper time? "There is only one frame of reference in which clock is at rest, and there are infinitely many in which it is moving." What does it mean?

- #2

haushofer

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I'm not sure what you mean by "solving proper time", though.

- #3

Dale

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Given some time like worldline, proper time is the time measured by a clock traveling along that worldline. It is given by ##\tau=\int_P \sqrt{1-v^2/c^2}dt##What is proper time? How can I solve proper time?

- #4

Ibix

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If it is possible to get from one event to the other without exceeding the speed of light then the proper time of a clock moving inertially between the events is the same as the coordinate time between the events in a frame where that clock is at rest.

Dale gave the correct formula to calculate the proper time between two events along some path. However, do note that in the case where the clock is moving inertially, v is not a function of t and the integral is trivial.

- #5

Chestermiller

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Proper time is the simplest sort of time. There are more complicated notions of time. I am guessing that your notion of "time" includes some notion of "now". The notion of now requires some mechanism to tell when two events at different locations in space occur "at the same time", this is usually called "synchronization".

Proper time, being the simplest sort of time, doesn't require any notion of "now". It only requires clocks - stopwatches, basically.

If you want to know more about other notions of time and how they relate to proper time, ask. But I think the above explanation of proper time is sufficient to answer what you asked, though it may or may not tell you what you wanted to know. If it's not sufficient, perhaps asking more questions would clarify what you needed.

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Chestermiller

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The questions you asked in your initial post were very general. Maybe it would help if you asked more specific questions. Is this your only discomfort with the basics of special relativity? Or are other aspects of special relativity limiting your ability to understand property time.

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Does it mean that each observer is correct whatever they state of what they have observed?

- #11

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The questions you asked in your initial post were very general. Maybe it would help if you asked more specific questions. Is this your only discomfort with the basics of special relativity? Or are other aspects of special relativity limiting your ability to understand property time.

My teacher told me that there is a computation for proper time and I as I browse in the internet the formulas are confusing. I think I need a step by step instruction to solve it.

- #12

Chestermiller

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If the two observers are at rest relative to one another (and, thus, they are both physically present at both events) their clocks will both show the same elapsed proper time. If the two observers are in relative motion, then they can't both be physically present at both of the two events.

- #13

Chestermiller

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Dale gave the equation in post #3. Is this the equation you are finding complicated to solve? Which part are you finding complicated?My teacher told me that there is a computation for proper time and I as I browse in the internet the formulas are confusing. I think I need a step by step instruction to solve it.

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Is it the same with inertial reference and relativity of simultaineity?If the two observers are at rest relative to one another (and, thus, they are both physically present at both events) their clocks will both show the same elapsed proper time. If the two observers are in relative motion, then they can't both be physically present at both of the two events.

- #15

Chestermiller

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Sorry, I have no idea what you are asking here. It seems to me your problems are much broader than just not understanding proper time.Is it the same with inertial reference and relativity of simultaineity?

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Dale gave the equation in post #3. Is this the equation you are finding complicated to solve? Which part are you finding complicated?

Yes Sir. That formula is too complicated for me.

- #17

Chestermiller

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In what way? Have you not had integral calculus?Yes Sir. That formula is too complicated for me.

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My problem is how am I going to teach the concept of proper time to my classmates and how am I going to show some problem solving to them.Sorry, I have no idea what you are asking here. It seems to me your problems are much broader than just not understanding proper time.

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Yes Sir. I haven't learn integral calculus yet.In what way? Have you not had integral calculus?

- #20

Chestermiller

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Let's see your attempt to do this so far. What is your best shot at explaining this?My problem is how am I going to teach the concept of proper time to my classmates and how am I going to show some problem solving to them.

- #21

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Maybe I'll draw an illustration showing an observer inside the event and another observer outside the event. Then I'll ask them if who among the two know the proper time. Then the answer will be both have observed the event at a different time but both of them has the proper time in their own reference.Let's see your attempt to do this so far. What is your best shot at explaining this?

- #22

Ibix

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- Interval ##\Delta s^2=c^2\Delta t^2-(\Delta x^2+\Delta y^2 +\Delta z^2)##

- Worldlines

- Block universe

- Events

- Minkowski diagram

The block universe is 4d spacetime. Events are points in space at a given time. Worldlines are lines joining events - your worldline joins all the events you passed through in your life. Interval is the generalisation of Pythagorean distance to spacetime. You may wish to look up the relationship between proper time and interval, and then think about what a worldline's proper time means.

Note also that "proper" in this context is being used in its original Latin sense of "one's own", rather like "property". Not in the modern English sense of "correct".

- #23

Chestermiller

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If you confine attention to inertial frames of reference that are in relative motion with respect to one another with velocity v, then the equation simplifies to ##\Delta \tau=\sqrt{1-\left(\frac{v}{c}\right)^2}\Delta t##. Imagine that you have a single observer with a clock that is at rest in his frame of reference, and measures the time interval between the two events ##\Delta \tau## (he is physically present at both events). Imagine that this observer is moving with velocity v relative to a (stationary) group of observers strung out along the route from the first event to the second event, and the two observers physically present at the two events write down the times on their synchronized clocks at which the two events occur. They then get together and compare notes, and, when they do, they find that, according to their clocks, the time interval between the two events is ##\Delta t##. The equation above will tell you the relationship between ##\Delta \tau## and ##\Delta t## (which will not be the same).Yes Sir. I haven't learn integral calculus yet.

- #24

Chestermiller

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Only the observer who is at rest and personally observes the two events can be physically present at both of the events. The other observer you are referring to (in a different frame of reference) can be physically present at either of the events, but not both of them.Maybe I'll draw an illustration showing an observer inside the event and another observer outside the event. Then I'll ask them if who among the two know the proper time. Then the answer will be both have observed the event at a different time but both of them has the proper time in their own reference.

- #25

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This one formula is much easier than before but I think I need to try this one first. May I ask if you have any problem solving for me to solve?If you confine attention to inertial frames of reference that are in relative motion with respect to one another with velocity v, then the equation simplifies to ##\Delta \tau=\sqrt{1-\left(\frac{v}{c}\right)^2}\Delta t##. Imagine that you have a single observer with a clock that is at rest in his frame of reference, and measures the time interval between the two events ##\Delta \tau##. Imagine that this observer is moving with velocity v relative to a (stationary) group of observers strung out along the route from the first event to the second event, and the two observers physically present at the two events write down the times on their synchronized clocks at which the two events occur. They then get together and compare notes, and, when they do, they find that, according to their clocks, the time interval between the two events is ##\Delta t##. The equation above will tell you the relationship between ##\Delta \tau## and ##\Delta t## (which will not be the same).

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