# Confusing definition of proper time – which is correct?

I have googled for „definition of proper time“

This source https://www.collinsdictionary.com/dictionary/english/proper-time gives the following definition:

• proper time ... measured by a clock that has the same motion as the observer. Any clock in motion relative to the observer ... will not, according to the theory of relativity, measure proper time.

However, according to this answer Confusing time dilation - proper time is higher?

„In other words, it is the time registered by a clock that is carried from one event to the other“ exactly the moving clock measures proper time interval and this time interval is the shortest due to time dilation.

• It may help to realize that "proper" here means "belonging to oneself," as in "the Vatican doesn't lie in Rome proper." It doesn't mean "correct."
– user4552
Commented Dec 4, 2019 at 15:05

The definitions are both trying to say the same thing, but they are not quite managing to avoid all scope for misunderstanding. For a non-technical appreciation of the meaning of proper time you should start with the principle that proper time is the time experienced at any point in one's own reference frame. As you sit at your desk marvelling at the clarity of my answer you are experiencing proper time in the reference frame in which you are stationary. Any clocks that are stationary relative to you will record time at the same rate you experience it.

Anybody moving relative to you will experience their own proper time, which will be faithfully recorded by any clocks moving with them (ie clocks that are stationary in that person's reference frame).

The Collins definition was insufficiently precise. It should have said that any clock moving with respect to an observer will not measure proper time in the observer's frame of reference.

If a clock is moved between two other clocks that are stationary relative to each other, the time it records is a proper time for that clock's frame of reference, and it will be shorter than the time that appears to have elapsed according to the stationary clocks.

• If I am stationary, any clock that is at rest relatively to me, here or there, measures my proper time, which must be the fastest. It was the slowest in that answer. Second, lets‘s better speak about measuring time intervals. There are two ways – I am at rest and measure interval by means of two clock (this interval is larger), the moving clock was present at departure and arrival (measured this way interval is shorter). Why measured by moving clock interval (the shorter one) is the proper one? Which way to measure (and compare) intervals is in accordance with measuring proper time interval? Commented Dec 4, 2019 at 15:55
• The time that elapses on a single clock is the proper time for that clock. If a clock moves between two stationary clocks, the proper time it measures will be different from the time interval according to the readings on the two stationary clocks. Commented Dec 4, 2019 at 16:04
• Sure it will still be shorter. So what, our proper times are different? Why that clock must measure proper time interval different way than I do? In that clock’s frame its proper time must be longer and my shorter (dilated). "That clock" can also measure interval by means of two separated clocks in "its own frame", measured this way interval will be longer in accordance with definition of proper time in Collins. Then my single clock would be “present at both events” in that frame and would measure shorter interval. So why exactly does a single moving clock measures proper time interval? Commented Dec 4, 2019 at 16:40
• how many clocks does a stationary observer have? One or two? How many clocks does moving observer have? Why they measure proper time interval by means of a single clock, that is moving in their frames? Commented Dec 4, 2019 at 17:09
• Hi Mark, I think you are confusing two things. Proper time is by definition the time experienced by a single observer. The time you experience is your proper time. The time that ticks away on any clock is its proper time. That is what proper time means. If two or more clocks are stationary relative to each other, then their proper times will agree (in the absence of gravitational effects). So if you have ten clocks in your pocket they will all measure the same proper time for you. Commented Dec 4, 2019 at 17:41

A 'propre' French word for own, propre time later polluted as proper time of an object is the time that is measured by a clock which is at rest w.r.t. the object, not only at rest but is must be locally attached to it as in case of GTR, it is the case that two objects on first and second floor of a building ticks at different 'rate', The magnitude of four-velocity is $$c$$. Which is defined as $$\textbf{U} = d\textbf{x}/d \tau$$ $$|| \textbf{U} ||^2 = \textbf{U} \cdot \textbf{U} = c^2$$

For a frame of reference where spatial velocity is $$\vec{v}=\vec{0}$$ only 'temporal velocity exist' and

$$(cdt/d\tau)^2=c^2$$

When all of the weight of four velocity is carried by the temporal velocity or loosely speaking when temporal velocity becomes $$c$$ or the fastest an object can travel through time is with $$c$$. (Very loosely speaking) that is only possible when there is minimum dilation i.e when spatial velocity is 0 or things own clock.

The proper time is the time evolved between two events in your reference frame. In other words, it is the time measured in your clock.

Proper time is the clock you carry with you and it is measured from your frame of reference. If you are on a craft traveling at 0.99999 the speed of light to alpha Centauri it will take you about 4.3 years to get there from earth. If you return immediately the round trip will take you about 8.6 years in your time (proper time to you). But, an observer on earth who can get very old will have to wait 1833 years for your return because their clock is moving much slower compared (key concept!) or relative to yours. In their proper time 1833 years pass Crazy stuff…

Proper time must always be explained in relation to an observer. One has to imagine 2 systems K and K' with relative velocity "v", and 2 observers A in K, and observer B in K'. The time they both measure with their clocks is the same. But A would imagine (acc. to SR) that B's clock runs slower. and B would imagine (acc. to SR) that A's clock runs slower than his. So the proper time for both is the same. But A, acc. to t'=t/gamma calculates that every 1 second in K', would be shown t=(1)(gamma)>1sec on his clock. and B thinks the same about the time in K. So the proper time is what B experiences in K' and A in K. contrary to Einstein, the time dilation arises from the definition of time and not slowing the moving clock. ref. Zur Elektrodynamik bewegter Koerper, 1905 A. Einstein.

you are right. A formal definition in textbooks (already in A.Einstein) is simple but technically and practically confusing; formal- that integration along the path (on a diagram) as contrary to a coordinate time in the "at rest" observer (with a clock, rather two synchronized clocks at the distance x=vt). 1) Lorentz equations are symmetric in nature-when you switch coordinate systems: changing the description from (x,t) to (x',t') you will get a reverse number for both times. 2) The translation from one CS(coordinate system) into another is only a kinematical and not dynamical (as it is claimed in Twin Paradox Absurdity)- pointed rightly by M.Sachs. 3)The confusion is already in A. Einstein' article in 1905; there, he does not at all specify a type of a real Theory clock but only about an ideal light clock (that is just a model and nothing real)! In a practical experiment with atomic clocks, the difference between (so-called)"proper" and "coordinate" time arises from the Relativistic Doppler Effect - such clock mechanism counting acts as a "wave-field"(counting depends on the period or frequency wave of source emission); a flying atomic clock/GPS' frequency depends on the gravitational potential which is different on Earth's ground and above it; such clocks don't even test Lorentz formula for the inertial frame (centripetal acceleration in the opposite direction of gravitational one = the Lorentz formula, but it tests...GR and not SR (there both clocks would count the same number of clock ticks as they both have the same "unit time"-the physics of a clock does not change when one observes it from another reference system! (Analogically with "moving radioactive substances" called muons or other radioactive "particles"(rather the quanta of "matter(Broglie)wave"-Lorentz formula helps to explain the behavior of a system of "muon quanta-s" and not a one "muon"; a statistical "muon" is not a particle or a living object like a twin;more,for the counting time longer than half-time of "radioactive objects" it will show none difference as one sees easily on the diagram of disintegration (K.S.Krane,Intr.Nuclear Physics,1987)

The question arises: what is the "proper unit time"? If you use the same atomic clocks (as is assumed in both systems, at rest and moving one); then, a "unit time" must be applied to at rest coordinate system and not that of the "moving" clock attached to the body"(a textbook expression- a horror) because such unit time would be changed according to Doppler formula: unit t=1/(1-(v/c)^2)^1/2.At the same time,Theory assumes the "unit measure" of distance and time in both reference systems (x,t) and (x',t') is equal 1 (one) as both systems, "moving, and "at rest" are equivalent; hence, one sees immediately, that this new "moving" clock unit time is just a mathematical (fiction) transformation formula (between two coordinate systems) and not about any physical change in the mechanism of a "moving" clock (this "moving" clock is at rest in his own reference system!). The mechanism of such clock and its unit time (or period) does not depend on the velocity but as mentioned above if a special only clock, a "wave-field"clock,i.e. atomic clock in a different gravitational potential will count differently! Concluding: "proper time" is just an imaginary(mathematical) one that physically corresponds to so called "coordinate time" recorded by a clock or two synchronized clocks in the rest coordinate system. ps.Textbooks misuse the Minkowski diagram to graphically explain Theory idea in...forgetting to present the same diagram from the point of a "moving" reference system that would be at..rest! (Minkowski himself was ...fooled while he in his 1908 article assumed a symmetry of both systems while counting the "length" of an "electron" but not in the case of "time" parameter few years later!