# How did Einstein Define Time

Salman2
Perhaps someone can post where in the literature (publication, page no. text) where Einstein directly stated a definition of time. Does he have multiple definitions that are contradictory ?
Thanks for the help.

Note: please, I do not want this thread to be how anyone else defines time...please limit the discussion to explicit literature citation of how Einstein defined time.

Gold Member
Look at the first part of his famous 1905 paper introducing Special Relativity.

http://www.fourmilab.ch/etexts/einstein/specrel/www/

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Mentor
In his 1905 special relativity paper (On the Electrodynamics of Moving Bodies), he defines the time of an event basically as "the reading on a suitably-synchronized clock located at the same position as the event."

The “time” of an event is that which is given simultaneously with the event by a stationary clock located at the place of the event, this clock being synchronous, and indeed synchronous for all time determinations, with a specified stationary clock.

(from Section I.1, Definition of Simultaneity)

[ghwellsjr slipped in while I was fiddling with my post]

Salman2
Thank you ghwellsjr & jtbell.

So, if an event is thought to be the moment when a train arrives at a point A at a train station, then Einstein would define the time of that event as instantaneous to be "the reading on a suitable-synchronized clock located at the same position as the event", that is, suppose the clock at point A reads 7:00 pm the moment the train arrives at point A, then the time of that event is 7:00 pm. Would that be correct ?

Now, suppose the train leaves point A the same moment the clock at point A reads 7:02 pm, and arrives at a distance point B at the same moment that a second clock, synchronized with the one at point A, reads 7:12 pm. Thus, would Einstein say that the time of event as duration of "moving between point A and B" is t= [tB - tA] = 0:10 min. ? That is, time of event as duration between two moments (such as the movement of a train) is the difference [or that which is intermediate] between the readings on two well synchronized clocks located at two different positions (A and B) ? Would this be correct ?

If both above are correct, then would not Einstein have two different and valid (not contradictory) definitions of time (1) time of event as instantaneous (as one moment) and (2) time of event as duration (that which is intermediate between two moments)?

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PatrickPowers
Perhaps someone can post where in the literature (publication, page no. text) where Einstein directly stated a definition of time. Does he have multiple definitions that are contradictory ?
Thanks for the help.

Note: please, I do not want this thread to be how anyone else defines time...please limit the discussion to explicit literature citation of how Einstein defined time.

I seem to recall that somewhere Einstein defined time as "that which a clock measures." It is what is called an operational definition. Then he details what exactly such clocks do relative to one another. It can become very complicated.

Einstein proved that time is not a simple fundamental property of the Universe. It may very well be fundamental, but it isn't simple.

I also claim without proof that due to quantum uncertainty it is not possible to make a clock that accurately measures very short periods of time.

Gold Member
Thank you ghwellsjr & jtbell.

So, if an event is thought to be the moment when a train arrives at a point A at a train station, then Einstein would define the time of that event as instantaneous to be "the reading on a suitable-synchronized clock located at the same position as the event", that is, suppose the clock at point A reads 7:00 pm the moment the train arrives at point A, then the time of that event is 7:00 pm. Would that be correct ?

Now, suppose the train leaves point A the same moment the clock at point A reads 7:02 pm, and arrives at a distance point B at the same moment that a second clock, synchronized with the one at point A, reads 7:12 pm. Thus, would Einstein say that the time of event as duration of "moving between point A and B" is t= [tB - tA] = 0:10 min. ? That is, time of event as duration between two moments (such as the movement of a train) is the difference [or that which is intermediate] between the readings on two well synchronized clocks located at two different positions (A and B) ? Would this be correct ?

If both above are correct, then would not Einstein have two different and valid (not contradictory) definitions of time (1) time of event as instantaneous (as one moment) and (2) time of event as duration (that which is intermediate between two moments)?
The term "event" has a much narrower meaning when used in the context of Special Relativity than it does in common parlance. We normally can talk of an event as something that has a duration, such as a football game or a concert and something that can cover a broad area, such as an arena or theater. But in SR, all events apply only to an instant in time at a particular point in space, whether or not anything is actually happening at that time and location.

So, getting back to your questions, your use of the term "event" is exactly correct in your first paragraph but not in your second paragraph. There is only one definition of time as given by (1) in your third paragraph. Your second definition is not part of Special Relativity.

However, there is something that may be like what you are considering to be a duration and the is a "spacetime interval". You can look it up in wikipedia if you are interested.

Salman2
The term "event" has a much narrower meaning when used in the context of Special Relativity than it does in common parlance. We normally can talk of an event as something that has a duration, such as a football game or a concert and something that can cover a broad area, such as an arena or theater. But in SR, all events apply only to an instant in time at a particular point in space, whether or not anything is actually happening at that time and location.
OK, thanks, this is very important to know. Do you have a literature citation exactly where Einstein "defined event" in the narrow context you indicate ?

ghwellsjr said:
There is only one definition of time as given by (1) in your third paragraph. Your second definition is not part of Special Relativity.
Well, I know in his 1905 paper Einstein had this to say about time and its relationship to his relativity principle "judgements in which time plays a part are always judgements of simultaneous events".

So, if you look at the example for the second definition of time I suggested, the judgement of the time number (the 0:10 ) is derived completely from judgements of two simultaneous events, that is, it is the mathematical difference of the two judgements.

Don't you think Einstein would view as important that both 7:00 (time as instantaneous) and 0.10 (time as a duration, e.g. elapsed time) ARE BOTH NUMBERS derived purely from making judgements about simultaneous events ?

Is it possible that the concept of "elapsed time" (time as duration) is a concept that needs to be added to Special Relativity to make it complete ? Just asking, but I do wonder how Einstein would deal with the concept of "elapsed time" (time as duration), which is such an obvious phenomenon that humans experience daily ?? If the number 0.10 from my second example is NOT A JUDGEMENT OF TIME...what the heck is it a judgement of ??

yoron
He defined time locally. To define it as the same, at two different locations, he used synchronized clocks. The synchronization was thought of as a light pulse going from A to B and then back again.

==

Suppose there is a clock at point A and another clock at point B. Let a light ray be sent from A to B, then reflected back from B to A. '
Let

tA = Reading on the clock at A when the ray leaves A.
tB = Reading on the clock at B when the ray arrives at B.
t'A = Reading on the clock at A when the ray returns to A.

The two clocks are synchronous by de nition if;

tB -tA (time light took to travel from A to B.) = t'A - tB (time light took to travel from B to A.)

tB-tA = t'A-tB
==

Time is very much a local phenomena.

" The "time" of an event is the reading obtained simultaneously
from a clock at rest that is located at the place of the event,
this clock being synchronous . . . with a speci fied clock at rest.
We have de fined time by means of clocks at rest in the rest
system; because the time just defi ned is related to the system
at rest, we will call it "the time of the rest system." "

From Einstein.

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yoron
As for your question of durations and 'proper time'?

There doesn't exist a 'absolute time'. You can always destroy a system by introducing a new party moving relative that system. And it all comes from his definitions. He don't need to be corrected, and nobody really has, in the last hundred years as he got down to his definite definitions. What we have done is to introduce ways of defining those equations in new ways, reaching sometimes extremely weird conclusions. But as far as I know his final definitions in SR and GR still holds, as stated by him.

Salman2
As for your question of durations and 'proper time'?
Thank you for your two posts.

So, when we say that Einstein "defined time" in SR, what we really say is that Einstein defined "rest-system time". Does this mean there is another sense of the concept of time that Einstein did NOT define, and would that other sense of undefined time be "proper time" ? Or, does Einstein define "proper time" somewhere ?

I understand that there is not an absolute time for Einstein, not even "rest-system time" is absolute. The only absolutes are the speed of light and that fact that instantaneous events exist (as a moment in time) that can be used to define time...correct ?

Also, I would appreciate if someone could point in the literature where Einstein defined the concept 'event'. It would be nice to read how he constrained the concept 'event' to be local and instantaneous by definition.

yoron
A event can by definition only be instantaneous locally (intrinsically), if you consider the speed of light. If you mean two events happening simultaneously inside your railway car, they will to an observer outside, watching you pass, happen differently in his 'time'. It's about 'clocks', and how to define them, your 'local' clock will never lie to you, and it will always give you the same, invariant, correct 'time' relative your heartbeats. Proper time is what you find your wristwatch to give you locally, you being 'at rest' relative Earth for example. But, it's also about 'inertial frames' but that one I will jump for this.

Being 'at rest' with something means that it to you all will seem as you have an (approximately) 'synchronized' time in that 'frame of reference (earth)' loosely speaking here. And if we define it as you're being 'at rest' in a uniform motion, and if ignoring all 'local gravity' inside your spaceship, we can speak of it as some absolute synchronization. But in reality gravity is everywhere, and clocks will differ with it. But, when defining this kind of concepts you want to make them simple, so in general you can define it as a 'uniform motion' is the place of being 'at rest'. Earth isn't 'at rest' in that motto as it is 'gravitationally accelerating' but you might assume two 'point particles' following a 'geodesic', uniformly moving that is, to be 'at rest' relative each other.

The other thing to consider is 'durations', what is the best 'clock' you know?

And what is weird with those durations, as shown by 'c'?
Isn't it the way it always will present you with the same speed 'locally', just as your wristwatch, no matter its 'source', or your 'detectors/sinks' relative motion. It will always be 'c' locally. So if you look at it from radiation, your 'time', if defined by radiations clock, never can differ. It's always 'c'. What will differ is the 'time' you see other things to take (frames of reference) and their 'distances'.

Being 'at rest' in a 'uniform motion', and finding a 'gravity/constant inertia' in a acceleration I find two of the most fundamentally upsidedown turning definitions made in modern history.

Combine those with 'c', and there will be a lot to question when it comes to those definitions we used to believe in. Distance, motion, time. You name it. And this last one ('c' as the absolute 'clock') is the one Einstein didn't define, as far as I know? Because he had the concept of SpaceTime as a whole thing, undifferentiated as I think of it. The moon would still be there when he slept as a example, even though this is a slightly different definition. But I think you can define it this way too, and still find it 'undifferentiated', as long as you accept that it is 'c', and 'gravity' that 'holds it together' in our observations.

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Gold Member
The term "event" has a much narrower meaning when used in the context of Special Relativity than it does in common parlance. We normally can talk of an event as something that has a duration, such as a football game or a concert and something that can cover a broad area, such as an arena or theater. But in SR, all events apply only to an instant in time at a particular point in space, whether or not anything is actually happening at that time and location.
OK, thanks, this is very important to know. Do you have a literature citation exactly where Einstein "defined event" in the narrow context you indicate ?
If you look in the above referenced 1905 paper, in the first article, the sixth paragraph starts out:
If at the point A of space there is a clock, an observer at A can determine the time values of events in the immediate proximity of A by finding the positions of the hands which are simultaneous with these events.​
Since the hands of a clock are always moving, there is only one moment in time that is simultaneous with a position of the hands.
There is only one definition of time as given by (1) in your third paragraph. Your second definition is not part of Special Relativity.
Well, I know in his 1905 paper Einstein had this to say about time and its relationship to his relativity principle "judgements in which time plays a part are always judgements of simultaneous events".

So, if you look at the example for the second definition of time I suggested, the judgement of the time number (the 0:10 ) is derived completely from judgements of two simultaneous events, that is, it is the mathematical difference of the two judgements.

Don't you think Einstein would view as important that both 7:00 (time as instantaneous) and 0.10 (time as a duration, e.g. elapsed time) ARE BOTH NUMBERS derived purely from making judgements about simultaneous events ?

Is it possible that the concept of "elapsed time" (time as duration) is a concept that needs to be added to Special Relativity to make it complete ? Just asking, but I do wonder how Einstein would deal with the concept of "elapsed time" (time as duration), which is such an obvious phenomenon that humans experience daily ?? If the number 0.10 from my second example is NOT A JUDGEMENT OF TIME...what the heck is it a judgement of ??
Einstein did not give any special attention to the duration as the difference between the time coordinates of two events because this duration is based on coordinate times and is relative to the Frame of Reference in which they are defined. Instead we use a term called Spacetime Interval which is a calculated value based on both the spatial differences in the two events and the time difference in the two events and which turns out to be the same value no matter which Frame of Reference we use to define the two events (assuming a proper transform using the Lorentz Transform. Note that the term "interval" can be applied to both space and time so it is a much better term than "duration" which can only be applied to time. If you want to learn more about Spacetime Interval, look it up in wikipedia.

Gold Member
Thank you for your two posts.

So, when we say that Einstein "defined time" in SR, what we really say is that Einstein defined "rest-system time". Does this mean there is another sense of the concept of time that Einstein did NOT define, and would that other sense of undefined time be "proper time" ? Or, does Einstein define "proper time" somewhere ?
I'm not sure if Einstein used the term "proper time" but it simply means the time on a clock that is usually moved around and so it experiences time dilation. In contrast is the term "coordinate time" which is the time on the clocks that remain at rest within a Frame of Reference that are used to define the time coordinate at the space coordinates where they are located. Usually these are imaginary clocks as well as the "rulers" that used to measure out the space.
I understand that there is not an absolute time for Einstein, not even "rest-system time" is absolute. The only absolutes are the speed of light and that fact that instantaneous events exist (as a moment in time) that can be used to define time...correct ?
Yes, I think you've got it.
Also, I would appreciate if someone could point in the literature where Einstein defined the concept 'event'. It would be nice to read how he constrained the concept 'event' to be local and instantaneous by definition.
I pointed this out in the previous post.

yoron
Yeah, I tried to look it up (proper time) ghwellsjr, as I wasn't sure of if that was his definition, or a later one, but I can't find who 'invented it', although I think I've read Einstein use it too somewhere? When it comes to 'invariant SpaceTime intervals', then that is what I would call the Jello, made from the spatial and time like directions, relative 'c'. But that we find a symmetry to them do not guarantee that they are a 'whole SpaceTime', as I see it.

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Salman2
ghwellsjr and yoron. I greatly appreciate your time and explanations. I have another question concerning the concept of 'event' for Einstein.

Ghwellsjr...you provided this comment "Since the hands of a clock are always moving, there is only one moment in time that is simultaneous with a position of the hands."

So, "one moment in time" = one event for Einstein...correct ?

But, if so, would Einstein say that time is not "in the event" (in the moment), since it is the moment that is in time that is simultaneous ?

Consider for example how we say that odd and even number are "in the number line". In the same way would Einstein say that one moment, one event of a position of the hands on the clock, is in time ?

The reason I ask is that it seems to me that what Einstein calls "one moment in time" would be what is also called the "present" or the "now", and it makes perfect sense to me to say that there is no time within the now or the present, but instead to say that the present (now) is a moment in time...what Einstein would call "an event".

Not sure if I am making myself clear, but any help with understanding is appreciated. What I'm trying to do is to see how Einstein would relate the concepts of [event...moment...present...now] (seems to me Einstein would say they are four words of the same concept, and that all are outside of time, but are the limit of time ?).

PatrickPowers
ghwellsjr and yoron. I greatly appreciate your time and explanations. I have another question concerning the concept of 'event' for Einstein.

Ghwellsjr...you provided this comment "Since the hands of a clock are always moving, there is only one moment in time that is simultaneous with a position of the hands."

So, "one moment in time" = one event for Einstein...correct ?

But, if so, would Einstein say that time is not "in the event" (in the moment), since it is the moment that is in time that is simultaneous ?

Consider for example how we say that odd and even number are "in the number line". In the same way would Einstein say that one moment, one event of a position of the hands on the clock, is in time ?

The reason I ask is that it seems to me that what Einstein calls "one moment in time" would be what is also called the "present" or the "now", and it makes perfect sense to me to say that there is no time within the now or the present, but instead to say that the present (now) is a moment in time...what Einstein would call "an event".

Not sure if I am making myself clear, but any help with understanding is appreciated. What I'm trying to do is to see how Einstein would relate the concepts of [event...moment...present...now] (seems to me Einstein would say they are four words of the same concept, and that all are outside of time, but are the limit of time ?).

The way I would put it is that there is no such thing as a moment in time.

Time is measured by counting oscillations. There is a quantum fact that the smaller the interval in time, the less certain the amount of energy in that interval. Since all oscillators involve energy, that means the smaller the interval the less certain we are of the period of the oscillator, which means the idea of time breaks down.

It is easy to think that time is OK and only our ability to measure it fails, but I think the idea of time really does break down and things begin to behave quite differently from what we are used to.

yoron
Yep, very nicely put :) If I use 'c' as, eh, my 'clock of choice', then it should break down at Planck length, as that is where 'light' moves one Planck length in one Planck time. And discussing smaller quantities/values may be possible, but we don't have any distinct definition of such, as I know.

But then we have Heisenberg's uncertainty principle too, and that seems to operate at larger values. As I see it, the 'speed' we have defined is arbitrarily made, in such a motto that it is a ruler of choice, measured in durations of choice (clock/times arrow), that defines that speed. But using another ruler won't make light fail, as the 'constant' it is, and will be then too.

So, to my eyes, HUP becomes very interesting there.
==

although, I do see a arrow, invariant, always the same locally, same as 'c'.

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Gold Member
ghwellsjr and yoron. I greatly appreciate your time and explanations. I have another question concerning the concept of 'event' for Einstein.

Ghwellsjr...you provided this comment "Since the hands of a clock are always moving, there is only one moment in time that is simultaneous with a position of the hands."

So, "one moment in time" = one event for Einstein...correct ?
You also need the three components of space, x, y z plus t to specify an event. Just like x, y, z specifies a point in space and t specifies a moment in time, the combination of all four components define an event in spacetime.
But, if so, would Einstein say that time is not "in the event" (in the moment), since it is the moment that is in time that is simultaneous ?
Einstein would certainly say that a specific time is in an event, plus a specific point is in an event. Each event takes all four components.
Consider for example how we say that odd and even number are "in the number line". In the same way would Einstein say that one moment, one event of a position of the hands on the clock, is in time ?
Yes, odd and even numbers are in the number line but so are an infinite number of fractional numbers included between each odd/even pair of numbers, just as there are an infinite number of different events between noon and one second after noon at a single location. And there are an infinite number of events between x=0 and x=1 with the other components unchanged. Same for y and z. So if we specify an event as [t,x,y,z] then you can see that there are an untold number of events between [0,0,0,0] and [1,1,1,1] if we allow each parameter to vary independently of all the others.
The reason I ask is that it seems to me that what Einstein calls "one moment in time" would be what is also called the "present" or the "now", and it makes perfect sense to me to say that there is no time within the now or the present, but instead to say that the present (now) is a moment in time...what Einstein would call "an event".
Yes, except that the time component of an event doesn't have to be connected with "now" or the "present" any more than the spatial components have to be connected with "here". They are just coordinates that allow you to refer to any place at any time you want; past, present or future, here, there or anywhere.
Not sure if I am making myself clear, but any help with understanding is appreciated. What I'm trying to do is to see how Einstein would relate the concepts of [event...moment...present...now] (seems to me Einstein would say they are four words of the same concept, and that all are outside of time, but are the limit of time ?).
No, but I hope my previous comments have cleared this up for you. If not, ask again.

Gold Member
PatrickPowers and yoron, just like relativity is unconcerned about the mechanisms of time dilation and length contraction, it is also unconcerned about the granularity of time and space. And I doubt the forums where those topics should be discussed concern themselves with relativistic Frames of Reference.

yoron
Ah, but they do. Check on Smolin.

But you're right, got carried away here. A event is something that needs three spatial, and one temporal component to be defined. It's locally defined by your local watch 'proper time', and all other 'events' you observe relative your 'proper time' will have to consider lights speed in a vacuum, to fit your local clock (via Lorentz transformations).
=

And mass/energy too, thinking of it.

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Gold Member
A event is something that needs three spatial, and one temporal component to be defined. It's locally defined by your local watch 'proper time', and all other 'events' you observe relative your 'proper time' will have to consider lights speed in a vacuum, to fit your local clock (via Lorentz transformations).
This is a confusing mixup of several different concepts.

The time that is used in an event is the called the coordinate time, not the proper time, even if they happen to be the same which they only will be if you and your local watch remain stationary in the chosen Frame of Reference and started out with your local watch synchronized to the coordinate time or if your local watch happened to be the master clock by which all the other clocks that remain stationary in the chosen Frame of Reference were synchronized. And this synchronization process has nothing to do with Lorentz Transformations.

The time coordinate of an event is defined only for a specific Frame of Reference. In other words, the four coordinates making up events are defined for a specific Frame of Reference. The time component is called coordinate time.

The Lorentz Transform is used to convert the coordinates of an event defined in one Frame of Reference to the coordinates of the same event in a second Frame of Reference moving inertially (no acceleration) with respect to the first Frame of Reference.

We use the term "proper time" to refer to clocks that do not remain stationary in the chosen Frame of Reference so this cannot apply to the clocks that are used to define the time coordinate of that Frame of Reference. And the reason we have a separate term for these clocks is precisely because they differ from coordinate time.

yoron
You might be right, I shouldn't use 'proper time' so loosely, but in my mind it doesn't matter if I define a 'proper time' on Earth or in another accelerating frame aka the equivalence principle. As for then defining any other frame of reference from that it follows naturally to me that my 'clock' will be the master clock, as yours will be for you.

To define it otherwise is naturally possible, but only when comparing frames of reference, and then also defining the clock you don't go under as the 'right one'. But as you say, I do mix a lot :)

Gold Member
But we're talking Special Relativity in this thread where the equivalence principle doesn't apply and where the Lorentz Transform only works with inertial frames, not accelerating frames. It's OK for you and your clock with its Proper Time on it to accelerate in any inertial frame of interest and this is where your clock will have a different time on it than the Coordinate Time at whatever location your clock is present at. That's the meaning of Proper Time.

Even though you and your clock may accelerate and move with respect to me and my clock (whether or not I accelerate and move), when we are talking Special Relativity and using the Lorentz Transform to discuss multiple Frames of Reference, we need to talk about one inertial Frame of Reference at a time. Both of us and our clocks exist in every Frame of Reference and we don't want to use one FoR for you and a different one for me, that will lead to paradoxes. One FoR at a time, please, and use the Lorentz Transform to get from one to the other, no loose ideas here or we're in for trouble.

yoron
You know, I'm thinking of it as 'local time' actually, proper time is a somewhat of a misnomer to me, in that is differs between special and general relativity. I should have avoided that word, it slipped through my fingers here.

When I look at how Einstein thought of it I see only 'local time'. And that is how I think of it. That's the only frame you can measure directly in a local setting, and that's the frame I see as defining all other frames. And 'inertial frames' is a tricky subject

"In classical mechanics the inertial frame and time are best defined together by a suitable formulation of the law of inertia: It is possible to fix the time and assign a state of motion to the system of coordinates (inertial frame) such that, with reference to the latter, force-free material points undergo no acceleration; furthermore it is assumed that this time can be measured without disagreement by identical clocks (systems which run down periodically) in any arbitrary state of motion.

There are then an infinite number of inertial frames which are in uniform translational motion relative to each other, and hence there is also an infinite number of mutually equivalent, physically preferred states of motion. Time is absolute, i.e. independent of the choice of the particular inertial frame; it is defined by more characteristics than logically necessary, although - as implied by mechanics - this should not lead to contradictions with experience.

Note in passing that the logical weakness of this exposition from the point of view of the stipulation of meaning is the lack of an experimental criterion for whether a material point is forcefree or not; therefore the concept of the inertial frame remains rather problematical. This deficiency leads to the general theory of relativity. "

And that's why I didn't wanted to discuss 'inertial frames', the better definition is the one from GR as I see it, with SR to me being a limited description in that a inertial frame doesn't exist in any gravitational positional system, if not assuming 'force free points'.

"To harmonize the relativity principle with the light principle, the assumption that an absolute time (agreeing for all inertial frames) exists, had to be abandoned. Thus the hypothesis is abandoned that arbitrarily moved and suitably set identical clocks function in such a way that the times shown by two of them, which meet, agree. A specific time is assigned to each inertial frame; the state of motion and the time of the inertial frame are defined, in accordance with the stipulation of meaning, by the requirement that the light principle should apply to it. The existence of the inertial frame thus defined and the validity of the law of inertia with respect to it are assumed. The time for each inertial frame is measured by identical clocks that are stationary relative to the frame."

That one you can see two ways, you can either define it such as there can be no 'common ground' for a same clock rate anywhere, except, when defining some sort of synchronization by light in uniform motion, also presuming absence of 'gravity'.

But then you have the idea of your own 'local' clock never changing its 'duration', or 'time rate', relative your own 'frame of reference'. If every experiment you do locally only show you the same durations/time rate locally, and if you then also find that no matter where you go, or how fast you move relative some arbitrary frame of reference, that this hold then you have a slightly different definition in my opinion. If it also hold true for you changing your 'SpaceTime position' to some system that you before found to have a different 'clock' relative you, then you have a definition of a 'local time' that never change its 'shape' relative your local experiments. And it is that one that will hold both in SR and GR, all as I see it. I find 'inertial frames' tricky, in that I don't see them, other than as a conceptual description. Not that it isn't a beautiful definition in its own right though, as the way it proves Lorenz contractions and time dilation.

http://www.nobelprize.org/nobel_prizes/physics/laureates/1921/einstein-lecture.pdf

Salman2
Einstein would certainly say that a specific time is in an event, plus a specific point is in an event. Each event takes all four components...I hope my previous comments have cleared this up for you. If not, ask again.

I do have one question however. If I understand what you are saying, it is that for Einstein the "time" represented by each "event" within the (x,y,z,t) system would be a type of time called "coordinate time"...correct ?

But, if so, I am confused because at this Wiki link below, it clearly states that "coordinate time" for Einstein would not be within an event, but is "the time between two events".

http://en.wikipedia.org/wiki/Proper_time

Do you see my confusion ? Either "coordinate time" for Einstein is (1) as you say, within the event as being the t in any (x,y,z,t) event, or, (2) as stated by Wiki, it is the time that is between two events, each of which are measured using the two t's found in two different (x,y,z,t) events. Both explanations cannot be a correct understanding of how Einstein defined coordinate time.

Also, from the Wiki link I read how the concept of "proper time" relates to what I called "elapsed time" previously, and that proper time is given the tau symbol to distinguish it from coordinate time. But, the Wiki site also claims that proper time is a type of time between two events, only curved, whereas coordinate time is a straight line between two events.

What I am trying to clarify from my OP question is, does Einstein define "time in general" as being "coordinate time", "proper time", both or neither ? This is still not clear to me.

Gold Member
Yes, I see your confusion but it is easily cleared up once you realize that a clock is keeping track of the time between two events.

To help you understand, let's think first about stopwatches. They display an elapsed time between two events, the first event occurs when you start the stopwatch and the second event is when you stop it. Or you could just let the stopwatch keep running without stopping it and then the second event is whenever you look at it.

A stopwatch has a reset button that let's you set the initial time to zero but a clock has several buttons or knobs that let you set the display to any time you want. This would be the first event. The second event would be whenever you look at it.

So the first event with coordinate time is when you synchronize the clock. The second event is when you look at it.

With proper time, the first event is when you set it to the local coordinate clock or when you reset two clocks or set two clocks to the same time and then take one of them on a journey so that its time goes out of sync and later return it to the second clock to observe that it has elapsed less time, for example.

So Einstein defined coordinate time when describing his convention of synchronizing all the clocks that are used to define a Reference Frame. This is what he talked about in the first two or three sections of his 1905 paper (see link in post #2). He defined proper time when he described what would happen to a moving clock in relation to a coordinate clock. This is what he talked about at the end of section 4 of his paper. Now he may not have used the same terminology that is in use today, but that is what he meant. You can see another change in terminology at the end of section 3 where he uses β for what we now call γ. We now use β for a speed as a fraction of the speed of light. So we shouldn't get overly concerned about the specific terms that were used over a hundred years ago compared to the terms that are in use today.

Does that clear things up for you?

Salman2
Does that clear things up for you?

1. But just so I am sure I understand you...we can conclude then that there are two completely different and non-contradictory "time" concepts for Einstein, (1) coordinate time that we use t to symbolize within (x,y,z,t), and (2) proper time that uses tau as symbol. This then would be the final answer to my OP question...how did Einstein define time ? Makes sense to me, but please let me know if I error.

2. Also, in your stopwatch example. Suppose we have a runner moving between points A and B. Would it be true that Einstein would say there are two different measurements of "time" possible for this circumstance. So, the first, would be coordinate time, and would be measured by an observer using a stationary stopwatch (say at a position midway between A and B) to determine the time for the runner to move from A to B. The second would be proper time measured if the runner carried the stopwatch and was both runner and observer. So, in theory, Einstein would say the two different time measurements should not be the same for the same race (if we could design a watch sensitive enough to measure the difference at such slow speeds)...would this be correct understanding of Einstein and his use of the concepts of coordinate time and proper time ?

Gold Member

1. But just so I am sure I understand you...we can conclude then that there are two completely different and non-contradictory "time" concepts for Einstein, (1) coordinate time that we use t to symbolize within (x,y,z,t), and (2) proper time that uses tau as symbol. This then would be the final answer to my OP question...how did Einstein define time ? Makes sense to me, but please let me know if I error.
Einstein is credited with having said, "Time is what a clock measures". This would be the proper time. Then he uses the proper time on a non-accelerating clock to synchronize the proper times on remote clocks at rest with the first one as part of his definition of a Frame of Reference. It's because all these clocks are not allowed to accelerate that allows the proper times on all these clocks to be used as coordinate time for the FoR.
2. Also, in your stopwatch example. Suppose we have a runner moving between points A and B. Would it be true that Einstein would say there are two different measurements of "time" possible for this circumstance. So, the first, would be coordinate time, and would be measured by an observer using a stationary stopwatch (say at a position midway between A and B) to determine the time for the runner to move from A to B. The second would be proper time measured if the runner carried the stopwatch and was both runner and observer. So, in theory, Einstein would say the two different time measurements should not be the same for the same race (if we could design a watch sensitive enough to measure the difference at such slow speeds)...would this be correct understanding of Einstein and his use of the concepts of coordinate time and proper time ?
Not just two, but an infinite number. Time is relative, not absolute or narrowed down to just two types.

The proper time is what any clock measures, whether it is accelerated or not. But if it's never allowed to accelerate, then we can use it as coordinate time. But remember, another clock moving with respect to the first one will be running at a different rate and if it is not allowed to accelerate (once it gets to its constant speed), it can be used as coordinate time in a different coordinate system (Frame of Reference).

Let me take the opportunity of your question about a runner to have a little fun with this. I'm going to assume that these people don't know anything about relativity. Here we go:

Let's say that a bunch of runners start their own stopwatches when the gun fires at the start of a race at point A and then they each punch the lap button on their stopwatches when they each arrive at point B. The lap button displays the elapsed time but allows the stopwatch to continue to run and you can see this accumulating time when you punch another button. So they all record their individual elapsed times and punch the other button to allow their stopwatches to continue to display the time since the start of the race. They do this because they want to see if all the runners started their stopwatches at the same time.

And what do they find? First, they realize that all the stopwatches are now ticking at the same rate. In other words, whatever the differences are between the stopwatches remains the same, so they believe the clocks are accurate.

But the second thing they find is that the accumulating time on the first place winner's stopwatch is earlier than all the others implying that he may have punched his start button later than the others in an attempt to give himself a better time. And the same with all the others in the order in which they arrived at the end of the race. The slowest runner's stopwatch is displaying the latest accumulating time. So this puts into serious doubt the actual race statistics.

So these people decide they will get some unbiased measurements of the race times for each runner. They get a whole bunch of people, each with their own stopwatches and they place them all along the race route. They are each instructed to start the stopwatch when the gun fires at the start of the race and to record the time displayed on the stopwatch when they see each runner reach the end of the race. What will they find?

Again, each one will measure a different time for each runner. The one closest to the end of the race will have the shortest times and the one closest to the start of the race will have the longest times. Why is this? It's because the one at the end of the race is starting his stopwatch later than the one at the start because he has to wait for the image of the gun firing to travel to him and he doesn't have to wait any time for the image of each runner to reach him because he is right there at the end of the race. Not only does the one at the start of the race not have to wait any time to start his stopwatch but he has to wait for the image of each runner to get back to him, making his measured time even longer than the one at the end. And all the timers located along the track will have proportionately different times between these two extremes. So there are so many different measurements of the time it takes for each runner to get from point A to point B. How are they going to make sense of it all?

Well, some smart guy among them realizes that if they ran the race in the other direction, and assuming that the runners ran at the same speed as before, they should get the same elapsed time for each runner as before. When they do this, they discover that the person who is measuring the racers at the midpoint is the only one who gets the same time for each runner in both cases. So they decide from here on out to make a new rule when timing races: they will put their official timekeeper at the midpoint of each race.

That was fun. But keep in mind that they have just defined the meaning of time on remote clocks at rest with one another, the same way that Einstein did. They still realize that the accelerated clocks (the ones the runners carry) will have a different concept of time.

Salman2
Einstein is credited with having said, "Time is what a clock measures". This would be the proper time.
Excellent ! I was always under the impression this was the coordinate time that Einstein was talking about in this famous quote.

So, what you say below seems to me to be the correct answer to my OP question about how Einstein defined "time"...I never made all these mental connections between proper time and coordinate time...your explanation is incredibly clear...thank you ! This thread is closed for me.

ghwellsjr said:
"Time is what a clock measures". This would be the proper time...

Then he [Einstein] uses the proper time on a non-accelerating clock to synchronize the proper times on remote clocks at rest with the first one as part of his definition of a Frame of Reference (FoR). It's because all these clocks are not allowed to accelerate that allows the proper times on all these clocks to be used as coordinate time for the Frame of Reference...

The proper time is what any clock measures, whether it is accelerated or not. But if it's never allowed to accelerate, then we can use it as coordinate time. But remember, another clock moving with respect to the first one will be running at a different rate and if it is not allowed to accelerate (once it gets to its constant speed), it can be used as coordinate time in a different coordinate system (Frame of Reference).

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