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How did Einstein Define Time

  1. Oct 23, 2011 #1
    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.
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  3. Oct 23, 2011 #2


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

    Here's a link:

    Last edited: Oct 23, 2011
  4. Oct 23, 2011 #3


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    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."

    (from Section I.1, Definition of Simultaneity)

    [ghwellsjr slipped in while I was fiddling with my post]
  5. Oct 23, 2011 #4
    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)?
    Last edited: Oct 23, 2011
  6. Oct 24, 2011 #5
    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.
  7. Oct 24, 2011 #6


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    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.
  8. Oct 24, 2011 #7
    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 ?

    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 ??
  9. Oct 24, 2011 #8
    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. '

    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.
    Last edited: Oct 24, 2011
  10. Oct 24, 2011 #9
    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.
  11. Oct 24, 2011 #10
    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.
  12. Oct 24, 2011 #11
    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?
    Radiation? wouldn't you agree?

    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.
    Last edited: Oct 24, 2011
  13. Oct 24, 2011 #12


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    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.
    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.
  14. Oct 24, 2011 #13


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    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.
    Yes, I think you've got it.
    I pointed this out in the previous post.
  15. Oct 24, 2011 #14
    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.
    Last edited: Oct 24, 2011
  16. Oct 25, 2011 #15
    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 ?).
  17. Oct 25, 2011 #16
    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.
  18. Oct 25, 2011 #17
    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'.
    Last edited: Oct 26, 2011
  19. Oct 26, 2011 #18


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    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.
    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.
    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.
    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.
    No, but I hope my previous comments have cleared this up for you. If not, ask again.
  20. Oct 26, 2011 #19


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    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.
  21. Oct 26, 2011 #20
    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.
    Last edited: Oct 26, 2011
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