What’s the ‘Proper Time’?

Today’s post revisits one of my favourite themes in Theoretical Physics – time. In previous posts we’ve looked at the idea of the present and how the theory of Special Relativity refutes its absolute existence – and we’ll be drawing on this idea again here. Today I want to discuss the idea of ‘proper time’ and tell you what it is, alongside a deeper explanation of the geometry  of spacetime.

Back in the day it was believed by many, including the great Newton who put together the three laws of motion, that time was absolute. This meant that wherever you went in the universe, a clock at one end of the cosmos would be ticking in synchronisation with one at the other. As though, there was a universal time, running on an almighty clock in the sky and all other clocks in the cosmos would adhere to its pace. Not so. With the discover of Special Relativity, we learn that the ticking of one’s clock and the time measured between events, depends on where you are in the universe. It depends on whether you’re near a gravitational field and how fast you are moving. The closer you move to the speed of light, the slower your clock will tick. The closer you are to a heavy mass, the slower your clock will tick. Let me just caveat here – this is not a special property of just clocks! The is the property of time as we know it, itself. A clock is just a mechanical object that we have devised, which has a constant periodic tick, from which we can then measure other events against. It is not just this tick that slows down, it is all atomic processes. The beating of your very heart would slow down in a strong gravitational potential or when travelling at a fast speed – for in essence your heart (if regular in its beating I hope!) is nothing more than a type of clock. If you need a reminder of how time is warped by relativistic effects I refer you to these two posts ‘Does the present really exist‘ and ‘Black Holes: #1 Falling In‘.


When describing an object we use 4 coordinates, three for the spatial position of the object and one for the time: x, y, z, t. Now the framework used to describe the geometry of everyday space is called, by mathematicians, Euclidean geometry. Another very useful tool employed to visualise spatial geometry is a standard two-dimensional graph. If we plot on a page two axes – y and x, one representing one direction e.g. North and the other a direction perpendicular to it e.g South and then plot the relative positions of two objects on this graph, the line joining them represents the distance between these two objects.


Of course in real life there are three spatial dimensions, so we can also plot a three dimensional graph. Imagine a room. The z axis protrudes out the floor straight up to the ceiling, and the x and y axis exist in the floor at right angles. Your feet exist at one point in this graph and the door knob at another, the straight line across these three dimensions represents the distance between your feet and the door. Simple right? I’m sure you knew that already. Where am I going with this? Bear with me.


(A 2D representation of a 3D graph!)

Next step. How do we describe the geometry of four dimensions? Well this is the geometry of space-time. The graph we use here is called a space-time graph or space-time diagram. Now unfortunately I can’t create a nice visual analogy for you this time, because if you can visualise four-dimensions you’re a super-human (or an alien). We have the three-dimensional graph from before with an extra axis, protruding out in an extra fourth dimension representing time. Now again we plot two things into the graph – we call these things events instead of objects now because they include time. For example, Event A could be Big Ben chiming at 12pm on the 18th June 2017 and Event B could be New Year’s Eve 2017 at the Eiffel Tower. Now what does the line on the space-time graph connecting these two events signify? Clearly not distance. The line connecting two events on a space-time four-dimensional graph represents a quantity theoretical physicists called proper time. 

Proper time?! What on earth is that I hear you say. Let me explain. Proper time is a construct made from the difference in the four coordinates x, y, z, t between two events (along with a factor of c – the speed of light). And whereas the time (t) between two events is not always measured to be the same because of relativistic effects (somebody running fast will measure the time between two events to be less than somebody standing still) any observer, regardless of their place in the universe or their speed will always measure the proper time (the combination of the change in all x, y, z and t) to be the same. This is very profound indeed – we’ve found a quantity, composed of the spatial and temporal coordinates that is invariant. The symbol for proper time is tau, τ. The equation is given here:


Why do physicists call it proper time? Well my inkling is because, as I mentioned before, we  as humans are so deeply unsettled by the fact that time is not measured the same for all that we wanted to give the quantity that we did find to be fixed, a connection to our beloved time.

So just to re-iterate the key points here. A space-time graph, is a graph of four dimensions which is exists in four-dimensional space-time geometry (x, y, z and t). Two events are plotted on the graph and the magnitude of the line joining them represents the proper time between the two events. This quantity is measured to be the same for any observer, regardless of their motion. So as not to confuse these special 4D line with 2D or 3D lines in normal Euclidian geometry, we call the lines in four-dimensions worldlines. 


(A 2D representation of a 4D space-time graph – even worse! You can ignore the world sheet and world volume for today.)

In a way this discovery does alleviate my unsettled feelings to do with the relative nature of time. With proper time there now does exist a quantity, composed of all four dimensions whose measurement remains invariant between any two events in this universe. The invariance, we initially believed held for time, exists instead on a higher dimensional level, incorporating time as a component. And thankfully it does, for a universe where everything was truly relative and nothing absolute wouldn’t sit well with our burning desire to seek out an underlying simplicity to nature.


44 responses to “What’s the ‘Proper Time’?

  1. Just a couple of points. It seems to me a one dimensional line in space might incorporate both north and south. Wouldn’t a two dimensional configure require east and west? Secondly light, by definition, travels at the speed of light. So why does light take time to travel any distance? As I am rather alien in much of my behavior I must admit that the fourth dimension is still rather puzzling, just as the bulk of the rest of the 11 dimensions now in fashion.


    • Hi Jiisand, we seem to have some similar areas of thinking. I do not see any other responses to your questions so i hope my comments may be of some assistance for future thinking.

      Re: your first point – many humans have shared this thought, it is both how and why maps work and allow us to succesfully negotiate our way about our planet! 🙂 Just how a 2 dimensional plan works to let us navigate a 3 dimensional sphere does get my mind a little boggled sometimes but as it seems to work well i relax a little and trust maps do what i want them to without digging too deeply :-). Personally, in a more general sense of the 1D 2D thing i prefer to use the terms positive and negative (relevant to the dimension being considered) rather than less specific terms like N, S, E and W. It does get a little tricky for my human brain to identify though, when you have positives and negatives all in 3D to know exactly what is opposite to what! It gets worse when you add in the complications of symmetry, mirror symmetry and rotational symmetry in 1,2 and 3D.

      Re: your second point. If we go with the standard ‘flow’ and think of light travelling it is very important to understand that while light might be the ‘fastest’ thing we know of in the Universe the speed of light is NOT constant within it. The speed of light VARIES depending upon which medium it travels through at the time. Light moves fastest through a vacuum and slower through more dense media. If you split a light beam into two seperate beams and have them travel the exact same distance to get to a single collector and have one beam travel in a vacuum and one through glass say, the beam in the vacuum will hit the collector before the beam passing through glass! Crazy huh? As for the time it takes? Consider what it is we mean by speed: speed is a distance divided by the time it takes to move that distance eg. miles per hour or metres per second or in astronomy we use the term light year (speed of light times a certain time) to measure a distance. (D = c(m/s) x time (in years) or c = D/t).

      But here’s a thought… we say light is an electromagnetic WAVE. A wave on the ocean can travel from one side of the Pacific Ocean to the other BUT no particle of that wave will move any more than a few feet from it’s original location. The water particles move more vertically than they do horizontally and yet we ‘see’ the wave top travel continuously for thousands of miles (assuming we can account for the interference of other waves on the surface.) A surfer can travel with a wave horizontally for many metres but the water underneath him stays put (until the wave ‘breaks’) as is evidenced by the wake he leaves behind.

      Now apply this thinking to light – light ‘particles’ don’t actually move along the light beam they simply do what water particles do and transfer their energy to the next ‘particle’ making the energy seem like it is physically moving in one direction when the real movement, a (cyclical sine wave form: 0,+,0,-,0) vibration, is perpendicular to the apparent direction of movement.

      Of course, exactly how this principle would apply in a vacuum where there are no ‘particles’ i have yet to fully comprehend 🙂



  2. “The symbol for proper time is tau, τ.”
    And, of course, any similarity to the ancient word TAO is purely coincidental, accidental, or an inside joke.
    And so we created the math to force the Universe to fit into our
    pre-conceived notions. How convenient for us.

    Liked by 1 person

      • Tao
        [dou, tou]
        Dao (noun)

        Liked by 1 person

    • The seen and the unseen (known and unknown, aspects of Yin and Yang) are both equally vital aspects of True Reality. Science does not do ‘unseen/unknown’ all that well! 😉 Science seems to me to believe everything that is hidden has to be brought out (and dissected) into the cold hard light of day and that the darkness of night should be banished forever as it is something inherently ‘evil’ or wrong and should have no place or value in our life.

      While i do see a value in scientific understanding i believe humans would be better served if the above were better understood and our ‘worship’ of science as the only way to understand our life and universe we live in was not so all pervasive or cock-sure of itself.

      Knowing there are things we don’t know or have not considered enough are very healthy for us limited human beings in the long run. 😉


      Liked by 1 person

  3. Sorry about my first comment. Your north-south business is, obviously, correct. But the fact that light travels in a zero time span still puzzles me.


  4. What Physists don’t account for is the variable of awareness or consciousness. There is no frame of reference without it. All variables follow a particular analogy or algorithm only because they all are empowered by this life variable. The day this is discovered only then all algorithms will Fallon place
    Time on moon or for a tortoise or a humming bird varies as interpreted by human beings. There is no physist on moon or for the bird. Man alone has this concept. While it’s so nice to go through these equations etc they may not completely provide the answer.
    There is but one time, if at all, ie Now.
    PS I fully respect the author n the science behind the topic.

    Liked by 2 people

    • Yes, you raise a deep philosophical idea over whether time is a by product of a consciousness understanding of nature, which I really appreciate. Though the way I see it change happens regardless if a human is there to perceive it. A tree falls even if nobody is watching and if that tree falls there is an interval of time that exists between its upright state and its changed fallen state. These changed states to me at least give evidence for an independent flow of time. Thank you for reading and your insight!


  5. Pingback: What’s the ‘Proper Time’? | SHOUT OF A KING·

  6. Time is part of the creation, everything has a time on its own, but it’s relative for the one who lives it.
    P.S. did you have the time to check the post “second hand dreams”?


  7. Reblogged this on Richard's Watch and commented:
    Time for my readers to get another update on how scientist’s regard time (see Science & Scripture hub). Here, theoretical physicist Mekhi reminds us, ‘the theory of Special Relativity refutes (time’s) absolute existence.” NOW that fact has already been well-known from the days of Jesus Christ’s first followers for, as His lead-disciple Peter wrote, “But do not forget this one thing, dear friends: with the Lord a day is like a thousand years and a thousand years are like a day” (2 Peter 3:8 NIV). I submit, nevertheless, that the concepts she espouses of ‘proper time’ and its associated ‘world-line’, ‘world-sheet’ and world-volume’ could be a way into scientifically grasping how the scriptural equivalent of Newton’s classical laws of action and reaction – ie sowing and reaping (Gal 6:7-9 ‘rule of life’) – actually manifest spiritually as well as materially through generations. Also, events of modern history foretold in biblical prophecy may also come into such a study. Mmm, most interesting Mekhi, thank you very much.


  8. “The beating of your very heart would slow down in a strong gravitational potential or when travelling at a fast speed.”
    This isn’t something we usually think about when studying relativity theories. I don’t know that I’ve ever seen it put quite like that. Thank you for that thought!


    • Thank you! Yes when studying relativity theories it is often clocks that are used to evidence the slowing down of time but for me this doesn’t explain the point clearly enough as clocks are just man-made products we have designed. The second, we have chosen as the standard clock interval means nothing in nature – it is just a measurement of time we chose in fact because it was similar to a human heart beat! Something very familiar to us. So yes I like to use this example to really emphasise it is the processes of nature that all run slower at fast speeds or in strong gravitational fields!


  9. Time to me just records everything that happens. Every detail of everything.The only other thing that I can say is that when I go travel out of body. One day in another realm is only one hour here on earth. Not sure why but it’s like that.


  10. Pingback: What’s the ‘Proper Time’? — Rationalizing The Universe | Aheadguide·

  11. Pingback: Timespace Part 3 – G. Stephanie Morey·

  12. Interesting… Thank You Mekhi.

    I was thinking about time and our 4D world recently. One thought i had was to do with symmetry and the peculiarity time has in that unlike any of the spatial dimensions where we can assign our current position as an ‘Origin’ and them move in either a positive or negative direction from said origin we can only ever move in the ‘positive’ direction in time, we can imagine time as a negative quantity (like remembering the past for example) but we can not reverse our time direction like we can all other movement?

    The other thought i had was that since the time of the Big Bang practically all anti-matter has annihilated most of the matter and we are left with just a little of the original matter that creates the observable Universe. Would a Universe created of anti-matter therefore balance out the time imbalance by having anti-time or backwards moving time??

    Finally, if time is an actual dimension that is capable of being ‘swapped’ with any of other the three dimensions to be mathematically equivalent to our 3D reference frame, could we then travel backwards in time while keeping the new fourth dimension a one-way vector (i.e. having only zero or non-negative movement)?



    • Very interesting thoughts lwbut, let me address them one by one as best as I can!

      Firstly yes that is the peculiar nature of time as opposed to the other spatial dimensions. With x,y,z we are free to move in the negative and positive direction but with time we are confined to only traverse forwards. It is been mused by some physicists, Kip Thorne for example, that there may be higher dimensional beings that are 4D (as we are 3D) that could traverse time in both directions – but this is all hypothetical of course. If you’re interesting in this read the chapter titled ‘Bulk Being’s in ‘The Science of Interstellar.’ We sadly are stuck going forwards.

      Interesting idea! I myself have read no papers that have drawn on this theory. A point that makes me think this is interesting it that in Feynman diagrams when one draws an anti-particle they indicate the time arrow as pointing in the opposite direction (backwards) to the other particles. I’ll see if there are any thoughts on this idea floating about.

      And no unfortunately the mathematics stops the time dimension being easily swapped with any of the spatial dimensions. If you see my equations above for Tau you see the time symbol does not have a negative sign in front of it while x, y and z do. This sign allocation distinguishes time from the rest of dimensions.

      I hope this was helpful! Thanks for your interest in the blog, Mekhi


  13. Well done Mekhi I can relax along with you egg-heads knowing there is something unchangeable about our universe. At 75 I have a sneaking suspicion even my old- fashioned real time is running out.

    Liked by 1 person

    • Thank you for your support as always kertsen! Yes real time is cruel. I’m always trying to find a way to seek some solace in theoretical physics from the knowledge my real-time clock is ticking.


      • ‘ Ah, make the most of what we yet may spend,
        Before we too into the Dust descend;
        Dust into Dust, and under Dust to lie
        Sans Wine sans Song, sans Singer, and –sans End!’


  14. just remember: numerical-theory by itself can’t/doesn’t properly-explain the true nature of reality. 1 + 1 =3 has been demonstrated to be true ‘ on paper’. but when one goes outside, collects a rock, then collects another-rock, a ‘third’-rock is guaranteed to never somehow self-materialize out of nowhere. one has to go and get it ( a rock ) himself. ‘then’ one correctly has three-rocks ( i.e. 1 + 1 + 1 =3 ; 1 + 2 = 3 ). forgive me if am not a big-fan on numerical-theory. it seems like almost ‘anything’ is possible with numbers on paper , which, again, is ‘not’ the nature of reality.


    • Hi trex363 thanks for your comment. I can appreciate the concern over whether mathematics can truly be representative of nature – i’ve watched far too many documentaries on this myself. Do tell me though, who has managed to demonstrate 1+1=3 to be true on paper?!


      • Hi Mekhi,

        I took the approach that since it has been stated as true it must be true (The White House approach!) and therefore tried to figure out the proof for myself.
        My workings were as follows:
        We have all heard it said of someone that they took 2+2 and came up with 5 (2+2=5).
        We know that 1+1=2 so we can restate the previous equation as (1+1) + (1+1) = 5 or 1+1+1+1+1=5
        removing 1 from both sides gives us an equivalent equation so 1+1+1+1=4, and doing the same again ‘proves’ that some people can state 1+1+1=3 🙂 Q.E.D.
        Next time: Black = White.



  15. Thanks, Mekhi for helping us think.

    Though a beating heart slows down, and indeed all atomic processes slow down, at high speeds or in strong gravitational fields, could that be an observation of the physical properties by which we measure time and not necessarily the passage of time itself?

    Time might be defined as the property necessary to effect any change. Without time there could be no movement, in fact no change at all. Even thought requires time to change from premises to a conclusion. Could Time be more like a medium for the familiar dimensions? To me, this begins to explain why Time only moves forward.

    I have written a little on this idea. See https://ectorward.wordpress.com/2017/08/27/the-time-axis-and-a-4-d-universe/


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