Q: Do time and distance exist in a completely empty universe?

Physicist: This is a classic philosophical question!

For a while, it was generally assumed that without matter distance and time would still exist.  After all: why not?  Time is time and space is space, and the material things in them are just “actors on a stage”.  If you remove all the actors, the stage is still there.

That’s not a proof one way or the other, but it does present a salient point: “what’s the damn problem?”

However, that stance took a hit when relativity came along.  First, Galilean relativity, that states that the physics describing how things move around works whether you yourself are moving or not.  His example was someone dropping a stone from the mast of a ship: from the perspective of someone on the ship the stone falls in a straight line (along the mast), and from the perspective of someone on the shore it falls along a curved path.  Both of those people perceive and describe the world exactly as though their “stage” were stationary around them.  Point is; there’s no way to tell whether or not you’re the “correct one” just by chucking rocks about.

Time and space, as seen in Stephen Massicotte’s “The Clockmaker”.  If Galilean relativity starts to sound too complex, keep in mind that it’s just talking about a stage and a clock.

The take-away from Galilean relativity is that, for any pair of events that happen at different times, perspectives moving with respect to each other (boat vs. shore) will see them happen at different relative locations.  Say you’re floating in a void and two firecrackers go off, one after the other.  If you’re moving in the right direction, at the right speed you can “catch” them both and see them both go off right in from of you (it’s important to have protective eye wear in an infinite void).  From most perspectives the firecrackers went off in different places and you had to move to catch them, but from yours, you were stationary and they moved so that they would explode in the same place.

(Left) The firecrackers are sitting still and as the cloudthing whips past they explode.  The explosions are in different places.  (Right) The exact same situation, but with the cloudthing sitting still and the firecrackers exploding (in the same place) as they pass it.  In relativity, there’s no way to tell which is “correct”.  In both diagrams time points in the upward direction.

Still, there’s no problem with there being some particular “stage” with everything in the universe moving around on it.  Heck, the Earth is moving all over the place, but you’d never notice.  The important thing is that a given object will take up a given amount of space (have a set size) that everything can agree on, and will experience the same amount of time as everything else.  In Galilean relativity, the size of objects, the distance between two events that happen at the same time, and time itself are all fixed.  So the dude on the boat and the dude on the shore will always agree on what time it is, as well as how far apart they are at any moment.

The only problem so far is that you can’t tell what’s moving and what’s not.  But there’s nothing to say that somebody out there is standing still.

The issues really start rolling in when you switch over to Einstein’s relativity (also known as “relativity”).  Both Galilean and Einsteinian relativity state that all of physics works the same independent of movement, but Einstein’s relativity includes the added rule “the speed of light is the same to everything, regardless of how that thing is moving”.

That extra rule has a lot of weird consequences that you have to be some kind of Einstein to figure out.

Just like in Galilean relativity, different observers can disagree about where an event can happen, but unlike Galilean relativity, in Einstein’s relativity they can also disagree on when.  Worse than that, the physical size of objects is different, and the duration of events is different, depending on how you’re moving.  You genuinely cannot talk meaningfully about much time or space things “actually” take up.

What you can do, is establish a particular “reference frame”.  Essentially, you measure time and distance from the perspective of some object (one might say “relative” to the object).  In a single reference frame (from the perspective of anything moving at the same speed as the particular object) everything has a size and a position and a time.  The unfortunate thing is that as soon as you look at the same things from a different reference frame, sizes, positions, times, and durations all change.

So finally, to the point.  If there’s nothing at all in the universe to base a reference frame on, then how do you define distance and time?  Keep in mind that you can’t point at a location and say “here” because there’s no you to do the pointing either.  You can easily talk about the size and age of an object in the universe, but the “stage and clock” of the universe itself, on its own, has no particular size or age without something to reference.

Or maybe it does!

Impossible to tell for sure.

The clockmaker image was stolen, without pitty, from http://www.post-gazette.com/pg/10034/1032914-325.stm.

The “cloudthing” is from Hertzfeldt’s opus: Rejected.

This entry was posted in -- By the Physicist, Philosophical, Relativity. Bookmark the permalink.

17 Responses to Q: Do time and distance exist in a completely empty universe?

  1. steve says:

    So then spacetime is just plain ol’ space in the absence of matter/mass?

  2. The Physicist The Physicist says:

    Not even that!
    The problem is that distances and times don’t make sense outside of some form of reference.

  3. Alex says:

    Let’s say we have a given reference frame and all positions and speeds of all objects at a given time in a matrix. Is it possible to transform that information to a different reference frame by a linear function? Is it like the change of bases? Or is this nonsense?

  4. Andrew says:

    I just started Lee Smolin’s “Three Roads to Quantum Gravity” (Perseus Books, 2001) and he takes a definite side. His opinion is that space cannot be an empty stage (absolute space) any more than a sentence can remain a sentence with all the words removed. I’m still pondering that.

  5. The Physicist The Physicist says:


  6. Orien rigney says:

    Let me answer by saying, with no references to neither “time or distance”, nothing can be used to describe an empty universe., The continuum it now exists in has no parameters, thereby making an empty universe impossible. It would simply be a part of the continuum.

  7. akshit says:

    time and distance were defined by humans there is no proof that they really exist or not one would say that when we move we cover distance and when things happen they require time to occur but it is just our means to describe things which surely are helpful to us but not necessary that true .in the question the important thing is not that Do time and distance exist in a completely empty universe? but the important thing is how you will define this empty universe? the basic parameters of our thinking are time and distance and if they are taken away then we have nothing to define empty universe.for example if you say that large black voids with nothing in them is empty universe then your imagination itself has included both time and distance,because darkness will be spread over a distance and nothing present or we can say that nothing has developed as time has come to a pause .

  8. Anthony Rose says:

    I think we don’t have to measure something to know it exists, as long as it has been measured before. Even more so the dimension we were using to measure it by. So if you took everything out of this universe, time, being a dimension*, would assuredly still be going on at any point for speeds less than light, despite the fact that we have no reference for that point nor anything there to experience it. To say that we may not think of time and distance in regarding such an empty universe is to beg the question, surely. And the words in the sentence analogy fails because a sentence has no dimensions beyond its words – unless you include the paper it was written on.

    * (Time must be a dimension of the universe rather than matter and energy because our relative experiences of it, as effect, cannot also be the sole cause or measure of it. Otherwise, what is the effect? What are we measuring?)

  9. Deson Bowenford says:

    Fresh link for “Rejected”. http://www.youtube.com/watch?v=MuOvqeABHvQ

  10. Ledar Augusto says:

    What assumptions can be made about a planet whose day is equivalent to 1000 earth days? Can anything be assumed about the planet’s size or distance form earth?

  11. The Physicist The Physicist says:

    Pretty much any planet can turn at pretty much any speed. There basically nothing you can say about a planet’s size or location based on it having a 1000-Earth-day day.

  12. Robert says:

    Hi, nice website. Whenever I Google phys/maths I invariably always get directed here. Would you be able to expand on the topic by reference to the thermodynamic arrow of time (entropy) at all? i.e. If all the matter in the universe were to suddenly disappear, there would be no moving particles to infer time from? Thanks.

  13. The Physicist The Physicist says:

    I hadn’t thought of that, but that’s true! Without anything to define entropy on there shouldn’t be a good way to tell if the “film is being played forward or backward”.

  14. Mitch says:

    I think your explanation was referring to special relativity only when you described the impact of “Einstein’s relativity.” Wouldn’t GR speak more directly to this question, since “matter tells space how to curve?” GR tells us that “the stage” changes if we start removing the players, and doesn’t have any form at all if there’s no mass/energy at all.

    Also, the SR effect that “when” and “where” don’t have fixed values without a frame of reference might not count as a full answer to the original question, since that’s true whether the universe is empty or full of stuff. SR instead gives an alternative to time and space (“space-time”) that does provide objective locations (“events”) and measurable separation between them (“intervals”). I suspect we can talk meangfully about this “stage” in an empty SR universe. For instance, even if we knew that all the matter in the universe was about to disappear, we could calculate the interval between the point in space time where I posted this comment and the point in space time at which the next president would have been sworn in. Hopefully we would find better things to do with our remaining time, but in an SR universe that calculation would be possible. Once we add in/switch to GR, that wouldn’t make any sense.

    Factoring the vacuum energy of “empty space” into this whole discussion is… left as an exercise for the reader.

  15. SM says:

    How could you have an “empty universe” ,as the question was posed, how can there be space without bodies within the space to thus define it. And vice-versa, how could you have the bodies without the space in which they may exist in. Either one is impossible without the other it seems.

  16. Mitch says:

    @SM, do you think the following alternative question sheds any light on the original?
    “If everything in our universe were suddenly removed, would it still make sense to talk about time and space?” There are at least two ways of thinking about this question, “would time and space still exist” and “could anyone say anything interesting about it?.”

    Gallilean relativity suggested that the second (“epistemological”) question should probably be answered “no.” But that doesn’t resolve the first “metaphysical” question, at least according to Newton who followed and appreciated Gallileo but still unselfconsciously talked as if space and time were absolute.

    I think Newton woud have been reasonably comfortable discussing e.g. what would happen in this universe after some supernatural event simultaneously removed every object in it. He could still assign coordinates to where Jupiter would have been next year, could tell you how you would have had to orient your telescope to spot Jupiter at midnight on December 1st. It would all be relative to where e.g. Cambridge “would have been,” but that’s merely an epistemological challenge not a metaphysical one — space would still be there, even if you would have trouble mapping your location without landmarks.

    I think Leibnitz, a contemporary of Newton, might have disagreed. He might feel that it couldn’t be the same universe if pretty much anything were removed, since the relationships among things would be profoundly altered.

    Fast forwarding to the 20th century, I think Special Relativity sharpens the epistemological problem, and General Relativity introduces a serious challenge to whether space would really be there at all if everything were removed. According to SR, casually referring to “midnight on December 1st” is simplistic, since even when there were observers they wouldn’t agree on the date. According to GR, Leibnitz was basically right: space-time is defined as a relationship among all the things in it.

  17. SM says:

    @Mitch, thanks for the reply.

    To your alternate question: “…would time and space still exist?” Sometimes I like to trace back the original meanings of words as I find it can shed some light on things. The etymology of the word “exist” is ultimately from latin: to stand forth, to emerge, appear. From this, you could reword your question “…would time and space still emerge”, or in other words, without the things within space/time from where would space/time emerge. I know, this sounds awkward, but the reverse might be a little more cogent: without (empty) space/time, from where would the things within it emerge from? Or, the part standing out from the whole, the part by itself doesn’t really make any sense. The perspectives of SR, GR and Leibnitz are largely in agreement with this, in that the relative nature of things are due to their mutual interdependence.
    And so the question of whether space/time exists without the bodies within it maybe is analogous to questioning whether there would still exist backs if all fronts were removed. Or how could you have a “back” without a corresponding “front”. From the Buddhist perspective, one indian scholar on Sunyata (emptiness – all things being empty of inherent existence) was quoted as saying: “Everything that exists does so dependently and everything that is dependently existent necessarily lacks independent objective existence.” Maybe some taoist somewhere might say that the object cannot be without the subject observing it.

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