Q: Since the Earth is spinning and orbiting and whatnot, are we experiencing time wrong because of time dilation?

Physicist: A little!

The movement of Earth, as well as the Earth’s gravity, change how much time we experience compared to other objects in the universe.  If we were to occasionally compare our clocks to clocks in tight orbits around black holes or neutron stars we’d find they run slower than ours, and if we compare with clocks floating deep in the middle of nowhere we’d find that those clocks run a little faster than ours.

However, there’s no “true” time to experience; you can never experience time wrong.  Time is relative which means that we can compare how time is passing for any two things, but there’s no ultimate “clock of the universe” to compare with.  Your watch, no matter where you are or how you’re moving, will always read 1 second per second.  That is, you’ll never see yourself in fast-forward or slow-motion.  In that sense we can’t help but experience time correctly.  Each of us may as well declare that our clock is the One True Clock, and everyone else’s is wrong.

Simply moving fast in a straight line isn’t enough to make your clock objectively run slowly compared to other clocks.  If two folk run past each other they both see the other experiencing less time and, weirdly enough, this isn’t a paradox and they’re both “right”.  There are two effects that do objectively (in a way that everyone in the universe can agree) cause clocks to run slow: the very poorly named “twin paradox” and gravity.

In spacetime the “length” (spacetime interval) of a trip is measured by a clock that makes that trip.  It turns out (this is not obvious, but it can be understood) that the shortest trips are the ones that are the most circuitous.  If you watch the ball drop on New Years and stay put for a year until the next ball drop, then you’ve made a pretty straight trip (in spacetime) between those two events.  This path is straight, so it’s long, and your clock will read more.  Instead, if you spend that year zipping around the solar system as fast as you can before coming back for the next New Years, then your path was decidedly not straight (in spacetime).  This all-over-the-place path is short and your clock will read less.  “The longest spacetime distance between two points is a straight line” may sound utterly insane, but it works.  Long story short: if your trip involves a loop, then your clock is falling behind.

As it happens, the Earth spins on its axis and orbits the Sun and, along with the rest of the solar system and all the stars that we can see, orbits the galaxy as well.  Each of these are loops, not straight lines, and each time the Earth makes one of these circuits it falls a little behind any clock that didn’t.  This is a little hypothetical: in order to get a clock to sit in the same place while the Earth does an orbit to meet up with it every year, it would need a big rocket (it’s not orbiting the Sun, so it should be falling into it).

As fortune would have it, you can just use the gamma function, \gamma = \frac{1}{\sqrt{1-\left(\frac{v}{c}\right)^2}}, to find the time dilation caused by running in a loop (for more complex paths, like those with different speeds, you still use the gamma function but you need calculus too).  The velocity of the spinning Earth at the equator is about 0.5 km/s, we orbit the Sun at about 30 km/s, and the whole kit and kaboodle orbits the galaxy at about 200 km/s.    The difference in time experienced between people living in Longyearbyen (near the pole) and people living in Ecuador (near the equator) is about one part in a trillion, which gives those proud Norwegians an extra second every 25 thousand years.  Don’t spend that second all in one place, Norwegians.

The time dilation from the biggest of these speeds, our movement around the galaxy, amounts to one part in 4.5 million.  That amounts to an extra second every couple months or an extra half solar year for every galactic year.

The second effect to consider is the curvature of space time caused by (or which is) gravity.  Things that are lower experience less time than things that are higher.  This can be explained (and even verified) by measuring how the frequency of light changes when it travels vertically in a gravity field.  The details are terrible, but for most practical purposes (“most practical purposes” = “not black holes”) you can find the time dilation between two altitudes by figuring out how fast something would be moving if it fell from the higher to the lower and plugging that v into \gamma = \frac{1}{\sqrt{1-\left(\frac{v}{c}\right)^2}}.

It’s reasonable to say that if you’re infinitely far away from something then you’re outside of its gravitational influence and your clock should be running “right”.  If you fell from “infinitely far away” to the surface of something big, you’d be moving at the excellently named “escape velocity” of that big something.  If you try leave a planet moving slower than the escape velocity, then eventually you’ll fall back.  Excellent name.

To escape the Earth from the ground you need 11 km/s.  More difficult is escaping the Sun (from Earth’s orbit) which requires 42 km/s.  To leave our galaxy (from here) you need somewhere between 500 and 600 km/s.  This time dilation from the Milky Way’s gravity has the biggest effect of those mentioned here.

The spinning of the Earth and the orbiting of the Sun do affect the amount of time you experience, but not by a lot.  Despite being closer to the Earth than the bulk of the galaxy, it’s our orbits around, and position in, our galaxy that affects our experience of time the most.

The Milky Way: a really big, really ineffective, time machine.

The Milky Way: a really big, really ineffective, time machine.

By virtue of being a member of the Milky Way, we experience about 1 second per week less than someone hanging out deep in the intergalactic void.  Most of that comes from the effects of our galaxy’s gravity directly; not from the motion of our planet.

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22 Responses to Q: Since the Earth is spinning and orbiting and whatnot, are we experiencing time wrong because of time dilation?

  1. Francisco Lebre says:

    Is it possible that Time is a complex dimension of Space?

    We can imagine an X axis with points connected side by side.
    Those 2 adjacent point are conected and would represent the smallest possible distance between 2 points over X axis.
    Lets call that distance “dx”

    We can also imagine an Y axis with points connected side by side.
    Those 2 adjacent point are conected and would represent the smallest possible distance between 2 points over Y axis.
    Lets call that distance “dy”

    Let’s also suppose that the size of “dx” equals the size of “dy”

    Whatever the smallest “dx” and “dy” are , they allways would be “Cathetus” of a right triangle existing in that plan. The correspondent “hypotenuse” will be greater than either “dx” and “dy”.

    So it would be impossible to have continuity in that plan, because if we considere “dx” and “dy” made with connected points , than the hypotenuse would allways be greater that the connected points “dx” or dy” and therefore NOT connected. (It will be impossible to have continuity in the hipotenuse direction.)

    That would be right except if:

    we could construct a plan where the hypotenuse is the same size of the Cathetus. That is : The hipotenuse would be the same size of cathetus dx and dy .

    How could that be possible?

    Let’s name “dx” =”dy” , the distance between 2 conected points , “L”

    L= dx= dy

    Now imagine that “dx” and “dy” in that plane (spacial) is associated with another ortogonal dimension (T = Time).

    Sqr (dx*dx + dy*dy + dT*dT) = dx=dy

    Sqr ( L*L + L*L + T*T) = L
    (considering Time T we could have the dimension of cathetus and hypotenuse equals to L )

    what do we get?

    L=iT

    T=iL

    Time is a complex dimension of Space. Time is the Phisics dimension that allow Space to be continuos.

    And now we have to considere that not in the 2 dimmensional plan but in a 3 dimensional space.

    Any spacial plan have an ortogonal temporal dimension called Time.

    hummm ? Is that possible?

    Francisco Lebre

  2. Doug says:

    Since there is not “one true clock” by whose clock is the universe’s age measured as 15 billion years? There could be different experiences of time so in some frame you would find a different age.

  3. Tero says:

    Interesting area. Dilation because of movement. And different speed because of gravity. Also makes you think about size. If atom works at different speed in gravity, could we say that size of the atom is changing. So curved space would be actually curved with sizes as well. And let’s say dark matter or some sort of gravity fields set the size of the atoms in space. And how do these work. As we can leave from earths gravity field with rocket, but we are still in suns and milky ways gravity field. So we are not really in empty space.

    So for distance, let’s say milky way as whole would be collapsing. We maybe can’t see that if everything in milky way would be collapsing (all including size of the atoms). So how would we actually see that would be that space around milky way would seem to expand. Like in net example. If we pull area from large net closer, near by objects are coming closer and closer together. But net in large scale does not change size. It just seems like that when close by objects are moving closer and closer each others.

  4. Niko D says:

    Isn’t it possible to use the Cosmic Microwave Background to determine some sort of neutral clock, which anyone in the universe can use to keep track of things?

  5. Rob says:

    “… you can find the time dilation between two altitudes by figuring out how fast something would be moving if it fell from the higher to the lower and plugging that v into (gamma)”

    Isn’t the speed you would be travelling at when you fall from a height h to the center of a body the same as the speed needed to travel in a circular orbit around a body? So to use the gamma factor you would use the same v for gravitational time dilation as for translational time dilation which would always result in the the effects cancelling out for a circular orbit at any height h?

  6. The Physicist The Physicist says:

    @Rob
    Nope. If you’re really close, then there isn’t much speed gained by falling and you’d have to orbit really fast. If you’re really far away, then you orbit slowly and would gain a lot of speed by falling. For orbits there is an altitude where the effects cancel, but definitely not all altitudes.

  7. Pingback: Time on Earth moves SLOWER than in space | TKG News

  8. Pingback: Le temps s’écoule plus rapidement sur Terre que dans l’Espace ! | La société solidaire et durable

  9. Alena says:

    Hey! This post could not be written any better! Reading through
    this post reminds me of my good old room mate! He always kept chatting about this.
    I will forward this post to him. Pretty sure he will have a
    good read. Many thanks for sharing!

  10. The Dro says:

    Next time I’m late for something, I’m just going to boast that time is relative…

  11. Ed says:

    Hi,

    Can you please note somewhere in your answers that time may or may not exist and all those devices that has been constructed to “measure time” are really not time measuring machines?

    There are so many assumptions in this answer that is becoming a disservice to your efforts to help us understand some of this issues.

    Clocks do not measure time.

    Regards,

    Ed.

  12. Avante says:

    @Ed So what do clocks measure, and what are you getting at?

  13. Tim Crowe says:

    This question seems to be asking if their is a slower reference frame from which to view the universe than that the reference frame of earth. If I understand correctly earth’s reference frame, including speeds of our galaxy and cluster movement, is at about 20% the speed of light if background radiation is 0% the speed of light. Or, the slowest speed we can go.

  14. Angel says:

    @Ed:

    Time exists. Time is a coordinate of the Euclidean temporal space curvature. However, this curvature is distorted by tensors that result from forces and energy. This distortion allows for time to be experienced differently, in complement with the speed of light which is equal in all frames of reference. There could exist such a thing as correct time: if you were located infinitely far away from a center of mass, assuming no other forces are present, with absolutely zero motion and zero energy, then there would be a correct time. However, considering that those conditions are inherently impossible — for requiring zero entropy, among other things — we cannot experience time correctly. However, given that time is relative, because any other frame can be chosen in the scheme of the universe, there is no such a thing as correct time. The conditions described above are the ideal conditions to choose time because it creates the simplest foundation; there is no particular obligation to choose that one whatsoever. Spatial time curvatures are a mathematical element. Mathematical elements do not exist in the physical world. However, the concepts we attempt to represent with those elements and their nuances exist because they are manifested directly unto the physical world. Of course, that is assuming that the physical world exists. Which I believe we all assume.

  15. Angel says:

    @Doug:

    Scientists have suggested to conclude that the universe is 13,798 thousand of million years old on the basis that the light from the cosmic radio microwave background has been traveling towards us for about that much time.

  16. Ed says:

    @Angel
    We all?
    https://www.youtube.com/watch?v=wgSZA3NPpBs

    From your answer:

    “Time is a coordinate of the Euclidean temporal space curvature”
    “Spatial time curvatures are a mathematical element.”
    “Mathematical elements do not exist in the physical world.”

    Regards,

    Ed.

  17. Marcela shu says:

    The time dilatation for me is just consequences of properties geometrical as the variations of the curvatures is equivalent for the variations of spacetime.how the speeds between two bodies in relative motions is not given by physical interpretations,but yes by geometrical interpretations,then the time dilatation and contractions are observed conjugated for the variations of speeds the relativistic level are variables,then how much major the speed major the curvatures of spacetime.then the time dilatation and contraction of space are just geometrical,linked at the 4dimensional spacetime continuum,are physical,as the biological cells must not suffer the same variations of time in speeds near the speed of light than the subnuclear particles.are things completely differents.the twin paradox are not real,but just show the differences of the velocities in relative motions or in accelerations,when the spaceships change it direction to return the earth,forget not than the antiparticles traveling backward in time cancel the time dilatation,because the time dilatation said is linked to the different styles curvatures of spacetime associated the variations of curvatures with the velocity.

  18. Angel says:

    @Ed

    You know what I meant by ‘we all’. It is clearly a blanket statement. There is not one thing 100% of humans agree in, but at least a significant majority would say the universe does exist. Particularly, those commenting here, most would assume so.

    @Marcela

    I am afraid you misunderstand some of the concepts you are talking about. You mentioned that antiparticles travel backwards in time, but there is no substantial evidence saying so; this is at most a conjecture. Even if there are evidence, traveling backwards in time does not cancel time dilation. Time dilation is the phenomenon of perceiving time faster or slower than the “usual” (note that usual is in quotation marks because technically there is no such a thing as usual, but you probably understand what I meant). It has nothing to do with traveling forward or backwards in time. Also, N.A.S.A is currently conducting an experiment on the Twin Paradox. So far, it does look real.

  19. Pingback: einstein's clock tower

  20. Ed says:

    @Angel

    Of course I understood, but poked some fun at the statement with the link as a way of showing that in science, specially what we perceived as a “reality”, could actually not be.

    My link in the reply to Avante while simplistic is a good description of what clocks measure and how they really work. I am aware of most of the documented experiments performed on time dilation and they suffer from different problems.

    Using clocks whether atomics, quantum logic or pendulum based are a poor way of analyzing time dilation since they don’t measure time.

    Are there variations on cesium decay or aluminum ion vibrating between two energy levels at different conditions (including speed)? I would probably say yes.

    Good reads:
    http://www.nist.gov/public_affairs/releases/aluminum-atomic-clock_092310.cfm

    http://www.nist.gov/pml/div688/logicclock_020410.cfm

    https://en.wikipedia.org/wiki/Hafele%E2%80%93Keating_experiment

    https://en.wikipedia.org/wiki/Ives%E2%80%93Stilwell_experiment

    https://en.wikipedia.org/wiki/Time_dilation_of_moving_particles

  21. Nova says:

    Clocks do not measure time, they measure and display the result of a mechanic inside of them completing a cycle, I.e 1 gear rotation = 1 unit of movement. Time is not measurable in the fashion, it can theoretically be derived as 1 unit of time = 1/the maximum number of events possible in the smallest unit of space without exceeding light speed.

    Please correct me if I’m wrong and post why.

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