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The way I usually see spacetime explained, it says that if you just sit still, you are moving at 0kph and so you are moving at maximum speed through time (ie. time for you is flowing at maximum speed). However, sitting still we're moving at the speed of our galaxy through space, which is about 600km/s. The speed of light is about 300,000km/s. So for simplicity's sake, let's say the galaxy is actually moving through space at 1,000km/s. Does this in fact mean that if I sit still on Earth, time for me is actually flowing 1/300th slower than if I were sitting still with respect to the universe? And does it also mean that if the Milky Way were travelling at 99% the speed of light, time for me would be flowing at 1% the rate of the flow of time for someone that was sitting still with respect to the universe?

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  • $\begingroup$ It is funn that you accept as answer an invitation to study (not to call it a reprimenda). Let me have some fun as for I have been criticised and even downvited for a correct answer to an ill-posed question :) $\endgroup$ – Alchimista Jan 9 at 23:46
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Your question has a misunderstanding at its root: You say, "So for simplicity's sake, let's say the galaxy is actually moving through space at 1,000km/s". The problem here is that the whole point of Relativity is that the idea of movement with respect to space is meaningless -- the only thing that has meaning is movement with respect to other bodies.

Time dilation is also relative. If you're moving at 1000kps relative to Fred, Fred sees your clocks as running slower, and in his "reference frame" they are. But you, in your reference fame, see Fred's clocks as running slower! (This is the essence of the famous Twin Paradox.)

You're being led astray by your intuitions about space and time. (And don't be ashamed about that. Newton, who was probably the greatest physicist ever, even greater than Einstein, and Kant (one of the great philosophers) and many, many others had the same intuitions. Yet experiment has taught us that they were wrong.) Neither space nor time is absolute, and an understanding of Special Relativity (which is much easier to understand than it was to discover in the first place!) is required to ask as well as to answer your question.

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  • $\begingroup$ Do you mean that 1) our galaxy has no proper motion to speak about 2) that no observer can be conceived still respect to a reference frame in which our galaxy has the above motion. ? Note that the op compare himself sitting on earth to a nearby observer still respect to universe (comoving). How do extrapolate so much errors from the op text? I also used the expression "moves through space with speed ...." obviously vs a reference. Where the op let you conclude that he believe in an absolute space? The important point is its clock vs that of another observer happily comoving. $\endgroup$ – Alchimista Jan 9 at 20:07
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    $\begingroup$ @Alchimista Proper motion, and "motion through space", are very different things. The former is motion relative to a reference - the center of mass of the Solar System. The latter makes no sense, because space is not a thing and motion cannot be measured relative to it. OP is definitely thinking of the erroneous idea of "motion through space". The correct answer is to properly define the basic concepts so they can reconsider what it is that they're asking about. $\endgroup$ – Florin Andrei Jan 9 at 20:54
  • $\begingroup$ @Florin Andrei. Ok perhaps the OP thinks something on your line but I did not notice anything special to deduce that. Nor that the answer here does indeed answer the question even if the latter is ill-posed. In no way op suggested to think of a not specular outcome or that time dilation is observed by only one of the two. I did edit to avoid misunderstanding and perhaps help OP to reconsider the real meaning of the Q. $\endgroup$ – Alchimista Jan 9 at 23:03
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As far as you are considering the proper motion of the galaxy towards the Great Attractor the speed is less than a percent of the speed of light c.

Although astonishing this speed doesn't require a relativistic correction.

Of course if we were to sit on a galaxy moving at, say, 0.9 × c, then we would be like the travelling twin of the famous "paradox" as compared to someone still nearby and watching us.

However for calculating the time dilation you can't go by % proportion as in your question but apply the relativistic formula

$$\Delta t^\prime = \frac {\Delta t}{\sqrt{1-\frac{v^2}{c^2}}}$$

which expresses the fact that the moving observer's period of the clock $\Delta t^\prime$ is longer that the period $\Delta t$ in the frame of the clock itself.

that I copied from https://en.m.wikipedia.org/wiki/Time_dilation

It might be worth pointing out that the formula is valid for both observers and thus they will see each other's clock ticking slower.

Related but more general questions and discussion by following How does space time differ between galaxies?

in which the effect (lack of) of galaxies on spacetime is attacked from a general relativity point of view (how does galaxy's mass influence the spacetime curvature).

edit after receiving comments I am not mirroring anymore the wording "moving through space" as it leads to think, or that the authors of the Q and the A think, of absolute motion in absolute space. I also add that the conclusions for the observer on the galaxy and the one still coincides and both are right (unless the galaxy for some reason turns back ;)

Nevertheless

I would like to point out that moving through space is a perfectly sensible sentence in both common speaking and in physics. Through what something should move when its spatial coordinates are changing if not space? :)

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  • $\begingroup$ There is no such thing as "motion through space". All motion is relative to some other object. Space is not an object. OP's question is misplaced, and this answer perpetuates the mistake. $\endgroup$ – Florin Andrei Jan 9 at 20:42
  • $\begingroup$ I completely disagree as for the wording might be to adherent to that of the question but I do think that the OP and certainly not me think of a kind of absolute motion. He is comparing the watch of him sitting on milky way to that of him sitting still out of the galaxy. Obviously the still observer is it so vs whatever reference (great attractor, CMBR or whatever lead him to conclude that the galaxy move with a certain speed). You and others do not notice what is asking at the very end. $\endgroup$ – Alchimista Jan 9 at 22:17
  • $\begingroup$ 600 kms divided by 300.000 kms is 0.2%, not 2%. Also the Twin paradox has less to do with high speeds, than acceleration that breaks symmetry between observers. $\endgroup$ – AtmosphericPrisonEscape Jan 9 at 22:52
  • $\begingroup$ @AtmosfericPrisonEscape thank for signalling the speed data plus 1. No really clear what do you mean by breaking the symmetry. We do not have to solve any so called paradox here. Which by the way isn't removed by acceleration that is redundant in SR. I did mention the twins because if the galaxy were to move fast enough then yes the two observers will experience time dilation. Wonder if you have read. minus 1 $\endgroup$ – Alchimista Jan 9 at 23:18

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