B Time Dilation b/w Galaxies: Dark Matter Impact?

[AndrewDes]

If time slows down near a black hole then doesn't it stand to reason that time is slower in our galaxy than inbetween galaxies. If that's the case, wouldn't our measurements of distant galaxies be over estimated do to time being faster intergalacticly. Would this time dilation help explain part of dark matter?

 

[PeroK]

If time slows down near a black hole then doesn't it stand to reason that time is slower in our galaxy than inbetween galaxies. If that's the case, wouldn't our measurements of distant galaxies be over estimated do to time being faster intergalacticly. Would this time dilation help explain part of dark matter?

Dark matter is postulated to explain the rate of galaxy rotation, which is higher than expected if we consider only visible matter. See here, for example:

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

Gravitational time dilation effects on observations from Earth are effectively negligible. If you do the maths, you are talking about something like milliseconds per century difference.

 

[Ibix]

If time slows down near a black hole then doesn't it stand to reason that time is slower in our galaxy than inbetween galaxies. If that's the case, wouldn't our measurements of distant galaxies be over estimated do to time being faster intergalacticly.

Not to any significant extent. Even super-massive black holes have negligible time dilation effects at this distance.

Would this time dilation help explain part of dark matter?

No. Galactic rotation rates vary with distance from the core because they aren't rigid discs, and the difference between their observed rotation profile and the prediction based on visible matter only isn't a constant factor, which it would need to be if it were to be explained by a mis-calibration of our clocks.

 

[Ibix]

Not to any significant extent. Even super-massive black holes have

Just to put a number on this - if you replaced the Sun with a million-solar-mass black hole, Earth clocks would tick 1% slow compared to a clock in intergalactic space (i.e., in the time it took an Earth clock to tick an hour, a clock in intergalactic space would tick an extra 3.6s). If, instead, you replaced Alpha Centauri with that same black hole then Earth clocks would tick something like 0.000005% slow (if I counted zeros right that means the intergalactic clock would get less than an extra millisecond per Earthly hour). The galactic core is a long way further away than that.

 

[AndrewDes]

Just to put a number on this - if you replaced the Sun with a million-solar-mass black hole, Earth clocks would tick 1% slow compared to a clock in intergalactic space (i.e., in the time it took an Earth clock to tick an hour, a clock in intergalactic space would tick an extra 3.6s). If, instead, you replaced Alpha Centauri with that same black hole then Earth clocks would tick something like 0.000005% slow (if I counted zeros right that means the intergalactic clock would get less than an extra millisecond per Earthly hour). The galactic core is a long way further away than that.

Im suggesting that our preception of time is being slowed because of the combined energy well of our entire galaxy, not just the black hole. Even if it's a small difference between our time and intergalactic Time, it would have a compounded effect on something we are perceiving as being billions of light years away.

 

[PeroK]

Im suggesting that our preception of time is being slowed because of the combined energy well of our entire galaxy, not just the black hole. Even if it's a small difference between our time and intergalactic Time, it would have a compounded effect on something we are perceiving as being billions of light years away.

No it wouldn't. And, if you say it does, then let's see your calculations.

 

[AndrewDes]

No it wouldn't. And, if you say it does, then let's see your calculations.

I don't have the math skills to do such a calculation but if a million solar mass object replacing our sun would slow time down 1%, then looking at the 1.5 trillion solar mass of the milky way as 1 object would slow time down significantly more as compared to space unaffected by gravity. Also speed affects Time, that's why the ISS time travels. So wouldn't the speed at witch our planet is moving+the speed the sun is moving+the speed the galaxy is moving all add up to some effect? Combine our relative speed with being in that 1
5 trillion SM gravity well and we must be getting into some sort of significant difference compared to being stationary in intergalactic space.

 

[Vanadium 50]

I don't have the math skills to do such a calculation

So how can you say that those who do are wrong?

 

[jbriggs444]

I don't have the math skills to do such a calculation but if a million solar mass object replacing our sun would slow time down 1%, then looking at the 1.5 trillion solar mass of the milky way as 1 object would slow time down significantly more as compared to space unaffected by gravity.

One million solar masses at one A.U. distance versus 1.5 trillion solar masses at some 25,000 light year average radius?

So about 1500 times more mass and about about 25,000 times 62,000 = 1.5 billion times more radius. That's about a factor of one million less gravitational time dilation

[Gravitational time dilation scales with gravitational potential. Gravitational potential scales proportionately to mass and inverse proportion to radius]

Also speed affects Time, that's why the ISS time travels. So wouldn't the speed at witch our planet is moving+the speed the sun is moving+the speed the galaxy is moving all add up to some effect? Combine our relative speed with being in that 1
5 trillion SM gravity well and we must be getting into some sort of significant difference compared to being stationary in intergalactic space.

No. Unless you can do the math, chattering on about small things adding up to big things does not cut it. Sometimes they do. Sometimes they don't. Math is what can tell us which it is.

 

[Ibix]

Im suggesting that our preception of time is being slowed because of the combined energy well of our entire galaxy, not just the black hole.

No - a (relatively) tiny volume around a black hole is the only place in the galaxy where time dilation is at all significant. All of the rest of the dynamics is well explained by Newtonian gravity, meaning that time dilation is completely negligible.

Even if it's a small difference between our time and intergalactic Time, it would have a compounded effect on something we are perceiving a

I don't know why you'd think that. Typical gravitational time dilation calculations (like the one I did) compare a clock at some finite distance from a massive body to a clock at infinity. There's no further compounding to be done.

if a million solar mass object replacing our sun would slow time down 1%, then looking at the 1.5 trillion solar mass of the milky way as 1 object would slow time down significantly more as compared to space unaffected by gravity.

A 1.5 trillion solar mass object compressed into a few trillion kilometers diameter would cause significant time dilation for objects orbiting close to it, yes. The galaxy is much, much, much more spread out than that, and consequently its gravity is much less intense. Nowhere is its gravitational potential so high that you get significant time dilation.

Also speed affects Time,

That's a serious oversimplification, but for orbital motion it's close enough.

So wouldn't the speed at witch our planet is moving+the speed the sun is moving+the speed the galaxy is moving all add up to some effect?

Nothing significant. Stellar speeds are nowhere close to the speed of light, so the effect is negligible again since kinematic time dilation is proportional to $1/\sqrt{1-v^2/c^2}$.

 

[PeroK]

I don't have the math skills to do such a calculation but if a million solar mass object replacing our sun would slow time down 1%, then looking at the 1.5 trillion solar mass of the milky way as 1 object would slow time down significantly more as compared to space unaffected by gravity. Also speed affects Time, that's why the ISS time travels. So wouldn't the speed at witch our planet is moving+the speed the sun is moving+the speed the galaxy is moving all add up to some effect? Combine our relative speed with being in that 1
5 trillion SM gravity well and we must be getting into some sort of significant difference compared to being stationary in intergalactic space.

Most of the mass of the Milky Way is too far away to entail gravitational time dilation on Earth. The Earth is not in a deep gravitational well. In this respect, the calculations are everything.

 

[PeterDonis]

dosnt it stand to reason that time is slower in our galaxy than inbetween galaxies.

Slower in principle, yes. Slower by enough to appreciably affect any of the measurements you describe, no.

 

[PeterDonis]

The OP question has been answered. Thread closed.