Why do all cosmological models assume time flow is the same for everyone in the universe?

[Aki Tendo]

Hi.  The question above arises out of things like "The universe is 13 trillion years old." The assumption seems to be that everyone experiences time at the same rate, even though we know this isn't true. Relativity posits that as anyone accelerates, time slows down.  GPS satellites have to take this skew into account to even work.  So why does this get ignored in cosmological models?

Consider the following thought experiment.  I get in a spaceship that can accelerate to any speed less than c. It stands to reason that such a craft could go fast enough that its clock would only move 1 year in the time that the vessel went from here to the nearest star.  Yet, as it looks back at earth, it would see 4, possibly 5 orbits completed (depending on the exact fraction of c necessary to cause this degree of time dilation).

When we look at other galaxies the stars are moving too quickly to stay gravitationally bound to the system. Is Dark matter (or a portion of it) simply an optical illusion born out of time flowing in that galaxy at a different rate than ours? Can the observed motion in galaxies be slowed down enough to become gravitationally bound without using dark matter? If so, is this impossibly slow? Will it be the same for each galaxy (I predict no, see below).

Two points define a dimension, a ray.  Our present time and the "big bang" are 13 trillion years apart. Consider now an observer on a planet flung by a black hole to .9c some 10 trillion years ago. If that observer measures how old the universe is would they come up with the same answer? No.

Also, speed is a "change of position over time." c is ~300,000 km/s. Whose second though? Ours? The observer on the space ship that will perceive itself to reach Proxima Centari in a year even though far more pass on earth? The observer flung to .9c as observed from earth?  How do we know we aren't the ones going .9c relative to another observer?

Other galaxies are on different points of this literal timeline. For that statement to be false there would have to be a privileged reference frame, and that's already been proven not to exist through GPS satellites and other experiences. Everything on the line is moving away from the origin - the big bang. 

Are the stars of the Milky Way moving too fast to be bound to the gravitational center?  I ask this because, presumably, the stars in our galaxy should be in close to the same relative time frames - but not exactly. Stars near the center are moving faster through space, and therefore slower through time. Matter close to black holes should be moving the slowest of all through time.

In summary, I have grappled with these questions in my head a long time, but keep arriving at the conclusion that at least some of the problems observed with dark matter, possibly dark energy, come from shoehorning our own reference frame of time when we should know better given what we know of relativity. 

Or, more likely than not I'm missing something.

 

[beecee]

17 minutes ago, Aki Tendo said:

Hi.  The question above arises out of things like "The universe is 13 trillion years old." The assumption seems to be that everyone experiences time at the same rate, even though we know this isn't true. Relativity posits that as anyone accelerates, time slows down.  GPS satellites have to take this skew into account to even work.  So why does this get ignored in cosmological models?

Consider the following thought experiment.  I get in a spaceship that can accelerate to any speed less than c. It stands to reason that such a craft could go fast enough that its clock would only move 1 year in the time that the vessel went from here to the nearest star.  Yet, as it looks back at earth, it would see 4, possibly 5 orbits completed (depending on the exact fraction of c necessary to cause this degree of time dilation).

When we look at other galaxies the stars are moving too quickly to stay gravitationally bound to the system. Is Dark matter (or a portion of it) simply an optical illusion born out of time flowing in that galaxy at a different rate than ours? Can the observed motion in galaxies be slowed down enough to become gravitationally bound without using dark matter? If so, is this impossibly slow? Will it be the same for each galaxy (I predict no, see below).

Two points define a dimension, a ray.  Our present time and the "big bang" are 13 trillion years apart. Consider now an observer on a planet flung by a black hole to .9c some 10 trillion years ago. If that observer measures how old the universe is would they come up with the same answer? No.

Also, speed is a "change of position over time." c is ~300,000 km/s. Whose second though? Ours? The observer on the space ship that will perceive itself to reach Proxima Centari in a year even though far more pass on earth? The observer flung to .9c as observed from earth?  How do we know we aren't the ones going .9c relative to another observer?

Other galaxies are on different points of this literal timeline. For that statement to be false there would have to be a privileged reference frame, and that's already been proven not to exist through GPS satellites and other experiences. Everything on the line is moving away from the origin - the big bang. 

Are the stars of the Milky Way moving too fast to be bound to the gravitational center?  I ask this because, presumably, the stars in our galaxy should be in close to the same relative time frames - but not exactly. Stars near the center are moving faster through space, and therefore slower through time. Matter close to black holes should be moving the slowest of all through time.

In summary, I have grappled with these questions in my head a long time, but keep arriving at the conclusion that at least some of the problems observed with dark matter, possibly dark energy, come from shoehorning our own reference frame of time when we should know better given what we know of relativity. 

Or, more likely than not I'm missing something.

 

Your first faux pas is that the universe is around 13.83 billion years old. Secondly everyone's time, everywhere, moves at 1 second per second: It is only when we in our frame, view another person's frame that is moving relative to us that we notice there time as dilated, just as they notice our's as dilated.

DM is certainly needed to explain the rotation curves of galaxies, and while originally a fudge factor, has much supporting evidence now, including the http://chandra.harvard.edu/press/06_releases/press_082106.html and gravitational lensing.

 

[Roamer]

Why do all cosmological models assume time flow is the same for everyone in the universe?

Lel.

Time doesn't flow, things move, generally at different speeds, due to different(multiple) factors.

When reading explanations/theories and they use terminology implying time is a thing and not a concept,

i see that as a clear sign it wasn't written by a scientist(or someone genuinely trying to be one)

[Lord Antares]

2 hours ago, Aki Tendo said:

/cut

Good question. You are correct in that there is no universal age of the universe. As I understand it, the the most ''neutral'' way to calculate it is from the cosmic microwave background, which would be equivalent to calculating it from ''aboslute space''. That is, picking a point which is completely at rest, only moved by the expansion of the universe. Since time moves the slowest for objects at rest, this is the maximum possible age of the universe. Obviously, for someone theoretically travelling at the speed of light since big bang, the universe isn't even a second old.

Now, if you search a bit on this, you will find some people saying that 13.8 billion (not trillion!) years is relative to us on earth, but you can even easily accept that since the difference between CMB and the earth is miniscule. Calculating the age of the univers from almost any point within the universe will give roughly an equal value, simply since the expansion of space is the biggest factor in movement for a vast majority of objects in the universe. There are exceptions like black holes, but this generally holds true.

Here is a short article which gives exact values and also concludes that you can consider the universe to be pretty much of the same age throughout the universe.

http://www.askamathematician.com/2017/07/q-if-time-is-relative-then-how-can-we-talk-about-how-old-the-universe-is/

EDIT: When you say everyone's frame of reference is different, you are correct. However, Anything moving at high speed tend to be short lived. For example, a person speeding in a space rocket is going to be moving fast (relative to an earth-bound observer) for an insignificant fraction of the time elapsed since the big bang. By and large, the majority of matter's movement is going to be mostly by the expansion of space, hence the conclusion that measuring the age of the universe from different points within it is going to differ by only a small amount.

Edited October 15, 2017 by Lord Antares

[swansont]

7 hours ago, Aki Tendo said:

Hi.  The question above arises out of things like "The universe is 13 trillion years old." The assumption seems to be that everyone experiences time at the same rate, even though we know this isn't true. Relativity posits that as anyone accelerates, time slows down.  GPS satellites have to take this skew into account to even work.  So why does this get ignored in cosmological models?

How big is the shift in a GPS satellite? The gravitational contribution is ~45 microseconds per day. So it's of order a part in a billion. For the solar system and galaxy it will be somewhat larger, but even at a part in a million the shift is smaller than we can ascertain with the precision of our measurement of the age of the universe. You would have to be much deeper in a gravitational well for it to be measurable.

[Janus]

8 hours ago, Aki Tendo said:

When we look at other galaxies the stars are moving too quickly to stay gravitationally bound to the system. Is Dark matter (or a portion of it) simply an optical illusion born out of time flowing in that galaxy at a different rate than ours? Can the observed motion in galaxies be slowed down enough to become gravitationally bound without using dark matter? If so, is this impossibly slow? Will it be the same for each galaxy (I predict no, see below).

 

You have to consider how we measure these star velocities. We do this by measuring the Doppler shifts of stars in in these galaxies. This works best if the we are seeing the galaxy nearly edge on.   We measure the Doppler shift from stars on one side of the Galaxy and compare them to those on the other side.  By measuring stars on both sides, we can account for any over-all shift that might be a part of the shift we see (by the galaxy itself moving towards or away from us for instance.).  From these measurements, we know that any time rate differential is way too small to account for the fast star velocities we see.  

For instance, for the galaxy M-33, the measured speeds for outer stars are three times what they should be given the visible matter in the galaxy.  For that to be a result of any type of time dilation, the galaxy would have to be moving towards us at a good fraction of the speed of light. (gravitational time dilation couldn't be the reason simply because it would cause us to measure slower star velocities, not faster ones, and besides the amount of mass that the galaxy would need to have to exhibit a time dilation of this magnitude would have been more than enough to account for the faster star velocities, so in either case the galaxy would have to have more mass than that we see.) However, when we average out the Doppler shifts for the stars of M-33, we get a relative speed to our Sun of only 179 km/s , which would only result in an apparent increase of 0.06% in the star velocities.

In addition, it is not just the higher speed of the stars, that we are dealing with,  it is also how the velocities change as you move outward from the center. Near the center, the velocities match pretty much what we would expect and then diverge as you move outward.  If the higher velocities were due to some difference in time rate between these galaxies and our own, the velocities would vary from the expected values by the same factor at all distances from the center.

 

[Mordred]

To add to this, we can also infer from the above the luminosity to mass relations, accounting for the above Doppler shifts influences upon spectral index measurements. This is in regards to understanding how Zwicky determined the missing mass problem. The mass to luminosity correspondance to rotation curves showed a considerable amount of missing mass.