The expansion of time, probably ad nauseum...

Clue+less

Okay, I was reading another post on PF about the expansion of time and most of the detractors stated things like "time equals itself" so there can be no "expansion" of time. The proponents tended to say things like "if space can expand and we can relate the expansion of space to time, why can't time expand and we relate the expansion of time to space?" I sort of agree with the second point, at least to the extent that I have grossly generalized it.

My question about the expansion of time is slightly different though. Doesn't the concept of expanding time dovetail nicely with the whole 'arrow of time' concept? While theoretically possible to move forward and backward in time, empirical evidence shows us that we cannot move backward in time. If time is expanding right along with space though, it makes perfect sense that we cannot move 'backward' in time, right? Because time has 'expanded' past the point at which you dropped your coffee or were dumped by your girlfriend. Time follows the arrow of time because it is expanding right along with space, in all directions, all the time.

Clue+less

Anyway, if someone would set me straight, I would appreciate it. I really don't know very much about, well, anything. Thanks all.

Drakkith

Expansion means that the distance between all points increases. Expansion does NOT equal travel when talking about spacetime. For example, the expansion of the universe causes galaxies to recede from each other. However these galaxies do not get closer to any other galaxy. Ever. They are not moving "through space" towards another galaxy. So your idea of expanding time fitting with the arrow of time is simply not correct.

Also, I am curious as to what "expanding time" would really mean. Is it measurable?

marcus

I never heard of "the concept of expanding time" in the context of professional cosmology research. I don't know what the concept would be. what would the words signify in terms of a mathematical model of the universe?

In ordinary mainstream cosmo, distances expand OVER time. In a million years time you see distances grow by about 1/140 of one percent. The year stays the same, you keep using the same clock---it is only the distances that increase.

On what timescale would time be "expanding"?

I think Drakkith's right about this.

Chalnoth

The FLRW metric in flat space is:

[tex]ds^2 = dt^2 - a^2(t)\left(dx^2 + dy^2 + dz^2\right)[/tex]

Here we see the expansion factor [itex]a(t)[/itex] multiplying all of the spatial components of the metric. But time is left alone. What happens if we also multiply the time factor by this same value?

[tex]ds^2 = a^2(t)\left(dt^2 - dx^2 - dy^2 - dz^2\right)[/tex]

But this is just the flat space-time Minkowski metric (the metric that describes special relativity) multiplied by some function. It is pretty easy to show that the function multiplying the whole thing is meaningless: it's just an overall coordinate scaling that doesn't impact the physics at all.

So by adding expansion of time, you've removed the expansion entirely.

You might ask about the situations such as what happens if we let the expansion factors for time and space be different, or if we give time an expansion factor but not space, but these situations are the same as an overall function multiplying the FLRW metric above.

So in the end, though we can examine a metric with "expanding time", it turns out to not add any new physics than what we already have with either the FLRW metric or the Minkowski metric. And those two metrics are generally much easier to understand.

Clue+less

Drakkith, Chalnoth, Marcus,

Thank you, I'm honored by your replies. And please don't mistake me for someone who knows anything about cosmology or just about anything else. I'm simply an avid reader of whatever I can get my hands on relating to cosmology, relativity and physics. I'm also curious.

It occurred to me the other night that the problem with the arrow of time, as I understand it, is that we should be able to move forward and backward in time because physically, there is no difference. If time were expanding, right along with space (and I do understand that no two points in the universe are moving towards each other and that expansion is not a measure of distance), then the arrow of time problem could be "explained" (?). Or at least, expanding time would accommodate the 'arrow of time' only moving in one direction.

Drakkith, you asked if expanding time would be measurable. Surely not, not in any way that we currently measure time because any artifact we use to measure time would be subject to the same expansion, thereby eliminating any possibility of an answer other than 1.

Forgive me, but I cannot get around the fact that Einstein brought space and time together but we measure the expansion of one (space) independently of the other (time) though the two are entwined.

Again, I appreciate your answers. I still have much to think on and many avenues to pursue.

petm1

Why don't we think of this as the gravitationally bound part of the universe, after all we know time is a local variable yet its motion is always dilation?

Chalnoth

I'm really not sure what you mean. Any observer will see the clock of a different observer moving rapidly with respect to them as ticking more slowly than their own clock. That is, if we both have clocks and you move past me at high speed, I will see your clock ticking slowly, and you will likewise see my clock as ticking slowly.

This is a perspective effect that has nothing to do with expansion, one way or the other.

marcus

That's a very reasonable thing to worry about and be puzzled by! In popular accounts they don't tell you the whole story.

In bare general relativity (as distinct from cosmology, where you have matter e.g. a primordial hot gas, and the ancient light from it which we still see) there is no criterion of rest and no distinguished time.

However in cosmology we do have a criterion of rest. We live in a bath of ancient light.
this is redshifted by expansion so it is no longer in the visible range. It used to be the slightly orange-ish color light given off by 3000 kelvin (hot) gas. Like the surface of an orange-ish star. But now the wavelengths are stretched out by a factor of about 1000 and it is in the microwave range. Socalled microwave background. A kind of invisible soup of light that you need a horn antenna to detect.

IF YOU MOVE fast enough in some direction you will see a DOPPLER HOTSPOT in the ancient light in that direction.

If you are at rest the ancient light will be the same low temperature, approximately same mix of wavelengths, in all directions. No Doppler hotspot in the microwave sky, for an observer at rest.

So there is a criterion of rest. It has a definite meaning. And in accordance, then, with general relativity, there is a preferred time.

That is the basic time we use in cosmology and it is the time that the AGE of the expanding phase of the universe is stated in terms of.

Observers anywhere in the universe who are at rest relative to Background---who measure the same temperature we do in all directions---will estimate approximately the same age.

In effect, our clocks are synchronized with those of all those other observers---or would be if they existed (which we don't know for sure).

Drakkith

Consider the following.

1. Is moving forward and backward in time equally valid? Would there be a physical difference? Keep in mind that time is a coordinate to measure the position of objects in spacetime relative to other objects. (As far as I know at least) Could you, or anyone else here, tell me what "moving backwards in time" would mean in this context? If an object moves through time in the opposite direction as something else, is it's displacement in the time coordinate still a positive number?

2. How can you explain the arrow of time through expansion of time? The arrow seems to indicate that things only travel in one direction through time. How is expansion going to explain that? What keeps someone from simply going the other way?

IF expansion of time were happening, then that should affect the way events in the distant past are viewed. We can see upwards of 13 billion years into the past. Would expansion of time affect our observations in some way? If so, what? (Forgive me if Chalnoth already explained this in his post, but I don't understand what that equation really means. Chalnoth, what is ds² and what does it mean?)

Clue+less

Once again, thank you all for your replies and reasoned discourse on a topic which most likely has no intellectual value. You have all provided more fodder for my somewhat addled brain to chew on and for that, I'm in your debt.

Drakkith, you pose excellent questions for me to think about.

Marcus, I appreciate your explanation of the (reasonably) absolute nature of time and what cosmologists consider 'rest'. I didn't realize we could use the CMB to define a resting state.

Thanks all.

Naty1

As you know now, expansion of space [really distance] is in our main cosmological model; expansion of time is not. In any case, your stated premise is incorrect. Nearby distances, even in our solar system, even in our galaxy, are not expanding. Increasing distances are limited to vast cosmological separations, not in our local vicinity which is dominated by mass and energy lumpiness. The model that leads to increasing distances does not apply locally.

The criteria for expanding distances results from assumptions of an isotropic and homogeneous universe..,.those cornerstone assumptions have not led us to expansion of time.

As far as is known, only two things affect the relative passage of time: relative velocity and different gravitational potentials. [You can read about GPS time corrections between earth and orbiting satellites for detailed explanations and see how they correct to make time constant between the two.] This serves as experimental evidence that time is pretty darn constant.

Clue+less

Naty1, thank you for your reply.

However, your argument for time being "pretty darn constant" seems to me to be an argument for time being not constant at all. If time is affected by gravity and velocity, both of which abound in the universe, then time is infinitely variable, isn't it?

Naty1

yes, in a sense time IS infinitely variable since all observers will in general record different times. But the difference between observers is a steady difference over distance as far as we know. For example, if two observers move apart at a steady velocity over time they will
each record the others time as fixed slower tick rate as their distance increases [after accounting for local gravitational differences.

[But even this description can be easily criticized...as 'velocity' and distance in curved spacetime [large distances] becomes ill defined. ]

Chalnoth's post with the FLRW metric is a nice mathematical way to think about the steady tick of time.

Chalnoth

I think a better way to say it is that you can always define a time that is "steady" as measured by some observer.

Clue+less

Thank you Chalnoth, Naty1, I appreciate the instruction.

petm1

I was not thinking about reading each others clocks, I was thinking more along the lines of the red shifted photon from space and from a gravity well. One caused by an expanding spatial component the other by a dilating temporal component.