# md65536

Senior Members

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7

1. ## Is expansion meaningless where it is not measurably happening?

Yes, that seems valid. It doesn't matter whether they would measure it or find meaning in it, just that it's possible they could. It seems their meaning would basically be, "if there were other things not bound by gravity, the space between them is expanding." Just to add to what it all means: From https://en.wikipedia.org/wiki/Expansion_of_the_universe Expansion of our universe is stated in terms of comoving coordinates where general galaxies (or "comoving observers") that have not been accelerated by forces or gravity, have fixed spatial coordinates. Their distances would be considered at a common comoving time, where "The comoving time coordinate is the elapsed time since the Big Bang according to a clock of a comoving observer and is a measure of cosmological time." So for example if you had 2 galaxies not gravitationally bound to each other, on a line, one located at (0) in comoving coordinates and the other at (1), we say their locations are fixed and that the measure of distance between them is increasing. Say we call the distance between them "one intergalactic unit", which I just made up. Here, the meaning of "the measure of distance itself (in these coordinates) is increasing" is that an intergalactic unit is equal to an increasing number of lightyears, over time. The measure of a lightyear can remain fixed. It doesn't mean that every possible measure of distance is increasing, which would be meaningless (see several other threads) because a change in a measure of distance is relative to something else.
2. ## Is expansion meaningless where it is not measurably happening?

I agree, but then the topic's question could be reframed by that. Our universe and this toy universe are expanding due to vacuum energy or dark energy, but it would collapse if gravity was increased (put everything closer together, and/or add more mass). So if there was still this vacuum "expanding" influence on everything, but the universe collapsed, is there any way in which it could be said that the space itself is still expanding? Or is the metric still expanding? I no longer think this is a scientific question because the definition of expansion (as far as I know it) just doesn't apply. I think the question might be philosophical, and similar to asking "what is the true nature of the universe beyond what can be measured?" Conversely, for example say you have a toy universe with vacuum energy but where everything is gravitationally bound and collapses, except for one particle that is distant and not gravitationally bound, and separates at an ever-increasing rate. This fits the definition of expansion and I'd say that the space between the particle and the rest of the universe is expanding. This might be a stretch because the definitions are based on a universe that appears homogeneous.
3. ## Is expansion meaningless where it is not measurably happening?

Yes, but the effect of gravity would diminish as the energy was carried away. This is what I thought you were talking about when you first mentioned photons. In a Newtonian analysis, a symmetric "shell" of outbound photons (or an expanding shell with mass equivalent to the photons' energy) would stop attracting a mass to the center of the shell as soon as the mass was inside the shell (shell theorem, which also implies the gravitational effect would not diminish before that happened). Based on that, you could reason something like, the photons from the first mass that pass by the second mass stop attracting the second mass toward the first, and start attracting it away.
4. ## Is expansion meaningless where it is not measurably happening?

But what is space without matter? Isn't it just distance, and specifically distance between things? Isn't the vacuum itself observer-dependent? Space isn't made of some "stuff" that is measurable independent of other things, I think. Anyway I think scientific answers don't depend on those questions, because science deals with definitions and measurements. If expansion is defined as "expansion of the metric", and not of "space", then it doesn't matter what space is. If expansion is defined only for gravitationally unbound objects, and defined as their increasing separation, then I think there's no expansion without that separation, and no way to apply it to gravitationally bound masses. But yes, it doesn't make sense that matter would "stop" expansion. For example, consider 2 comoving distant galaxies that are separating due to expansion. Then say there are 2 gravitationally bound small masses somewhere between them. There is metric expansion between the 2 galaxies. It seems fine to say that space is expanding everywhere throughout the distance between them. What is happening between the 2 small masses? The definitions can answer that! In comoving coordinates, the galaxies have fixed coordinates, and the measure of distance itself is increasing. In these coordinates, for the 2 smaller masses to remain a fixed distance from each other in their local coordinates, one or both must be changing location in comoving coordinates. That gives the answer, that space is expanding between the gravitationally bound masses and they're moving through that space (at the very least mathematically!). But then, we can also consider the local coordinates of the gravitationally bound masses, where in this example they're stationary. You really can say that the masses aren't moving through space (which means nothing more than that they're not changing location in these coordinates). The metric is covariant but I'm still not sure if expansion would be something that is an absolute part of the metric, or dependent on the coordinates. I think it's reasonable to say "space is still expanding here" but with the implication that it's referring to space generally, or in other coordinates, not space in local coordinates. Interesting, I hadn't thought of the physics of the model beyond being an example. I think that even a bunch of photons scattered in all directions would start separation because of decreased mass density.
5. ## The speed of time

It doesn't violate GR. It is a prediction of GR given the values of several measured variables.
6. ## Is expansion meaningless where it is not measurably happening?

Well I changed my mind again. Geodesics aren't some set of lines that remain fixed relative to absolute space, because there is no such thing. Whether something's moving or not will always (I think) involve a choice of coordinates. Also, whether 2 masses are gravitationally bound depends not just on their locations, but their relative velocity. So for example, two comoving fairly distant galaxies can be unbound and separating due to expansion, while two similarly located galaxies can be gravitationally bound just by giving them enough velocity toward each other (basically an "unescape" velocity to overcome expansion). So I think the answer to whether some specific effect is expansion or not, can depend on a choice, and doesn't have a single answer. To get around that, the definition exists only where it is applicable, eg. per wikipedia "The expansion of the universe is the increase in distance between any two given gravitationally unbound parts of the observable universe with time." As well, to say whether something is moving or not, "comoving coordinates" are used, not because that represents absolute motion or anything, but because most of the observable universe approximately fits them pretty well. I think whether expansion is occurring on smaller scales between gravitationally bound masses is literally undefined, and a definitive answer would require some extra definitions and that would necessarily involve making some arbitrary choices of what's moving and what's not.
7. ## Is expansion meaningless where it is not measurably happening?

I think it's confusing because the expansion "breeze" would have to blow in all directions and not push on the ball bearing at all. But, the idea of expansion contributing and gravity contributing to the whole, makes sense. As for atoms expanding, what I've read is that that would only happen if the vacuum energy increased boundlessly, so that the scale at which expansion dominates gets smaller over time, approaching zero. But that would be speculative. I thought of 2 analogies that help me make sense of this. 1. Imagine the Earth is a perfect sphere and it's expanding uniformly. A rigid tectonic plate or island could represent a gravitationally bound region. This is analogous to universal expansion at all scales, since even though the island doesn't change in size, the underlying size of the Earth's surface does. Note that for the island to stay a fixed size, some other part of the crust would have to expand more than the average expansion, for the whole Earth to expand uniformly. 2. Imagine a patch of live skin cells that all slowly divide over time, so that any given area of skin doubles over some long time. A scab or patch of dead cells on it could represent a gravitationally bound region. In this case it's not needed for another area to expand faster to make up for the scab, because the whole isn't expanding with global uniformity and the distortion caused by the scab would be like curvature of spacetime. I think the second is a closer analogy to expansion in the universe, because it's attributed to local vacuum energy rather than some global expansion of the volume of space. I think the island analogy is wrong in that it confusingly represents space both as the crust (including the island) but also as some extra underlying thing that doesn't have a real analog in the universe. But beyond analogies as thought experiments, I think the technical answer needs to be based on the actual definition of expansion. Expansion refers to "metric expansion" which is a change in the measure of distance itself, rather than just a change in the distance between specific things. Well that's not helpful to think about, but what does it mean? The closest I've seen to a description of the technical meaning of expansion is that it involves a divergence of geodesics over time. I think in the case of a static gravitationally bound region, geodesics wouldn't diverge. It wouldn't matter how the rest of the universe was expanding, it would be like tattooed lines on a rigid scab. The geodesics would be like the fan and magnet contributing to a whole, or vacuum energy and gravity contributing to one metric. It would not be like the Earth analogy where one could imagine separate geodesics for an expanding Earth and a static island through the same place.
8. ## The speed of time

I don't think anyone said it cannot fit? Just that it is meaningless. In fact there are published papers that propose exactly what you're saying, they're just not accepted as mainstream science, mainly because they don't account for everything that the accepted science does. Accepted science is always changing (usually slowly) but it changes to better account for actual observations, not imagined alternatives (unless it's a useful improvement). A lack of evidence doesn't prove your alternative doesn't fit, just that it doesn't improve anything. What it looks like to me, is that you're suggesting the possibility that instead of using GR to account for the universe as we observe it (where it fits very well for cosmology and large scales), we use it to account for something different than what we observe, and add in your proposals to account for the difference.
9. ## Is expansion meaningless where it is not measurably happening?

The cosmological constant (CC) is associated with vacuum energy and its corresponding expansion, which is the accelerating expansion that dominates on the largest scales. There's also expansion (or contraction) in the Einstein field equation (EFE) without the CC (as in the original form of the EFE which didn't have the CC. The CC was first added to try to avoid expansion/contraction and allow for a steady-state universe). So, not all of expansion is an 'add-on'. That might provide the answer I was looking for. If the vacuum energy is contributing an expanding influence to the curvature of spacetime that is still present even at small scales, but the Einstein tensor overwhelms it and the net effect is no expansion or even contraction at small scales (eg. within a galaxy), then there's simply no expansion. So expansion is the end result, meaning space between comoving stuff is actually increasing, rather than just a component such as the influence of vacuum energy alone. I think my mistake is in thinking of space as a thing that is independent of the stuff in it, where for example the vacuum can expand without the stuff moving apart. I think I should consider it just as coordinates, but quickly get lost trying to think of expansion that way.
10. ## Is expansion meaningless where it is not measurably happening?

I was about to reply to this saying basically that I think that space is expanding at all scales, but on smaller scales (even between Milky Way and Andromeda), gravity overwhelms expansion so that the galaxies are "moving through" space relative to each other faster than expansion can separate them. A google search shows only results that disagree with my view, and seem to suggest that if two things (in an otherwise empty universe, say) aren't separating, then I guess there's no meaningful way to say that that space is expanding? If two more-distant galaxies are separating at an increasing rate due to expansion, people use phrases like, "gravity has no effect at those distances" due to expansion, which is also not what I thought. Say for example you have 2 masses in an empty universe where their gravitational attraction exactly balances expansion of space between them, so they remain at a fixed distance. Would you say, space is expanding between them, but gravity accelerates them through that space at a rate that keeps them at the same distance? Maybe even there is a measurement that shows that gravity still applies and that expansion is also happening. Or would you say there is no expansion of space and no gravitational effect between the 2 masses in this system? It's nonsense to say the masses are moving through space or accelerating, because those only make sense relative to something else, and they're not moving relative to anything. There is no way to distinguish expansion and gravity, because any effect (like redshift) of expansion that would otherwise cause the 2 masses to separate, would be exactly cancelled out by an opposite effect of gravity that would otherwise cause the 2 masses to converge, and so no such effects are measurable. Is either correct? Could you also say that "gravitational effect" and "expansion" are just emergent effects of the metric, and are not fundamental and separate parts of the metric or the universe? It is the metric that has these two masses relatively stationary, and gravitational attraction and expansion are simply zero for these 2 masses? If so, then I think you could model or label the system so there is both a gravitational effect and expansion of space between the 2 masses, but you would only do that if you had a reason to separate them, otherwise it is simply an unnecessary complication. It seems, I shouldn't think of expansion as some intrinsic process that's happening throughout the universe, but is just a measurement that is a consequence of our universe's particular metric tensor?
11. ## On Lorentz transforms.

What is the time measured by a clock moving 0 m with velocity 0 m/s? How would you define an hour measured with a stationary clock? If time can be measured without motion, why would the "most basic" definition require motion?
12. ## Time dilation (split from The speed of time)

http://curious.astro.cornell.edu/about-us/102-the-universe/cosmology-and-the-big-bang/the-big-bang/586-did-time-go-slower-just-after-the-big-bang-advanced has the closest to an answer that I've found so far. From there: It seems everyone agrees there's not a lot of physical meaning to comparing such clocks. I don't understand "clocks were slower because mass density was so high" enough to believe it. A "shallow gravitational field" doesn't make sense to me, I think he means higher relative gravitational potential, but like in the first post I'm not sure that gravitational potential even makes sense here. It seems that to compare the "gravitational depth" here, it would be more correct to compare "the metric tensor of the universe in local coordinates of a clock in the past, to the metric tensor in local coordinates of a clock in the present." Is that the right way to say it? It still makes no sense to me, because if you could compare those, why can't you just compare the clocks? But basically it sounds like evolving from a high density uniform universe to a lower density uniform universe due to expansion of space, can be considered to be moving to a higher gravitational potential --- and when I write it like that it sounds just plain wrong because there's nowhere to fall to, where the gravitational potential is relatively lower. However it seems like it would be measured as if it was the same, for example light from an older clock would redshift as it traverses through expanding space, losing energy as if it were climbing out of a gravitational well. So, I'm still confused. Edit: Or is it, the metric in local coordinates of a modern clock, could tell you the gravitational (only) time dilation factor between the two clocks? Or is it pointless to talk about metrics without a better understanding first?
13. ## The speed of time

Does this mean it could be done (compare a clock with itself in the past while accounting for any effects related to the location of everything in the universe relative to the clock)? The implication is that any expected difference in the rate of the clock over time can be attributed to a change in the universe relative to the clock, leaving nothing that could be attributed to a change in time itself, in accepted theory? If it's made up and can't be measured, how can you possibly draw a useful conclusion from it? What's stopping you from imagining it to be something where the rate of time varies wildly relative to what we measure, and someone else imagining it to be something where the two measures are the same?
14. ## The speed of time

It could, but I think you'd have to remove any effects that depend on location, if you're trying to measure changes over time alone and not over space.
15. ## The speed of time

Everyone in this thread (except AbstractDreamer) seems to be using the following: 1. Time is what clocks measure, by definition. 2. The only way to measure or reason about the rate of time, is to compare time measured by one clock to that of another clock. 3. A clock will always tick at 1 s/s compared to itself, there's simply no room for a clock to disagree with itself. AbstractDreamer, I can't make sense of what you're saying without knowing what definitions you're using or where you disagree with these 3 things. I suggested this before but it was split off and buried: To test for a changing rate of time you would compare observations of the rate of a clock from earlier in its history, relative to the clock now. You would need to account for any effects not attributable to time, and then any deviation that's left over would have to be due to changing rate of time. Or, compare a clock now to one in an environment that is identical to the environment in the first clock's past. Or, you could compare a clock at two different times, against a reference clock whose rate can be considered constant. I'm sure this is possible to reason about, because you could say "A clock speeds up as it climbs out of a gravitational well," and it makes implicit sense, I think, using any of these 3 methods. I think this is what AbstractDreamer is trying to ask about, specifically about expansion of space or other possible unknown effects in the history of the universe. What I still don't get is whether GR can and/or does predict that expansion would have an effect on a clock like this, or whether the rate will still be constant because there is always something else other than time to account for any observations (eg. redshift in older images of a clock would be due to expansion of space, not an increase in the rate of time), or if it still makes no sense because there is no reference clock that can be defined "outside the universe" to escape the effects of expansion, or no way to compare a space that's undergone expansion to one that hasn't, etc.
16. ## What is happended to time in black hole?

In some ways, not others. No: The possible paths of light depend on where a light source is relative to a black hole, but does not depend on the speed of the source. In diagrams of flat spacetime, the lines representing light do not rotate for different observers. The lightcones don't distort or rotate. Yes: In some ways you can treat the spacetime around a black hole as if it's falling into it (and taking the light cones with it). You can apply SR in a local spacetime for insights on how for example an inertial in-falling observer sees things differently than one hovering above the event horizon.
17. ## Time dilation (split from The speed of time)

Then I'll stick to expansion, unless inflation gives different answers to the main questions. You're talking about time dilation between distant clocks, right? But that doesn't say anything about how a clock compares to itself in the past. Also, the original topic isn't just whether expansion of space on its own would cause a clock to change its rate. I can't see any reason to think it would, because locally nothing's changed. Rather, could the changes in our universe's past caused by expansion, change the rate of a clock? Or more generally, would a clock in a uniform (flat?) space with very high density of matter, tick differently than a clock in a uniform space with low mass density? And if there's no way to connect the two to compare them, without some curved space in between, could they describe the same clock before and after expansion, and be compared?
18. ## Time dilation (split from The speed of time)

Oops, I was thinking of gravitational redshift and often mistakenly call it gravitational Doppler shift. I was assuming that if there was a difference in the rate of time due to inflation, it would be due to a change in spacetime curvature. Can there be spatial flatness, but curved time, with a constant speed of light? Or would a changing rate of time require a changing speed of light? I think it does. I assumed "speed of time" meant rate, and interpreted it to mean "How would the rate of a clock now compare to the rate of the same clock shortly after the big bang (assuming the most general case possible)?" The more I think about it the less sure I am that it even makes sense to ask. For example it makes sense to say, "I've aged one year less than my twin because of those two years (Earth time) I spent traveling when I aged at half the rate that I'm aging now," but this only makes sense with that second clock to compare to. In another frame, I'm aging at a half rate now, relative to some time I was traveling. Trying to "define things in a vacuum" as you mentioned, I was always aging 1 yr/yr and never aged slower. But then again!, I can just treat myself now and in the past as 2 different clocks and I can compare them, basically label my past self my "twin", and it's fine to say my past self in a different reference frame aged slower relative to me now, and for my past self to say "my future self will age slower relative to me now!" But back to the case of inflation, I was thinking maybe it's possible to measure your own past clock relative to your current clock. For example if you could define a light clock where the only thing that changes over time is gravitational time dilation (is that even possible to do?), then there might be a red or blue shift occurring in the light clock over time. But how? For example you could make the clock inertial, and say it has 2 mirrors and you keep the mirrors relatively stationary throughout time. But if space is expanding during that time, keeping them stationary for one observer (you) means moving the mirrors according to another observer, so are you really making gravitational time dilation the only thing that affects the redshift? Anyway I got stuck without figuring that out. Without a way to measure it, I can't make sense of what it means to compare the rate of a clock in the past with itself now. Using another clock to compare to is fine, the "standard clock" you asked for, but like you say: how? For example in flat spacetime in SR you can define a reference clock free from the effects of time dilation simply by making it inertial. But how would you bring a reference clock through an era of inflation without having it affected by it?
19. ## Time dilation (split from The speed of time)

Gravitational potential is only meaningful in some simpler metrics like Schwarzschild. Assuming our universe is flat on the largest scales, do we say it's flat because it has uniform mass distribution, and is that independent of the total mass? Then, assuming it's flat and that the big bang happened, theoretically it was always flat? Or is it flat specifically because it has very little average density, and wasn't always flat? If what I wrote above makes sense, you'd be trying to compare a clock in flat spacetime, to a clock in flat spacetime after inflation. Could it make sense to do it with a Doppler analysis? If you compared clocks at different places, the Doppler shift would mostly be due to inflation, but would there also be a gravitational shift over time even for a single inertial clock? If gravitational time dilation requires curvature, and the curvature of the universe didn't change in general, then I would guess there's no measurable change in the rate of time for an inertial clock (in the general case) now relative to the same clock earlier, and no theoretical change either.
20. ## On Lorentz transforms.

The transformation doesn't tell you what x and t are, you can choose that and it works for anything. If you make t a constant, then x(t) can describe a single event. You don't need objects at all. x = vt+r for a constant r gives you the world line of an object that is at rest relative to O' (the x coordinate changes over time, but x' doesn't). x = r gives you the world line of an object that is at rest relative to O (the x' coordinate changes over time). x = 2vt is an object not at rest relative to either. x can be independent of v. So: no, there's no implicit object that is moving at v, it is the reference frame O' that is moving at v.
21. ## On Lorentz transforms.

With x and t being anything, the case where x=vt describes a particle that is at the origin of O' at time t, and the meaning of gamma(x - vt) = 0 is that a distance of 0 will always be 0 no matter what the length contraction factor, or in other words if two things are at the same place and time, you can't change that just by transforming their coordinates. Conversely if you have 2 events 1 m apart, you can transform to another coordinate system where they're 0.5 m apart. Eg. let x=vt+1 be a particle that is 1 unit (according to O) away from the origin of O', then x' will depend on gamma.
22. ## The energy of the Universe

In general and specifically in our universe, a frame of reference in curved spacetime is a strictly local thing, right? There's no global frame of reference that can be used to consider all the energy in the universe. The best we can do is say that for a local frame of reference, what we measure or predict is either consistent or not with the speculation that the total energy of the universe is zero. As far as I know, everything is consistent with it being 0, but there are too many unknowns that we can't measure, to say that it is so. You can talk about the total energy of the universe, but not in terms of a frame of reference. So if you have a model where say the universe spontaneously comes into existence from nothing, and energy is conserved, and it ends up with curved spacetime and no global frames of reference, there are still ways to describe the energy of that system being 0, but it wouldn't be described using things like a conservation law that applies to frames of reference. There are different descriptions of energy, some frame dependent and some invariant. Is this right?
23. ## The energy of the Universe

You could choose a frame of reference where the entire universe has some great momentum, just by using an observer that's travelling at high speed relative to most stuff. It probably doesn't mean much to give a net momentum to the entire universe (because that's relative to what?). Or you could choose a frame where the universe has no net momentum. If you can do that, you can consider the "invariant energy" of the universe. Adding to what joigus wrote, I think anywhere you are in the universe you can define an observer where, measured locally, the net momentum of the universe is zero? I hope this isn't a gross misrepresentation of GR. Basically, such observers everywhere don't share a frame of reference with each other, because space is expanding between them, but they're also not moving through space relative to each other, so they can each be "at rest relative to the local zero-momentum frame of the universe"... I think.
24. ## Gravity wells (split from A Question for Curved Spacetime)

Well it depends on what you're looking for, a model that shows things in a simple way, or a rendering of what would be seen by your eyes. The movie Interstellar shows visual effects around a black hole, and I think they needed a lot of time on a supercomputer to render them. In the SR game above, it doesn't include all the effects of SR, and yet the result is still confusing enough to the eye that you can't easily see what's going on. For Interstellar, they ignored the Doppler effect for artistic reasons. So even these are simplifications relative to what would actually be seen.
25. ## I can my self move any megalithic stone on hundreds of tons with physics

Edit: I missed the double-negative and only now see I'm agreeing with you, but I can't find where/if the statement you're quoting was resolved in this thread... How can you one possibly think that it follows, when you can do experiments in the kitchen sink with water and glasses that show that it's complete nonsense? You're Others are forgetting (but it looks like mistermack pointed it out long ago) that the space displaced by the mass that you're floating, does not need to be filled with mercury! So for example, say you have 700 kg of mercury in a container, filled right to the top, and you put in a 600 kg weight and it floats, displacing 600 kg of mercury. This is acceptable, agreed? However, the 600 kg of mercury has spilled over the top, so now you have a 600 kg weight floating on 100 kg of mercury, in the space that can hold 700 kg of mercury. Having tight seals or an "already floating" mass doesn't matter. If you have a stone sitting in a container that is just a little larger than the stone, you can float it using as little mercury as it takes to fill up the space not taken up by the stone.
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