md65536

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.

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.

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?

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?

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?

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?

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.

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.

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.

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?

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?

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.

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.

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.

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?

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.

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.

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.

This demonstrates visual effects of SR by the way, not GR, and is not applicable to this thread. I wasn't paying attention to which topic I was in!

There's http://gamelab.mit.edu/games/a-slower-speed-of-light/ It doesn't have a lot of options but it's built on an open-source Unity toolkit. The description says it shows time dilation (objects should be slower the closer you are to the speed of light) but I don't see it, and I also don't see delay of light (objects should appear faster as you approach them); it might be the effect is too small for me to notice.

Based on context and the forum we're in, the model must be a relativistic one. The quantum argument sounds reasonable but you can't make that claim about a gravitational singularity without a theory of quantum gravity. I don't see how lack of a clear cause is a useful argument. If you use that reasoning, you can claim that spontaneous particle decay can't happen at all. Yes, it seems accepted theory is moving away from the idea of an initial singularity. My limited understanding is that the singularity is considered speculative, shown to be not necessary in some theories, and not possible in others. However the issue isn't settled because to do so would require a theory of quantum gravity. Therefore making claims as if it's settled, is speculation only. I haven't followed OP's arguments, I'm only addressing yours.

Why not? Are you implying that a point particle can't decay?

I think this is the key to understanding it. I also think most people's approach is not best, whereby they imagine a contraption and explain if or how it works. If instead you ask yourself, given that the air is still and the ground is moving at a constant rate relative to it, is it possible to extract usable energy from that? It's obviously "yes". It's obvious that it could be done without breaking the laws of physics. Then other misconceptions easily fall away too. How much energy can be extracted? Now what swansont said is obvious, you would want a bigger propeller to extract more energy (the more you let the ground pull, the more you must push against the air). It's obvious that the moving ground could provide enough energy to overcome friction in a well-engineered device. It's obvious you wouldn't want a weightless vehicle, if you need a downward force against the ground to capture energy from its motion. Then, "How might that energy be turned into thrust, and does the device in the videos etc. conceivably do that?" is easier to think about.

I don't think the light has to be confined, and a system consisting of a glass prism with light shining through it should have more mass than just the prism. As a thought experiment, consider a massive particle at rest, and a photon moving with +x velocity. The photon has no mass, but considering the two particles as one system, this is not its rest frame. In the system's rest frame, the massive particle has some -x momentum balancing the photon's momentum. As a system, the particles' kinetic energy contributes to the system's rest mass. Likewise the prism+light's rest frame would be different from the prism's rest frame. I don't know if this is meaningful in general, since spacetime curvature depends on how the mass is distributed, and I can't imagine how to describe the effects of unconfined photons. However there are cases where it is meaningful, such as with a "kugelblitz", a black hole created by a dense concentration of light energy for example.

Yes, but gravitational potential is a Newtonian thing, and that applies (always) in a Newtonian analysis. I was going to use gravity assist / planet flyby as an example of how an object can climb out of a gravity well using less energy, in a changing gravitational field. However, in Newtonian physics, the planet's gravitational force acting on the object equals the force of the object acting on the planet, and the object still uses the same energy to climb, it just gets it from the planet. So it's not the case that a dynamic system alone breaks gravitational potential's path independence. GR is a different system, and I don't understand where and how the analogy to gravitational potential fails. But for example, I read that if you separate two masses, the GR analog to gravitational potential depends on if the masses are spinning, but the Newtonian gravitational potential doesn't.