Iggy

Ignoring the cosmological constant (just as an approximation) if the distance you are talking about is [math]D[/math], the measured density of the area you are talking about is [math]\rho[/math], the measured velocity of the "far out-into-deep-space" point as compared to the starting point is [math]V[/math], and the gravitational constant is [math]G[/math] then the area will expand if, [math] \rho < \frac{3 \left( \frac{V}{D} \right)^2}{8 \pi G} [/math] and will contract if, [math] \rho > \frac{3 \left( \frac{V}{D} \right)^2}{8 \pi G} [/math] You can get this by solving the escape velocity of an expanding sphere.

At rest relative to the CMB. ...edit... The CMB frame is the local frame in which the universe appears to be expanding at equal velocity in every direction. It is, like you said, the frame where all of the peculiar velocities o fgalaxies nearby tend to cancel out. Because that frame is used in cosmology to give a meaningful notion to 'cosmic time' and space as well (spatial hyperslices) it is sometimes mistaken for a privileged frame. ...edit... Bouncing light there and back would measure the distance, but light is not at rest with A and B. Nature has chosen the space-time interval to be invariant and nature has chosen spatial distance to be variant. It doesn't matter if you like space-time or not, and it doesn't matter if you really want spatial distances to be invariant or not. These facts follow from your definition of space and time. If you arbitrarily decide to ignore them then you are arbitrarily deciding to ignore the nature of the world around you.

Relativistic factors can be measured at low velocity. If you are relatively at rest with an object then the object has zero momentum. Perhaps you can understand that 'zero momentum' is not the only correct momentum for an object. If you are relatively at rest and very near a GPS clock then you measure the rate of its clock at 1 second per second. Since you feel it necessary to compare the GPS clock to the center of the earth you should understand that 'one second per second' is not the only correct measure of the clock's rate. If you and all your measurement equipment are at rest with points A and B then the distance [math]\overline{AB}[/math] is impossible to measure. I think the earth is moving about 600 km/s relative to the microwave background and the gravitational potential of earth's surface with respect to the Milky Way is 130 GJ/kg so the time dilation wouldn't be much... our clocks would run slow by a factor of 0.999997 in that frame if my quick calculations are correct.

Perhaps we don't need someone better versed in SR, but someone who can explain the concepts leading up to a variable hypersurface of the present in simple terms. Owl, please feel no need to respond. Tar, maybe this post will do something to answer... A frame of reference... A person can always consider themselves the origin, at rest, at the center of their own coordinate system. Your frame of reference moves with you because you can never leave yourself behind or send yourself ahead. The following is a 2 dimensional coordinate system describing 'your' frame of reference. Each line marks 5 feet further from you. It shows you walking down the street past an intersection (perhaps not the best thought experiment, but it is the first that comes to mind), The positive numbers (to the right) mark the distance in front of you and negative numbers (to the left) mark distance behind you as you walk. At t=0 the street is 50 feet in front of you. At t=10 seconds you have reached the center of the intersection and at t = 20 the intersection is 50 feet behind you. If you carry a stopwatch with you, that is what it will read at those locations. The street moves a total of 100 feet in 20 seconds. Speed is change in position divided by change in time -- 100 ft / 20 sec = 5 feet/second -- so the speed of the street relative to you (i.e. its speed in your coordinate system or its speed in your frame of reference) is 5 feet per second or 3.4 miles per hour. To add another frame of reference to the situation... as you walk along a girl named Sue passes you and walks ahead of you. She is trying to keep up with her dog we'll say. Your two coordinate systems now look like: According to Sue's frame the position of the intersection changes from +50 (50 feet in front of her) to -20 (20 feet behind her) while 10 seconds pass. The velocity of the street in Sue's coordinate system is... change in position (70ft) / change in time (10 s) = 7 ft/s. Sue also notices that her distance to you goes from zero to 40 in 20 seconds. Your velocity in her frame is 2 feet per second. Every second she gains 2 feet on you. Galilean Space-Time Diagram... Eliminate the vertical spatial axis that wasn't really being used and replacing it with a time axis makes a space-time diagram with one spatial dimension and one temporal dimension. This diagram doesn't involve special relativity -- just a Galilean space-time diagram, The objects that were dots are now lines. They are extended in space and time. Even though the diagram is not animated, it shows how the objects move and interact. At zero seconds (the very bottom of the diagram) Sue, the dog, and 'you' are all in the same spatial location. They are all at zero feet. The gray line is the street intersection. At zero seconds it has a starting position at x=50 feet. At t=0 it is 50 feet from the other two objects. As time moves along (moving up along the y-axis of the diagram) the intersection approaches the other three objects. The dog is the closest, followed by Sue, then 'you'. Two events are marked in this coordinate system. At P2 Sue crosses the center of the intersection. This happens in your coordinate system at x=14.29 feet, t=7.14 seconds -- 7.14 seconds into the thought experiment and 14.29 feet from you. At P1 (x=0, t=10) you cross the intersection. All of this will match the "your frame of reference" animation. All of the information in the animation is also in this diagram. For example, "how far is Sue from you at the end of the thought experiment?" is answered by how far the top of the red line is from the top of the black line. In a space-time diagram the tilt of a line tells you how fast that object is moving in that coordinate system. The gray line moves up by 2 units for every 10 units it moves across. For every 10 feet there are 2 seconds. Its speed is 10/2 or 5 feet per second. The black object (you) does not move horizontally on the diagram just like the black dot doesn't move on the "your frame of reference" animation because it is your reference frame. If you don't understand how the "your frame of reference" space-time diagram matches up with the "your frame of reference" animation then stop, go back and look at them and read again. Nothing else is going to make sense unless it is understood how these diagrams correspond. This is Sue's reference frame as a Galilean space-time diagram, Now in this frame with these coordinates, it is Sue who remains at x=0 ft. throughout the thought experiment. The events P1 and P2 are the same physical events, but in Sue's frame they are at P1 = -20 feet, 10 sec. P2 = 0 feet, 7.14 sec. To put that into words, Sue crosses the intersection at 7.14 seconds, and 'you' cross at 10 seconds when you are 20 feet behind Sue. To transform the events of one coordinate system to another, since this is Galilean (classical) space-time, the Galilean transforms are used, [math]x'=x-vt\,[/math] [math]t'=t \,[/math] where [math]v[/math] is the velocity between frames (2 ft/s in this case); [math]x[/math] and [math]t[/math] are the time and position in the first frame; and [math]x'[/math] and [math]t'[/math] in the second frame. In our first frame, 'your' frame, P1(x=0 , t=10), P2(x=14.29 , t=7.14). Solving Sue's frame gives, P1: [math]x'=0-2 \cdot 10 = -20[/math].... [math]t'=10[/math]... (-20,10) P2: [math]x'=14.29-2 \cdot 7.14 = 0[/math].... [math]t'=7.14[/math]... (0,7.14) Those numbers match our diagrams. The Galilean transformations reflect the classical rules of mechanics where space and time work the way Galileo and Newton expected them to. They tell us what should happen in one frame knowing what happens in another. They are the rules that tell us how to transform from one frame to another. The Galilean transforms assume a universal now -- if an event happens at [math]t[/math] in one frame then it happens at the same time ([math]t'=t[/math]) in any other frame. The transforms also assume absolute distance -- if you measure some distance between events, everyone else will measure that same distance in their frame. This method of kinematics is how people intuitively expect the universe to work so it is understandable that people have a hard time rejecting it, but it is empirically wrong. The actual thing that should be the same between every frame is not distance and not duration, it is a particular velocity. The speed of light, 300 thousand km/s, is the same in every inertial reference frame. This is not something that one can easily get their mind around, so let's look at it in terms of space-time transformations. In a Galilean transform, just like we saw before, everything is skewed over from one frame to another. Here we have two frames. You are the black line and Sue is again the red line. You shoot a laser to the right and Sue chases the laser at 0.6 times the speed of light. This is your frame and hers according to classical mechanics (i.e. galileo transforms), The three lines and the coordinate system have been skewed over like a deck of cards. This might be more apparent if we put both coordinate systems on one image: It seems to make sense, if light is moving away from you at 1c and Sue is chasing that light at 0.6c then Sue is going to think the light is moving 0.4c... just like the diagram shows. This means that both reference frames share the same present. To make this clear, the green events that I marked all happen at the same instant for both observers. They both happen when all of the clocks in both reference frames read 0.5 seconds. But, this also means that light does not have the same velocity in both frames. For light to have the same velocity in both frames we us Minkowski space-time with the Lorentz transformations. Minkowski Space-Time diagram... here is an empirically correct diagram of the same thought experiment depicted above with both coordinate systems: It is messy, so first keep in mind that this shows the same situation where Sue is chasing the laser from 'your' perspective. Find the event marked with a green dot. To see where this event is in your coordinate system (the black coordinate system again) follow from the green dot down the black line to the black spatial axis. It is at one light-second. Also follow the green dot left along the black line to the black time axis. It is at one second. The event is at one second and one light-second in the black coordinate system. The green event is along the ray of light, so we have found that light moves one light-second per second or 1c according to 'you'. In the red coordinate system follow the red line down from the green event to the red spatial axis. It is 0.5 light-seconds. Again follow the red line left to the red time axis. It is 0.5 seconds. Light moves 0.5 light-seconds per 0.5 seconds or 1c according to Sue. The same thing can be done with any event that can be marked on the diagram. You would find that Sue moves 0.6c to the right in the black coordinate system and you move 0.6c to the left according to Sue's coordinate system, and both of you find that light moves 1c. This corresponds to the empirically correct set of transformations -- the Lorentz transformations. The horizontal black lines are a single moment in time in the black coordinate system. All of the events along those lines happen at the same time according to 'your' clock. The horizontal-ish red lines mark a single moment in time in the red coordinate system. There is no absolute now across different reference frames. To make this clear I'll mark a present instant at t=1 in both reference frames: All of the events along the green line happen at the same time for 'you' -- at t=1 on your clock. All of the events along the blue line happen at the same time for Sue -- at t=1 on her clock. They do not share the same present in Minkowski space-time and Minkowski space-time is the construct that keeps the speed of light invariant. That diagram got very complicated, so let me simplify it... Here is a corollary description of absolute time and Galileo space-time... http://www.phy.syr.edu/courses/modules/LIGHTCONE/galilean.html http://www.phy.syr.edu/courses/modules/LIGHTCONE/maxwell.html And of special relativity and Minkowski Spacetime... http://www.phy.syr.edu/courses/modules/LIGHTCONE/minkowski.html If you can't make a Minkowski diagram then you would have no hope of discussing the ontology of space-time.

You are confusing together signal delay, classical doppler shift, and time dilation. When the clocks reunite they do not read the same. Time dilation is an additional factor to doppler shift and signal delay.

Correct, gravitationally it wants to collapse. FLRW assumes that the universe is homogeneous. There are no variations in density. Because of this, it is only accurate at very large scales. It does not predict, and no one would expect, small dense areas like a solar system to expand. The choice between a kinematic coordinate system and an expanding coordinate system has nothing to do with whether or not dense areas of space are gravitationally bound. The critical density inside a galaxy is different than the critical density of the universe as a whole.

You have said that clocks and rulers which are not at rest give bad measures of time and distance. You have said that clocks and rulers which are at rest give the correct and accurate results. How do you know if something is at rest? You honestly can't answer this?

I agree it is arbitrary, but I think it is appropriately arbitrary. If we want to know if a galaxy will expand then r would be rather small. To find out if a supercluster is going to expand indefinitely then the sphere under consideration, and its r, would be quite a bit bigger. It is good that we can examine any size sphere we want, so good I think to have r be an open variable. I agree you could find the gravitational potential and kinetic energy of the mass in an area of space to see if that area will eventually collapse, but it is really the same thing as the previous equation. The equation is derived by comparing the gravitational potential of an area to the kinetic energy of the mass constituents. It is a simplified form of that equation. The only variables needed are density and velocity (assuming the area is homogeneous, velocity increases with distance, and omitting the cosmological constant).

Your description of the history does not sound very familiar to me. A doppler shift interpretation and a metric expansion interpretation should be different coordinate choices for the same situation. Whichever way you look at it you should get the same physical outcome. Both interpretations are valid. A couple of articles saying this... I agree FLRW doesn't have that function because it assumes as an approximation that the universe is homogeneous. The formula, [math]\rho_c = \frac{3 H^2}{8 \pi G} [/math], works not only for finding the critical density of the visible universe as a whole, but any particular part of it as well. If you draw a sphere around an area of interest and you want to know if that area will collapse or expand in the future then mark a point in the center of the sphere. The velocity between the point and the edge is [math]H[/math]. Using that to find [math]\rho_c[/math] and comparing it to the real measured density, [math]\rho[/math], will say if the area will eventually collapse or expand. The important point, i think, is that inhomogeneities existed in the past. Some areas were above their local [math]\rho_c[/math] and some areas below. The areas of segregated mass that we see now are a result of that.

Thank you. I'm curious. Would you expect the scale of atoms to be twice today's scale at z=1, and at what rate would you expect macroscopic things like stars and planets scale as a function of redshift?

I think "void" is a relative term. Some areas of the universe, the majority to be sure, have a current density below the critical density, [math]\rho_c = \frac{3 H^2}{8 \pi G} [/math] (#1) of their local area, and they have a tendency to expand. Other areas have a density above the critical density and they will want to collapse. In the past the critical density was no doubt different and the actual density was different, but I'm sure there still would have been a density inhomogeneity where some areas were above the critical density of the time and others below. #1: ...where lambda is zero and H is the recession velocity in the area under consideration

pantheory, have you related redshift to distance? How long ago would you expect z=1?

Viewing a statue from the front makes a two dimensional projection and a two dimensional perception. Looking at the statue from the side gives a different two dimensional projection. The statue appears different. For example, the width of the statue as viewed from the front is two meters and the width of the statue as viewed from the side is one meter. The width is different not because the statue itself has changed between the various perspectives, but because the three dimensional geometric relationship between the statue and the observer is different between perspectives. The one meter width (viewed from the side) and the two meter width (viewed from the front) are equally real, equally correct, and equally accurate. They represent different arbitrary two dimensional cross sections of a statue that has three spatial dimensions. Relativity is the same situation, and I believe the captain makes an excellent metaphor of it. Each frame of reference is a three dimensional cross section of a four dimensional world. Each three dimensional cross section of an object doesn't just appear different, it is different. But the object in four dimensional space-time is the same regardless of various arbitrary three dimensional perspectives. The Lorentz transforms are a rotation in space-time. Just like rotating a statue in 3D gives a different 2D cross section, so too will a rotated object in 4 dimensions have a different 3D cross section. The object in four dimensions doesn’t itself change, it is the four dimensional geometric relationship between the object and observer that is different. With that considered, it would take either a willful omission, a pretty bad misunderstanding, or no knowledge at all of scientific theory to think length contraction is subjective idealism. If someone wanted to limit their understanding to two dimensions then they could characterize the changing width of the statue with the changing position of the observer as subjective idealism too. How can the width of the statue be different unless the observer's perception is changing the object?

I agree, but I still don't understand your idea of velocity because you didn't define it like I asked and you didn't answer, "how do you decide if something has high velocity?" Let me put it this way, when you say something like this: if one of those clocks is in the Andromeda galaxy and the other is in the Milky Way then which has a higher speed and therefore ticks slower? Is it the one in the Andromeda galaxy or the one in the Milky Way? I'm assuming you don't intend to compare both to the center of the earth again. You say that not all inertial frames are equal... you say the rest frame is the only "accurate" frame -- so how do you decide which is which? Which galaxy has a higher velocity and slower clocks? How do you decide what velocity an inertially moving body has? How do you define velocity so that you can say "this thing has a high velocity and its clock will tick slow"?

I maybe didn't ask very clearly. I'm asking what you mean by "at high velocity". How do you decide if something is "at high velocity"? ...edit... the question would be "how do you decide?", "how do you know", "what definition of 'high velocity' tells you that some things are at high velocity and some things are not" ...edit... For GPS clocks, are you saying that all GPS clocks, no matter what direction they are moving, have a "higher velocity" than the surface of the earth? For the big bang, do you think big bang cosmology proposes a point in space that is, or was, the origin of the bang from which earth is quickly receding? Hopefully I worded these very clearly

speaking of "what is it", what is "at high velocity"? Is the milky way at high velocity?

Can anyone think of a philosophical reasoning that this wouldn't be true, specifically by describing some definition of distance that has meaning without the presence of matter? Here is where I pulled that quote. I think it explains the context of his reasoning. If coordinates are not real but just an arbitrary means of labeling matter... then without matter there really would be nothing left.

All definitions are rhetorical tautologies. The word and the definition are one and the same, or at least they should be. You had trouble with this, Space is to empty volume as dog is to angry bull terrier. 'Space' is not the same as 'empty volume' just like 'dog' is not the same as 'angry bull terrier'. They need to be the same.

I think it is fair to say that you cannot have time without space and matter. Einstein said also, "People before me believed that if all the matter in the universe were removed, only space and time would exist. My theory proves that space and time would disappear along with matter"

Like I explained in my last post, it is not generally assumed that duration is something that exists in and of itself. Einstein held that space-time coordinates do not have an independent, substantial, ‘life of their own’. Relativity, he said, proves this. You might think of it like this... things that have a "life of their own" can be counted. You can count the number of swans in a lake or the number of stars in the Milky Way. You can't count a duration in the same way. If duration had an independent existence then you should be able to count the number of durations between a person's birth and death, but any count would be an arbitrary counting of events. Don't get me wrong, I believe duration is real -- just that it isn't independent -- doesn't have a life of its own. It depends on other things, one of those things being frame of reference. If you believe duration has a life of its own then you are making a reification of time, which is fine, but it is not supported by relativity. A series of events make a clock. You do not understand that an instant is a function of reference frame and there is no absolute reference frame -- therefore no universal instant or universal present instant. People have tried to explain why this is true, but without a basic working knowledge of relativity I don't think it's going to hit home. Your statement has the same meaning (or lack thereof) as the often repeated old saw, “Time is that which clocks measure,” which is a meaningless tautology. A rhetorical tautology... that's all it is... that was my point. That is correct, it does not. Relativity does not introduce any kind of medium or aether that dilates. There are no postulates or assumptions of that sort. Velocity is not an environment or an environmental factor. There is no such thing as a "fast environment" or "slow environment". People knew this going back to Galileo in the 1600's. It should be possible to derive relativity without reference to clocks and their mechanics or any other physical process. I think you have in your mind that clocks slow down because some force is being applied to them or something physical is interacting with them and affecting whatever mechanism makes them work. Is that right?

Well... not units per se. Wikipedia's dimensional analysis page makes a good distinction of dimensions and units, The way I understand the OP -- it is essentially asking 'If length and time are measurable dimensions, what about these other things -- can they be considered dimensions too?' That is to say: What are the dimensions of weight and entropy... or are they dimensionless? I would just answer that entropy can be dimensionless in mechanics so it would certainly not be a dimension like length or time. Weight has dimensionality (mass times length over time squared), but in case the OP meant 'mass' where it says 'weight'... yes... mass is often considered a base dimension just like length and time. Here is a paper treating entropy's dimensionality in the same light: Perhaps I'm not following what you meant by "units" or "confusing the issues" and perhaps I'm being a bit obscure with the OP's idea of "dimensional property"... quite likely. [... edited for clarity... ]

I may be a little (or a lot) off base here, but to me "dimensional properties" can mean something different and perhaps something rather worth getting into. In classical dimensional analysis a dimension is a fundamental physical property -- which is to say, it can't be defined as a combination of more fundamental properties and can't be measured as a combination of more fundamental units. The fundamental dimensions usually given are mass, length, time, electric charge, and temperature (although, electric charge and temperature aren't always allowed in the club). A dimensionless quantity, on the other hand, is a value that doesn't change when the units used to measure the fundamental dimensions of the value change. If I were to answer the OP, thermodynamic entropy has units of joules / kelvin or dimensionality of energy per temperature. Energy is mass • length2 / time2 so entropy all together would be, [latex]\frac{M \times L^2}{T^2\times K}[/latex] where M is mass, L is length, T is time, and K is temperature. But, temperature can be expressed as an energy, so entropy would be... [latex]\frac{M \times L^2}{T^2 \times \frac{M \times L^2}{T^2}}[/latex] and... yeah... that cancels, or I should say, it simplifies to 1. It is dimensionless, or at least can be expressed that way. Weight has the same units and dimensionality as force which is Kilograms times meters per second squared, or M • L / T2, so that will have dimensionality in the classical fundamental units.

Yeah, I remember that I remember we talked about it in a thread called "can we see it" and I did (or we did) bring up presentism in that thread. I also remember saying that I didn't think your idea would be consistent with special relativity... I mean... I asked Owl for a "physics theory consistent with relativity's confirmed predictions and presentism" and I think your idea would indeed be consistent with presentism, but not the confirmed predictions of relativity. In fact, I think I remember saying that exactly in the thread. Let me find that... Yeah -- so I agree that your idea was consistent with presentism but not that it is consistent with the observational consequences of special relativity. Good reference though... I only hope I'm not contributing too much to taking the thread off topic (I'm sure I am -- sorry).

By definition, the meaning of a year is "31.5576 Ms (megaseconds or 'million seconds')" (definition) where one second is defined as "the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom"[/i] (definition). The definition of "year" in a scientific context actually doesn't contain any reference to the earth or sun. To explore the philosophy of time clearly a few things have to be established. Proper time is a measurement. It is a measurement of a physical process. For example, an oil lamp could burn so that all of the oil is used up. lighting the wick of the lamp when it is full of oil is an event and when the lamp goes dark from running out of oil, that is another event. Between those two events is a duration. Everyone, in all frames of reference, agree on the physical process. They agree that the lamp burned completely -- that there were two events -- that the one event happened before the other. The duration of the physical process, however, is variable and relative to velocity and gravitational potential. This means that someone with an identical lamp in a different reference frame could himself burn, for example, two lamp-fulls of oil between the events in question. The duration between events could also be measured with a mechanical clock. The person in the frame of the first lamp (lamp 1) measuring the duration of its burn could get 5 minutes on a stopwatch. The person in the different frame of reference using an identical stopwatch measuring the burn time of lamp 1 would get 10 minutes. It doesn't matter what units of measure are used or with what physical process they are defined. The units are arbitrary, which makes the number of units equally arbitrary. Relativity works regardless of the units used (you can pick any you like) and that is the reason Einstein said "according to the general theory of relativity the four coordinates of the space-time continuum [space and time] are entirely arbitrary choosable parameters, devoid of any independent physical meaning." Values like "2 lamp-burns", "5 years", or "20 seconds" do not themselves have independent physical meaning. "5 minutes" is not a thing that exists between two events. This is why it is so weird that you say relativity makes a reification of time -- it actually does the opposite. In relativity time is just the measurement of a clock -- that's all. Time dilates because identical clocks disagree about the duration between the same two events. For example, I had a birthday this year and I had a different birthday last year. Between those two events the earth orbited exactly once. Everyone, no matter what frame of reference they are in, would agree that the earth orbited the sun once between those events. If, however, there were an identical solar system to ours near the center of the Milky Way it would measure a different value based on its orbit. It would not orbit exactly once between the events because it would 'tick' at a different rate. I think you would have to understand these basic concepts of relativity and time dilation before you could consider what they imply about time.

Can you give backup for the idea that "the present is present, i.e., now everywhere", for example, a physics theory consistent with relativity's confirmed predictions and presentism? I would be very interested in looking at that theory. The duration of a bang/cruch cycle depends on the gravitational potential and velocity relative to the CMB of the frame measuring it. In the usual big bang metric the duration of the cycle would be equal for all observers, but only because all observers are assumed not to have a peculiar velocity or a peculiar gravitational potential. Observers in reality don't exactly follow that simplifying approximation, so the time since the big bang -- or the time of a bang/crunch cycle -- is not constant, but depends on reference frame.