md65536

But compare the number of earth orbits (actual years, by the definition of what the word "year" means) to the "clocked years" on I ME's rocket, as above and the former will have observed ten orbits on the "earth orbit clock" while the latter will have recorded only five years on the rocket clock/calendar.

If relativity insists that both are correct, then relativity is wrong. The rocket clock is clearly in error because of the well known relativistic effect, but that is no problem, because the correction provided by relativity adjusts for the five year discrepancy... just like GPS adjustments, which are essential for positioning accuracy.

The Earth orbiting the sun can be considered a clock. All clocks experience the same relativistic effects under SR/GR. Different clocks tick at different rates due to relativity*, not due to mechanical error. Yes, different clocks ticking at different rates can be considered correct.

But wait, perhaps you are right. The Earth orbiting is a really big clock, and I can see how that would make it authoritative. The solar system is our homeland. Obviously it should be treated as a privileged frame of reference, even though theory and experiment show that there is no such thing. Even if we say we accept the principles of relativity, the theory must be wrong because I still don't get it. I suggest we get the word out by spamming science forums on the internets.

Then again... in your example, every observer agrees that 10 years and 10 orbits have occurred in the Earth frame while the rocket was traveling. Some just see that happening faster than others. Everyone is still correct.

* In that sense, time can be considered somewhat malleable. If you consider "traveling forward through time at different rates" to be time travel, then time travel is an experimentally verified reality.

PLEASE address this issue.

Hasn't this issue been addressed literally trillions of times in these forums, for this issue and an essentially identical issue regarding "space" as well as "time"?

I'm no expert but I'll stab at it once again:

SR and GR deal specifically with the rate at which clocks tick. The essence of time according to GR is that time is what a clock measures. Einstein defined time (as far as he dealt with it) as what clocks measure.

And by clock I mean anything that measures time. A mechanical clock is a clock. A person is a clock, with their age a measurement of time. Rotting fruit can be a clock -- obviously some of these are more precise than others and some of them vary greatly depending on the environment. But here's the thing: constant velocity is not an objective aspect of the environment, yet relative velocity precisely affects the rate at which clocks tick. I'll explain what I mean: Velocity is relative, which means that if you have 2 inertial frames moving relative to each other, neither frame is "preferred", ie. neither frame can be said to be absolutely at rest while only the other is moving. Practically, what this means is that any clock you have has no absolute meaning of being at rest vs being in motion, and is therefore unable to detect any clue about such a non-existent thing, and therefore behaves the same relative to an observer in its same inertial frame whether it is at rest or moving relative to another inertial frame. Therefore, different clocks in the same inertial frame will not behave differently from each other due to relative motion vs another frame. If you have 2 otherwise identical environments, such as rocket interiors, all clocks will keep time the same in them whether moving or at rest relative to something else. (Anything that makes the frame a non-inertial frame can be an exception, so you may have clocks that "behave weird" during acceleration phases. Mechanical pendulum clocks should behave differently under acceleration. However, these cases are exceptions, and SR and GR apply to the general case, so we don't have to go into these exceptions to discuss either the consequences or the validity of SR or GR (which can deal with the exceptions anyway)).

In summary the choice of clocks or the mechanics of those clocks don't matter. SR/GR applies to all clocks.

Now, you are certainly more concerned about "what time really is" and all that, beyond "time only as measured by clocks."

But GR is NOT concerned with that.

For one thing, time as measured by clocks is ALL that GR needs, as far as being a theory.

For another thing, GR does NOT imply anything more than that about what time "is".

It would be a MISTAKE to derive a greater ontological meaning of time more than what clocks measure, from GR, because it simply does not say more about time than that.

And this is a mistake you've made.

If you have interpreted GR as making specific claims about time being some "thing" or whatever, something more than what clocks measure, then this is an interpretation of GR, and not a part of the central theory. Certainly, there are multiple possible interpretations of GR, and the interpretation (ontological aspects?) have not been settled. The accepted interpretation will certainly change over time (especially since it's not exactly complete, as far as I know).

Your ontological study of time transcends GR. But certainly, your interpretation of time must account for GR in one way or another if it has any chance of being correct, because GR is experimentally supported.

In summary: Interpret time however you may wish, but 1) you may not be able to prove that certain ontological aspects of that interpretation are correct, yet 2) if your interpretation does not agree with GR then it can probably easily be proven incorrect (unless you can experimentally prove GR incorrect). Perhaps you can consider GR's implications of time as a minimalist ontological description of time, that any other ontological interpretation must accommodate.

Assuming GR says more about time is a mistake. Asking people to explain how GR deals with your specific interpretations and misinterpretations is illogical.

Expecting GR to explain any more about time than it needs to is like demanding blood from a stone. Asking people to extract more information about time from GR is like repeatedly demanding to know the blood type of blood from a stone, and this is also illogical.

Suppose you want to prove the statement "All crows are black".

You can't do it logically, it has to be done empirically. One way is to go out and look at every crow and note its color. Every black crow would be a confirming instance of the statement, and increases (however slightly) the likelihood of the statement being true. The more black crows you see, the more likely the statement is to be true. The statement could only be proven if you could examine every crow and find that each is black.

Now consider this: The statement "all crows are black" is the logical equivalent of "all non-black objects are not-crows". So if you go out and see a purple cow, that is a confirming instance of the statement, and increases the likelihood of it being true by an infinitesimal increment.

But... a purple cow is also a confirming instance of the statement "all crows are white".

How can one thing increase the likelihood of two opposite statements being true?

Keep in mind you've defined the problem as "not a logical problem", even though there is some intuitive logic in this example.

If you generalize this problem then you're basically talking about making statements about a set based on a sampling of the set.

When you make probabilistic statements based on samples (whether you take enough samples or, as the above example, not), you don't just have a probability that something is true, but you have a confidence interval or whatever. With your example, the "error bars" would be so big that the possibilities of the contradictory statements overlap or something.

Also... treating this as a general example and not a real-world example, you allow the case that there are no crows at all.

In this case, both statements about crows in the set are true.

If you sample objects and none of them are crows (as you did in your example), you increase your confidence in this case being a reality.

If you sampled all objects in the set and found that none of them were crows, you'd prove both statements with 100% certainty.

If you sampled all but one object, and none were crows, the error bars on the probability of both statements would still cover various contradictory statements about crows in the set.

Yes.

But then, what is this one phenomenon on which all are correct but on which all disagree?

Nobody technically disagrees. They can all measure certain aspects of the same phenomena differently (time, distance, etc -- while other aspects which are invariant would be measured the same by anyone).

But all the different measurements are consistent with each other. They do not fail to correspond; by definition they don't disagree.

You can say they disagree on the values of 2 measurements made from different frames if you want. Another way of saying that is "the measurements are relative."

Also... while everyone may see things slightly differently, they all agree on what each other should see.

I hate to burst your bubble, but in terms of differential geometry a cylinder is flat. You can roll the surface isometrically onto a plane.

 

Maybe you should regroup and learn enough mathematics to understand curvature a it. There is no simple explanation of Riemannian curvature.

I've abandoned the cylinder idea.

I'm simulating an oscillating point in one dimension along a line on which is a gravitational mass.

I still haven't dealt with flat geometry or curvature properly.

I tend to do things the hard way. :/ I try to figure things out for myself, come to the conclusion "that doesn't make sense", and then try to learn the proper way of doing it. It's not the best way to learn.

Yes, learning the math would be the smart way to start.

The main value of the simulation is not the results themselves but what you might learn by doing it.

So far I've learned that I have no idea about the things I've been talking about! I have mental ideas of what curvature means, but then if I try to do calculations based on that, I'm stuck. Which means my "understanding" is not usable, which means I don't really understand curvature. I really need to learn the math.

But of course that didn't stop me. I found a post on another site which said that the curvature caused by Earth is in the range of 1mm.

As a guess I figured the effects of this curvature might be inversely proportional to r (I also tried 1/r^2 but 1/r seems to work better... not perfect though).

I was going to describe the calculations I'm using but I realize it must be wrong because it doesn't have a property of local flatness. So I think I must be overestimating the effects of curvature. Which is unfortunate because to get results close to Newtonian gravity, I had to use a curvature of 17.6mm instead of 1.

But when I tweak values, I can get results that are close to Newtonian. It is tempting to try to get them to match (eg. I wonder if I can make it match by including the effects of time dilation etc), but that's a red herring if I'm not even using curvature even remotely right.

Another problem to address is numerical error. I'm adding tiny values (the difference in x after leaping back and forth a very small distance) to very large ones (x is around the radius of the earth). I'm surprised I got values at all. I may be able to mitigate this by separating big variables from small, and making sure no variable includes both big and small. For example, I would have 2 variables for x... one for its position ("big") and another for the distance it traveled since the beginning of the simulation (small, at least to start with). Also I'm using mainly Euler method. Also I'm using a huge leap distance of 0.1m (otherwise I'd have to simulate billions of oscillations without getting anywhere)... I have to find a way to approximate a few billion tiny oscillations in a single calculation, while making sure the errors are kept small.

Implementing this forced me to figure out a way that acceleration plays a part. The best I have so far, is this:

Suppose a particle leaps 1 unit in one direction, and then 1 unit in the opposite direction, but due to changing measurements of distance, say it is 1 trillionth of a unit away from its initial position.

The time that it has taken to make these leaps at a speed of c is t = d/v = 2/c. It has moved 1 trillionth of a unit in a time of 2units/c, which I'm treating as a tiny change in velocity that the particle gets to "keep"... if it leaps once, it acquires a tiny additional velocity and keeps moving with that velocity while continuing to oscillate. That would mean that after a trillion (an arbitrary example number here) oscillations, it would approach a significant fraction of c (I'd have to include time dilation and length contraction if the velocity gets large).

So in summary: Don't know what I'm doing yet, but I can fudge this in several ways to force some results. At this point I don't expect it to work if I make some reasonable corrections, but I'll try to figure out some corrections.

If I didn't have a computer how would I be able to work that out in a mathematical way?

Well, if you compute the answer (whether the computer is electronic, or your brain, or water logic gates or anything) you'd use a computer.

If you say had a huge lookup table of binary numbers with one-bit add results (a sequential list of numbers?) you could find the answer without computing it.

But I think what you're asking for is an algorithm to work out the answer by hand or in your head.

A simple algorithm for adding numbers can be the same for binary or decimal. When you add a 1 to an arbitrary decimal number, you are using an algorithm.

For example, a typical way for people to add 2 arbitrary numbers is this:

1. Add the least significant digits together. If it exceeds the maximum value of a digit, then carry the one to the next least significant digit.

2. Add the next least significant digits plus the carry. Again carry the 1 if there is one.

3. Repeat step 2 for all digits.

For binary numbers the only other information needed is to know how to add 2 bits plus a carry:

0 + 0 = 0

0 + 1 = 1 + 0 = 1

1 + 1 = 0 with carry

0 + 0 + carry = 1

0 + 1 + carry = 1 + 0 + carry = 0 with carry

1 + 1 + carry = 1 with carry

This is typically how humans add: Memorize a table of one-digit addition, and use a loop and simple rules to compute arbitrarily large numbers. Computers use logic that doesn't require the loop or "cascade".

For adding just a single bit, there are simpler algorithms.

http://www.wikihow.com/Add-Binary-Numbers might explain it simpler.

Is this a "free energy" device/perpetual motion machine?

Why is it called The Unified Theory?

Would it be possible to harness energy from the orbit of moons?

 

I had an idea about extending alternators to near the orbit of the moon and having a solar powered magnetic field generator built on the moon so when the moon passes close to each alternator it induces a current in the device, the energy then transferred back to earth, would this be possible, would the power generated by too negligible for it to be practical?

 

If we could build that, would it work?

I don't think this would be practical.

Assuming you had a stable orbit (orbiting in the opposite direction that the moon orbits relative to Earth might work?), then extracting energy would involve some net force between the moon and "alternator", which would quickly pull it out of a stable orbit. Unless it's possible to extract energy from the process of returning to a stable orbit? Eg. every orbit might involve "sling shotting" around the moon and then extracting energy while slowing down.

I don't know if that's possible but I can't imagine it being practical compared to other possible methods, given the complications and the relatively low power output I'd expect.

I'm thinking I should try simulating this on the computer, unless anyone knows why this might be a waste of time.

What I would simulate is this:

On a one-dimensional line, have a mass at x=0 with some familiar value (such as Earth's mass) and a test particle at some arbitrary x₀.

Calculate distances on this line using some kind of spacetime equations (which hopefully I can find on wikipedia!), set up with curvature based on the mass.

"Leap" the test particle back and forth along this line by some fixed distance in the particle's frame, at a speed of c.

Edit: Somehow accumulate and apply the test particle's velocity.

Plot the location of the test particle over time.

Questions to answer:

How does the leap distance matter?

Does a random speed < c and/or random leap distance give better results? If so how quickly does the result converge?

A successful outcome would involve fully accounting for gravity when using real-world constants, within some reasonable error.

A failed outcome would involve no definitive acceleration in the test particle.

A possible outcome according to replies to this thread would be that any simulated acceleration is negligible compared to g₀.

If such an experiment would be valueless, I might avoid trying to do it. Would the results of a simulation matter?

Could gravity be as relative as light and thus could a black hole be "gravity-dilated" due to relative velocity/gravity? Why does GR assume relative spacetime and absolute gravitational relations? Is that too abstract a question for this thread?

The force of gravity is proportional to mass, which is relative and depends on relative velocity. I don't think gravity is absolute in any sense.

Edit: I just read some posts in the original thread and it looks like this reply is completely wrong.

Is that what T-symmetric means? that the result is the same for t positive and t negative?

Perhaps "the result is symmetrical" would be more precise than "the same"?

I think that to be exactly "the same" with respect to the sign of t, means the process doesn't depend on the direction of the arrow of time, which would be a more specific case of T-symmetry? Eg. constant velocity would be T-symmetrical (reverse time and you reverse the movement), while zero velocity (ie relatively at rest) is not just T-symmetrical, but also "the same" regardless of whether time is going forward or backward.

What I am confused about is what we mean by T-symmetry in general relativity.

I'm also confused more generally... Is a process T-symmetrical if and only if it is reversible? By reversible I mean able to return exactly to a previous state.

I haven't been precise with my wording, but with the conjecture that gravity works "the same" under time reversal I mean that it is an attractive force either way, which would mean that it is not T-symmetrical. If gravity is T-symmetrical, then reversing time would mean reversing gravity, and just like playing a movie in reverse, it would appear to be a repulsive force.

The conjecture is based on other conjectures. I accept that I can't claim anything meaningful or provable at this point.

If you had an arbitrary vector (βr,βphi,βtheta), could you not apply a rotation matrix to rotate it onto the r axis, then apply the boost matrix for the Cartesian x axis, using r instead of x (they should be equivalent if the axises are aligned), and then apply an inverse of the rotation matrix to get it back to your original direction? Multiply these 3 matrices to calculate a general boost matrix?

My maths ain't so good, but I'm curious... would that work?

Accordingly, the drag force that I posited in the lab frame is maybe fully alive and well in the CM frame?

I thought about this some more and I think I see what you're saying...

In my example, in the launcher's frame, light from M2's launcher seems to be moving somewhat forward to catch up to M1.

Meanwhile from M1's frame, that same light is moving toward M1 totally perpendicularly.

This is why everything in the launcher frame appears slanted to the moving M1; light that appears to be coming from behind M1 according to one frame, appears to be coming from the side in another frame.

But then... isn't it true that according to the launcher's frame, gravitons would also "approach M1 from behind and slow it down"?

The answer is... no, the paradox resolves itself exactly the same way.

Just as from M1's frame, everything in the launcher's frame appears slanted, everything in M1's frame appears slanted according to an observer in the launcher's frame (the launcher frame can be considered moving relative to M1's frame equally validly as M1's frame can be considered moving relative to the launcher's frame).

So now... sorry for the complication... consider this...

Imagine another observer in the "middle of the football field", equidistant from M1 and M2, which observes them passing by in the middle of their "race".

Imagine also a ruler connecting M1 and M2.

Since the M1+M2 frame is moving relative to the Middle observer, the ruler will appear bent to her. It would be the same as if the Middle observer were moving toward the midpoint between M1+M2 while M1, M2 were at rest. The middle of the ruler would appear farthest forward in the race according to Middle, while the M1 and M2 edges would slant back toward the launcher positions.

Now if you imagine photons or gravitons emitted from M1 or M2, as seen by Middle, they would appear to always travel along the ruler. They would travel in a straight line according to Middle (or according to anyone), but different parts of the apparently bent ruler would coincide with that straight line at different times, because the ruler is moving.

Any observer would see M1 and M2 being pulled by each other in the direction of the ruler, even if that ruler is bent according to some observers.

It's weird but it's consistent.

So M1 and M2 converging would be essentially involve the ruler shortening.

The direction of the ruler represents M1's "side" in any frame. So, weirdly, you might say that Middle sees photons from M2 approaching the moving M1 from behind, but they hit M1 on the side, even though Middle sees that side slanting forward! This is only possible because M1 is moving forward while colliding with the photons.

Any additional details can make it more complicated, but it should always work out perfectly.

So, at any subsequent time, t, each test mass MUST be experiencing a force that is directed to a point that is less distant from the opposite launcher, than either mass perceives itself to be from it's own launcher. This means that the net force on M1 and M2 will ALWAYS be mysteriously directed a bit toward the other's launcher, EVEN THOUGH ORTHOGONALLY TO THE SIGHT-LINE OF IT'S OWN LAUNCHER. Accordingly, the drag force that I posited in the lab frame is maybe fully alive and well in the CM frame?

Yes, you might think of it that way, but remember that in M1's frame everything off to its side in the Launcher frame appears to be slanted forward (along a line that is angled slightly forward of perpendicular). The point on the Launcher frame that is "less distant from M2's launcher" is also offset forward in M1's frame by exactly the same distance, making that point appear perpendicular in M1's frame.

You can prove that it works out "magically perfectly" simply by considering that light moves relative to each and every inertial frame, and imagining the path of a photon relative to M1.

Remember that a photon in M1's inertial frame will behave as if this is a rest frame. If you consider M1's frame to be moving forward relative to the launcher frame, then all the photons in M1's frame must also be considered moving forward or "dragged along with the frame" -- it's less confusing simply to treat it as a rest frame with any other frame moving. Since M1 doesn't "leave the photons behind" as it moves, the lateral delayed images never appear to be from behind.

Just to further clarify that point: All photons can be considered to "be in" every inertial frame. You can consider the launcher frame at rest and imagine photons relative to that frame, and then switch to a different frame and consider the same photons relative to that other frame... the same photons behave as if any inertial frame they are considered from is at rest.

All of the SR "paradoxes" I've seen so far are similar:

1. Relativity seems weird, and you can imagine weird situations.

2. Describe that situation without considering relativistic effects, and you deduce impossible situations.

3. Consider ALL applicable relativistic effects (time dilation, length contraction, lack of simultaneity, etc), which seem like further complications, and everything ends up working out perfectly.

They're all puzzles and this one's a good one.

It's not due to coincidence that relativistic effects happen to make everything work out by just the amount you need. They are essential to the consistency of the scenario.

The aberration of light occurs between objects that have a relative velocity with respect to each other, it does not occur between objects that do not have a relative motion, such as in the example.

The aberration occurs between the moving rockets' frames, and the "launcher" frame. Think of it like 2 (very fast) runners on a (very large) football field. Due to aberration, the yard lines would not appear perpendicular to the runners, but instead slant forwards.

This is crucial to this example because each of the traveling objects appears in their own frame to have a head start. During the head start, the other object appears to be in the launcher/football field frame; during the head start there is relative motion between each object and the other (from their own frames of reference). But due to aberration (a form of length contraction), they only appear to be catching up to a perpendicular line to each other, rather than appearing to have left the other behind. During the head start, the start line (including the other object) appears slanted forward.

When they are at the same speed, there is no relative motion, and they are perpendicular to each other from either object's view point (or any viewpoint on the football field equidistant to each). But they still never appear to be at the same yard line, from either of the object's viewpoints. The yard lines do not appear perpendicular to them.

Further, this allows for each object to appear to themselves to always be ahead in the race relative to the launcher/football field frame (which must be the case due to the delay of observations of the other object), and yet remain neither ahead nor behind the other in their own frame where the other is relatively stationary.

This is the solution to the paradox. You can't ignore lack of symmetry from the objects' perspectives, so you can't ignore relative motion at the start of the "race", and so you can't ignore length contraction and still expect it all to work without problems (which also means that if you're doing the numbers, you can't ignore time dilation either).

Exactly. For massive particles we can interpret the parameter t as the proper time. As you see passing from t -> -t does not affect the geodesic equation.

 

For massless particles we cannot interpret the affine parameter as a proper time. We still have the T-symmetry formally but it does not have such a clear interpretation as for massive particles.

So a geodesic is the same path, passing from t -> -t?

I think that implies that spacetime curvature is the same for t as for -t? Or at least, there is no inversion of the curvature that would make time-reversed gravity into a repulsive force.

If you send a signal to the moon and time-reverse the process before it gets there, it will reverse course and return to you.

If you drop a neutron off a building and time-reverse the process before it lands, it will continue to fall (I speculate).

Admittedly, this depends on some of my own interpretation, which is not accepted science. As you say, there is no clear interpretation.

Time doesn't exist, you certainly can't run it backwards

Ignoring whether my examples describe practical or possible realities, figuring out the theoretical implications can be useful in figuring out what is possible in the universe and hopefully ultimately how it all works.

Large-scale T-symmetrical time reversal is probably impossible (this very thread speculates one of several reasons why), and certainly impossible in any universal way that requires the existence of a fictional concept of "universal time", but it's useful in very small scale interactions such as those described by Feynman diagrams.

Spoken like a true dogmatist. Not all cosmology is based on GR. And "curved spacetime" as a central concept is still a hot debate among ontologists (whom of course you despise, to your discredit.) It would broaden your horizons to study those papers on spacetime compiled by Deiks and all those references provided by Ross.

owl, you are a fool.

You are a pigeon, crapping on the chessboard that is this forum.

Since you don't understand analogy, I don't expect you to understand metaphor, so I apologize for my inaccurate insult.

Philosophy of science is fine and it has its place, but you are using it to discredit GR.

This is a Relativity forum, not a philosophy forum; hence the pigeon analogy and now metaphor.

If you can prove that GR is wrong using philosophy in a way that is generally accepted, then those philosophical arguments are relevant here.

But around here, GR is generally accepted science that has not been refuted in any accepted way, regardless of any "hot debate".

You have a LONG WAY to go to disprove GR using philosophical arguments. Until it is generally accepted, THOSE ARGUMENTS DO NOT BELONG HERE.

If you wish to try to refute GR using arguments that are not already accepted science, do it in the speculations forum.

You have two choices: 1). Learn and understand the concepts on which the theory is built. 2) Continue to babble incoherently making inane, irrelevant and nonsensical comments..

There's another choice: 3) Stop posting.

I'm a fool myself. But I'm trying, Ringo. I'm trying real hard to number 3.

I read in Carl Sagan's Cosmos that traveling near the speed of light would warp things so that things that were behind you would squish into your forward cone of vision, but I never really made sense of that until now.

I believe that my post fully resolves the paradox but no one has acknowledged or refuted it.

If two rockets are separated by one lightsecond and are launched at the same time in their rest frame, they will each see themselves start to move one second before the other does.

But length contraction will make perpendicular lines that are in the launchers' frame appear to curve forward.

The other rocket will appear ahead of me (on one of those curved lines) until I catch up to it exactly at the point where it reaches the same speed as me. While traveling with the same velocity they are relatively at rest, and will be exactly perpendicular to each other, even though they each witnessed having a head start over the other.

In short: The effects of length contraction ensure that nothing impossible happens. My previous post explains more.

The principle is essentially this: http://en.wikipedia.org/wiki/Aberration_of_light

I'm assuming that gravitons and photons behave identically.

What if instead of thinking of the early universe of the big bang as expanding spacetime in some abstract sense, you just thought of it as a small, dense ball of matter? Then, think of the expansion of that ball as a process of stretching the contents out despite a limited amount of space between them. So instead of the contents "expanding into" space, they are actually stretching space between them like trying to expand a vacuum within the atmosphere. Another way to describe this would be to say that gravity originated as perfectly contracted spacetime and henceforth began expanding to allow more distance between particles/objects, yes some areas remain(ed) less expanded (e.g. galaxies, stars, planets, interstellar clouds, etc.) In this way, would it be necessary to view gravity as a force, or could it be viewed as simply varying degrees of expansion of spacetime? Also, could it be that the expansion was caused not by a "bang," i.e. pushing force from the center, but rather a "pull" as its surroundings were drawn outward for some reason?

If the universe were thought of as an expanding (inflating) ball... (it might not be valid to do this)...

Yes, I think you could define a changing measure of distance, such as "one unit = radius of the universe". Then using that measurement, the universe remains a ball with radius of one unit, and everything inside it shrinks and contracts into "patches" of greater density.

You might be able to reconcile gravitational acceleration with the equivalence principle, in that a frame under the influence of gravity is equivalent to an accelerating frame.

Perhaps something like... the strength of a gravitational field is related to the rate at which it contracts.

Everything shrinks relative to the size of the universe, so it always seems like there is more room in the universe... it appears to be expanding relative to everything.

Upon re-reading your post, I don't think this is what you're talking about.

When you say "expand a vacuum within the atmosphere", do you imagine pushing everything else out of the way, so that the atmosphere (analogous to the universe) remains the same size, and everything outside of the vacuum gets pushed together (analogous to gravity)?

Or do you imagine that the atmosphere is being pulled larger, and everything in stays where it is, so that the distance between things remains the same but those distances diminish relative to the increasing size of the atmosphere? If you mean the latter, then no I don't think that the expansion of the universe explains the effect of gravity.

One interesting side-effect of imagining the size of the universe being fixed and the size of everything else changing relative to that is this: If the universe started out as a singularity, couldn't it be considered to still be a singularity?

I must be blind. Where is it T symmetric?

t only shows up squared, so the equation has the same value whether it is positive or negative. ???

It makes sense that a particle traveling along a geodesic would travel in the opposite direction along the same geodesic if time were reversed.

I am not sure about T-symmetry in general relativity as a whole as we do not usually have a good notion of space and time, rather just space-time.

 

However, one can think about T-symmetry in the context of the path of test particles.

 

The geodesic equation is

 

[math]\frac{d^{2}x^{\lambda}}{dt^{2}} + \Gamma^{\lambda}_{\mu \nu} \frac{dx^{\nu}}{dt} \frac{dx^{\mu}}{dt}[/math].

 

Clearly the above is T-symmetric.

Gravitationally accelerated test particles do not move along a single geodesic.

If a black hole were time reversed and "became a white hole", yet we at an external perspective were not time reversed, the white hole would continue to gravitationally attract us.

What I'm not sure of is whether the particles inside that white hole would follow full reverse paths and appear to be gravitationally repelled from the white hole, or if they would only follow reverse geodesics, and remain gravitationally attracted to the white hole. Only the latter makes sense, because (I assume) the spacetime curvature of the time-reversed black hole would remain the same as before, and that curvature is what dictates the gravitational acceleration.

But then again, like you said we don't have a good notion of space and time. I'm mistakenly thinking of curvature only as spatial curvature, so time reversal might imply changes to spacetime curvature that I can't clearly imagine.

This is the same as the "light clock" example. Start off by bouncing a light back and forth between the objects. As seen from either object, the light passes directly between the two. Now accelerate the objects equally. repeat the experiment. The light will still bounce back and forth between the objects, and neither will see the light as coming "from behind" the other object. You can't tell any difference between before and after acceleration.

But how do you accelerate the objects at the same time according to all observers? You can't.

If I have a viewpoint from which the 2 objects are symmetrical, and I synchronize the start of their acceleration, then they'll always be symmetrical to me.

But each of the objects will see that they appear to have had a head start vs the other.

Assuming gravity waves behave exactly like light, an object's gravitational pull on me will always appear to come from exactly where the object appears to be.

So let's restate the problem with a different example:

Imagine 2 objects P and Q at the start of a race.

Imagine a very long start line, many light seconds long, with the objects separated by 1 lightsecond.

A light signal equidistant to P and Q starts the race. Suppose P and Q instantly accelerate to some significantly fast speed (so we consider only 2 inertial frames: at rest relative to the start line, and moving relative to it).

From P's perspective, it started the race 1 second ahead of Q. P won't see Q start the race for 1 second, and vice versa.

The resolution to the paradox is this: If we imagine any photons moving through space, we can imagine them moving along with whatever inertial frame we choose to consider, correct? So, imagine photons emitted from Q a fraction of a nanosecond after Q starts to move (assume it is essentially at the starting line) and traveling along the start line, perpendicular to the velocity of P and Q. From P's moving inertial frame, these photons will "move along with P" and remain incoming from a perpendicular direction.

This must mean that the start line appears to curve "forward" according to P. When it switches frames, it sees the start line stretching out to the side but now stretching slightly forward of perpendicular. It appears as if Q is "already ahead" of it. After 1 second, it appears to catch up to Q laterally at the same time that Q appears to start moving. They would remain "side by side" except for that first second (and if they stopped at the end line, Q would appear to be behind P for only that last second).

I read in Carl Sagan's Cosmos that traveling near the speed of light would warp things so that things that were behind you would squish into your forward cone of vision, but I never really made sense of that until now.

I came across a definition of a white hole as a "time-reversed black hole."

I assume that a white hole would only let light out.

However, this doesn't make sense to me. If you have a curved geodesic contained within a black hole event horizon, wouldn't light travel along the same path whether it was going forward in time or backward in time?

It seems to me that spacetime curvature would determine whether light etc would be confined to a space, or unable to enter that space.

A time-reversed black hole would be gravitationally identical to a black hole.

Perhaps its spin would be reversed or something, but essentially its influence on the universe would be the same???

A white hole then would be a "spacetime inversion of a black hole", where the curvature is inverted or negated or something.

Extrapolating, it seems clear that gravitational attraction is independent of the direction of the arrow of time (it's probably still dependent on the rate of time or the magnitude of the arrow, if that makes sense). Gravitation is a one-way process, regardless of whether or not time is. ???

Or would a time-reversal of a black hole allow light to escape along the same paths that let it in?

It sounds like you're trying to imply some form of absolute perception. My point is that particles are only ultimately relative to each other insofar as they interact directly. Beyond direct interactions, you're only dealing with abstract spatial relations, which can't be more than a composite of overlaid orientations derived from various observations.

No, I agree everything's relative. I just think the additional dimensions are important. Since you reduced location to distance, I assumed you were talking about spherical coordinates while considering only the distance dimension.

Your example of orbiting the sun is not the best example, because the sun is essentially the same in any orientation. But if instead you were orbiting Earth, and say you wanted to land, then yes your relative distance is important, but if it mattered where on Earth you landed, and whether you landed on your head or on your butt, then relative orientation also matters.

But this is all beside the point because as soon as you add a third point that's not collinear, an angle dimension becomes relevant, and if you add a fourth point that's not coplanar to the other 3, a 3rd dimension becomes relevant. With 4 non-coplanar points, I don't think your example of choosing an arbitrary axis and origin where you can ignore a dimension, will work.

Certainly, the distinction between whether locations are considered relative or absolute is relevant to the thread, and I hadn't considered it in the original post. But I think that any theory that attempts to describe reality would have to consider locations to be relative.