md65536

Refraction is due to the slowing of light — light follows the principle of "least time" in getting to its destination — it gets there as fast as it can, and given that it has to slow down, that's not a straight line. It travels faster in the air, so by bending towards the normal line you minimize the time spent in the medium.

 

A piece of glass is pretty uniform, overall. If it weren't you would get distortions of the light. (If the nonuniformities were of a particular pattern, you'd have a lens) A chunk of glass 1cm on a side is going to contain about 10^21 molecules. Any small inhomogeneities are going to average out over the path the light travels.

A single 1cm "row" of glass molecules would have 10^7 molecules. The number of interactions of transmitted light could be far less (if photons bypass most molecules) or more (if photons interact with multiple rows of molecules). Smaller wavelengths (violet) refract more than longer (red) so the former must involve more interactions.

Have scientists observed or modeled the path of photons and the number of interactions?

If a photon is absorbed and then re-emitted when passing through glass, it would still have to obey causality. I assume that if a photon is absorbed at one point and time, and emitted at another point and time, the energy that makes up the photon will be found to have traveled some distance at a speed of c. Uncertainty might disagree with that. But I suspect that both uncertainty and causality apply: The exact location of energy is uncertain, but where it is observed, it is observed to have traveled at a speed of c.

Does it make sense to speak of the path of photons between when they are absorbed and re-emitted? They might not be considered photons after being absorbed. It might not even be the same energy that gets re-emitted??? But if it does make sense, you could call the path of the energy a curved path along which the energy travels at a speed of c?

The conjecture seems to be compatible with the principle of "least time".

The principle says that the path of light takes the least time to get from P to Q while traveling at different speeds through different media.

My conjecture would state that the speed of light is constant through all media, and follows a path of least distance (and thus least time) getting from P to Q. Since the distance inside the glass is different due to curvature than the same distance measured by an external observer, it doesn't appear to be the least distance to an outside observer. It might even be the case that the bent path "feels" straight to the photons??? A traveling photon (imagined to be moving in some pseudo-classical sense) might not experience any change in direction, nor any interaction with molecules, when passing from air to glass, but might instead experience a sudden warping of space as it passes from the spacetime curvature of one medium to the curvature of another. Infinite length contraction makes this impossible to imagine, and possibly meaningless.

However, this doesn't seem to be compatible with reflection, and I would assume that the behavior of reflected light is very similar to the behavior of refracted light, in terms of photon/matter interaction.

Part 1: Slow glass...

From a thread in the Relativity forum:

Reminds me of a book about something called slow glass, great stuff, lets you see back in time....

http://en.wikipedia....ight_in_fiction

"'Slow glass' is a material where the delay light takes in passing through the glass is attributed to photons passing '...through a spiral tunnel coiled outside the radius of capture of each atom in the glass.'"

Suppose you had complete control over the path of light through some volume.

Even with light traveling at c, a long curving path would take longer for light to travel, and could be used to delay light.

A fractal path on an arbitrarily small section of a plane can have an infinite length.

Quantum limitations might make a true fractal path impossible, but using arbitrarily large volumes of "slow glass" and being able to cross paths and use 3 dimensions should allow you to make an arbitrarily large path for light.

If you had the path determined by some repeated crystal structure, such that the path of light entering from any specific angle at some specific point, would be the similar to the path of light entering from the same angle at any other point, you might be able to implement slow glass (possibly restricted only to a specific incoming and outgoing angle, eg. you might make it work only for light that is normal to the surface).

Part 2: Refraction

Can refraction and the "slowing of light in a physical medium" be described as the light traveling a greater, curving distance through the medium than it would if it were traveling through a vacuum?

My (poor) understanding of refraction is that photons traveling through a medium with an index of refraction > 1 will interact with chains of molecules one after another, making light appear to have a speed lower than c, when instead it is just being delayed due to these interactions. But I can't make sense of that. The arrangement of molecules should make light behave differently depending on its angle through the medium. How can light through eg. glass be so perfect unless every path of given length through it intersected with the same number of molecules, regardless of direction? How could the atomic structure of glass be so isotropic?

INSTEAD... I imagine that, say you have a 1 cm thick pane glass, then the distance across that pane, as measured from inside the pane, is greater than 1 cm. It might be that the path of light is simply curved or bent in some uniform way as the light interacts with the matter (ie. all glass is a type of "slow glass"). Another possibility is that the matter of the glass curves its interior space so that what appears as a straight line of 1 cm from outside, becomes a straight line greater than 1cm inside. Then light need not directly interact with the matter; it just follows a longer curved path through a vacuum inside the glass (ie the mostly empty space between the subatomic particles of the glass), and the length of that path is determined by the curvature caused by the matter.

Can anyone imagine this?

One problem is that refractive index depends on light wavelength, so the curvature of space within a medium would need to be variable. I can imagine curving spacetime looking like a curved funnel of typical spacetime "rubber sheet analogy" drawings, with different wavelengths of light going on different locations on the funnel, resulting in different distances being traveled through the glass.

To rephrase the conjecture: Matter causes local spacetime curvature, that causes light of a specific wavelength to travel a longer path through the medium than it would through a vacuum.

Then it's easy to conjecture that if a material is opaque to light of a certain wavelength, that means that the curvature is too extreme for the light to escape, similar to a black hole. Could the absorption of light energy be equated to light entering a black hole?

I do agree that neither time nor space are entities. As for space-as-emptiness, my "problem" with the quote is that emptiness does not "disappear" when matter disappears as entities existing in space. The lack of matter in space is emptiness.

Suppose you have some space and you take everything but the space away (if such a thing is possible). Does the space still exist on its own, independent of all other things? If yes, then it is an entity. If no, then Einstein's quote holds (sorta... the quote speaks of space without "matter" while I'm speaking about space without "everything").

If it's impossible to take everything out of space, then space can't exist on its own. So the quote holds.

 

 

We can measure the different rates at which clocks "tick" in different environments, and call these differences "time dilation" (implying that time is an entity.)

No, it does not imply that at all.

What if we didn't call it "time dilation", but instead called it "time differences"? Does that make time an entity?

What if we just called it "differences in the measurements of the rates at which clocks tick in different environments"? Does that make time an entity?

Does giving something a name (like "time dilation") give it a physical presence?

I really think you're making a huge imaginative and misunderstanding-filled jump from "statements about time" to "time is an entity".

I think that SR/GR is closer than you think, philosophically, to your own beliefs about time. I think that because SR makes claims about time (or the measurements of clocks) that you don't understand, you are assuming that it's claiming that time is a "thing", when really it is not.

Time dilation does not imply that time is an entity.

My speculation was: by virtue of its properties antimatter may put itself in a different space time to that of matter. This would explain why antimatter disappears (into another time zone?) whenever we try to manufacture it. If this were true then a large accumulation of antimatter may manifest itself to us as 'dark matter' - something which obviously exists as it effects gravity but cannot be directly detected. Or have I had one glass of wine too many?

I think the general idea's worth investigating, but I disagree with your details:

- The properties of antimatter are actually very similar to matter, in terms of visibility, behavior, mass, etc. The only thing different is charge, as far as I know.

- Antimatter annihilates with matter. If you are conjecturing that this involves moving to a different "time zone" or dimension or whatever, then what happens to the matter that is also annihilated? ALSO, annihilation releases a lot of energy, consistent with e=mc^2. Though it disappears, there's nothing missing when its gone.

- The properties of known antimatter are fairly well known. If a lot of dark matter is made up of antimatter, it's not made up of "regular" known antimatter. But I think that's okay; we don't know the properties of dark matter, and I don't see why it couldn't be antimatter or somehow related.

Dark matter is matter that doesn't interact with the electromagnetic force. Anti matter does interact with the electromagnetic force ( it is electrically opposite matter, and thus by necessity must interact with it), so Dark Matter can not be Antimatter.

Given your definition of dark matter as "matter", can we assume that there is also an antimatter equivalent? "Dark antimatter"? And since dark matter doesn't interact with matter, I presume it wouldn't interact with antimatter??? (Or would it? Would it annihilate, which is a different interaction from EM force interaction???) Dark antimatter probably wouldn't interact with antimatter, and might also not interact with matter, nor with dark matter.

This doesn't help explain dark matter at all, but it might provide a possible explanation for why there seems to be so much more matter than antimatter in the universe. If all the antimatter is hiding in the form of dark antimatter, it might be possible that the total mass of matter equals the total mass of antimatter.

I would guess that dark antimatter (vs dark matter) would be as scarce as antimatter is vs. matter. However, if matter can be converted into dark matter and/or vice versa, then some version of the OP's conjecture might be tenable.

while time remains an artifact of measurement

Be careful with your terminology. Time is the measurement. Otherwise we'll be mired in questions like "an artifact of a measurement of what?" and that gets you nowhere. Then all your questions could be answered and you can still imagine there must always be something more to wonder what it is.

 

I think the above ontology is actually a more restricted sense of time than an expanded one... just elapsed time during all physical movement rather than some unexplained local variable "time environment."

 

Okay so I thought you were saying that time must be something more than what SR/GR says, but are you instead saying it is something less?

Again, I believe it is a mistaken interpretation of SR to say that it suggests that time is an entity, or even that it is unexplained.

If SR/GR's definition of time is no good, what can be added, changed, or removed to improve it?

What specific observable (measurable) phenomena might be predicted differently by GR vs. this new definition (Note that all observed phenomena so far are consistent with GR)? If none, then how would you clearly describe the difference between the new definition and GR's definition of time, precisely enough for it to be useful?

My point is, how can you define time by anything other than that which can be measured (ie. by a time measuring device)? If you propose some aspect of time that is not a consequence of what is observed, then how can you evaluate its validity? On the other side of the issue, if you propose some aspect that can be removed from GR's definition of time, how do you account for all of the observed phenomena that are consistent with GR?

To the same point, say we took a small scale example... a box full of objects (matter.) We take all the stuff out of the box and now the box is empty. It makes no sense to say that the space inside the box disappears. Discussion?

Well sure... the box can define a space. But I think Einstein was talking about removing everything, including such a box.

Einstein's saying that space and time don't exist on their own.

If something exists on its own, when considered as independent of other things, this implies that it is an entity (by the very definition of entity), agreed?

But time is not an entity, agreed? Therefore, time does not exist on its own.

Similarly space is not an entity, agreed? Therefore, space does not exist on its own.

If you agree with all these things, where's the problem with Einstein's quote?

Once upon a time, sailing ships dominated intercontinental transit. Today, passenger jets have replaced the function sailing ships once had. Do you think it would be possible for sailing ships to bear all intercontinental traffic once again? If they did, do you think intercontinental travel would decrease due to the inconvenience or do you think sailing ships could provide sufficient convenience to satisfy modern consumers despite the long travel duration?

Partly, technology adapts to fit our lives, and partly our lives adapt to fit available technology. To replace all passenger jets, you're talking about a major change in lifestyle. The world would be a very different place. But I think people and lifestyles could adapt to it.

I envision a future that has overlapping phases of both increased technology (and travel speed), and reduced resource use due to scarcity. That might involve perhaps "floating cities" that use wind power or similar, where people can freely drift all over the world, while at the same time there may be space planes that get you anywhere in an hour, but that are only used by few people or in rare circumstances. This is a very different lifestyle than the "work in one place; get away as quickly as possible" lifestyle.

Anyway, there are a lot of possibilities to imagine. I think that the only thing that would reduce the number of people traveling or greatly increase the travel time, would be resource scarcity, and when that happens it will happen along with some major changes in lifestyle and technology. Hopefully it would be evolutionary and not disruptive.

It's conceivable, but I doubt it, because...

1) Anti-matter looks and behaves like normal matter. If dark matter can't be detected, making it antimatter doesn't make its invisibility any more explained.

2) Large amounts of antimatter probably do not exist in observable space. If they did exist in places, we would likely see evidence of annihilation of matter and antimatter in such areas or along the boundaries between areas of matter and antimatter.

Oops... I didn't realize that your conjecture goes beyond this. Perhaps "dark antimatter" is different from antimatter, but evidence suggests that matter and antimatter have no problem coming into contact.

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. It doesn't address "What dilates" in "time dilation", for instance, the ontological question.

That which clocks measure, dilates. ie time. If that's unsatisfactory, can you give us a concrete example or speculation or anything of what time might be other than "that which clocks measure"? Is there any reason to suggest it is something more?

And a follow-up: Is there any observable or testable prediction or consequence (even if indirect) of such an expanded definition of time? Or is there any way in which you can notice the effects of time, for which it is insufficient to say that it is "that which clocks measure", so that the definition of time used by SR/GR is insufficient?

And, in case there is no way to notice the effect of any consequence of an expanded, ontological definition of time, then how would you verify that it was true, especially versus any other supposed ontological definition of time that also can't be verified or falsified, including of course the obvious possible case that it is nothing more?

I have never claimed that different rates of 'ticking' are due to "mechanical error."

I should have omitted "mechanical". Clocks ticking at different rates due to relativity are not due to any sort of error.

Clocks ticking at different rates will not remain synchronized. GPS corrections etc involve re-synchronization of one frame's clocks to another's, not correcting for errors in time-keeping.

In what sense is time "malleable" if it is not some kind of "stuff," an entity? (Ontology.)..."traveling forward through" what?

If "time travel is an experimentally verified reality" then can we travel forward to the end of that horse race (from the time travel thread) and then bet on the winner? How about visiting dead ancestors before they died, or is going backward in time off limits?

It is malleable in that it is adjustable, even controllable (though neither easily nor arbitrarily, but it certainly happens as an everyday phenomena on a negligible scale). It adjusts to changing circumstances.

"traveling forward through time" has the same meaning as "time travel" except it is limited to change in the same direction of the arrow of time. It does not imply any extra "stuff". If the word "through" bothers you, I'll change it to "one-way time travel". If that still bothers you perhaps you can define what you mean by "time travel" in a way that doesn't evoke "stuff".

Going backwards is more complicated and really depends on what you mean to even begin discussing if it's possible. For example, universal time doesn't exist according to SR, so having everything go backwards in time while synchronized by all (universal) observers is impossible. An individual particle might be able to go backward in time. Some types of time travel might be possible with faster-than-light travel, which is itself impossible.

I would say a safe bet is that any type or meaning of "time travel" that breaks the rules of causality, is impossible.

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.