md65536

If your model predicts some observations simply or more accurately than the standard model, that's great, but for a model to replace the standard model it would pretty much have to predict all known observations that fit the standard model. The weird or complicated stuff is usually there because of specific observations.

 

In your example, the round-earth model is better than the flat-earth model, but the round-earth model still predicted all the observations that had been made which had fit the flat-earth model.

 

 

(One possible way around this would be the discovery of some new evidence that trumps all existing observations. If for example someone from antiquity had a round-earth model that predicted that the oceans would fall off the planet, this flawed model should still be preferable to a flat-earth model given the evidence of someone traveling into space and observing that the Earth is in fact round. I can't imagine what possible observations might disprove the standard model. "Many things can be answered" alone would not do that. For "many things can be answered", you'd want a model that is pretty compatible with the standard model and all its complications.)

So I got completely confused in this other thread...

 

Suppose an observer moves along the x axis in some known way at speeds where length contraction is significant.

Is it possible to synchronize the movement of another object on the x axis, at some distance from the observer, such that the object always appears the same distance away according to the observer?

 

 

For example, suppose the observer and object are relatively at rest separated by 1 light second, and then at a predetermined time the observer moves in the direction of the object at v=0.866c for one second (with negligible acceleration time) and then stops. Is it possible to move the object in such a way that it always appears 1 light second away according to the observer, despite any length contraction that the observer might experience?

Continued...

 

In this example the ship is 1 LY from Rear to Front, and there is a travel distance of 1 LY from Front to Destination. v = 0.866c; gamma = 2.

Assume negligible acceleration time.

 

 

Okay so if we let the Front get a half??? 1.15??? year start (according to Rear), and stop one year some time in advance (again according to Rear but this time in a different frame), Rear never sees the length of the ship change ???????, although it is certainly affected by length contraction.

 

So if the distance to Destination contracts to 1 LY according to Rear, but the ship also remains at least 1 LY long, then what gives?

 

 

Okay so after the Front's head start, Rear travels at 0.866c for 0.577 years local time, covering 1 LY of rest distance in the Destination's frame (ie. the total distance of the trip).

At the start of its trip, the distance to the Destination (rest distance 2 LY) contracts by gamma = 2 to 1 LY, and continues to decrease as the rocket approaches. In other words, it contracts to closer than the front of the ship. BUT the observations of this still take 1 LY to reach Rear.

 

Before Rear can observe the Destination contracted to closer than the Front, after 0.577 years rocket time it stops, undergoing a frame shift, and changing its simultaneity relative to Destination. Any observations of the Destination being closer than the Front are unobservable, because they happen too far away to be seen in the time that Rear remains in its moving frame. The frame shift essentially changes what has not yet been observed.

This brings up an interesting consequence of SR: If an event is predicted to happen, but then becomes unobservable due to an update to simultaneity, then that event didn't happen. Only observable events actually happened.

 

So in conclusion: The ship will also be affected by length contraction (relative to the observer on the ship), BUT if the front is ever calculated to be beyond the destination, it will only happen for a short enough duration to make it unobservable, which means it never actually happens.

 

 

 

If you read all that... sorry...

(2) The 'phone number of the girl I met in the pub on Friday (sorry, I didn't get her name- it was a bit loud and I wasn't entirely sober).

0113 876 0760

Curious. I keep coming up with an answer of infinity.

 

 

I couldn't help thinking some more about this problem.

 

 

Let's simplify the problem further.

Suppose we have an observer at the back of the ship, and the front of the ship is one unit away (1 LY say). We'll consider the front and back of the ship as 2 separate entities, with nothing in between; we'll ignore the rest of the ship so we don't have to worry about how it behaves.

Suppose one unit beyond the front of the ship is a destination.

 

The destination is 2 units away from the observer. Length contraction of gamma = 2 will bring the destination to the same distance as the front of the ship; any higher gamma and the destination will be closer than the front of the ship.

 

 

The ship can't start moving as a single unit at a single time according to all observers. At best the start time can be synchronized according to some location. This can be done by sending a signal to start, to both the front and back of the ship. Suppose this is done from the middle of the ship. From that perspective, equidistant to front and back, both start at the same time. But according to the observer at the back, she gets the signal to start before she observes the front of the ship starting.

 

Another alternative is that the front of the ship sends the signal to start. Then, the observer at the back observes the signal to start at the same time that she observes the front of the ship also starting. In this case, the observer sees the ship starting as a single unit.

 

Using this synchronization method, it's clear that there are only 2 cases: The observer will begin moving before observing the front of the ship starting to move, or at the same time as observing the front of the ship starting to move.

 

Case 1: Observer begins moving first.

Until the observer sees the front of the ship moving, the front of the ship will be in the same inertial frame as the destination.

The length of the ship will contract by a factor of gamma, the same ratio that the distance to the destination contracts. The front of the ship will never be seen to be beyond the destination.

 

... Then there are a bunch of details I don't want to try to figure out and am skipping, in the timing of this.

 

Case 2: Observer begins moving at the same time as the front.

With gamma=2, what the observer sees is that the distance to the destination contracts to half its length, and the front of the ship appears to have instantly reached the destination, at which point it stops and becomes part of the destination's inertial frame (thus again, now length-contracting by the same amount with the front never appearing to be beyond the destination).

 

This is consistent with what other observers would see: From another perspective, the front appears to have a head start, the ship stretches, and the front of the ship reaches the destination early.

 

 

Again there's a bunch of details that can be worked out, but this is enough to resolve the paradox:

Unless the front of the ship passes the destination (according to all observers), then an observer elsewhere on the ship will necessarily see her own ship length-contract (for at least part of the duration) along with the destination, such that she never observes the front of the ship passing the destination.

 

 

 

---------

Edit: I think I got this at least partly wrong. It should be possible to set this up so that the rear observer never observes any change in the length of the ship.

I think I was forgetting about the travel time of light.

 

Dammit complicated relativity, you are ruining me.

Note: the following turned into a huge mess when I tried to correct errors in the original.

 

 

Alright say for example the ship is 1 LY long, and the front travels a further 1 LY to reach its destination, at v=0.866c with gamma = 2.

The time it takes, according to an observer in the destination's frame, is 1 LY /0.866c = 1.15 years.

According to the front of the ship, it has to travel a length-contracted distance of 0.5 LY at 0.866c, taking half as long or 0.577 years local rocket time.

 

If the front of the ship gets a 1.15 year (destination frame time) head start, the length of the ship becomes 1.15 year * 0.866c = 1 LY longer according to the rear, but the distance is length-contracted by a factor of gamma=2 before the rear starts moving, to a distance of 1 LY. Sorry... confused...

If the front of the ship gets a 0.5 year (destination frame time) head start, the length of the ship contracts by a factor of 2 to 0.5 LY, so it takes 0.5 years for observations of this to reach the rear. But if the rear observer begins moving at the same time as this observation reaches her, she is now at rest relative to the front and observes herself moving in sync with the front, keeping an observed ship length of 1 LY.

In the destination's frame, the rocket is 1 LY + 0.5 year * 0.866c = 1.433 LY long. If the front stops while the rear is still moving, their distance according to the rear will contract to half that, 0.7165 LY. (Ugh, sorry these calculations got a lot more complicated than I expected..) Now if the front stops by a time of t earlier than the rear, then the rear will continue to move forward at 0.866c while the observation of the front having stopped travels backward at c... we want (1+0.866)*t = 0.7165 LY. t = 0.3839 years... If the front stops 0.3839 years before the rear, then the rear will observe this after 0.3839 years... at which time it stops. Having traveled 0.3839 years*0.866c = .332 LY, the rocket is now 1.433 LY - 0.332 LY = 1.10 LY long.

SO! I don't know if I've just thoroughly confused myself and everyone trying to read that,

or if I've demonstrated that if the scenario is set up so that the rear observer observes being in sync with the front (and thus never experiencing extreme length contraction relative to the front), then the rear cannot remain at 1 LY away from the front (ie. it's impossible to keep the ship always appearing to be 1 LY long).

I'll try to figure out the rest of the details sometime later. I'm probably still wrong here so far, somewhere. Feel free to correct me!

Then he stumped me: it should therefore be theoretically possible to arrive at a speed sufficiently close to c such that the entire universe seems to contract to shorter than the length of his spaceship. The front end would essentially have shot passed his destination and the back end would essentially have regressed behind his point of origin. How does one resolve this paradox?

With these extremes you can't treat the spaceship as one unit. You have to take relativity of simultaneity into account. Different parts of the ship would experience the situation and its timing differently.

 

To simplify the situation, we can consider the viewpoint only from the back of the ship (to begin with, at least).

Let us set up the timing such that from this viewpoint, the observer never moves relative to the front of the ship. We can make the ship very long (a lightsecond, say) if it helps.

To simplify, rather than considering the entire universe we could consider only some distant "destination" point, for the front of the ship to reach.

Let's assume instant acceleration and deceleration.

 

I think the paradox resolves as follows:

With extreme enough velocity, the destination would indeed contract to a length less than the length of the ship.

However, the travel time (according to the observer's clocks) to reach the destination would be shorter than the time that it takes light to travel from the front of the ship to the back (someone please correct me if that's not certain).

 

When the ship instantly accelerates, it experiences an "update to simultaneity" relative to the destination.

Before the observer can observe anything happening at the front of the ship, the ship has reached its destination, and the observer experiences another "update", and at no point has the observer observed the front of the ship being farther ahead than the destination.

 

 

If the ship instead passes the "destination point" and keeps going, the observer simply observes it all happening with different timing than the front of the ship would.

If the front of the ship crashes into the destination while the observer continues moving forward, the length of the ship would be decreased to the length between observer and destination before the observer could witness anything impossible happening.

 

 

 

I have a feeling this explanation is missing something in the details though...

I'm not sure what use this could possibly have.

Say for example if you wanted to calculate everything.

The problem I see lies in the units... Let's say the unit for time is seconds and the unit for space is in meters... How can "Everything" be defined in Meter Seconds? You need to define your "Everything" better. Is there a use for this equation your suggesting?

Perhaps Infinity I is multidimensional. Perhaps Everything is Meters³ Seconds. Then it makes sense.

 

However, a decimal with an infinite number of zeroes followed by a one in not equal to an infinite number of zeroes followed by a zero.

 

I think it's equal.

It is because of the mathematics shown above, that no two points will ever be able to come together due to scaling.

Perhaps I missed something but how is it that scaling by a factor of 0 is disregarded?

 

 

 

In other words, on the one hand you seem to agree that earth does not actually move closer to the sun, as length contracted measurements would have it. On the other hand, all that physics seems to be an argument for the opposite, i.e., that the 19 million km distance, as seen from the fly-by frame is accurate in 'the real world' and that, by the above "magic" somehow the heat diminishes with the shorter distance and time of exposure.

 

Again, I do not deny that the voyager "will see the earth as being closer to the sun." But it still looks like a distortion effect of relativity to me. Same with earth's diameter. It does not shrink just because extremely high speed frames of reference from which it is measured make it look like a 1/8 sized mini-earth.

What you are talking about is known as "rest distance".

You are arguing that rest distance is more definitive of the concept of distance, than is relativistic distance.

You can argue for that, except that it leaves the distance between moving objects undefined, which is not very useful.

It might be okay for describing a static universe, or ideas that we've known for 100 years to be false.

 

In fact, all of your "ontological studies" seem to advocate a return to early 1800s understanding of time and space, back when the metre was defined as a fraction of the Earth's circumference. Your ontological arguments involve undoing 200 years of understanding and progress, but I don't see anywhere that they offer a means forward beyond what was known back then.

 

 

Edit: Erased discussion-stifling comments.

Actually, we don't fry, because of how length contraction works.

I would have thought that it could also be answered in terms of time dilation.

 

With gamma = 8, the earth would receive "8 minutes worth of radiation in 1 minute of observer's time" (ie. 1 AU's worth of radiation in the time it takes light to travel 1/8th AU) due to length contraction ???,

but the sun would emit 1/8th the radiation per minute of the observer's time, due to time dilation.

That is true but you still age at the rate that is normal for you and you still spend time in time, just a slowed down version in relation to others who are not moving in relation to you. When i think of time travel i think of simply stepping into a machine and arriving at a destination as though you are going to the mall or the next room. You have a valid point but to me that is not visiting the future independent of time but still with in the "Now" of everyone else. You simply age slower, there is no disconnect with time that time travel implies.

Traveling relative to a universal time is impossible because there is no universal time. Time travel "independent of time" makes no sense. Existing anywhere but (your) "now" makes no sense.

 

The time travel you describe (stepping into a machine or going to the mall or next room) and the time travel that A Tripolation describes can be united. If you travel close enough to the speed of light, then even a small duration for you can mean a large duration for whatever you're moving relative to. Whatever you do, you will age along with your own clocks, and the actions you described (stepping into a machine, going to the mall or next room) take time. Even if you spend only a second in the time machine, if you travel fast enough, you could have years pass outside the time machine.

 

Not only does the technology not exist, the energy requirements would be ridiculous, and it involves changes in velocity that would probably turn you into a "quark soup" or worse.

 

At 0.99999 c, 1 second in such a time machine would get you only about 3 minutes 43 seconds into the future.

 

0.99999999999999 c for 1 second would get you 81 days into the future (if my spreadsheet remains accurate to those decimal places). Each extra "99" tacked on gets you about 10x farther into the future, so

0.9999999999999999999999 c for 1 second should get you over 2 thousand years into the future.

 

Or just spend a minute at 0.99999999999999 c to get 13 years into the future.

 

No guarantees at all on the accuracy of these numbers.

 

given time dilation/relativity that perhaps in the

 

future we may be able to "jump" forwards in time

To jump forward in time by only exploiting special relativity, you'd have to travel at the speed of light.

 

 

Astronauts and muons aging more slowly and living longer and clocks ticking slower are physical processes that slow down with higher velocity. (No dispute.) This does not make time something that expands (which dilation means.)

Interesting... you've nixed the accepted definition of time in favor of a new definition that includes only the concept of duration, but you're also saying that all physical process durations can change (ie. become longer durations, due to slower processes) independently of this new definition? In other words, your "EDPP" isn't "something" that can be changed, and remains defined for a relatively moving observer exactly as it does for an observer at rest, even if there are no unchanged durations to define it?

 

Or did I get that wrong, and EDPP can dilate but time can't?

 

 

 

 

 

 

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.

Thanks. A lot of that is beyond my understanding, but it seems to clear things up, for me.

 

What I gleaned from it: Distance is meaningless or undetermined (not undefined) for "nothing".

You can define distance with respect to nothing, but you can do so in many different ways, each equally valid with nothing to determine the metric.

 

 

The same argument applies, of course, to the meter stick (in hand, at rest frame) staying one meter long even while the near 'C' fly-by guy measures it as a tenth (or an eighth) of a meter.

Out of curiosity, how would you apply your definitions to the following situation?

You have 2 meter sticks, one in each hand. You move one of them and it is (imperceptibly) shorter than the other. Which stick is 1m, if they are different lengths? The one at rest I presume?

 

Now suppose a friend is holding on to the other end of each stick. Suppose you pull on one stick (making it shorter to you due to length contraction), and your friend gets pulled along with the stick. The shorter moving stick for you, is the longer "at rest" stick for your friend. Which of you is correct?

It seemed off-the-wall and irrelevant to the above argument. I obviously missed the significance of your point. My verification would be the same as Newton and his apple falling from a tree... what goes up will also come down in my living room. (??) Plus, I stick to the floor like everyone else rather than levitating.

 

 

The relevance is that you accept that gravity applies beyond experimental evidence (eg. in your living room) but dismiss evidence of relativity beyond experiments.

This view might make more sense if relativistic effects (like length contraction) were just parts of a theory devised to explain observations of high-energy particle experiments, which you've suggested that you believe. However, relativity is a theory devised to explain other observations... namely those of the speed of light, and measurements thereof in different forms over a century or two. Length contraction and time dilation are consequences of relativity and of the observations of light. The theory came before experimental observation of relativistic effects. Particle experiments support the theory; they did not spawn the theory.

 

Maybe ontology is clouding my judgment

Yes, I think this is true. I think it makes the most sense to consider only the properties of time that you can reason about (and do so precisely, ie. mathematically), and ignore everything else (because if you can't reason about it or test it, you can't validate it, and there would be no way to tell what is "true" from what is simply made up, or what is "cloudy"). For me a good ontological study would begin with what you can experimentally observe about time, and end with what you can logically deduce -- or perhaps a step further into interpretation(s). If ontology requires more (determining "what it is" when any potential answer can't be validated or evaluated), then I don't think ontology has scientific merit, besides being a source of imagination that can inspire new ideas. If ontology exceeds experimental validation, it is similar to me to visionary science fiction.

 

But I think this is an aspect of philosophy in general, where it is good to think of ideas without limits, whether or not those ideas can be experimentally verified. Philosophy considers the meaning of things, and if you're trying to figure out something like time, that can definitely make things cloudy.

That, contrary to relativity theory, there is a preferred frame of reference... at rest relative to that which is being measured.

Come to think of it, I think the technical name for that is "local frame of reference" (or perhaps "inertial frame of reference"?).

You might say that every observer prefers their local frame of reference, but that is not the accepted meaning of preferred frame. Considering all frames, none are generally preferred over others.

That, contrary to relativity theory, there is a preferred frame of reference... at rest relative to that which is being measured.

Isn't this just what "frames of reference" are in general? Things in an observer's inertial frame are at rest relative to the observer.

 

 

Problems with this definition:

- Every observer's frame is a preferred frame of reference, since every observer is at rest in their own frame.

- How do you measure the distance between moving objects? For example, consider measuring the distance between 2 rockets moving away from each other. Where is the preferred frame, at rest relative to that which is being measured?

 

 

I'm glad to see some specific ideas besides "SR is obviously wrong".

I must conclude that my initial idea was wrong.

We can define space in such a way that it is defined for nothing, simply by having the definition not depend on things like matter.

 

 

More practically, we can consider distance in terms of curvature, and discuss what curvature is like away from matter.

I think that GR might not define curvature in the absence of all matter, but it does define curvature remote from matter, to any distance (since spacetime is homogeneous). ?

I still "believe" that spacetime might not be homogeneous and there is some way to express some kind of curvature where distance "ends" or something, but this belief is based on ignorance.

 

 

But I think there may be some insights into the topic in the question of "How would you measure a distance of nothing without sticking any matter into it?"

(I think it's an interesting question, because if space curves due to matter, then measuring it with matter changes it, and then the real answer might be the answer to another question: "Do we assume that measuring space changes it very little, due to assumptions, or due to extrapolation?")

 

 

So back to the question of how might we measure distance where there is no matter?

If you beam photons into it, you will never get information back from them?

Is there a way to beam energy into a void, and have it change direction without interacting with anything? Perhaps you can have something photon-like that decays into other photon-like energy that is emitted in different directions, at least one of which can be intercepted? Or perhaps shooting 2 converging beams into nothingness... would you be able to detect information from the point of convergence?

And is putting energy into nothing the same as putting matter into it?

No more lectures on SR, please. I have actually studied it in depth.)

I am not a mathematician, but I am seriously trying to understand how length contraction comes out of the particle accelerator and applies to earth's diameter and our standard astronomical unit. If those lengths really "contracted," how is it that earth's diameter, earth itself does not shrink, and we do not actually get closer to the sun. I thought these were fair question deserving more than implied ridicule for answers (and another demerit in the popularity contest department.)

I'm surprised that you never came across these answers while studying SR in depth. I find that sometimes, pages of books I'm reading get stuck together and I skip over things without even realizing it. You might look over your notes to check for this. Perhaps you accidentally skipped a few chapters.

 

Since you have studied it in depth, you will know how length contraction follows as a logical consequence of the principles of relativity, and you will know what observed evidence must be incorrect if length contraction is false.

 

 

Yes. But if it is just "Event Duration of Physical Processes" (my coined acronym for time, EDPP) then slowing down of physical processes is the empirical observation and does not fall into the pit of "time" reification, i.e., that "it dilates." OK?

EDPP... I like it. It's less confusing than "time" and it's clear from the words exactly what it means (ie. it means what we really mean when we're talking about "time"). It doesn't roll off the tongue quite like "time"--I will pronounce it "Edpeepee"--but it is good.

 

Of course, the Edpeepee still varies due to relativity; that is, the durations can be longer ie. dilated, but since the wording is clearer we can know that we don't have Edpeepee reification, when we say that it is a logical consequence of the principles of relativity and a fact of nature, that "Edpeepee dilates".

I asked (again) recently if anyone actually believes that earth's diameter or earth-sun distance actually varies with different frames of reference from which they are measured. Apparently no one wants to look foolish enough to affirm contraction/expansion of that diameter or the one AU distance, but relativity's "length contraction" insists on their variability.

I believe it because it does vary.

 

The distance between Earth and Sun is the distance between Earth and Sun according to any observer.

Distance between Earth and Sun varies even without length contraction since Earth's orbit isn't a perfect circle (wikipedia says "The Earth is 1.00 ± 0.02 AU from the Sun").But an AU is defined as a number of meters, which vary due to length contraction.

 

What doesn't vary is c, which I think is key to grounding all of these concepts and making them meaningful despite all the variability.

 

(I was baiting the forum with this example to see if anyone actually knew anything about this field, or if blind prejudice would prevail. It did.)

Curses! You've once again proven me a fool by my taking of your bait and replying to your posts!

I'm currently siding with the opinion that information that does not have an effect on anything else, does not exist.

Is this true (or false) based on definitions ("exist" etc) or scientific laws?

 

 

Why I think it's true:

- If it has or can have no effect on anything, then it doesn't matter if it exists or not (there is no difference in the observable universe), and it seems like existence would require such a thing, by definition.

 

Why I think it might be false:

- Conservation laws; symmetry etc. If you have energy and you lose it, you know by conservation laws that it is not destroyed, and you can deduce that it still exists. I don't think this is valid, because it would require an assumption of the existence of things we have no way of knowing anything about. If we know that some energy has been lost (if there is some evidence of it left in the known universe, this constitutes a "memory" of the information, which might be considered an observable effect of the information??? This might require the distinction between "observable information", "deducible information", "lost information" (unknown information that might be found again), and maybe "destroyed information".

 

 

 

Examples:

- If you beam light into deep/empty space, and in the case that it may never come back, is that information lost? If it doesn't interact with anything, it is undetectable(?). Wouldn't this have happened with the big bang, where a lot of light would have escaped and continued outward forever, with no way for us to measure? Is there some unknowable amount of energy that is assumed to have escaped the big bang, or are there clues left behind to be able to determine the total energy of the big bang?

 

- If you send a light signal across empty space (say from Earth to moon), that light does not seem to exist except where it is sent and where it is received. For the duration of its "flight", the photons have no effect on anything, and they are undetectable (except by something that changes their destination, in which case they still only exist where they have an effect). There is no observable difference between photons flying from one place to another, vs. photons jumping from one place and time to another.

 

- If an event is completely forgotten (no memory of it, not written down anywhere, no evidence of it, no lasting effect on any energy or particles), is there any meaningful definition that says the event actually happened? This might get into many-worlds interpretation etc.

 

- If you have 2 entangled particles and lose one, can you deduce the existence of the lost one from the known one? Are there such clues about all possible particles, found in all known particles?

I was not quoting you but making a general summary statement. It would have been more clear if i had said “If time and space are not entities...” then how did “spacetime” become a malleable medium, curved by the gravity of mass?

 

Imagine a circle.

What is it made of ("the ontological problem of the imaginary circle")?

Is it curved?

Can things that do not have physical presence (ie. non-entities) be curved? If no, then how did your imaginary circle become real?

 

 

I don’t understand this at all. Do they not routinely make very precise adjustments to GPS clocks (which vary in ticking rate) to yield precise positioning information?

Yes, a wind-up clock submerged in water will slow down a lot, and no one would call it time dilation, but saying “time dilates” under other familiar conditions (changes in gravity field, velocity, etc.) does mean that something “time” is changing, not just the “ticking” rates of clocks? If there is a difference, what is it?

The difference is that in one situation (eg. due to gravity), all clocks slow down... ie. time dilates.

In the other (eg. under water), not all clocks slow down.

 

So for example if you put a clock underwater you can see that it's slowing down, but if you're traveling at near c with a clock, you can't see any change in time (in fact there is none relative to you) because your brain is also affected the same way that the clock is. Time dilation is only experienced relatively, from other frames of reference. AND because there is no privileged frame of reference, you cannot say that a clock is absolutely slowing down, from within an inertial frame of reference.

 

If this doesn't make sense, it is because relativity is a very confusing thing to get, at many different levels (from general concept to exact details of particular examples), and you're not going to understand it without researching it. I could not and would not try to explain it all in an internet forum.

 

 

"So defining time with a tautology is no problem for science."

 

All this evaluation of wording is beside the point.

The point is:

- time is well-defined and consistent

- its definition is meaningful, in that it applies to aspects of real-world observations (unlike your example of auras and aura-meters)

- it is complete in that the definition ("time is what clocks measure") does not fail to account for any "time-like notions of reality".

Sorry my wording is not exactly scientific.

 

Any proposed evidence to the contrary would be interesting.

The problem you are confronting I believe is. If space is totally flat (or spacetime if you prefer) then it does not warp; there is is a contradiction.

[...]

You also mentioned gravity waves. Of course it has not been proven that gravity waves exist but there is evidence that they might, and a Nobel Prize given for the evidence to suggest them. If they exist then, the question becomes, "what do they do." Some think that they are the cause of gravity but in GR, gravity is caused by warped space. Others including myself believe that gravity waves are simply waves produced by very massive objects and are unrelated to gravitational effects. They are more like De Broglie waves IMO.

 

Well, my reasoning is as follows:

- Distance seems to be defined between any 2 points in space.

- Distance also seems to be defined "around" matter, since mass curves spacetime. But to what extent? There seems to be no intrinsic limit based only on length (distance from the mass). I don't have a firm handle on curvature but I think curvature due to mass approaches 0 (flat) as distance approaches infinity, but it is still non-zero at any arbitrary distance???

- However, there is an intrinsic limit to distance based on time. A mass cannot have any effect on anything outside its light cone, ie. no information can travel faster than c. This is the law of causality. To me it means that a mass cannot define the curvature of space at a distance farther than where light (or eg. gravity waves) could be able to travel in the time that the mass has been around. In other words, space could not be defined farther than c * age of the universe away from any matter (even if inflation allows the matter to escape other matter's "causal horizon", which might allow for "gaps in space").

 

 

 

 

That spacetime warps (consistent with SR and GR) is a fact of reality that I accept. The universe appears (to the limit of our measurement) to be flat*; these are not mutually inconsistent statements. I don't understand it enough to say why.

If there is infinite matter in the universe (which I don't believe is true) and it's evenly distributed, then distance would be defined to infinity in any direction.

 

 

* Admittedly, this is pretty meaningless, because it's like saying "To the limit of my vision, the Earth appears to be flat."

 

Another point concerns your idea of infinite space. If space is defined by matter as in the BB model or other finite universe models and Einstein (according to his quote in the O.P.), then space is not infinite by definition.

I agree.

 

I believe that there's a finite amount of mass, all within some distance (related to the big bang), and that spacetime and distance is not defined beyond some limit (the union of all causal horizons of all matter and energy in the universe, I guess), and that spacetime is probably flat instead of closed. I don't think that all these beliefs are mutually consistent, and I'm missing some understanding of the meaning or implications of curvature, or mixing up the meanings of a flat universe and flat spacetime.

 

Distance can be defined abstractly, so that the distance between imaginary points is still defined, and this doesn't depend on what space is defined as (because we can always (maybe???) define an abstract space as well that is infinite and covers any "nothing" we want to consider).

 

It seems that if space is flat (infinite) and homogeneous and isotropic then an abstract definition of distance would match a real definition of distance?

 

Then, even if we couldn't measure distance in nothing without putting something into it, we could extrapolate it. This relies on the assumption that spacetime curvature is homogeneous to an infinite distance in any direction, which kinda implies that infinite distance is defined. I'm confusing myself now, but there must be something in this statement. Matter causes spacetime curvature at a distance. That curvature can be measured or extrapolated. Or is spacetime curvature the same as distance, and could be argued to have no meaning except between given reference points?

 

Without figuring out the meaning of nothingness or space, I would guess that the calculable effect of spacetime curvature caused by mass would allow for a definition of distance, and this curvature is defined within the light cone of that mass.

 

 

So I think that on the "real" end of the spectrum, distance is measurable between points of matter,

and on the "abstract" end of the spectrum, distance is defined abstractly in an infinite flat geometric space,

and somewhere in between, there is spacetime, which is defined only within the union of all light cones of all matter, and that distance is defined throughout and only throughout all of spacetime. But then, I don't know whether or not nothing would be defined to be exclusive to spacetime, or within spacetime, or both.

 

I think you would have to allow nothing within spacetime, or spacetime would have to be considered "something" and there's no good reason to do that.

 

 

 

Alright I've talked myself in circles but it comes back to the original idea: Even if distance is only defined between things, doesn't all matter "radiate information" (for example in the form of gravity waves) that define distance within that matter's light cone, all around it? Or does information only exist if it causes an effect -- only if there is something out there to receive it?

This is a digression of the "ontology" thread...

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"

 

 

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?

 

How could you possibly measure (or express) distance of nothingness? Isn't 1m between nothing the same as a billion light years between nothing?

 

How can you measure distance without using matter? If you stick a tape measure in it, the matter of the tape measure defines distance. If you shine a light into it, you receive no information back (unless spacetime is closed). Is there any example of distance that is defined without requiring some form of matter at its extremities?