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Time does NOT Exist - Math Proof

  1. Mar 1, 2005 #1
    Many, myself included, tend to think of time as if it were flowing from the past into the future and in some mysterious way changing things as it passes, but I think this is demonstrable wrong. Really we never observe time. "Time" need not, and probably does not, exist and this can be demonstrated with mathematical rigor. Now for that demonstration:

    What we actually observe is something changing, not time. I'll take a changing observable related to time, the continuously moving hands of a clock, but any changing observable would do. (The mathematical formulation I give is general.) These hands advance in relation to some other change, specifically in the case of a grandfather clock, they correlate with the swings of the pendulum.
    Let me now state it more generally: Event "A" is an observable changing function of time, "t" or A(t) = a(t) where the functional form of a(t) could be 15sin(7t) if the observable event A were the oscillatory positions of a pendulum, swinging with amplitude 15 in some system of units. (I use this example, despite its having repetive occurances of "A" because the inverse function has a well know name and that helps in my specific illustration/example.) Likewise some other changing observable event, say B(t), which if you still need specifics you could consider to be the position of Mars in its journey around the sun, but lets be general.
    We have two equations:
    A(t)=a(t) and B(t)= b(t). Inverting (Solving each separately for "t") we get: t=a'(A) and t=b'(B). As I fear some are already confused, i.e. not with me any longer, I will briefly return to the specific example: This inversion of the equations with the prior specific example: A(t) = 15 sin(7t) leads to 7t = arcsin(A/15) or t= {arcsin(A/15)}/7 which for convenience and generality, I have called a'(A). (The function form of a' ,which was an "arcsin" in this specific example, is only expressible in the general case symbolically and I have chosen a'(A) to represent it.)

    Becoming more general still by considering some other observable, C, I get:
    t = c'(C) etc. for every observable in the universe. Now eliminating time from all equations of the universe (and this is the proof that it is not needed to describe all observables in the universe) we have:
    a'(A) = b'(B) = c'(C) = .....
    That is every observable in the universe can in principle be related directly to any other observable without any reference to time.

    Eliminating time from all physics would be an extremely useless thing to do. It is much easier to describe all event as if they were function of this wonderful, but unobservable construct of man, we call time. But the "passing of time" is not the cause of anything. (Events cause events.) Time is a very convenient invention of man, a parameter in our equations, as I have just demonstrated with mathematical rigor. Becoming specific again to make sure all can follow:

    I am not growing older because of the passing of time. I am growing older because of causal events in my body. For example, in my joints small crystals are forming, when my cells divide, their telomares are growing shorter, etc. "Time passing" has nothing to do with my aging. Time causes nothing.
    Man invented time, but not by any conscious process. It is just the way we tend to think, like we once did that the world was the center of the universe, sun going arround, etc. ("natural assumptions", formed prior to knowledge) Without education, science and math we would still have more of these naturally assumed truths and hold them strongly. Slowly, one by one, man is gaining a more correct view.

    Summary: Time can not be observed. Time does not cause or modify anything that can be observed. Time is not necessary for a complete description of the universe or the changes of its state. Time’s existence is a “natural assumption” of most humans and a very useful parameter in the equations of physics.

    Unfortunately, few yet realize (and few will even accept despite the aforegoing mathematical proof) that time is one of these "natural assumptions" of man and not any real thing that flows from the past to the future, making changes as it passes. Is any one willing to agree with me on this? If not why not? Can your refute the math?
    Last edited: Mar 1, 2005
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  3. Mar 1, 2005 #2


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    Math proof is weak, but from a thought experiment, there are a few points

    Time has been used to synchronize series of events, and in a sense that an event A preceeded an event B, you will have a vector of time associated with their difference. Then there is this hardwired law of physics where time, distance, and speed are related. And what do ya know, acceleration is based on time too.

    Then there is a weak force and halflife decay - sure they can be said to be sequences, but overall the way to quantify it has been to use time, so now we have forces that are inter-related through this nice indexing variable we call 'time'. As you run more and more experiments you arise to a conclusion about nature of space and how it relates to this index 'time' - not nature of time itself, which is still, just an index
    Last edited: Mar 1, 2005
  4. Mar 1, 2005 #3
    Please show me specifically where, and I will try to improve it.
    I agree that "t" and delta "t" are often used as you describe. I agree that F=ma, etc. have the very units of time in these equations. but there are many different ways to describe physics. I do not understand it but I believe that at one time there were eight different description of some fundamental physics events etc, that all appeared to be equally valid models of the experiments. (Fortunately some clever mathematicians were able to show that these formulations were the same in a few years.) Quantum Mechanics has both an analytic equations and Matrix description. Newton and Lipzig had different descriptions of calculus. The fact, to which I readly agree, that "t" is a very useful parameter in the more common descriptions, does not negate the fact that my proof elimates "t" entirely in an essentially useless (because of its complexity, not any error) alternative description of the universe.

    Since your post I inserted the following brief summary:

    Summary: Time can not be observed. Time does not cause or modify anything that can be observed. Time is not necessary for a complete description of the universe or the changes of its state. Time’s existence is a “natural assumption” of most humans and a very useful parameter in the equations of physics.

    It seems to me that anything with these characteristic, can fairly be said to not exist. Perhaps you disagree with some point in this summary? If so which and why?

    I fully agree "t" is a nice indexing variable - that was my point: time is a great paramter for relating events in our equations, data sets, life insurance tables, etc., but this fact says nothing more than "t" is convient and a very "natural assumption" or parameter. Nothing about the existence of some thing or invisible massless flow from past to the future. If you think time really is something that actually exists, please tell me where I can get some to study.

    I will grant you one point: I may have overstated my case by saying that "events cause events." Spontaneous radioactive decay does seem to be an "uncaused event", but then again, perhaps AE was correct - we just don't know about the "hidden variables" that occasionally combine in some special way to cause the decay, so I reserve to right to restore "events cause events, not time" to its full former strength, If AE should turn out to be right again.
    Last edited: Mar 1, 2005
  5. Mar 1, 2005 #4


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    Ok reason I said the math used here is weak is because you used "the swings of the pendulum". When a pendulum swings there are forces that act upon it - gravity, air friction, etc. The 'gravity' part of which is based, again, on time. It also happened to be one of the 4 fundumental forces in the Universe. So your pendullum is in fact based on gravity - which is based on mass, and a gravitational constant. There are so many variables along the way, but its ok, because in Physics, everything is relative. Even if we are moving at 30 km/second around the Sun right now, and some ~370 km/s around the Universe (based on Microwave Radiation Observation) - we are still at 'rest' since its all 'relative'

    But time is there - the past, the right now (which was actually right RIGHT now minus 2 seconds ago), and the future (which is RIGHT now). In a sense I agree with you that 'time' in itself doesnt really exist - but for different reasons. People assume there is a 4th "dimension" and that its a real but not really real dimension. Then there are 8 or so more for M-theory.. and all that - but in fact all those dimensions are used not on experimental data, but on a mathematical hypothesis - because when you used 12 dims everything fits nicely and easily, but speaking in relativistic terms:

    (x,y,z,t) the t doesnt really exist - there are only 3 dimensions and an index of time, "t", which is used solely to distinguish sequences of events
    Last edited: Mar 1, 2005
  6. Mar 1, 2005 #5
    Thanks. You are of course correct. I was trying to keep things simple for the philosopheres here. (no offense intended - I can't understand a lot of your writting.) What I should have written is:

    a'(A,B,C....) = b'(A,B,C,....) = c'(A,B,C....) = ......etc.

    To some extent, I did at least acknowledge this when I said it would be totally usless to try to do physics when each of the function depend uon a large number of observables. My simple version of original post is some what like say saying the sun's gravity determines the Earth's orbit (neglecting Jupiter etc.) When the full solar system interactions are projected far into the future, it is my understanding that even this epitemy of "classical behavior" is chaotic!

    Thanks again for providing / stimulating me to be more correct.
    Last edited: Mar 1, 2005
  7. Mar 1, 2005 #6


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    i've not took the time for a proper, thorough reading of your math (i will at some .. time later;)), but i've always thought of time as a unit of measuring what truly does exist: changes. "//" this much changes from one fixed point to the next.
    therefore, to your thesis, that time isn't a physical, observable "thing", to that end i agree.
  8. Mar 1, 2005 #7


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    If time isn't real, then energy isn't real, because QM tells us E=hf, where f is frequency and h is plancks constant. But then mass isn't real either, because E=mc^2. The fact is, we don't know if any of our physical quantities are really real, but they are helpful in making predictions, and that's all they need to do.
  9. Mar 1, 2005 #8


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    If there is causation, then there is time... How can there be causation without a sequence of events in time?

    Yes, time can be eliminated from two equations, and you can relate the remaining variables... but I don't see how this proves that time does not exist.

    What are valid observables... something from each of the five senses? Sight (position in 3 dimensions), sound, smell, touch, taste...

    I think the question should be, just how observable is time? Do we actually observe a sequence of events? My personal belief is that time is directly observed... the flowing nature of our experience, the changing nature... is direct proof that there IS such a thing as "change".

    If it is an illusion, how can we maintain the idea of causation?
  10. Mar 1, 2005 #9


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    Billy T: keep digging man, you are on to something

    However a word of advise: You need to find a good example among partial differential equations, perhaps a complex system
  11. Mar 2, 2005 #10


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    I've Just read this thread. Have any of you read the article in this week's (or maybe by this time last week's) New Yorker on Einstein and Goedel? I believe it was called Time Lords or something cute like that. The point of the story is that both men, who hobnobbed together during their last years, denied the reality of time. E was misunderstood and patronized, G was ignored as a "clown of philosophy". Times are changing and perhaps Billy has hit the right note.
  12. Mar 2, 2005 #11


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    Perhaps I'm missing something, but a couple of objections pertaining to this argument (but not necessarily to the conclusion itself) occur to me.

    The general strategy to this proof is to solve all time-based equations for the time variable and then equate these, thus eliminating any explicit mention of a time variable in the first place. However, as we can solve these equations for t, their units will necessarily be things we take to be measurements of time, such as seconds. How do we account for what a 'second' is without referring to time?

    Also, it seems to me that this strategy can be reproduced for just about any singular physical variable for which we can solve. By the reasoning of this proof, can we not (say) solve all equations involving mass for m, equate them all, and thereby conclude that mass does not exist? (If this cannot be done with mass for whatever reason, there surely must be other physical variables that we can use and come to the same general conclusion.)
  13. Mar 2, 2005 #12


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    Yes precisely, thats why I said that we need to look for partial changes with respect to statistical data of a complex system

    Taking into account that time would be a vector between the events, its easy to see that time exists. But not in a physical sense, as in there is no such thing as a '4th' dimension - its only a mathematical plane that we need to use to distinguish one event from another. That being said, time travel is impossible - or is it?

    To travel back in time would require to either (i) restore all events in current event B to their positions and properties in event A. (f: B -> A , card(B) = card(A) where f would be sequence event transformation as a function of time) -- clearly this is impossible since it would require so much energy to change things back to their original shapes/properties, and even positions!

    (ii) Worm hole concept - that space warps and you can get from one instance to another? I'm no expert on this, but even if you can travel through a wormhole - you will end up millions miles away from your original position, and you can only 'see' the past as light traveling from that position through a telescope of some kind. That is one way to see them dinosaurs, but then there is another quirk - how do you travel through a wormhole at v=0.9c, and still manage to get farther away from (x,y,z) -> (x',y',z') during t->t' where the distance travelled would be far greater than the amount of distance you can travel at speed of light, in effect going faster than speed of light, without actually going faster than light - if that makes sense
  14. Mar 2, 2005 #13


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    Well (said he, working both sides of the street) I think that time is more than a convention in present day physics. I am thinking of the trouble that Tomonaga and Schwinger had in defining a manifestly covariant quantum field theory of electromagnetism. The problem was to generalize the handling of time that had served Dirac in his relativistic one-particle theory. If time had been purely a convention, this generalization would have been easy, but time interacted with how a field theory behaved, in a nonconventional way that was difficult to conceptualize and incorporate into a consistent mathematical model. Tomonaga's name for this model was "many times", which doesn't mean actual multiple time lines, but approximately that different observers will have differently pointing time arrows. But the field had to consistently link all thhese neighboring time values.
  15. Mar 2, 2005 #14


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    I think time travel is impossible on dynamic grounds: The universe, as I see it, is a big non-linear dynamo in its chaotic regime. Think of the Lorenz Attractor: Trajectories NEVER cross. Same for the Universe in my opinion: to travel back in time would require crossing trajectories and to do so would entail "jumping" to another attractor (a different universe). Anyway, looking at it that way works for me.

  16. Mar 2, 2005 #15
    No, if you have an equation for the displacment of the QEII and solve for the mass of the QEII, I'll call it M. and another equation using the mass of a flea and solve it for m, I do not think it valid to set m=M!
    Mass is a real observable thing (Please lets not get too philosophical, especially now that the thread has been moved.) Mass is not like time. The time parameter is the same thing in all equations, althought its numerical value will deppend on the system of units (Measurement in year being different numbers that days etc.)
    Time is not observable and despite what many believe, not even measurable. What is measurable, and mistaken for time, is, to take a simple crude example, event B follows event A and after A,but prior to B the pendulum of a grandfather clock has swung 38 full cycles when event B occurs.

    Again events cause events. Time has no effect upon anything (Read again why I am growing older in my first post this thread. That too is not caused by time "passing") Consequently time can not by itself move anything, such as the hands on a clock (the spring or battery energy decreasing is the relativly continious sequence of events that moves the hands, not time.) If time can in truth do nothing how could it be measured? Unlike mass, time is just a very convient parameter in equations. A "natural assumption" of man that it is a flowing thing, dragging events along much like man's "natural assumption" that the earth is flat once was.
    Last edited: Mar 2, 2005
  17. Mar 2, 2005 #16


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    How is this not an observation of time though?

    You have a sequence of events: A, B...

    What kind of sequence is this?
  18. Mar 3, 2005 #17
    As I do not know how to make my original text appear in this response, I will ignore for the time being your first question. Stay tuned, and I may reply to myself and give more about it later.
    Your sequence of events,A, B..., is ordered and I agree we would commonly say "in time." but really it is only a chain of cause and effects.

    There is a play, which was made into a musical (good music to, but I have forgotten all the songs) and can no longer be confident in the spelling of the play's name, but I will try: Brigadoon.

    It is the story a a small village up in the Scottish highlands that for centuries was without any contact with the rest of the world. When contact began, in the view of the elders (local priest? - I for get who) was concerned that the outside world would corrupt their honest pure way of life. God granted their prayer that each night when they went to sleep, they would wake up and 100 years would have passed. One of two non Brigadoon hunters falls in love with a Brigadoon lassie, and is as is usually the case in such stories, their love is so strong and his grief so deep and sincere when that eve of their meeting Brigadoon disappears for another 100 years, it magically reappears and he can join her.

    Let us suppose (as most people do) that time is real, does exist, that the passage of time is what is making me age, that somehow that B follows A as if riding on the "river of time" flowing from past into the future, etc. and that Brigadoon is our solar system and all of the near by objects in the heavens for which we can notice a change in their position against the more distant stars. That is suppose that after a period of 24 hours time stops for us and 100 years pass for the distant stars and then our next 24 hours start running again - (very much like we were the characters in a two reel movie and the second movie projector in the projection booth was broken so that the second reel could not be faded in as the first was ending. I.e. the movie audience must wait for the reels to be changed on the only working projector.) Because I do not think time is real I did not like to say:
    "... time stops for us and 100 years pass for the distant stars and then our next 24 hours start running again..." I would have preferred to say: "every atom cease to move or change its internal structure and then 100 years later resumes exactly as it was" in the "greater solar system Brigadoon."

    How do you know my my "greater Brigadoon supposition" is not true? You think a sequence of events B, after A, proves time is real, but really all it shows that there is as I say a causal chain and time need not have anything to do with it and certainly does not cause change. "Events cause events" is becoming my mantra.
  19. Mar 3, 2005 #18
    Billy T, you are suggesting that "time" does not exist, in order to disprove something one must have a defintion for it (as one must have a definition for a thing which one is trying to prove the existence of). So you are saying "time" does not exist, what exactly are you saying does not exist?
  20. Mar 3, 2005 #19
    In a recent post I told outlined the story of Birgadoon. Suppose that there is a kind God and there is on Earth an modern day Noah, his very faithful servant, who happens to be an astronomer. who has been carefully recording Pluto’s position for the last few years. The small variations in Pluto’s orbit, after correcting for Neptune’s (an all other known mass’s) perturbations still do not account for his observations. He tries postulating other masses (perhaps hoping to become famous for the discovery of a new significant object) but the perturbations are still small and steadily growing, not like anything bound to the sun and orbiting it, so he starts trying to fit his data to an open trajectory and gets a good fit with a 2.2 solar mass object approaching our solar system from the north polar region.

    Going back through all his records and those from years earlier made by others, he becomes convinced. And begins to speculate what this object could be. If ordinary matter, it should have been observed in telescopes by now. Thus is either completely transparent of perfectly black. Never having heard of anything that fit’s the first alternative, he concludes it is a stellar core black hole. His trajectory data (from best fit of Pluto’s residual perturbations) projects it will pass 12 AU form Earth near the end of 2008, going N to S thru the ecliptic. (Here is were this story departs from my strange physics textbook, Dark Visitor Here “Jack,” the astronomer of Dark Visitor, is Noah, God‘s most faithful servant.)

    So Noah prays to his kind God for a “10 year Brigadoon effect” for the solar system - No one will know, because only Noah knows about the approaching black hole. Everyone will wake up in 10 years, and have their morning coffee and not know that during their Rip Van Winkel night the approaching black hole passed far from the solar system (which God stopped moving ,along with all the atoms in it did) and is “now” safely back in deep space.

    How do you know this did not happen?

    For those of you who wish to know what less pure Jack does (how he makes a lot of money etc.) or just want to know why I would wrap up/ hide a lot of physic in a scary story visit : www.DarkVisitor.com For those of you who want to know more now, skip next paragraph and read read remainer of this post. I hope those who think I am spaming will read next paragraph before making that opinion firm.

    At the web site, I tell how to read Dark Visitor in its entirety for free. Thus, unlike spammers, my motive is not profit - I doubt if I will ever recover my investment and certainly will get less than $1/per hour for my effort to help the western world not lose leadership in science to the hard working, very studious Asians, as it has already lost technological leadership. (What western country can make a robot that walks while it plays a bugle?) My motive was not fame either. Billy T is the author of Dark Visitor, but that is not my name. I wrote the book to appeal to young people, not currently interested in physics, who would never pick up a physics textbook, nor Dark Visitor if they new it is full of physics. (A sub page of the site lists all the physics hidden in it.) Dark Visitor is a recruiting tool for physics. The first four chapters are a historical account of the origins and troubles of the principle characters and have little physic in them (Hopefully my target readers are “hooked” and will continue reading even when they realize that they are painlessly learning a lot of physics.) Dark Visitor is like no textbook you have ever seen. It even has “Easter Eggs” hidden in it to encourage students to carry it around on campus, filling idle moments by searching for these eggs, and offers the “World Class Egg Hunter” certificate to those finding five or more. More below if interested. If you still think I am spamming that is your right, but I think I am trying to do a good deed for the western world, and my grandchildren, who I hope will have more interesting jobs available than cutting someone’s hair or selling fast food (Jobs that can’t be exported to Asia as most can and are being moved now.)

    There have been many "cosmic disaster" stories, some made into movies. Unfortunately, most require something from space (usually an asteroid or comet) to hit the Earth and this is not very probable, in a time period of interest to most of us.

    Dark matter excepted, perhaps, the most common objects in the universe are small black holes. The cores of stars bigger than about 6 solar masses end up as stellar-core black holes. There have been many generations of stars before the sun was born. Back in the early history of the universe, it was much smaller. Then the gas clouds, from which stars formed, were much more dense. Then as now, most gas clouds formed pairs of stars. (If only one were formed, it would need to rotate too rapidly to collapse enough to gravitationally heat to fusion temperatures. Also the density within the gas cloud is not uniform, so typically the two most dense regions eat up most of the gas to form a pair of gravitationaly bound stars, rotating about their common center of mass. Being big, they rapidly age into Black Holes pairs.)

    Thus, probably at the present age of the universe, the most common objects in the universe are gravitationally-bound, small, black hole pairs. (all those prior generations of big stars are now "stellar core" BHs with typically a few solar masses each.)

    What would happen if one with 3 solar masses should pass "near" our solar system, say five times more distant than Pluto is from the sun and in the same azimuthal sector of the sky as Pluto, just to take a specific example? Well, since Pluto is in a relatively weak gravitational field of the sun, it could be strongly disturbed. Perhaps even its orbit plane would be tilted from the ecliptic. Neptune is also far from the sun. If not in too different a sector at the time of the BH's passage by our solar system, as it was about 90 years ago, it too would be disturbed.

    To cut to the chase: In the late 1920s Neptune was disturbed. Based on this disturbance Percival Lowell predicted an unknown planet, "planet X," many times more massive than Earth, would be found roughly where Pluto was found a few years later. (He had been planet hunting for years. He founded the Flagstaff observatory and hired someone whose sole task was to hunt for Planet X, and he found Pluto. For a long time, may be still, I don’t know, the symbol for Pluto was the superposition of the letters L&P.)

    For years it was assumed that Pluto had mass much greater than the Earth, as this is necessary for it to make the observed perturbations to Neptune (from Pluto's orbit, which is always at least 17AU from Neptune). We now know Pluto is in fact smaller than the moon. It was hard work searching a specified region of the heavens plus luck that found Pluto. It would not have taken so long as it did to find if Pluto's orbit plane were essentially in the ecliptic, like all others are.

    Now back to the fact that stellar-core BHs come in pairs: The thesis of Dark Visitor is that the second member of this "1928/2008 pair" of stellar-core BHs will pass thru solar system in 2008. The good news is: it has only 2.2 solar masses. The bad news is: it misses the Earth by only 12 times the distance to the sun (A 12 AU miss is much more likely than the "direct hit" concept of other "cosmic disaster" stories.)

    I used the Dark Visitor story as a vehicle to teach a lot of physics, without the reader being aware how much he / she is learning. All the physics and a lot about climate is all woven into the story. For example, Keppler's three laws are explained and used but never even named, certainly not taught like you will find in a normal text book. The Earth's orbit will be changed by a bout 10% after 2008. A permanent ice age develops, but unlike all prior ones, it is confined to the Northern Hemisphere. We Southern Hemisphere dwellers get to live, no ice, but you would not believe the floods that wash away most of our cities. Explaining why all this is so is the vehicle I used to painlessly teach about the mechanism of climate.

    I am trying to recruit students to study physics. The western world has already lost technological leadership to hard working Asians and is process of losing scientific leadership as well. (Not because of cheap wages - people who can design a robot that can walk while playing a bugle do not come cheap.) Visit site www.darkvisitor.com to learn more, to get list of physics and climate painlessly taught, and see how to read entire book free. (My motive for writing it is as stated, not profit of fame. - Billy T, the primary author of Dark Visitor, is not my real name.

    The book's astronomer, Jack, provides most of the physics as he explains it to Billy T. The climate information comes from their mutual friend, George, brother of Jack's wife, who worked for NOAA. (Jack is too busy looking for slight deflections of background stars as the approaching BH passes in front (to refine the trajectory of approach) to write the book himself.) Jack and Billy T were college roommates at HARVARD, etc. Billy T tells about Jack's PhD astronomy project - another vehicle to painless teaches physics, etc.

    It is called Dark Visitor because being a BH, it reflects zero sunlight - telescopes do not see it coming. It may be, and someday will, but probably not in 2008. The unexplained late 1920 disturbance of Neptune may have been the first indication that our solar system would be visited by two gravitationally bound BHs, the most common objects that exists in the universe! If Neptune's perturbation was something else, it is still true that someday we will be visited by a pair of "dark visitors."
  21. Mar 3, 2005 #20
    The common understanding of time is what I am sayng is false. The subject of that understanding is what I say does not exist. As for me it is non existent, it is hard to be more precise. You give me a discriptive definition of an angel and I will try to give you one of time. (not really - just trying to make you understand why I can't. Your angel definition should at least tell how big are they and where their wings are attached and how they are powered etc.) You get my point, I presume.
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