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1 + 2 + 4 + 8 + 16 ... = -1 Overflow the universe - Page 2 — Parallax Forums

1 + 2 + 4 + 8 + 16 ... = -1 Overflow the universe

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  • Heater.Heater. Posts: 21,230
    edited 2016-05-29 17:10
    There is no punch line. It is not a joke. It is not "wrong".

    In the history of mathematics there has been all kind of conceptual, common sense, "wrongs".

    For a long time we had no zero. That makes no sense. A number to count nothing, crazy! The Romans did not even have a zero. That idea came from India and took a long time to be accepted.

    Negative numbers were also problematic. I can have one cow or two cows. How can I have a negative cow? Crazy.

    Pythagoras and his crew were really upset by the square root of 2. A number that cannot be written, or even exist, as a fraction like p/q where p and q are actual tangible integer numbers.

    Cantor showed that there were infinitely many more real numbers than there were the infinite number of fractions. WTF? Weird but true.

    Then came "i". As I think I mentioned above. The square root of minus one. There is no such thing. It's crazy!

    Heck, even the Newtonian differential calculus effectively divides zero by zero, a meaningless undefined thing to do, and arrives at correct results.

    Turns out that all these non-intuitive "crazy" concepts have proven very useful. Zero, negatives, real numbers, imaginary numbers, science and engineering as we know them would not exist without accommodating these crazy concepts.

    These weird results for infinite sums also seem insane. But make your definitions the right way and you have results that are consistent and useful. In quantum mechanics for example. Not that it ever showed up when I was studying it decades ago.

    It think the mathlogger video I linked to above shows this nicely. He shows exactly when alarming liberties are being taken with infinity and clocks them up on his "insane-o-meter". But then goes on to show how one can make sense out of all of this.
  • Heater. wrote: »
    It think the mathlogger video I linked to above shows this nicely. He shows exactly when alarming liberties are being taken with infinity and clocks them up on his "insane-o-meter". But then goes on to show how one can make sense out of all of this.

    I'll watch that, but he's talking about -1/12, not -1.

    The first video, however, is subtracting two different series from each other, but pretending they are the same.
  • Heater.Heater. Posts: 21,230
    edited 2016-05-29 17:53
    You see. You are getting the hang of it already. Instead of writing out the series you just refer to them by the sums -1/12 and -1. :)

    The same conceptual weirdness applies to both those sums and videos.

    I think the key here is in "pretending".

    In the same way we pretend there is a square root of two or pretend there is a square root of minus one. Or we pretend that dividing zero by zero gives a sensible result in differential calculus.

    Heck, I think we are pretending when we talk about numbers at all. I don't see any numbers out there in reality. Do you ?

    The idea is to formulate rules that might allow for such crazy manipulation of pretend quantities, like infinity, whilst being consistent with with the rest of our "pretend" mathematical logic, and hopefully being practically useful at some point. As has often proved to be the case.




  • TorTor Posts: 2,010
    edited 2016-05-30 01:04
    As for objects in the universe moving away from each other faster than light, yes they can do that, and no, it doesn't violate Einstein special relativity because those objects are not moving through space at that speed. They're not moving at all actually. Just like us (if we ignore our slow spin around the center of the galaxy, and movement caused by the gravitational attraction between our galaxy and nearby dwarf galaxies for example).

    Found a link about this too: http://curious.astro.cornell.edu/the-universe/cosmology-and-the-big-bang/104-the-universe/cosmology-and-the-big-bang/expansion-of-the-universe/1066-can-two-galaxies-move-away-from-each-other-faster-than-light-intermediate
  • Beau SchwabeBeau Schwabe Posts: 6,566
    edited 2016-05-30 02:03
    The speed of light is also relative...

    The Earth spins at about 1000 miles per hour, we orbit the Sun at approximately 67 thousand miles per hour, our solar system is moving through space at it's own remarkable clip ... and who knows how fast we are moving within the arm of the galaxy and about 450 thousand miles per hour in the arm of the galaxy we are located in, but for argument sake, suppose it's 1/2 the speed of light. (Actually 1/1500th the speed of light) If nothing can travel faster than the speed of light, then that would mean that in one direction at least, the speed of light would max out at half of what you would expect. ... and that doesn't happen or else all of our time of flight measurements would become "universe direction/orientation indicators" depending on which way you pointed them. <-- That would be cool though ... even if there was a slight Doppler detection in time of flight based on orientation.

    Still at 1/1500th the speed of light you should be able to detect a Doppler effect or a "cosmic cap" limitation if there was one
  • TorTor Posts: 2,010
    But the speed of light is not relative, that's what it's all about. Time itself bends instead (and distance measurements). So there's no universal tick, no 'real time', as Heater said. There's only individual time. When I walk into the kitchen, and somebody else walks in a slightly different direction, into the living room for example, we both have our own individual time that we carry with us. They're not the same, although the difference is tiny. But it's there. It's measurable when one of you are in an airplane, and easily measurable if one of you are on the ISS. I'm not really talking about one of you experiencing time slower than the other, that's not what it's about. If I move away from you, or you move away from me, or we both move away from each other (there's not really any difference there), I can observe you and determine, from watching your wristwatch very carefully that your time is moving slower than my time. And you can watch my wristwatch, and determine that my time is moving slower than your time. And the thing is, we would both be right. That's what I mean by 'individual time'. We all carry it with us. Except for photons, or other particles with no rest mass. They don't have a time field, they don't observe any time.

    Whatever trick we try for measuring the speed of light as something else than C, we'll fail. It'll always be C (not considering measuring in non-vacuum, e.g. air, it's "slower" just because what really happens is that photons keep getting absorbed and re-emitted by electrons, and other such effects). So, in special relativity, C is absolute, not relative.

    Of course this crashes head on, apparently, with quantum mechanics, in particular entanglement, where people keep talking about things happening "at the same time" for items physically removed from each other, maybe very far away. There's no such thing as that kind of "same time" in special relativity. Because there's no "universal tick". So 'at the same time' does not make any sense.

    There must be a way out of that, but so far we don't know how.
  • Heater.Heater. Posts: 21,230
    edited 2016-05-30 14:54
    Beau,

    The speed of light, measured in a vacuum is always the same. C.

    If you stand by the road and I travel towards you at 100mph in my car, I can measure the speed of light from my head lamps as C. You can measure the speed of light from my headlamps and it will be C. Not C + 100mph.

    See Michelson Morley experiment here: https://en.wikipedia.org/wiki/Michelson–Morley_experiment Especially the section on Special relativity.

    The consequences of this were worked out by Einstein. Length, as measure by different observers, changes according to the relative speeds. Clocks keep different times, relative to each other depending on their relative motion.

    Next up Einstein flys with the idea that the effects of gravity and acceleration are the same. This leads to the conclusion that clocks keep different time depending on their positions in gravitational fields. Space bends under gravity, and so on. This is general relativity.

    All this has been know for over a hundred years now. The results have been verified by numerous experiments and observations. Atomic clocks on jet planes flown around the world do keep different time than those kept at home. The GPS system does not work with out taking relativity into account. That is to say, the speed of light is a constant.

    (When I say "known", I mean some people are smart enough to understand the maths and have spent years doing so. The rest of us have "known" it but have to take a lot of it on trust. The maths of special relativity is OK, but General Relativity is over my head.






  • Heater,
    I agree to disagree on some counts. ... Since there is no "universal tick" then C can be assumed to have no directional value and "time" as we experience it on Earth is a byproduct of mass (the Earth) moving through spacetime... from our perspective on Earth C 'can' be measured, but on the Moon that measurement would have a different value because the mass of the Moon is different, however one could argue that the equipment used to take the measurement would scale/stretch that time frame accordingly and in fact the result would be the same for C on the Moon as it would be on the Earth. ...in the depths of space, the results would again be the same because the time dilation with regards to mass and spacetime would again have proportional scaling and stretching. So is this an error in our perception or the way in which we try to measure C ? I think a little of both.

    What if C doesn't move at all, and C is the energy of life and it is everywhere at all times, where it doesn't have to move at any universal "tick" because it doesn't move, instead it defines all of space. Only does it manifest under the influence of mass moving through spacetime (<-aka C) such as our planet can we perceive the passage of time in "ticks". .... looking at the bigger picture "We" (all of us) constitute the essence of C ... because without any of us, Einstein included, this discussion wouldn't exist.
  • Heater.Heater. Posts: 21,230
    Beau,

    I have read your post through five times and I have no idea what you are trying to say.

    Point is that if you ever try to actually measure the speed of light, on the earth or on the moon, or wherever, and no matter where that light comes, from you will always get the speed of light, C.

    We don't need to get philosophical or spiritual about this, it's a measurable thing. The maths agrees with the measurements. Or is that the other way around?

    I might ask, what do you mean by time?

    Is it the count of the ticks of a good old pendulum clock? Or the count of some oscillations of some rubidium?

    How do you know that I get the same number of ticks as you do?

    Don't forget, if you cannot measure it, it does not exist.




  • No, I'm just saying that if there isn't a universal "tick", then any unit you apply to it is arbitrary and has no meaningful weight. If the unit is arbitrary then set C to zero so C doesn't move or that it's a constant, which is what has already been established anyway. On the same token, since C is constant and doesn't move in any direction then it must be everywhere at all times already. ... but if you are saying that C does move, then it must have direction and therefore have some measurable "delay" between two or more points. A measurable delay means that there is some kind of "tick" that must be referenced, but yet there is no official "tick" to quantify that measurement with. ... Many of the hypothesis attempt to describe the speed of light as though YOU or an object is traveling at some speed and that's just it... what if C doesn't move and your motion or the objects motion through C is misinterpreted as C actually moving when indeed it does not move at all?
  • Heater.Heater. Posts: 21,230
    edited 2016-05-30 22:52
    Beau,
    ...any unit you apply to it is arbitrary and has no meaningful weight...

    No. Here is the deal.

    I can make a measure of distance, let's say that meter stick in Paris, or whatever stick I have. I can also make a measure of time, say a good old fashioned pendulum clock, or a spring based escapement, or the oscillations of a rubidium clock.

    From that I can make a measurement of the speed of light. That is meaningful to me.

    Now, you can clone my meter stick, or whatever stick I have, and you can clone my clock, whatever it is. And sure enough, you can measure the speed of light, just like me and get the same result. No surprise there. That is meaningful to you also.

    Except, if you take the apparatus that you have cloned from me into a different gravitational field, or go running around at high speed with respect to me, all of a sudden we find that your clone of my apparatus has always told you the same speed of light, as we expect, but it turns out your clone of my clock is no longer in sync with mine.

    For whatever reason, time for you, as measured by the clone of my apparatus, is not the same as time form me.

    WTF?

    But that's how it is.

    See Einstein.




  • TorTor Posts: 2,010
    Just to add - when I mentioned "universal tick", I meant that there's no 'preferred frame', as the physicists say. That is, there's no universal time which everything else relates to. So there's no such thing as 'same time' for two entities not in the same place.
    Makes sense, in a way, as time doesn't exist unless you have mass. So time must be an emergent property of the universe.
  • tritoniumtritonium Posts: 543
    edited 2016-05-30 23:10
    Hi
    how does this fit in?
    If light enters any substance with a higher refractive index (such as from air into glass) it slows down. The light bends towards the normal line. If light travels enters into a substance with a lower refractive index (such as from water into air) it speeds up. The light bends away from the normal

    ...and different colours have different frequencies... or is it a particle...

    which light are we talking about?

    Dave

    I KNOW I'm going to regret posting this!
  • rjo__rjo__ Posts: 2,114
    edited 2016-05-30 23:37
    Heater,

    "Now we have found that the universe is expanding, and expanding at an increasing rate. This means there is a limit to how far out into space we can see. Light from objects beyond that limit can never reach us."

    There is actually no proof that the universe is expanding at an increasing rate. This "Universal Expansion" is a conclusion, based upon the assumption that there is a certain type of star, which explodes in a very precise manner... and that this "type" of star has existed and invariably exploded in the same way since the beginning of time.

    If you accept this kind of nonsense then you accept a Universe that is expanding at an increasing rate,
    but if you don't... well, that hasn't been looked at yet. I'm not holding my breath.

    You have to ask yourself: is there anything in the environments of such stars that might have changed over the last 13 billion years... is it possible that the environment of such a star would determine when it will explode and precisely how? A reasonable answer should be "yes" to all three questions.

    This kind of misdirection must exist for a reason... it can't be shear stupidity. If it were stated as a speculation, the assumption would be immediately attacked. But hidden within a major thesis, it is somehow passed along as gospel.

    When physics insists on painting itself into a corner with these kinds of assumptions, there isn't much for rational people to do except ask "where is the real physics?"

    It isn't in the textbooks... or on television. It is all nonsense excepting experimental physics, which at best incompletely reports experimental conditions and at worst, systematically misreports data... all for reasons I can understand and with which I can sympathize...but which leave us where?
  • Heater.Heater. Posts: 21,230
    rjo__
    There is actually no proof that the universe is expanding at an increasing rate....
    Not sure what you expect for "proof" but the guys that found this were actually looking for the opposite, a collapsing universe. It was a bit of a surprise.

    I'm not sure why you call it "nonsense". I expect a hydrogen atom to be the same out there as it is here. We have to assume physics is the same everywhere in the universe else we can say nothing about it.

    Of course if you want to say that different rules apply out there, then we might as well give up. Frankly I can't accept that.

    You talk about "nonsense" and "misdirection" as if the physics community was some kind of mafia or religious cult that wanted to deceive you for some reason.

    As far as I can tell nothing could be further from the truth, these guys love to prove each other wrong, by experiment or mathematical deduction.
    It is all nonsense excepting experimental physics, which at best incompletely reports experimental conditions and at worst, systematically misreports data.
    I'm sorry but what do you mean? Are you suggesting physicists are lying about the results of experiments? If so who?
    When physics insists on painting itself into a corner with these kinds of assumptions, there isn't much for rational people to do except ask "where is the real physics?"
    I don't know what to say about that.

    "Rational people" used to think that having zero as number was crazy.

    "Rational people" used to think that negative numbers were crazy.

    "Rational people" used to think that the square root of minus one was crazy.

    "Rational people" used to think the world was flat.

    "Rational people" used to think everything rotated around the Earth.

    "Rational people" are incredibly boring and it turns out wrong! :)
  • rjo__rjo__ Posts: 2,114
    edited 2016-05-31 01:16
    I agree that rationality isn't all it is cracked up to be. Both the gravitational and the electromagnetic environments of the early Universe are known to be vastly different than they are now. To say that these differences cannot possibly have lead to different conditions for stars in their terminal throws seems unnecessary and possibly wrong. And then we have to ask... how could we know? If we really cannot know(which is most likely), then we need two theories... one that includes a reasonable alternative.

    The problem that I have is that we are taking this single assumption... which seems very open to question and creating a single model for celestial mechanics, when we could easily have two alternative explanations (equally supported by the evidence) and then judge the merits and implied physical mechanics of each.

  • rjo__rjo__ Posts: 2,114
    Here is what thatspace.com/11642-dark-matter-dark-energy-4-percent-universe-panek.html corner looks like right now:)

    All the consequence of one assumption.
  • TorTor Posts: 2,010
    The never-visible part of the universe is a much older concept than the idea about the universe expanding at an increasing rate. The latter isn't what causes this. The universe passed that point a long time ago - afaik the estimated size of the universe is some 40 billion light years, which is quite a bit more than the 13.7-13.8 billion light years we can theoretically see. Those far away parts of the universe are already moving away from us very fast. Even if you don't increase the expansion rate (that came up around 1998 or so IIRC), every part will still get away from the other parts faster and faster. Imagine the galaxies as raisins in expanding dough. Or dots on an expanding balloon.
  • rjo__rjo__ Posts: 2,114
    edited 2016-05-31 05:05
    Tor,

    It all depends on a very long list of unknowns. Do the inverse square laws hold at all distances? We really don't know. There might be some distance, beyond which no force is transmitted.

    Even within distances where inverse square laws are known to hold... can any force exist, which does not include some material exchange... however we equate mass and energy?

    Right now the best argument that I have seen for dark matter and energy is that they can account for why the pattern of orbital velocities of galaxies doesn't seem to mirror the pattern of a solar system.

    Isn't it also possible that there is a more prosaic explanation for these orbital differences having to do with how gravity works at very long distances?

    One thing that we do know is that the moon is drifting away... among the explanations that I have never seen is this: "gravity causes an object to loose mass but not momentum."

    It sounds like the silliest idea, but if gravity isn't free... how do we account for the cost?





  • evanhevanh Posts: 15,916
    Tor wrote: »
    ... Imagine the galaxies as raisins in expanding dough. Or dots on an expanding balloon.

    There's that apparent medium showing up again! What's the story here?
  • rjo__rjo__ Posts: 2,114
    edited 2016-05-31 06:10
    And then there is the issue of the effect of gravity on light.

    There are very famous experiments that show that when light passes a large mass, the
    direction of that light is changed. If we accept that light is indeed subject to the laws of gravity,
    then what can we expect when a photon travels directly toward or directly away from
    the center of a large gravitational mass?

    Because of symmetry, the direction of light can't change.

    By assumption, the velocity of the light cannot change.

    Therefore, the only other possibility is that the apparent frequency would have to change.

    Is it reasonable that the only effect on light, which is non-intersecting and non-orthogonal to a large mass is to
    change direction?

    Or is it possible that there a mixture of frequency and direction change always takes place except at the extremes of orientation?

    One conclusion might be that the red shift of a photon arriving at a detector from a distant star is a function of the distribution of masses along
    the path of that photon as it travels from origin to detection. On average, it might very well be true that the red shift of a photon is
    directly correlated with the distance traveled. But it might also be true that the comparative shift of two photons relates more to the density
    and distribution of masses along the path which the photon travels from emission to detection.

    From this, we can also conclude that the only light lost from our potential view, is that light which originated near the exact center of mass of the Universe. The rest
    will eventually circulate enough to have a chance of reaching us... unless the inverse square law does not hold at some great distance.


  • TorTor Posts: 2,010
    edited 2016-05-31 06:23
    rjo__,
    I don't have any issues with questioning dark matter/dark energy. That's indeed quite open. But that has nothing to do with the forever-invisible part of the universe, the speed and distances are there, now, and dark energy isn't needed to explain that. And dark matter is mostly about why galaxies hold together, a different issue.

    As for why the moon is drifting away, there's no fancy physics needed for that. It's a simple transfer of momentum between the earth and the moon (addon: Due to the tides, on both bodies, their rotation slows down relative to the other body. The moon is already down to zero (tidally locked to the earth), the earth is still working on it - the day is much longer now than in the past. When the earth's spin slows down, the momentum must go somewhere. And it does: The moon's speed around the earth increases. Thus it drifts away. Slowly.)

    evanh,
    Don't confuse the analogy with the the reality - if they were the same, it wouldn't be an analogy anymore.
  • rjo__rjo__ Posts: 2,114
    I didn't even read it as an analogy:) ROFL pretty late on my side of the planet.

    Thanks for responding;)
  • rjo__rjo__ Posts: 2,114
    Tomorrow... I answer analogy with analogy.
  • evanhevanh Posts: 15,916
    Tor wrote: »
    evanh,
    Don't confuse the analogy with the the reality - if they were the same, it wouldn't be an analogy anymore.

    Well ... I kind of figured we aren't swimming in cookie dough. But the implied analogy is of a medium of some manner.
  • TorTor Posts: 2,010
    edited 2016-05-31 08:11
    No, the analogy isn't about how it expands, it's about the effect: The farther away the dots on the balloon are from each other, or the raisins in the dough, the faster they move away from each other (the second part of the analogy is that with the balloon you can't point to any part of the surface where the dots (galaxies) are and say 'this is the center (of the universe)'.
  • evanhevanh Posts: 15,916
    edited 2016-05-31 09:02
    There is the medium of the rubber balloon that spreads the dots. Which implies some medium that spreads the galaxies. So space is made of something.

    EDIT: Okay, the analogy is a bad one then, because "the how" is a pretty damn important part of analogies.
  • Heater.Heater. Posts: 21,230
    Great, there is a lot of interesting speculation going on here.

    When I said "Rational people", the quotes were important. What I was talking about was "common sense" that feeling that we all have about things that are so "obvious"
    that it must be the way we think about it and to think otherwise is crazy talk. Common sense comes about when we have limited evidence and haven't spent much time reasoning about it. Common sense has historically been wrong a lot of the time. Even to the point of killing those who dare question it.

    Seems to me that rationality, what ever that is, think mathematics and logical reasoning, is the only tool we have to make any progress here. Historically it has been incredibly successful in describing and modelling the universe. Enabling predictions to great accuracy.

    We can all speculate. We can all question the base assumptions used by mathematicians and physicists. That's easy. The hard part is proposing a theory based on whatever new assumptions one may have that fits all the available experimental and observed evidence.

    For sure physicists are trying to do that all the time. There is not just one true physics. There is an ecology of competing proposals and theories. Think string theory, of which there seems to be many. Think all those crazy ideas of multi-verses and such as a way to look at quantum mechanics. In this ecology theories compete and fight for survival always keen to prove themselves right and the other guys wrong.

    This is all good stuff. It means a lot of people do a lot of thinking about it. It means we do experiments, think CERN, Hubble etc that aim to get the evidence to support, or not, this theory or that.

    Admittedly we seem to have run into a major problem. We have theories that on the one hand try to describe something on the other hand seem to be fundamentally unobservable. How could we ever prove what it was like before the big bang or immediately after? How could we ever prove that our ideas of the end of the universe are correct? What about that multi-verse thing?

    On the other hand, when Einstein found his model led to the bending of light travelling around massive objects he pretty much ignored it. To him it was obvious that the effect would be so small that we would never be able to detect it. No point in thinking about it then....
  • evanhevanh Posts: 15,916
    You've got me doing a couple of searches at least. :) Wikipedia's article on the Graviton seems a good read - https://en.wikipedia.org/wiki/Graviton

    I've just realised that the "Standard Model" is of quantum theory, and does not take General Relativity into account.
  • Channeling the 11th Doctor:

    Think of the galaxies as raisins in cookie dough, the galaxies aren't really raisins of course, but if it helps you then think of them that way.
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