We are developing the social individualist meta-context for the future. From the very serious to the extremely frivolous... lets see what is on the mind of the Samizdata people.

Samizdata, derived from Samizdat /n. - a system of clandestine publication of banned literature in the USSR [Russ.,= self-publishing house]

Samizdata quote of the day

“One finds that time just disappears from the Wheeler-DeWitt equation,” says Carlo Rovelli, a physicist at the University of the Mediterranean in Marseille, France. “It is an issue that many theorists have puzzled about. It may be that the best way to think about quantum reality is to give up the notion of time – that the fundamental description of the universe must be timeless.”

Carlo Rovelli. Remember this next time you turn up late for an appointment.

48 comments to Samizdata quote of the day

  • chuck

    The crackpots seem to get all the coverage these days, probably because they make the most extravagent, yet imprecise, claims. I blame Bush. But not everyone thinks that Rovelli is a wonderful physicist and in this case I see no reason to doubt Lubos Motl’s evaluation from several years back concerning this particular claim.

    Does time exist?

    Carlo Rovelli believes that time does not exist. That’s a kind of vague statement. One would have to define what “time” means in the most general theory, and what does it mean for this time to exist. I might agree if he said that time is not an exact concept after all. There is a simple yet powerful argument composed of two parts supporting the viewpoint that time is not an exact concept:

    * the progress in string theory shows that space is emergent, approximate concept – it is just the manifestation of some particular light modes in your theory, but there can be many other light and heavier modes. T-duality is able, in fact, to exchange the translations in space with a phase redefinition of fields depending on their winding number. Whether something is space or not is a matter of convention, especially if this space is small
    * special relativity that is still exactly preserved by local physics – at least if the space is large – says that “whatever holds for space, holds for time as well”. This means that if space is emergent and approximate, time should be emergent and approximate, too

    This is a nice exercise in logic, but it may be a futile one. Unlike Carlo Rovelli, I think that all theories that will ever be accepted to have something to do with physics will have to show that time emerges from them – because we simply know that time exists. Perhaps, time won’t be an exact observable – and there won’t probably be any general exact Hamiltonians in quantum gravity. On the other hand, a Hamiltonian could always exist with an appropriate gauge-fixing. But even if you work with the S-matrix that does not allow you to study the evolution “moment by moment”, you can still exactly distinguish the future from the past. Time will always have to “reappear” in one way or another. Physics only emerges if we have time, at least some time. There is no physics without time.

    When Rovelli tries to clarify his point of view in detail, I think that this clarification makes his proposal even more obsolete. He literally compares spacetime to the “surface of the water”. The latter is eventually made of atoms, and so forth. Jesus Christ, this is not just analogous – it is exactly the 19th century idea of luminiferous aether. Everything that can carry waves must be made of “atoms”, they thought. Einstein with his special relativity had to throw away this garbage of luminiferous aether – and it’s exactly what makes Einstein so special. I believe that in the 22nd century, only a few very specialized historians of science will remember these specific “discrete” attempts to revolutionize physics, and they will consider these physicists as late 20th century followers of the wrong 19th century ideas of aether – who had nothing new to offer. But I can’t prove it.

    Lubos seems to have a low opinion of Rovelli’s competence on the whole.

    Several readers have asked me what I think about a new attempt to derive the graviton propagator in loop quantum gravity, an attempt described as a groundbreaking paper by a fellow blogger and included in the unfinished revolution by another blogger. It would be far too dramatic to say that I am flabbergasted but one thing is clear. The work is so manifestly incorrect that I just can’t fully comprehend how someone who has attended at least one quantum field theory course can fail to see it. But of course, yes, I am happy that people are still trying different things and some of them don’t get discouraged by decades of failure – and I always open such papers with an enthusiastic hope that a new breakthrough will appear in front of my eyes. 😉

    The paper linked above is supposed to be a more complete version of Rovelli’s previous graviton propagator paper. Indeed, you can see that several pages in these two papers are identical. Most of these two papers’ assumptions are misguided, nearly all the nontrivial steps are erroneous, and the results are incorrect, too.

    I am not a theoretical physicist (IANATP?), but I do have some familiarity with mathematics and physics and Lubos’ comments strike me as reasonable. The complete memo is here.

  • Time is what keeps everything from happening all at once.

    This is elementary.

  • Billy, do we definitely know that?
    Fascinating; do two events happen simultaneously in different places, or MUST they be seperated by a finite difference in time?

  • chuck

    Fascinating; do two events happen simultaneously in different places

    The concept of simultanaity is not an invariant, that is to say, it depends on the reference frame: two events simultaneous in one frame will not be so in another. The idea of simultanaity went out the window when the theory of special relativity came along 102 years ago, that is one reason the theory was so revolutionary.

  • Sigivald

    I’m no physicist either, but Motl’s spot on that time exists – the experience of it is unavoidable and (in the most plain sense of the word) essential.
    To say that it doesn’t “really exist” is either flim-flammery, or a very precise and technical use of the terms “really”, “exist”, and/or “time”, that doesn’t apply to any other context (or at least to the global, macro level).

    That in some theoretical equations nobody’s been able to get to work (“No one has yet succeeded in using the Wheeler-DeWitt equation to integrate quantum theory with general relativity.”), time disappears, means nothing.

    (If time is, as Rovelli suggests, really just an emergent property of the extra-quantum scale, that still leaves us wondering

    a) why that means it doesn’t “exist” – since it still plainly does, at the macro level


    b) why it’s so damn consistent (in that it works in one direction, not that it’s consistent from place to place in some non-relativistic way).)

    Though really the problem is the headline on the writeup; even Rovelli isn’t claiming time “Doesn’t exist”, just that it’s not a fundamental property at the quantum level – though he can’t demonstrate it (always the problem with quantum theorising, it seems).

  • The reference frame is reality.You are attempting to impose a percept-driven model on a theory, which must be conceptual.

  • My concept is of reality existing simultaneously at all points in existence; the question I asked was whether events are simultaneous too.
    To attempt to link reality to a particular frame of reference would be a great way of winning a conflict, except that the bad guy has a frame of reference also.
    Soon adds up to a big, non-functioning, mess.

  • Midwesterner


    Time and space are both relative. I think it is not meaningful to say “at the same time”, but rather to view time as an object linked perception. One might perceive two events as happening at the same time, but the perceptions are traveling from and through different space, therefore, “at the same time” is meaningless except ‘at the same place’ in which case, it is the same event. Which could, of course, be perceived as two or more separate events if the perception arrivies via different space.

  • eoin

    “Time and space are both relative.” Time is constant to the observer, which is what counts.

    Clearly time exists. A mathematical theory can be solved to prove the Earth is the centre of the solar system. It will work to predict future movements of the stars, and planets relative to the Earth.

    Mathematical models are just that. Models. Mathematics is just a tool. Solving a mathematical equation which “proves” that time does not exist is not even up the standard of heliocenticism which tried, at least, a model to explain the world as it is, rather than use a trick to solve an equation which had no basis in reality. String theorists have more than one theory , too, but an infinite number seemingly, clearly unfalisifable, all replete with numerous constants which they “hand-tune” ( which is mathematical charlantanism) / Even then they need 25 spatial dimensions which is 22 more than actually exist ( but they are really small, see!), and if they needed 5,602 dimensions to solve an equation they would get that too.

    utter nonsense.

  • Mid-a train sets off from Denver at 3pm; another train sets off from Tulsa at the same time(adjusted for local variation).
    The Tulsa train didn’t ‘perceive’ the Denver train, nor vice versa.
    Are you going to tell me that only the one I’m on is real?
    If they are on a collision course, I will find out that they are both real when they collide, but they only collide because they are and always were both real.
    My subjective perception is irrelevant until it becomes a tool with which to undermine conceptual reality.
    Then you might see what was really intended.

  • Midwesterner


    They are both real. But being in different places, they are just not in the same time. It is easier to imagine if you think instead of interstellar travel at high speed. That makes the time distortions more understandable.

    Once they attempt to occupy the same space, they are in the same time. As we say in racing, “contact!”

  • Paul Marks

    Perhaps one day physics people will hold Erwin Shrodinger in higher regard than they now do. And remember (for example) that the example of the cat was NOT to show that the universe was a cool wacky place – but that the cat was either alive or dead at a given moment of time (not in some in between state till observed).

    Matter is energy which is organised in a certain way – but this energy is a real thing (not just a lot of numbers) and electons going round a nucleus may just be waves of energy (wave-particle duality is not something I am qualified to discuss) – but this energy is real (not just numbers and probabilities).

    Still enough of the nonscientist (me) trying to make understand science.

    After all I have not studied science since I was 16 – and that is many years ago.

  • They are both real.
    They are both on the same track.
    They definitely will, therefore, occupy the ‘same time’.
    But wait.
    When they were hundreds of miles apart, this was still true.

  • Pa Annoyed

    Mid, Pietr,

    The relativity of time and space is not a matter of saying that either is unreal, but that the division between them is an artificial one to do with the way you look at it. It’s like asking whether the directions “forwards” and “sideways” are meaningful – obviously they are in some sense, since walking forwards corresponds to a perfectly real activity, but “forwards” points in different directions for different people.

    Think of “forwards” as time and “sideways” as the position in space. Then if two people both walk “forwards” across an open field at the same speed but in slightly different directions, each will see the other not only moving sideways (according to their own definition) but also drifting slowly backwards. They appear to be going more slowly through time (forwards). This is what the dictum that “moving clocks run slow” actually means. Not only that, but both observers sees the other’s clock running slow, just as each walker sees the other falling behind them, without any paradox.

    “Simultaneous” in this analogy just means “in line with each other sideways”, and therefore depends on whose sideways you’re talking about. All the events (the locations in the field) are perfectly real and definite – it’s only the choice of coordinates that we use to describe it all that are in any sense unphysical.

    As for Rovelli’s point about time, I suspect he probably doesn’t mean what he appears to mean. The problem of time result from trying to do my field-walking exercise not on a flat field, but one covered in hills and valleys. Now when you try to extend lines “forwards” and “sideways” the directions wobble all over the place to follow the landscape. There isn’t any way of defining a simple consistent time everywhere, even from the point of view of one observer. So we fudge it, and pick a particular arbitrary slice across the landscape without worrying about whether it is in any sense straight/simultaneous, and then work out your equations on that. If you do that, then the bit of maths that normally says how things change with time instead turns out to equal zero. That tells you something – it constrains what’s allowed to happen on your wobbly slice – but it doesn’t tell you what happens next.

    That’s probably something to do with the fact that your recipe for working out the physics assumes there’s something like a time variable, and this is just plain wrong. Rather than doing it in terms of forwards and sideways, you’ve somehow got to do it in terms of the landscape.

    Well, I found that an interesting diversion – if a little incongruous in the context of this blog. Are people putting up the occasional maths/physics/philosophy item to keep us scientists happy? If so, my thanks!

  • Midwesterner

    Well P.A., that saved me a lot of work and thought. I like the walking in a field with hills visualization and will probably use it for other conversations. The following is what I had already written and was previewing this before your answer came up and I think my brief answer, in its simplistic way, is true.


    The fact is that they are on a collision course and will soon meet in space and time. But they are not synchronized in time. You are not allowing for differences in their speeds. Let’s say two spaceships are on a collision course. One is going 1/4 the speed of light, one is going 3/4 the speed of light. They are in different time frames right up to the moment of contact.

  • Midwesterner

    I should add that my statements of speed are based on a third party (standing by the rails) observation point.

    Without having given it too much thought, it seems to me that two objects in total isolation (no observation point, not ‘track’) would not have separate speeds, but rather a single ‘closing’ speed. Is that a correct?

  • Pa Annoyed


    Yes, what you say is true, but it sort of gives the impression that the two frames have nothing to do with one another, that there is no relationship between them, as if they were in separate universes or something. I think that’s what Pietr was objecting to.

    Whereas the forwards/sideways analogy makes it clear that they’re both occupying the same domain, everything is real and definite, and there is going to be some sort of fairly simple geometrical relationship between how each sees the world. There can be only one spacetime. But that because the concept of ‘sideways’ is observer-dependent, there’s no absolute sense in which events can be said to be simultaneous. To one of the people two widely separated points might be simultaneous, but to the other person they occur one after the other.

    [Full disclosure: The only slight twist in the tale is that space and time isn’t quite like directions on a flat field, because the geometry is slightly weird. You may remember from school Pythagoras talking about the square on the hypotenuse of a right-angled triangle being the sum of the squares on the other two sides? Well in the weird geometry used by spacetime it turns out to be the difference of the squares on the other two sides. Following through the consequences of this one small modification, the whole of special relativity can be reduced to simple schoolboy geometry.]

  • Pa Annoyed

    And yes, considered in isolation, there’s no concept of absolute speed either. That will also depend on what coordinates you choose for space and time.

  • Midwesterner

    You’re right about the perception. I was trying to figure out how to convert the rather complicated pictures in my mind to something I could type. Your walking model did it. In my mind I visualize timelines surrounding objects. Objects are clearly in the same reality, but still in their own times.

    I am very interested in what you said about Pythagorean theorem and relativity. Can you give me any pointers to more info? School boy geometry, I can enjoy.

  • Midwesterner

    Follow up question:

    Using a 3-4-5 right triangle, when you say “the difference of the squares on the other two sides.” do you mean 4 sq =16 minus 3 sq =9 for a difference of 7? Or a difference of the sq rt of 7 as in the sq of the hypotenuse is 7? So the hypotenuse of a right triangle 3-4-H would be ~2.646?

    By my quick head games, that is still a right triangle by normal rules, except now the shortest, instead of the longest side is the hypotenuse.

    If so, what would be the smallest whole numbers that would yield a right triangle? 3-4-5 again? With 3 being the hypotenuse?

    And when you say geometry used by spacetime, could you be a little more specific? I live in space and time and the Pythagorean theorem works normally for me. I’m confused.


  • Pa Annoyed


    The ‘length’ ds of a timeline through spacetime is given by
    ds * ds = dt * dt – (dx * dx + dy * dy + dz * dz)
    where (dx,dy,dz) are the changes in position.
    (The space part follows the normal Pythagoras rule.)

    So if you take 4 seconds to travel 3 lightseconds (that’s 3/4 of the speed of light) then the length of your path is Sqrt(4*4 – 3*3) = Sqrt(16 – 9) = Sqrt(7), or 2.65 seconds. The number comes out the same in any moving frame of reference – in particular your own, in which you travel zero distance in 2.65 seconds.

    Similarly, if you take 5 seconds to travel 4 lightseconds, it will take you 3 seconds to do it.

    I’ll try to post more later. Have to dash.

  • What ‘time-frame’ is the stationary observer at the contact point in?
    As long as the (high speed:)) trains don’t get too close to the speed of light, he will see both of them approaching.

    The point I make is that whatever the relative(ity) effects may be, the reality is singular; ie all three exist simultaneously.
    My original debating question was whether reality operates like a multi-threaded computer, switching CPU ‘event reality’ time, or whether there is in fact actual simultaneousness.

  • Midwesterner

    What ‘time-frame’ is the stationary observer at the contact point in?

    His own.

    As long as the (high speed:)) trains don’t get too close to the speed of light,

    As long as you don’t get too close to the speed of light, relativity’s effect is so small as to be practically not meaningful. It is there, but as P.A. pointed out to me earlier, Newtonian mechanics is all that is needed for navigating space ships in our 21century technology.

    he will see both of them approaching.

    Even at high speeds he will see both of them approaching, but he will be seeing them through the lens of time variation. Which can warp much like looking at a coin in a pool. The coin IS there. It is where it is. It just isn’t where it appears to be from your veiwpoint. But as the pool is drained, much like an object approaching your time frame, it appears much closer to it’s actual location perceived from your viewpoint.

    I certainly think everything in all of this corresponds to a singular reality. The question is with using the word ‘simultaneously’. Hypothesize two clocks that are synchronized at the moment of contact. Now project their indicated times into the past. The clocks on the two vehicles will not by any requirement be in synch with each other. It is possible, but more likely they won’t be.

    When our resident mathematician returns, I think he will do a much better job of explaining it. He’ll probably find some errors in my descriptions but I only have a layman’s grasp of it all. Meanwhile, he gave me some stuff to puzzle through, so I’m going to spend free time staring at the corner of the ceiling for a while.

  • I don’t disagree with any of what you just said Mid.
    Great stuff.
    But reality does contain certain invariant consequentials;
    the trains(going at 3c/4-TGV Narf!) will collide, and it should always be possible to predict when even with high speeds, whether you put your time elapsed in terms of train1, 2 or the ‘stationary’ observer.
    What is stationary anyway in an expanding universe? And can we define a stagnation time frame for base reference?

  • Paul Marks

    According to Maxwell (long before Albert Einstein) if light is fired off away from two men and one dashes after it at 30 miles an hour (say on a fast horse) and the other man just stands there – the light gets further away from both men at the same rate (not minus 30 miles an hour for the man dashing after it).

    That was the point I stopped being interested in physics.

  • Midwesterner


    But reality does contain certain invariant consequentials;

    Tell me! My own most memorable consequential involved two vehicles attempting to occupy the same place in the space time continuum. Consequential, indeed.

    it should always be possible to predict when even with high speeds,

    Given enough knowledge, yes. In hypothetical models where all the inputs can be known, certainly. The question is, is it certain that in a real case, inputs can be perceived with certain accuracy? Can precise information be exchanged between the trains and the observer? (This also raises the topic of determinism. I will purposefully avoid that topic. This thread I am assuming is about the space/time relationship.)

    A side note about the expanding universe, I’ve always wondered just a little bit if the expanding universe is an ‘illusion’ caused by the same thing that makes the gravity that holds us to earth indistinguishable from the ‘gravity’ one feels while accelerating in a zero G environment.


    Am I correct in understanding that “4 seconds” is in the ‘stationary’ time frame of the course and a fixed observer, “3 light seconds” is also in the time frame of the course and the fixed observer, and “2.65 seconds” is in the ‘on-board’ time frame? Otherwise, I am having trouble correlating the “4” and the “3” to the “2.65”.

    And is the Pythagorean theorem just a useful mnemonic or does it have a deeper significance?


    That was the point when I became interested.

  • Pa Annoyed


    In the sense in which you mean it, you are correct. All three – the two trains and the trackside observer – exist together all the time. There is only one reality, and as far as special relativity is concerned, events can occur simultaneously in the reference frame of any of the participants. That the participants don’t agree on which events are simultaneous and which are not doesn’t, I think, affect your point.

    At a deeper level, the question of whether events can be simultaneous is trickier. Certainly the idea of a single multi-tasking processor jumping from event to event, handling one at a time, is not valid. Reality is more like separate computers at every single point of space and time, all working in parallel, connected by a network. But when you start trying to mix quantum mechanics into things, clocks start to act really weird. They do things like only ticking when you’re not looking at them (the quantum Zeno effect), sometimes running backwards, and blurring in a way that depends on the energy with which you probe them. At finer resolutions than about 10^-44 seconds, the structure of space and time break down, and it isn’t clear that it is meaningful to assign times to events shorter than that.

    So the answer to your question is probably no – not because reality hops from one event to another, but because reality is slightly blurry, and the relationships defined between events not perfectly precise. But most of that is at a level more than twenty five factors of ten below anything we can possibly observe yet, and not relevant to anything really. For all practical purposes you can assume the answer to be yes.

    Does that answer your query?

  • Pa Annoyed


    When I say you move so many light seconds in such and such a time, I mean those are the times and distances in the reference frame of some other observer, who of course considers himself to be stationary. Since everybody considers themselves to be stationary, it is another term, along with “simultaneous”, that doesn’t have any absolute meaning.

    The 2.65 is the ‘onboard’ timeframe, the time shown by a clock moving between those events. The 3 is the time shown by the ‘stationary’ observer’s clock.

    The Pythagorean theorem isn’t just a useful mnemonic. It has to do with the concept of distance. In ‘normal’ space, what we call Euclidean space, distance is defined in a particular way, which Pythagoras’s theorem happens to calculate. In spacetime, which is sometimes called Minkowski space, the points are arranged differently and the distances between them behave in a different way. What the concept of ‘distance’ is to Euclid’s geometry, this concept is just as important to spacetime. There’s a sort of generalisation of distance that includes both Euclidean and Minkowski types, and lots of others, that locally can always be put into some sort of sum-of-squares form, but showing that involves a bunch of matrix algebra which I don’t think you would be so entertained by. It has a lot of elegant properties that mean it is arguably the simplest way things could be while being complicated enough to be interesting, but I don’t think we really understand if there’s a deeper significance. We use it because it works (at least, it does above 10^-44 seconds), and that the best reason of all.

  • Midwesterner

    Can you explain just a little bit (type slowly and use small words:-) what Minkowski space is and how it relates to Euclidian space (which I assume is the one where Newton’s stuff is plenty accurate enough to be useful).

  • Pa Annoyed

    Oops, sorry, that was a typo.

    I meant “The 4 is the time shown by the ‘stationary’ observer’s clock.”

    Incidentally, it’s worth mentioning that I used lightseconds as my units of distance in order to keep everything simple. It means that space and time are measured in the same units. If you don’t, and use something like metres and seconds, you need a conversion factor. It’s like measuring distances “forward” in miles and “sideways” in centimetres. The reasons are historical of course, since we didn’t realise until recently that they were different aspects of the same thing.

    If we call our conversion factor c (‘c’ for conversion, of course) then the formula I gave above for the interval becomes:
    ds * ds = c * dt * c * dt – (dx * dx + dy * dy + dz * dz)

    We can divide this through by dt^2 to get this:

    (ds/dt)^2 = c^2 – ((dx/dt)^2 + (dy/dt)^2 + (dz/dt)^2)

    The quantity (c, dx/dt, dy,dt, dz/dt) is the spacetime equivalent of the velocity.

    While we’re at it, we can recall a few things from Newton’s mechanics about force. Everyone knows the one about force being mass times acceleration, but there are a couple of other quantities that are also important. The momentum is what you get if you accumulate a force over time. And the energy, or work done by a force, is the accumation of force over a distance.

    So if we think of force being one ‘thing’ in spacetime, it’s accumulation over space and time also has to be one ‘thing’ (because space and time are the same, and interchangeable), which follows the same geometrical rules as our distances do. That means that energy and momentum are different coordinates of the same thing, just as time and distance are. In fact, energy is the coordinate in the time direction times c (because we’re accumulating over distances with different units), while momentum is its coordinates in the space direction. (E/c, px, py, pz) where E is the energy, and (px,py,pz) the three spatial components of the momentum.

    One other thing – remembering our old force = mass times acceleration, we know that if we accelerate for a while we get a particular change in velocity, so that tells us that in Newtonian physics, momentum is mass times velocity.

    Can we do the same with our energy-momentum thingy in spacetime? Well, we know what the velocity is, because we calculated it above. So we can multiply by m to get:
    m*(c, dx/dt, dy/dt, dz/dt)

    The space coordinates are the ordinary Newtonian momentum, as we wanted, but what’s that time part? We’ve got m*c, which is equal to E/c. So that tells us that the energy and mass are related.

    In fact:
    E = m* c^2

    There! You’ve always wanted to know how that was done, haven’t you?!

  • Pa Annoyed

    Yeah, sorry.

    Minkowski space is the mathematical name for a space that behaves the way space and time behave. You just say “what if we swapped the signs round here and left everything else the same?” and see where it goes.

    It’s sort of like the difference between spherical geometry (distances on the surface of a sphere) and plane geometry (distances on a flat plane). If you fly from the States to China, the line doesn’t look straight on the map, and the distances along the sides of triangles don’t add up. In fact, it’s possible to have a triangle with three right-angles in it! Just think of the north pole, and two points on the equator 90 degrees in longitude from each other.

    Mathematicians love playing with the rules to see what breaks if you change them. There are lots of different things you can do – Euclidean space and Minkowski space are just two different examples.

    Anyway, got to dash again. I’ll probably be back in a few hours time.

  • Midwesterner

    I looked up Minkowski space on wikipedia and that makes a lot of sense. I understand the 4 vectors, Euclidian is basically the last three, right? The 1st one is future or past ‘timelike’. But I’m a little confused about how the Pythagorean theorem would behave differently with the addition of a time vector. It seems that with the time vector = zero, it should work normally. In which case how does a timelike vector ≠ zero change things?

    It also sounds like Minkowski space becomes less useful for the full scope of this discussion because it doesn’t work with gravity (and acceleration?). As I understand the whole “manifold”/”tangent space” thing it is like a flat map for a globe. It works progressively less well as the flat map tries to include more of the sphere. Except instead of a sphere, we are talking gravitational distortions. I assume there must be a way to try and adjust for those distortions much as the percentage of a sphere covered by a right triangle effects the angles. Or have I got this all wrong?

    If I am annoying you (or whoever’s thread this is) just say “go away.”

  • Pa Annoyed


    You’re not annoying me at all. If anything, I feel slightly guilty for enjoying myself so much. I like talking maths/physics.

    I’m dead impressed that you found the Wikipedia article making sense – it’s pretty mathematical. Yes, the last three work exactly like Euclidean space. With time non-zero, everything gets a bit closer. When the time offset is equal to the space offset, the distance can actually be zero – the two cancelling each other. This applies to light rays, and what it means is that for a light ray there is no time and space is flattened to a plane. What happens is that as you get closer to lightspeed in your spaceship, the journey time gets shorter. (External observers say it is because your onboard clocks run slower, observers on the ship say it is because the universe is moving relative to us and therefore contracts. Our geometrical discussion explains that the two effects are essentially the same thing.) As the speed approaches lightspeed, the clocks grind to a halt, and the universe flattens to zero length, so at light speed the photon arrives at its destination at the very moment it set off, the two being zero distance apart.

    This is one of the major peculiarities about Minkowski space that show how different it is to Euclidean – you can get non-zero vectors with zero length. (But it’s probably no weirder than triangles with three right angles.)

    For somewhat slower speeds, the subtraction of the squared time component reduces distances along the direction of motion – we say that moving objects shrink.

    You’re quite right that Special Relativity doesn’t handle gravity properly, and correct about how it goes wrong. The flat map of the world is exactly the right analogy. That’s what General Relativity is for, and that is most definitely not schoolboy geometry. It does give a complete solution, though.

    If you want a moderately accessible introduction to that, I recommend Roger Penrose’s book The Road to Reality. There are a number of points in the more speculative areas of physics I disagree with him on, but when it comes to explaining complicated maths the guy has a real talent. It’s probably still incomprehensible to most people, but comparatively speaking it’s about as good as it gets when it comes to explanations.

    Even General Relativity can be explained. This website has a go. But it’s undeniably difficult, and anyone who tells you otherwise is lying.

    Acceleration is handled in special relativity (you may remember I was playing with mass times acceleration earlier), although accelerated frames of reference are where the special theory meets the general. In fact, a lot of the general theory was developed by looking at how special relativity worked in accelerated frames, and extending the results to to assume gravity worked the same way.

    If you want a serious problem to think about, try thinking about the rotating disk. We have a large disk that rotates about its centre very fast. The circumference is moving at an appreciable fraction of lightspeed, and therefore shrinks along its direction of motion, but the radius of the disk remains the same, since it is at right angles to the direction of motion. So if the circumference of a circle shrinks, but the radius stays the same, does that mean that Pi changes its value? Certainly something pretty odd is going on.

    I assure you that the rotating disk can be explained, the circumference does shrink, the radius stays the same, but Pi has the same old value it ever does. Everything can be fitted in to a simple consistent picture. However, I’m not going to explain it.

    The space in the rotating frame of reference is curved, although I’m not going to attempt to describe the shape. If you can figure it out yourself, I will be very impressed, but you shouldn’t worry about not being able to do so. A lot of professional physicists don’t know the answer either, or get it wrong, and some seriously world-class physicists have devoted significant time to studying it. Or you could look it up – the internet knows all. It’s an important problem though – think about how they define a global time using atomic clocks when you’ve got all this going on in your rotating world.

  • Midwesterner

    With time non-zero, everything gets a bit closer.

    Okay, so I’m imagining a cube with the timelike vector as a dot in the middle of it. As time goes non-zero, does the cube shrink in one dimension or all three? I’m viewing the time vector as a positive or negative intensity since the three directions are already taken up by Euclidean geometry. But if the cube shrinks only in the direction aligned to its travel, ???

    Or is it more useful to imagine the cube of Euclidean directions as a bead on the string of time? This would allow visioning the next sentence, “When the time offset is equal to the space offset, the distance can actually be zero” as somebody running on one of those moving walkways like airports have. While the walkway is traveling one way (time) they are running the other way (distance) and if they run at the speed of the walkway, they stay put. Time ‘stands still’.

    But I see a problem with that image. If the guy runs the other direction on the walkway, he could pass through a hunk of Euclidean space at twice the speed of light. Tut tut. Oh, wait a minute. Never mind. He would be running in Euclidean space, not in time. And Euclidean space is traveling on the walkway. With time’s inexplicable arrow, he can only run ‘into’ time, not ‘with’ it.

    Your last three paragraphs will give me something to enjoy. I’ll think on it. I ordered the Penrose book.

  • Midwesterner

    My computer is so slow right now that it is literally minutes between screens. (Drums fingers.) But it’s given me some time to think about your riddle.

    It seems likely to me that the outer edge would rotate forward or backward and lay against itself. The radius would go ‘straight’ out in a ‘curve’ to reach the perimeter.

    But I’ll keep thinking and see if any other possibilities occur to me.

  • nick g.

    They tell us now that we have ‘atomic’ clocks. I think they should stop there! If we had quantum clocks, they would always tell us, ‘The time is NOW’.

  • PA-I have two more days left of driving a newspaper delivery truck;and yes! The clock does only tick when I’m not looking at it!
    But I mean…. I knew white van drivers went fast, but fast enough for relativistic effects?

  • Paul Marks

    According to Euclidian ideas of space and time, if two objects each head towards the other at three quarters of the speed of light, their combined (or collision) speed is one and half times the speed of light.

    It is things like this (of course) that lead to modern physics rejecting Euclidian ideas of space and time.

    So we end up with principles such as distance being shortened to someone on a spacecraft moving at close to the speed of light (because otherwise the slowing of time, another principle, will lead him to measureing his own movement to his objective as being faster than light).

    I do not deny that the universe is this wild and wacky place, there is no reason why the universe should be in accord with the “common sense” principles of the human mind.

    However, I suppose it was only one more step on from all this to start denying any objective reality to matter/energy at all (or at least treating it as if it had no objective existance) and treating it all as numbers.

    It was a step that Einstien never made – but others did.

    Only the other day I watched a Q.M. physics person (with a long string of Harvard qualifications after his name) explain how meditation could change what we call reality (his example was the stock market – he was on Neil Cavuto’s show) as perception of reality determined what reality was.

    But why stop there? Why not just deny that there is a stock market, or a New York City (or any external universe at all).

    Of course, I can not prove that there is an external universe – after all if I kicked this man he could simply explain that away as false data.

    Still, on the positive side, Q.M. is a useful thing to hit determinists over the head with.

    Actually Q.M. is nothing to do with agency/choice (randomness is not agency), but if modern physics denies determinism for particles and stuff – why should human beings be subject to the “laws” of determinism?

    Although, of couse, if they were subject to determinism humans would not be “beings” at all.

  • Pa Annoyed


    Yes, the cube shrinks in all directions for a non-zero time offset. I was trying to talk about too many interesting things at once, and made it confusing by jumping topics too fast. Sorry.

    It’s a horribly inaccurate analogy, but think of a painting of the landscape, and the correspondence between points on the painting, and the real points that they’re a painting of. Small moves on the canvas correspond to large movements in the real world. As you get closer and closer to the image of the horizon in the painting, you go faster and faster in reality. As you move up to touch the horizon, you go faster without limit, but it doesn’t make sense to talk about moving when you’re actually at the horizon, since it’s a zero width line. There’s no width to cross, so it takes no time to cross it.

    In fact, the painting analogy fits an entirely different sort of mathematical space, called a projective geometry, and is quite different in its properties to Minkowski space. But it was the best I could think of at short notice.

    Your stockbroker is as much a “QM physics person” as the average snake-oil salesman is a medic. He’s either a nutcase (and qualifications are no sure guard against that) or he’s a scam merchant (and there’s no law that says clever, qualified people can’t be criminals. Well…, OK, there is; but you know what I mean.)

    But there’s no easy way for the layman to tell the difference. Someone selling something outrageous like reality-bending meditation is possible to spot, but I can quite see how my discussion of the more outre elements of QM above would be pretty much indistinguishable. The default position is that when someone tells you something crazy-sounding, you should not trust it. That doesn’t mean that it is definitely wrong, but you should insist on a lot of very good proof before betting your own money on it being right.

    The universe is weird only in very specific ways – not just any old weirdness is allowed.

  • Paul Marks

    Pa Annoyed.

    The man was not a stock broker, and he was not trying to sell anything.

    He was an academic (or ex academic) with a group of people who had hit upon the stock market as an example of what they could do.

    Of course in “my reality” the stock market fell like a stone (about 7% over the week), but who knows what happened in “their reality”.

    You are quite right that I know little or nothing about physics.

    I am used to economists knowing nothing about economics and historians making all sorts of absurd mistakes about history (and as for the philosophers…..)

    But these are subjects I have some knowledge of. Physics is a subject I can make no judgements in.

    In physics I can just hear people talking “weird stuff”, and you are right that I have no way of telling what is the “true” weird stuff and what is not.

    I despise the American “pragmatist” school of philosophy, but in physics I am forced to their “does it work” position.

    If people can predict lots of things correctly (positivist style) and come up with principles that allow other people to build useful things, then I am forced to accept that the science they come out with is “true” – even if it seems like insane ravings.

  • Midwesterner

    I’m not sure I understand the painting analogy. I can’t quite figure out what corresponds to what.

    And that shrinking in all directions is interesting. How big might a photon be if we could stop it still? Hhmmm…

    Projective geometry sounds like a precision calculation of what we were taught in 7th grade art class. Disappearing points and that kind of stuff.

    Cool. I looked it up and the third sentence of the description is “Projective geometry originated from the principles of perspective art.” So I’m on the right track.

    I ordered that book (Penrose, The Road to Reality). I already got a shipping confirmation this morning. Should be here soon. 🙂

  • Midwesterner

    Well, P.A., I don’t know if you are still checking the thread. I know sometimes you do. The book arrived Tuesday morning. I am on page xx of the xxviii pages at the beginning. After that I can start reading pages 1 though 1099. At over eleven hundred pages and 2 and 3/8s pounds weight (in the paperback), I think you’ve given me food for thought for a while.

    I found the subtitle to be humorously ambitious in a Hitchhiker’s Guide sort of way. “A Complete Guide to the Laws of the Universe”. Hhmmm…

  • Pa Annoyed


    I wasn’t checking it regularly, but planned to give Amazon a little time to deliver the book.

    It’s best to take it slowly. He explains in one book what others have taken a bookcase or two of textbooks to do, and to make it even marginally comprehensible is a grand achievement. But it is by no means easy, because this is the real thing, not the nursery school version. He refuses to patronise the reader by assuming they could never understand, and instead gives it straight. The only other books I’ve seen that even come close to doing that were Richard Feyman’s, and even he fudges a lot of the maths. (For example, QED was an excellent book, but you won’t find any path integrals in it.)

    But as Roger says in his introduction, you can’t really understand a lot of modern physics without the maths, so he devotes a large chunk of the book to teaching enough of it to understand what’s going on. It’s well worth the effort – or at least, I think so anyway.

    Since you read the Wikipedia article on Minkowski spaces and liked it, I figure you should be up to it. Just don’t try to go too fast, or give up because it’s proving hard work. I hope you enjoy it.

  • Midwesterner

    It is going to be a slow read, that’s for sure. I saw that part in the intro about refusing his editor’s instructions to leave out math and was both anxious and encouraged. It means that Penrose understands his audience and is going to try anyway. I may stand a chance.

    My big problem is that due to the nature of my work, I have been unable to have more than two hours of personal thinking time at a stretch for about three years now. (24/365) Most of my Samizdata time comes in five and ten minute bits. But in the past I have often gone into pure, all alone by myself, thought spells lasting as much as two or three weeks (both as a carpenter and a farmer I could take time to do that). But all I can do in two hours is try to remember previous thoughts, learning is difficult. Missing day dream time is long term as bad as missing night dream time. The brain steadily loses functionality.

    Definitely it will take me a long time and there will be a lot of rereading, but worth it, I hope.

    During preview, I just realized a big part of the problem with short thinking spells. I can figure things out tenuously, but to retain it requires turning it around in the brain, experimenting with it and in general becoming familiar with it. This is the part of the process I am missing so much. The bits learned flutter away in the wind before I can get them filed.

  • Midwesterner

    One more question. Is there a guide somewhere to phonetically sounding out equations and symbols? One of my primary memory storage buffers is the sounds of things but without knowing how to sound out the various equations …

    If you know of a link or anything, I’ve looked in the past and not found anything.

  • Pa Annoyed

    I’m not aware of one. You may find it helps if you expand the symbols into what they represent (velocity, mass, the-rate-of-change-of-, etc.), or try to express it in words – it’s a useful exercise anyway in understanding. So rather than x, y, z, and t, you could use ‘forward, sideways, up, and time’. Or say ‘the three space coordinates and time’ instead, which is even better.

    I don’t know if that will help – but if you’re doing it for self-study, you can probably make up your own sounds/names for them. Whatever works.

    If it’s any comfort, Richard Feynman described in one of his books how the fact he learnt his maths from books meant he couldn’t pronounce the names correctly – when he went to college he started talking to people about the Bernoulli equation and nobody had any idea what he meant, because he didn’t realise it was pronounced ‘bare-nooey’.

    Many mathematicians have their own fairly descriptive private names for stuff: ‘curly d’, ‘vertical bar’, ‘x-hat’, ‘x-dash’, “x-bar’, ‘dot’, ‘star’, ‘squiggly’, ’round-e’, ‘curvy-e’ ‘right-arrow’, and so on that aren’t the official names for the things, but are often quicker to explain. You can find the Greek alphabet on Wikipedia – it can be potentially embarassing for a professional mathematician if you call omega ‘curly-w’ in an important lecture, but nobody will worry if you get xi and zeta mixed up, or phi and psi. The wonder of maths is that it still works, whatever you call them.

    But as a general rule, you probably shouldn’t be wasting your time trying to remember equations. If it’s an important enough equation that you see it very often, you will remember it anyway. If it isn’t, then just try to remember the types of quantities involved and that they are somehow connected. You can always look up the precise equation again if you need it. Concentrate on the ideas instead.

    Incidentally, daydreaming about physics is an excellent technique for doing it. Einstein did a lot of his best work based on his ‘gedanken experiments’. It’s not to everyone’s taste, so don’t do it if you have other topics you prefer, but you might find involving a bit of exotic physics can give you more scope for the imagination. Study shouldn’t be taken too seriously – if you’re not being paid to do it and you’re not having fun doing it, it’s probably best not to do it.

  • Midwesterner

    I had no idea the verbalizations were so casual. As for concentrating on the ideas, when it is somebody else’s ideas I usually look at the ideas first and then bounce back and forth to the equation until all the funny squiggles are accounted for. I often come up short. Sometimes too much knowledge is assumed.

    I think calling them what they represent is probably the best, and the Greek letter pronunciation guides can help. The only classical language I studied even a little (very little) was Latin. I wanted to avoid learning an alphabet. Then I learned to read and write a little Russian on a night class/I’m bored lark. That was probably twenty years ago and I’ve forgotten it all now. Too many things that all sound like ‘zzhhh’ to me.

    Feynman is one of my favorites. The cloud chamber at Princeton(?) story is priceless. As is the safes at Oak Ridge story.

    I crave having a really good think. Oh well. Not for now. I wonder though, would an imaginary tokamak be a ‘gedanken donut’? Maybe that’s only funny in America. Maybe it isn’t even funny here.


  • Pa Annoyed

    “Gedanken donut” – well, I laughed.

    In professional circles things are a little more formal, and when trying to explain something to someone else it is usually useful to be able to use more precise terms, but really it doesn’t matter and I’ve heard some pretty wacky descriptions of particularly unusual notation even in professional circles. Informally, anything goes.

    There is no arcane secret knowledge about it. A lot of mathematicians have only ever seen it written in books too and therefore are in exactly the same position you are, and so it’s mostly just common sense. Anyway, for anything that isn’t a standard book method (and sometimes for things that are, if the standard notation is inconvenient for some reason), mathematicians are used to just making up notation on the fly, and so long as you define your terms you can call it anything you want.