Dear Daryl,
Very pleased to see time utilised so elegantly here - well done. Your essay is both relevant and interesting. I think you've used excellent arguments and find myself agreeing with them. Hopefully if you have time, you will take a look at my essay which perhaps shows an arrow of time emerging when utilising simplexes of their respective n-dimension to explain entropy.
Best wishes for the contest,
Antony
Israel,
On the last point, in the reference I suggested, Einstein concluded (though you should probably still read how he got there):
"[Minkowski space], judged from the standpoint of the general theory of relativity, is not a space without field, but a special case of the g_ik field, for which--for the coordinate system used, which in itself has no objective significance--the functions g_ik have values that do not depend on the co-ordinates. There is no such thing as an empty space, i.e. a space without field. Space-time does not claim existence on its own, but only as a structural quality of the field.
Thus Descartes was not so far from the truth when he believed he must exclude the existence of an empty space. The notion indeed appears absurd, as long as physical reality is seen exclusively in ponderable bodies. It requires the idea of the field as the representative of reality, in combination with the general principle of relativity, to show the true kernel of Descartes' idea; there exists no space 'empty of field'".
And this brings me back to the first point. In effect, you're claiming that Newton thought no more about space and time than a naive child. That he wasn't guided by the development of physics. That somehow brilliant Descartes had really thought deeply, then Newton stood up and said "actually, I've got this other idea that's basically been knocking around in my head since about eight that I'm going to run with." That Newton, who based his entire system on naive intuition, gave no compelling reasons for doing so, and people accepted it for centuries because, apart from a couple of real thinkers such as Leibniz, no one else really thought of the problem past their own childish view of reality for centuries until Mach set us back on the right path and Einstein took up the torch.
You began your first post with "As far as I can see our discrepancies may be a matter of semantics," yet I disagree with what you wrote after that on every level. As I said, I've already discussed this a lot with John below, so if you want a sense of some of my reasons for thinking differently from you, you could read that discussion. I'm heading out of town tomorrow, and don't have the time to re-iterate.
Daryl
Daryl,
The issue here is; What is space?
Physics treats it as a measure. As Einstein said, "Space is what you measure with a ruler."
So now there are 2 measures; That which is being measured by how far light travels in a given time and how far two points of reference are away from each other.
So are they both measures of the same space, or are they completely distinct from one another? Presumably they are of the same space, since they are being compared to one another. In that case, which is the denominator and which is the numerator? Which is the reference frame and which is the variable? Presumably the denominator, the reference frame, is the measure of "real" space and the other is distance being denominated in the units of the other.
Now it would seem that you are using lightyears as the denominator, yet you are saying the distance between two points/galaxies, is the "real" space. So if "real" space is expanding, what is the basis of lightyears? You say the light is not measuring the real space, but there just seems to be this stable metric the light is traveling, yet it is just assumed. What makes it "constant," if it is not measuring the "real" space?
John,
Why do you want to consider a ratio of the distance light travels through expanding space through time, to an instantaneous distance? True, they're both measures within the same space-time metric, but they're very different [Actually, as I read this over, I see this is your point. Please keep reading and I'll talk about this at the end].
If you're referring to the comoving coordinate separation, that's not a distance at all. What's the distance between the north pole and the south pole of a sphere? You can't answer that unless you know the magnitude of the radius in some unit of measure. Same goes in cosmology. The scale-factor, in whatever unit, is multiplied by the coordinate positions.
By "Now it would seem that you are using lightyears as the denominator", I can only take you to mean that you think lightyears is not just the unit of measure, but actually the magnitude that distances are scaled against. Sure, it can be, but you're missing something. You're not thinking about this the right way at all, and I fear I may have confused you at some point. Please think of it this way: space-time (the geometry of the Universe's evolution) has a well-defined metrical structure, so we can use an algebraic coordinate representation to describe it. We assume continuous coordinates which are multiplied by a scale-factor, which provides the unit of measure, and it is an increasing function which *sets the scale* *throughout time*. Therefore, if the distance between two points A and B, say on opposite sides of spherical space (that's their coordinates) is 1 m at one time (that's because of the value of the scale-factor at that time, which sets the scale and defines the unit of measure) and then the scale factor doubles in size, then they will be 2 m apart at the later time.
That example considers only spatial distances at an instant and not distances travelled over the course of time. As I've said, in order to calculate distances travelled over the course of time you do need to use calculus and consider the space-time metric, not just the metric of space at one time, because that changes as the scale factor increases with time.
[Now, getting back to that point from above: the metrical structure of space-time allows us to consistently compare distances in any particular unit of measure throughout space-time. We can therefore determine how far light moves through expanding space over the course of a year and call that our unit of measure. Due to the metrical structure of space-time, we can then even use that as our unit of measure when referring to instantaneous distances throughout space.]
I do need you to try to meet me halfway on this. In my last post, I gave examples in which the distance travelled through space in a minute varied even though you jogged along at a constant rate and therefore always actually jogged the same distance in a minute. I need you to either concede that what I said makes sense to you or disagree with it. It's an example that I think should eventually help, or I wouldn't have written it down.
I'm sorry if this is even more confusing. I'm trying.
Daryl
Daryle,
I do think I understand your point. It just seems to me that you are absently using a given without considering that it needs a source.
Consider: "Therefore, if the distance between two points A and B, say on opposite sides of spherical space (that's their coordinates) is 1 m at one time (that's because of the value of the scale-factor at that time, which sets the scale and defines the unit of measure) and then the scale factor doubles in size, then they will be 2 m apart at the later time."
So: At one point in time, the sphere of the universe is one million lightyears across. Subsequently at another point, it is 2 million lightyears across. This seems to correspond to your description. Yes?
So my point is; Where does the metric of space/distance come from, that sets the speed of light? Presumably, if the speed of light is being determined by the same set of coordinates as A and B, it will always be one million lightyears, because the set of coordinates and the speed of light are determined by the same metric of space, but they are not. There are two metrics of space, that between A and B and that (m) set by the speed of light.
Consider: " in order to calculate distances travelled over the course of time you do need to use calculus and consider the space-time metric, not just the metric of space at one time, because that changes as the scale factor increases with time."
If lightspeed was determined by the space-time metric, it would change along with the scale, but it doesn't, so it is not determined by the space-time metric. So my question, again, is: What metric determines the speed of light?
Daryl,
Sorry for the name misspelling. My mac is old and the spinning wheel is getting more distracting.
John,
(no problem about the misspelling. I know you know how to spell my name.)
Consider the line-element
ds^2=-c^2dt^2+a(t)^2dx^2,
where c and a(t) are in metres and the coordinates x and t are unitless.
At t=1, what is the distance between x=1 and x=2? Again, you can't answer that, because I haven't told you that a(1)=1 m; therefore, the distance is 1 m (dt=0, so s=1 m*integral over dx from x=1 to x=2; therefore, s=1 m*1=1 m). If a(2)=2 m, then the distance between x=1 and x=2 at t=2 is 2 m. Depending on the value of a(t) at any particular t, the distance between the fixed locations x=1 and x=2 varies.
Now to the speed of light. Light moves along null lines in the metric, where the conserved quantity ds is zero. A little rearranging of the line-element tells us
dx/dt=(+/-) c/a(t),
so the coordinate velocity of light certainly changes in time with a(t). As a(t) increases, light doesn't get as far along x in equal amounts of time. But c is just a constant which is defined as such in the line-element.
Daryl
Hi John,
Now I want to change things and define the units as dimensional quantities. This is perfectly allowable, mathematically, and really about half of cosmology textbooks define a dimensional scale factor and half use a dimensional radius. So consider the same line-element,
ds^2=-c^2dt^2+a(t)^2dx^2,
where t is in seconds, x is in metres, c is in m/s, and a(t) is dimensionless. The point I want to make regards the value of the constant c. We can set it equal to 300,000 m/s and scale our entire description accordingly, calling that "the speed of light". The reason is given by the second equation above, with a=1. I see your point about "but how do we define "space", and compare the "speed of light" to it, describing that as constant, when space is expanding?" Indeed, as the above example shows, the coordinate speed of light is not constant, and as we've said over and over light will make it further away from us through expanding space this year than it will next year.
But do you see that c really is just a constant. The lightyear is defined by multiplying that constant by the number of seconds in a year. From the metric, we can integrate to determine distances at an instant or distances through expanding space. For light, which moves along null (ds=0) lines, we can calculate how far it goes in a year when the scale factor changes in some way. We can state the values in "lightyears" in just the same way that, in the above example, we can say that you jog along the moving walkway at a rate of 2 m/s, and in a minute you travel 120 m, regardless of how far you actually make it along the moving walkway, which is something that also depends on the walkway's speed.
How's that?
Daryl
Daryl,
I'd love to say, Ah ha! I see your point, because you have been far more patient than anyone else in the physics community has ever been, but....
If I'm jogging along, however the larger frame is moving, there are basic physical reasons why my speed is constant, but with the speed of light, you remove the validity of a stable metric of space, assigning that the expanding scale, yet still take it as a constant for granted.
As you say, it "moves along null (ds=0) lines."
Wouldn't this constitute as basic a metric of space as you could describe?
Yet you then turn around and say, " the coordinate velocity of light certainly changes in time with a(t). As a(t) increases, light doesn't get as far along x in equal amounts of time."
The irony here is that since the coordinates increase, relative to that, the change in the coordinate velocity of light must be to slow, since it doesn't travel as far. Yet because you take the speed of light as a constant so much for granted, then the assumption is it is the coordinates which vary, ie. increase.
It is still the same problem; The coordinates grow further apart, while the speed of light remains constant. Which is the measure of space in this equation and which is the distance being measured?
Lets put it in the context of me jogging; Say I live in some funhouse reality, where my stride is constantly being warped and shrunk and swollen and there is no way to judge what each step will be. One might only be a few inches, while the next could be hundreds of feet. It would no longer be a useful constant now. So it is only because each is governed by the same processes and covers the same relative amount of ground that it can be considered a constant. The same goes for the speed of light. Whether the universe is 1m, or 2m, or 3m, m is still the constant. It is the distance between the coordinates that changes.
Dear Daryl
You said: people accepted it for centuries...
I don't think so, most people (including Newton himself) knew that totally empty space was an absurdity, but we have to understand the reason why Newton left space totally empty in his theory. Newton mostly agreed with Descartes' view of space. For Newton space was a substance and the medium that convey gravity between celestial bodies was the aether, but he realized that Descartes' view was so complicated to put it in mathematical terms that he decided to leave space in his theory as an empty container. As we all know, the empty container view of space is mathematically represented by Euclidean space. This is space, as we all know, has no substantial or material properties per se and the same occurs with any other geometrical space (you should check Riemann's original paper on this subject). The view that space was an empty container was always seen as an anomaly of Newton's theory but the anomaly remained for centuries because that was the only game in town since nobody could come up with a better formulation of space until Minkowski arrived in 1908. Similar to Euclidean space, Minkowski space-time represented emptiness although its metrical properties are certainly different (the discussion of Minkowski space-time as a real space is still a hot topic among the philosophers of science and some physicists, Veselin Pektov is one of the advocates of the physical existence of Minkowski space-time). When the aether was rejected in 1905, Einstein left space again totally empty, just as in Newton's theory. According to Newton's theory celestial bodies were interacting at a distance in totally empty space, which for Newton himself was an absurdity. At this point, it is convenient to quote Newton's opinion about this topic, I'd like to show you that he was basically following Descartes' view. The quote was taken from one of his letters sent to Bentley in 1692:
It is inconceivable that inanimate brute matter should, without the mediation of something else which is not material, operate upon and affect other matter, without mutual contact, as it must do if gravitation in the sense of Epicurus be essential and inherent in it. And this is one reason why I desired you would not ascribe 'innate gravity' to me. That gravity should be innate, inherent, and essential to matter, so that one body may act upon another at a distance, through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity, that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it.
So, as we all know, the discovery of Minkowski space-time didn't and doesn't solve the problem of how celestial bodies interact. Minkoswki space-time continues to be an empty container. At first, Einstein disliked Minkowski's formulation but later he recognized its scientific value. He realized that treating inertial frames in terms of space-time could be useful to extend his SR to non-inertial frames. Since, it is assumed that GR is an extension of SR, at some point the metrics in GR should reduce to the Minkowskian metric. He then argued that the Minkowskian metric is a special case of the general case g_ik where the gravitational potentials are contained. Einstein said that even if the energy-momentum tensor were zero, we still have the gravitational potentials contained in the metric tensor which at the end gives meaning to space. Minkowski metric, is then a special kind of gravitational potential with constant coefficients. According to Einstein, empty space is inconceivable, for him the g_ik tensor gives physical meaning to space, this object in Einstein view is the new "aether". But we should not mix the concepts, this is the metric of space not space itself. In Newton's theory the mathematical object that represents the notion of physical space is the Euclidean manifold not its metric. Similarly, in GR what represents space-time is not the g_ik but the pseudo-Riemannian manifold. And a manifold has no intrinsic material or substantial properties associated with it. In GR, space is not a medium as Descartes' aether was. Space-time is still a container with metrical properties defined by its material content but the manifold itself doesn't represent a substance.
Now, Einstein said that g_ik is the fundamental field, but what is a field made of? If we ask this question to Maxwell, he would certainly reply that an electromagnetic field is a state of a material medium, in his time, such medium was the aether which filled the empty space. I must make clear that I don't follow this dichotomy, for me aether and space are the same thing, therefore, a field is a state of space, understanding space as a material substance and so one can say that space is a material field. The fact that the permeability and permittivity of the vacuum are not zero tells us that the vacuum behaves as a paramagnetic medium and only material substances have these electromagnetic properties. If space were Minkowskian these properties would be zero. In contrast, for Einstein, an electromagnetic field is a different entity from space, is a physical reality that fills and propagates through space. And for him the properties of space itself are defined by the metric tensor that gets its "substantiality" from the gravitational potentials. But again, this is not a medium in the sense of Descartes, Newton or Maxwell because a medium is material and has no curvature. It is absurd to talk of a curvature of a medium, that term only makes sense only for geometrical spaces (manifolds). I hope I had made clear why I don't follow the notion of geometrical space-time. I have read your discussion with John and I support's John's view. I think you are getting it in the wrong direction.
Best regards
Israel
By the way, did you hear about the work that claims that the universe is not expanding? The argument is that the mass of the particles in the past was different and that's the cause of the redshift that astronomers observe today, what do you think? I don't think the masses changed, that hypothesis cannot be experimentally proven. But it seems that it;s gaining support from some people.
http://www.nature.com/news/cosmologist-claims-universe-may-not-be-expanding-1.13379
Regards
Israel
And I think you're going in the wrong direction. C'est la vie. Regardless of what we think, though, it ultimately comes down to whether a consistent physical description can be formulated which consistently accounts for the phenomena, etc.
No I haven't read that article. I find much of physics these days to be purely speculative mathematics, motivated by a shut up and calculate dogma. Why think, when you can do advanced algebra? That's what that sounds like to me.
Thanks for sharing. I suppose that sounds insincere from what I wrote, so I should stress that I really do mean that. Sincerely,
Daryl
Hi John,
First of all, thanks. It means a lot to know that you appreciate my effort. Just to let you know, I appreciate you pressing the issue. It's good to think about these things, and always helps to reevaluate the justification of ones ideas.
Second of all, sorry I'm taking so long to respond. I'm traveling right now, with a few hours to kill in Zuerich, but won't be able to properly respond until after I'm settled. That may not be quick because I'll be busy while I'm here, so I'll post on your site again to let you know when I do.
Best regards,
Daryl
Hello darryl - Have you had the time to take a look at my post, above?
John
Hi John,
Yes I did get it as I was preparing for a trip. I've just arrived in Lausanne for a metaphysics of time workshop tomorrow, but I will read your essay. Thanks very much for reading mine, and for rating it (you gave it a 6, right?). I will read yours.
Daryl
Dear Daryl
You have your approach and I have mine. I think I'm right, you think you are. As you said: Regardless of what we think, though, it ultimately comes down to whether a consistent physical description can be formulated which consistently accounts for the phenomena, etc. I agree with this but perhaps you are ignoring one important component of science. There was a time in the past when science was about unveiling the true behind the appearances, but that view is in the past. Today science is more a business than science. I brought the case of that paper not to bother you but to let you know that the weight of media has something to do with the establishment of new approaches. You may wish to ignore it, but the general public will not. I'd like to quote something that Lee Smolin said and that I sympathize with:
Science is not about what's true or may be true... Science is about what people with originally diverse viewpoints can be forced to believe by the weight of public evidence.
"Public evidence" means "evidence widely known". As long as our ideas are not widely spread by mass media they'll be ignored by the physics community. I have read the story of how Einstein and his theory became famous and many commentators ask why the same situation didn't occur with QM. It was the mass media of that time, not the theory itself, that created the legend and the greatness of relativity and its author, not only among the general public but also among the physics community. Finally, I'd like to quote what Oliver Heaviside said in 1919 with respect to the understanding of gravity and the future of theoretical physics:
Newton, as was known, did not understand the nature of gravitation. We do not understand it now. Einstein's theory would not help us understand it. If Einstein's third prediction [gravitational redshift] were verified, Einstein's theory would dominate all higher physics and the next generation of mathematical physicists would have a terrible time. Such things as university courses for all practical purposes would be continued upon Galilean and Newtonian dynamics, but the Einstein school could not fail to interest, sooner or later, every intelligent man.
He sounds like prophet because he knew that the view of space and time of GR will blind future generations of physicists. Now, here we are all, a hundred years after still trying to unify gravity with the other forces and discussing these topics because after all we are starting to realize that GR didn't help us understand it.
All the best and don't be cranky, there's no reason to be like that, life is too short!
Israel
Dear Daryl,
I have studied your essay and this gave me further motivation to go back to the related Wheeler's paper you refer to.
I found your essay very well written and interesting.
"Understand the quantum as based on an utterly simple and -- when we see it -- completely obvious idea.
Explain existence by the same idea that explains the quantum...
Reduce time into subjugation to physics."
If you read my essay
http://fqxi.org/community/forum/topic/1789
you will see that the Riemmann surface concept, favoured by Hermann Weyl, may be made in a good correspondance with the quantum.
Good luck,
Michel
Good Paper. Starts off slow, repeats the same stuff about Wheeler found in other essays in this contest. Then goes on to discuss our language issues with the notion of time, and makes some rather interesting points.
I wholeheartedly agree that Minkowski spacetime does not exist. However, the relationship between space and time does exist down the single direction of propagation of quantum particles, not in some empty manifold we call Minkowski space. "Elements of reality" are therefore bounded by the emitter and absorber atoms. This is where an "interval" in time can be considered. In section 3, your claim that "no interval of time exists..." needs a reference.
I am not convinced by the world-line argument. This is just another attempt to regenerate a form of simultaneity surfaces. World-lines do not exist unless something travels along it. I do not find the argument for block universe compelling, even if it is a dynamically warping and molding thing.
The section on Minkowski space was a little jumbled and confusing.
I enjoyed the description "relativity of synchronicity." Very nice.
This is a strong entry and I gave it a good rating. The author would have done better with a shorter introduction and a focus (in two sections) on the Newtonian and Einsteinian inconsistencies in the relativity of synchronicity, then in the concluding section added the claims of novelty that he wished to make.
All in all, a worthy paper I will look forward to reading other works from this Author.
Daryl,
Good luck on the trip. Not a problem getting back to this. Patience is a necessity. Not that I always have any, but I'm good at keeping myself distracted.
Hello Daryl
Richard Feynman in his Nobel Acceptance Speech (http://www.nobelprize.org/nobel_prizes/physics/laureates/1965/feynman-lecture.html)
said: "It always seems odd to me that the fundamental laws of physics, when discovered, can appear in so many different forms that are not apparently identical at first, but with a little mathematical fiddling you can show the relationship. And example of this is the Schrodinger equation and the Heisenberg formulation of quantum mechanics. I don't know why that is - it remains a mystery, but it was something I learned from experience. There is always another way to say the same thing that doesn't look at all like the way you said it before. I don't know what the reason for this is. I think it is somehow a representation of the simplicity of nature."
I too believe in the simplicity of nature, and I am glad that Richard Feynman, a Nobel-winning famous physicist, also believe in the same thing I do, but I had come to my belief long before I knew about that particular statement.
The belief that "Nature is simple" is however being expressed differently in my essay "Analogical Engine" linked to http://fqxi.org/community/forum/topic/1865 .
Specifically though, I said "Planck constant is the Mother of All Dualities" and I put it schematically as: wave-particle ~ quantum-classical ~ gene-protein ~ analogy- reasoning ~ linear-nonlinear ~ connected-notconnected ~ computable-notcomputable ~ mind-body ~ Bit-It ~ variation-selection ~ freedom-determinism ... and so on.
Taken two at a time, it can be read as "what quantum is to classical" is similar to (~) "what wave is to particle." You can choose any two from among the multitudes that can be found in our discourses.
I could have put Schrodinger wave ontology-Heisenberg particle ontology duality in the list had it comes to my mind!
Since "Nature is Analogical", we are free to probe nature in so many different ways. And you have touched some corners of it.
Good Luck,
Than Tin
