Speed of light

Cecil's Columns/Staff Reports
41

But:

Now, the only thing I can imagine you’re calling a “contention” from the sentence you quote from me is “This was a clear implication of the material of the article,” where “this” referres to the idea that “there could be entities which percieve the same world we do as a two dimensional one.”

While the thing I just quoted doesn’t say exactly that, it does “clearly imply” it just as I said. The creatures living in this alternative sort of spacetime described can’t determine which dimensionality their universe has, but might be physiologocally predjudiced in favor of one description or other. I don’t see any reason to think that all creatures in such a universe would have to be physiologically prejudice in the same way–if evolution occured several times in that universe, its likely that some would be prejudiced one way, some prejudiced the other, just as some might have wings, and some might have tentacles.

The thing I quoted is not talking about our universe, but about an alternative sort of spacetime, but a following section of the article serves to pointedly fail to rule out that this mathematical trick may work for our universe as well, albet in a slightly modified fashion.

It explains why the technique can’t work on our universe exactly as it does in the case of the alternative spacetime just discussed

But then goes on to explain that there is a mathematician who may well have found a way to apply the technique which may well work for universes like ours:

Now, Exapno, a lot has happened since the post from me that you quoted. Mathochist has given a bit of an explanation of what’s going on. I’ve given a much better summary of the article, based on a fresh reading of it, then the one found in the post of mine you quoted. Later material on this thread is much more relevant to the ongoing discussion on this thread than any material from that post of mine you did quote from.

Also, I can’t understand your use of the word “contention.” Contentions are never hedged by phrases such as “I don’t remember if” and “I remember thinking.”

You’ve asked in another thread whether you forgot to put on deoderant. I can assure you from this distance, I have no olfactory experience of you whatsoever. So that must not be the problem.

-FrL-

42

It’s a very common topic in complex analysis. Basically it goes like this (polar coordinates on the plane used everywhere and TeX where needed).

Given a harmonic function u(r,t) on the unit disk, consider its restriction to the boundary f(t) = u(1,t). This defines a smooth function on the circle. So far so good.

Now we define a special function on the disk, the “Poisson kernel”:

P(r,t) = (1 - r^2)/(1 - 2r cos(t) + r^2)

We can think of this as a family of functions on the circle parametrized by r: fixing a value of r we get a function of t, which is the coordinate on the circle.

Now we can use the Poisson kernel to turn a function on the circle into a function on the disk. The procedure is called “convolution”

u(r,t) = \int_{-\pi}^{\pi} P(r,t-x)f(x) dx

It turns out that most of the nice properties of the Poisson kernel (including the fact that it’s harmonic) transfer over to v. In addition, if we start with a harmonic function, restrict to the boundary, and then convolve with the Poisson kernel we get the original function back. Conversely, if we start with a smooth function on the circle, convolve with the Poisson kernel, and restrict to the boundary we get back the original function on the circle.

In glib terms, the upshot is that convolution with the Poisson kernel “solves the Dirichlet problem for the disk”. That is, it finds a harmonic function (a function satisfying a certain kind of partial differential equation (PDE)) satisfying certain boundary value conditions.

So what does this mean for “holographic” physics? Well let’s say that the universe is a four-dimensional ball, with the “boundary” being really really far away[1]. Einstein’s equations are a PDE describing the gravitational field, which is a description of the geometry of 4-d spacetime. The field restricts (in a sense) to the boundary sphere, where it describes a 3-d geometry there satisfying a different PDE (and so being essentially different than GR). So the translation from 4-d GR to this new 3-d theory on the boundary is just another Dirichlet problem.

[1] This isn’t as weird as it sounds. Escher’s Circle Limit IV shows a disk with a hyperbolic geometry. All the angels and all the devils are “really” the same size, and from their perspective the edge of the circle is infinitely far away.

43

Hey guys, glad to be here. This looked like a good place to introduce myself. I don’t know if Murduck was satisfied with the replies or not, it seemed to get a little :smack:
Yeah, Harvard physics conducted several tests which manipulated the speed of light a few years ago. Ya see, the speed of light is not really constant. It is referred to as a constant when measured in a vacuum with no interference and under the laws of physics as observed in the universe at present. It can be increased when there’s a big suck helping it along.
Not that I cleared up the muck Mr. Duck. I just wanted to say hello to everyone.

especially you Unca Cece. :slight_smile:

44

It can’t be increased. The usual experiments involve firing a laser pulse through a medium, where the exit pulse is produced nearly instantaneously by the lased media. But the entry pulse is annhilated in the process, and both laser pulses move at the usual <c speeds (since they are not moving through a vacuum). In effect, the information contained in the pulse is used in a superluminal way to produce a new pulse. But neither pulse breaks the c-limit.

These are wierd experiments, and the press nearly always gets it wrong.

45

I don’t know about the press in regards to the experiments I read. They were conducted by Dr. (I can’t recall her name) at Harvard. I studied the results as she presented them in regards to the manipulation of light speed. As far as the increase is concerned, that is theoretical. I’m not aware of any actual experiments that have produced “faster than light” speeds. Since the experiment would have to simulate the absence of a universe. It would in fact have to produce one hell of a vacuum to which our physics may not apply. I doubt the theory could be presented as an actual hypothesis. Considering our idea of space/time in comparison with what we might imagine in a universe of singular dimensions, it is entirely plausible that light could travel across the universe instantaneously. But if the universe was in singularity as some “time” in it’s history. It’s dimensions would be undefined as well. The idea of infinity goes both ways as I’m sure you are aware.

46

This is gibberish in which the only correct words I can recognize are “I’m not aware of any actual experiments that have produced “faster than light” speeds.”

You do understand that the speed of light is shorthand for Einstein’s constant “C”, not the actual transmission of photons, don’t you? Einstein’s C is what shows up in the equations. Measurements of phase velocities and maybe group velocities can exceed C but that is not at all the same as faster than light speeds for information or objects.

Start with Wiki’s article on faster than light and see if it helps clarify some of these notions for you.

And what is your background in physics? If we knew what level you were at, it would be easier to pitch our explanations.

47

I can see that some folks take offense at opposing ideas. But to say the idea of a one dimensional universe is any more “gibberish” than a 4D or 5D universe is a bit childish. I understand quite well the physics involved since I studied astrophysics in college. I know enough to realize that we still have a lot to learn. I submitted a thesis on dark matter in the universe.

of course

If you grasp the idea of a universe expanding from a singular point in “space” you should be able to realize that “lightspeed” is meaningless as we understand it at this point in time. After the growth of the universe stabilized and became constant itself, then space/time (speed) took on meaning. That is the basis behind lightspeed being constant. If we could travel faster than light (NOW) we could theoretically travel beyond our own universe. Now you are entering multi-dimensional planes of existence which are also not subject to our current knowledge of physics. Sorry… more gibberish, huh.
How big was the universe before the bang vs. how big was it one second after the bang? Better yet, how big is it now vs. how old is it? It is bigger than time allows for it’s expansion.
Take into consideration the energy behind the matter (the whole universe) and the absolute void into which it filled. Replicate that experimentally. Physics as we TRY to understand it is inappropriate. There are plenty of cites describing the exponential rate of growth during the first few seconds after the bang.

But Marduck’s op was “can anyone contradict this assertion?” Obviously many people did.
Apparently I misunderstood the OP and my point of view was not asked for, sorry.

48

No… definitely not your body odor… something else…

-FrL-

49

Yup, gibberish. The Universe didn’t expand from a single point in space; space is, rather, a part of the Universe. And the growth of the Universe certainly isn’t a constant now, and I’ve never seen any evidence that it ever was. If we could travel faster than light, then we’d be able to leave our observable Universe, but it’s no big deal to point out that our obeservable Universe isn’t all there is.

50

Check, and mate.

51

Huh?

I don’t see how your comment here answers the implicit comment of my post. Chronos’ rudeness (which was less inappropriate than your own BTW, since he was taking up a “gibberish” gauntlet thrown down by JBeam himself already) does nothing to lessen the fact that your own comment was inappropriately rude.

Here’s what you should have said.

“I can’t understand what you mean by several of these sentences, and here’s why:…”

and then list specific problems in the text which illuminate your point.

This phrasing politely, and constructively, allows both for the possibility that you are the one who needs to be educated, and that JBeam is the one who needs to be educated. No matter how clear it may be to you that the latter is the case, it can’t be clear to JBeam at the early stage in the conversation in which you offered your post to him, and to prejudice the discussion at that stage is simply to invite JBeam to defend himself to the point of irrationality or leave. Neither of these fulfills your educative intent. And furthermore, whether or not you like it, you might be wrong: JBeam may be onto exactly the right ideas and you may simply be misunderstanding him. It may be you who needs to be educated.

Anyway, reword things this way, and people will not jump on you for saying “the same thing everyone else is saying” as you put it in a previous post.

-FrL-

52

Well actually it is commonly accepted that the universe did originate from a point of singularity. I said “space” note the quotes. I didn’t mean to imply that space as we observe it existed then. So far most of what everyone has said thus far is gibberish.
There is no checkmate involved, especially when postulating theories about how the universe was “created”. At least we’re staying away from religious creation.

BTW I should’ve brought up the concept of a zero dimensional universe.
I thought I’d check it out a little more. There are a number of experiments which have produced faster than light speeds which are proven. Although they manipulated the medium through which the light traveled. (cesium gas vapors IIRC)
Sorry I even said hello in the first place.

53

I’ve been waiting to dip my toe into this charlie foxtrot here. Everything you’ve said about cosmology seems to miss the fundamental point of the unity of spacetime, and that goes doubly for this point here (pun sorta intended).

Spacetime in GR exists as a single four-dimensional manifold equipped with a smooth metric of signature (1,3) (or (3,1)). “Time” is just a direction like any other. You can try to slice spacetime into a family of spacelike hypersurfaces (parametrized by “time”), but there’s no way of doing this that’s better than any other, and even when you (essentially randomly) pick one, you can’t say that point A in slice 1 and point B in slice 2 are “the same” or not in any meaningful sense whatsoever.

So the single point in the big bang model is a single point of spacetime, which has no meaning in whatever spacelike hypersurface you define as “now”. That’s what people mean when they say there’s no center of expansion of the universe.

Study astrophysics all you like, but take a differential geometry course and learn how the model really works.

54

Yeah Mathochist, I get all that and I know the model to which you refer. You imply that only one exists and yours is the correct one. Singularity does not necessarily refer to a point in space/time. It does also refer to the concept of a zero dimensional universe where all matter is infinitely small. I realize there is no “center” of the universe. We don’t even have an agreed upon shape of the universe much less it’s dimensions or growth rate.
Perhaps the universe existed of cesium vapors before it “exploded”. Who knows what the universe was before time? You?

thanks Fry… I appreciate the open mind.

55

You seem to be saying that this “zero-dimensional universe” is the initial singularity, which “exploded” and evolved into the present three-dimensional one. If this is what you mean, you are completely throwing out general covariance (you’re picking a preferred foliation by hypersurfaces), which is not to be done at all as lightly as you seem to be.

If you mean something different, you’re going to have to explain more thoroughly.

By the way, we’re not closed to new ideas, but none of these are new ideas. Some of us (like Chronos) live in theoretical physics, while others (like myself) have furnished vacation-homes there. We’ve seen this before and it just doesn’t measure up.

56

You don’t know enough about this subject to comment on it. I’ve been trying to educate you on that point all along. Enthusiasm and badly remembered and misunderstood popular science articles are not physics.

Why not learn from people like Chronos or Mathochist who actually know what they are talking about? Or even me? Theoretical physics isn’t something that’s up for debate by amateurs.

No. There aren’t. Again, see phase and group velocities.

The same should be said for you: Enthusiasm and badly remembered and misunderstood popular science articles are not physics. Cesium vapors did not precede our universe.

Physics is amazing and wonderful on its own. An open mind is absolutely necessary to grasp what the physicists say. You can lose yourself in its depth easily. That’s still not at all the same thing as making up your own physics and insisting that others appreciate it.

57

Ahem, you’re welcome but (to be honest I can’t make heads or tails of your posts either. I just don’t think it’s right to kneejerk a “gibberish” call on it just because I don’t understand it.)

-FrL-

58

There is an absolute rule in Internet science discussions that if a writer asks you to keep an “open mind” the theory/hypothesis/subject at hand is gibberish. There are no known exceptions.

59

In our last exchange on this thread, I showed that I had correctly understood the implications of the SciAm article I “badly remembered” and you had not understood those implications even though you had just read it. You’ve succeeded in “educating me” on no point whatsoever, and this wasn’t due to any lack of learning ability on my part.

I do know enough about the subject to comment on the appropriateness of your tone as far as it befits your intention in posting, and on the reason people react badly to your posts sometimes as you have attested.

Here’s what happened between me and Mathochist:

I disagreed with him, cited my reasons and my readings, and when he explained the physics and math to me to show how I had not perfectly understood what was going on in the article, I acknowledged this. I then asked him to show me something about harmonic functions.

So, since what you request in the above quote is what I’ve already done in this very thread… I have no comment here.

Exactly right. But the socratic method can be a very effective way to teach in a forum like this. So if I, a student, have questions or even disagreements with my teachers, then I, as a student, should be corrected constructively, rather than slapped around the head and berated in ways I may not even be able to understand.

More of the same. Who here do you think is concieving of themselves as “making up their own physics?” People are here trying to understand and communicate what they (at least think they) understand about these topics. When they are incorrect, or when they are communicating unclearly, the appropriate way to “fight ignorance” is to show them why they are wrong, or how they are being unclear. To simply say “this is gibberish” and then post up facts which fail to clearly engage what they were talking about, is not to “fight ignorance” but rather “to praise one’s own (sense of a) lack of ignorance.”

-FrL-

60

Oops… you know you just undermined a previous comment of yours, here, right? :smiley:

But I know what you mean, anyway.

-FrL-