Speed of light

Cecil's Columns/Staff Reports
21

As we’ve explained over and over here, they’ve tweaked the group velocity, not the phase velocity, as the link clearly states. When they say “faster” and “slower” they’re still always talking about speeds below c. In fact, the article even explicitly states that they can create the illusion of superluminal propagation.

Please, for god’s sake shred your copies of The Tao of Physics and The Dancing Wu Li Masters. They’ve done far too much harm already.

God, the old “sound barrier” trope.

The sound barrier was regarded as a technical impossibility, not as a strict physical limitation. Of course things moved faster than sound, but aeronautical engineers didn’t think they could make a plane do it. The speed of light is enormously different, since at every instant for every point of spacetime we’ve observed so far (and that’s really quite a lot), causality is preserved. If there is a mechanism for superluminal propagation of signals, then it’s really on its proponents to exhibit it by now, and further to explain where all relativistic physics is somehow wrong.

22

If you’re refering to the Inflation Theory…then matter didn’t excede the speed of light.The expansion of space did.The Theory of Relativity says that nothing can travel THROUGH* space faster than light.It places no limits on the speed of the expansion of space(and mater trapped within that space).When the expansion of space excedes the time it takes for light to cross that space it’s no longer visable to you…hence eventually everything will be dark to anyone left around to look.

Basicly space expanded faster than light and took the matter with it but no speed limits were broken because the mater didn’t travel through space faster than light…it stayed in the same place…space expaned.

23

You think wrongly.

You believe incorrectly.

There is an enormous difference between saying that we have not been able to completely understand the universe - which is what all good scientists say - and saying that therefore anything and everything is possible.

As real working scientists and mathematicians have already shown in this thread, true understanding of science explains many more things than assertions from those who fail to understand even the basics of current science, let alone the difficult bits.

The OP asked a model question. When a seeming contradiction arose, he or she asked for an explanation - without offering any opinions or beliefs as to what science was or how it worked. If you’re not already an expect, that’s the way to knowledge and eventually understanding.

And if you really want some Zen wisdom, there are always the words attributed to Yogi Berra: You can observe a lot by just watching.

24

I was confused by something else in that staff report.

He or she seemed to be saying that Relativity could be construed as saying that we can’t know which is the correct reference frame. But I had always thought Relativity asserts there’s no such thing as a uniquely correct reference frame.

As I think about it, I begin to wonder what the practical difference between these two assertions would be–maybe there’s no practical difference.

But still, the latter is what I’ve always heard, and the former I’ve always thought would be a mistaken way to understand Relativity.

Comments?

-Kris

25

It’s a rather subtle point in ontology, and really shows the evolution of the underlying thought as relativity has grown up.

Early on, writers would generally talk in terms of, “well, there might be a ‘proper’ coordinate system, but there’s no way to tell the difference so we may as well not mention it.” Nowadays you’ll hear more, “there’s no such thing as a ‘proper’ coordinate system. They’re all equally good.”

In practice, the two are identical. It’s more a question of how physicists think about physics than about physics itself.

26

Is there any way you could get me started on doing some research on the evolution of this kind of talk in Relativity theory?

This is, amazingly and coincidentally, directly relevant to an important (to me) paper I’m working on right now.

-Kris

27

If you want to be strictly correct, you can say something like “There is no experiment which can be performed the results of which would distinguish any particular reference frame from others”. If you define a “privileged” or “proper” coordinate system as one which can be experimentally distinguished from all others, then no, there’s no privileged coordinate system. If you define “privileged” in some other, metaphysical manner, then all we can say is that we don’t know if there’s such a frame, and if there is, we can’t know what it is.

28

Best I can offer offhand is to go back and read Einstein’s original papers (SR and GR), and then read a few texts written at points through the last century.

29

Ref: And if you really want some Zen wisdom, there are always the words attributed to Yogi Berra: You can observe a lot by just watching.

Advice that Schrödinger evidently followed regarding his alleged cat. He later reported it was a very unsatisfactory experience.

30

pistachio, I sympathize with you. Relativity is very difficult to understand. It’s also difficult to believe. One book on relativity for the layperson stands out from all the rest that I’ve looked at, which is a lot of books. It’s called “Relativity Visualized” by L.C.Epstein. He could have taught Einstein a thing or to about explaining his theory. I was able to understand Einstein’s book for the layman only after reading Epstein’s.

By the way, the specific question of the barn with the apparently-too-long ladder moving at high speed through it, is dealt with in the book.

I hope this helps. I found reading the book very enjoyable. This book is readable. I take my hat off to Epstein.

31

That was in response to a claim that we say there are four dimensions only because that’s the way we percieve things.

It may be that the person who made that claim got it from the sources you name, or that s/he concluded it his/her own self after a session of pop-philosophy.

But I wanted to point out that in fact, at least some physicists are making a claim a lot like this one. It was in a SciAm article within the past three years (sorry I can’t be more specific than that!). The idea was that you can build up a two dimensional physics which does just exactly as good a job of predicting events in our world as our current three dimensional physics does, and that there is a method for developing in the same vein a four dimensional physics, a five dimensional one and so on. Part of the point of this was to say that it’s, so to speak, “undecideable” which of these mathematical models is the “real” one. I don’t remember if it was explicitly concluded that there could be entities which literally percieve the very same world we live in as a two dimensional one, or not. But I remember thinking, at least, that this was a clear implication of the material in the article.

I hope someone can sweep in with a cite. I looked a bit around but could find no material.

This article frickin’ blew my mind, by the way. That’s why I’m so stupid now.

-FrL-

32

As weird and crazy as this is, it is one of the key mechanisms used in the quantum computers being built in research labs.

33

The statement was “our 4 dimensions … only exist because that’s the only way we can percieve things.” This carries so much hand-wavy, new-agey ontological baggage that it’s complete nonsense as it stands.

As for making physical models with various numbers of dimensions, it’s trivial to do so, but there’s no evidence that more than one choice of “dimension” for a given theory will accord with observations. Two different models can give the same (or at least similar enough) predictions for different settings of “the number of dimensions”, but that’s because they describe things in different ways.

For instance, there’s a kind of function that comes up in mathematics called “harmonic” which turn out to be completely described by their values on the boundaries of their domains. You can talk about harmonic functions on the unit disk in the plane (2-d), while I can talk about smooth functions on the unit circle (the 1-d boundary of the disk), and we can translate between the two. So is the theory “one-dimensional” or “two-dimensional”? Without specifying what general model you’re talking about, making a choice of its number of dimensions is all but meaningless.

But all that’s as maybe. There’s evidence that while some models can be formulated in any number of dimensions, the models for different regions of physics can only fit together for very special choices of dimension.

Upshot: there is only one reality. There may be many ways of modelling it, but you can’t sensibly talk about the number of dimensions unless you pick one sort of model. In this thread we’re discussing relativity, which can be formulated in any number of dimensions, but four gives the best agreement with observations. Nature always has the last word.

34

No, no, I’m sure you have this wrong. Not that “science” in general disagrees with you, but rather, the scientific community is open to the posisbility that you’re wrong.

To my recollection (but note that now I’m resolved to go try to track down the article if I can so I can get really clear on this,) The idea is that you can do a two dimensional model which conforms to observations just as well as a different, three dimensional model does, which in turn conforms to observations just as well as a different, four dimensional model does, and so on through all numbers of dimensions. And just to be clear, this isn’t a vaccuous “they all confrom to observations as well as all the others because they all barely conform at all” type claim. :slight_smile: I mean to be saying the all conform to observations just as well as our normal four dimensional contemporary physics does.

Of course, I’ve just remembered, the article is probably better categorized as being about quantum physics than about relativity. That may be relevant to the point you were making.

But now I feel like I’m remembering there was something in there about the math behind all this providing a promising bridge between the two.

Seriously, I gotta go find the article. I’ll return if and when I do.

Back later…

-FrL-

35

This is the article, but unfortunately, I don’t have access to the full thing, just the first two paragraphs:

http://www.sciam.com/article.cfm?chanID=sa006&colID=1&articleID=000AF072-4891-1F0A-97AE80A84189EEDF

So I can’t go back and reread it online to make sure I’ve got my summary correct.

Sorry. Ignore me I guess! :stuck_out_tongue: :smack: :frowning:

-FrL-

36

I’m wrong about what? There being a single objective reality? Nature always having the last word? Or that “dimension” is a technical term regarding a particular model that doesn’t necessarily hold its same meaning from one class of models to another?

And the fundamental ontologies of these different models are generally different. I’m pretty sure you’re either thinking of so-called “holographic” models (which are analogous to the example of harmonic functions and their boundary values I mentioned) or of a “there may be higher dimensions”, which nobody seriously disputes anymore. What those articles take as read is that the point is to adjust the dimensionality of this model of relativity and that model of quantum field theory until at some point they can be fit together.

This is another sticking point. Four dimensions hasn’t been “contemporary” to working physicists for a very long time. Back into the '70s (maybe even '60s), quantum field theorists allowed the dimension of spacetime to be a variable in the theory. That doesn’t mean that they thought all different values were equally good – just that it should be open until there was good reason to pick one value.

37

Exactly as I thought. It’s about a holographic model, which is a fundamentally different sort of model from the standard ones. It’s exactly analogous to the situation for harmonic functions I was talking about before.

You talk about harmonic functions on the disk, I talk about smooth functions on the circle, and we can translate back and forth. The two models are completely different sorts of things, though, and in physics the holographic models have a much different ontology than more conventional models.

If you talk about a model of relativity theory, fixing the number of dimensions has a meaning. If you talk about a model of a holographic theory, fixing the number of dimensions has a completely different meaning. The models are different, and the terms have different meanings in each.

38

Well… I’ve happened upon a copy of the entire article online, but I strongly suspect this copy is not supposed to exist where it exists, since it’s proprietary to SciAm and this web address is not a SciAm web address. So I guess it is not allowed for me to link to it.

And I guess it is not allowed for me to quote passages from it.

I’ll try to summarize some though it’s complicated:

Leonard Suskind at Stanford showed that the entropy of a given area of space is directly related to its boundary area, not to its volume. Susskind thinks a good way to explain this is by appeal to facts about holographic surfaces (I’m not 100% clear what that means) and it is apparently a consequence of these facts about holographic spaces that, given an area of space and a physics holding within it, a physics holding just at that area’s boundary is mathematically equivalent, even though that physics is of a dimensionality one smaller that the dimensionality of the area itself.

So if you’re talking about a 3D area, there’s a 2D physics describing the physics of the surface of that area which is, apparenly, mathematically equivalent.

This could even apply to our universe at large, if we can model it as having a boundary of some kind. Some theorists (unnamed in the copy of the article I’m looking at, apparently named in a sidebar in the original) have shown that a universe described by a superstring theory in a particular sort of spacetime is mathematically equivalent to a quantum field theory defined only on the boundary of that spacetime.

If there are creatures inhabiting such a universe, there would be no means for them to (or even sense to the notion of) determine(ing) whether they “really” live in the 5D spacetime or the 4D surface.

And for all we know right now, our 4D world is the surface of a 5D spacetime, or else, has a 3D surface which is such that other entities in our universe may find it more natural to talk about space as though it were 2 dimensional with a single temporal dimension.

My earlier summary wasn’t totally right, but you can see what’s going on here. Kind of mind boggling IMO.

Could we determine about another entity that he was percieving space as 2 dimensional (or 4 dimensional) instead of 3 dimensionally like us? It seems to me that if the entity uses language, this would issue in a dead giveaway. But if they have a language and they also see things so differently than the way we do, how could we ever understand their language? But surely we should be able to interact with them as meaningfully as we could with any aliens who are percieving 3Dimensionally like us–we are all living in the same world, moving the same objects around in the same ways. We just “see” it differently.

I can’t wrap my mind around it.

-FrL-

39

When I said “no no I’m sure you’ve got it wrong” I didn’t mean you were wrong that there’s only one reality. I was expressing an idea that this one reality may not be inherently of any particular dimensionality, but can rather be modeled as having any of a number of different dimensionalities.

I now understand your original reply to me much more clearly having re-read the article and your more recent posts. I see you and I don’t really disagree, though you are in posession of a few more facts than I am. :slight_smile: (Most relevantly, the fact that, as you put it, “There’s evidence that while some models can be formulated in any number of dimensions, the models for different regions of physics can only fit together for very special choices of dimension.”

Hey, umm, is there anywhere online where I can begin to learn about the harmonic function/boundary function duality (for lack, to me, of a better term at present) which you mentioned? I’m reasonably intelligent, though I know little more than beginning calculus. If its impossible, I understand.

-FrL-

40

Yes, the article can easily be found and the following is a fair use cite of the relevant paragraphs:

This is exactly as Mathochist described the notion, and Frylock, your earlier contention that “I don’t remember if it was explicitly concluded that there could be entities which literally percieve the very same world we live in as a two dimensional one, or not. But I remember thinking, at least, that this was a clear implication of the material in the article.” is quite wrong.

There are a number of problems with 2 and 4-dimensional spatial universes. In neither do gravity behave the same as in a three-spatial-dimensional universe, e.g. We can easily show that neither describes our space. This is not at all equivalent to the notions talked about in that article.