General Relativity.

In my effort to understand general relativity, I have pondered the attributes of space as is required. I have tried to build a model of understanding that is consistent with what I understand regarding other things, and I am sure this is how most understanding comes about. Most analogies of this curvature are done so as a two dimensional representation as opposed to a three dimensional one due to the difficulty in visualizing a 3-D model. This bothers me to the point at which I feel that since the space we are familiar with is three dimensional, then we should be able to visualize this three dimensional curvature. The only analogy that I can use to make sense of this is to ascribe a “density” to space, and therefore an increase or decrease in “density” for space that is curved. This leaves me wondering with respect to what is this “density” increasing or decreasing?I come about with this idea because one idea calculus reveals to me is that the slope, or curvature, of one “thing” is dependent upon the instantaneous value of another, wholly independent, absolute “thing”. The curvature of space depends upon your location in space relative to a gravitational field. I see the curvature of three dimensional space as being the increased or decreased density of volumes of conventional spatial units (call them Planck lengths) per “something”. Is the “something” I am referring to a gravitational field itself (I wouldn’t think so considering the magnitude of a gravitational field varies according to your location in space and not absolute as my definition requires)? Is matter compressing “empty space” as it occupies this region of “something” and therefore “compressing” “empty space” relative to this “something”? If not, then where is matter located? Does it make sense to ask what is inside an electron or a quark, and if there isn’t anything (or if there is no "inside"), then where is the space that it “occupies”, or does the space simply become part of the matter? Is this “something” an entity separate from space and subsequently an absolute property of the universe with respect to which all things can be considered?Is this a correct line of thinking considering, as I understand it, there really is no sense in ascribing density to something such as space since it is merely a void? After all, how do you have more of a void in one location? How do you have more units of “space” per unit space, hence my calling the latter “something” instead of space? Perhaps I have completely missed something in my attempt to understand these things, thus the immense confusion, or perhaps this is why a three dimensional model is never used as an aide in understanding.

Cavediver: I am aware of this as this is the consequence of the increasing and decreasing density of spatial curvature. It would seem to me that all things traveling at constant speeds are actually traveling in straight lines, it is simply the fact that the space they are traveling through is more or less dense, making their trajectory appear to be curved due to the way in which we perceive space.What confuses me about this idea though, is with this increase in density of space around an object with mass, why does your speed increase when you have to traverse more space? I’ll clarify; if you are traveling at a constant velocity, I assume this means that you are flowing through a certain number of spatial units per unit time and this ratio is constant, regardless of an increase in spatial density (I don’t want to misuse the term metric-field, but perhaps this is what it is). If you approach an object with mass, this number of spatial units is becoming more numerous and there are more “lines of magnitude” of a metric-field, I suppose.This would seem to tell me that your motion relative to this object from a third observer would appear to decrease as you approach this object since you are having to move through more and more spatial units the closer you get (after all, you are moving at a constant velocity through curved space). This seems counter to the idea of gravity since gravity should increase this ratio of spatial units per unit time. It seems that either I have it backwards, meaning the density of space decreases around an object with mass so that from a third observer your velocity increases, or I am just thinking of it incorrectly.Of course using this approach, you would still think you are traveling at a constant velocity the whole way, and so would the object you are moving toward. Is this freefall? Maybe this is where my confusion arises; is the distance between two objects a measure of the amount of spatial units between them, or is there some other standard of measure that is independent of spatial density?I will digest the rest of your last post regarding the link between mass and curved space for a bit longer before I reply, I’ll leave you with this for now.

Xeriar: Regardless of how a third observer perceives my motion relative to theirs, I would experience time just the same, right? Perhaps that's what the "more appropriately ..." was about. If my clock were ticking slower, and I were traversing fewer spatial units per these slower ticks (from 3rd observer's perspective), perhaps they would cancel? But if they cancelled, there would be no revelation, and they would only cancel if they were inversely proportional, which they aren't. So, if apparent motion slowed more than time dilates, (one slowed down tick allows me to traverse less space) my apparent motion through space would decrease, which wouldn't match observation. Conversely, if time dilated more than my apparent motion slowed (one slowed down tick allows me to traverse more space), there would be a resultant apparent increase in my motion relative to the 3rd observer which matches observation. Does this seem to make sense?By the way, thanks for the insight cavediver and xeriar!Edited to clarify previously potentially indiscernible post.This message has been edited by madeofstarstuff, 09-21-2005 02:32 PM

I don't think that intensity of light and energy of a photon have anything to do with each other because energy is merely an attribute frequency, not intensity. As for answering Ben's question, no clue here, good one though.This message has been edited by madeofstarstuff, 09-21-2005 05:00 PM

I was talking about individual photons, as was Ben, I believe. I thought the photoelectric effect showed that the energy of light is directly related to its frequency and comes in packets. If you crank up the intensity of low energy (low frequency) light you don't get electrons. If you increase the frequency, remaining at a low intensity, you get electrons. If you increase the intensity of high frequency light, you get more electrons. Higher frequencies of the same intensity give you faster moving electrons. This is how I thought it worked. As for the intensity of an individual photon, I've never come to an understanding of this idea. Perhaps this is where I am misunderstanding.I must have misread someones post originally as it all seems fairly correct now that I reread it. Either way, this really has nothing to do with the intent of Ben's question in the first place.

The picture you chose here lays it all out. The way I understand it is as follows, someone tell me where, if I am wrong. The energy associated with any given single, solitary photon is related to its frequency, and also varies with varying frequencies. A coherent (completely in phase and of the same frequency) light wave (many photons) oscillates at some frequency with its amplitude defined as the number of photons in that wave having the same frequency. The amplitude of a light wave is the intensity of that light wave. Inquiring about the amplitude of a photon is the same as inquiring about the intensity of a photon. I would assume from this (perhaps this is where I misunderstand) that the intensity of any individual photon, regardless of it frequency, is the same, namely one (choose your unit of measure) photon. This is where I come to the understanding that the energy of a photon corresponds to its frequency and has nothing to do with its intensity since intensity is the same for any one photon.This message has been edited by madeofstarstuff, 09-28-2005 12:07 AMThis message has been edited by madeofstarstuff, 09-28-2005 12:11 AM

RL: What is the volume of a photon? It seems intuitively obvious that a single photon should have an amplitude. Most things in this realm, however, go against some level of intuition. I just don't see, given the results of the photoelectric effect, how intensity/amplitude should differ between one photon of one frequency and any other photon of any other frequency? I further conclude that the energy of a photon is independent of its intensity/amplitude?Why this is so, and what frequency and energy have to do with one another outside of just saying that E=hf, is what Ben is asking about, I assume. If amplitude and intensity are synonymous in your usage here, then you have to adopt a different understanding of light due to the results of Einstein's work on the photoelectric effect.

Yes, I realize that, and it is way over my head! I tried picturing it, but still couldn't completely get my ind around it. I will have to reread again.

"To find the intensity, take the energy density (that is, the energy per unit volume) and multiply it by the velocity at which the energy is moving."Taking this to heart, then seeing as though the energy of a photon is dependent upon its frequency, and the velocity of light is constant, then for the same intensity of varying frequencies the energy of the light is varying as well. Another indicator of intensity of light not influencing the energy of that light."The term intensity has a particular meaning here: it is the number of waves or photons of light reaching your detector; a brighter object is more intense but not necessarily more energetic. Remember that a photon's energy depends on the wavelength (or frequency) only, not the intensity."from Electromagnetic RadiationThis site specifies that energy is dependent upon the frequency only, no mention of amplitude. Nowhere can I find a description of the amplitude of a single photon. This is all very interesting as I have never thought of all of this in this way. I am familiar with the self-sustaining, propogating, electric and magnetic fields, as that is what a beam of light is. I never thought they were in phase as it appears to be shown in the latest picture, I thought they were ninety degrees out of phase as well as ninety degrees perpendicular. Oh well.Any help on finding something regarding the amplitude of a photon particularly would make me feel better, as the only thing I see is in regards to Intensity = amplitude^2, which requires many photons, as I see it.This message has been edited by madeofstarstuff, 09-28-2005 08:41 PM

I have also found this: at this location: http://members.aol.com/photonics/willis.htm#AmplitudeI would have only linked the website if it were short, however, this was pretty far down the page. This says that the amplitude for every frequency of every individual photon is the same. Does this seem right?

RL: How about, the frequency of a photon is a byproduct of its energy. Is that better wording or more accurate? But what I am trying to say is that you can't increase the amplitude of an individual photon because every individual photon's amplitude is the same regardless of the frequency. If you want more amplitude, you add more photons, which, in turn, increases the intensity of the light. I'm not so sure about this. White light isn't composed of a bunch of photons all having the various characteristics you mention of white light. I think it is a bunch of photons of all different frequencies, and consequently colors, that make it appear white, as white is an amalgam of all colors. These can be separated, as I'm sure you know, through diffraction. Your statement is only true, as I understand it, for a coherent light source, i.e. laser.All of these things being said, I maintain that the frequency of a photon is directly related to its energy and that the energy of an individual photon only changes for changing frequeincies. The amplitude of a photon of any frequency is the same, and intensity is a measure of photons (smallest possible packet of energy still related only to frequency) per unit time and related squarely to amplitude. I have seen no evidence contrary to this, only more evidence corroborating this. You have provided insight, but only relating the wave properties of photons to sound, which doesn't seem totally analogous. Perhaps there is something lost in the translation of thinking about photons as sound waves.

Thank you Justin, I realize that I don't totally understand all about light, but am trying. I have said that something is lost in the translation of thinking about photons as sound waves, but it seems that some things are gained as well. I knew that it wasn't totally analogous.By the way RL, just because your reasoning was sound in the following revelation, I had to find out: Microwaves | HowStuffWorksJust because I didn't know and it is pretty interesting.

I have posted some ideas I have regarding GR and am curious as to whether they are even in the right ballpark. They are now at least a couple of pages back due to the slight departure from topic. If anyone who knows a lot about this stuff can take a look, I would appreciate it, thanks.

I didn't take it as condescension, it is a confusing yet fascinating topic that leads the layman such as myself down the rabbit hole. Nevertheless, we all perceive it, so it seems that there should be some way of seeing its true colors some way (pun intended).

I just watched the first one and it was very interesting, thanks. I have never before heard the relation of the spinning vector determining the probability, that was a bit insightful. I will watch the rest when I have more time.