General Relativity.

What is the exact relation between Special Relativity and General Relativity?Is it just that in SR spacetime isn't curved? As in, two straight lines through spacetime (constant speed and direction) view each other as inertial, yet in GR two inertial frames can be viewed as relatively accelerating from each others frames, which is a prediction of spacetime curvature?Also, does spacetime curvature just mean non-Euclidean geometry? In this way, it's not necessary to view spacetime curving into other dimensions as we see in the analogies involving two dimensions?

Here's another one I don't quite understand. How does time dilation, length contraction, and relativistic mass fit into general relativity?In other words, how does the time dilation that is caused by a gravitational field relate to time dilation between relative observers with different velocities?I can understand these phenomena based on Lorentz transformations and the fact that they are analogous to "rotations" in spacetime, so at different velocities observers are witnessing different "angles" of each other. But how do I interpret these effects caused by a gravitational field?

That was actually kindof illuminating. Through I'm having a trouble seeing how you are moving wrt your light cone when you accelerate. Do you mean that you are moving with regard to the axis of your light cone?This message has been edited by JustinC, 09-16-2005 06:55 PM

One last question that may clear things up for me. In GR, is there a distinction between "real" acceleration and apparent acceleration. Because I know that if two observers are following intertial trajectories in curvered spacetime they will view each other as relatively accelerating, but is this relative acceleration different than the acceleration in the light cone you are referring to?

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You are now effectively moving wrt your light-cone. You have also accelerated to get there, and if you think about this in SR-terms, you are going to experience a real time-dilation. It is quite possible that you are not now moving wrt a distance observer. But you are still moving wrt to your light-cone. E.g. stood on the earth, where you light-cone is pointing inwards towards the centre of the earth (actually, slighlty to the side becasue of the rotation) Thus you would expect to see a real time-dilation wrt someone who isn't fighting their light-cone so hard.

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I'm trying to think about this in terms of the "Clock Postulate" of special relativity. The problem is, I can't see where the symmetry is broken between the two relatively stationary observers.If two observers are accelerating at different magnitudes, and we want to know how they view each other's clock rates at a given instant, we just take the instantaneous velocity and find gamma. They will both view each others clocks as slowed down by that factor. Is this a correct consequence of the "Clock Postulate"?If it is, where is the symmetry broken when two people are at different heights in a gravitational field? Even though they are fighting their world lines differently, wont there still be an instantaneous velocity (using their accelerations with regard to their respective world lines) between them and wouldn't special relativity imply a symmetry in how they view each others clocks?Where am I going wrong?

I think you guys are extremely confused about the nature of light. You are trying to combine the particle model and wave model into one unified model. There is no easy way to do this. The subject that deals with predicting the behavior of photons is quantum electrodynamics.

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frequency is related to the amount of energy in that, in a period of time, a higher frequency will carry more energy than a lower frequency.

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This is not true. The formula E=hf determines the energy of a photon based on the frequency of light. This energy is delivered in a packet, a quantum. There is no mention of any period of time going by.

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but the actual amount of energy carried by a photon is measured by amplitude.

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If light was a wave, then the energy of light would be determined by the amplitude. It's not, as several experiments have shown. Look up the photoelectric effect.

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frequency is measured by oscillations per unit of time. how is that not mentioning time? the way i see it, a higher frequency has more oscillations, that means the 'waves' of the electric field and the magnetic field are closer together. this means that the packets of energy are closer together. therefore more energy would be transfered in one second of a 2Hz wave than in one second of a 1Hz wave. am i right?

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I'm not an expert on this subject either, so don't take what I say as gospel. Light was traditionally thought of as a wave in an electromagnetic field. Different types of light were ascribed frequencies. Later, around the turn of the century, it was discovered that light is actually composed of particles, called photons.One piece of evidence for this is the photoelectric effect. Light was shined on a metallic surface. As you increase the intensity of light (I= Energy/Time/Area) the kinetic energy of the electrons coming off the surface was the same. This only makes sense if light is composed of discrete packets of energy, quantum (actually, it can also be interpreted as the electrons only absorbing a certain amount of energy, but further experiments have confirmed that light is a particle). E=hf is the formula we use to figure out how much energy these packets deliver. When light was interpreted as a wave, it was ascribed various frequencies. These frequencies can be related to the energy of the photons of that light by that formula. h is called planck's constant, and is a constant of proportionality.Quantum electrodynamics says that light is composed of photons (actually just one type of photon, different observers view it differently from different frames of reference, i.e., red shift and blue shift). In order to see what will happen in a give experimental setup, you have to figure out every path the photon can take. This gives a probability that the photon will start at a given point and end up at a specified point.In some setups, there is an interference pattern, i.e., it seems like it is behaving like a wave. But it is not a wave. You can dim the light so that is only sends one photon through a given experiment. Each will produce a tiny mark on a photosensitive screen. As more photons go through the setup, an interference pattern develops. Photons of different energy produce different interference patterns, and this was interpreted as different wavelengths/frequencies of light.In different experiments, no interference develops. It all depends on the experimental setup.This may be unclear, so look of the "Two Slits Experiment" to see what I mean.

You guys should pick of the book, "QED", by Richard Feynman. It is based ona series of lectures he gave to the laymen in New Zealand on the subject of quantum electrodynamics. Very informative with regard to the nature of light, and the mysterious wave/particle duality.Feynman is probably the greatest physics teacher of all time, so the book isn't hard to read at all but gives one a deeper understanding of the subject. You may not be able to explain light to someone at the end, but you'll be able to spot mumbojumbo from a while away.

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yeah i've read a little bit about planck's constant. its just hard to remember so much, especially when i've learned most of it in the last few days. the two slits experiments is a pretty easy way to show wave-particle duality, but it seemed more and more clear to me as i studied this how wave-particle duality worked. i don't know if thats from naivete of the subject or what. early in my investigations i saw how frequency was the amount of oscillations, or number of crests in the wave, per second. then what 1.61803 said made me realize that these oscillations are the movement of a photon and some other particle

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This is where you are going wrong. An electromagnetic wave is not a photon travelling up and down as it traverses as distance. In the wave model, light is a distrubance in an electromagnetic field. The field is the medium and it self propogates (i.e., the electric part of the field induces the magnetic part which induces the electric, ad infinitum). Remember, a wave is energy. No "thing" actually traverses the distance the wave is travelling, only the energy. Think of a water wave, the peaks and troughs travel the distance, the water only travles perpindicular to the distance and eventually rest back to where they started (ideally). For light, you can think of the electromagnetic field as the medium through which the wave travels (i'm not too sure how accurate this analogy is, but I've heard it before). Waves can have different frequencies. When different light was projected on the two slits experiment, different slits formed. This was interpreted as different frequencies. This is also true of many other experiments.The particle model describes light as packets of energy, photons.Photons are not mentioned in the wave model and waves are not mentioned in the particle model. You can't think of a photon travelling up and down like a wave.These two models were combined in quantum electrodynamics. Synopsis: Light is particles. In some instances when you calculate the probability of events, it produces interference patterns, in others it produces no interference. It acts like waves and particles. The same goes for all subatomic particles.Now a key point is that QED doesn't provide any sort of mechanism for picturing this. It isn't a mechanistic theory. The core is that only probabilities of events can be calculated. Why? No one knows. No one understands it.This message has been edited by JustinC, 09-30-2005 06:02 PM

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your second paragraph seems to further my premise that amplitude is the energy carried by individual photons, or packets as you put it, and not the entire group.

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Amplitude has no meaning in terms of photons, seeing as they are particles. Niether does frequency for that matter. But for practicle matters, one can think of light of light as different frequencies and this gives good results with experiments.

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Why would faster spinning of that little vector mean higher energy?

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Keep in mind i'm a layman.It seems you are trying to think of QED as a mechanistic theory. The spinning vector has no physical analog. It is a device used to calculate the probability of events.Maybe a better question would be "why do higher energy photons have faster spinning vectors in QED." This probably has to do with the deeper math of QED, which Feynman greatly simplified for us mortals with his notation of spinning vectors. I think it's more of a mathematical notation question than a physics question, since there is no physical analog of a spinning vector.That's my two cents.

What he's talking about is slightly different. According to quantum mechanics, light is a particle, like electrons, quarks, etc. These have properties which we would normally associate with waves.But what is a particle? That's what that quote is talking about. I'm pretty sure the implications for that apply to all particles. Cavediver talked about this a couple time (i think), but it is way beyond me.I'm just talking about QED, which is probably the most verified theory in existance. I'm not sure the coupled oscillator interpretation deduces to QED and whether it is a highly accepted interpretation. Either way, it is beyond me.Even if that is the correct interpretation, you should definately learn QED first then move onto stuff like that if you wanna get a deep understanding. Going straight into that stuff would be like learning General Relativity your first day of physics. You need to appreciate Newtonian Mechanics and then Special Relativity and then General Relativity.It's seems the analog with light would be: wave properties, particle properties, QED, then phyics which will make the feeble mans mind explode.This message has been edited by JustinC, 10-01-2005 01:42 AM

You keep mentioning "the spiritual" in your posts. Explain what you mean by the term and why we should believe that such things as "spiritual universes" exist.