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Ecowiz Returns
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Portugal
Aug 2001
time: 05:18
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quote:
Originally posted by Lung
Another way to look at it is this:
If you walk along the equator and see a longitudinal line perpendicular to the equator. Just to be sure, you measure the angle, and sure enough, it's 90 degrees. You walk another couple of hundred miles, and you see another. Again, you find it's 90 degrees. You turn and follow the longitudinal all the way to the north pole, only to find the other longitudinal line you passed earlier! However, if they were the same angle, they must be parrallel, right? Wrong. Why? Because you've applied 2 dimnesional geometry to a 3-dimensional world. Applying 3-dimensional geometry to 4-dimensional spacetime will also fail. in other words, your straight line is another dimension's curve.
At least that's my understanding of the geometry of multidimensional spacetime  |
Lung:
Although your example gives a good explanation on the efects of aplying 2 dimensional geometry to a 3 dimensional world the problem I see is this:
In your example, the two 2 dimensional paralel straight lines are actually two 3 dimensional intersecting curves. Ultimatelly, if I were to walk in a 2 dimensions straight line, forever, I would ultimatelly drawing a circular form.
In time-space we are called to believe that a 3 dimensional elipse is actually a 4 dimensional line which is, exactly, the oposite result.
How can this be?
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Lung
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of my princess Anastasia!
Mar 1999
time: 15:18
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quote:
Originally posted by Ecowiz Returns
In time-space we are called to believe that a 3 dimensional elipse is actually a 4 dimensional line which is, exactly, the oposite result.
How can this be? |
Buggered if i know!  
Sorry, i think it was just my way of grasping something i read from Stephen Hawking or Timothy Ferris (not the INXS variety!). I guess the point i was making was one of perception. When you walk around the world you are of course walking in an enourmous circle, even though you appear to be walking straight. It is a perception that is misleading. We do apply our 3-dimensional geometry to space, and end up with the confusion over how gravity works.
Another way, i found, of viewing space in a gravitation field is having a 3-dimensional grid where an object, such as a planet, draws the gridlines into it by a degree relative to it's mass. At a certain speed, a small object passing the planet will follow the gridlines, so in a way, it is moving straight. The point is that gravity distorts space, and i found this to be a good way of conceptualising it.
I may be wrong, but i feel i understand gravity. Am i deluding myself? 
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MrWhereItsAt
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New Year's Resolution: 2005 is the year of Where It's At - come get some.
Nov 2001
time: 17:18
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In the current theory, no particle can travel FTL, thus limiting the EM force to this speed. Thus, if you have two particles that can interact electromagnetically at opposite ends of the universe, the "information" of interaction from one to the other would take that 14 billion years or whatever to reach the other, and vice versa. BUT, unless the particles were created from energy (can energy in any form NOT interact with anything else?), the particles were always there - including at the beginning of the universe, when they were in the same place.
But at this point the laws of Physics are open season. After some expansion of the universe, the forces we know of, Gravity, EM, Strong and Weak, "crystallize" out and become distinct. At this point, the two particles could start interacting. BUT, since their interaction can only travel at the speed of light, if the Universe itself was expanding at FTL (and how would you define or measure this, since your measuring device is expanding at the same velocity!), then these two particles, unless they moved closer together by some other means, would NEVER be able to interact! That is, unless the Universe DOES eventually slow down and start to contract.
And all this is conditional on the speed of light being absolute, not just in the Universe as we measure it, but absolute when measured by some hypothetical way OUTSIDE our Universe, looking at the expansion of the Universe as well!
As if I haven't confused everyone (and myself) enough, I just had to say something in response to someone's post on the first page that sent me into paroxysms of Physics-class induced horror - there is no "universally accepted" quantum theory of gravity at present. String theory is not convincing enough to be taught as part of any GUTS or TOES.
Though one can hope.
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Rogan Josh
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I just wrote a lenghty response to Lung and Mrwhereitsat and then the bloody browser crashed!!! 
Briefly....
Lung: it really depends what you mean by 'interaction' . If you mean 'exchange a photon' (which is how I would define 'interact') then yes it would take them 14 billion years. If you include the collapse of a mutual wavefunction in your definition then it is instantaneous. Your objection then becomes the EPR paradox.....
I wanted to point out to Mrwheritsat that the expansion of the universe is a large scale expansion. The metric locally is not expanding in this way, otherwise you would not be able to observe the expansion because your 'ruler' (and you) would also expand making everything look the same.
quote:
Originally posted by LightEning
A virtual photon is "sent" (forgive me for not knowing the proper vocabulary) from electron A to electron B (A and B being, of course, as far away from each other as necessary). However, before the virtual photon gets there, electron B bumps into a random positron C that got into its way, and annihilates. What happens to the photon? (since I have never seen the answer to this question, I figure it's probably irrelevant, but I'd like to know it anyway) |
this was what I was meaning earlier about the idea of virtual particles being misleading. In some sense, the virtual particle is guaranteed to meet the other particle before it is emitted, or put another way, it would not be emitted if it wasn't going to meet the other particle. This doesn't really make sense in terms of cause and effect but the quantum theory which is underlying the analogy is still sound. It is just the analogy which is breaking down. Indeed, in what sense can the virtual particle be said to exist at all since it is by definition, unobservable.
Feynman's explanation was that there is a sort of sum over all possible histories. The virtual particle takes all possible routes out from its parent, and the physical reality is a superposition of all of these possible realities weighted by the exponential of (i times) the action (I am not going to go into the definition of the action, but think of it as how 'difficult' the journey of the particle is). The paths with high action interfere with one another and cancel out, leaving the actual reality as (approximately) the path with least action.
Hmm... this is hard to explain without the maths....
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Rogan Josh
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quote:
Originally posted by Adalbertus
Btw: Is there someone who has studied the subject who can tell if gravitational waves can be deduced from Einsteins Field Equations? If gravitational waves are more than speculation, gravitons can be "simply" explained as the quanta of gravitational waves in the same way as photons are quanta of electromagnetic waves. |
Yes. Since Einstein's Field equations are exactly that - field equations - they have solutions which are fields, and therefore gravitational waves. Therefore, a graviton can be thought of a quantum of these fields. The theory actually looka a lot like electromagnetism.
The problem is that when you make the theory quantised you find that every observable depends on the physics applicable at the Planck scale (or some other cut-off scale). In other words there is no factorisation between the physics of gravity at our energy scale and of very high energy scales, meaning that we have to understand the physics at these high energy scales to explain the physics in our realm of experience. This is not nice (technically we say the theory is non-renormalizable).
There is an even better problem with gravity though (which I mentioned earlier but was ignored). Why is it so weak? If gravity is so much like electromagnetism, shouldn't it have a similar strength? But look at the molecules in your body - they are held together by electromagnetic effects, but these electromagnetic effects are strong enough to counter the gravitational pull on the atoms from the entire Earth! If electromagnetism and gravity were of similar strangths we would all be crushed to nothingness - ripped apart by the Earths gravity!
In fact gravity is roughly 10^17 times weaker than elecromagnetism. This is a huge number and is thus far, completely unexplained.
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Ecowiz Returns
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Portugal
Aug 2001
time: 05:18
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quote:
Originally posted by Adalbertus
A fixed point in space isn't necessarily at rest in any inertial frame (in the view of general relativity). Someone falling out of a plane is at rest as long as you can neglect air resistance. When you are sitting on your chair, you are not. |
That much I can understand.
What i have some trouble in visualising is how something that is (more or less) "drawing" a closed curve in a 3 dimensions representation is said to "draw" a straight line in a 4 dimensions one.
For the sake of the argument lets assume that the Earth indeed draws an exact elipse around the sun, in our intuitive 3 dimensional scope.
If I disregard time, I could state that the Earth would eventually return to some point in space where it already had been.
When I add the time dimension I have to say that, in fact, the Earth never returns to the same space-time point, for time as elapsed. We would have a kind of cilindrical elipse, but hardly a straight line, wouldn't we?
The way I see it, it is not intuitive at all that, by adding another dimension to someting I end up with a simpler, rather than more complex geometrical shape.
I really can't see where I'm wrong, although I'm sure I must be (otherwize, someone else would have stated this same argument, I supose).
I also don't see the use of that "curve is actually a straigh line" rational in explaining the "small hole" is space-time caused by mass that seems to ilustrate the gravitational effects.
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Adalbertus
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Cologne, Germany
Feb 2001
time: 06:18
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quote:
What i have some trouble in visualising is how something that is (more or less) "drawing" a closed curve in a 3 dimensions representation is said to "draw" a straight line in a 4 dimensions one. |
You've answered that part already in your post, in four dimensions the path of the moon is a sort of spiral.
quote:
When I add the time dimension I have to say that, in fact, the Earth never returns to the same space-time point, for time as elapsed. We would have a kind of cilindrical elipse, but hardly a straight line, wouldn't we? |
In some sense, it is. The problem is that we normally think to know what is a straight line. Then you have to define it in some way. The most practical way is to take the paths of the light in vacuum as straight lines, also in four dimensions.
On earth, this fully agrees with our notion of straight lines.
One of the first tests of General Relativity was to take a photograph of the sun and surrounding starts during a solar eclipse, and of the same stars later when the sun was far away. One has found that the stars that appeared close to the sun apparently moved apart, and that even stars were visible that should have been hidden by the sun. The reason is that the gravitational field was such that the sun attracted the light (from a flat geometry point of view), or that spacetime around the sun was curved.
Note that we cannot know the "truth" about the geometry. We can measure the universe as we like to. You can make up a theory with a flat spacetime, and an attractive force of the sun to light. The only problem is that this theory would become way more complicated than the theory with a curved spacetime is.
(To get a better notion of the problems with a curved geometry you might find something in a good atlas, when it comes to the problems of drawing a world map. It is impossible to draw a flat world map in which all shortest paths on earth show up as straight lines on the map. Things are similar in a curved spacetime).
So the next thing you'll probably ask is the following: The deflection of light by earths gravity is not noticeable, one has a hard time to see this from the sun, why is the path of the moon so much more curved than that of light?
The answer: Earth curves spacetime but the moon does, too. This gives a far stronger effect than of the earth alone. And the path of the moon is not very strongly curved. You can see this by a short estimate: The velocity of light is the conversion factor time - space. The moon is a bit more than a light second away from us. It takes one month for a turn around the earth. Which is that said spiral has a ratio of radius :thread height of about 1:2419200. To me, this is quite straight.
quote:
In fact gravity is roughly 10^17 times weaker than elecromagnetism. This is a huge number and is thus far, completely unexplained. |
The antropic principle would simply state that if gravity were as strong as electromagnetism, everything had ended up in a black hole or complete void, as gravity is (at least mostly) attractive; thus there were nobody to notice that situation. Of course it doesn't help here.
I just had a look in a handbook of physics, and found a table of the strengths of the fundamental forces
strong interaction 1
electromagnetism 1/137
weak interaction 10^-14
If the numbers are comparable to what you state, gravity should go in as something like 10^-19, which I would not see as too far off. Electromagnetism and weak interaction were the first to be unified.
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Adalbertus
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Cologne, Germany
Feb 2001
time: 06:18
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quote:
If you want to talk coincidental numbers - |
Given the error some of your data have, such as "number of particles in the universe" or "size of universe", it's rather coincidental orders of magnitude.
Let's discuss real numbers, small ones:
We perceive four dimensions, one of which (time) is somewhat weird.
We perceive four fundamental forces, one of which (gravity) is somewhat weird.
Why?
quote:
This thread isn't teaching me about gravity sadly, though that's entirely my fault I'm sure |
Maybe it's not only your fault, there are many intelligent people who don't have a clue on general relativity. And there are two inherent difficulties: Most people who are untrained in university maths have difficulties in understanding geometries other than the usual Euclidean, or a spacetime other than our normal Galilean. And even if they did there are huge problems in communication inherent to the subject: To get some decent and mathematically correct understanding of GR, you have to take a one year's course at the university (I didn't get through all of it because of other interests...), after having done physics for some time. It is close to impossible to fit the essentials of what you've learned in this time into a post which roughly stays in limits (Imagine writing a data compression software such as zip which reduces the size of any given file by a ratio of 1:10000). And scientists aren't really famous for their communication skills.
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26-03-2002 15:53
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