FAQ (Frequently Asked Questions) - Read this before posting!

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FAQ (Frequently Asked Questions) - Read this before posting!

Postby Keiji » Fri Mar 17, 2006 9:36 pm

Q. Has anything related to the fourth dimension ever been observed?
A. Not that we know of as yet.

Q. How to visualize 4D?
A. For some people this is easy, for others it is hard. There are many Java applets around however that can get you used to seeing in 4D - e.g. by showing a rotating tesseract.

Q. What does this term mean?
A. Take a look at the glossary.

Q. Isn't time the fourth dimension?
A. Some people consider this so. However, on this forum the general assumption is that time is not a dimension. If you wish to discuss time as a dimension, head to the Relativity & Time Travel forum.

Feel free to add more quick questions to this topic. Any silly posts in this topic will be deleted without warning.
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Postby moonlord » Sat Mar 18, 2006 7:26 pm

Q. Has it been proven there is / there isn't a fourth spatial dimension?
A. None of them. We are working on pure hypothesis.
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Postby jinydu » Thu Mar 30, 2006 8:42 am

Q: What is a dimension?

A: Mathematically, the dimension of a vector space is the number of vectors in a basis for that vector space. That is, the dimension is the minimum number of vectors {v1, v2, v3 ... vn} such that any vector, v, in the space can be written in the form

v = c1v1 + c2v2 + ... + cnvn

where c1 ... cn are scalars

Q: Is it possible to study 4D space (and higher dimensional spaces) without being able to visualize it?

A: Yes; it can be done solely through mathematical reasoning. There are already many theorems about higher dimensional spaces in calculus, geometry and topology.

Q: Why is it not possible to reach the speed of light?

A: According to Einstein's Special Theory of Relativity, the energy of a particle (in a particular reference frame) is:

E = sqrt((mc^2)^2 + (pc)^2)

where m is the particle's rest mass, p is its momentum and c is the speed of light

Furthermore:

p = gamma * m * v = (1-(v/c)^2)^(-1/2) * m * v

As v -----> c, gamma -----> infinity, so p -----> infinity and thus E -----> infinity.

Thus, an infinite amount of energy is needed to accelerate a particle to the speed of light.

Caveat: This argument does not take into account potential energy. But unless you can find a way to make potential energy decrease by an infinite amount, the argument still holds.

Q: Is it true that according to relativity, when your speed approaches the speed of light, time slows down, lengths contract and your mass increases?

A: Special Relativity is mainly concerned with two things:

1) Determining which quantities are the same in all inertial reference frames.

2) Given a description in one inertial reference frame, determining what happens in another reference frame.

The second objective is done by expressing everything in the original frame in terms of four-vectors, and then applying what is called a Lorentz transformation (i.e. multiplication by a 4x4 matrix of a particular form).

Time and length are quantities that vary from one reference frame to another. Suppose we have a clock and a ruler, with no relative motion between the two. Let S be a reference frame where the clock and ruler are stationary. Suppose that in the reference frame S, the period of the clock is T and the length of the ruler is L.

Now suppose we have another reference frame, S', moving parallel to the ruler, with a speed v with respect to S. What is the period of the clock (T') and the length of the ruler (L') according to S'? According to Special Relativity, the answer is:

T' = gamma * T
L' = L/gamma

where gamma = (1-(v/c)^2)^(-1/2) [as implied in the answer to the previous question]

Thus, clocks run slow and rulers contract in a reference frame where the clock and ruler are in motion. Since all inertial reference frames are equally valid, there is no "true time" or "true length".

Also, the effects are totally symmetric. A clock at rest in the S' frame will appear to run slow to an observer in the S frame.

Q: So that means that everything is relative?

A: No. As hinted in the first goal of special relativity, there are quantities which are the same in all inertial reference frames. Examples are

c [the speed of light]
(ct)^2 - x^2 - y^2 - z^2 [called the spacetime distance]
m [rest mass]
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Re: FAQ (Frequently Asked Questions) - Read this before post

Postby papernuke » Thu Aug 31, 2006 11:02 pm

Rob wrote:quick questions


Jinydu that dosen't look quick.
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Re: FAQ (Frequently Asked Questions) - Read this before post

Postby Nick » Thu Sep 14, 2006 10:28 pm

Icon wrote:
Rob wrote:quick questions


Jinydu that dosen't look quick.


... or frequently asked.
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Postby quickfur » Mon Nov 06, 2006 6:39 am

On the "4th dimension is/isn't time" topic, I recently found this timely quote from H.S.M. Coxeter's lovely book, Regular Polytopes, which neatly sums up the accepted view here:

Little, if anything, is gained by representing the fourth Euclidean dimension as time. In fact, this idea, so attractively developed by H. G. Wells in The Time Machine, has led such authors as J. W. Dunne (An Experiment with Time) into a serious misconception of the theory of Relativity. Minkowski's geometry of space-time is not Euclidean, and consequently has no connection with the present investigation.

(p.119, emphases his, not mine.)

Coxeter, for those of you who may be unfamiliar with him, was a professor most of whose career was at the University of Toronto, and one of the foremost geometers of this century. He specializes in higher dimensional space, and so has contributed much to our cause on this forum. :)
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Postby houserichichi » Mon Nov 06, 2006 7:15 am

I agree that it's a common and terribly frustrating thing to have the same question raised time and time again. Time is "a" fourth dimension, but in the context of physics and not of geometry - and since the physics that uses a fourth "temporal" dimension is not Euclidean, in fact it's actually a Lorentzian manifold which is locally Minkowski - the two topics are rightfully in separate parts of the forum.

Now, were one to question what a tesseract would look like in 4+1-dimensional spacetime as it neared the speed of light...well THEN we'd be in business!

\\having just wrote "forum" into actual words I suddenly felt very ancient greek. Anyone else get that feeling from time to time? :)
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Postby bo198214 » Mon Nov 06, 2006 9:47 am

houserichichi wrote:Now, were one to question what a tesseract would look like in 4+1-dimensional spacetime as it neared the speed of light...well THEN we'd be in business!

Oh, it siimply looks contracted in the direction of movement, thats all :P

having just wrote "forum" into actual words I suddenly felt very ancient greek. Anyone else get that feeling from time to time? :)
Sometimes words become strange if singled out, though it happened not yet for me with the word "forum". So where was your past life? ;)
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