Faster than light

[M-CaTZ]

LoL blike and faf, cant we all just get along??

[fafalone]

He knows he's wrong, he's just trying to piss me off.

[KHinfcube22]

I think it was like Einstein or some messed up guy like stephen hawking who said the whole molecule thing.

[Raider]

I heard once that if one travels at the speed C, the will expand and "become" the universe, in a manner of speaking. Is this true?

 

No. If you *accelerate* to c, you have infinite energy but that isn't possible as far as we know.

[blike]

I still think I'm right. I'll let some others respond before I post what I found when I checked up on it tonight.

[fafalone]

If you looked at the simple vector issue I presented you'd realize the absurbity of stating v(t) for all objects is equal to c.

[KHinfcube22]

I believe, (and this has nothing to do what Blike's talkin about,) that if something has never been done, there is no proof it can't be done. Wouldn't it be cool to have an infinite amount of cheese?

[blike]

Originally posted by fafalone

Position in space-time is defined as s(t) = x(t)i+y(t)j+z(t)k, and velocity is ds/dt.

 

How can this be constant if a <> 0, let alone be constant at c?

 

I looked around at the bookstore and asked around on this issue and I found out that I am right. We are always travelling through spacetime at C. The problem with your statement above is dt. dt with respect to who? According to einstein time is relative.

 

We'll start with what you have: position in spacetime is p=(t, x, y, z)

 

We'll denote p as the 4-vector position in spacetime and q as the 3-vector spatial dimensions (x,y,z). V is the velocity of the 3-vector (x,y,z)

 

p = (t, q)

 

In classical mechanics velocity would be the dertivative of q (x,y,z) with respect to time, v = dq/dt

 

However, time is relative to so we need to use a time that everyone will agree on: :tau:.

 

So now we have v = ( dt/:tau: , dq/:tau: )

 

We can establish a relationship between :tau: and the coordinate time with the time dialation formula..

 

dt/d:tau: = :gamma: = (1- (u/c)^2)^-1/2 where u is the classical speed.

 

Now, applying the chain rule to the velocity formula yields:

 

v = ( :gamma:, dq/dt * dt/d:tau: )

v = ( :gamma:, :gamma: * V )

 

The magnitude of a vector in relativity is given by

 

p^2 = (ct)^2 - x^2 - y^2 - z^2

or

p^2 = (ct)^2 - q^2

 

When applied to velocity we get

 

v^2 = (c^2:gamma:^2) - (:gamma:^2 V^2)

 

or

 

v^2 = :gamma:^2 (c^2 - u^2) [where u is the classical velocity denoted by V^2]

 

remember that :gamma: = (1- (u/c)^2)^-1/2

 

so substituting that for :gamma: yields:

 

v^2 = ((1 - (u/c)^2)^-1/2) ^ 2 * (c^2 - u^2)

 

v^2 = c^2

 

The square magnitude of the velocity vector is equal to c squared.

 

See the attached image for Prof. Greene's explanation. His is a bit more complex, and makes assumptions that there are certain things you already know about the formulas.

 

Motion through the three spatial dimensions takes away from our motion through the fourth dimension, time. However we are alway moving at C, split up among the dimensions. Its from this line of reasoning that when we're moving through space at C, theres no way we can be moving through time AT ALL without changing our velocity through spacetime (why the time dialation approaches :inf: as velocity approaches C). This is what prompted my statement about photons being ageless.

___________________________________________

sources: Hurkyl, dave, Briane Greene

[fafalone]

The fact that makes your solution ultimately incorrect is that you cannot separate spacial coordinates from their 4th, t, coordinate.

[blike]

It must be handled differently because of its relativistic properties. Notice that time is handled differently in the 4-vector. This is straight out of physics books. Check out relativistic kinematics.

 

This was einstein's idea, and lorentz also toyed with it. I can cite sources for all this.

[MajinVegeta]

Originally posted by blike

I bless you with another homemade graphic.

 

We're always traveling through spacetime at C, though most of our motion is through time.

 

I agree with Fafalone. You seem to have no knowledge of Lorenz transformations in particular. Yes, we are traveling at c, and we are not. It depends on your frame of reference. Each perspective is relative; to us, we are not traveling fast. From an external observer's point of view, we are traveling fast.

Another thing to consider is that traveling at c is paradoxical because if you start traveling at c (esp. c+), you will return before you left.

I have a solution to this paradox. If anyone's willing to here it, I'll be more than happy to type it up(not a long solution, I assure you).

[blike]

Originally posted by MajinVegeta

I agree with Fafalone. You seem to have no knowledge of Lorenz transformations in particular. Yes, we are traveling at c, and we are not. It depends on your frame of reference. Each perspective is relative; to us, we are not traveling fast. From an external observer's point of view, we are traveling fast.

Another thing to consider is that traveling at c is paradoxical because if you start traveling at c (esp. c+), you will return before you left.

I have a solution to this paradox. If anyone's willing to here it, I'll be more than happy to type it up(not a long solution, I assure you).

 

You're misunderstanding me. Spatial motion is not always C. But the sum of all our motion is always C. This is why time contracts as motion through space(xyz coords) increases.

[NSX]

Originally posted by MajinVegeta

I have a solution to this paradox. If anyone's willing to here it, I'll be more than happy to type it up(not a long solution, I assure you).

 

I'd like to hear it.

[MajinVegeta]

oops!! Sorry, blike. I know YOU are like an expert in Lorenz Transformations (and you too, fafalone). hehe....

[blike]

Originally posted by MajinVegeta

oops!! Sorry, blike. I know YOU are like an expert in Lorenz Transformations (and you too, fafalone). hehe....

 

Haha, its ok to disagree

[fafalone]

Just for clarification, blike hasn't even taken physics 1, and is by no means knowledgeable in physics.

[blike]

Originally posted by fafalone

Just for clarification, blike hasn't even taken physics 1, and is by no means knowledgeable in physics.

 

You're right, I havn't taken physics one. I should assume this makes it all the more embarassing for you.

[MajinVegeta]

Originally posted by NSX

I'd like to hear it.

 

Multiple History theory is the key to my solution. When you leave now, and you return before you left, you are not returning to the same history, but another one because when you come back, you are changing the past. This directly calls for a new history to arise. (history=parallel universe. I think history is more of a discriptive word). So provided you return in a different history in the past, it is not paradoxical.

[fafalone]

Why is being right embarassing? Relativistic effects are perfectly accountable for without separating space from time. I strongly doubt Einstein said we exist anywhere other than space-time, since he basically came up with space-time.

[blike]

Originally posted by fafalone

Why is being right embarassing? Relativistic effects are perfectly accountable for without separating space from time. I strongly doubt Einstein said we exist anywhere other than space-time, since he basically came up with space-time.

 

Eh, no one is separating space and time. They are interwoven, hence the reason for all that math. If space and time were seperate, then time NOT be relative and this whole discussion wouldn't be taking place. Where did I say einstein said we exist outside of spacetime?

[fafalone]

Since space-time cannot be separated, your q and V vectors are meaningless. Just because a book says something doesn't make it true... don't forget that not all math people show is correct. Think back to the people who came here proposed GUTs.

[blike]

Originally posted by fafalone

Since space-time cannot be separated, your q and V vectors are meaningless. Just because a book says something doesn't make it true... don't forget that not all math people show is correct. Think back to the people who came here proposed GUTs.

 

q and V vectors must be separated from time because they can be handled in a classical manner and time cannot [hence einstein, relativity, and this discussion].

 

If you would like them to be handled the same, I hope you would enjoy living in a newtonian universe! This is so fundamental to special relativity I don't see how someone can claim to fully understand the implications and yet ignore the very thing einstein was pointing out. This is not "one book" that I've scoured through. Every physics book dealing with relativistic kinematics will agree, I guarantee it. This is out of einstein's notes, its not something some lone author pulled out of the air.

 

I challenge you to find me a legit source that will say otherwise. I also challenge you to provide a mathematical model to find velocity in 4vector coordinates which will work for all observers regardless of their graviational field or velocity and does not apply any special relativistic principles to time [hint, ds/dt won't work].

[fafalone]

No, they cannot be handled classicly as you claim. Motion of objects is dependent on not only the relativistic effects of time, but also of gravity.

 

You're completely misinterpreting what you've read. The very fact that your fingers are moving relative to something else proves my point.

[blike]

I'm not misinterpreting, trust me, thats the first thing I suspect. I've had like 15 people that I've emailed respond affirming this. I've read books that explain it in laymans terms. I've plugged through books that explain it mathematically. I provide you a model (and yet another from an Oxford professor) and the best you say is that "space and time cannot be separated"?? (which if they were separated, time would not even be included in the vector). Seriously this stuff is in the first chapters of books explaining relativity.

 

Don't be so foolish to believe that I would seriously contradict you without triple checking everything. Again, my challenges stand. Until then my only recommendation is that you read up a little. I can sit here and say with a straight face that you are wrong.

[fafalone]

So explain how anything can move in laymens, you should be able to.