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# Geometry of Spacetime

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Author Topic:   Geometry of Spacetime
New Cat's Eye
Inactive Member

 Message 7 of 41 (701446) 06-19-2013 11:09 AM Reply to: Message 1 by Iblis06-18-2013 10:11 PM

 if time is in fact a 4th dimension at right angles to space

I don't think it is. Here's my current conception of it, though I may be wrong:

The time coordinate is at a right angle, but the time direction of your path is only at a right angle to your distance when you're at rest. As you increase your velocity, the angle of the time direction becomes more acute. When you start approaching the speed of light, the time direction approaches being parallel to your space direction, and that's how you get length contraction.

Stand with your arms pointing straight out to your side at 90 degrees and look straight forward. You're going to be moving forward in the direction you're looking, but while your standing still you're arms are pointing in the perpendicular direction. The amount that your arms are pointing forward towards the direction you are looking (traveling) is how much time contributes to your position, which is zero right now at rest. As you begin moving faster in the forward direction, move your arms towards the direction you are facing. This is an increase in the time component of the distance. More of your path includes the time direction the faster you are going. When you reach the speed of light, your arms are pointing straight forward and time component makes up all of your distance (the space component is contracted). A photon doesn't really experience passing through space, its more like the spot it is going to is contracted to its current position.

But all that is just off the cuff so I'm sure I screwed something up. Still, I think that's the jist of it.

 This message is a reply to: Message 1 by Iblis, posted 06-18-2013 10:11 PM Iblis has not yet responded

 Replies to this message: Message 9 by NoNukes, posted 06-19-2013 6:44 PM New Cat's Eye has responded

New Cat's Eye
Inactive Member

 Message 8 of 41 (701447) 06-19-2013 11:11 AM Reply to: Message 4 by Coyote06-19-2013 12:02 AM

 Why do you + x, y, and z but –t? Why not +t?

It "takes" time to gain distance.

 This message is a reply to: Message 4 by Coyote, posted 06-19-2013 12:02 AM Coyote has not yet responded

New Cat's Eye
Inactive Member

 Message 13 of 41 (701510) 06-20-2013 10:47 AM Reply to: Message 9 by NoNukes06-19-2013 6:44 PM

 The time coordinate is at a right angle, but the time direction of your path is only at a right angle to your distance when you're at rest.

What does it mean to be 'at rest'?

The impossible state of not-moving. Since everything is moving, there's always going to be some contribution to your path from the time direction. That is, it would never be at a true right angle.

 This message is a reply to: Message 9 by NoNukes, posted 06-19-2013 6:44 PM NoNukes has responded

 Replies to this message: Message 14 by NoNukes, posted 06-20-2013 11:51 AM New Cat's Eye has responded

New Cat's Eye
Inactive Member

 Message 15 of 41 (701520) 06-20-2013 12:05 PM Reply to: Message 14 by NoNukes06-20-2013 11:51 AM

The way I understand it, the only way for the time component of your path to be at a true 90 degrees would be if you were not moving. I suppose you could achieve that with the proper inertial frame, but that didn't seem to be what the OP was asking.

 This message is a reply to: Message 14 by NoNukes, posted 06-20-2013 11:51 AM NoNukes has acknowledged this reply

 Replies to this message: Message 16 by nwr, posted 06-20-2013 3:28 PM New Cat's Eye has responded

New Cat's Eye
Inactive Member

 Message 17 of 41 (701537) 06-20-2013 4:10 PM Reply to: Message 16 by nwr06-20-2013 3:28 PM

 And the way I see it, is that in space-time there is no such thing as "true 90 degrees" between a time-like direction and a space-like direction. It is all relative to the observers frame.

Sure. But if you have a particle that is at rest (in whatever reference frame), then aren't the time-like and space-like directions at 90 degrees?

 This message is a reply to: Message 16 by nwr, posted 06-20-2013 3:28 PM nwr has responded

 Replies to this message: Message 18 by nwr, posted 06-20-2013 7:34 PM New Cat's Eye has not yet responded

New Cat's Eye
Inactive Member

 Message 26 of 41 (701948) 06-28-2013 9:48 AM Reply to: Message 24 by Iblis06-28-2013 12:14 AM

Re: Anybody?
Have you studied calculus?

 This message is a reply to: Message 24 by Iblis, posted 06-28-2013 12:14 AM Iblis has not yet responded

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