Space = Time?

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Space = Time?

Postby ralfcis on March 10th, 2017, 3:56 pm 

What does that mean and is there a missing list of caveats, conditions and disclaimers that go with that statement?
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Re: Time to pay attention.

Postby Faradave on March 10th, 2017, 9:28 pm 

It seems that we never stop reviewing this.

Our continuum requires four numbers to geometrically specify one location (a "spacetime event") in relation to another. Thus it's description as 4-dimensional. Conventionally, these are specified as 3 of space and 1 of time (though other coordinate designations have their uses). In any case, the most fundamental property of a dimension is the potential for geometric separation.

One of the dimensions is unidirectional, providing forward-only freedom. Each of the three spatial dimensions are characterized as bidirectional. Either way provides for separation. This means that coordinates assigned in one reference frame will "transform" some degree of the dimensional designations given in a different reference frame. In different inertial frames, there is appears to be an exchange in the proportion that the temporal and spatial components of each contribute to a given separation.

The three spatial dimensions exhibit a Cartesian relation in that the separation (r) between any two locations in space at a given time (i.e. within "a simultaneity" or "spatial foliation") is given by the Pythagorean sum: ∆r2 = ∆x2 + ∆y2 + ∆z2.

More general spacetime intervals are however, not that simple, as they involve a difference between the squared spatial (∆r2) and temporal (∆t2) components. This is attributed to a hyperbolic relation between them.

P.S. We haven't mentioned rotational freedoms, which are important, interesting and fairly simple but I don't think that's what you were after.
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Re: Space = Time?

Postby BurtJordaan on March 11th, 2017, 3:22 am 

ralfcis » 10 Mar 2017, 21:56 wrote:What does that mean and is there a missing list of caveats, conditions and disclaimers that go with that statement?

I avoid this statement for this very reason. Loosely speaking, time is placed on equal footing with space by multiplying it with c and placing it on a 4th orthogonal axis, as part of spacetime. Looking at a single event, with a set of 4 spacetime coordinate values, it does not matter which one you call time. Have two events and it is not so easy - now it depends whether these two events are separated by a spacelike, lightlike or timelike spacetime interval, or more specifically, whether one could be the cause of the other or not.

If one could be the cause of the other (in whichever way), there exists an inertial frame in which the events happened at the same place (zero space separation), but have a time interval separating them. But there cannot exist an inertial frame in which these two events were simultaneous, (zero time separation), and have only a space interval separating them.

So for me, causality dictates that there must be a difference between space intervals and time intervals.

There obviously exist inertial frames in which the two events have spatial and time separations that are both non-zero.
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Re: Space = Time?

Postby ralfcis on March 11th, 2017, 7:49 am 

Well why didn't you say so, that was a fantastic, clear, concise explanation. You're firing on all cylinders lately in my book. I'm sure it was what Faradave meant to say but honestly I don't absorb information regurgitation very well, makes me very unpopular on physics forums.
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Re: Space = Time?

Postby vivian maxine on March 11th, 2017, 8:06 am 

ralfcis » March 11th, 2017, 6:49 am wrote:Well why didn't you say so, that was a fantastic, clear, concise explanation. You're firing on all cylinders lately in my book. I'm sure it was what Faradave meant to say but honestly I don't absorb information regurgitation very well, makes me very unpopular on physics forums.


Unfair advantage, ralfcis. Jorrie wakes up before you do. Which proves - I think, in my later-yet hour - that there is such a thing as time.
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Re: Space = Time?

Postby ralfcis on March 11th, 2017, 8:11 am 

Time is relative and there's a spatial difference between us so he actually wakes up later than I do relative to clocks in our respective frames.
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Re: Space = Time?

Postby ralfcis on March 12th, 2017, 7:52 am 

So I guess all that's left is to explain this

http://sciencechatforum.com/viewtopic.php?f=84&t=8621

in terms of Jorrie's explanation in this thread. The math will need to show that only length contraction can explain the phenomenon. Unfortunately the math may not be simple algebra anymore and the terminology will take some getting used to. Still I can't see if the time and space vectors are interchangeable, at what point in the proof do they cease to be. Sounds above my pay grade to figure out.
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Re: E = M

Postby Faradave on March 12th, 2017, 11:23 am 

This is a short, simple (and imperfect) version of Lincoln's expert note, linked above.



P.S. I once had a cat named "ion". But unlike actual cations she had a distinctly negative personality.
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Re: Space = Time?

Postby BurtJordaan on March 12th, 2017, 11:41 am 

ralfcis » 12 Mar 2017, 13:52 wrote:So I guess all that's left is to explain this

http://sciencechatforum.com/viewtopic.php?f=84&t=8621

in terms of Jorrie's explanation in this thread.

I guess that you have meant Lincoln's explanation?
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