Geometry of Spacetime

If the events were simultaneous, what would the t represent?

Did you even bother to look at the example calculations in those wikipedia articles I recommended?

even bother

I enjoyed studying the example given in the article on Proper Time, I gave the results of my understanding above. Here is a bit of it for reference

wiki writes: Let there now be another observer B who travels in the x direction from (0,0,0,0) for 5 years of coordinate time at 0.866c to (5 years, 4.33 light-years, 0, 0). Once there, B accelerates, and travels in the other spatial direction for 5 years to (10 years, 0, 0, 0). For each leg of the trip, the proper time is

I plugged in my 3 and 4 and got the same 2.64etc I have been going on about for more than a page. No problem.

I am not finding any similar examples in the article on Proper Length. This is the article from which you have lifted your mistagged definition and one equation, which do not appear to fit together. I am noticing that there are other equations in the article, and some multiplication by c-squared and so on.

But I'm giving you the benefit of the doubt. It would be cruel and senseless of you to pretend there were examples in a place where there aren't any, so I just must not be able to see them for some reason. Please feel free to post them here, thereby alerting the 3 or 4 people in the universe who do not yet know that I am a retard of their duty to throw rocks at me in honor of your pithy wisdom.

I am not swearing out loud in a coffee-house right this very minute.

I am noticing that there are other equations in the article, and some multiplication by c-squared and so on.

Yes, but when distance is measured in light-years and time is measured in years then c squared = 1.

But I'm giving you the benefit of the doubt

Don't be silly. There are no proper length examples. However the discussion in the article answers the question you asked me. If you believe I've provided you with an improper equation, I'll be happy to acknowledge and correct that.

the discussion in the article answers the question you asked me.

What discussion? Here's the total dialogue from the talk page

... spacelike events in a frame of reference in which the events are simultaneous. Doesn't it mean timelike? If I remember correctly, spacelike events can be in the same spot, but not at the same time. Timelike events, however, can be at the same time, but not in the same place. You don't remember correctly. Timelike events can be related through time. So they can be at the same place but not at the same time. Similartly spacelike events can be related only through space. --EMS

an improper equation

Here's the actual equation

L=\sqrt{\Delta x^2 + \Delta y^2 + \Delta z^2 - c^2 \Delta t^2},

As given there, yes it's hideous but it probably ought to be

If the c² is just 1=discardable, then my proper length appears to be the same as my proper time only imaginary, ie the root of -7.

Here's another boggle

Proper length is analogous to proper time. The difference is that proper length is the invariant interval of a spacelike path or pair of spacelike-separated events, while proper time is the invariant interval of a timelike path or pair of timelike-separated events.

Proper time actually turned out to be the relative time experienced by my astronaut when I walked the example. This was cool, I wanted that. So why is it being called invariant and likened to a number that supposedly represents a nonrelative view, ie

f the two events occur at opposite ends of an object, the proper length of the object is the length of the object as measured by an observer which is at rest relative to the object.

Am I just misunderstanding the language? Is this really a calculation of the relative distance? Is there some number I should be plugging in along with my 3²-4² that will make the root of it a real number?

Why is this article so shitty compared to the other one, and what in the world makes you think it's sufficient?

Maybe I will just post the whole thing and ask for votes on the shittiness quotient™

Edited by Iblis, :

Edited by Iblis, :

If the c² is just 1=discardable, then my proper length appears to be the same as my proper time

With c² = 1, the equation appears to be exactly the same as what I posted. Thanks we can do away with that accusation.

By discussion I definitely don't mean what's posted on the talk page. Instead I mean the discussion that talks about the meaning of proper length and proper time.

the meaning of proper length

1) In special relativity, the proper length of an object moving at velocity close to that of the speed of light is its length as measured by an observer in the rest frame of the object.
Will: Dude, that 30cm ruler travelling at the speed of light looks to be only about 28.5cm.
Nathaniel: Yeah, that's because it's proper lenth is 30cm

2) A massive shit.
Nathaniel: Dude, I just crimped out a proper length.
Will: Yeah, thats a proper brown length.

http://www.urbandictionary.com/define.php?term=Proper%20L...

So why is it being called invariant

Imagine an object moving relative to the earth. The observed length of the object varies with the velocity relative to earth, but the proper length is independent of the relative velocity. The proper length then is a property of the object, while in general, the observed length is not.

I yield. This is not fun anymore, and I usually enjoy talking about relativity.

Edited by NoNukes, : No reason given.

NoNukes writes: The observed length of the object varies

Yep, got it. That's when I posted the urbandictionary above, which helped make it clear to me.

Proper Length has nothing to do with the distance traveled, it is the vehicle that is getting dilated in a sort of "doppler effect" of the dimension in line with trajectory. The only relation to my original question is the symmetry with proper time for elucidation, and perhaps that it was, or at least could put me closer to, what Son Goku was talking about. Yes?

Back to the actual question, I'm totally headfucked about the distance part of relativity, aren't I? I e there's no dilation of the distance traveled from the viewpoint of my astronaut, he perceives himself as having traveled 3 light years. He just thinks he did it in 2.64etc years, at warp factor 1 point something.

I think I will tell my crowd of Believers that it is 2.35ish anyway. It will be ok! They will Believe it, that's what they do ...

not fun anymore

Yes, that's fine, you're off the hook. No need to answer this even, why I made it General.

Thanks for helping !!!

That first ² doesn't really belong there does it?

Good catch, I've corrected it in my original post.

I'm taking this to mean that I can keep working in terms of just two components, distance and time. They are sufficient, in the same way that the distance on the ground from me to the bottom of a flagpole, plus its height from the ground, would be sufficient to calculate the true distance from my feet to the top of the pole.

Yeah, you can do this for simple calculations alright.

Look, in my original dealie, distance is 3, the square is 9; time is 4, the square is 16; 9-16=-7, the root of minus 7 is a broken calculator. This is telling me that it is slower than light travel that is impossible / absurd !!!! my ftl version comes out a perfectly tolerable 2.64etc. Please tell I just got the terms backward or something. Please?

For this reason we usually use:

for the distance rule (metric), because it's nicer to have the slower than light distances come out real.
It actually makes no difference, since the important thing is that they are imaginary with respect to each other.

The whole point is that displacements which we call "slower than light" are ones with the time displacement being larger than all the spatial ones. These are called time-like displacements.

Faster-than-light displacements have larger space components and are hence called "space-like".

If you use:

then spacelike distances are imaginary, if you use

then timelike is imaginary.

However in calculations of physical quantities the imaginary number drops out and the spacelike displacements always come out with problems (infinite-energy, e.t.c.) regardless of which one you initially give the imaginary value to.

Of course in some cases the time and space displacements are equal and you get 0 as the interval, which is called "light-like" since light moves along this displacements or "null" because of the 0 result.

I should say there is nothing wrong with faster-than-light travel in Special Relativity itself. Some particles can move along time-like displacements (the particles we are made of) and others along space-like displacements (known as tachyons).

All relativity prevents is crossing over between the two domains. No amount of energy can change one type into the other.

It's quantum mechanics however that rules out tachyons completely. Since every particle must be an excitation of a quantum field, there would need to be a tachyon field.

However, first of all, tachyon fields are unstable. Basically two tachyons would have less energy than none, four would have less energy than two and so on, so very quickly the field would produce an infinite number of particles.

However quantum mechanics forbids* an infinite particle state like this and so the only way such a tachyon field can obey quantum mechanics and still exist is if it remains frozen in its "no particle" configuration. However interaction with any other field would kick it out of its ground state, so basically the tachyon field cannot interact with anything and might as well be non-existent.

*This is quite difficult to explain, but basically a field with an infinite particle state like this, simply cannot exist mathematically, attempting to write one down is basically like writing down 1=2. Rather than forbidding it, quantum mechanics says it is logically inconsistent.

actually makes no difference

Thanks brother, this is helping a lot. I'm sure you see what I am doing here, but I'm going to continue because it really is making me smarter. Or call it, less stupid

imaginary with respect to each other

So would it be correct to say that this business we hear widely in the media and in physics classes taught by coaches, about how ftl is "impossible" because of the square root of negative 1, is just a pedagogical canard?

Or would it be better to say that since the theory uses Minkowski space, and Minkowski subtracts instead of adding like Pythagoras, and the theory has been proooven right, and we see plenty of cases of traveling slower than light, then it is ftl that must be imaginary?

Or am I going to far here? I know that time dilation due to gravitational influences has been supported, but I can't find any references this minute that show data for a real-life test of dilation due to acceleration.

in calculations of physical quantities the imaginary number drops out

Are you just saying that, we don't have any real-world ftl events to measure? Or is there deeper stuff here I'm not flashing on presently?

---

I'm still missing something in this "proper length" stuff. The relief of realizing it had less to do with my question than one might think has passed and I'm left a curious monkey going huh. I can't seem to make a real world example cause I'm not flashing on what I should use for the t quantity there. Is the c stuck in to make sure I realize it is speed I should plug, not 0 = "simultaneous" ? An example might help, showing how fast my yardstick is traveling vs how long it looks.

Still looking ...