Today Special Relativity dies

[Hurkyl]

Ok, now to start getting to the point of drawing this diagram.

Rather than thinking of the universe as being some spatial "thing" that only exists "now", we can think of the universe as consisting not only of now, but the past (and the future?).

The thing I'm getting at is that instead of thinking of the animation in picture #1 which shows the universe at a given instant of time, and show how the universe changes as time changes, we can think in terms of the diagram I draw which shows the whole of space-time all at once.

In this representation of the universe, we can recover our classical notion of "now"; a point in time corresponds to a horizontal line on this diagram, and everything occupying that line is what we, classically, think of the universe looking like at that time.

Agree?

 

[ram1024]

if the moving picture stops 1/2 way through that diagram where the green lines cross then yeh i'd say that looks pretty accurate.

 

[ram1024]

horizontal cut = now
vertical cut = where

yesh... proceed

 

[wespe]

this picture displays the 'center...stance light travels is the same for a and b.

 

[ram1024]

no idea what you're getting at since i never combined those two

 

[wespe]

no idea what you're getting at since i never combined those two

then why do you say "changing JUST the observer to BE moving changes the distance that light will travel hence change the intercept times." ?

 

[ram1024]

Case #7
Step: 1

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======================================

Step: 2

                     [u](o)                                        <-)|[/u]
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                     [u](o)                                  <-)|[/u]
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Step 4:

                     [u](o)                                        <-)|[/u]
                        [u](o)                                     <-)|[/u]
                           [u](o)                                  <-)|[/u]
                              [u](o)                               <-)|[/u]

===============================


Step: 3

                     [u](o)                                        <-)|[/u]
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                     [u](o)                                                 <-)|[/u]

Step 5:

                     [u](o)                                        <-)|[/u]
                  [u](o)                                           <-)|[/u]
               [u](o)                                              <-)|[/u]
            [u](o)                                                 <-)|[/u]

i move them around so you can do the comparison easier.

 

[ram1024]

for each step, pulse a light from the emitter at line1 and assume it hits the observer on line 4.

it's pretty easy to see that the simple changing of "who's moving" doesn't make for an equivalent picture. in 2 and 3, no relative distance is made <progress> of the observer towards the location of the light emission source (not the emitter, but where the emitter WAS in line1 when it pulsed)

in 4 and 5 relative motion IS noted between the light emission source and the observer(this time since the emitter source is stationary, the light emission source occupies the same location)

 

[wespe]

Case #7
i move them around so you can do the comparison easier.

Yes, the distance is measured by observer and emitters differently, and so is the elapsed time, due to length contraction and time dilation. So what? I will provide you numerical examples to make you understand what value everyone will measure. Wait..

 

[Hurkyl]

$$\begin{picture}(500,240)(0,0)<br /> \put(100,210){\textcolor{red}{\line(0,-1){210}}}<br /> \put(300,210){\textcolor{red}{\line(0,-1){210}}}<br /> \put(100,210){\textcolor{green}{\line(-1,-1){75}}}<br /> \put(100,210){\textcolor{green}{\line(1,-1){180}}}<br /> \put(300,210){\textcolor{green}{\line(-1,-1){180}}}<br /> \put(300,210){\textcolor{green}{\line(1,-1){180}}}<br /> \put(200,210){\textcolor{yellow}{\line(0,-1){210}}}<br /> \put(166.7,210){\textcolor{blue}{\line(1,-3){70}}}<br /> <br /> \put(100,210){\line(3,-1){360}}<br /> \put(325, 135){\circle{4}}<br /> \end{picture}$$

Ok, I've extended the diagram a little so I can talk about some additional things.

Once we permit ourselves to think about the universe in terms of a space-time, we can ask a "what if" question...


We know from geometry that all lines are the same. Sometimes we pick two perpendicular lines to be axes, but we can always rotate and pick different axes. So...

What if we allow lines that aren't horizontal to be "when" and lines that aren't vertical to be "where"?


Nonvertical lines reprsenting "where" have been around a long time; the blue line represents a "where"... the train. Other lines parallel to the blue line also represent "where"; places at a fixed position relative to the train.


The thing that makes SR different than Gallilean relativity is that SR also permits diagonal lines to represent "when". The black line I've drawn on the diagram is a line that, according to SR, represents "when" in the train's frame.

Now, before you jump on this and call it stupid, consider this: even if you think it's stupid to let a diagonal line represent "when", we can identify this black line in reality. We could define a collection of lines parallel to the black line, and define something by these lines.

So, whether or not you consider this a measurement of time, it is certainly a measurement of something physically meaningful in reality.


In this diagram, I hope you can see how SR can say that in the train's frame that the emissions aren't simultaneous. If we're using these diagonal lines to measure "time", instead of horizontal lines like we're "supposed to", then it's clear that this different way of measuring "time" will not measure the two emission events as occurring at the same time. In particular, if we're using these diagonal lines to measure time, then the emitter on the right will fire before the emitter on the left!


I extended the picture so I could also talk about the "center of emission". Again, if I'm using these diagonal lines to define "when", then the points where the right photons intersect the black line correspond to the same "time". The little dot I drew is the midpoint between these two intersections. If I'm using the black line to define "when", then that dot should be the "center of emission", because it is the point midway between the photons.

Again, this diagram shows how we can be referring to the same reality, but disagree on the "center of emission".


Each frame of animation #2 can be generated by drawing one of these diagonal lines. The black line I drew corresponds to the frame in animation #2 when the left emitter fires. Notice that, along this black line, the right photon is much closer to the yellow observer than the left photon is, the train is located at the midpoint of the photons, and the right center of emission is located a little to the right of the right source. If you look at animation #2, the frame where the left emitter fires will conform precisely to this description. (including your green fuzzy dot!)

 

[ram1024]

no, there is no distance measured differently... light CLEARLY travels farther if you switch the frames like this.

in the emitter reference we have the emitter moving away from the "light emission source" which has NO impact on when the observer will receive the photon.

in the observer reference we have the observer moving away from the "light emission source" which has TOTAL impact on when the observer will receive the photon.

not "time gets skewed" because the observer is moving but "it's not even the same situation"

 

[ram1024]

$$\begin{picture}(500,240)(0,0)<br /> \put(100,210){\textcolor{red}{\line(0,-1){210}}}<br /> \put(300,210){\textcolor{red}{\line(0,-1){210}}}<br /> \put(100,210){\textcolor{green}{\line(-1,-1){75}}}<br /> \put(100,210){\textcolor{green}{\line(1,-1){180}}}<br /> \put(300,210){\textcolor{green}{\line(-1,-1){180}}}<br /> \put(300,210){\textcolor{green}{\line(1,-1){180}}}<br /> \put(200,210){\textcolor{yellow}{\line(0,-1){210}}}<br /> \put(166.7,210){\textcolor{blue}{\line(1,-3){70}}}<br /> <br /> \put(100,210){\line(3,-1){360}}<br /> \put(325, 135){\circle{4}}<br /> \end{picture}$$

i don't see how the black line can be the train's "where" because it never gets hit by the light from emitter(L)...

explain the black line to me once more :(

 

[ram1024]

ah okay nevermind you said it's a "when" line

 

[ram1024]

it was informative, but it doesn't tell me much except that non-simultaneity for that frame is a direct consequence of light speed measured constant for the observer.

allow for a moment light to be subjected to normal physics in the sense that the emitters impart whatever velocity they have to the light when it is emitted, as would be if light were a normal mass attribute object.

here is my version of events allowing inertial velocity to be added to the light sources (making the light travel with the emitters) in order to preserve a true reference frame according to the stationary train as an observer.

http://www.imagedump.com/index.cgi?pick=get&tp=89150

<changed the background, white hurts my eyes>

[edit] explaining that a little bit for you, the white line is the skewed "when" line for the now "stationary" train. i shifted the train back over to the original location, since it "doesn't move". i allowed the emitters to carry their inertia from movement over to the photons so that they're moving along with added velocity of the source (if you check my earlier case #7 you'll see why this is necessary to ensure constancy). the red lines are the moving emitters. the "dotted" red lines are theoretical emitter locations if they were not moving.

 

[Hurkyl]

Informing was my goal. I wasn't trying to convince anyone of anything; I was mainly trying to clear up how, according to SR, the two different frames could be corresponding to the same "reality" despite the disagreement over things like simultaneity and centers of emission.

I just recall that, when I was learning this stuff, I never really "got" SR until I tried understanding it from these diagrams instead of from wordy descriptions and algebra. Thought it might be helpful while we wait for Tom to dig up the meaty stuff.

 

[kurious]

Today special relativity dies...

Kurious:

It will die in space-time...

 

[ram1024]

my diagram makes sense right? I've never messed with this space-time stuff, it was good of jscd<sp> to point out how useful it could be for explaining stuff.

in any case, i hope you can see that on my diagram <allowing for relative motion of the observer towards the "light emission centers"> his space/time is skewed but he still calculates simultaneous "when" emissions on his skewed line

i think grounded has the mathematics for such a transform already in place, he's just missing the "light emission centers" bit in there which according to how we'd plotted it would be a simple geometric rotation of the observer's spacetime "worldline"

 

[ram1024]

woops my bad, jdavel suggested space-time diagrams

 

[wespe]

no, there is no distance measured differently... light CLEARLY travels farther if you switch the frames like this.

in the emitter reference we have the emitter moving away from the "light emission source" which has NO impact on when the observer will receive the photon.

in the observer reference we have the observer moving away from the "light emission source" which has TOTAL impact on when the observer will receive the photon.

not "time gets skewed" because the observer is moving but "it's not even the same situation"

Ram, I now think "time gets skewed" is the resolution to your apparent paradox.

I found that other link again. Please take a look:
http://casa.colorado.edu/~ajsh/sr/paradox.html

Note that vermilion and cerulean do not agree on where the centre of emission is. So the centre of emission is relative too.

In your example, no one will agree on times and distances due to SR effects, that's normal. But, what confused me was: time dilation and length contraction don't depend on direction of speed. So they don't explain the difference between 2/4 and 3/5. But, relative simultaneity does depend on direction, and that is why there is a skew in time, not a shift. So, I think the resolution to your paradox is the skew. I hope you can work it out with the spacetime diagrams.

 

[ram1024]

In your example, no one will agree on times and distances due to SR effects, that's normal. But, what confused me was: time dilation and length contraction don't depend on direction of speed. So they don't explain the difference between 2/4 and 3/5. But, relative simultaneity does depend on direction, and that is why there is a skew in time, not a shift. So, I think the resolution to your paradox is the skew. I hope you can work it out with the spacetime diagrams.

see the main thing i see as "the problem" is that light itself does NOT obey physical laws of the universe, so when you put it in a position where the frames get switch you cannot expect light to behave the same.

case in point the picture i submitted most recently which is a spacetime diagram of the train stationary, but the light sources moving AND the photon light emission centers being tied to the emitters.

in this diagram it is clearly obvious <by taking "whens" on that diagonal <the train's view> you can see that even according to the train, emission IS simultaneous.

but BECAUSE light is not tied to its source <not the case with other physical mass bearing things in the universe> if you shift the frames and don't compensate for this, it's not the same situation.

i had the same problem when i was prooving .999~ doesn't equal 1. people were functioning under the limit that infinity was an absolute limit, then got all confused when numbers at the limit didn't behave the same way as numbers anywhere else on the line. remove the limit and everything still works the same.

same thing here, compensate for your limitations and everything still works fine. no time dialation, no length contraction, no simultaneity nonsense.

no relative to the viewer light speed, but i do believe that's solely an error based on how they're calculating their measurments. we'll see when the data arrives.

 

[Alkatran]

But .999~ does equal 1?

 

[wespe]

see the main thing i see as "the problem" is that light itself does NOT obey physical laws of the universe, so when you put it in a position where the frames get switch you cannot expect light to behave the same.

I wouldn't say light does not obey physical laws of the universe. It's a special case because of its zero rest mass. Then again you might say light is not physical but it does interact with mass.

case in point the picture i submitted most recently ...

I don't have the time to decipher your diagram so I can't comment..

same thing here, compensate for your limitations and everything still works fine. no time dialation, no length contraction, no simultaneity nonsense.

But everything doesn't work fine with Galilean relativity. GPS for example. MMX null result. And of course experiments in particle accelerators. What about muon decay? Muons live longer and travel longer when they are moving fast. You can't ignore all these.

no relative to the viewer light speed, but i do believe that's solely an error based on how they're calculating their measurments. we'll see when the data arrives.

Are we expecting new data? What are the errors? Do you have a consistent theory to correct the errors?

 

[ram1024]

But everything doesn't work fine with Galilean relativity. GPS for example. MMX null result. And of course experiments in particle accelerators. What about muon decay? Muons live longer and travel longer when they are moving fast. You can't ignore all these.

without data i can only offer conjecture on these topics.

my thoughts are as follows

GPS still works because of triangulation. it doesn't work PERFECTLY, but then again it's all consistent so if they're running off the same system and all give the same error who's to know it's actually an error? being peak technology for that kind of thing the only way you could check it would be to use cruder technology

MMX null result is of no consequence because i don't believe in "aether" anyways.

does a muon decay at the same rate in space as it does on earth, subjected to atmospheric pressure, gravity, and element interaction? not enough data to conclude.

so without that kind of data, i can't give you much

 

[Alkatran]

GPS still works because of triangulation. it doesn't work PERFECTLY, but then again it's all consistent so if they're running off the same system and all give the same error who's to know it's actually an error? being peak technology for that kind of thing the only way you could check it would be to use cruder technology

I think they would notice if the GPS satellites made an error. Even if they all made the same error people would notice when it said they were 2 km from where they actually were.

 

[ram1024]

well... the only way they'd be able to detect it is if you had other GPS satellites going the OTHER direction (orbit) and i don't think they do

 

[ahrkron]

In a sense, they already do. The GPS satellites orbit Earth in a nice symmetric pattern. Here's a representation:

http://www.gisillinois.org/gps/GPSDEF/sat.htm

If there was a systematic shift, how much it would affect you would depend on where and when you took the reading. Sometimes it would point one direction, and sometimes the opposite, depending of where the visible satellites were with respect to you at the time of the evaluation.

It would be quite chaotic, which it isn't.

 

[ram1024]

i went and looked up a lot of references on GPS and relativity, and apparently there's still a lot of controversy as to what is going on up there.

apparently regardless of how they correct the system they still get errors, so the whole thing has to be continually recalibrated.

they're saying that how things operate up there is MORE consistent with Lorentz Relativity than Special Relativity.

but General relativity seems to be holding for gravity effects <shrug>

now i got to go figure out what the difference is between Lorentz Relativity and Galilean/Einstein relativities :O

 

[wespe]

Ram, I think your skepticism is fine. But one thing seems certain: there is no going back to Galilean relativity. Current data fits into Einstein's relativity much better.

they're saying that how things operate up there is MORE consistent with Lorentz Relativity than Special Relativity.

If I'm not mistaken, SR includes LET as a subset but LET includes an aether which is just another frame in SR, if LET is what you mean by Lorentz relativity.

 

[ram1024]

still trying to figure out what it means myself... :D

 

[russ_watters]

i had the same problem when i was prooving .999~ doesn't equal 1.

Oy - not only is every physicist wrong, but every mathematician is wrong too? Ram, you have a problem that we can't help you with here.

apparently regardless of how they correct the system they still get errors, so the whole thing has to be continually recalibrated.

Every system has errors. GPS clocks are quite good (easily good enough that they notice time dilation), but they still need to be synchronized periodically.

One little tidbit: GPS satellite clocks are calibrated according to the predictions of GR/SR and as such, when on the ground, they don't keep accurate time. Once in orbit, they do keep accurate time. What does that tell you?

In any case, it is clear from your statements that you don't know how GPS works, nor do you know its implications for SR/GR. You also don't understand the significance of the Lorentz transformaions an their relationship to SR. You should choose to learn these things instead of just assuming that you are right, choosing to believe that despite your admitted ignorance you know something that thousands of scientists don't, and choosing not to look at the mountain of evidence that says otherwise. Maybe that's not a choice you are capable of making. I don't know.