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Author Topic:   Speed of Light Barrier
cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 8 of 178 (223078)
07-11-2005 5:27 AM
Reply to: Message 1 by JustinC
07-10-2005 1:15 PM


Brian Greene's explanation mentioned further up the posts is a very good way of describing it... and the analogy is not so flawed as the poster inferred. But the idea of a "reserve" can be expressed better:
I use the following picture with my students...
Imagine the space around you (in your room, office, etc) is representing space-time, with left-right, and forward-backward as your space dimensions, and up-down as your time dimension.
Take a 1m (or 3ft) ruler. This is your 3-dimensional (2space +1time) velocity vector. Let's call its length "c". Point it straight up.
As you can see, your velocity vector is pointing entirely within the time-direction and not pointing in any spatial direction. This is you, moving through time with "time-velocity" c, and not moving through space at all.
Now tilt the ruler over by 5 degrees from vertical. Your velocity vector is pointing slightly sideways, and so you have a small spatial velocity, but your "time-velocity" is hardly changed. However, because of the magnitude of c, this small spatial velocity is actually enormous in our terms.
Now tilt the ruler further to 45 degrees. You have now made a measurable impact on your "time-velocity". You also have a large sideways, spatial velocity.
Finally, tilt the ruler until it is horizontal. You now have NO time-velocity at all, but all of your velocity is in the spatial direction. How much velocity? c of course... the length of the ruler is fixed.
You should now start to understand simultaneously the reason for a max speed limit and time-dilation (and if you think about it hard enough, length-contraction)...
The speed-of-light is a maximum simply becuase it is THE ONLY SPEED. It just depends in which direction of four-dimensional space it is pointing! You are always travelling at the speed-of-light, just not always spatially.
Can you now understand that what we call velocity is really just a ROTATION of a fixed length higher-dimensional vector?
Asking how to go faster than the speed-of-light is the same as asking "what angle can I turn my ruler through to make it longer than 1m?". As you can see, the question makes no sense. Our ideas of velocity are screwed becasue we think of it as a rate of translation, where-as it is actually a rotation.
Hold a second ruler perpendicular to the first, so it starts pointing in a purely sideways / spatial direction. As we start moving spatially, we rotate and now our spatial vector is pointing slightly downwards. The important point is that the ruler does not now point as far in the spatial direction because of its rotation. Rotate 90 degress to "the speed-of-light" and the spatial ruler no longer points spatially at all. This is length-contraction.
Once you realise that all the bizarre notions of special relativity simply come from having a restricted 3d viewpoint on a 4d universe, you are well on your way to learning the subject.
This message has been edited by cavediver, 07-11-2005 05:30 AM

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Replies to this message:
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cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 9 of 178 (223101)
07-11-2005 8:50 AM
Reply to: Message 3 by Chiroptera
07-10-2005 2:07 PM


Just a quick addition to what I wrote above... this whole business with "relativistic" mass is just another example of measuring the wrong thing. We're looking at a 3d concept and expecting it to make sense in a 4d universe. Length, velocity, time and mass as we naively understand them are merely PROJECTIONS of the true 4d quantities which don't change. Think of shadows: shadows are 2d projections of actual 3d objects. The shadows themselves can change shape markedly, without the object doing so. In fact, this is why we see various quantities going to infinity... it is only the projection moving out of its range of validity.

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Replies to this message:
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cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 11 of 178 (223111)
07-11-2005 10:27 AM
Reply to: Message 10 by Chiroptera
07-11-2005 9:59 AM


Then, it it appears that people may understand this, I mentions stuff about rotating coordinate axes through imaginary angles.
Or just teach them the hyberbolic trig... they always wondered what that sinh and cosh stuff was on their calculators! You haven't done the barn paradox until you've drawn it on a hyberbolic grid :-)

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cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 13 of 178 (223316)
07-12-2005 7:13 AM
Reply to: Message 12 by Tony650
07-11-2005 8:47 PM


Anyway, my point is that I'm just wary of how closely I associate intuitive physical analogies with the actual phenomena they describe. It seems, from what I've heard, that the only way to really understand certain physical models is mathematically.
Absolutely. This is the key to getting over all the naive preconceptions and objections. My description was not an analogy. It was an actual depiction of the 3+1 dimensional mathematics (with a little simplification of course!)
You can produce analogy upon anaology, but until you understand the mathematics, you cannot see how it all fits together as one incredible whole.
Off-topic here, but you've just touched on my personal obsession. You seem quite knowledgeable of this so, if you can help me in any way, please feel free to contribute your own thoughts.
Hmmm, interesting thread. Shame I wasn't around for it. The funny thing is that as you get more into the mathematics, topics such as extra dimensions lose their mystique and become the ordinary!
The best way to learn is to devote your first three decades to the subject :-) That's how I did it. Otherwise, if you have a desire and the patience to get into the mathematics, try "The Road to Reality" by Roger Penrose. It's an attempt to bridge the enormous gap between the layman approach to fundemental physics and the post-graduate. I'm not sure it quite suceeds, but he writes well and he sees a lot further and deeper than many of the others out there, even if he does have some quite bizarre ideas.

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cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 16 of 178 (223853)
07-15-2005 4:02 AM
Reply to: Message 14 by Tony650
07-12-2005 8:47 PM


Again, I apologize for my lack of clarity.
Heh, no worries. I wasn't being critical, just emphasising the important points as I see them.
I find it to be a kind of double-edged sword, really. I like descriptions, such as Greene's cars, that are clear and easy to understand. At the same time, though, I worry that the more simplified the description (for ease of understanding), the less accurate it will be in describing the actual model. It's tough trying to understand physics purely through the concepts themselves, and knowing none of the math.
This is the trouble with fundemental physics. It has no obvious physical description. The analogies are the best you will get. And they become poorer the deeper you go... ever considered how you get attraction by particle exchange? That's why the maths is so important... check out the thread I opened in the coffee shop on mathematics.
If you have anything you can add to it you're more than welcome.
Well, the only obvious comment I had on the whole thing was on the justification for extra dimensions. When string theory is popularised, the extra dimensions are always pointed out as a major problem, where-as to any quantum gravity guy/gal that was one of the principle benefits... we've had a good idea that extra dimensions would play a key part for neraly 100 years
My ultimate goal, though a long shot admittedly, is to achieve the same intuitive perception of four-space that I have of three-space.
Hmmm, if that's your ultimate goal, then what are you going do about all the dimensions above 4? My first work was in bosonic strings and there we work in 26 dimensions

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Replies to this message:
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cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 18 of 178 (223863)
07-15-2005 4:42 AM
Reply to: Message 15 by JustinC
07-15-2005 2:42 AM


I never heard it put that way, though I like to think I'm pretty well read on the subject.
To be honest, neither have I. It's my own way of teaching the concepts. SR is rarely taught by actual relativists so even physics undergrads don't have a good picture of what's going on. And populist books are either written by people with too little understanding or too much. But as I stressed above, it's not really an "analogy"... it's an accurate-ish description of the mathematics. The inaccuracy comes because I'm describing it using normal trignometric rotations/geometry where-as it's actually hyperbolic trig geomtry (you know, using sinh and cosh, not sin and cos).
I'm having trouble understanding the "length-contraction" in that analogy.
Ok, that was a little vague... the horizontal vector simply represents a length, say of the ruler itself. As the ruler's "velocity increases" its 4-velocity vector starts to tip out of the vertical as decribed above. But the horizontal vector tips with it, so now the spatial extent of the ruler is pointing slightly through time and slightly less through space. So from a spatial perspective it is shorter. Hold a ruler out in front of you from left to right. Now rotate it slightly into the front-back direction so you now see it obliquely. Does it not look shorter? This is length-contraction except instead of front-back, you are rotating into time. Does that help?
Chiroptera showed that mass will increase as velocity increases, but only by assuming there is a limit to the speed of light. I took that post as "mass will increase since there is a speed of light limit," not "there is a speed of light limit because mass increases."
Yes, that is right. The "mass" increase is just another optical effect, as with the length contraction.
Actually, in many ways so is the speed limit: You do realise that if you travel to another star, you will have no max velocity... you can travel there as fast as you like... have I just confused everything
You gave me a good way of visualizing special relativity concepts, but only by assuming a fixed length to the ruler.
It's not that the length of the ruler is fixed... it doesn't have to be... the point is that its length doesn't change by rotating it!
Based on Maxwell's equations, light is a self-propogating E-Field and B-field. The only way it is self propogating is for it to be moving, but if you were traveling at the speed of light it wouldn't be moving relative to you, so it wouldn't exist. Then if you slowed down, it would either: 1.) reappear (something from nothing) or 2.) continue to not exist, although from another persons reference frame (whose was moving slower than c the whole time) it would still be there, right next to you. These scenerios seem pretty illogical, and it seems intuitive to assume one simply can't go faster than c.
This is more implying the relativistic velocity addition law, but essentially yes. It was Einstein's genius to put himself close to the speed of light and observe the universe from that vantage point, at the same time demanding some sort of sense. This is why I claim relativity is OBVIOUS once you look from the correct vantage point.
His other great Gedanken experiment was observing the two vehicles colliding across a junction. If light transformed as per Galilean relativity, you would see an approaching vehicle swerve for no good reason as the other crossing vehicle was still some way off, and then a moment later the second vehicle would also swerve for no reason at all as the other vehicle had left the scene. Constancy of the speed of light ensures that you always "see" what actually happens.
Oddly, this is of course exactly what happens with sound. You would hear the horn blaring of the approaching vehicle and then some later after the incident hear the second horn.

This message is a reply to:
 Message 15 by JustinC, posted 07-15-2005 2:42 AM JustinC has replied

Replies to this message:
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cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 19 of 178 (223865)
07-15-2005 4:50 AM
Reply to: Message 17 by Wounded King
07-15-2005 4:19 AM


Maybe its like 'Magic Eye' and all you need to do is really unfocus your eyes, and maybe your brain.
Hmmm, was it From Beyond (a very bad Lovecraftian film ) where the guy's Pineal came out on a stalk... I always wanted one of those to help with dimensions 8 and 9... always had a problem with those
Actually, it's not just higher dimensions. A friend of mine published several papers on Kleinian space-time, which is 2+2 rather than 3+1 (i.e. two time and two space). That did my head in...
This message has been edited by cavediver, 07-15-2005 04:51 AM

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Replies to this message:
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cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 21 of 178 (223872)
07-15-2005 5:58 AM
Reply to: Message 20 by Wounded King
07-15-2005 5:03 AM


Yep, that's the one. Take a square piece of paper... connect the top side to the bottom side and the left side to the right side with a twist... a Klein bottle.
The same without the twist: a torus (do-nut)
The same but twisting on top and bottom as well: RP2 (Real-projective plane in 2-dimensions)
All exceptionally important in string theory
When I mentioned about us knowing that higher dimensions wre a good thing for neraly 100 years, this is down to Klein as well.
Kaluza-Klein theory puts General Relativity in 5 dimensions. The extra one is postulated to be compacted into a very small circle (sound familiar?). When you do the maths you find you have effectively GR in four dimensions but also the whole of Maxwell's electromagnatism has appeared as well!!! This still blows my mind and is the first example of unification of gravity with anything else. So GR in higher dimensions leads to unification with the other "forces".
Actually my first major post grad calculation was a repeat of this in string enhanced general relativity. Now that took a few days

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cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 23 of 178 (223971)
07-15-2005 4:58 PM
Reply to: Message 22 by JustinC
07-15-2005 2:53 PM


Why yes, yes you have. Can you maybe expound that a little
Sure As you travel towards a distant star, the star is moving towards you, as is the length or distance between you and the star. So the length contracts, firstly because you are moving towards the star, and secondly becasue of length contraction. We measure speed as distance over time. Well, the distance is shrinking at a much higher rate than expected... so we must have a much greater speed, so V_effective >> V. In the limit of V=C, the distance shrinks to zero and we have traversed the distance in zero time implying infinite V_effective. So as far as you are concerned, given a spacecraft with sufficient thrust and fuel, you can visit any part of the universe in as short a period of time as you like. Just don't expect anyone to be around when you get home...

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Replies to this message:
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 Message 25 by NosyNed, posted 07-15-2005 5:28 PM cavediver has replied
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cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 27 of 178 (224040)
07-16-2005 5:21 AM
Reply to: Message 26 by JustinC
07-15-2005 7:54 PM


I'm muddling this a little. V1 is your velocity wrt say an observer's frame on Earth. V2 is your velocity from your moving frame. Neither will go above c, because although you're dividing by an ever decreasing time as you approach c, you're also dividing into an ever contracting distance. V_effective is the rest-frame distance divided by your moving-frame time_elapsed. This is actually just gamma x c. For example, travel to Sirius, about 8.1 Lyr. Travel at .999c assuming negligible acc and dec times. sqrt(1-v2/c2) is .045, and elasped time will be 8.1*.045 = 133 days. So V_effective is 8.1 lyr/133days = 1/.045 = 22c. 22 times the speed of light, which is Warp 2.8 if I remember from a VERY old star trek book of mine

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cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 29 of 178 (224062)
07-16-2005 9:02 AM
Reply to: Message 24 by Chiroptera
07-15-2005 5:01 PM


I've never did the calculations to verify this, though.
Yeah, as soon as any of us have to integrate, we find something else to do
I have to say that over the last 20 years I have spent at least 30% of my total time sat on the loo trying to come up with a plausible 1g drive. One day...

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cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 30 of 178 (224064)
07-16-2005 9:11 AM
Reply to: Message 25 by NosyNed
07-15-2005 5:28 PM


Re: Tau Zero
I must check it out... One thing that really annoys me is the invention of all sorts of psueudo-physics for Sci-Fi, when the real physics is far more amazing and exceptionally ameniable to great stories. I've been meaning to get round to writing something based on this particular idea for a couple of years, but sounds like I may have been pipped to it

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cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 32 of 178 (224108)
07-16-2005 2:03 PM
Reply to: Message 31 by Ben!
07-16-2005 12:50 PM


Re: Why 3x10^8m/s?
In this view, does it fall out directly from the hyperbolic relationship between spatial coordinates and time coordinates?
Exactly... as to its value:
Very short answer: it just is
Short answer: if it was much different to 3x10^8m/s you wouldn't be here to ask the question
It's one of the constants that you hope will drop out of whatever TOE happens to be your favourite.
Just one point:
light travels such that the vector has no time component
Be careful here. A photon's 4-velocity certainly has a time component, but it also has an "equal" space component. It's the magnitude of the vector that is zero.

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Replies to this message:
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cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 35 of 178 (224214)
07-17-2005 1:04 PM
Reply to: Message 33 by Son Goku
07-16-2005 3:59 PM


Re: Why 3x10^8m/s?
However, because of the way we see the world, humans call 300,000,000 meters in time 1 second.
Yes, and the whole question is why is the number 3x10^8 and not say 2x10^8. The units are a given, it's the magitude that is of interest.
There is a similar reason for all the constants.
If you mean, why they have their given dimensions, then this is obvious. Their magnitudes are not obvious.

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cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 36 of 178 (224216)
07-17-2005 1:14 PM
Reply to: Message 34 by JustinC
07-17-2005 12:52 PM


Re: Why 3x10^8m/s?
From your vector "analogy", it seems that if something is travelling through space at c, it won't be traveling through time.
It's time for you to start answering your own questons
clue: which frame are you talking about? Do you see light rays travelling through time... or not?
Even better than this, do you recommend any books on general and special relativity?
If you mean textbooks, then there's always Misner Thorne and Wheeler's Gravitation... the bedrock of relativity... literally given its size. But I do like Ray D'Inverno's Introduction to General Relativity. And the book I mentioned earlier, Penrose's "The Road to Reality" is a great bridge between layman and graduate textbook. If you mean layman's guide... then no, cause I haven't written mine yet Seriously, I have yet to find a decent guide. These days everyone's so desperate to rush into explaining string/M-theory that they miss out any deoth in relativity. Seriously, all this talk of branes is deadly dull compared to a good talk through of Reisnner-Nordstrom or Kerr geometry (electrically charged black hole and rotating black hole respectively)

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