Register | Sign In


Understanding through Discussion


EvC Forum active members: 65 (9162 total)
4 online now:
Newest Member: popoi
Post Volume: Total: 915,815 Year: 3,072/9,624 Month: 917/1,588 Week: 100/223 Day: 11/17 Hour: 0/0


Thread  Details

Email This Thread
Newer Topic | Older Topic
  
Author Topic:   Speed of Light Barrier
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

This message is a reply to:
 Message 14 by Tony650, posted 07-12-2005 8:47 PM Tony650 has replied

Replies to this message:
 Message 17 by Wounded King, posted 07-15-2005 4:19 AM cavediver has replied
 Message 48 by Tony650, posted 07-20-2005 3:37 PM cavediver has replied

  
Wounded King
Member
Posts: 4149
From: Cincinnati, Ohio, USA
Joined: 04-09-2003


Message 17 of 178 (223858)
07-15-2005 4:19 AM
Reply to: Message 16 by cavediver
07-15-2005 4:02 AM


Hmmm, if that's your ultimate goal, then what are you going do about all the dimensions above 4?
Maybe its like 'Magic Eye' and all you need to do is really unfocus your eyes, and maybe your brain.
TTFN,
WK

This message is a reply to:
 Message 16 by cavediver, posted 07-15-2005 4:02 AM cavediver has replied

Replies to this message:
 Message 19 by cavediver, posted 07-15-2005 4:50 AM Wounded King has replied

  
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:
 Message 22 by JustinC, posted 07-15-2005 2:53 PM cavediver has replied

  
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

This message is a reply to:
 Message 17 by Wounded King, posted 07-15-2005 4:19 AM Wounded King has replied

Replies to this message:
 Message 20 by Wounded King, posted 07-15-2005 5:03 AM cavediver has replied

  
Wounded King
Member
Posts: 4149
From: Cincinnati, Ohio, USA
Joined: 04-09-2003


Message 20 of 178 (223868)
07-15-2005 5:03 AM
Reply to: Message 19 by cavediver
07-15-2005 4:50 AM


Kleinian
Is this the same Klein as in the Klein bottle?
TTFN,
WK
This message has been edited by Wounded King, 07-15-2005 05:06 AM

This message is a reply to:
 Message 19 by cavediver, posted 07-15-2005 4:50 AM cavediver has replied

Replies to this message:
 Message 21 by cavediver, posted 07-15-2005 5:58 AM Wounded King has not replied

  
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

This message is a reply to:
 Message 20 by Wounded King, posted 07-15-2005 5:03 AM Wounded King has not replied

  
JustinC
Member (Idle past 4843 days)
Posts: 624
From: Pittsburgh, PA, USA
Joined: 07-21-2003


Message 22 of 178 (223943)
07-15-2005 2:53 PM
Reply to: Message 18 by cavediver
07-15-2005 4:42 AM


quote:
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?
Yes, that helps alot. The length that is projected into the space direction is less and less as you you rotate more.
quote:
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
Why yes, yes you have. Can you maybe expound that a little.
quote:
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!
Ah yes!

This message is a reply to:
 Message 18 by cavediver, posted 07-15-2005 4:42 AM cavediver has replied

Replies to this message:
 Message 23 by cavediver, posted 07-15-2005 4:58 PM JustinC has replied

  
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...

This message is a reply to:
 Message 22 by JustinC, posted 07-15-2005 2:53 PM JustinC has replied

Replies to this message:
 Message 24 by Chiroptera, posted 07-15-2005 5:01 PM cavediver has replied
 Message 25 by NosyNed, posted 07-15-2005 5:28 PM cavediver has replied
 Message 26 by JustinC, posted 07-15-2005 7:54 PM cavediver has replied
 Message 49 by Tony650, posted 07-20-2005 3:52 PM cavediver has not replied

  
Chiroptera
Inactive Member


Message 24 of 178 (223975)
07-15-2005 5:01 PM
Reply to: Message 23 by cavediver
07-15-2005 4:58 PM


I think that I read somewhere that under a constant acceleration of 1 g (so that you can experience earth-like gravity), you can go just about anywhere in the visible universe in about 30 or 40 years. I've never did the calculations to verify this, though.

This message is a reply to:
 Message 23 by cavediver, posted 07-15-2005 4:58 PM cavediver has replied

Replies to this message:
 Message 29 by cavediver, posted 07-16-2005 9:02 AM Chiroptera has not replied

  
NosyNed
Member
Posts: 8996
From: Canada
Joined: 04-04-2003


Message 25 of 178 (223982)
07-15-2005 5:28 PM
Reply to: Message 23 by cavediver
07-15-2005 4:58 PM


Tau Zero
For an imaginitive play on this idea the decades old SF novel by Poul Anderson - "Tau Zero" is fun.

This message is a reply to:
 Message 23 by cavediver, posted 07-15-2005 4:58 PM cavediver has replied

Replies to this message:
 Message 30 by cavediver, posted 07-16-2005 9:11 AM NosyNed has not replied

  
JustinC
Member (Idle past 4843 days)
Posts: 624
From: Pittsburgh, PA, USA
Joined: 07-21-2003


Message 26 of 178 (224005)
07-15-2005 7:54 PM
Reply to: Message 23 by cavediver
07-15-2005 4:58 PM


quote:
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...
So what is the difference between V effective and V? Why can V effective go above c but not V?
I'm kindof getting stuck in a loop when I think about this. If you start off moving towards the star at .5c, due to length contraction you are moving faster towards the star than .5c? And when you then factor that in, the distance again contracts? Ad infinitum.
Basically, whose reference frame are you moving in V and whose in V effective?

This message is a reply to:
 Message 23 by cavediver, posted 07-15-2005 4:58 PM cavediver has replied

Replies to this message:
 Message 27 by cavediver, posted 07-16-2005 5:21 AM JustinC has replied

  
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

This message is a reply to:
 Message 26 by JustinC, posted 07-15-2005 7:54 PM JustinC has replied

Replies to this message:
 Message 28 by JustinC, posted 07-16-2005 8:35 AM cavediver has not replied

  
JustinC
Member (Idle past 4843 days)
Posts: 624
From: Pittsburgh, PA, USA
Joined: 07-21-2003


Message 28 of 178 (224060)
07-16-2005 8:35 AM
Reply to: Message 27 by cavediver
07-16-2005 5:21 AM


Thanks, got it.

This message is a reply to:
 Message 27 by cavediver, posted 07-16-2005 5:21 AM cavediver has not replied

  
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...

This message is a reply to:
 Message 24 by Chiroptera, posted 07-15-2005 5:01 PM Chiroptera has not replied

  
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

This message is a reply to:
 Message 25 by NosyNed, posted 07-15-2005 5:28 PM NosyNed has not replied

  
Newer Topic | Older Topic
Jump to:


Copyright 2001-2023 by EvC Forum, All Rights Reserved

™ Version 4.2
Innovative software from Qwixotic © 2024