Naked Science Forum

Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Magnus Westberg on 14/12/2010 17:30:03

Title: What is special relativity?
Post by: Magnus Westberg on 14/12/2010 17:30:03

Magnus Westberg  asked the Naked Scientists:
   
As I understand it, according to the Lawrence equations of special relativity, when you get to the speed of light, time stands still, your mass becomes infinite and your length becomes zero.
 
Does that mean I become some sort of 2 dimensional black hole?

What do you think?

Title: What is special relativity?
Post by: Bill S on 14/12/2010 17:39:59

 Hi, Magnus,
If ever you reach the speed of light, do tell us about it.  I would love to know what a 2 D black hole looks like.  [???]

One thought, while you are waiting for a real answer; photons travel at the speed of light, and they are (probably) not black holes of any dimensionality; at least, not in our F of R.

Title: What is special relativity?
Post by: imatfaal on 15/12/2010 11:59:58

Quote from: Magnus Westberg  on 14/12/2010 17:30:03

Magnus Westberg  asked the Naked Scientists:
As I understand it, according to the Lawrence equations of special relativity, when you get to the speed of light, time stands still, your mass becomes infinite and your length becomes zero.
Does that mean I become some sort of 2 dimensional black hole?
What do you think?

Magnus - it's the Lorentz Transformations (same sound different name) that I think you are referring to.  These transformations allow you to compare and convert two diffrent observer's measurements from different frames of reference (FoR) with a relative velocity.  Distance and time are converted from one FoR to another using formulas and the Lorentz factor(γ):
γ = 1 / √(1-v²/c²) with v = relative velocity and c = speed of light.
You will be able to see that at normal human speeds v²/c² will be tiny, thus γ will be damn close to 1, and everything will be as we intuitively think it should be.  But as v gets very high and approaches c, weird things happen and from the fixed FoR distances in the direction of travel within the moving FoR will be contracted and time measurements will be dilated.  There are excellent pages on Wikipedia about Special relativity (http://en.wikipedia.org/wiki/Special_relativity) and the  Lorentz transformations (http://en.wikipedia.org/wiki/Lorentz_transformation) linked here; and if you want a numerical idea of the changes check out this link for time dilation and length contraction (http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/tdil.html#c2)

Quote from: Bill S on 14/12/2010 17:39:59

I would love to know what a 2 D black hole looks like.  [???]

The dreaded black spot of pirate literature of course - who would have thought Robert Louis Stephenson would predate the world's physics community in his investigation of reduced-dimensionality black holes?

Title: What is special relativity?
Post by: Bill S on 15/12/2010 14:39:23

This is timely.  I have just been asked to explain this to someone who has even less maths than I.  If t = 20yrs in the following equation, would some kind person check my figures before I risk subjecting some poor soul to a load of rubbish. Thanks in anticipation.                          

                         1.t′=t x √1-v^{2                                                                       
                                 2.t′= 25 yrs x √1-0.82                                                         
                                 3.t′= 25 yrs x √1-0.64
                                 4.t′= 25 yrs x √0.36
                                 5.t′= 25 yrs x 0.6
                                  6.t′= 15 yrs.}
                          
                       

Title: What is special relativity?
Post by: imatfaal on 15/12/2010 16:20:11

Bill
t = γ(t'-vx/c2)
t is time position
v is relative vel
c is light speed
γ is 1 / √(1-v²/c²)

You can crunch through figures to get elapsed time T from the basis of the difference of two t measurements - the transformation of this T through its own Lorentz boosts gives
T_fixed = T_moving . γ

If the moving person experiences 25 years (btw your calcs had different figures in intro and sums)
then the fixed person experinces 25 years multiplied by 1/√(1-v²/c²).  If you using (which I think you must be) v = 0.8 of the speed of light then

T  = γ.T′
T  = T'/√(1-v²/c²)
T  = T'/√(1-0.8²/1²)
T  = T'/0.6
T  = 25/0.6

And I have just realised that I have done the other way than you were getting at  [:o]
If the fixed person experiences 25 years the moving person will experience 15 years
ie
T' = T/γ
T' = 25.(1-v²/c²)
T' = 25.(0.6)

And now I am convinced that I have lost it entirely - ah well just press post; the hoards will tear it apart if I got it wrong

Title: What is special relativity?
Post by: Bill S on 15/12/2010 17:00:33

 Thanks.  Now I wish I'd left it well alone.  [xx(]

Title: What is special relativity?
Post by: yor_on on 16/12/2010 14:58:55

t = t0/(1-v^2/C^2)^1/2

            t = time observed in the other reference frame.
            t0 = time in observers own frame of reference (rest time)
            v = the speed of the moving object
            c = the speed of light in a vacuum

(And ^ = the exponent = 'raised to')



Let v = .95c
t0 = 10 years

We will solve for t which is the time that the earth bound brother measures.

        t = 10/(1- (.95c)^2/c^2)^1/2
        t = 10/(1- .95^2)^1/2
        t = 10/ .312

t = 32 years (the time the earth bound brother measures)

==

Nope, not mine :)
Just shortened it.

And when it comes to reaching the speed of light for matter it seems to become a infinitely steep slope.
                    

(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fwww.phy.olemiss.edu%2FHEP%2FQuarkNet%2Fgr_timedial.gif&hash=1144838f9e26590b92dfb348d7c01105)

But if you could?

Maybe you could see it as a variation of the Bekenstein bound? (http://www.thenakedscientists.com/forum/index.php?topic=25747.msg333528#msg333528) naively speaking, as they say? Those, ahem, Mega Boffins ::))

(phieew... All those little ^ What ever are they good for?
                Only disturbs my tranquility they do:)

Title: What is special relativity?
Post by: Bill S on 19/12/2010 20:15:43

Quote from: imatfaal

(btw your calcs had different figures in intro and sums)

I should have mentioned that my craft was travelling at 0.8c. Would that have removed the apparent discrepancy?

Title: What is special relativity?
Post by: JP on 20/12/2010 01:33:06

Quote from: Magnus Westberg  on 14/12/2010 17:30:03

Does that mean I become some sort of 2 dimensional black hole?

Hi Magnus,

You don't become a black hole. This is simple to see because, although someone outside your ship would view your ship as getting thin and high-mass, you would be stationary on your ship and it would appear to be normal size and mass to you.  It would be odd indeed if the outside observer saw you become a black hole, while you did not. 

The more in-depth reason why you don't become a black hole is that the equations of GR say that it's not just mass that matters.  There's a more complicated quantity than mass, called the stress-energy tensor that actually determines if matter forms a black hole or not.  The stress-energy tensor takes into account the energy and momentum of matter as well as it's flow in space and time (the mass can be computed from energy and momentum).  Your moving spaceship has high energy and momentum, but it's moving, and the fact that it's moving saves you from becoming a black hole.

Title: What is special relativity?
Post by: Magnus W on 20/12/2010 12:27:56

Thank you so much for all the good answers :-)

"Your moving spaceship has high energy and momentum, but it's moving, and the fact that it's moving saves you from becoming a black hole."

Thank you JP I think that was the answer I was looking for.

Title: What is special relativity?
Post by: yor_on on 23/12/2010 21:10:23

Just a thought I've had and wondered about before. We know that the 'gravity well in fact will be created behind the spaceship, right? So what's stopping that potential point to become like a black hole. Not the ship but that weird 'point'.

And if it would?
What would happen to the ship?

Title: What is special relativity?
Post by: Bill S on 23/12/2010 22:59:40

Quote

And if it would?
What would happen to the ship?

Would that not depend on whose F of R the black hole appeared in?

Title: What is special relativity?
Post by: yor_on on 23/12/2010 23:06:01

Well, considered from how I think of it I believe the black hole created and the ship are in the same frame of reference? As they have to share the same 'room time geometry' as I call it. But I'm not sure. If you looked at it as 'forces' it becomes truly weird as the 'gravitation' is a direct result of the spaceships acceleration, expending energy, so you might be able to state that it's the force of the spaceship that creates the 'black hole' which then somewhere sometime maybe? eat the spaceship. Reminding me of a snake (formerly known as worm) eating itself :)

==

Worm= sounds like = orm = meaning snake in Swedish
gotta to watch that :)

Isn't that a sign used by the medical profession btw?
==

Eh, not worm.. No no no, Yes! A snake eating itself..
I meant.
==

Nope, it's a snake pole-dancing :) isn't it?
Dam*d 6:y sign, never thought of the medical profession in that light before..

Title: What is special relativity?
Post by: yor_on on 23/12/2010 23:29:38

And yeah Bill, looked at as forces they are 'action and 'reaction' as you need the acceleration to get the gravity. Looked at as 'frames of reference I'm not sure? Looked at the way I should think of it, when I remember that is, they are 'relations'. And I'm not sure how to look at it from a 'room time geometry'.

It's like the Lorentz contraction you will perceive outside your accelerated frame. I believe the ship to share the contraction meaning that if you went out to measure 'space' you would find it to 'fit' your yard stick, which it would anyway, I know :)but if you see how I mean? And if that is so then that BH should belong to it as it travel with the ship. But there is one little problem, according to Einstein gravity travels with the light of speed in a vacuum. So there is a difference in the Black Holes gravitational waves, as it have to grow with the acceleration, and what the ship perceives.
==

But if we consider it a constant 'uniform' acceleration at one G the Black Hole would be able to create a stable configuration, maybe? Or maybe not as it still increases? A brain teaser definitely.
==

If you like rename Black Hole to 'Gravity potential point' or as we say in the business a GPP.

Let, us now pray "Oh mighty GPP .."
But it becomes strange :)

As the GPPO (Gravity Potential Point Origin) still is the ship?

So do the GPP live without a GPPO?
Yep..

I like that one :)

Title: What is special relativity?
Post by: yor_on on 23/12/2010 23:49:25

I think one G would create a stable 'field' thinking of it inside its own 'Room time geometry' aka frame of reference. Yep, they are the same thinking of it :) its just my way of pronouncing the 'idea' that we all have our own 'frame of reference' when 'looking out' at SpaceTime. one that to us always will be the same, as Soul Surfer said too. always giving you the same 'clock ticks' and length measurements.
==

And looked at that way, what you have created is one singular SpaceTime in equilibrium, that from Earth or some other frame of reference should be perceived as a constantly growing acceleration creating 'measurable' (pretending here) gravity waves that will be constantly time dilated relative the ship as they constantly need to 'catch up' at light speed.

But in your frame (room time geometry) there can be no such gravity waves.

And that is weird.
Isn't it?

Title: What is special relativity?
Post by: jartza on 24/12/2010 00:14:42

Here square object whizzles past a small ball, no black hole is created.

Then the square object wizzles past a ball that is two times bigger than the small ball, and moving quite fast, no black hole is created.

Then the square object wizles past a ball that is two times bigger than the small ball, and not moving, a black hole is created.

 [ Invalid Attachment ]

Note that leftmost ball observes just as dense square object wizzzling by as the rightmost ball does.

Title: What is special relativity?
Post by: yor_on on 24/12/2010 01:25:28

You're talking about 'frames of reference' Jartza. But I don't think you ever will see a black hole created by acceleration. The 'point' I refer too you might look at as a 'defect' in SpaceTime or as a point of gravitational potential that we might, if we assume a starting point for gravity waves relative the ship, describe possibly as a Black Hole at some stadium. But not really, as you always is able to think of another ship accelerating beside our first one, and that ship will be able to see it as it is as they in a sense will be in 'uniform motion' relative each other.

It was more of a thought experiment, leading to some weird conclusions :) my idea, helping me to see a little clearer.

But if you can think up a 'frame of reference' from where there would be impossible for that ship to have a 'coasting' companion then there might be a difference.
==

Actually you can turn that expression. Imagine placing a black hole next to another black hole, would it be able to see through the event horizon? Okay, imagine speeding them up near lights speed coasting relative each other, would they now be able to see through that event horizon?

And if you say no again, you have proven the theorem (JP) above defining what a black hole is, at least to my satisfaction :)

Ah, take it with a pinch of salt please :)
I can't help it ::))

Title: What is special relativity?
Post by: yor_on on 24/12/2010 01:40:41

Maybe you could say that the metric for the 'gravitational potential' demands proper (invariant) mass for becoming so 'distorted' that the proper mass will, falling in on itself, create a singularity. It sounds reasonable, maybe someone :) can answer that one?

(Only a 'planet' aka matter able to become a Black hole)

Title: What is special relativity?
Post by: JP on 24/12/2010 01:55:09

I don't know how to do all the math, but if since the laws of physics should be the same in all reference frames, forming a black hole in one should mean forming a black hole in all.  Otherwise you'd introduce a very bizarre paradox...

Title: What is special relativity?
Post by: yor_on on 24/12/2010 01:58:58

Scientists observe how black holes eat matter through gravitational lensing (http://newsroom.melbourne.edu/news/n-305)

Title: What is special relativity?
Post by: jartza on 24/12/2010 02:00:32

Here is a accelerating rocket. The rocket crew lay behind a long wire. There's a blue line that marks the event horizon. It is impossible to pull back the part of wire that has crossed the blue line. The wire is also certain to break at the blue line if not earlier.

BUT a very strong trailing wire that is about to snap does NOT exert a very large pull on the rocket.

 [ Invalid Attachment ]

Title: What is special relativity?
Post by: yor_on on 24/12/2010 02:07:08

Maybe, there are other that say that if you just feed out the line fast enough you will be able to feed it past the apparent Event horizon for the ship without it breaking but only to a certain degree, and as you say they can never winch it back without it breaking.

Title: What is special relativity?
Post by: yor_on on 24/12/2010 02:17:01

There are some very weird things happening if you ever would take a ship there. I remember reading about how to prolong your life if stuck in a black hole, it was weird reading :)

For those interested. Here you can download a free cool book The Theory Of Relativity by C Moller. (http://www.archive.org/details/theoryofrelativi029229mbp)  In PDF format. It's still readable :)
==

And it starts with presenting relativity from Newtonian derivations which may make it palatable for those of you finding his universe the 'clearer one'. It's a cool book.

Title: What is special relativity?
Post by: Foolosophy on 24/12/2010 08:36:59

this problem may well be a purely theoretical excercise

if we accept the conclusions of special relativity as having a physical reality, then the practical implications of accelerating a body at rest towards the speed of light become nonsnesical as an INFINITE amount of energy would be required to achieve this.

So to transform a body of finite size and mass into an entity travelling at the speed of light with zero size and infinite mass is one for the philosophers.

Maybe thats why photons dont possess mass

Title: What is special relativity?
Post by: yor_on on 24/12/2010 14:03:38

Yeah Foolosophy :)

"We seek him here, we seek him there"

Ahem :)

Merry Xmas all :)

Title: What is special relativity?
Post by: yor_on on 24/12/2010 14:21:58

Jartza, were you thinking of it in terms of a black hole being 'stuck' at one place?
Even if we assume that you can still imagine a ship relative the ship at the 'black hole', and they will see each other. You need something else for it, tell me when you've got it.
==

Or will they :)
How far apart can they be before they lose 'sight' of each other?

Gravity 'bends' light right?

Title: What is special relativity?
Post by: yor_on on 24/12/2010 14:27:11

So the 'room time geometry' at a black hole will be very 'restricted' won't it?
Defining your 'frame of reference' very clearly.

Title: What is special relativity?
Post by: yor_on on 24/12/2010 15:24:06

And if we assume that one 'room time geometry' is equivalent to all other 'room time geometries'?

Which it should be.

What can we learn from such an example?

Title: What is special relativity?
Post by: yor_on on 24/12/2010 16:07:38

Why do I expect it to be 'equivalent'?

Well, we do expect the other 'room time geometries' to have a relevance to ours, don't we? They are as I call it 'relations', creating the 'room time' you see in your telescope, or binoculars, or just see.

Title: What is special relativity?
Post by: jartza on 25/12/2010 01:20:18

Here is a wire and a black hole. A red rod fiddles the wire. On the right is an observer, named Bob.
Bob observes that waves that arrive through the wire are kinda muffled, because waves lost their energy when climbing the uphill, or for some other reason. 
 [ Invalid Attachment ]



 [ Invalid Attachment ]
Here is a wire and an accelerating rocket. A red rod fiddles the wire. In the rocket is an observer, named Joe. We know that there is no reason why waves would lose energy when traveling through the wire. But Joe should observe that the waves are in some way muffled.

How do we solve this problem? Like this: Joe knows he is in a rocket. Joe thinks that the mass of the rocket decreases while the waves are traveling. Joe deduces that if the rocket had the same mass as it had at the time when the waves started the travel, then the waves would make the rocket shake just very slightly.

Title: What is special relativity?
Post by: yor_on on 25/12/2010 14:53:28

I don't know what you're talking about now Jartza? :)
Better explain what you saw yourself explaining when you drew them so I can see.

Just want to clarify what I wrote about all frames of reference being equivalent.
rigorously speaking we state it as "All constant velocity frames of reference are equivalent (including frames of reference that appear to be at rest — after all, a prolonged state of rest is motion with a constant speed of zero)."

And make accelerated frames a special case where the equivalence isn't as clear. For example a constantly accelerating frame of reference is according to the principle of equivalence primary equivalent with a gravity. And non-constant acceleration is not associated with anything, else than its own unique case, as I know it?

So when I spoke about all frames of reference as being the same it was in the general notion of them all describing a 'SpaceTime' for the observer, no matter what frame he is in. And that's another way to to see it, the Bekenstein bound (http://www.scholarpedia.org/article/Bekenstein_bound) exemplifies that view if you, like me, associate it with a description of what an observer are able to observe as his upper bound of information, in any frame thought up.

Well, it was Xmas yesterday, right:)
==
Ah western Europe, USA, and Russia too(?), have theirs today, right :)
A happy second Xmas then..