What happens as an object approaches c? (1 Viewer)

[seansci17]

I did the Space topic last term and was just wondering what would happen as an object approached the speed of light (c). Now according to the Lorentz transformations the mass will increase and the length decrease as the velocity of the object approached c. Also if the mass increased and the length decreased won't the gravitational field of the object also increase? By also assuming that at c the mass will become infinite and the length zero then won't the object create an event horizon just before it reaches c? Thus with the object behind an event horizon it has left earth's observable universe.

Now my problem was in determining at what velocity the object became sufficently short (in the direction of travel) and massive that it's gravitational field caused the formation of an event horizon. I tried to use 2.9999...x10^8m/s but it doesn't work... this is why

let x = 2.999...
10x= 29.999...
9x= 27
x= 3

What the hell!!! It seems that 0.999... is equal to 1.

How else can I find the velocity required to form the event horizon?

 

[me121]

Having myself done HSC Physics, but not yet uni physics, I am unable to comprehend what you are saying. In other words, I don't think you need to know this for HSC physics. I myself have never encountered it at all.

 

[seansci17]

Sorry I wasn't very clear, this isn't anything to do with the syllabus but i still find it an interesting problem. It's actually a smaller part of a paper I'm writing to convince my physics teacher that it is possible to leave the Earth's observable universe.

The point is I would like someone to find out how I can type 2.999... into my calculator so I can continue with my crazy ideas.

 

[davidbarnes]

The point is I would like someone to find out how I can type 2.999... into my calculator so I can continue with my crazy ideas.

Press the 2 key, then the decimal key, then the 9 key.

 

[samwell]

By also assuming that at c the mass will become infinite and the length zero then won't the object create an event horizon just before it reaches c? Thus with the object behind an event horizon it has left earth's observable universe.

Now my problem was in determining at what velocity the object became sufficently short (in the direction of travel) and massive that it's gravitational field caused the formation of an event horizon. I tried to use 2.9999...x10^8m/s but it doesn't work... this is why

let x = 2.999...
10x= 29.999...
9x= 27
x= 3

What the hell!!! It seems that 0.999... is equal to 1.

How else can I find the velocity required to form the event horizon?

Wat r u trying to say? Remeber that accordin to Einstein acheiving the "C" is almost impossible.
E=mc^2+0.5mv^2
The energy required to acheive the speed of lite or 2.99999x10^8ms^-1 is also quite impossible. Elaborate on ua qsn more{do we really need to noe this 4 the HSC on relativistic space probes}

 

[m.incognito]

it has to pass through B first.


AHAHAHAHAHA.

 

[me121]

Sorry I wasn't very clear, this isn't anything to do with the syllabus but i still find it an interesting problem. It's actually a smaller part of a paper I'm writing to convince my physics teacher that it is possible to leave the Earth's observable universe.

good on you. i am always happy to see students going beyond the syllabus and expanding their understanding.

What the hell!!! It seems that 0.999... is equal to 1.

You would need to consult someone with uni maths to answer this.

 

[xiao1985]

As far as high school physics are concerned, an object, in vacuum, can never travel faster than speed of light.

Now, your proposal that: "By assuming at c..." You will need to accelerate to c first. And to do that, you will already need an arbitarily large amount of energy (since mass dilates as you speed up.

And you also mentioned "then won't the object create an event horizon just before it reaches c". I think it's quite plausible that, as long as the object concerned is not at c yet, it still has a defined mass, a definted length, thereby, not a event horizon.

Though I do not specialise in physics, but I think it's sufficient to say that, by getting arbitarily close to speed of light, you are getting close to the event horizon.

 

[seansci17]

I believe there is a misunderstanding here. You seem to believe that an event horizon occurs when the object reaches c and its mass becomes infinite and its length zero. This is not true. As I understand it, an event horizon is the point above the surface of an object where the escape velocity is equal to the speed of light. This normally only occurs at singularities (black holes) but there should be a velocity just underneath c where the escape velocity equals the speed of light. At this velocity the combination of the length dilation and mass dilation should generate a gravitational field powerful enough to create such a large escape velocity.

I have run some quick calculations by hand and I've found that for an object that has a mass of 100,000 tons and a length of 400 metres an escape velocity of 1000.7m/s can be achieved when it is travelling at 2.999999999999999999999999x10^8m/s. You can see why I wanted to find a method for determining the number of nines required... its gonna be a very large number. I do ext 1 math and was gonna go back over the "series and sequences" topic when I get a chance this weekend, I think it will work if I approach it from that angle. Another idea was to tackle the problem by using a limit equation. Any ideas are welcome.

I suppose this thread might have fit better in an ext 1 forum but the inspiration came from physics. Again this next thing has nothing to do with the syllabus but its a good problem to chew on while your bored.

A thought I had on a way of interpreting why an object gets smaller and more massive when it speeds up is that you could think of the object creating a bow wave in space-time similar to a boat through water. Einstein's general theory of relativity points out that space-time is curved by the mass in it. It is this curvature that gives us gravity. If we were to look at an object moving through a fluid it creates a wave around it which then spreads out, this could very well be the same as the gravitational waves that exist in our universe. As the object moves faster a shock wave develops and closes around the object; this could represent space-time curving around the object thus making it shorter and possessing a stronger gravitational field.
There are two reasons why the mass of the object seems to increase with velocity, one is where it becomes more efficent to convert the accelerating energy into matter rather then kinetic energy; and two, where you are concentrating the same amount of matter into a smaller space as space-time curves around it.
My main idea is that once the object has reached such a high velocity that an event horizon closes around it the object breaks through space-time and god knows what happens then. There could be a massive gravitational shock wave similar to a sonic boom as it passes out of our 4D Universe but it is pure speculation. This is because not long after the event horizon forms the object will collapse to a singularity and our mathamatics breaks down. Its a bit of food for thought anyway although it is definetly way more thinking then I have the time for

 

[xiao1985]

Sorry for the misunderstanding. You have my HSC and 1st year physics knowledge completely stomped.

I'll have to say that I'm not familiar at all with the concept of event horizon (if I did not already).

 

[minijumbuk]

Didn't you know that 0.99999..... = 1?

Well, try this:

1 / 3 = 0.3333333333...
2 / 3 = 0.6666666666...
3 / 3 = 0.9999999999...

Oh, 3 over 3 is not 1???

My theory is that 1 cannot be divided into 3 perfectly :mad1:
I hate stuff without an end.

 

[veloc1ty]

http://en.wikipedia.org/wiki/0.999...

 

[seansci17]

Thanks Veloc1ty that helped clear up a few things.

 

[Captain Gh3y]

It might also matter that 2.9999...x10^8m/s > c

 

[yorkstanham]

hey, you can 'prove'0.999999....... does =1

x = 0.99999999999 ______ 1
10x = 9.99999999999 ______ 2

eqn 2 - eqn 1

10x - x = 9.99999999- 0.999999999

9x = 9

Therefore x = 1

hope that helps

 

[jcurry]

hey, you can 'prove'0.999999....... does =1

x = 0.99999999999 ______ 1
10x = 9.99999999999 ______ 2

eqn 2 - eqn 1

10x - x = 9.99999999- 0.999999999

9x = 9

Therefore x = 1

hope that helps

isnt that one too many x's meaning that it should be 9.99999999- 0.999999999
Therefore 9x = 8.999999991
x= 0.999999999 which brings you back to the beginning

am i wrong in thinking this or not?

 

[seansci17]

isnt that one too many x's meaning that it should be 9.99999999- 0.999999999
Therefore 9x = 8.999999991
x= 0.999999999 which brings you back to the beginning

am i wrong in thinking this or not?

Sorry but yeah you are wrong;

see we are dealing with 0.999... where the 9's repeat to infinity. Thus the method we got taught in 2 unit math prelim for turning repeating decimals appears to fail.

Let 0.999... equal x
therefore 10x= 9.999...
by subtracting x from 10x we are in effect cancelling out the repeating decimal and are left with
9x = 9
we then end up with x = 9/9

This has led me to the conclusion that numbers are not actual quantities... they are merely ideas to represent quantities. In other words a number does not neccesarily represent one quantity. Very very very strange idea...

 

[a-n-d-r-e-w]

0.99999....=1, other people have already beat me to it.
and are you using 2.999999x10^8 for c, if so maybe you should use 299 792 458 m/s as the speed of light, other than that i have no idea. Im quite intrigued by this event horizon business sounds cool. Hope it helps

 

[Forbidden.]

0.99999....=1, other people have already beat me to it.
and are you using 2.999999x10^8 for c, if so maybe you should use 299 792 458 m/s as the speed of light, other than that i have no idea. Im quite intrigued by this event horizon business sounds cool. Hope it helps

The radius of a black hole (or its event horizon) can be calculated using the escape velocity equation, using the speed of light as the escape velocity c = √2GM/r
then r = 2GM/c²

So if a star had the same radius and mass as Earth, the size of the black hole would be around 9mm if your calculations are correct.

 

[seansci17]

0.99999....=1, other people have already beat me to it.
and are you using 2.999999x10^8 for c, if so maybe you should use 299 792 458 m/s as the speed of light, other than that i have no idea. Im quite intrigued by this event horizon business sounds cool. Hope it helps

Thanks for that andrew but my main problem was simply trying to calculate at which point an object accelerating towards the speed of light will become so massive and small that, according to an observer on earth, the spaceship will become a black hole. The method will be absurdly simple when it occurs to us, my bets are on limiting sums and limits. I'm opening a thread on the ext 1 forum to deal with the question from a math approach.