Speed of light Question, need mathematician ?

[Tallaxo]

We experience the 4th dimension every day and are aware of it. it is duration otherwise known as TIME.

I am not sure if any of you have seen this flash presentation , but it tries to explain the string theory of 10 stacked dimensions. It is very well thought out and provokes some great ideas.

Enjoy

Jase

http://www.tenthdimension.com/flash2.php

Just click on the spinning tree of numbers to start .

 

[jrv]

The question I am dying to know the answer to is how long would it take, and how far would we have travelled, to reach the speed of light at a constant acceleration to maintain a force of 1G, and 1.5G respectively ??

As was said you can't accelerate and reach the speed of light.

To figure out what seems to happen you have to ask where the observers are, because they don't always see things the same. For example your starship may have a magical engine that always produces 1G of acceleration on the ship. At launch those on Earth will see the starship accelerate at 1G. But as the starship appears to approach the speed of light strange things happen – time seems to dilate on the starship (clocks seem to move slower) and there's less and less acceleration. Those on the starship don't see this: the clocks move at normal speed and they still see 1G acceleration. From the viewpoint of Earth it *never* reaches the speed of light.

(there are plenty of books on the weirdness of relativity. Also there's quite a bit of experiment showing that the relativity equations are right - it really that weird)

Well, photons do have mass, or else you would have trouble setting up a gravitational lens. You can calculate their mass by solving E=mc² for m, and say E is the photon's energy (h*f).
Actually, photons are not so special, if you start considering De Broglie's wave equation which says everything is a wave... hehe, gets really messy there.

E=mc^2 only works for objects that are at rest. A more general form of that equation is (IIRC) e^2=m^2c^4+p^2c^2 where m is the rest mass and p the momentum. It's possible to have energy even with zero rest mass.

A gravitational lens works because of the star or galaxy in the middle - the “lens” - not because of any mass in the photon. It's the lens that creates the gravitational curvature of space, and the photon just follows that curvature.

I prefer to say “photons are particles, and particles behave like that.” In other words, a photon is not some sort of cross-dresser that is sometimes a particle and sometimes a wave – a photon is *always* what it is and we just have trouble describing it – sometimes we try to explain it as a particle, sometimes as a wave, but it is always our descriptions and explanations that change, not the photon's behavior. Nothing we are familiar with in day-to-day life behaves the way a photon does (or any other subatomic particle for that matter) so we are stuck with various wave and billiard-ball analogies that only make sense some of the time.

 

[Chief-Eamonn]

the 2D axis is at a right angle to the original 1D axis and the 3D axis is at right angle with both the first and second axis the fourth is simple at right angle to all 3 of the original axis or the ones we know of..

also 3D shaped can be drawn on 2D paper and yes 4D shapes can be modeled on a 3D model.. (its been done before)

the problem is if you asked a 2D person to point in a direction other than front back left or right he couldn't he has no idea what up and down are just like how we find it hard to visualise a 4th dimension..

 

[philguy]

 Nothing we are familiar with in day-to-day life behaves the way a phone does

Yup, that's right - my calculator doesn't emit weird sound waves out of nowhere scnr, I know what you meant.

I think youn are right with the gravitational lens - it's misformed space, not the photons being bent.

About E=mc²: From what we learned, it is a generally valid equation - depending on what your mass is. So if you take an electron (E at rest =511keV), and accelerate it with 300keV, its new mass could be calculated by E=mc², solved for m, using 811keV as energy.

*going off to double-check*

 

[jrv]

Yup, that's right - my calculator doesn't emit weird sound waves out of nowhere scnr, I know what you meant.

I think youn are right with the gravitational lens - it's misformed space, not the photons being bent.

About E=mc²: From what we learned, it is a generally valid equation - depending on what your mass is. So if you take an electron (E at rest =511keV), and accelerate it with 300keV, its new mass could be calculated by E=mc², solved for m, using 811keV as energy.

Oops - photon, phone, whatever! ;D fixed!

The "m" in that equation is the rest mass. The increased energy from the acceleration shows up as momentum, which is a different term. If I'm remembering correctly that is - my last college class was almost 30 years ago ...

 

[xanatos]

4D model in 3D: google/wiki "Tesseract". Think of a box, each side opens. You open one side, fill it, close it, spin the box to the next side, open it and -voila! - the whole box appears empty. So you fill that side, close it, spin to the next side, and again, empty box. You can fill all 6 sides of the box before the tesseract is actually "full".

I really need one of those as my garage!!!!!

Dave

 

[Zarniwoop]

That would be the case if tachyons travelled at *infinite* speed. But aren't they defined as just travelling faster than light, which could be 1.00001 C? If so they'd still take a finite amount of time to cross space and couldn't be everywhere simultaneously.
(Man this is reminding me of the "infinite improbability drive".)

To revisit a previous topic... Correct me if I'm wrong, but escape velocity is the speed required to break free of a body's gravitational pull *ballistically*. You could theoretically climb a ladder (or a "beanstalk" aka. space tether) into orbit much slower.

 

[xanatos]

That would be the case if tachyons travelled at *infinite* speed. But aren't they defined as just travelling faster than light, which could be 1.00001 C? If so they'd still take a finite amount of time to cross space and couldn't be everywhere simultaneously.
(Man this is reminding me of the "infinite improbability drive".)

To revisit a previous topic... Correct me if I'm wrong, but escape velocity is the speed required to break free of a body's gravitational pull *ballistically*. You could theoretically climb a ladder (or a "beanstalk" aka. space tether) into orbit much slower.

I still laugh like a nut whenever I think of HGTTG when they were a ball of yarn, and they guy got sick & barfed yarn...

The gravity thing is pretty strange - ballistically you need to go (for the Earth) 25,000 mph to escape gravity, which means you have enough forward energy so that no matter how long you coast for, the Earth's gravity will never reduce your speed to a negative (Earth-returning) velocity.

The problem with the "long ladder" idea is that while in theory you could climb for a thousand years and get a LONG way away, gravity NEVER goes away completely (We even feel the effect of gravity from stars at the far side of the universe, though it is too small to measure). What this means is you climb and climb - you're 100000000000 miles out. Then you finally get tired and let go of the ladder. Slowly - imperceptibly at first (at first, meaning like for the next 20000 years) you begin slowly drifting BACK towards Earth! Left unchecked, you would quite surely accelerate and find your way back to Earth, substantially faster than you left, and would meet a fiery end on your reunion with your home world.

Of course this all assumes you weren't far enough out to be closer to another celestial object's gravitational influence, in which case you'd fry there instead.

So that's the deal with escape velocity. If at any time you find yourself in the gravitational influence of another body, it takes a certain amount of energy to exit that body's influence, else you find yourself coming back to it.

This is what we call marriage... Oops, wrong body!

Dave

 

[Zarniwoop]

Not to keep digressing from the starting topic, but this is fun...

So if I stepped onto the space elevator in my back-yard (I live next door to The Physics Shop where all the frictionless devices come from ), and rode it to the 22,600 Mile point (geosynchronous orbit), donned my space-suit, and stepped out, would I fall, or would I be in a stable orbit?

 

[xanatos]

IF you were remaining at a point fixed over the surface (geosynchronous as you mentioned), then you'd be in orbit. Why? Because you're actually NOT staying put - you're spinning around the planet at 1 revolution per day. This causes your centrifugal (or centripital - I get those two confussed ) forces to be equal and opposite to the force of gravity.

HOWEVER... if you were to do the elevator thing, and say your fictional elevator had the far end of the cable tied to Alpha Centauri, and you went to the 22,600 mile marker and stepped out, you'd fall! SLowly at first, but you would fall, as you would NOT be moving in a semi-circular path around a fixed point, so no centrifugal/centripetal forces to counteract gravity.

Thought experiments like this are a lot of fun (at least for those who enjoy such things) - but even more than fun - they are how many critical, key discoveries have been made in the sciences (and many other disciplines, in fact). These kinds of things are the very keys to scientific evolution... keep 'em going!

Dave

 

[BlueFusion]

[quote author=BlueFusion link=1200733275/0#14 date=1200828000]
Think of this. You can represent 3 dimensional space on 2 dimensions, like in a seemingly 3D drawing or graphic. It follows then, that you could represent 4 dimensions in 3.
A mistake a lot of people make here is trying to imagine 4 space dimensions, which there aren't.

Bold statements, young Jedi!

Okay, I dare you to
a) get me a 3D-Model of a 4D-world.
b) prove me wrong when I say "there is no 4th spatial dimension".

By the way: your first statement implies there is a fourth dimension of space.
Also, it isn't really that hard to picture a fourth dimension

I think this is really problematic as as we are 3-dimensional beings, the concept of movin not only "sideways and longways and slantways and any other way you can think of", but also "out of" this space. The problem becomes a bit clearer when you picture explaining a 3D-world to a 2D-guy.[/quote]


I can easily represent 4D space. Thing is, it isn't accurate as space is only 3D, time is 4th.

Imagine a net for a cube. 5 squares in a cross pattern plus one extra on one leg. So ow fold that into a cube, Then stack 1 cube on each face, and 2 on one face to get the same pattern. You now have a net for a 4 space dimensional cube.

Now this is a problem because the 4th dimension is time, not a space dimension. We move through it at a fixed speed, but the direction we move in it, is dimensions 1 to 3 essentially.

 

[Morepower]

The theory in my OP is something I had been wondering for 20 odd years, ever since I heard a scientist say the biggest 2 problems(at that time) with travelling great distances for human beings was if we were to accelarate to the speed of light we would be crushed, and the second was we would not have any significant bone mass left when, and if, we got there. Of course since then we have other thoughts of how we might be able to get to distant places in the Universe.
However I wonder how the 1 or 1.5G thing(instead of having to do it with centrifugal force which inherently has it's own set of problems) might work for travelling within our own Solar system ? Get to the half way point, turn the ship around and decelarate at a costant G force. There would be no bone loss, middle ear or cardiac problems to deal with and no rediculous amounts of wasted exercise time and more time for scientific experiments.
I guess though one of the biggest questions, for me at least, is what is the Universe. Surely it has to be a small part of something even bigger. Just like the smaller we look the more we find, like molecules are made of atoms, atoms are made of sub-atomic particles, sub-atomic particles are made of something that I can't remember right now, etc., etc..
Some other things I find intriguing is Dark Matter and Zero Point Energy.

And like xanatos said keep it going, this is very informative and enjoyable.

 

[simplysped]

This may seem kind of off topic but, if we could travel lets say twice the speed of light... And we did this for a year away from earth, and we looked back at earth with a telescope, would we see a year in the past?

 

[Tallaxo]

This may seem kind of off topic but, if we could travel lets say twice the speed of light... And we did this for a year away from earth, and we looked back at earth with a telescope, would we see a year in the past?

Simple answer: Yes.

Jase

 

[xanatos]

Well, allowing for the possibility that we could go 2C, without some significant distortion of the known universe for doing so (and assuming we didn't get galactic speeding ticket! ), then, yes, the light we would see coming from Earth would be a year old.

Of course this is nothing compared to what it is like NOW on other planetary systems... planets in the Regulus/Alpha Leonis trinary star system see light from Earth that left our planet 77.5 years ago!

There is a galaxy about 1.4 billion light years from Earth that, if they had super massive telescopes and could see Earth, would see us as we were 1.4 billion years ago (when I was young). Of course that's the least of their problems, because there is a super massive black hole devouring their entire galaxy, so they probably don't much care about what we were doing (or the dinosaurs) !!!

Dave

 

[philguy]

This may seem kind of off topic but, if we could travel lets say twice the speed of light... And we did this for a year away from earth, and we looked back at earth with a telescope, would we see a year in the past?

But I think you would have to look forward to "collect" the 1-yr-old photons flying before you.


@BlueFusion: I don't think it's that easy, maybe look up "http://en.wikipedia.org/wiki/Image:Dice_analogy-_1_to_5_dimensions.svg" or generally the 4D-topic on wikipedia.
Problem is, the cubes would need to "fold into themselves" (for your 3D-perspective), but the connections within these would be different that the "2d-Cube-cross".
Well, what can I say, I'm just a limited 3D-lander.


@Zarniwoop: Judging by your name, you should know...
Anyways, it depends on the situation. If you start out from your back yard and are "shot up" there, so that you only receive acceleration along the y axis (i.e. upwards or downwards), then your tangential speed (speed along the geostationary orbit) would be the speed you had in your backyard (i.e., R[sub]earth[/sub]*2*pi/(1 day)). But up there, you need the same angular velocity (1rev/day), which is R[sub]geostat[/sub]*2*pi/(1 day). So what consequence arises out of that? You are too slow, and therefore unable to fall around the edge (or rather, curvature) of the earth, and would crash down. It would be a whole different question where...
Were you to "climb up a pole", thus increasing your tangential velocity, too (pole fixed to the ground = same angular velocity), you'd be fine.



qmorepower: yup, esp. Zero-point energy thrills and freaks me...that is just plain "abhorrent"