A question about relativity

dgarrad

Ok,this may be incredibly obvious,but it's been bothering me for a while.What I was basically wondering was what happens at relativistic speeds when a n object starts to rotate?
Imagine a cylindrical object moving at 99% of the speed of light.In this example all the particles that make up the object are travelling at the same speed,and therefore experience the same time dilation and length contraction.
Now imagine that this object begins to rotate with the rotational axis being the direction of motion.Now the particles along the axis still travel along the same path as before,but the particles at any distance from the axis begin to travel in a helixical path.This means that they travel a greater distance than the particles at the centre.

Now what I want to know is what happens to these non-axis particles when the rotation begins to reach relativistic speeds too.Classicaly the rotational velocity should add to the forward velocity,but obviously this could not work at these speeds since that would result in the particles moving nearly twice the speed of light!

Can anyone help me figure out how this all works,cause as I said it's been bugging me for a while! (And if it's incredibly obvious feel free to slag me about it!)

Kaner

Hi dgarrad

Cool question.

Here's my 2 cents worth.

Seems to me that in the direction of travel all the particles have the same velocity.

My rationale is that if you add the all the vectors of the rotating particles their combined velocity will be greater. But the vector of their combined velocities will not be in the direction of travel. It will describe the helicial path.

If I am wrong and the rotating particles have greater velocity, then I imagine the mass of the offending particles would increase more than the non-rotating particles at relativistic speeds.

Capt'n Midnight

aren't you forgetting that dimensions change at high speed - but of course an observer sitting in the rotating cylinder will not notice that.

So if you were looking at the side (imagine a clock) would all the hours be the same size - no !
If the cylinder was heading to the right then from 9 to 3 the hand would be moving faster so the lengths would be shorter (it would not move as far in the same time) and those from 3 to 9 would be a little longer.

Salvador Dali watch anyone ?

dudara

If something is rotating, then it is accelerating, even if it's speed is constant. Thus when acceleration comes into relativity, I think it moves beyond special relativity and falls into the realm of general relativity, some about which I know absolutely nothing.

BattleBoar

If nothing else, finding the solution should give you plenty of practice on your tensor maths

Kaner

I am no PhD in pyysics but I think the main point here is that as far as we know, we cant go faster than the speed of light - c.

We would need to pump in a hell of a lot of energy into an object to get it to reach c. In fact it would need infinite energy, which means we cannot get an object to reach the actual speed of light. As we get close to the speed of light, then v begins to apprach c.

The E=m*c*c equation means that when v approaches c (a constant) then m will become the variable. So at relativistic speeds the mass will keep increasing so long as the energy keeps increasing.

After thinking about this some more, I believe that the answer to the question above is that the rotating particles mass will be greater than the non-rotating particles, because their total velocity will approach c before the non-rotating particles.

But this raises the question - will their size increase - in other words will the object deform to an observer on the rotating body. This might be important if we ever build a rotating spaceship that can approach the speed of light.

dgarrad

Well I'm glad it wasn't something simple that I'd overlooked!

The increasing mass would make thing very awkward to visualise,but by my understanding of things the lengths of the objects would also change,so you'd get an effect similar to the 'stretching' of normal spacial dimensions,in which the mass per non-moving unit area would stay the same.But again I could be wrong,my knowledge of special relativity is not very comprehensive.

But as Dudara says we made need to use general relativity to work things out,which I also know pretty much nothing about!

But thanks guys for helping out.I was really bored one day when I started thinking about this,and when I couldn't find a solution myself it really started to annoy me!But at least now I know a bit more,and also know that I'm not the only one who found it an awkward problem!

Sev

Originally posted by dgarrad
Now what I want to know is what happens to these non-axis particles when the rotation begins to reach relativistic speeds too.Classicaly the rotational velocity should add to the forward velocity,but obviously this could not work at these speeds since that would result in the particles moving nearly twice the speed of light!

Let say we have a barrel rotating really fast such that the walls of the barrel are moving at near light speed. Then if we are stationary beside the barrel.. All seems normal, barrel is floating in space rotating at the speed of light.. But.. if the barrel is moving at relativistic speeds, we must see time as having slowed down for the barrel. That means we wont see the barrel rotate as fast. And if the barrel is moving at the speed of light, we wont see it rotate at all. It will appear that time will have completely stopped for it. Your paradox explains time dilation, and time dilation explains your paradox? I dunno. Some day I'll have a good answer for you.

nadir

I dont think I understand the question(inparticular the helixical stuff), but I guess like its kinda something like the particles rotating on the outside will be going like .99 the spead of light relative to the axis particles. Then the object itself goes at .99 the speed of light relative to an external observer. So its all cool. I know its a bit of a retarded answer but like if you have a torch and you run with it, the light obviously isnt going faster than the speed of light.

zepp

ya if the object is rotating it is a general relativity problam not special. Bascally it will probally have the effect of warping space time around it which will cause resitance to the motion. but basically i think you will see the object warp and deform. but remember with all realitiy it is all realative so the object sees you deform.

Gleanndún

Originally posted by Kaner
But this raises the question - will their size increase - in other words will the object deform to an observer on the rotating body. This might be important if we ever build a rotating spaceship that can approach the speed of light.

first of all, no to this, because the MASS is increasing and not the volume. MASS and VOLUME are unrelated.

Originally posted by nadir
I dont think I understand the question(inparticular the helixical stuff), but I guess like its kinda something like the particles rotating on the outside will be going like .99 the spead of light relative to the axis particles. Then the object itself goes at .99 the speed of light relative to an external observer. So its all cool. I know its a bit of a retarded answer but like if you have a torch and you run with it, the light obviously isnt going faster than the speed of light.

Now this guy, though saying he's retarded, is the 1 w the right idea! i dont have a lot of experience in general relativity, but i dont really think u need it 4 this (a is perpendicular 2 v so i think we can ignore it, our favorite thing 2 do in physics;))In this scenario, i'm sure any measurements given of the rotating particles' speeds will b done so in the frame of the object. and as said above, if ur running w a flashlight, that doesnt move the photons faster than the speed of light. velocities dont add in relativistic physics. thats 1 of the main things that makes sumthing relativistic. unless theres sum special rules for this situation deriving from general relativity that i am unaware of, i would use the formula for adding velocities:

u = (u' + v)/(1 + vu'/c^2)

where u is the observed velocity, u' is the velocity in the object's own frame,
and v is the speed of that frame.

so the particles will be moving faster than the objects center, but the measured difference in that frame will not b the same as in ours. if the particles were spinning with a speed such that they approached the speed of light in the objects frame, say they were moving .99c relative to the axis, then employing the above equation, the speed observed in the "stationary" frame would b appr. equal to .9999494975c. so in the limit that both go 2 c, then the observed velocity of the particles becomes only arbitrarily close to c, closer than the speed of the object, but never reaching the speed of light, which i think is wut u were lookin 4.

Kaner

Gleanndun

My theory is that the volume will increase, and that mass and volume are related at relativistic speeds. I have not verified this as it is hard to find any publications on this matter.

It is a fact that electrons close to c have a mass about 2.5 times their rest mass. Particle accelarators are designed to account for this.

If the electrons in the object become more massive, then their angular momentum will increase and they will be forced into higher orbitals. This will increase the radius of the atoms in a way similar to the expansion of metal atoms when heated, except possibly to a greater extent. Assuming the atoms dont lose their electrons then they would be stable at the higher orbitals.

Capt'n Midnight

Originally posted by Kaner
My theory is that the volume will increase,

If the electrons in the object become more massive, then their angular momentum will increase and they will be forced into higher orbitals. This will increase the radius of the atoms in a way similar to the expansion of metal atoms when heated, except possibly to a greater extent. Assuming the atoms dont lose their electrons then they would be stable at the higher orbitals.

It's all relative I suppose,

Volume should shrink 'cos length shrinks at higher speeds
and unless I'm getting mixed up tween special and general relativity, from the electron's own frame of reference nothing has changed, chemical reactions depend on electron movement - taken to its conclusion you are saying that all chemical bonds would break down as you approach the speed of light, BTW: when metals get hotter they melt...

nadir

Originally posted by Kaner
Gleanndun
My theory is that the volume will increase, and that mass and volume are related at relativistic speeds. I have not verified this as it is hard to find any publications on this matter.

I think you are thinking about this wrong. Volume really doesnt have anything to do with it afaik. But im a bit confused, I mean volume is like an occupied area of space, but you are talking about particles and stuff, for which i think it would be almost impossible to guage the volumes in question, especially considering the bounding areas of such particles are not defined.

It is a fact that electrons close to c have a mass about 2.5 times their rest mass. Particle accelarators are designed to account for this.

I dont know about this either, erm where did you read that? at high speeds such as those obtained in accelerators, it can be observed that an electron can occupy two different positions in the same time frame. Are you just adding the masses in this frame? cause im not sure you can do that, taking into account that that frame is only relevant to the observer which in our case would be the speeding object and not the external observer, and thats quantum mechanics anyway, and kinda away from what we are talking about with special relatiavity. For a start the electron is the fundamental unit of mass 511 KeV. were it to become more massive then, erm well it wouldnt be an electron anymore.

If the electrons in the object become more massive, then their angular momentum will increase and they will be forced into higher orbitals. This will increase the radius of the atoms in a way similar to the expansion of metal atoms when heated, except possibly to a greater extent. Assuming the atoms dont lose their electrons then they would be stable at the higher orbitals.

ok so lets say you were right and that our electrons became something more than 'electrons' , again you cant take this to be any sort of general physics problem, because it involves quantized states you must take electron spin into account, but anyway thats all besides the point.

Originally posted by Capt'n Midnight
Volume should shrink 'cos length shrinks at higher speeds

again i dont get the volume thing. Maybe im totally missing the point here, please correct me if i am. as for chemical bonds and stuff, lol im afraid I cant remember much about that, what have you weak var del wall forces and what not. Dunno

Gleanndún

Originally posted by nadir
I dont know about this either, erm where did you read that? at high speeds such as those obtained in accelerators, it can be observed that an electron can occupy two different positions in the same time frame. Are you just adding the masses in this frame? cause im not sure you can do that, taking into account that that frame is only relevant to the observer which in our case would be the speeding object and not the external observer, and thats quantum mechanics anyway, and kinda away from what we are talking about with special relatiavity. For a start the electron is the fundamental unit of mass 511 KeV. were it to become more massive then, erm well it wouldnt be an electron anymore.

they mean in our frame--not the electrons frame.
and just 2 clarify, electrons in the observing frame can far exceed 2.5 times their mass. in fact, in the limit that their speed approaches c their mass approaches infinity, which is where we get that whole "u cant go the speed of light" thing from.

cf. m'=m/ã(1-v^2/c^2)

Woden

electrons are still electrons no matter how fast they are moving and as a result of how fast they are moving how massive they are. what people may consider somewhat fundamental is the rest mass of an electron due to the fact that the electron is considered point like with no known substructure at this time.

yes close to c electrons are a hell of a lot more massive then 2.5 times there rest mass. typically in particle accelerators they are so massive that their energy can just be consider to be equal to their momentum as the rest mass is negigble.

chemical bonds breaking down as you approach the speed of light? an interesting concept and i suppose it would depend on the method used to give the particles enough energy for them to reach speeds close to c, however at the moment i can't envision a method that would allow you to impart such large amounts of energy to a molecule and for it to not shake itself apart.

consider a typical chemical bond in the order of 500kJ per mole

which is 500000 J per mole

which is 5*10^5/6.023*10^23 J per molecule which is about 10^-18 J per molecule

then you consider a typical proton proton collider that can operate in the GeV range which is low enough these days. 1Gev = 1.6*10^-10 J iirc now even if you consider the fact that you had a gas like CO which would contain say 28 nucleons to acclerate (ignoring the fact that the neutron is not charge) this 1GeV of energy is orders of magnitude greater then the strength of the chemical bond.

Woden

electrons becoming more massive => increased angular momentum. are you thinking along the lines of L = r X p. if so not sure how applicable these classical non relativisitic expressions are here in this situation especially with quantised energy levels and such however again i suspect the energies required to signifcantly change the mass of electron would be well past the ionisation energy of any individual atom, the ionisation energy for hydrogen i think is may 13eV or something

Kaner

I am happy to see this topic has attracted some discussion, rather than the usual (and often illogical) attempts at slap downs you get on Boards.ie....ha ha.

Maybe the whole concept of humans travelling at the speed of light is for the birds.

Speaking of that, I saw a programme once that said if you travelled at the speed of light you would see the back of your head. Now I never came close to understanding that one - have any of you geniuses out there got an explanation for this.

Capt'n Midnight

As you approach the speed of light your head will increase in mass - you will become increadibly dense.
So dense that you brain will be a black hole that will bend light around corners.

No that ain't the correct explaination - but at high speeds you will travel nearly as fast as the rays of light from your head. It's like a fish looking up at the surface of water - they can only see things above the surface in a circle - as you approach the speed of light you won't enjoy the view - mainly because light won't be able to reach you the way it would normally.

Woden

when you travel as speeds close to c though light still travels at a speed c relative to you?

Gleanndún

light still travels at c relative 2 anything traveling at c, which is another of the main concepts of relativity: the speed of light is constant, no matter what speed u travel at. cf. the earlier equation:

u = (u' + v)/(1 + vu'/c^2)

If we say that v=c, and u'=c, then we have:

u = (c + c)/(1 + cc/c^2) = 2c/(1 + 1) = 2c/2 = c.

rde

I think everyone's making this a lot more complicated than it actually is (warning: ianap)
As our object approaches c, it'll get more massive. As it does, angular momentum must be conserved, so its spin rate will decrease. By the time it gets to the point where the outer reaches would've been going faster than c, it'd have stopped spinning so the problem will have disappeared.

ps: Gleanndún: can you please stop using sms shorthand in the same post as equations? Surely 'to' isn't that hard to type?

Woden

i've chatted to a couple of people about this anyway who've taken general relativity this year though i didn't get much info.

what i did find out is that there is no problem at all with things going faster then the speed of light, however for this to occur no information can be sent, it can't effect casuality and stuff. will look into this more.

data

planck2

I'll get back to this question after the exams, i.e. after the 24th of May

Gleanndún

Originally posted by rde
I think everyone's making this a lot more complicated than it actually is (warning: ianap)
As our object approaches c, it'll get more massive. As it does, angular momentum must be conserved, so its spin rate will decrease. By the time it gets to the point where the outer reaches would've been going faster than c, it'd have stopped spinning so the problem will have disappeared.

I think we have a winner:D

ps: Gleanndún: can you please stop using sms shorthand in the same post as equations? Surely 'to' isn't that hard to type?

my bad, ill try ...to (fighting habit>.<) lay off:p

planck2

No we don't have answer, I suggest that Einstein's book: Relativity; the special and general theory be consulted. It's quite easy to read and quite cheap too, only 12 euro

planck2

Imagine an observer in a reference frame K and another observer in a reference frame K'. In the first situation, i.e. K' is moving with uniform velocity 0.999c ( c = 3*10^8 m/s ) in a flat space-time of course. The usual consequences of such a situation are observed by the observer in K with regard to length contraction and time dilation.

Now let us move onto the situation where the reference frame K' is rotating as viewed by the observer in K. An observer in K' sitting on top of the rotating cylinder
can regard himself at 'rest' and he will experience a centrifugal force , i.e. a radially outward acceleration, which shall be resisted by his inertial mass.

The observer has no way of knowing, at least to first order, if this due to himself encountering a gravitational field or because his rest frame is linearly accelerating
( Einstein's Principle of Equivalence ).

The observer in K' wishes to know the nature of the space-time in his frame. What does he do to gather such information ? He could set up two clocks of the same material make up. One at the centre of the rotating cylinder and one at the top or the bottom of the cylinder. These two clocks in order for our measurements to make any sense must of course be simultaneously set off.

If the cylinder were not moving in uniform motion at 0.999c, but only rotating then we could say that from K no time dilation on the clock at the centre would be observed because it is not moving relative to K, but the clock at the top or bottom of the cylinder would have a time dilation. However, in our set up the cylinder is moving at 0.999c and rotating so as measured from K both clocks have a time dilation . If we carry out length measurement we do note length contraction, but due to rotation
and uniform linear motion we cannot say anything comprehensive because if we place a ruler along the rotation direction we note contraction as observed from K, but if we place it along the height of the cylinder we not e that when observed from K the ruler contracts in length when then angle that rotating cylinder makes wth the direction of linear motion is 0 or 180 degrees its length also contracts as noted from K. We cant really say anything about time or space data because measuring length we sometimes get a ratio bigger than pi = 3.14. Thus further investigations are needed to gain some precise data on the nature of space and tim with regard to K'.

Kaner

A couple or three things:

1. It seems to me that people are confusing travelling at the speed of light with relative motion.

If you are on an object traveling close to the speed of light certain phenoma occur, as described in the E=mc^2, ie, mass will increase. I don't think this mass increase depends on whether or not you are an observer. Hence "frames" are not "relative" to the argument. ;0)

The time and length contractions are only seen by observers.

2. Regarding an object coming to a standstill to conserve angular momentum. I am not sure that you could define stopping as conservation of angular momentum.

Correct me if I am wrong, but an increase in the mass of a rotating body will increase angular momentum, which is what is going on here. This a different thing than conserving it.

3. A rotating object does not necessarily mean that general relativity applies, since the acceleration of a rotating object is directed towards the centre of the object and will total zero.

Gleanndún

Originally posted by Kaner
A couple or three things:

If you are on an object traveling close to the speed of light certain phenoma occur, as described in the E=mc^2, ie, mass will increase. I don't think this mass increase depends on whether or not you are an observer. Hence "frames" are not "relative" to the argument. ;0)

the increase in mass occurs only in the "stationary" frame, because in the frame of the cylinder, it is this "stationary" frame that is moving, and the cylinder itself is stationary. If the cylinder gained weight in its own frame, then it would be able to tell that it was moving, which would violate the concept of relativity, i.e. there is no absolute frame, all movement is relative.

2. Regarding an object coming to a standstill to conserve angular momentum. I am not sure that you could define stopping as conservation of angular momentum.

Correct me if I am wrong, but an increase in the mass of a rotating body will increase angular momentum, which is what is going on here. This a different thing than conserving it.

momentum must be conserved because there r no forces acting in this scenario, therefore momentum of any kind cannot change. this is why angular momentum must be conserved, and since the equation for angular momentum is L=1/2Iw^2, if mass increases, then I will increase, which means that w must decrease for the value L to remain constant. in the limit that the speed of the cylinder approaches c the mass of the object goes to infinity, which mans that the moment of inertia I will also go to infinity, therefore to maintain L the angular speed w must go to zero. This also makes sense from another standpoint: ans speed increases the time for objects in the speeding frame will slow. as the speed approaches the speed of light, time dilates infinity, i.e. time stops. the cylinder is rotating at some speed with respect to time. if time stops for the cylinder, the amount of time for it to rotate any amount dtheta will be infinite, so the cylinders rotation will essentially stop as well.

3. A rotating object does not necessarily mean that general relativity applies, since the acceleration of a rotating object is directed towards the centre of the object and will total zero.

I'm not quite sure what you mean here...the acceleration will total zero?

Gleanndún

p.s. plank2, i couldn't really understand what you were saying. could you clarify that please?

Agent Smith

Originally posted by Gleanndún
p.s. plank2, i couldn't really understand what you were saying. could you clarify that please?

likewise

planck2

A few comments :

1. Frames are always "relative" to the argument because what I see is not what you see, but the laws of physics are still the same in every frame, i.e. there is no special place in the universe.

2. General Relativity applies to every physical situation ( apart from the region of a singularity in space time, black holes). Sometimes we don't need to use it for example in flat space we just use special relativity rather than general relativity.

3. For the time being can we just leave out this idea of increasing mass, if the cylinder is moving at 0.999c any object of mass m will have an infinite amount of energy already so the fact that the cylinder begins to rotate won't really make any difference.

4. Angular momentum L is Iw, i.e the product of the moment of inertia of a body times it angular velocity.

5. Most importantly c = the speed of light is the same for all observers.

6. Addition of velocities in general relativity is not quite the same as in special relativity, we have to take into account the acceleration.

7. For purely rotating refernce frames we can't really say anything about the nature of the space or time because time dilation occurs at some points in the frame and not at others and also because length contracts in the direction of motion and not along the diameter. For our cylinder we have both rotation and linear motion so we have time dilation at all points some points more than others and length contraction as well.

nadir

yea, i dig frames aswell.

thing is when our object gets more massive, thats just to the external observer right, it doesnt actually appear to be more massive to the object in question !!! ? !!! wouldnt it be best to take everything in frames and work regular newtonian physics on individual frames rather than to the problem as a whole and not try to apply newtonian physics concerning, momentum .etc to special relativity problems.

planck2

Yes that would be correct the object only gets more massive to the external observer who is at rest.

Special relativity is better because the Newtonian set up is a limitg case of special relativity that is to say if we let the velocity in Special Relativity go to zero we get the Newtonian equations of motion.

Woden

morning planck hows it going?

when the object gets more massive though does it occupy more space? or does retain the same physical dimensions, length contraction aside? i'm kinda thinking along the lines of density and volume here?

how applicable are these?

data

planck2

Evening Data, hope you kicked some good old french ass last night.

I know where your coming from, i suppose in an external frame the density probably would change but in GR we always talk about such things as the proper density of the matter distribution which I think means that basically all we ever care about is the density as measured in the moving objects rest frame.

There is also a thing in relativity where by there is no such thing as a truly rigid body only approximations to such a situation, the whole length contraction thing.

Getting back to the increasing mass, volume, density thing. We know the mass increases and the dimensions decrease so the volume must decrease also according to the external observer and so the density will probably increase. What do you think?

Woden

well if we see the see the object to decrease in length and we know it increases in mass then we how both things working together to give a larger density.

i presume though that the simple density = mass / volume relationship applies.

how does this catch ya? you accelerate something so much that its length contracts and its mass increases. as a result of the increasing density we reach a state where there is a fermi pressure due to the degeneracy pressure of the electrons, like a white dwarf, further acceleration over comes this degeneracy pressure, until neutrons are formed and there is degeneracy pressure form this effectively generating a small neutron star type thing and so on to a black hole....

however if its all to an external observer i dont' know, the question is does the mass actually increase or have we just observed/measured it to increase, coz according to the moving rod or whatever all of space has just contracted if i'm remembering this correctly?

data

Gleanndún

i dunno about the fermi thing bc im not there yet (im but a wee little freshman^^) but data, u gave me a good question: mass increases in the external frame, so does that mean that the gravitation force of attraxion also increases? because (to answer ur question) we kno that mass doesnt actually increase, and length doesnt actually contract, they merely appear to in the external frame. im not sure y mass appears 2 increase, but length contraxion is do 2 the fact that information cant travel faster than the speed of light, and it has 2 do with we cant really c the positions clearly cuz the obj is moving so fast, but im not sure how we percieve mass 2 increase. wow, this is a disorganized post, like my mind i guess:p, but neway, so my question is does F of gravity increase in the external frame?

Woden

the fermi thing basically means that if you squeeze an object hard enough it will start to resist as you are pushing electrons in to lower and lower energy levels. however it is impossible for the electrons all to occupy the same energy levels in a solid due to the pauli exculsion principle. so basically there is a pressure which resists your squeeze. this pressure is what stops white dwarf stars collapsing. and it is also a contribution to the pressure in the sun which stops it collapsing but for a star the mass and radius of the sun it is a negligble contribution.

data

planck2

Data thinking about it again I'm not so sure if the volume decreases however if view the mass to increase the density will stay thus increase whether the volume decreases or stays the same. However the situation you were enquiring about wouldn't happen though because what we see doesn't mean that actual goings on inside changes as well. We just see an external change in the space time and mass increase nothing more

Woden

yeah this is the type of stuff, that weirds me out a little, that the particles mass or lifetime for example hasn't increased really, we just observe it too. while from the particles point of view, decaying atmospheric muons for example the distance to the earth is contracted and so they don't exist for longer then they should according to them

bah damn relativity, i should be back on campus tomorrow planck not getting that much done at home

might cya then

data

Gleanndún

aye, the things only conracting 2 us, and we only see it to be contracted, but in its own frame its the same length.