A question about relativity

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.