Acceleration as a "side effect" of dimensional contraction?

[Daecon]

I have a kind of hypothesis, of sorts. But there was something I just need to clarify.

 

Does an object travelling at exactly half the speed of light, get contracted to exactly half of it's "rest" volume - thus exactly doubling it's "rest" mass?

 

What about at 25% of light speed, and again at 75% of light speed?

 

If this is not the case, is there any kind of reference chart to show the progression between an object at rest and the resulting volume/density (with regard to this rest mass) as it approaches the speed of light, where (at least in the way I'm working my hypothesis) would make it a two dimensional volumeless and essentially an object of "infinte mass"?

 

My hypothesis works from the perspective that energy is used in "dimensionally" contracting an object, and that what we call acceleration, is merely a result that we see from the effort of reducing 3 dimensional matter into 2 dimensions.

 

Of course the energy required to squueze anything to becoming actually two dimensional woud be infinite (as it shouldn't be possible) and the resulting mass of two dimensional physical objects would also be, theoretically, infinite.

 

However I was trying to figure out how such a sliding scale of energy/mass/volume would work, hence the question at the start of my posting here.

 

I'm aware that the mathematics behind such a scale could be quite complex and admittedly I'm not mathmatician - but I'm fairly certain there must be some pattern to the relation between speed and density, that can be worked out.

 

First of all, information on the theory behind mass/density and speed as a percentage of light would be appreciated.

 

Any constructive comments would, naturally, be appreciated.

[swansont]

The length contraction formula is not linear. [math]\gamma = (1-v^2/c^2)^{-1/2}[/math]

 

But no matter what, the rest mass is unchanged by the motion - it is a Lorentz-invariant quantity.

[J.C.MacSwell]

I have a kind of hypothesis' date=' of sorts. But there was something I just need to clarify.

 

Does an object travelling at exactly half the speed of light, get contracted to exactly half of it's "rest" volume - thus exactly doubling it's "rest" mass?

 

What about at 25% of light speed, and again at 75% of light speed?

 

If this is not the case, is there any kind of reference chart to show the progression between an object at rest and the resulting volume/density (with regard to this rest mass) as it approaches the speed of light, where (at least in the way I'm working my hypothesis) would make it a two dimensional volumeless and essentially an object of "infinte mass"?

 

My hypothesis works from the perspective that energy is used in "dimensionally" contracting an object, and that what we call acceleration, is merely a result that we see from the effort of reducing 3 dimensional matter into 2 dimensions.

 

Of course the energy required to squueze anything to becoming actually two dimensional woud be infinite (as it shouldn't be possible) and the resulting mass of two dimensional physical objects would also be, theoretically, infinite.

 

However I was trying to figure out how such a sliding scale of energy/mass/volume would work, hence the question at the start of my posting here.

 

I'm aware that the mathematics behind such a scale could be quite complex and admittedly I'm not mathmatician - but I'm fairly certain there must be some pattern to the relation between speed and density, that can be worked out.

 

First of all, information on the theory behind mass/density and speed as a percentage of light would be appreciated.

 

Any constructive comments would, naturally, be appreciated.[/quote']

 

In the context I think you are pondering, the volume at 86% of c would be cut in half of it's original wrt the original frame.

[Daecon]

But no matter what, the rest mass is unchanged by the motion - it is a Lorentz-invariant quantity.

Then why is it said that mass increases as you approach the speed of light, and that at 100% it would be infinite?

 

Or have I mis-read something?

[swansont]

Then why is it said that mass increases as you approach the speed of light' date=' and that at 100% it would be infinite?

 

Or have I mis-read something?[/quote']

 

Lots of thing are said that are incorrect, or without regard to proper definitions. Why? Because some people are sloppy. Others don't really know what they're talking about. Relativity is one of those subjects that people like to distill down for public consumption (journalists, I'm looking at you), and they do so to the point that it's wrong.

 

Note that I said rest mass. I have defined what I'm talking about. Others will use relativistic mass, which is just using m = E/c², where E is the total energy. Using that definition, m is a frame-dependent quantity. That limits its usefulness in calculations, so it really isn't used all that much. And it seems to hang like a millstone around the neck of the understanding of relativity, because it confuses the heck out of many in discussions where people don't differentiate between rest mass and relativistic mass by just saying "mass."

[Daecon]

Ah... I'm afraid I may be one of those people. Is there a resource you can point me to where I can look up the difference between rest and relativistic mass?

 

Unless you could explain it for me...?

[swansont]

John Baez's mass of a photon FAQ and the links therein.

[Daecon]

Okay, I'll modify my question slightly then: if mass is always constant regardless of speed, what about volume and density?

 

If volume is reduced to half at 86% of light speed, does that mean density is doubled at 86% of light speed - and so at c would it's volume be zero, and therefore it's density "infinite"?

[Severian]

Volume is frame dependent because of length contraction.

[swansont]

c isn't attainable, but yes, the observed density would increase at higher speeds as observed by someone else.