This Time It's Mass

Thanks for all the posts on my last thread "Question Of a Photon"

I now have some questions regarding what happens to mass when in motion, if anyone can help. Some of these are a little bit scenario specific:

1) What would an object with the mass of 1 Metric Ton (as measured under Earth gravitational conditions) weigh when traveling at 99.99% the speed of light? And what would be the time dilation effect? For example, if a clock was attached to the 1 Ton block, how long would it take for the hour hand to move from 12 to 1 o’clock as viewed from the observer reference frame?

2) Why does an object with ‘X’ invariant mass, increase its relativistic mass, when in motion? And does this increase in relativistic mass occur as soon as an object begins to move, regardless of how small the movement and resulting effect might be? And why does this increase in relativistic mass not translate in to an increase in the gravitational field?

3) Does an object with mass increase its time dilation as soon as it begins motion through space, regardless of how small the resulting effect might be?

4) Does the mass increase at an equal rate for all objects in the universe with mass, as they reach near the speed of light? And does the reduction in ‘movement through time’ also decrease equally for all objects in the universe as they increase movement through space?

5) If you were traveling in a hypothetical spacecraft at 85% the speed of light, would the photons being generated from the hypothetical light bulbs on-board also start traveling at the speed of light, or, would the effects of time dilation at this speed exhibit the same relative properties (as stated in Einstein’s Law of Special Relativity) to these photons as it would for all the other particles constructing the spacecraft and its inhabitants?

Thanks,

 

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6.) Can you do my homework for me?

 

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That depends on what mass convention you adopt. Relativity does not obligate us to say that mass varies with speed at all, and indeed most physicists today don't say that. They regard "mass" as the invariant magnitude of the 4-momentum (in natural units).

But if you wanted to know how to calculate the so-called "relativistic mass" you would use the formula m(v)=γm₀, where γ=1/sqrt(1-(v/c)²). Better yet, let this calculator do it for you:

http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/tdil.html

Scroll down to "Relativistic Mass". Notice that there are time dilation and length contraction calculators too.

To calculate that you would use the formula Δt'=γΔt, where Δt'=the elapsed time in the moving object's frame and Δt=the elapsed time in the Earth frame (I assume that is what you mean by "observer reference frame"). Δt' is the so-called "proper time".

As I said earlier, we needn't say that mass varies with motion at all. But if we do adopt that point of view, then you can see from the formula I quoted that mass is a continuous function of speed on [0,c). So the increase would start as soon as the object begins to move.

While the gravitational field of an object does vary with motion, this variation has nothing to do with "relativistic mass". If you adopt the relativistic mass convention then the equivalence between inertial and gravitational mass no longer holds. That's why the variation of m with v doesn't show up in the gravitational field.

Yes, it does. You can play around with the calculator at Hyper Physics to convince yourself of that.

If you adopt the convention m(v)=γm₀, then it holds for all bodies. The time dilation formula applies either way.

First of all, no one ever experiences time dilation. That is something that always happens to the other guy's clocks. And second, the speed of light is c in any inertial frame.

 

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Ah, I said the same thing at first, but now I don't think so.

 

Thanks for the pointer to the conversion calculator, very usefull. As I said in my first post, I'm not a physics or maths student, infact the last time I had a maths lesson was when I was 16, well over 10 years ago now.

Anyway, unfourtunatly I don't have a lecturer to validate my thinking so this seemed like the best place to ask people with the relevant knowledge.

Can I therefore bounce the following question of you...

Does time exist as a dimension because of the collective mass of the universe? From what I understand of what you have been saying, time is only experienced by objects which have mass (photons, gluons being exempt), so mass is crucial for time to be able sustain (probably not the right word) the continual interaction of the information which constructs the universe. It seems as if time and mass are closely intertwined.

Is this a justified view, or have I miss-interpreted the connection between the two, and should I throw this connection out of the proverbial window?

 

The connection between mass and spacetime is not made in SR, but it is made in GR. Unfortunately for me, I know very little GR. But in SR I don't think that the statement "time is only experienced by objects which have mass" can be shown true or false. We can say that massive objects do experience time, but we can't say much of anything about what the situation is like from the photon's point of view. Note that by "point of view" I mean "rest frame". Since a photon doesn't have a rest frame there's no way I can use SR to determine what's going on there.