Acceleration (split from Relativistic Mass)

[md65536]

5 hours ago, beecee said:

As a body gains speed, the harder it gets to get it to continue to accelerate, illustrated by the fact that the energy would need to be infinite to push it beyond "c"

If you were the body and accelerating yourself, do you know how this would feel or what you would measure? For example, if you're on a rocket accelerating away from Earth at ever-increasing speeds. I think that understanding that would help understand the issue.

(Hint: a simple rocket model implies constant proper acceleration, and is probably an easier answer. If instead you suppose constant acceleration relative to Earth you'd measure different things. You could also imagine accelerating in short rocket burns and then describe what you measure in between; what differences do you notice between subsequent burns?)

 

Another question that might help understanding: How would you describe your body's total energy (or "relativistic mass") in the frame of a muon generated by a cosmic ray in the atmosphere, relative to which your speed is over .999 c? In what way is it hard to accelerate yourself relative to it? This isn't a trick question.

 

Edited June 23, 2019 by md65536

[J.C.MacSwell]

11 hours ago, md65536 said:

 

 

Another question that might help understanding: How would you describe your body's total energy (or "relativistic mass") in the frame of a muon generated by a cosmic ray in the atmosphere, relative to which your speed is over .999 c? In what way is it hard to accelerate yourself relative to it? This isn't a trick question.

 

When you accelerate yourself with respect to everyday common frames the amount of energy used may not be very high, and the amount of acceleration with respect to those frames may seem quite considerable.

But these same accelerations with respect to your suggested muon frame? The energies measured (calculated) would be very high and the accelerations measured (calculated) relatively minor with respect to that frame.

[md65536]

17 hours ago, J.C.MacSwell said:

But these same accelerations with respect to your suggested muon frame? The energies measured (calculated) would be very high and the accelerations measured (calculated) relatively minor with respect to that frame.

Can you clarify "same accelerations"? It's confusing because a given acceleration wouldn't be the same in the two frames. Do you mean the same proper acceleration, which would be measured as relatively minor in the muon frame? Otherwise suppose the "quite considerable" acceleration is of 0.001 c, then accelerating that much in the muon's frame would be measured as an acceleration of 0.001 c (ie. quite considerable, not relatively minor).

 

Ugh, there's always complicated and simple ways to look at anything in relativity.

Complicated: Say you are at rest relative to Earth, and are able to easily accelerate to 0.001 c relative to Earth. While at rest on Earth, you are also traveling at say .999 c toward a muon. If you want that "same acceleration" of 0.001 c relative to the muon: You can't accelerate 0.001 c toward it (measured in its frame), but you can accelerate away (or decelerate) so that you're traveling at .998 c toward it. If you did this starting from at rest on Earth, you'd accelerate 333.556 times as much relative to the Earth (using more than that many times as much energy?), so you're now traveling at 0.333556 c relative to Earth (determined using composition of velocities formula).

 

Simple: When you're at rest you have a rest frame, and your mass is the same regardless of the relative velocities of other moving objects. In each of their rest frames, you're the one that's moving. You feel the same regardless of their motion (you can't distinguish between being at rest and being in a moving inertial frame), and proper acceleration is equally easy no matter which inertial frame you're in; the faster you go, the same it always feels. The difference is that a large change in velocity in your frame may be small in another frame, due to the way velocities add in special relativity, so you have to accelerate greater and greater amounts to achieve some specific acceleration in the other frame.

 

(Is this simplification valid? Can the change in total energy of an object as v approaches c, be found using composition of velocities formula, or is there something more to it?)

Edited June 24, 2019 by md65536

[J.C.MacSwell]

3 hours ago, md65536 said:

Can you clarify "same accelerations"?

Meaning the same event.

You seem to be recognizing this here...

4 hours ago, md65536 said:

The difference is that a large change in velocity in your frame may be small in another frame, due to the way velocities add in special relativity...

 

[md65536]

I just realized the topic was split, but I wanted to sum it up to bring this back to the original topic anyway.

Saying that it is "harder" to accelerate an object that is moving fast (as measured from some reference frame), can instead be said more precisely: A certain change in velocity of an object in a frame in which it is moving fast, requires a greater change in velocity (ie. higher rate of acceleration or acceleration for longer time) in a frame in which it is moving slowly, because the difference in the velocities is not the same in different frames of reference.

Edited June 24, 2019 by md65536