"Mass doesn't change with speed" DEBUNKED

[Farsight]

Do you also believe that Intelligent Design should be taught in schools?

I take exception to that.

Edit: no, I certainly don't believe Intelligent Design should be taught in schools. I very much dislike religion.

 

[Farsight]

By the way, your equations are wrong:

$$E^2 = m_0^2 c^4 + p^2 c^2 = h^2 f^2$$

only implies for a photon that

$$p = \frac{hf}{c}$$.

Huh? No they're not, and what's all this about?

IMHO the equation above relating energy to mass and momentum is an either-or fudge to cope with mass-ive or massless entities. It ducks the issue of what mass is.

 

[2inquisitive]

CANGAS,
As I said in my previous post dp/dt is not zero in your experiment since you need to accelerate the "flywheel" to the considered speed of 0.866C and so you have a net force F acting.
Initially, at t1, you have angular momentum p1. Finally, at t2, you have p2.
The difference is p2-p1=Δp.
Now, F=Δp/Δt which is the average force acting on the flywheel through the space-time during the interval Δt=t2-t1.

No, the observer could accelerate away from a flywheel spinning in space and the observer would still see the flywheel slow down in its rotational speed once the observer stops accelerating in his new inertial frame, according to Special Theory. It has been proven that accelerating an object (the observer) has no effect on the rate it counts time, only acceleration due to a gravitational field causes clocks to slow in the non-inertial frames.

Letting the flywheel free-fall in a gravitational field slows 'time' relative to a stationary observer as it nears the gravitating object, but what 'force' could slow the actual rotational speed of the flywheel itself?

 

[Pete]

Letting the flywheel free-fall in a gravitational field slows 'time' relative to a stationary observer as it nears the gravitating object, but what 'force' could slow the actual rotational speed of the flywheel itself?

No force (torque actually, since we're talking rotation) is applied.
Torque is the rate of change in angular momentum.
In this case, the angular momentum is constant. Of course, it immediately follows that angular momentum is not determined by the newtonian formula, since the angular velocity is changing while the angular momentum is not.

 

[martillo]

2inquisitive wrote:

the observer could accelerate away from a flywheel spinning in space and the observer would still see the flywheel slow down in its rotational speed once the observer stops accelerating in his new inertial frame, according to Special Theory.

There are two possibilities to see the flywheel slow down:
One is this cited above, changing the frame of observation and this one was already largely covered by Trilarian, Tom2, etc when they state that in that case the problem is that the momentum is frame dependent. Different observers measure different momentums of the same flywheel as the velocity is measured different. This happens also in Classical Physics!
The second one was the pointed one by CANGAS when he asked for the problem when the frame is maintained the same and the flywheel is accelerated to some velocity. This is the problem I covered finding that there is a non zero force F=Δp/Δt due to the unavoidable acceleration which causes the variation in the momentum.

They are two cases corresponding to two experiments physically very different.

 

[2inquisitive]

martillo,

One is this cited above, changing the frame of observation and this one was already largely covered by Trilarian, Tom2, etc when they state that in that case the problem is that the momentum is frame dependent. Different observers measure different momentums of the same flywheel as the velocity is measured different. This happens also in Classical Physics!

Are you stating that I will measure the rotational velocity of a flywheel as different if I am moving at a various non-relativistic velocities wrt the flywheel?

The second one was the pointed one by CANGAS when he asked for the problem when the frame is maintained the same and the flywheel is accelerated to some velocity. This is the problem I covered finding that there is a non zero force F=Δp/Δt due to the unavoidable acceleration which causes the variation in the momentum.

There may be some confusion about the flywheel's charateristics in this thread. I stated a flywheel rotating on frictionless bearings. How is the non-zero force (the acceleration) that slows the flywheel applied? My second example was of a flywheel in gravitational freefall anyway.

 

[2inquisitive]

No force (torque actually, since we're talking rotation) is applied.
Torque is the rate of change in angular momentum.
In this case, the angular momentum is constant. Of course, it immediately follows that angular momentum is not determined by the newtonian formula, since the angular velocity is changing while the angular momentum is not.

The part in bold is what I do not agree with. Why would a stationary observer see the angular velocity of the freefalling flywheel change? I agree that the stationary observer would see a change in a freefalling cesium clock's rate, but not a change in the rotational speed of a freefalling flywheel.

 

[martillo]

2inquisitive,
I'm sorry, I made a mistake.

Now I agree with Pete in that the angular momentum is measured the same in any relativistic frame since the factor γ in the definition of the momentum cancels with that of the change in the time variable corresponding to velocity.

CANGAS includes γ into the mass while Trilarian, Tom2, etc consider a non classical definition of the momentum where the same factor appears in the formula by definition. Actually the formulas are the same!

In both cases there is no change in the angular momentum which remains constant.

 

[martillo]

Something to be considered and that haven't been done is that Relativity's space-time transformation predicts that the velocity of different parts of the disk or flywheel are not the same at relativistic speed. The velocities parallel to the velocity of the center vary differently from those in other directions.
The disk/wheel is someway deformated!
Then it does not make sense to talk that the disk/wheel slows down, it acquires a complex distribution of velocities...

 

[Farsight]

I'm not quite happy with "complex distribution of velocities", martillo. I can't quite put my finger on why. In similar vein I've always been unhappy about passing a planet or sun at a relativistic velocity. It's going to look flattened, like a thick-crust pizza or a maybe a disk, but it's rotating.

 

[martillo]

farsight,
That's the relativistic prediction: in average it rotates but with some parts compressed and others decompressed.

 

[Farsight]

The flattened planet would look rather like this martillo:

(¯¯¯)

Sorry, that's a top view. It would actually look like this:

○

I hope you know what I mean. The transverse motion → would be faster than the forward ↓ and backward ↑ motion. It feels like a problem.

 

[martillo]

Yes, it would be seen (in Relativity all depends in how things are observed by different observers) as something elastic...

Do you believe in Relativity or have some scepticism?

 

[Farsight]

I'm fine with Relativity, but not with the interpretation, which I think has been skewed since Einstein's day. Anyhow it's not a matter of belief or scepticism. What's there is there, and that's what we want to find out about. What we see isn't necessarily what's there. It's a matter of ontology.

A planet is a rotating sphere. Not a flattened oval where the rotation speeds up at either end.

 

[martillo]

2inquisitive,

There may be some confusion about the flywheel's charateristics in this thread. I stated a flywheel rotating on frictionless bearings. How is the non-zero force (the acceleration) that slows the flywheel applied?

That is Relativity!
The flywheel doesn't change its state but its movement is observed differently at different velocities by an observer. This is a relativistic prediction which makes some sense since momentum and energy are conserved.

Everything looks strange with Relativity's predictions but we are told that our intuition is wrong and Physics don't need to agree with "common sense" isn't it?
I don't agree with this but I must recognize that Relativity has a large degree of mathematical consistency and that's why it is the "stablished" theory today...

 

[Pete]

The part in bold is what I do not agree with. Why would a stationary observer see the angular velocity of the freefalling flywheel change?

I don't know. It seems to be part of the nature of the Universe... I don't know why.

All I know is that it's what is predicted by the best models of the Universe that we have.

 

[BenTheMan]

Huh? No they're not, and what's all this about?

IMHO the equation above relating energy to mass and momentum is an either-or fudge to cope with mass-ive or massless entities. It ducks the issue of what mass is.

These are the correct equations, whether you accept them or not. As soon as something is moving, the mass-energy relation is the equation that I wrote down.

Mass is generated by the coupling of matter to the Higgs field. Case closed.

 

[Kumar]

"Mass doesn't change with speed"

Can "rest mass" be effected with energy intraction with mass, say heat with a substance? How mass in created?

Change of speed can also be considered an energetic interaction with mass.

 

[Farsight]

These are the correct equations, whether you accept them or not. As soon as something is moving, the mass-energy relation is the equation that I wrote down.

Mass is generated by the coupling of matter to the Higgs field. Case closed.

LOL, and the earth is flat because it says so in this here book.
Bah, you don't understand mass at all. Higgs field, LOL.

 

[(Q)]

LOL, and the earth is flat because it says so in this here book.
Bah, you don't understand mass at all. Higgs field, LOL.

What's the problem? If particles can acquire their mass from interacting with the Higgs field, then we can determine the mass by how strong the coupling. However, the Higgs field is more a requirement to understand the symmetries involved as opposed to merely predicting the mass.