Taking my girlfriend to Alpha Centauri on the Millennium Falcon 2

[Gian]

17 hours ago, swansont said:

 

17 hours ago, Halc said:

Time lords live in a universe with significantly different laws of physics. Same for Star Wars/Trek.

The problem is that there are two kinds of mass: proper mass (frame invariant) and coordinate mass (frame dependent). Use of the term 'mass' was sort of ambiguous until around 1950 when the term was formally assigned to mean proper mass. But using it to mean coordinate mass (as Einstein did) persists in pop sources to this day, and chatbots will likely still use it since those pop sources are the larger percentage of its training data.

 

 

Hi Mr Swansont and Mr Halc!

looks like co-ordinate mass is a location like the balancing point at the centre of a mass rather than the mass itself.

And whatever its nature the consequences are the same for space travel; that is in getting to c, mass  of my spaceship becomes infinite and so infinite energy is needed.

Co-ordinate mass and resting mass are still both mass?

Is that right?

Cheerz

GIAN🙂XXX

[swansont]

36 minutes ago, Gian said:

 

Hi Mr Swansont and Mr Halc!

looks like co-ordinate mass is a location like the balancing point at the centre of a mass rather than the mass itself.

And whatever its nature the consequences are the same for space travel; that is in getting to c, mass  of my spaceship becomes infinite and so infinite energy is needed.

Co-ordinate mass and resting mass are still both mass?

Is that right?

Cheerz

GIAN🙂XXX

The coordinate mass is just a proxy for total energy (rest mass energy and kinetic energy), so it’s redundant. The mass that shows up in most of the equations is the rest mass. 

Coordinate mass has nothing to do with center of mass calculations. “coordinate” and “proper” are used to refer to issues involving frames of reference 

[Halc]

1 hour ago, Gian said:

looks like co-ordinate mass is a location

No, not at all. As swansont points out, the term is used to refer to mass issues involving frames of reference.

Mass of any kind is a resistance to acceleration. Coordinate mass is simply a coordinate dependent mass that you've been speaking of:

1 hour ago, Gian said:

in getting to c, mass  of my spaceship becomes infinite

Say your proper (physical) mass is 80 kg and so is your coordinate mass relative to the frame of your shoe.  Relative to the frame of some muon, your mass is still 80 kg but your coordinate mass (some sites call it relativistic mass) would be say 500 kg. Notice that all we did was an abstract change of reference frames (coordinate systems) and there was no requirement for energy or acceleration. Mass is physical and frame independent: it is 80 kg in any frame.  But coordinate mass is a frame dependent abstraction,  ranging from 80 on up to any arbitrary value depending on the coordinate system chosen.

Notice also that no mention of location was made in any of that.

[Gian]

On 10/31/2024 at 7:35 PM, Halc said:

No, not at all. As swansont points out, the term is used to refer to mass issues involving frames of reference.

Mass of any kind is a resistance to acceleration. Coordinate mass is simply a coordinate dependent mass that you've been speaking of:

Say your proper (physical) mass is 80 kg and so is your coordinate mass relative to the frame of your shoe.  Relative to the frame of some muon, your mass is still 80 kg but your coordinate mass (some sites call it relativistic mass) would be say 500 kg. Notice that all we did was an abstract change of reference frames (coordinate systems) and there was no requirement for energy or acceleration. Mass is physical and frame independent: it is 80 kg in any frame.  But coordinate mass is a frame dependent abstraction,  ranging from 80 on up to any arbitrary value depending on the coordinate system chosen.

Notice also that no mention of location was made in any of that.

Hi Mr Halc, if the co-ordinate mass of the Falcon 2 is approaching infinte at 99.99%c, is it also true to say that objects stationary relative to the Falcon's velocity are kinda... much "lighter?" 
cheerz

DECLAN xxx😊

[KJW]

13 minutes ago, Gian said:

Hi Mr Halc, if the co-ordinate mass of the Falcon 2 is approaching infinte at 99.99%c, is it also true to say that objects stationary relative to the Falcon's velocity are kinda... much "lighter?" 
cheerz

DECLAN xxx😊

No. If an object is at rest relative to the Falcon 2, then its mass in the frame of reference of the Falcon 2 will be the rest mass of the object.

Note also that in the frame of reference of the Falcon 2, the mass of the Falcon 2 will be the rest mass of the Falcon 2. Also, in the frame of reference of the Falcon 2, the mass of the earth, which is moving at 99.99%c relative to the Falcon 2, will be approaching infinite.

 

Edited Monday at 07:42 PM by KJW

[Gian]

2 minutes ago, KJW said:

No. If an object is at rest relative to the Falcon 2, then its mass in the frame of reference of the Falcon 2 will be the rest mass of the object.

 

Thanx. I'm still having difficulty with the meaning of "relativistic mass." Sounds like "mass" isn't a very good word to use in it. But I guess it means a kind of "virtual" mass. If the Millennium Falcon2's engines are accelerating (by 1G) upto 99%c for some reason a helluva lot more energy is needed even though the rest mass of the Falcon2 is the same and the acceleration is the same.

Cheerz
DECLAN

[KJW]

The assumption is that the Falcon 2 is getting its power to accelerate from an external source, and that the rest mass of the Falcon 2 is not changing.

 

[Gian]

9 minutes ago, KJW said:

The assumption is that the Falcon 2 is getting its power to accelerate from an external source, and that the rest mass of the Falcon 2 is not changing.

 

But if the rest mass of the Falcon2 is the same at eg 95%c and the acceleration of 1G is the same as when the journey started, why does the relative mass increase? I know that's what the math requires, so I guess that's just the way the universe is constituted...🤯😊

Edited Monday at 07:57 PM by Gian

[KJW]

In special relativity, the energy-momentum vector is a four-component vector in spacetime. The time component corresponds to the energy, the three spatial components correspond to the momentum, and the magnitude of the vector corresponds to the invariant rest mass. (Note however that for dimensional consistency of units, E=pc=mc²).

 

49 minutes ago, Gian said:

But if the rest mass of the Falcon2 is the same at eg 95%c and the acceleration of 1G is the same as when the journey started, why does the relative mass increase? I know that's what the math requires, so I guess that's just the way the universe is constituted...🤯😊

Because it's being described in the earth's frame of reference, and in that frame of reference, the energy component of the four-component energy-momentum vector is increasing, though the invariant magnitude of this vector is not changing. The formula that describes the invariant rest mass in terms of energy and momentum is:

[math](mc^2)^2 = E^2 - (pc)^2[/math]

........................................

[math](m_{\text{rest}}\ c^2)^2 = E^2 - (pc)^2
\\
E = m_{\text{relativistic}}\ c^2
\\
p = m_{\text{relativistic}}\ v
\\
(m_{\text{rest}}\ c^2)^2 = (m_{\text{relativistic}}\ c^2)^2 - (m_{\text{relativistic}}\ \dfrac{v}{c}\ c^2)^2
\\
m_{\text{rest}}^2 = m_{\text{relativistic}}^2\ \left(1 - \dfrac{v^2}{c^2}\right)
\\
m_{\text{rest}} = m_{\text{relativistic}}\ \sqrt{1 - \dfrac{v^2}{c^2}}
\\
m_{\text{relativistic}} = \dfrac{m_{\text{rest}}}{\sqrt{1 - \dfrac{v^2}{c^2}}}
[/math]

 

Edited Monday at 08:46 PM by KJW

[KJW]

Also:

[math]\text{For }v \approx 0:
\\
\dfrac{1}{\sqrt{1 - \dfrac{v^2}{c^2}}} \approx 1 + \dfrac{1}{2} \dfrac{v^2}{c^2}[/math]

[math]\text{Therefore:}
\\
m_{\text{relativistic}}\ c^2 - m_{\text{rest}}\ c^2 = m_{\text{rest}}\ c^2 \left(\dfrac{1}{\sqrt{1 - \dfrac{v^2}{c^2}}} - 1\right)
\\
\approx \dfrac{1}{2} m_{\text{rest}}\ v^2[/math]

 

Edited Monday at 09:30 PM by KJW

[Halc]

2 hours ago, KJW said:

No. If an object is at rest relative to the Falcon 2, then its mass in the frame of reference of the Falcon 2 will be the rest mass of the object.

Note also that in the frame of reference of the Falcon 2, the mass of the Falcon 2 will be the rest mass of the Falcon 2. Also, in the frame of reference of the Falcon 2, the mass of the earth, which is moving at 99.99%c relative to the Falcon 2, will be approaching infinite.

Pretty much that answer, yes, except I don't remember Earth being involved in the question.

I had just chosen a frame where the ship (and Earth too) were moving at .9999c  But yes, in the frame where the Falcon is at rest, its coordinate mass and mass are identical, by definition.

[KJW]

43 minutes ago, Halc said:

I don't remember Earth being involved in the question.

No, but I had to dispel the view that if Falcon 2 is more massive from the perspective of Earth then Earth is less massive from the perspective of Falcon 2.

 

Edited Monday at 10:32 PM by KJW

[Halc]

5 minutes ago, KJW said:

No, but I had to dispel the view that if Falcon 2 is more massive from the perspective of Earth then Earth is less massive from the perspective of Falcon 2.

 

But the perspective of Earth was not mentioned.  Just "co-ordinate mass of the Falcon 2 is approaching infinte at 99.99%c", which is true of me now relative to some frame. No fancy ship needed.

But sure, if that speed is relative to some other object, then relative to the ship, it is the moving object (Earth??) that gains coordinate mass.

Gian also implies that acceleration and/or energy is required for something to have a large coordinate speed. This isn't true at all since several examples have been given of Earth moving at nearly c. It's a coordinate effect. Nothing is physically different in such a frame.

[KJW]

34 minutes ago, Halc said:

It's a coordinate effect. Nothing is physically different in such a frame.

Yes, it is worth keeping in mind that even as we sit in front of our screens, there are frames of reference relative to which we are moving at arbitrarily high speeds even if those frames of reference do not correspond to any observer or object.

 

[Halc]

3 hours ago, KJW said:

Yes, it is worth keeping in mind that even as we sit in front of our screens, there are frames of reference relative to which we are moving at arbitrarily high speeds even if those frames of reference do not correspond to any observer or object.

There's always an object stationary in almost any arbitrary frame choice, even if it's just a muon or neutrino somewhere.

Observer, no, but observers in relativity don't actually observe anything except instruments, which can be done by anybody regardless of motion.

For instance, a fast approaching clock is observed to run fast despite actually running slow in the observer's frame. His role is to run the the computations and provide a name for the frame, neither task requiring any actual observation.

 

As for my assertion that say length contraction is not a physical effect, there are examples that can demonstrate it so. Rotation is absolute so via rotation, coordinate effects have physical consequences.  A spinning ring will fit through an identical (*) ring not spinning. That's real contraction and not just coordinate like the barn pole thing is.

Another example is a circular train track packed with cars.  As they pick up speed, more cars will fit in the same track who's circumference is unchanged, despite the fact that relative to any one train car, the track just below it is shorter and one would think that relative to the cars, fewer would fit in the same contracted circle.  Not so.

 

* Unless really thin (2D), a spinning 3D object cannot be identical to a non-spinning one.

Edited Tuesday at 02:54 AM by Halc