B What if we use a non physical reference point to measure an object's mass?

[Malemsana]

TL;DR Summary

If we use non physical reference point to measure an object's total mass (rest+reletivistic/motion) mass. Than our non physical point is not bounded to laws of physics since it has no physical properties. Than we will see the object we are trying to measure mass has infinite mass, and thus becoming a blackhole.

Concider a planet A, which is a planet just same as earth (for familiarity).

When we try to mesure it's total mass (rest + relativistic mass), we have to mesure it from some reference. (Because motion is relative)

Let's put reference point as planet B which is moving away from planet A at a speed.

Now to calculate it's total mass, we need to add up all mass including its rest, relativistic, and any kind of other energies such as kinetic etc as energy= mass by Einstein mass energy equivalence principle.


For planet B's reference point,

Plant A's total mass is = rest + reletivistic.

Rest mass is a fixed quantity, however the reletivistic mass can be varied due to different speeds from different reference points.

Concider,

Our reference point i.e plant B is moving away from the planet A, and Planet A stays still. For B's reference point, it would appear A is moving away, this time time when B measure A' total mass, it would be higher as it would have higher speed this higher reletivistic mass.

Reletivistic mass is formulated by

m = m_0 / sqrt(1 - (v^2 / c^2))

where:

( m ) is the relativistic mass,
( m_0 ) is the rest mass of the object,
( v ) is the velocity of the object,
( c ) is the speed of light in a vacuum

If we use non physical reference point


Now, you know a point is a concept that has no mass, volume, not any physical thing. So it's not limited by laws of physics, which means there is no law that limit that that point B can't cross the speed of light.

A point has no physical properties and can be used as a reference point, perfect for our case

We can imagine a point moving away from planet B, as the speed of point moving increaseses, so does the total mass.

If we make the point reach the speed of light, than the total mass we measure of B will be infinite. Do thus with infinite mass, it becomes a blackhole for our point's reference point.
[Note: I am letting the point reach speed of light because it's just a mathematical concept and has no physical properties,]

This questions, if what our observation can be ultured so much that it becomes a blackhole, from a reference point, is there anything can be called a reality?


Thus, my conclusion is that everything has an infinite mass and is a Black hole from some perspective. This is obviously mathematical and philosophical rather than physics based.

 

[DaveC426913]

Sure. If you start with nonphysical premises, you will end up with nonphysical results.

But even if we took it at face value, your logic contains errors that render your conclusion moot

 

[Ibix]

This appears to be a collection of misunderstandings of relativity.

"Relativistic mass" is not the source of gravity, the stress-energy tensor is. So no, nothing "has infinite mass".

The formulae you are using assume you are measuring with an inertial frame, which implies that what you are calling "the reference point" is moving slower than light. Using it with a reference point travelling at or above $c$ is a self-contradiction and any results following from it are nonsense.

I usually recommend Taylor and Wheeler's Spacetime Physics (free to download via Taylor's website) or Morin's Relativity for the Enthusiastic Beginner if you want to actually learn the theory.

 

[DaveC426913]

Thus, my conclusion is that everything has an infinite mass and is a Black hole from some perspective.

This is just one of the errors.

You earlier stated that this "point" has no physical properties, and that it can move at the speed of light.

One of the other properties this poimt cannot have, then, is a perspective.

A massless object that moves at c is not a valid reference frame.

 

[Doc Al]

This is obviously mathematical and philosophical rather than physics based.

More importantly, it's also wrong, as pointed out by @Ibix (and @DaveC426913):

This appears to be a collection of misunderstandings of relativity.

I urge you to get one of the books recommended by @Ibix.

 

[Dale]

As others have mentioned the concept of relativistic mass has been discarded for several decades now. The concept of mass now refers to invariant mass. As the term indicates, the invariant mass is invariant and is therefore the same in all frames.

It is possible to use coordinates where the t axis is spacelike (faster than c). Whether you can call such a coordinate system a reference frame depends on the exact definition of reference frame. But regardless, in such a coordinate system the mass is still the same as any other system.

The existence of an event horizon is also an invariant global feature of the spacetime and doesn’t depend on the coordinates used.