More on what we were discussing earlier. Seems even Einstein struggled with inertiaL and gravitational mass 😉
https://bigthink.com/starts-with-a-bang/why-inertial-gravitational-mass-equivalent/
https://bigthink.com/starts-with-a-bang/why-inertial-gravitational-mass-equivalent/
Quoting from your Ask Ethan link:
If the object is in motion, we need to bring relativity into the equation, and that means considering “more than rest mass” for each component. An object’s “resistance to changing its motion” is no longer given by the m in F = ma, but is rather given by a more complicated formula involving a change in (relativistic) momentum over time.
Ethan's statement is in accord with the following statement I made earlier and suggested would be an avenue that you may like to explore:
In Newtonian physics, the "inertia" of a particle may be regarded as its "resistance to acceleration".
In Special Relativity, "inertial resistance" is more than particle "inertia" and originates from Minkowski spacetime structure.
Now we have a bit more flesh on the bones!
P.S. I didn't get the impression that Einstein was struggling with the concept.
Gravitational mass is just the inertial mass in the "at rest" reference frame of a system, aka proper mass.
‘P.S. I didn't get the impression that Einstein was struggling with the concept’
Perhaps struggling is the wrong word. This is what Ethan wrote:
‘The mass that gravitates and the mass that resists motion are, somehow, the same mass. But even Einstein didn’t know why this is so.’
Perhaps inertial mass aka weight only manifests whenever an energy transformation takes place. In Einstein’s equivalence thought experiment there is no large mass like there is on Earth to impart the 1G to the object during acceleration. However, when the object is accelerated, it is through an energy transformation of some kind that applies a force to the body. On Earth, energy transformations within the Earth’s mass curve space time so that’s why the object here feels 1G.
Perhaps struggling is the wrong word. This is what Ethan wrote:
‘The mass that gravitates and the mass that resists motion are, somehow, the same mass. But even Einstein didn’t know why this is so.’
Perhaps inertial mass aka weight only manifests whenever an energy transformation takes place. In Einstein’s equivalence thought experiment there is no large mass like there is on Earth to impart the 1G to the object during acceleration. However, when the object is accelerated, it is through an energy transformation of some kind that applies a force to the body. On Earth, energy transformations within the Earth’s mass curve space time so that’s why the object here feels 1G.
I'd call it a hypothesis and there's nothing wrong with taking a pop at it. I agree that the tone of the article is a little 'this is done and dusted' which it isn't of course. Are his results within experimental error? I don't know. It only becomes a theory if it makes predictions that can be tested and explains things better than anything it replaces (again, see Ethan Seagal who has written on this subject). For that reason, 'multi-verse' and string theories in my book are hypotheses because there is no way for the foreseeable future we can make testable predictions with these constructions, and that being the case, is it physics or pure mathematical conjecture? Nothing wrong with the latter, but there is a fine balance between physics and math and if you let the two get out of kilter, you stray off the straight and narrow IMV. Einstein seemed to embody this view because he used thought experiments, existing data (Michaelson-Morely, Maxwell's equations etc) and from that built SR and GR math that made testable predictions. In other words, the physics and the math were in lockstep.
here is a link to a very nice book about relativity BTW
https://ia800503.us.archive.org/11/items/einstein_relativity/einsteinrelativity.pdf
The opening post associated quark movement with the force of gravity.
That was a while ago!
Inertial mass is also known as weight?
Inertial mass is a measure of how difficult it is to accelerate a body, and is given by the m in F= ma.
Weight is the force a mass experience in a gravitational field and is given by the W in W = mg (g being the gravitational acceleration).
The first quantity is measured in kilograms and the second in newtons.
Therefore, I can't agree that inertial mass and weight are one and the same thing.
Your statement that an energy transformation results in a force sounds completely back to front to me.
More accurately, the application of a force may result in an energy transformation.
One example is of an astronaut in deep space applying a force to accelerate an object. In this situation the chemical energy (released from food) is transformed into kinetic energy.
Another example is an object accelerating in near Earth space under the influence of the gravitational force. In this case, gravitational potential energy is transformed into kinetic energy.
Now, more about inertial mass:
Newton originally stated his 2nd law of motion thus: "The unbalanced force (F) on a body is directly proportional to the rate of change of momentum of the body".
That is, F = (mv-mu)/t, where m is the inertial mass, mu is the initial momentum, mv is the final momentum and t is the time for the change.
(Note that F = (mv-mu)/t reduces to F = ma to give the form in which Newton 2 is more usually written.)
So with certainty we can say that where there is a momentum change there is an unbalanced force.
This extends to what Ethan said in your link (I paraphrase):
In relativity, an object’s inertial mass is not simply given by the m in F = ma, but is given by a more complicated formula involving a rate of change of relativistic momentum.
Weight on Earth and and the force experienced by an accelerated body are the same thing and that was Einstein’s great insight. He referred to it as a force of 1G experienced in each case, but you cannot have weight without gravity or without some accelerating force if in flat space time.
Your statement that an energy transformation results in a force sounds completely back to front to me.
How do you create a force of any kind without using energy of some form? If energy is being used in any form, it’s being transformed. That applies to acceleration, deceleration, heating a kettle of water etc.
In relativity, an object’s inertial mass is not simply given by the m in F = ma, but is given by a more complicated formula involving a rate of change of relativistic momentum.
I haven’t said anything that disagrees with your paraphrased summary above.
Your statement that an energy transformation results in a force sounds completely back to front to me.
How do you create a force of any kind without using energy of some form? If energy is being used in any form, it’s being transformed. That applies to acceleration, deceleration, heating a kettle of water etc.
In relativity, an object’s inertial mass is not simply given by the m in F = ma, but is given by a more complicated formula involving a rate of change of relativistic momentum.
I haven’t said anything that disagrees with your paraphrased summary above.
Nor did I say you did.
That "summary" appeared under "Now, more about inertial mass" and was therefore intended to be separate from the first part of my post.
You say an energy transformation of some kind "applies" a force to a body.
But does an energy transformation cause forces to happen or is it the other way round?
That's a matter for discussion, but I can say that Physics makes a distinction between energy and force:
Energy is a scalar quantity defined as the capacity to do work, i.e., to change velocity, position, temperature etc., whereas Force is a vector quantity defined as the rate of change of momentum.
I can apply a force to change the quantity of a particular form of energy in a system, e.g., to give a body more kinetic energy.
All I can say is that a force can be applied to an object without any change in the energy of the object.
For example, the Earth exerts a gravitational force on you, but since you are supported by the floor and standing still there is no change in your energy.
The Earth exerts a force of 1G on your body. But you use energy to remain standing, the metobolic energy involved in that and the energy needed when you move around in the Earth’s associated gravity field. So far from there being no change in energy, there’s actually a huge amount of ‘balancing’ [for want of a better word] energy involved. And a body in freefall in curved space time, although it doesn’t feel anything (Einstein noted this when he considered a man falling off a ladder), it accumulates kinetic energy as it accelerates as it falls. When the body hits the surface of the Earth, that kinetic energy is dissipated as heat energy, energy required to break bones, deformation of the body and the ground beneath it etc. The further you fall, the greater the energy accumulation.
I cannot think of a single case where a a force of any kind is exerted without it arising from an energy transformation, and that force in turn, resulting in some sort of further energy transformation. If this were not the case, energy would not be conserved surely?
(It’s ok to use energy transformation and energy dissipation interchangeably in these discussions- energy always remains conserved)
I cannot think of a single case where a a force of any kind is exerted without it arising from an energy transformation, and that force in turn, resulting in some sort of further energy transformation. If this were not the case, energy would not be conserved surely?
(It’s ok to use energy transformation and energy dissipation interchangeably in these discussions- energy always remains conserved)
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But does an inanimate brick use energy to remain standing on its end on a floor?
In this situation the downward force of gravity is balanced by the upward push of the floor so the brick remains stationary.
No work is being done by either force (there's no change in velocity or position of the brick) and consequently there is no transformation of energy.
What happens when you pick the brick up?
I’m suggesting space time curvature exists on the surface of the Earth is because there are energy transformations taking place within the mass of the Earth. So space time curvature and thus weight (inertial mass) arise as a consequence of energy transformations. The same happens in flat time space. Energy is used to accelerate the body and that gives rise to it experiencing weight. That energy comes about through an energy transformation (some sort of motive machine).
This is not at odds with Einstein because GR states that space time is curved by both mass and energy. There isn’t an accepted explanation for why in both situations a body feels weight as Ethan states in the article I linked to, but we know it happens in both bodies even though in one case there is no large mass involved.
I’m suggesting space time curvature exists on the surface of the Earth is because there are energy transformations taking place within the mass of the Earth. So space time curvature and thus weight (inertial mass) arise as a consequence of energy transformations. The same happens in flat time space. Energy is used to accelerate the body and that gives rise to it experiencing weight. That energy comes about through an energy transformation (some sort of motive machine).
This is not at odds with Einstein because GR states that space time is curved by both mass and energy. There isn’t an accepted explanation for why in both situations a body feels weight as Ethan states in the article I linked to, but we know it happens in both bodies even though in one case there is no large mass involved.
I don’t think it’s as simple as talking about upward forces balancing downward forces when you talk about an inanimate object of the surface of the Earth. Energy transformations are still taking place in both bodies (atomic, thermal etc). But, if you move the objects position it will require additional energy inputs. In the case of the object flat space time one could then get into a discussion about the energy required to move the objects relative trajectory from its existing trajectory which is somewhat similar to moving a body’s position on the Earth’s surface.
An upward force greater than the gravitational force must be applied to the brick in order to give it a brief period of upward acceleration.
During that brief period, work is done against both inertia and gravity which increases both the kinetic energy and gravitational potential energy of the brick.
What happens to the brick thereafter depends on the subsequent forces applied to the brick.
It's just elementary physics.
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But a human must expend energy to stay in the same spot, because there are too many moving parts and they are not all aligned with the center of the earth. Just one miserable bone off center and the muscles around it need to expend energy to keep it in place, relative to others. A brick is just one moving part, so it’s not that hard for it to maintain its center of gravity. If the end were tilted enough, even that wouldn’t happen and down it goes.