What would happen if there were no inertia?

[Sundown444]

This is a theoretical question, not based on anything in real life, only theory. A thought experiment. Now, say that something does not have any inertia, or mass, whichever term you want to use is fine. Now, if a force were exerted on this theoretical object, how fast would it accelerate? Also, if a force made it move to however fast it would go, and even if there were no forces acting on it? Even if it accelerates to the speed of light, is it still capable of being exerted on?

I know, maybe this is a silly question. Still, I'd like to know.

 

[PeroK]

Newton's second law is $\vec F = m\vec a$. You should be able to see for yourself that this can only apply when $m \ne 0$.

 

[Dale]

Now, say that something does not have any inertia, or mass, whichever term you want to use is fine. For this question, we will assume it does not become born at the speed of light like a photon or light itself does.

This is self contradictory. If it has no mass then it can only travel at c.

 

[Sundown444]

This is self contradictory. If it has no mass then it can only travel at c

A fault on my part. I just edited the original post on this topic.

 

[Dale]

Ok, so with the edited question, in principle a force is a change in momentum and massless objects still carry momentum, so it would make sense to have a force on a massless object.

Such a force could not change the speed of the object, only its direction and its energy. If a force were applied perpendicularly to the momentum then it would change the direction only and not the energy. The resulting radius of curvature would depend on the energy of the massless object.

All of the above is regarding a hypothetical classical massless object.

 

[Sundown444]

Ok, so with the edited question, in principle a force is a change in momentum and massless objects still carry momentum, so it would make sense to have a force on a massless object.

Such a force could not change the speed of the object, only its direction and its energy. If a force were applied perpendicularly to the momentum then it would change the direction only and not the energy. The resulting radius of curvature would depend on the energy of the massless object.

All of the above is regarding a hypothetical classical massless object.

So how easily does an object change direction without mass, may I ask? If usually? Should I describe what kind of energy is in this kind of situation?

 

[Dale]

So how easily does an object change direction without mass, may I ask?

I don’t know how to measure/quantify easiness of direction changing.

 

[Sundown444]

I don’t know how to measure easiness of direction changing.

I am assuming centripetal force is not going to apply here?

 

[Dale]

I am assuming centripetal force is not going to apply here?

Yes, a force applied perpendicular to the momentum is a centripetal force.

 

[Sundown444]

Yes, a force applied perpendicular to the momentum is a centripetal force.

Ah, well, what I meant would be, how hard would it be to use centripetal force to change the direction of a massless object?

 

[Dale]

Ah, well, what I meant would be, how hard would it be to use centripetal force to change the direction of a massless object?

I still don’t know how to quantify that.

 

[Sundown444]

I still don’t know how to quantify that.

What would you need to do so?

 

[kuruman]

Ah, well, what I meant would be, how hard would it be to use centripetal force to change the direction of a massless object?

It depends on how big a change you want to happen. The centripetal force you need to apply is $F_c=\dfrac{mv^2}{R}$. This says that the tighter the turn from the original direction (smaller $R$) the more force you need to apply given a certain speed $v$. Also, note that you cannot escape Newton's second law. The mass is still multiplying the (centripetal) acceleration. It is easier to change the direction of a canoe than the direction of a battleship moving at the same speed.

 

[Sundown444]

It depends on how big a change you want to happen. The centripetal force you need to apply is $F_c=\dfrac{mv^2}{R}$. This says that the tighter the turn from the original direction (smaller $R$) the more force you need to apply given a certain speed $v$. Also, note that you cannot escape Newton's second law. The mass is still multiplying the (centripetal) acceleration. It is easier to change the direction of a canoe than the direction of a battleship moving at the same speed.

I see. I think I know what you mean. So with that logic, would a massless object be easier to change direction than the canoe?

 

[Dale]

What would you need to do so?

I would need a clear scientific definition of easiness/hardness. Either an operational definition (how to measure it) or a theoretical definition (how to calculate it from known quantities).

 

[Sundown444]

I would need a clear scientific definition of easiness/hardness. Either an operational definition (how to measure it) or a theoretical definition (how to calculate it from known quantities).

Basically, it is how hard you have to push or pull the object with a force to change its direction. We'd be using centripetal force in that case. If you want more, let's make the radius 0.0001 meters. We should already know the mass and velocity here.

Anything else you would need?

 

[kuruman]

I see. I think I know what you mean. So with that logic, would a massless object be easier to change direction than the canoe?

Proportionally, less force will be required for a less massive object to achieve the same acceleration as a more massive object. The proportionality constant is the mass. Thus, a 1 kg object will require half the force as a 2 kg object to achieve the same centripetal acceleration at the same speed and radius. Would you say that it is easier to change the direction of the 1 kg object because it requires less force? If that is how you define "easy", then the smaller you make the mass of the object for the same speed and radius, the easier it is to change its direction. Unfortunately, if you let the mass go to zero, the acceleration goes to zero because the force will have to go to zero. (F = 0*a = 0) and the object cannot change its direction at all. That's the price you have to pay for defining "easy" in terms of a force in the Newtonian sense. Thus, it's not easy at all to change the direction of a massless particle. Photons are massless and to change their direction, you will need at least a mass the size of a star or, even better, a black hole. How "easy" is that?

 

[Sundown444]

Proportionally, less force will be required for a less massive object to achieve the same acceleration as a more massive object. The proportionality constant is the mass. Thus, a 1 kg object will require half the force as a 2 kg object to achieve the same centripetal acceleration at the same speed and radius. Would you say that it is easier to change the direction of the 1 kg object because it requires less force? If that is how you define "easy", then the smaller you make the mass of the object for the same speed and radius, the easier it is to change its direction. Unfortunately, if you let the mass go to zero, the acceleration goes to zero because the force will have to go to zero. (F = 0*a = 0) and the object cannot change its direction at all. That's the price you have to pay for defining "easy" in terms of a force in the Newtonian sense. Thus, it's not easy at all to change the direction of a massless particle. Photons are massless and to change their direction, you will need at least a mass the size of a star or, even better, a black hole. How "easy" is that?

You actually need something that big to change its direction? Why?

 

[Dale]

Basically, it is how hard you have to push or pull the object with a force to change its direction. We'd be using centripetal force in that case. If you want more, let's make the radius 0.0001 meters. We should already know the mass and velocity here.

Anything else you would need?

Sorry, I cannot translate that into a formula to use.

Look, it is getting kind of irritating repeatedly telling you that I don’t know how to answer this part of your question. So I am done here.

 

[Sundown444]

Sorry, I cannot translate that into a formula to use.

Look, it is getting kind of irritating repeatedly telling you that I don’t know how to answer this part of your question. So I am done here.

Understood. I am sorry if I irritated you.

 

[italicus]

@Sundown444

“ Massless object” looks like an oxymoron, unless you are talking of photons. Any material object has a mass. Its momentum, and any force applied to change it, either in intensity or direction , or both, is proportional to its mass. Even fictitious forces are called, better, inertial, because are proportional to mass.
Photons, and maybe other particles that I don’t know, have mass = 0; treating them in relativity, it can be shown that their momentum equals energy, and the four-momentum has null modulus.

 

[Sundown444]

@Sundown444

“ Massless object” looks like an oxymoron, unless you are talking of photons. Any material object has a mass. Its momentum, and any force applied to change it, either in intensity or direction , or both, is proportional to its mass. Even fictitious forces are called, better, inertial, because are proportional to mass.
Photons, and maybe other particles that I don’t know, have mass = 0; treating them in relativity, it can be shown that their momentum equals energy, and the four-momentum has null modulus.

That is why this is more so theoretical on the massless object part. Reaching zero mass in real life would be as impossible as reaching infinite relativistic mass, would it not?

 

[italicus]

Let’s hope Einstein forgive you! Any material particle has a mass, which is invariant, doesn’t change with speed. An electron has a mass of about 0.511 MeV/c² (if I remember well) , which doesn’t change even if it is accelerated to 99.999% c and further ( if possible ! This is just an example).

 

[russ_watters]

That is why this is more so theoretical on the massless object part. Reaching zero mass in real life would be as impossible as reaching infinite relativistic mass, would it not?

Since mass less objects already exist (photons), I'd say no.