Conservation of kinetic energy between neutral fundamental particles in a vacuum?

[exchemist]

Then kinetic energy would not be conserved. Isn't that right? The kinetic energy of the ball exiting at the speed of sound would be less than the kinetic energy of the ball that struck it, since it has supersonic speed at the point of collision.

I think this is where it gets hard, because the reality is that the collision would not be perfectly elastic and some energy would be lost as heat within the balls.

But onlooking this up I realise I have made a mistake. A shock wave can travel faster than sound in a medium.
https://www.britannica.com/science/shock-wave
So that I think will be the explanation of what happens. Instead of a sound wave within the balls, you will get a shock wave, which travels faster and can transmit the necessary kinetic energy to allow the previously stationary ball to acquire the same velocity as the incoming one, even though it is faster than the speed of sound in the material of the ball.

But not much of this will apply in the case of QM entities. Due to the uncertainty principle (or, to put it another way, the wavelike nature of these entities), we won't be able to define the details of the energy transfer process, so I don't think we can talk of a speed of energy transfer in such a case. The boundaries of the objects are fuzzy (we have to deal with the "cross section" as a measure of probability of a collision taking place), the repulsion between them will be due to things like electric charge or the Pauli Exclusion Principle and will build up in a certain way as they approach......it all feels very hairy........but no doubt a particle physicist would be able to comment a lot better than I can.

 

[one_raven]

This is why I framed the thought experiment as fundamental objects in a vacuum. A fundamental object in a quantized system would imply, I believe, incompressibility (therefore, also imply that without compressibility there would be no internal mechanics) therefore there could be no internal shockwave.

With an incompressible object in a frictionless environment, 100% of the kinetic energy would be transferred.

What are the implications of one of these objects being fired at the other at a rate of speed that is greater than the stationary object can physically absorb the amount of kinetic energy in the fired object?

 

[one_raven]

Where is James R. when you need him?

 

[exchemist]

This is why I framed the thought experiment as fundamental objects in a vacuum. A fundamental object in a quantized system would imply, I believe, incompressibility (therefore, also imply that without compressibility there would be no internal mechanics) therefore there could be no internal shockwave.

With an incompressible object in a frictionless environment, 100% of the kinetic energy would be transferred.

What are the implications of one of these objects being fired at the other at a rate of speed that is greater than the stationary object can physically absorb the amount of kinetic energy in the fired object?

What do you mean by a fundamental object, though? Once you get down to the scale at which the size of Planck's Constant becomes significant, you will get QM behaviour whether you like it or not. Your object will not have well-defined edges and there will be no moment of contact. You will get wave functions that are perturbed by the approach of another QM entity, and so forth. Incompressibility won't have any meaning.

 

[one_raven]

What if I ask this way…

What happens if you launch a steel sphere at an identical stationary steel sphere at a rate of speed that exceeds the rate at which sphere can absorb the kinetic energy from the launched sphere?

The target sphere should be deflected before it could absorb all the kinetic energy. With the Newton’s cradle analogy, it’s already deflected and has started its upswing before all the kinetic energy has been transferred, right? My intuition tells me the launched sphere has not depleted all its kinetic energy in the collision, so it won’t be stationary after the collision. No?

 

[DaveC426913]

What if I ask this way…

What happens if you launch a steel sphere at an identical stationary steel sphere at a rate of speed that exceeds the rate at which sphere can absorb the kinetic energy from the launched sphere?

It would deform. It might explode, but that's merely a special case of deformation.

What if I ask this way…The target sphere should be deflected before it could absorb all the kinetic energy. With the Newton’s cradle analogy, it’s already deflected and has started its upswing before all the kinetic energy has been transferred, right? My intuition tells me the launched sphere has not depleted all its kinetic energy in the collision, so it won’t be stationary after the collision. No?

In whatever shape it ends up in...

 

[one_raven]

I don’t know if it’s you, me, both or neither of us, but my question is clearly not coming across.
Thanks, anyway.

 

[DaveC426913]

I don’t know if it’s you, me, both or neither of us, but my question is clearly not coming across.
Thanks, anyway.

Maybe it's a little too much thought and not enough experiment?
What I mean is: why all the hypotheticals?

As you're finding out, there are basically as many valid answers as there are distinct particles in the Standard Model.

Why not make the scenario match the real world as much as possible, and invoke the thought experiment aspect only when absolutely required?

 

[one_raven]

Have you ever read/watched sci-fi and been able to pick out when a bit of the science is or is not consistent with that universe, regardless whether it’s consistent with ours?

 

[DaveC426913]

Have you ever read/watched sci-fi and been able to pick out when a bit of the science is or is not consistent with that universe, regardless whether it’s consistent with ours?

Of course. The hallmark of good sci-fi is internal consistency. It doesn't have to be like ours, but it does have to be consistent.

Not really applicable here though. You'd have to tell us what your particles are made of and what their physics are.

 

[one_raven]

I did say what their physics are, that was rejected.
They’re made from imaginarium.

 

[DaveC426913]

I did say what their physics are, that was rejected.
They’re made from imaginarium.

You asked what would happen if they collided faster than they could transfer kinetic energy.
How are we supposed to know if they're made of stuff not defined? Do they react to the sting nuclear force? Are they made of quarks?

 

[one_raven]

They’re incompressible and electrically neutral.
They’re whatever they need to be to ensure a perfectly elastic collision between two inelastic spheres in a vacuum. I have no idea how else I could say this to make it more clear.

 

[DaveC426913]

They’re incompressible and electrically neutral.
They’re whatever they need to be to ensure a perfectly elastic collision between two inelastic spheres in a vacuum. I have no idea how else I could say this to make it more clear.

Ah. OK.

The de regueur answer, then, is you get unicorns.

In the Einsteinian universe there is no such thing as a perfectly incompressible or perfectly rigid material. If such a thing existed, it would transfer energy at infinite speed - faster than c.

So it requires tossing out the laws of physics, which means the outcome can be whatever you fancy.

 

[one_raven]

Wouldn’t that be unicorn²?

 

[exchemist]

What if I ask this way…

What happens if you launch a steel sphere at an identical stationary steel sphere at a rate of speed that exceeds the rate at which sphere can absorb the kinetic energy from the launched sphere?

The target sphere should be deflected before it could absorb all the kinetic energy. With the Newton’s cradle analogy, it’s already deflected and has started its upswing before all the kinetic energy has been transferred, right? My intuition tells me the launched sphere has not depleted all its kinetic energy in the collision, so it won’t be stationary after the collision. No?

There is no limit to the rate at which kinetic energy can be absorbed. What makes you think there is?

I've explained the process: deformation of both spheres, creating a sound wave - or a shock wave - within the material of which they are made, which will accelerate the centre of mass of the stationary sphere and accelerate the centre of mass of the incoming one. This can occur at any speed.

(Actually, I've realised something else will happen in practice. As the material deforms and a wave is created within it, it can be expected to set up resonant vibrations in both spheres - spherical harmonics - which will convert some of the kinetic energy to vibrational energy. So the collision will not be fully elastic, if the material deforms, which in reality it must. Both spheres will "ring".)

 

[one_raven]

Nothing is instantaneous. Even on the most practical macro level, you can watch a slow-motion video of an elastic collision... Contact --> Absorption through deformity --> Pause at peak potential energy --> Deflection through restoration (to some degree) of the material shape

If there is an upper speed limit to the transfer of electromagnetic energy, why wouldn't it be reasonable to assume there is an upper speed limit to the transfer of kinetic energy?

I'm just trying to wrap my head around the concept of incompressible mass (however impossible it may or may not be). I'm trying to work out what the physical properties of a fundamental particle would be. If quarks are fundamental particles that exist as physical entities with mass, as opposed to energetic excitations of a field, that mass must be incompressible. If mass is incompressible, could there even be a transfer of kinetic energy, or does the transfer of momentum necessarily require mechanical deformation? What even is the mechanism of transfer of kinetic energy, if not deformation and rebound? If kinetic energy could be transferred between two incompressible particles with mass, there is certainly an upper limit to how much kinetic energy a particle could have (if solely because a fundamental particle must have invariant mass).

These are the types of puzzles that keep me up nights, and the only way I've ever been able to get to the bottom of them is to accept impossible premises in hypotheticals, in order to strip away variables and suss out the core dynamics in a thought experiment, then build back out to "reality" from there.

 

[one_raven]

Is it possible, perhaps, that "Dark Matter" can travel faster than c? We don't know it's properties (other than simply that it interacts what gravity). The fastest thing we've observed is the propagation of electromagnetic energy. This says nothing of free, "dark" particles that seemingly do not interact with electromagnetic fields. If Dark Matter is immune to electromagnetism, who's to say it's not also immune to the weak and strong forces? If it is, what if it is a fundamental, incompressible particle? If such a particle exists, immune to nuclear and field dynamics, the only energy it is capable of propagating would be kinetic energy, IF THAT is even possible without deformity. If transfer of kinetic energy between incompressible particles is possible, there's, effectively, an entire dimension of an energetic system everywhere around us, impacting us directly, that we are nearly blind to. We only suspect it exists because we think we see the shadow of a ghost from the corner of our eyes. How do things like this not keep everyone up at night?

 

[exchemist]

Nothing is instantaneous. Even on the most practical macro level, you can watch a slow-motion video of an elastic collision... Contact --> Absorption through deformity --> Pause at peak potential energy --> Deflection through restoration (to some degree) of the material shape

If there is an upper speed limit to the transfer of electromagnetic energy, why wouldn't it be reasonable to assume there is an upper speed limit to the transfer of kinetic energy?

I'm just trying to wrap my head around the concept of incompressible mass (however impossible it may or may not be). I'm trying to work out what the physical properties of a fundamental particle would be. If quarks are fundamental particles that exist as physical entities with mass, as opposed to energetic excitations of a field, that mass must be incompressible. If mass is incompressible, could there even be a transfer of kinetic energy, or does the transfer of momentum necessarily require mechanical deformation? What even is the mechanism of transfer of kinetic energy, if not deformation and rebound? If kinetic energy could be transferred between two incompressible particles with mass, there is certainly an upper limit to how much kinetic energy a particle could have (if solely because a fundamental particle must have invariant mass).

These are the types of puzzles that keep me up nights, and the only way I've ever been able to get to the bottom of them is to accept impossible premises in hypotheticals, in order to strip away variables and suss out the core dynamics in a thought experiment, then build back out to "reality" from there.

Well OK, then we get back to c, the speed of light.

It's trivially obvious that nothing can exceed that limit: no wave, no sphere in motion so, given that energy transfer processes involves matter or radiation moving, c will in practice represent a limit for energy transfer too. But so what?

I don't know why you are trying to wrap your head around incompressible mass. There is no such thing. Incompressible objects are a convenient fiction, one of many that physical science uses, to reduce the complexity of physical problems by ignoring some aspects in order to focus on the essentials. Another convenient fiction is the idea of a "particle". That allows one to ignore the physical dimensions of real objects in order to simplify problems.

By the way, it makes no sense to talk of mass being incompressible. Mass is just one property of an entity, like colour or electric charge, or energy. It is the entity itself that is or isn't compressible.

 

[one_raven]

It's trivially obvious that nothing can exceed that limit: no wave, no sphere in motion...

Is it, though? Why?
Sure, electromagnetic energy is restricted to c, but if Dark Matter is immune to electromagnetic energy, and we know nothing else about it, other than it does impact gravity throughout the known universe (at least) how can you be so sure?
Maybe it's just the restriction of the propagation of electromagnetic energy that limits the speed of complex macro objects. After all, if what we perceive as matter is just collective quantum wave fluctuations, it would make perfect sense that it couldn't travel faster than light. If Dark Matter is a "real" fundamental particle that's immune to electromagnetic forces (which is not outside of what we have observed) why would we expect them to share the properties of the quantum "particles" we can observe (albeit indirectly) that impose these velocity limitations on them?

I don't know why you are trying to wrap your head around incompressible mass. There is no such thing. Incompressible objects are a convenient fiction, one of many that physical science uses, to reduce the complexity of physical problems by ignoring some aspects in order to focus on the essentials. Another convenient fiction is the idea of a "particle". That allows one to ignore the physical dimensions of real objects in order to simplify problems.

That's part of what I'm calling into question. I remain unconvinced.
How can you be so confident of the properties of something we have no way of directly observing? It could be so many things. What if mass/energy equivalence is conserved at the quantum level by kinetic energy transferring between physical fundamental particles that we haven't yet been able to observe, simply because everything we can directly observe (so far) is through one means of electromagnetic radiation? It could be the medium that gives rise to quantum fields and/or virtual particles... It could be the building blocks of Standard Model "matter", as we had/have in the classical understanding of matter. We need new ways of observing. We are still major leaps and bounds away from unifying quantum mechanics with Newtonian mechanics. What if there's a bridge, or at least a thread, through Dark Matter? The only way to know its properties is to find a way to observe and measure its properties.
Simple fact is, Dark Matter is still a mystery. Ascribing properties to an unknown entity is religion, not science.

By the way, it makes no sense to talk of mass being incompressible. Mass is just one property of an entity, like colour or electric charge, or energy. It is the entity itself that is or isn't compressible.

Semantics. I do appreciate the clarity, but you did get my point.