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Sorry for taking your time with elementary problems, but this question seems to be so simple that the only people who take it seriously are the ones who don't know what they are talking about.

Consider the question of whether it is worse to be in a car hitting a concrete barrier of nearly infinite mass and negligible give, compared to a car that hits an oncoming car of the same mass and equal but opposite velocity.

Now, in a particle collider, the reason for arranging collisions of similarly-massed particles travelling in opposite directions is that the energy levels attained can be many thousands of times greater than bombarding a solid target with the same types of particles at the same velocities. I want to discuss why such colliders can achieve significant gains at all, and I beg someone who really knows what he is talking about, to come down from the levels of sophistication at which he (or of course, she) normally works and kindly make matters clear.

First: a matter of faith, dogma, confidence, logic, etc etc: The total amount of energy the collision yields cannot exceed the amount put into accelerating the particles, no matte what, no matter whether the particles are relativistic or not. In fact, there always will be losses to side effects of various types.

Consider a case first, of suspended steel balls, such as you could find in a Newton's cradle. Next to a single ball we put a smooth, near-as-dammit rigid steel wall. We raise the ball to a standard height and let it swing against the wall. In a perfect world it would bounce back to the starting position. As nothing really is perfect, It would only recoil most of the way till it bounces to a stop. We observe that a certain amount of energy is expended in the process, energy in the form of momentum, kinetic energy, potential energy etc.

Well then, we remove the steel wall and replace it with a second steel ball. We repeat the experiment, but this time we raise and drop BOTH balls, thereby priming the system with precisely twice the amount of energy that we started with before. And we see...

Both balls recoil to the same height as before, right? and bounce the same number of times, yes? In short, each ball experienced the same impacts and accelerations as before, with the same energy as before, no?

Near as dammit, of course.

But when we do the analogous thing in a particle collider, although we still get out no more energy than we put in, we find the process thousands of times more profitable than hitting even the most rigid of stationary targets. How much of that is because of relativistic effects, and how much of a role does relativity play? I assume that part of the problem is that at such energies there is no such thing as a "rigid" stationary target? That for such purposes atoms within say a diamond crystal do not differ significantly from atoms in liquid methane?

There is another thing of course. Our steel balls approximate to elastic rigid objects. Suppose that we replace them with crushable material, possibly something like putty. I would expect that the amount of deformation of the putty PER BALL would be effectively the same in both experiments.

Am I wrong? Why? Given the equation for kinetic energy of a given mass at a given velocity: e=0.5*m*v*v it is true that the amount of energy for a fixed mass rises quadratically with velocity; it then makes sense that having put twice as much energy into the two balls as into one ball, I should get out twice as much energy as when I dropped just one ball against the rigid barrier. And yet, I could argue that I am entitled to regard the two moving balls as one ball stationary and the other at twice the velocity bearing four times as much energy, instead of twice as much. But I did not put in four times as much; only the same old twice as much!

Why is this not true? What am I missing?

And for the two cars; will the drivers be worse off than the driver of the single car hitting a rigid barrier? And if not, who would like to demonstrate, using swinging eggs on strings -- eggs that he had paid for personally?

And why should matters be different for relativistic particles in collision? I realise that their velocities will not change much when their energies do, but even so...?

Anyone, please? Real, crushing, simple arguments? Equations permitted, even welcomed, but not as substitutes for sense please! Links to direct answers will do, if they are clear and pertinent, say, if they were in reply to essentially the same questions in the past.

Thanks for your patience and attention,

Jon

Consider the question of whether it is worse to be in a car hitting a concrete barrier of nearly infinite mass and negligible give, compared to a car that hits an oncoming car of the same mass and equal but opposite velocity.

Now, in a particle collider, the reason for arranging collisions of similarly-massed particles travelling in opposite directions is that the energy levels attained can be many thousands of times greater than bombarding a solid target with the same types of particles at the same velocities. I want to discuss why such colliders can achieve significant gains at all, and I beg someone who really knows what he is talking about, to come down from the levels of sophistication at which he (or of course, she) normally works and kindly make matters clear.

First: a matter of faith, dogma, confidence, logic, etc etc: The total amount of energy the collision yields cannot exceed the amount put into accelerating the particles, no matte what, no matter whether the particles are relativistic or not. In fact, there always will be losses to side effects of various types.

Consider a case first, of suspended steel balls, such as you could find in a Newton's cradle. Next to a single ball we put a smooth, near-as-dammit rigid steel wall. We raise the ball to a standard height and let it swing against the wall. In a perfect world it would bounce back to the starting position. As nothing really is perfect, It would only recoil most of the way till it bounces to a stop. We observe that a certain amount of energy is expended in the process, energy in the form of momentum, kinetic energy, potential energy etc.

Well then, we remove the steel wall and replace it with a second steel ball. We repeat the experiment, but this time we raise and drop BOTH balls, thereby priming the system with precisely twice the amount of energy that we started with before. And we see...

Both balls recoil to the same height as before, right? and bounce the same number of times, yes? In short, each ball experienced the same impacts and accelerations as before, with the same energy as before, no?

Near as dammit, of course.

But when we do the analogous thing in a particle collider, although we still get out no more energy than we put in, we find the process thousands of times more profitable than hitting even the most rigid of stationary targets. How much of that is because of relativistic effects, and how much of a role does relativity play? I assume that part of the problem is that at such energies there is no such thing as a "rigid" stationary target? That for such purposes atoms within say a diamond crystal do not differ significantly from atoms in liquid methane?

There is another thing of course. Our steel balls approximate to elastic rigid objects. Suppose that we replace them with crushable material, possibly something like putty. I would expect that the amount of deformation of the putty PER BALL would be effectively the same in both experiments.

Am I wrong? Why? Given the equation for kinetic energy of a given mass at a given velocity: e=0.5*m*v*v it is true that the amount of energy for a fixed mass rises quadratically with velocity; it then makes sense that having put twice as much energy into the two balls as into one ball, I should get out twice as much energy as when I dropped just one ball against the rigid barrier. And yet, I could argue that I am entitled to regard the two moving balls as one ball stationary and the other at twice the velocity bearing four times as much energy, instead of twice as much. But I did not put in four times as much; only the same old twice as much!

Why is this not true? What am I missing?

And for the two cars; will the drivers be worse off than the driver of the single car hitting a rigid barrier? And if not, who would like to demonstrate, using swinging eggs on strings -- eggs that he had paid for personally?

And why should matters be different for relativistic particles in collision? I realise that their velocities will not change much when their energies do, but even so...?

Anyone, please? Real, crushing, simple arguments? Equations permitted, even welcomed, but not as substitutes for sense please! Links to direct answers will do, if they are clear and pertinent, say, if they were in reply to essentially the same questions in the past.

Thanks for your patience and attention,

Jon

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