Science One Physics Lesson 21

Relativity of Simultaneity Relativistic Momentum and Energy Recap and Preview

Last class • Relativity of simultaneity, length contraction, time dilation

This class • Twin Paradox • Relativity of simultaneity • Ladder Paradox • Why is our current idea of momentum broken? • Relativistic Momentum and Energy In the frame of the train, observers see the light hit the front and the back of the train exactly at noon. In the frame of the track, shown above, what can we say about the time on clock at the front of the train when light hits the back of the train.

A) The clock at the front reads 12:00. B) The clock at the front reads earlier than 12:00. C) The clock not he front reads later than 12:00.

In the second picture, the back clock reads noon, but the front clock reds earlier than noon, since the light hasn’t hit it yet. Spacetime Drawings Frame of train Spacetime Drawings Frame of track Relativity of Simultaneity

The Ladder Paradox

Barn Frame Ladder Frame

Simultaneous events in the barn frame are not simultaneous in the ladder frame. Principle of Relativity

Frame of the train if it were moving with the green ball (same horizontal velocity).

Frame of the train if it were moving with the green ball (same horizontal velocity).

Relativistic Momentum

The momentum that is conserved is

Note that

This means that an increase in x-velocity increases the momentum in the y- direcon.

Relativistic Energy

It turns out that the energy that is conserved is

This comes about by considering conservaon of momentum in different frames. Worksheet Question 1 Relativistic Energy

At low speeds the relavisc momentum recovers the familiar formula for momentum we use in our day to day lives.

However, taking gamma to zero doesn’t give us a familiar formula from classical physics, but it probably should if physics works.

Let’s do it in a more controlled way.

Worksheet Question 2 Approximating a function near a point Relativistic Energy

Classically (for small velocies): 1) Mass is always conserved 2) kinec energy only conserved in elasc collisions.

In Relavity:

1) The combinaon of these two is conserved in all processes. 2) Mass isn’t conserved, but we can convert mass to kinec energy and back again.

Gold-Gold ion collisions at RHIC Cosmic Rays (1 TeV Proton Collision) Q: What is Mass?

When the object is a rest we see that

We can use this as another definition of mass (as opposed to shooting peas at space salmon)

Q: What is Mass?

Generally,

Binding energy: this is oen negave for stable systems, so stable systems generally have less mass.

This definion agrees with previous definions of ineral mass and gravitaonal mass.

Which configuration of steel balls and magnets has the lower mass?

A)

B)

C) Impossible to tell. D) They have the same mass. Which configuration of steel balls and magnets has the lower mass?

A)

B)

C) Impossible to tell. D) They have the same mass.

Configuration B is more tightly bound. It’s harder to pull the right ball from B than it is to pull the left ball from A. This means that B has a lower overall potential energy, and thus has a lower mass.

M = 3 mball + mmag+ (thermal energy)/c2 + (potential energy)/c2 potential energy is more negative for more tightly bound state.

The Higgs Doesn’t Give You Most of Your Mass

The Higgs gives mass to fundamental particles like quarks. Only ~10% of the mass of the proton and neutron come from the mass of the quarks.

1 extra up 2 extra ups and and 2 extra downs 1 extra down bunch of other bunch of quarks quarks and and gluons gluons

90% of the mass comes from the kinetic energy of the massless gluons. We’re mostly neutrons and protons, so most of our mass doesn’t come form the Higgs. Previous Definitions

Using momentum:

Mass = amount of impulse to change v by a certain amount

This is called “inertial mass”.

Using gravity:

an object’s weight Mass = g (its free fall acceleration)

This is called “gravitational mass”

All three agree!