synchronized锁住的对象能否被修改

线程1通过synchronized将obj锁住，线程2还能否并发修改obj的内容？
代码示例:

public class ThreadTest {
    private String name = "step1";

    public void step1(){
        synchronized (this){
            try {
                System.out.println("********t1 sleep******1 name=" + this.name);
                Thread.sleep(10000);
                System.out.println("********t1 sleep******2 name=" + this.name);
            } catch (InterruptedException e) {
                e.printStackTrace();
            }
        }
    }

    public synchronized void step2(){ //synchronized保留与否有啥区别？
        this.name = "step2";
        System.out.println("********t2 update****** name=" + this.name);
    }

    public static void main(String[] args) throws Exception{
        ThreadTest threadTest = new ThreadTest();
        Thread t1 = new Thread(new Runnable() {
            @Override
            public void run() {
                threadTest.step1();
            }
        });

        Thread t2 = new Thread(new Runnable() {
            @Override
            public void run() {
                threadTest.step2();
            }
        });

        t1.start();
        Thread.sleep(100);
        t2.start();
    }
}

运行结果:

********t1 sleep******1 name=step1
********t1 sleep******2 name=step1
********t2 update****** name=step2

如果将step2()方法的synchronized去掉，运行结果:

********t1 sleep******1 name=step1
********t2 update****** name=step2
********t1 sleep******2 name=step2

说明：即使对象监视器被锁住，非synchronized修饰的方法依然可以修改对象监视器的值。