free falling clocks

Lets say that the rocket on Figure 7 turn around 180º and accelerates downwards, and that when it reaches 20,000 Km from Earth’s CG at a speed of 6.3 Km/s (escape velocity) it runs out of fuel and it begins to free fall to Earth. As it begins to pick up speed and gets closer to Earth, the gravitational field also increases. See Figure 8 for an illustration of the event, where gravitational time dilations are represented by an upward EVV and the speed by a downward vector. These two vectors, as described earlier, grow at the same rate. The sum of these two vectors is always zero. Time dilation is zero. This means that clocks in free fall at the escape velocity do not slow down. Is this a point where the model breaks down or where it really shines? This effect makes part of the equivalence principle a true identity, it says that objects in inertial state are identical to objects in free fall. It is important to note, that at speeds other than the escape velocity (higher or lower), the difference between the vectors gets smaller as the object falls. Time dilation effects get smaller for both cases. Earlier it was discussed in section 2.3 that launching a clock towards a BH at the escape velocity would make time stop twice at the event horizon. It turns out that not only it never stops, it doesn’t even slow down.

gravitational and velocity time dilations

Figure 8.

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2.6 Free falling clocks do not slow down Lets say that the rocket on Figure 7 turn around 180º and accelerates downwards, and that when it reaches 20,000 Km from Earth’s CG at a speed of 6.3 Km/s (escape velocity) it runs out of fuel and it begins to free fall to Earth. As it begins to pick up speed and gets closer to Earth, the gravitational field also increases. See Figure 8 for an illustration of the event, where gravitational time dilations are represented by an upward EVV and the speed by a downward vector. These two vectors, as described earlier, grow at the same rate. The sum of these two vectors is always zero. Time dilation is zero. This means that clocks in free fall at the escape velocity do not slow down. Is this a point where the model breaks down or where it really shines? This effect makes part of the equivalence principle a true identity, it says that objects in inertial state are identical to objects in free fall. It is important to note, that at speeds other than the escape velocity (higher or lower), the difference between the vectors gets smaller as the object falls. Time dilation effects get smaller for both cases. Earlier it was discussed in section 2.3 that launching a clock towards a BH at the escape velocity would make time stop twice at the event horizon. It turns out that not only it never stops, it doesn’t even slow down. Figure 8.