# A simple SR problem

1. Mar 29, 2005

### The Rev

I'm pretty new to the ideas of relativity, so maybe this is old ground to cover for some of you. However, I need to know how to resolve an apparent paradox.

Person A is travelling at relativistic speeds holding a stone over his head. The stone weighs just slightly less than the maximum weight that he is able to hold up. Person B is an observer, watching Person A. From Person A's point of view, the rock is unchanged, so he continues to hold it up. From Person B's point of view, however, the rock grows heavier due to relativistic increases in mass, and falls on Person A's head, killing him.

Now, how does Person A, who is alive from his own point of view, communicate to Person B that he really isn't dead?

The Rev

2. Mar 29, 2005

### jcsd

SR doesn't deal with gravity and unfortunately relativstic descriptions of grabity can never be that simple. Also remember F=Ma isn't generally true in SR anyway.

3. Mar 29, 2005

### pervect

Staff Emeritus
It turns out the rock never gets heavier in SR. It either has the same weight, or it gets lighter! (By "weight" I mean "force").

It's the same weight (force!) if the force points in the same direction as the observer is moving.

It's lighter (a lower force) if the force points at at an angle to the direction of motion.

This comes from the transformation laws, which can be derived from the folowing defintions.

4-force = dp/dtau, where p is energy-momentum 4-vector, and tau is the "proper time".

4-forces transform like any other 4-vector.

3-force = dp/dt - where p is the relativistic momentum (the energy-momentum 4-vector with the energy part omitted), and t is the coordinate time, rather than the proper time.

From the above, it can be seen that the 4-force and the 3-force are related by the time dilation factor, dt/dtau, i.e. (dp/dtau) = (dp/dt) * (dt/dtau)

4. Mar 29, 2005

### JesseM

Just to avoid confusion, the weight cannot get lighter in the frame of the man carrying the boulder, since that would provide the man with a way of measuring his absolute velocity...I guess the resolution would be that even if the force from the boulder pushing down on the man weakens as seen in some other frame, the force upwards from the man pushing on the boulder will also weaken as seen in that frame, so this frame will also predict no change in how high the boulder is held up.

5. Mar 31, 2005

### kleinwolf

Jscd : This is an interesting problem you put forward :

1)in SR, time and space change depend on the relative speed
2)in GR time and space depend on the relative position towards the source of gravitation.

shouldn't in GR space-time depends on the relative motion of the observer towards the source of gravitation too ?

6. Apr 5, 2005

### Antiphon

For the guy hodling the rock, the weight he must hold doesn't change because his
time is slowing down. A heavier rock in slower time doesn't weigh more because there
is a time derivative in computing the force.

7. Apr 15, 2005

### Gza

just for the record, what force are you talking about, and in regards to what time derivative?