Measuring Speed of Light Relative to Earth

[Chris84567]

The question:
If the max speed I can go in the universe is the speed of light measured from?

Background:

If there are three rocks in a vacuum along a line (the x axis), one is stationary (rock 1), one is moving 5 m/s in the x direction (rock 2) and one is move -5 m/s in the x direction (rock 3). All rocks are going 0 m/s relative to themselves. Rock 1 is moving -5 m/s relative to rock 2 and 5 m/s relative to rock 3. Rock 2 is moving 5 m/s relative to rock 1 and 10 m/s relative to rock 3. Lastly Rock 3 is moving -5 m/s relative to rock 1 and -10 m/s relative to rock 2.

Then in theory I can reach the speed of light relative to Earth because I am not moving relative to myself.
__________________________________________________________________________________________

I hope you can help clear this confusion up.

Thanks

 

[phinds]

The question:
If the max speed I can go in the universe is the speed of light measured from?

Background:

If there are three rocks in a vacuum along a line (the x axis), one is stationary (rock 1), one is moving 5 m/s in the x direction (rock 2) and one is move -5 m/s in the x direction (rock 3). All rocks are going 0 m/s relative to themselves. Rock 1 is moving -5 m/s relative to rock 2 and 5 m/s relative to rock 3. Rock 2 is moving 5 m/s relative to rock 1 and 10 m/s relative to rock 3. Lastly Rock 3 is moving -5 m/s relative to rock 1 and -10 m/s relative to rock 2.

Then in theory I can reach the speed of light relative to Earth because I am not moving relative to myself.
__________________________________________________________________________________________

I hope you can help clear this confusion up.

Thanks

Since all motion is relative your speed is always relative to some given location. Pick a point and start your trip. No matter how fast you are moving, when you shine a flashlight out in front of you, the beam leaves the flashlight at c. Your confusion about the situation you describe is quite common because novices to this stuff are not aware of the way that relativistic speeds add. Google "relativistic velocity addition"

 

[Chris84567]

I watched this video and I am still a little confused.



Are the ships in different positions depending on the observer?

 

[phinds]

I really have no interest in watching a 6 minute video. Try to express in words what you are confused about.

 

[Ibix]

@Chris84567 - If you say an object is moving at velocity $u$ and I say you are moving at velocity $v$, what is the velocity $u'$ that I think the object is going at?

In Newtonian physics the answer is simple: $u'=u+v$. So if you are a cop doing v=30mph relative to the ground and a car overtakes you at a speed your radar gun says is u=30mph faster than you, its speed relative to the ground is 60mph.

In relativistic physics the answer is $$u'=\frac {u+v}{1+uv/c^2} $$You are welcome to work out what difference the existence of the denominator makes to the example I gave above. My estimate is one part in 10²¹. However, it makes a lot of difference when u and v approach c. In particular, you may be interested in the case where "the object" is a pulse of light moving with $u=c$, or $u=-c$.

 

[Janus]

The question:
If the max speed I can go in the universe is the speed of light measured from?

Background:

If there are three rocks in a vacuum along a line (the x axis), one is stationary (rock 1), one is moving 5 m/s in the x direction (rock 2) and one is move -5 m/s in the x direction (rock 3). All rocks are going 0 m/s relative to themselves. Rock 1 is moving -5 m/s relative to rock 2 and 5 m/s relative to rock 3. Rock 2 is moving 5 m/s relative to rock 1 and 10 m/s relative to rock 3. Lastly Rock 3 is moving -5 m/s relative to rock 1 and -10 m/s relative to rock 2.

Then in theory I can reach the speed of light relative to Earth because I am not moving relative to myself.
__________________________________________________________________________________________

I hope you can help clear this confusion up.

Thanks

Assume that Rocks 1, 2 and 3 start off separated and pass each other and separate again. At the moment of passing, a flash of light is emitted from that point.
In this example we will assume that Rocks 2 and 3 move at 0.5c relative to rock 1.
This are events according to anyone at rest with respect to rock 1, The expanding white circle is the light flash.

Note that all three rocks remain inside of the expanding flash. With rock 1 remaining at the center of the Flash

Now we consider the same scenario from the rest frame of rock three

Now rocks 1 and 2 approach from the left, and recede from rock 3 to the right. The same flash of light is emitted when they meet. But now rock 3 remains at the center. All three still remain inside of the flash boundary. It is important to note that this is the same flash of light as shown in the first animation, the only difference is it is being seen from different frame of reference. Note, that if we were to use Newtonian rules for adding the Rock's velocities here, rock 2 would be moving at c relative to rock 1 in the second animation and would be right at the edge of the expanding light. If the relative velocities between rock 1 and the other two rocks was 0.6c, then Newtonian rules would conclude rock two as moving faster than the expanding light, and escaping outside of it.

Thus we would have two different frames with two different realities. One where rock 2 stays inside of the light and one where it passes beyond the light.
Actually, there would be three different realities. An animation shown from rock 2's rest frame, would show it as remaining in the center of the light and rocks 1 and 3 moving from right to left.
Adding the velocities relativistically avoids this problem. That is not to say that the relativistic addition formula was derived as a sort of "fix". It fall out naturally from the axioms of Relativity.

 

[nitsuj]

with that animation is the difference in length between 3 and the light edge the comparative length contraction to when we see it at rest with 3.

If we plotted "3's light flash" using 1's at rest frame/coordinates would it be a very elongated shape?

 

[Grinkle]

No human will intuitively predict the speed of anything is not relative to one's own velocity, this includes the speed of light. One must accept experimental evidence that the speed of light does not depend on one's own motion and reason from that forward.

You own velocity relative to any other object is not going to affect your measurement of the speed of light. This is not intuitive, its just an observed phenomena.

 

[Janus]

with that animation is the difference in length between 3 and the light edge the comparative length contraction to when we see it at rest with 3.

All three Relativistic effects come into play. For example, imagine that Rock 3 has a measuring rod with clocks lain out on it, which are all synchronized to each other in Rock 1 frame. This rod extends in the direction of the relative motion. According to Rock 3, the the light travels along the rod, reaching each clock when it read a given time. In Rock 1's frame, the light has to hit each of those clocks when it reads the exact same value as it did according to Rock 3's frame. But according to Clock 1's frame, the distance between the clocks on Rock 3's rod is length contracted, the clocks run slow, and the clocks are not synchronized with each other. All of these have to be taken into account when determining how far ahead of Rock 3 the light flashes edge is according to rock 1's frame.

If we plotted "3's light flash" using 1's at rest frame/coordinates would it be a very elongated shape?

It doesn't matter whether the flash was emitted by rock 1, 2 or 3 in this scenario, it expands out the same. In other words, in the Rest frame of each Rock, it finds itself at the center of the expanding circle, regardless of whether the flash was emitted by a source at rest with respect to that frame or not.