# How do Reference Frames Work? And What are the Consequences?

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How do reference frames affect experiments, and how do they come into play in general and special relativity?

I'm doing A-level physics, so I have a general understanding of certain aspects of physics, but this is an area (all be it small) that makes my head hurt.

And thank you in advance for any relevant explanations or answers given.

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If I'm floating out in space and I see a rock floating toward me, is the rock moving or am I?

Relativity states that it's equally valid to say that I am at rest watching a rock come toward me, and to say that the rock is at rest watching me move toward it. The case in which each of us is at rest is our rest frame.

In my frame of reference, the rock is moving at 100 km/h and I'm moving at 0 km/h. In the rock's frame of reference, I'm moving at 100km/h and the rock is moving at 0 km/h.

Let's say I throw a stick at the rock at 10 km/h. I see the stick moving at 10 km/m away from me. The rock sees the stick moving at 110 km/h towards it (10 km/h faster than it sees me moving).

So a reference frame is just a coordinate system for measuring speeds because you have to select something as being at rest in order to measure speed, with the resultant speed being relative to the rest frame.

The weird part comes from the fact that if I shine my flashlight at the rock, I will see the light moving away from me at the speed of light, and the rock will see it approaching at the speed of light, exactly the same speed despite the 100 km/h difference in our reference frames.

That leads to a varsity of implications about the variability of the rate at which time passes as well as how far distances actually are depending on how fast your going.

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How do reference frames affect experiments, and how do they come into play in general and special relativity?

A reference frame is no more than a choice of local coordinates on space-time.

In special relativity we have a prefered class of coordinate systems, but not a prefered frame itself, known as the inertial coordinate systems. These are the systems in which Newton's laws hold. Other classes of coordinates can be used in special relativity such as rotating systems, but here we have to be very careful and take care of fictitious or apparent forces. These are not true forces in the standard sence but reflect the fact we are not in an inertial coordinate system. Using non-inertial frames in special relativity gets us almost to general relativity...

Einstein realised that gravity itself can be seen as the curvature of space-time, or in other words the fact that we do not have truly inertial coordinate systems when gravity is in play. (Other than locally, but we risk getting technical here). In general relativty we have no prefered classes of coordinate systems. However, this should not be confused with the fact that there maybe more natural coordinate systems to describe the exact system you are interested in. For example, the space-time around a star as a rotational symmetry and it makes sense to exploit that.

With all thar said, we have the "gauge principal" which states that nature does not care about how we chose to describe it. Meaning that any truly fundamental notion in physics will not depend on the choice of local coordinates. In this sence, the choice of reference frame has no affect on experiments.

In practice this is not quite what happens. One will usually have to pick some coordinate system to use to make sence of the measurements made. There is no problem in doing this, just one must be careful will frame dependent effects and the "true physics".

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You have probably been using reference frames already if you've been solving physics problems. When you have a collision problem to work out, you are free to choose a frame of reference where e.g. the target is at rest, which makes the math easier. Or defining where potential energy is zero in a problem — at the top of the motion or the bottom, or some other convenient place. You are not forced into making one choice, and you are free to make another choice if it helps. The physics is the same, and you will get the same answer, assuming you consistently apply your conventions.

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