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Ch 37: Special RelativityWorksheetSee all chapters
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Ch 37: Special Relativity
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Inertial Reference Frames
Special Vs. Galilean Relativity
Consequences of Relativity
Lorentz Transformations

Concept #1: Inertial Reference Frames


Hey guys, in this video we're going to talk about one of the most important concepts in special relativity which is the concept of an inertial reference frame let's get to it now you can broad the break up reference frames which are just cooridinted systems that you construct arbitrarily to measure things right if we're trying measure displacement let's say if an object starts at some point X. Y. and moves to some new point X.1 Y.1 the only way that we can say that it started at some position X Y and ended at some new position is if we construct a coordinate system right in this case a cartesian X.Y. regular horizontal vertical coordinated system to measure the initial and final positions so that's coordinate system dependent and the coordinate system just represents a reference frame something with which we can refer to right to make a measurement so you can broadly breakup reference frames into two categories inertial reference frames and non inertial reference frames inertial reference frames are ones that move at a constant velocity. So the frame itself is either at rest or moving at a constant velocity a perfectly good example is a frame which is at rest right just you standing somewhere in a lab making measurements. A good example of a moving inertial frame is a car for instance if your car is going at 20 miles an hour when you're sitting in the car you feel as if you're at rest and you can make measurements inside the car within your reference frame but to an observer outside the car standing on the side of the road. They see your reference frame moving at a constant velocity so the measurements that you make in your reference frame aren't going to be the same necessarily as the measurements the outside observer makes in his reference frame but they're still inertial frames because your car is moving at a constant velocity and the guy on the sidewalk is at rest both of those are inertial frames non inertial frames as the name implies are frames that are not inertial and if inertial frames move at a constant velocity non-inertial frames move at changing velocity which means right that they have acceleration. So accelerated reference frames are non inertial frames constant velocity frames are inertial frames. Inertial frames are typically subdivided into two once again broad category's the lab frame and the moving frame or sorry rest frames and moving frames rest frames are frames that have a quote and quote 0 velocity and I put the quotes there specifically and I'll get to those in a second moving frames as the name implies have a quote and quote non 0 right velocity.

The lab frame is the most common type of rest frame and it's just a frame that's at rest with respect to the earth or specifically the earth's surface that's where you construct a laboratory you built it on the surface of the earth you put tables you put instruments and you're making your little measurements inside that stationary reference frame in the lab that is by far the most common type or the most common example of a rest frame. Frames that move at some velocity sorry at the same velocity as some event is specifically how I worded it here and this is typically how special relativity is done you're interested in events you are interested in things that are happening so if that event let's say it's a particle that's unstable that can decay. So there's a little atom that's moving along it's not very stable so eventually it's going to break apart that decay that breaking apart that's the event that you're interested in that atom can be moving very quickly in the lab frame like 1% speed of light 10% the speed of light the lab frame is what the scientists at rest in the lab and they're going to see that atom whizzing by but if you were construct a reference frame that moves with the atom. That would be considered what we would call the proper frame, the proper frame is the one that moves at the same velocity as an event right I put event in quotes that's exactly what I was just explaining that we care a lot about events when discussing relativity and so the proper frame is the one that's going to be going with the event. One of the most common events that you're going to discuss in relativity is going to be a ticking clock I know that doesn't really sound like an events but this is typically how physicists phrase it a ticking clock can be moving or can be stationary for instance you could be standing and on your wrist you could have a little watch right that's ticking by or somebody who's in a car moving past you could be wearing a watch that's ticking by if you're interested in your watch than the lab frame or the rest frame is the proper frame but if you are interested in this guy's watch then the moving frame the frame moving with the car is the proper frame.

Now something that I need to key in on because I set it specifically here are these quotes why are they in quotes why is it zero and non-zero in quotes well it's because that doesn't actually mean anything what does velocity mean I said the lab frame which is the most common type of rest frame is at rest with respect to the Earth there's no such thing as absolutely at rest or absolutely moving that's not an actual physical concepts everything is moving relative to one another or at rest relative to one another but there's no sort of universal coordinate system where you can say something is definitely at rest or something is definitely moving, typically special activity problems are going to sort of be anchored to the earth because that gives us as people right I mention it here us as humans write us as people an easier way to understand the problems and what's going on if you anchor things to the surface of the Earth you see the surface of the earth is at rest if you're measuring things relative to the surface of the earth they're at rest if you're measuring things moving relative to the surface of the earth than they are in motion that just conceptually is a lot easier for people to understand out in space though which there are quite a bit of special relativity problems that are not anchored to the Earth but a occur out on space. You can't use the Earth as a reference point you can't say that the earth is stationary and so everything's stationary relative to the earth is stationary everything moving relative to the earth is moving you can't say that because you don't have that anymore so you just have to arbitrarily choose one lab frame so popular instance or popular example is let's say that there is a spaceship chasing another spaceship. You can consider both of these to be moving frames if you want or you can consider one of them to be stationary and then the other is moving relative to the stationary one this is all stuff that's probably really confusing right now and it's really confusing to everybody when you first see it but stick with it and what you'll see as we start covering problems is that it will start to make more and more sense it'll start to click but these reference frames are really hard to get used to at first

So near the surface of the earth right wee would typically consider write a lab frame to be at rest relative to the surface of the earth and a moving frame to be moving relative to the center of the earth we usually call lab frames as S and the moving frame as S prime now that's entirely up to your professor your book what is what but that's just the typical convention that I've always come across and that's the convention that we're going to use in these videos and also U is typically used for the velocity of a frame whereas V will be used for velocities of things within the frame so if you see this U right here is the velocity of that S prime frame the moving frame relative to the surface of the earth and conversely relative to the lab frame over their frame S right because S is at rest with respect to the earth so if S prime is moving at U with respect to the earth it's also moving at U with respect to the lab frame because the lab frame once again is at rest with respect to the earth so if there are some object.

Moving at a speed V or a velocity V I could say in the lab frame if we were to measure the velocity in the moving frame it would be a different velocity V prime, by the way don't think about these two reference frames as being spatially separated I just have to show them separated so that you can pictorially really understand it so you can visualize it but imagine if this guy was 1 meter into that frame this guy could be 1 meter into this frame as well so this is the difference between S the lab frame and S prime the moving frame and those velocities V and V prime they're not going to be the same. Now the last thing to discuss before we wrap up this video on inertial frames is that non inertial frames aren't important what is important or stand is that they are ignored in special relativity special relativity never deals with non-inertial frame special relativity only deals with inertial frames general relativity the second theory of relativity published by Einstein much later on actually 10 years later that deals with non inertial frames. Now technically the earth the surface of the earth is moving in a circle and since it's technically moving in a circle it is actually a non inertial reference frame right it's just that the Earth rotates very very slowly so we don't really notice the rotation of the earth when we are in a car and the car starts to accelerate you feel the acceleration of the car but when you're just standing on the surface of the earth you do not feel that acceleration because it's almost unnoticeable at such a small acceleration. Now the fact though that the Earth is a non inertial reference frame does actually have real life ramifications specifically there's a Coriolis force which is responsible for how hurricanes rotates and then the centrifugal force. Which actually alters slightly the gravitational acceleration at the pole of the earth and at the equator so if you have the earth and here is the equator the gravitational acceleration here is going to be slightly different then the gravitational acceleration would be at the equator because of the centrifugal force it's an almost it's a very very very small and hard to measure difference but the difference is actually there but once again these aren't important to our discussions they're just real life ramifications of non-inertial frames. Alright guys so that wraps up this introduction to inertial frames even if you don't quite understand them at this point that's because we're going to be using them continuously throughout our discussion of special reletivity and the best way to really understand them is to start seeing problems where we start using those inertial frames. Alright thanks so much for watching guys and I'll see you in another video.