Відео

Thank you for your suggestion. I will consider this for a future video.

The minus sign comes from the fact that the second frame x' moves along the positive x direction with respect to the first frame and any measurements of distance or length in the x' frame along the x direction has got to be smaller than the same measurement made in the x' frame. You can imagine this by placing a rod or metre stick parallel to the x-axis and making measurements of the same in both the frames. You would find that, as x' moved towards the right (positive x-direction) for a time t with a velocity v, and hence a distance vt, the measurements of any point on the rod is less (-minus) by vt when compared with the measurements of the same point in x frame.

It is not a minus sign from the velocity direction as you might think. It comes from the relative motion of the two frames. The velocity direction could be assumed positive or negative which will not affect the equation here as such.

You are most welcome to suggest a better title for what I have done in this video that I could use in my subsequent videos of similar nature. Thanks in advance.

Thank you. Yes, I have plans to upload more Physics videos.

I have used multiple sources. 1) Modern Physics textbooks such as Beiser, Krane, Tipler, Thornton etc.,. 2) Special Relativity texts such as Resnick, French etc.,.

Here it is.. ua-cam.com/video/cl-CBZ4Ta5c/v-deo.html

I shall soon try to post a video on Ehrenfest paradox.

@@TheUltimatePhysicsChannel I will be keenly awaiting for this video. Thank you

Here it is....ua-cam.com/video/cl-CBZ4Ta5c/v-deo.html

Thanks for your appreciation and suggestions. I shall soon try to post a video on the Ehrenfest paradox.

​@@TheUltimatePhysicsChannel thank you for considering my suggestion

@@shrivatsa8604 Good suggestion, and nicely framed!

@@r2k314 thanks I'm keenly awaiting for his video on this topic

Here it is..ua-cam.com/video/cl-CBZ4Ta5c/v-deo.html

To answer your first question, there are a few different ways in which we can explain the situation. First I have to make something clear here. Maxwell’s electromagnetic theory which has at its core his four equations along with the Lorentz force equation (which pertains to your second question btw) precedes Einstein’s Special theory of Relativity by at least four decades. In fact, Einstein, while proposing his special theory and his general theory later, wanted to ensure that his theory was consistent with Maxwell’s electromagnetic theory including one of its major tenets that the electromagnetic waves travel at the speed of light and its invariance nature (in all inertial frames of reference). At the end of the day, we should remind ourselves that these two successful theories are eventually theories only. This also means that these two are two different ways of looking at the Physical Reality. Both make successful predictions and both are experimentally verifiable. Both these ‘theories’ make accurate predictions about the physical reality, which in the context of your first question is the electric and magnetic fields. Now, the fact that special relativity is able to explain a situation without invoking another field (a ‘special’ ‘magnetic’ field) is all the more interesting and adds to its simplicity in certain ways. One of the desirable qualities of any theory is that it should be simple with minimalist principles. Coming to your specific question, let us say there are two parallel conductors each having positive and negative charges in equal numbers so that each are electrically neutral. Now, when current passes through any of these two conductors, we see a force of attraction between the two or a force of repulsion depending upon the current directions. We know that current can flow in either of the two directions along the conductor but not perpendicular to it (relevant to your second question btw). The convention is to assign the current direction to be opposite to the direction of electron flow. This means the positive charges can be assumed to flow in the opposite direction to that of the electron flow thereby along the direction of current flow. But we know that in reality the positive charges (which are basically metal ions in a conductor) does not flow at all. But in order to understand what is actually happening, this is just a simple assumption to get the larger picture. Coming back to the context, you could imagine either type of charge in each of the two conductors as being at rest with respect to your frame of reference and see that the other type of charge moving at twice the speed. If you are fixed to the moving electrons in conductor 1, the positive charges on the other conductor (which causes an attractive force) move in the opposite direction at 2v speed with respect to you (since you were anyway moving at speed ‘v’ with respect to the lab frame). If you are fixed to the frame of the positive ions in conductor 1, you would see that the electrons in conductor 2 move in opposite direction at twice the speed. So, each type of charges moves at speed ‘v’ with respect to the lab frame but at speed 2v with respect to each other in either of the two conductors. This 2v speed results in a larger Lorentz contraction of either type of charge with respect to the other type of charge in the other conductor not the same conductor. This point is important to be understood well. Read it again if you don’t. This is where relativistic way of looking at things is different from the non-relativistic way of approach. The non-relativistic approach fails to understand the situation in terms of simple Coulombic attraction or repulsion as the case may be and rather invokes a special ‘magnetic’ force to understand the situation. So, your test charge has to identify itself with any of these four charge groups in our two conductors namely positive charges in conductor 1, electrons in conductor 1, positive charges in conductor 2 and electrons in conductor 2. Since your test charge behaves akin to one of these four types of charges, the description provided above should answer your question. 2) There are a few people who argue that the Special Theory of Relativity is more of a ‘smart’ theory rather than an ‘original’ theory. I personally don’t agree with this argument. Einstein drew ideas from different people (drawing inspiration and knowledge from their theories) but made his own theory. He did not copy from anybody. The difference between a genius and a copycat is this. If you let your brain free, it will come up with something original and novel while drawing inspiration from everywhere. Einstein let his imagination free and let it go wild. He needed some luck and a stroke of genius, He had both. The same Einstein could not accomplish similar success later on. He was not lucky. His brain was not the same either. What he was at 26, he was not the same later on. Lorentz and Poincaré 2) Maxwell 3) Minkowski (his teacher btw) were some of the names from whom Einstein drew a lot of inspiration. Einstein knew about the work of each of these people fairly thorough by the time he proposed his special theory. You might be wondering how this answers the second question. Read again what I have written and Now read ahead. In the context of special relativity, the Lorentz force law is extended to account for the four-dimensional nature of spacetime and the relativistic effects. In relativistic electrodynamics, the Lorentz force is described using the four-vector formalism. In special relativity, physical quantities are often represented as four-vectors, which combine time and space components into a single entity. For a charged particle, the relevant four-vectors include: Four-position and Four-velocity. And the electromagnetic field is described by the electromagnetic field tensor which is a rank-2 tensor that combines the electric and magnetic fields. Therefore, the relativistic form of the Lorentz force law can be written using the four-velocity and the electromagnetic field tensor. Thus we can write the four-force acting on a particle with charge based on this and thereby its equation of motion as well. To sum it all up, the relativistic explanation of the Lorentz force involves using the four-vector formalism and the electromagnetic field tensor. This approach unifies the electric and magnetic fields and ensures that the laws of electromagnetism are consistent with the principles of special relativity. Hope that answers your second question. Why did this video not address the larger picture? The larger picture is more complicated for the scope of this video. This video tries to explain what is happening between two conductors at the undergraduate level. A more thorough course on Special Relativity or relativistic electrodynamics should definitely address this in detail.

@@TheUltimatePhysicsChannel thank you once again

You're welcome

Thank you. Please check this one on this channel.. On Minkowski diagrams.. ua-cam.com/video/KPQFVMq79t4/v-deo.htmlsi=gUfRoIpToGez3dO7

To answer your first question, there are a few different ways in which we can explain the situation. First I have to make something clear here. Maxwell’s electromagnetic theory which has at its core his four equations along with the Lorentz force equation (which pertains to your second question btw) precedes Einstein’s Special theory of Relativity by at least four decades. In fact, Einstein, while proposing his special theory and his general theory later, wanted to ensure that his theory was consistent with Maxwell’s electromagnetic theory including one of its major tenets that the electromagnetic waves travel at the speed of light and its invariance nature (in all inertial frames of reference). At the end of the day, we should remind ourselves that these two successful theories are eventually theories only. This also means that these two are two different ways of looking at the Physical Reality. Both make successful predictions and both are experimentally verifiable. Both these ‘theories’ make accurate predictions about the physical reality, which in the context of your first question is the electric and magnetic fields. Now, the fact that special relativity is able to explain a situation without invoking another field (a ‘special’ ‘magnetic’ field) is all the more interesting and adds to its simplicity in certain ways. One of the desirable qualities of any theory is that it should be simple with minimalist principles. Coming to your specific question, let us say there are two parallel conductors each having positive and negative charges in equal numbers so that each are electrically neutral. Now, when current passes through any of these two conductors, we see a force of attraction between the two or a force of repulsion depending upon the current directions. We know that current can flow in either of the two directions along the conductor but not perpendicular to it (relevant to your second question btw). The convention is to assign the current direction to be opposite to the direction of electron flow. This means the positive charges can be assumed to flow in the opposite direction to that of the electron flow thereby along the direction of current flow. But we know that in reality the positive charges (which are basically metal ions in a conductor) does not flow at all. But in order to understand what is actually happening, this is just a simple assumption to get the larger picture. Coming back to the context, you could imagine either type of charge in each of the two conductors as being at rest with respect to your frame of reference and see that the other type of charge moving at twice the speed. If you are fixed to the moving electrons in conductor 1, the positive charges on the other conductor (which causes an attractive force) move in the opposite direction at 2v speed with respect to you (since you were anyway moving at speed ‘v’ with respect to the lab frame). If you are fixed to the frame of the positive ions in conductor 1, you would see that the electrons in conductor 2 move in opposite direction at twice the speed. So, each type of charges moves at speed ‘v’ with respect to the lab frame but at speed 2v with respect to each other in either of the two conductors. This 2v speed results in a larger Lorentz contraction of either type of charge with respect to the other type of charge in the other conductor not the same conductor. This point is important to be understood well. Read it again if you don’t. This is where relativistic way of looking at things is different from the non-relativistic way of approach. The non-relativistic approach fails to understand the situation in terms of simple Coulombic attraction or repulsion as the case may be and rather invokes a special ‘magnetic’ force to understand the situation. So, your test charge has to identify itself with any of these four charge groups in our two conductors namely positive charges in conductor 1, electrons in conductor 1, positive charges in conductor 2 and electrons in conductor 2. Since your test charge behaves akin to one of these four types of charges, the description provided above should answer your question. 2) There are a few people who argue that the Special Theory of Relativity is more of a ‘smart’ theory rather than an ‘original’ theory. I personally don’t agree with this argument. Einstein drew ideas from different people (drawing inspiration and knowledge from their theories) but made his own theory. He did not copy from anybody. The difference between a genius and a copycat is this. If you let your brain free, it will come up with something original and novel while drawing inspiration from everywhere. Einstein let his imagination free and let it go wild. He needed some luck and a stroke of genius, He had both. The same Einstein could not accomplish similar success later on. He was not lucky. His brain was not the same either. What he was at 26, he was not the same later on. Lorentz and Poincaré 2) Maxwell 3) Minkowski (his teacher btw) were some of the names from whom Einstein drew a lot of inspiration. Einstein knew about the work of each of these people fairly thorough by the time he proposed his special theory. You might be wondering how this answers the second question. Read again what I have written and Now read ahead. In the context of special relativity, the Lorentz force law is extended to account for the four-dimensional nature of spacetime and the relativistic effects. In relativistic electrodynamics, the Lorentz force is described using the four-vector formalism. In special relativity, physical quantities are often represented as four-vectors, which combine time and space components into a single entity. For a charged particle, the relevant four-vectors include: Four-position and Four-velocity. And the electromagnetic field is described by the electromagnetic field tensor which is a rank-2 tensor that combines the electric and magnetic fields. Therefore, the relativistic form of the Lorentz force law can be written using the four-velocity and the electromagnetic field tensor. Thus we can write the four-force acting on a particle with charge based on this and thereby its equation of motion as well. To sum it all up, the relativistic explanation of the Lorentz force involves using the four-vector formalism and the electromagnetic field tensor. This approach unifies the electric and magnetic fields and ensures that the laws of electromagnetism are consistent with the principles of special relativity. Hope that answers your second question. Why did this video not address the larger picture? The larger picture is more complicated for the scope of this video. This video tries to explain what is happening between two conductors at the undergraduate level. A more thorough course on Special Relativity or relativistic electrodynamics should definitely address this in detail.

@@TheUltimatePhysicsChannel thank you for the answer is there a way for us to visualise the transformation of the electric field in such a way that it can accomplish the effects of magnetic field based on question number 2 because in mathematical point of view the four vector transformation indeed explains the effect of magnetic force acting on a charge that is moving perpendicular to a current carrying conductor but the visualisation part is what makes me curious as in a special relativity point of view how might the charge experience a force when it is moving perpendicular to the current sideways like if the current is moving from left to right and the charge is moving away from the current carrying wire let's say in the positive Y direction the force acting on the charge acts to the right in the direction of current obviously so how might be visualise this effect as we can visualise the effect that you explain in one of your videos prior to this one

I feel such a visualization should be possible by using transverse Doppler effect but probably not with just Lorentz transformation alone, since length contraction occurs only longitudinally.

@@TheUltimatePhysicsChannel I do have a way of visualising it and I am interested in how you think about this view so basically if a charged particle is moving perpendicular to a current carrying wire let's say that the current carrying wire has linear and uniform charge distribution of positive charge and assuming that its infinitely long positioned on the x-axis as its moving in the direction of positive x-axis generating the current in the same direction now when we have a positive point charge moving in the positive Y direction then in a observation we see the magnetic force acting on the charge in the positive X direction but before hopping into the charges frame first we need to hop into the wires frame where the electric field can be visualised using a Gaussian surface being perfectly cylindrical and using the Gauss's law we can find the electric field exactly at any point changing the parameter of the cylinder so if we view the cylinder in only two dimension and search in such a way that the parameter is a square now after hopping into the point charges frame this square which is the 2D view of the Gaussian surface will be moving in a direction such a way that it is moving parallel to the diagonal of the square rendering one of its diagonals length contract and changing the parameter and the shape itself to a parallelogram this means that the radial Axis has to tilt at an angle and this angle is precisely the direction of the electric field which alliance said to be not straight to the axis of force acting on the charge in the stationary frame of US hence the force acting on a charge will be acting at an angle thats not 90 ° explaining the direction of the electric field and this effect we perceive in our frame as magnetic force that acts as a horizontal force component to the over all resultant force,I am keen to know your view on this

I have a few issues with your way of visualising the situation here. First, you talk about ‘the wire frame of reference’. I assume that you mean ‘lab frame’ by that. Then you talk of charges’ frame of reference. Remember that the positive charges are in the same frame as the ‘lab frame’ for our purpose. So, I assume you meant ‘the frame of the negative charges’ here. You have written that ‘we see the magnetic force acting on the charge in the positive X direction’ which can’t be true since the current flows along this direction. The direction of the magnetic field is along a circle around the wire varying as we move around the circle (Fleming’s right hand rule). So, I assume that you want to visualise a Gaussian surface in lab frame around the wire which is cylindrical which is correct. But to assume that it would take the shape of a square or a rectangle in 2D is not an accurate description of the geometry here. And to assume that such a Gaussian surface moves when we ‘hop’ on to the reference frame of the charges is beyond me. First, let us make something clear. The Gaussian surface that you construct in problems involving electric field calculations in electrostatics is merely a ‘construction’. It is not a physical reality. Therefore to assume that the geometry of a ‘slice’ of such a surface (when we go down by one dimension) would change and undergo Lorentz contraction would not be correct. Lorentz contraction is in a sense a physical situation when we compare measurements between two frames of reference which are in relative motion. A Gaussian surface is not. It is merely a geometric construction that makes our life easy when we attempt to calculate the electric fields of objects possessing certain shapes such as a point charge, or a spherical charge distribution, a wire carrying charge. And such fields can be calculated for static charges. When charges begin to move as in our case, things are very different. These moving charges would give rise to magnetic fields and when they accelerate they would produce electromagnetic fields. So, the validity of a Gaussian surface is in question in your visualisation.

Good day to you too. Sorry. I don't use Whatsapp for non-personal communication. You can reach me at theultimatephysicschannel@gmail.com. Thanks.

You're welcome.

Actually I do have an answer of my own but this is related to relativity of rotation which is a very complicated topic although I can give you a rough idea of it if you would like

Thank you.

Your inconvenience is regretted.

Thanks

Yes it has been demonstrated by experiment - time and time again. Tiny brains don't get to challenge real physics.

@@everythingisalllies2141 coz it's proven

@@shrivatsa8604 BS. Its not "proven". Its not even possible to prove such a thing. And its illogical and irrational.

You are welcome.Glad it is helpful.

Ask it then