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Kanhaiya Kumar posted an Question
March 09, 2022 • 21:51 pm 30 points
  • IIT JAM
  • Physics (PH)

Please anyone define homoginity of space, homoginity of time and isotropy of space with the help of only newtonian mechanics

Please anyone define Homoginity of space, Homoginity of time and Isotropy of space with the help of only Newtonian Mechanics

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    Anshum Sharma best-answer

    Homogeneity of Space: No point is space is special, so the same basic laws of physics should govern all of space. For instance, if electrons repel each other on Earth, we don't expect electrons to attract each other in the Andromeda Galaxy. More generally, if Maxwells equations hold on Earth, we also assume that they hold in the rest of the universe. Homogeneity of Time: No point in time is special, so the same basic laws of physics should govern all of time. So again, if Maxwells equations are valid today, there is no reason to expect the equations to suddenly become invalid tomorrow. Isotropy of Time: No direction in time is special. One way to visualize this, is to look at a simulation of Brownian motion for a classical gas at equilibrium, and then run the video in reverse -- the particles behave in the exact same way! For example, you are measuring the period of a pendulum on the Earth. If you go to the Moon, it changes (you would be able to distinguish where you are). Does this mean that the space is not homogeneous? No, it means that you have to consider the effect of gravity. So you would have to move the Earth-Moon system. Of course, you can't move everything in the Universe because then you a pure tautology. So when you do some transformation you have to do an extra effort and rearrange some parts of the experiment. Those statements are VERY abstract results of what is called Noether's Theorem. In plain english, it says that: The laws of physics are the same here as anywhere else (e.g., General Relativity holds at all places in space.) The laws of physics are the same for all possible values of the time coordinate. F=ma now and at 10,000,000 BC for example, and into the future. The laws of physics do not depend on the direction of time. The laws work if you run time forwards or backwards.

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    So, if a ball is thrown from a certain height it will bear the same potential energy and shall result in same kinetic energy no matter when the experiment is conducted. Because the duration of falling is least liable to change given the conditions are perfect. Implying that the motion shall also remain same and the velocity shall also remain same. As you know Suppose that potential energy U is function of time explicitly then d(U+T) =curly dU/Curly dt That means energy of system will conserved only when there is no non conservative force as well as Potential energy of the system do not depend on time explicitly... Homogeneity of time is related to Curly dU/Curlt dt=0

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