Timeline for How do we prove that the 4-acceleration transforms as a 4-vector in Special Relativity?
Current License: CC BY-SA 4.0
9 events
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| Oct 27, 2022 at 18:59 | comment | added | Voulkos | @mike stone ...Thanks for your important note : indeed, $\mathrm d(\mathbf{v\cdot v})/\mathrm d\tau=\mathrm d c^2/\mathrm d\tau=0$ but $\mathrm d(\mathbf{a\cdot a})/\mathrm d\tau=\mathrm d(-\Vert \boldsymbol\alpha_0\Vert^2)/\mathrm d\tau=-2\boldsymbol\alpha_0\cdot\mathrm d\boldsymbol\alpha_0/\mathrm d\tau \ne 0$ in general, where $\:\boldsymbol\alpha_0(\tau)\:$ is the acceleration 3-vector with respect to the rest frame of a particle. | |
| Oct 27, 2022 at 15:33 | comment | added | mike stone | What do you mean by "constant", as @Frobeneius says, ${\bf a}\cdot {\bf a}$ is an "invariant" , meaning independent of reference frame, but is not a "constant" as (unlike ${\bf v}\cdot {\bf v}=-c^2$) it can vary with with $\tau$. | |
| Oct 27, 2022 at 15:02 | comment | added | John Doty | @Frobenius If you don't connect your definition to physical reality, it is pure mathematics. | |
| Oct 27, 2022 at 14:57 | comment | added | John Doty | @Frobenius Every test of relativity versus Newtonian mechanics is a test of the physical utility of your definition. | |
| Oct 27, 2022 at 14:47 | comment | added | Shaashaank | @Frobenius thank you for replying, I meant that, for four velocity, we can show that it’s dot product is a constant, but for acceleration do we just assume it?. | |
| Oct 27, 2022 at 14:43 | comment | added | Voulkos | In mechanics I define the following named "stupid 3-dimensional momentium" $$\mathbf{s3m}=m^2\upsilon\,\mathbf n$$ What is the meaning of the "experimental test" of my definition ??? Note that I don't mention for what purpose I will use this 3-dimensional quantity. | |
| Oct 27, 2022 at 14:22 | comment | added | John Doty | @Frobenius But if that definition did not lead to results confirmed by experiment, we would reject it as irrelevant to physics. | |
| Oct 27, 2022 at 14:11 | comment | added | Voulkos | The 4-accelaration is defined and by its definition is a priori 4-Lorentz vector, see @mike stone's answer, not proved by experimental tests. | |
| Oct 27, 2022 at 13:40 | history | answered | John Doty | CC BY-SA 4.0 |