It's not just the Lorentz factor that you need to use to find correct solutions, it's the Lorentz Transformation that will link them together mathematically.AdamBenHamo said:I've recently been thinking more about special relativity, and while I understand the Lorentz factor and how to apply it to find correct solutions, I'm still stuck on the link between the effects of length contraction and time dilation, are they permutation of the same thing from different reference frames? How do they link together mathematically? Any light shed on this at all would be really helpful! Thanks in advance!
AdamBenHamo
AdamBenHamo said:Thankyou ghwellsjr, but that doesn't quite answer my question, it's no so much the solutions that I have a problem finding, but the symmetry between the two phenomena that I can't quite get my head around!
AdamBenHamo said:...on the link between the effects of length contraction and time dilation, are they permutation of the same thing from different reference frames? How do they link together mathematically?
Time dilation is a phenomenon where time appears to pass slower for objects that are moving at high speeds or in strong gravitational fields. This is due to the stretching of time and space as described by Albert Einstein's theory of relativity.
Time dilation occurs because the speed of light is constant in all frames of reference. This means that as an object moves faster, its perception of time slows down in order to maintain the speed of light as a constant. Additionally, the effects of gravity can also cause time to pass slower in stronger gravitational fields.
Length contraction is a consequence of the theory of relativity that states that objects in motion will appear shorter in the direction of their motion when observed from a stationary point of view. This effect only becomes noticeable at extremely high speeds, close to the speed of light.
Length contraction and time dilation are both effects of the same underlying principle, which is the constancy of the speed of light. As an object's perception of time slows down, it also experiences a contraction in its length in the direction of its motion. These two phenomena are interconnected and are both consequences of Einstein's theory of relativity.
Yes, time dilation and length contraction can be observed in everyday life, although the effects are very small and only become noticeable at extremely high speeds or in strong gravitational fields. For example, the Global Positioning System (GPS) has to account for the effects of both time dilation and length contraction in order to provide accurate location data. Additionally, particle accelerators and experiments involving atomic clocks have also provided evidence for these phenomena.