Baseless assumption. Length contraction and time dilation are both real in each FoR they are measured, and each FoR is as valid as the other. Basic SR.
Disagree
Measured to outside perspective or within perspective ?
Baseless assumption. Length contraction and time dilation are both real in each FoR they are measured, and each FoR is as valid as the other. Basic SR.
Do you have trouble in comprehension? Or just trolling?Disagree
Measured to outside perspective or within perspective ?
Your argument is math based ; what of reality .
To the Universe OUR perspective ; is just this ; our perspective ; and so is the mathematics .
K is free parameter in test theories of space-time that span Galilean Relativity, Newtonian Absolute Space and Time and Special Relativity.
In Galileo's/Newton's description of physics, K=0. In Special Relativity, $$K = \frac{1}{c^2}$$. Galileo's and Newton's experiments were too slow and imprecise to distinguish the difference between these quantities.
In the test theory, we simply write K and let experiment decide what value of K best matches the data.
(Test theory) Space-time transformation in one-dimension of space: $$ \Delta x' = \frac{ \Delta x - u \Delta t }{\sqrt{ 1 - K u^2 }} \\ \Delta t' = \frac{ \Delta t - K u \Delta x }{\sqrt{ 1 - K u^2 }}$$
The evidence for a particular value of K comes from precision experiments designed to test aspects of this relation:
(Test theory) Law of composition of velocities in one dimension of space: $$v_3 = \frac{v_1 + v_2}{1 + K v_1 v_2}$$
In 1859, it was empirically discovered that when $$v_1 \approx 10^8 \, \textrm{m} \cdot \textrm{s}^{-1}$$ that $$K= \frac{1}{c^2}$$ was preferred. This formula is derived from the Space-time transformation, so evidence for the latter is evidence for the former.(Test theory) Law of Proper elapsed time (time dilation): $$\Delta \tau = \sqrt{1 - K v^2} \Delta t$$
Experiments on unstable particles and clock in fast-moving vehicles such as satellites and jets have strongly supported $$K= \frac{1}{c^2}$$. This formula is derived from the Space-time transformation, so evidence for the latter is evidence for the former.(Test theory) Law of co-moving distances (length contraction): $$L' = \sqrt{1 - K v^2} L_0$$
Observations on unstable particles created at the top of Earth's atmosphere reaching the ground and the engineering of synchroton radiation devices have strongly supported that fast-moving particles treat lengths as contracted and so $$K= \frac{1}{c^2}$$ wins. This formula is derived from the Space-time transformation, as in my earlier post, so evidence for the latter is evidence for the former.(Test theory) relation between kinetic energy and momentum: $$\frac{p^2}{E - E_0} - 2m = \sqrt{m^2 + Kp^2} -m \approx K \left( \frac{p^2}{2m} - \frac{K p^4}{8 m^3} + \frac{K^2 p^6}{16 m^6} - \dots \right)$$
In the 60's they raced electrons to measure their momentum and energy. $$K= \frac{1}{c^2}$$ wins. This formula is derived from the Space-time transformation, as in my earlier post, so evidence for the latter is evidence for the former.
So we, unlike Newton's assumptions, appear to live in a world where $$K$$ is non-zero and is approximately $$ 1.11265 \times 10^{-17} \, \textrm{m}^{-2} \cdot \textrm{s}^2 = 11.1265 \, \textrm{TJ}^{-1} \cdot \textrm{mg}$$ in SI units. But those numeric value are not natural inventions but represent our human choice to describe the world in certain units.
While that is admirable and the right course of action to take, should not this thread and its ridiculous unsupported claims that have inevitably been shown to be wrong, be also moved to the appropriate section?Moderator note: absolute-space has been permanently banned from sciforums, after admitting that he was using a sock puppet.
Moderator note: absolute-space has been permanently banned from sciforums, after admitting that he was using a sock puppet.
The thread question is a legitimate one, and it's an interesting matter to discuss. Unfortunately, this particular thread went down a cranky path fairly early on. In the end, I've decided to move it and to leave a redirect in Physics.
A while back there was a question about the muon experiment "What if it were the other way round?" From the context this was clearly - assume the Earth is moving and muons are stationary. In reality the only movement is relative and "the other way round" would be for the muons to have 'Earth detectors' spaced (say) 10km apart - then the events would be 'detector 1 hits Earth' and 'detector 2 hits Earth'. The distance in the muon frame would be 10km and zero in the Earth frame. The invariant spacetime interval would be the same in both cases.Agreed. It is a pity it went off track.
http://www.atmosp.physics.utoronto.ca/people/strong/phy140/lecture32_01.pdfA while back there was a question about the muon experiment "What if it were the other way round?" From the context this was clearly - assume the Earth is moving and muons are stationary. In reality the only movement is relative and "the other way round" would be for the muons to have 'Earth detectors' spaced (say) 10km apart - then the events would be 'detector 1 hits Earth' and 'detector 2 hits Earth'. The distance in the muon frame would be 10km and zero in the Earth frame. The invariant spacetime interval would be the same in both cases.
Howdy. The muon example is so nice because it only works if special relativity has a special* type of consistency.A while back there was a question about the muon experiment "What if it were the other way round?" From the context this was clearly - assume the Earth is moving and muons are stationary. In reality the only movement is relative and "the other way round" would be for the muons to have 'Earth detectors' spaced (say) 10km apart - then the events would be 'detector 1 hits Earth' and 'detector 2 hits Earth'. The distance in the muon frame would be 10km and zero in the Earth frame. The invariant spacetime interval would be the same in both cases.
I think banning absolute space from a scientific forum is not a good idea, given that it is part of many important scientific theories like Newtonian mechanics.Moderator note: absolute-space has been permanently banned from sciforums
A while back there was a question about the muon experiment "What if it were the other way round?" From the context this was clearly - assume the Earth is moving and muons are stationary. In reality the only movement is relative and "the other way round" would be for the muons to have 'Earth detectors' spaced (say) 10km apart - then the events would be 'detector 1 hits Earth' and 'detector 2 hits Earth'. The distance in the muon frame would be 10km and zero in the Earth frame. The invariant spacetime interval would be the same in both cases.
I think banning absolute space from a scientific forum is not a good idea, given that it is part of many important scientific theories like Newtonian mechanics.
(Yes, I have understood that this is about a user with this name, but SCNR)
Nobody has banned the concept of absolute space. A user who pretends to ask an innocent question, when in fact it is a pretext for introducing a crank agenda, has been banned from part of the forum.
Hm. Do you read a post before answering? In case not, I repeat: Yes, I have understood that this is about a user with this name, but SCNR
I apologize for having not added 20 smilies and a "warning: satirical content" spoiler.