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Markus Hanke

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Markus Hanke last won the day on September 18

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  1. This is true only if you choose to parametrise the path using proper time - which physically just means that photons don’t have a rest frame. However, you can choose a different affine parameter, which will yield a non-zero result. Also, the world lines of the train’s constituent particles are time-like, so there shouldn’t be an issue.
  2. I’m afraid I don’t follow you on this (maybe my fault). In this spacetime all the relevant components of the metric are explicitly time-dependent, so if the histories of these clocks differ, then they aren’t guaranteed to remain synchronised. Also, the dilation factor relative to the distant clock will be time and coordinate dependent. But maybe I misunderstood your thoughts.
  3. Yes, exactly right. Note that the metric determines all relevant gravitational phenomena, so there’s really no need at all to try and carry over gravitational potential from Newtonian physics. How so? Time dilation between two points would be a time-dependent function rather than a single value, since all of spacetime here is filled with gravitational radiation.
  4. Are we not overthinking this a bit? An object such as the train mentioned in this thread is just a collection of (many) individual world lines. The geometric length of each individual world line between given events is something all observers agree on; thus, the volume implied by an entire bundle (congruence?) of such world lines should also be something everyone agrees on. Or am I seeing this wrong?
  5. Basically, the concept is meaningful only if it is independent of the specific path taken between the two events. This requires the presence of certain symmetries - which not all spacetimes have. For example, consider what happens if the spacetime is not stationary, such as in a binary star system. The work required to escape to infinity from any point within this system depends not only on where that point is, but also on when the escape happens, and what specific trajectory is taken. In other words, it depends on the path taken through spacetime, the metric of which now explicitly depends on both time and space coordinates. As such it isn’t possible to assign a single unique value that signifies gravitational potential to any point in that spacetime.
  6. I didn’t mean to suggest that. Of course this needs to be done according to the proper rules and procedures of differential geometry in spacetime - the language of exterior calculus naturally lends itself to this. I remember MTW has a section that shows the proper procedure to construct volume integrals on semi-Riemannian manifolds; it’s that I was thinking of.
  7. In 4D, you account for both space and time. If a boundary is contracted in space, it is expanded in time by the same factor, leaving the overall volume in spacetime unchanged. Or to put it more technically - the volume element in 4D is an antisymmetric tensor, so any volume constructed from it by integration will be a covariant quantity.
  8. Well, the universe is a 4D structure, yes. But my main point was that in order to find quantities that all observers can agree on (ie that are independent of reference frame), you need to always go into 4D. So, length (3D) and time (1D) depends on observer, but hypervolume (4D) does not, for example. So the ontology of objects in spacetime is 4D.
  9. Perhaps I should have been a bit more precise - it’s measurements of length that are relational, and the relationship depends on angles and orientation in spacetime. In practice that means that length contraction is observed along the direction of motion, but not perpendicular to it. Thus, for example, the initially spherical gold ions in the RHIC become flattened disks in the lab frame - and physically behave like flattened disks at the point of collision. So no, shape also depends on the observer. If you want to know about properties that do not depend on the observer, you need to consider all four dimensions of spacetime, and not just 3D measurements. For example, the train you previously mentioned would trace out a (4D) hypervolume in spacetime between two given events; this would be a quantity all observers agree upon, even if they don’t agree on isolated measurements of space and time. Thus, ontologically there are covariant and invariant quantities - but only in 4D. You always need to consider both space and time. It’s only our cognitive habit of separating these that creates confusion and misconceptions.
  10. It is meaningless to ask about “size” separate from a specific observer, since this measurement designates a relationship between two frames in spacetime. It’s not an intrinsic property. Thus there’s no contradiction, because we are dealing with relational properties, so the ontology of this is also strictly relational. In other words - all observers are right, but only in their own local frames.
  11. Can you not see that you are going down a very slippery slope here? You are now starting with a conclusion (‘photons must be waves‘), and try to force available data to fit that predetermined solution. This is the opposite of the scientific method. The correct explanation is already given in the experiment which I linked - the rest of your post is just wild speculation that doesn’t even seem to be related to the specifics of the LHC setup, or even to any established particle physics. To be honest, I think we’re done here.
  12. They have been observed at the LHC in March 2019, with a statistical significance of ~8 sigma, which is way above the ‘discovery’ threshold: http://cdsweb.cern.ch/record/2667214
  13. I have quite fond memories of my years on the Atari ST...for all its faults it was nonetheless a great machine, with a nice community of users around it. I taught myself to program on it, in several languages. I was really into it at the time!
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