When looking at energy distributions in statistical mechanics and time evolution of quantum systems, inverse temperature is equivalent to imaginary time.
Wick Rotations: specifically the section on statistical and quantum dynamics
When looking at energy distributions in statistical mechanics and time evolution of quantum systems, inverse temperature is equivalent to imaginary time.
Wick Rotations: specifically the section on statistical and quantum dynamics
It may comfort you to know that, while measurements of both space and time are inconstant in different reference frames, there’s a combination of space and time measurements that is invariant in all reference frames. By way of comparison, if I have a stick, I can lay it flat on the ground and say it’s (say) five feet long but has almost no height at all, or I can stand it upright and say that it’s five feet tall, or I can tilt it over at an angle and say that it’s three feet long and four feet tall. Height and length are thus variant depending on how I orient the stick. But in all cases, if I take the height squared plus the length squared, I’ll get the same value.
That’s what I took you to mean, actually.
Measurements of both spatial distances and temporal intervals will vary depending on the relative velocities between observers and the things observed. So if the varying nature of time measurements bothers you, and leads you to conclude that time doesn’t really exist, then the same reasoning ought to apply to space – or so I would think.
Also, as Chronos points out, there is a combined spacetime “distance” you can compute between any two events, whose value is independent of all observers. It’s hard (at least for me) to see how this quantitiy could be real, reliably and consistenly real, without the quantities it depends on also being real – in some form. More complicated maybe than what our everyday human perceptions tell us, but still real.
The point I was going for is that if you see an object, way over yonder, and it looks blue, you don’t immediately know whether it is “inherently” blue (it emits or reflects blue light when observed in its own reference frame), or whether it’s really inherently green and moving toward you rapidly, or is violet and moving away from you rapidly. You have to bring in other knowledge about the object, assuming you have any, in order to resolve that question.