I Is Heart Rate Invariant in Different States of Motion?

[aclaret]

just something i think about, maybe it difficult to answer.

i know, from study, that any observer moving along his world-line - in any state of motion - will not himself notice any difference to the rate which time passes for him. example: his heart-rate will feel normal (well, so long as he not stressed ;) !), his watch tick at normal rate, whatever (even, maybe he could use his heart as a clock!). and of course, the “time he experience” is nothing but integral of d$\tau$, the natural parameterisation (“propre” time) along world-line.

I "know" this to be true, from books, but i sometimes like to know how to deduce things beyond any doubt. is it possible to give a simple argument, to convince anyone that your heart indeed beat the same way for any observer?

see - at first i thought this obvious - it because if law of physics invariant in every inertial frame (heart rate govern by chemical reaction, govern by electromagnetism, govern by law of physic...), then could ask: “well, suppose it do beat faster in a certain given state of the motion, then which one does it beat faster or slower in?". then, by symmetry, you forced to admit it beat same in every inertial frame. BUT, we know that heart-rate would also feels the same for an observer in non-inertial motion. so maybe, this argument not sufficient.

 

[Vanadium 50]

If your heart beats once per second and your watch ticks once per second, they are always in sync. All observers must agree with this.

 

[aclaret]

If your heart beats once per second and your watch ticks once per second, they are always in sync. All observers must agree with this.

yes, that indeed is certain.

yes, suppose could say "well, proper time is define as time experience by observer, and if that proportional to heart rate, proposition follow". but it not intuitive to me, at least not at deep level, why proper time is constrain to correlate with "time experienced". i certain it correct, but if i wanted to explain say, my mom, why - i do not know I could provide intuitive answer.

also, at least in IRF, proposition follow from symmetry. but for non-inertial frame, not obvious to me how to set up similar argument.

 

[PeroK]

It's effectively a postulate of GR that the length of a spacetime path is the time measured by a clock traveling along that path. This needs to be be tested, as I wouldn't assume it's intuitive. On a non-inertial path, the clock must remain accurate and not be affected by the forces on it.

In general, using things like heart rate to measure time is a bad idea as it's not something that can be relied upon. If someone goes on a rollercoaster, then their heart rate is likely to go up, so the number of heartbeats may not be an accurate measure of how long they spent on the rollercoaster.

The test of the postulate, therefore, would be to count physical processes that you expect to be unaffected by the non-inertial trajectory.

 

[aclaret]

PeroK, you hit the nail on the head. makes me relief that I'm not a complete failure just because i could not reason intuitively why proper time constrain to correlate with time measure by clock ;)

ok, after your post i am satisfied. thank :)