If entropy is a method for determining “Time” does hawking radiation prove time displacement in a meaningful way?

[u/Little_Vehicle_6671]

If we have a baseline for how thermodynamic reactions SHOULD OCCUR…

And yet Blackholes radiate at 1 trillionth of a kelvin..

We could extrapolate backward from that, and say “Given this mass this is what we WOULD EXPECT to see”

So by measuring the low intensity of hawking radiation do we use this to confirm “Yes time is definitely running slower inside the black hole because of this relationship of energy out, vs what should be happening inside if time were 1:1”

Sorry I KNOW we already accept time dilation is a thing that occurs …Im just specifically asking if measuring the entropy of a black hole, also confirms the same things with no discrepancies.

[u/MarsMaterial]

Entropy isn’t really a way of measuring time. The second law of thermodynamics says that entropy must always increase, but it says nothing about how fast it increases. It can increase slowly or quickly, it all depends on the situation.

[u/Little_Vehicle_6671 → u/MarsMaterial]

But we use rates of entropy to confirm passage of time, relatively.

Which is why we see red shifting and blue shifting.

We use our frame of reference to establish “All thermodynamic reactions in this frame of reference , equal something” which we can measure and model as “Given this radiation source we can determine how much stuff is bring converted into energy”

We determine MASSES, energies, and TIME SCALES, soley based on these assumptions from very far away observations.

So if that is TRUE.

Would I expect the hawking radiation to MATCH what should be thermodynamically be happening inside a black hole…

And the estimated time dilation within the event horizon…

Or does it all become meaningless

[u/fractalife → u/Little_Vehicle_6671]

Which is why we see red shifting and blue shifting

No, red/blue-shifting has to do with relative motion, not anything to do with entropy.

Hawking Radiation does not tell you anything about what's happening inside a black hole. It's arbitrary quantum fluctuations happening at the surface of a black hole. They don't have anything to do with what's going on on either side of the event horizon.

[u/Little_Vehicle_6671 → u/fractalife]

Ok. So those quantum fluctuations are just ….pair productions? Or interactions with the interstellar medium??

[u/triatticus → u/Little_Vehicle_6671]

No it's because observers in accelerated frames do not agree on the particle content of the vacuum, and you would be in an accelerated frame to be stationary with respect to a black hole. This can be shown to be equivalent to being in a thermal bath of particles and as such the black hole radiates energy away losing mass (This is known as the Unruh effect, the current explanation for hawking radiation though not necessarily the only one). We have yet to actually observe this radiation though so we cannot verify anything yet.

[u/Little_Vehicle_6671 → u/triatticus]

Thanks for something to look into for a while. I might have more specific questions :D tomorrow anyway.

[u/joeyneilsen → u/Little_Vehicle_6671]

But we use rates of entropy to confirm passage of time, relatively.

This isn't really a thing. Entropy tends to increase as time passes. But there is no usable relationship between a time interval and a change in entropy, nothing that would tell you in general how much some measure of entropy should increase just due to the passage of time alone.

Hawking radiation is derived from black hole thermodynamics, and finding the black hole temperature is what makes it possible to calculate the entropy of the black hole in the first place. These things are all self-consistent. There's no expectation for Hawking radiation that doesn't match everything else we understand about black holes.

To the extent that Hawking radiation is thermal radiation, a detection of it would allow you to determine the temperature and then the mass of the black hole, and if you knew the mass via some other channel, you could test whether the prediction was accurate. But this scenario is extremely unlikely.

[u/Little_Vehicle_6671 → u/joeyneilsen]

Ok. Im liking all of this.

“No useable relationship between a time interval and a change in entropy”

But we know time dilation exists.

So if we know what a half life is for a given polonium 210 nuclei….

And we observe them.

But say someone managed to SLOW DOWN relative to earth that our reference frames changed …

Or where Earth Accumulates more relative time and the source accumulates less relative time

OR VICE VERSA.

Either should be possible.

In which case the observed decay emissions , could be DETECTED as slower, or faster than normal (Not saying C changes, but events become compressed or decompressed) over TIME.

(Except muons dont travel at C)

But this does get at my issue where Im looking at “shouldnt we see evidence of amounts of stuff or ..populations of stuff?”

[u/joeyneilsen → u/Little_Vehicle_6671]

There's a similar experiment in special relativity called the muon experiment. Basically: muons decay so quickly that most of them produced in the upper atmosphere shouldn't reach the ground. But a lot more do reach the ground than you'd expect if you ignore relativity. But when you account for time dilation or length contraction, the results match the predictions precisely. http://hyperphysics.phy-astr.gsu.edu/hbase/Relativ/muon.html

You could do the same experiment in general relativity. Time dilation is the same as time dilation, though, so the result would just be that if you had radioactive sources lower and higher in a gravitational field, you'd detect relatively more decay products from the one higher in the gravitational field.

[u/Little_Vehicle_6671 → u/joeyneilsen]

Ok …..ok…because wed see interactions along the whole path AT C….and those events would be generated along the entire vector at C … from the source.

Yeah I think Im just trying to hard to invent scenarios that are obvious if I had some actual years in schooling.

[u/lizardman49 → u/Little_Vehicle_6671]

The second law of thermodynamics is time independent. Entropy has nothing to do with relativistic doppler effects.

[u/Little_Vehicle_6671 → u/lizardman49]

Im hitting a block here.

Entropy is a meaningful model to say “This state should be more disordered than this state”

The rates of respective “Ordered to disordered states” is NOT only entropy

But it is HOW we measure time. Fundamentally.

And for radiation to exist, things have to emit radiation, and drop into more uniformly disorganized states.

This is HOW we monitor time because radioactive decay etc all comes down to this.

So for RADIATION to be coming from a black hole at 1 trillionth of a kelvin.

That Suggests WOW very low emissivity.

From what SHOULD be an incredible radiation source (its just shielded behind an event horizon)

My question is if we assumed the black hole was NOT time dilated, we would expect “X energy” as the singularity undergoes rapid entropy.

It CLEARLY DOES NOT.

So if we look at how “Infinitely slow” the event horizon seems to be …. Compared to what the energy release SHOULD be if we shared the same time and space …

Does the hawking radiation MATCH that in a way we could confirm “Ah yes , this looks exactly like a 100 billion solar mass object , radiating on a scale of time X 0.000000000000000000000000000000000000001

Or something.

Im asking if this is yet ANOTHER way we cn confirm time
Filation

T

[u/MarsMaterial → u/Little_Vehicle_6671]

To answer your question: the concept of time dilation becomes meaningless inside a black hole. Time doesn’t merely travel at a different speed, it travels in a different direction. Space becomes timelike, time becomes spacelike, they switch roles.

[u/nicuramar → u/MarsMaterial]

This is not true locally, for an observer falling inside the black hole. This role switch is a coordinate artifact. 

[u/MarsMaterial → u/nicuramar]

OP is explicitly talking about things from the perspective of an external observer, so I stand by the point. Different reference frames tell a different yet consistent story, such is how GR works.

[u/Little_Vehicle_6671 → u/MarsMaterial]

Ok but are you interested or not interested in directly addressing my question about the radiative flux of a black hole, and how it MESHES with the expected time dilation.

Or are we just accepting answers…

We have a real mechanism here. Radiative emissivity.

And PROPOSED interactions inside the event horizon.

Something is getting out.

Does it make sense?

[u/MarsMaterial → u/Little_Vehicle_6671]

That’s just not how it works. Temperatures are not directly associated with the speed of time like that, you can’t calculate one from the other.

[u/BananaBird1 → u/Little_Vehicle_6671]

The second law does not imply the rate of entropy change is constant, so its rate does not establish the passage of time.

Entropy only relates to time in that the relative entropy difference between states of a stochastic process implies a relative ordering in time, under conditions where the second law of thermodynamics holds (an isolated system with sufficiently many degrees of freedom, observed for relatively short periods of time).

Hawking radiation is entirely due to the curvature of space outside the black hole. In fact, as far as an outside observer is concerned, all knowable properties of a black hole exist at the exterior boundary (mass, charge, spin, and the entropy of these three properties). Anything specific to the interior spacetime of a black hole is entirely unobservable outside it.

Hawking radiation does match a black body spectrum, and we can use this to define a “temperature” of a black hole. But this temperature is not a true thermodynamic temperature caused by interior particle motion. It is just an effective temperature to define the black body spectrum. It is caused by a relaxation in exterior spacetime curvature.

[u/MxM111]

Entropy is not a method for determining time. Entropy is a method for determining direction of time. Big difference.

[u/Little_Vehicle_6671 → u/MxM111]

Ok. Now that this has been established can we get to the MEAT of the question ???

Wow Im sounding mean :(

I just feel too misunderstood sometimes.

[u/MxM111 → u/Little_Vehicle_6671]

The answer is no, there is no reason to think so. Hawking radiation is due to event horizon and it just can’t give information what is going on inside the horizon, and your analogy does not work either because the premise was wrong to begin with.

[u/Little_Vehicle_6671 → u/MxM111]

Ok. I do not understand why.

Now, my thinking was ….if emissivity is “Our observation” of thermodynamic events happening under time dilation ….

It WOULD make sense that the radiation (not accounting for accretion at all) was us SEEING delayed thermodynamics ….

But I still dont understand why that was the case.

Or why your statement is true.

But Im going to roll with you guys and take the punches.

[u/Uncynical_Diogenes → u/Little_Vehicle_6671]

Your thinking is not good.

You are awash in false premises, at the mercy of faulty understanding, and far too trusting of shaky ground.

You need to go back to the drawing board and read a lot before you draw anything new.

You keep calling nouns other nouns. Stop it. This isn’t poetry. Words mean things in physics.

[u/Little_Vehicle_6671 → u/Uncynical_Diogenes]

Annnd are the upvotes you got going to EXPLAIN anything?

I

[u/Uncynical_Diogenes → u/Little_Vehicle_6671]

No they’re just illustrating that you aren’t currently exhibiting a very pleasant or useful attitude.

[u/Little_Vehicle_6671 → u/MxM111]

Yeah but until we confirm entropy can run backwards. Then its pointless to add that distinction right ? Andnit doesnt get us closer to the question I asked.

[u/MxM111 → u/Little_Vehicle_6671]

Entropy cannot run backward, it sets direction of time.

[u/Little_Vehicle_6671 → u/MxM111]

I never said it could. I said Until we confirm that it CAN.

Which one of us said it could ?

Either statement is TOO assuming hence why I made neither.

[u/MxM111 → u/Little_Vehicle_6671]

We cannot confirm that it could run backwards. The sentence makes no sense.

[u/Optimal_Mixture_7327]

Time isn't some thing floating out there in space that runs.

Time is the length along a matter world-line.

A detector world-line at infinity should measure an increase in temperature from a black hole.

[u/Little_Vehicle_6671 → u/Optimal_Mixture_7327]

Ok. Im going to slow down and think. I cannot describe what I mean when I model stuff in my head.

My weak vocab is actually a problem that makes me become a dick. I like your model though.

Yes .. we agree that a detector at infinity is clearly going to “Pick up something” because it exists and …on infinite scales failures always occur.

Or in this case. Successes always occur…

Im trying to force a specific relationship :/ due to my own limited understanding. Because its just my way of thinking around the problem.

Im thinking …. “hawking radiation is just our way of seeing thermodynamics happen AT A REDUCED rate from within the black hole” a rate so tiny, that It might …explain the tiny bits of radiation we see.

[u/Optimal_Mixture_7327 → u/Little_Vehicle_6671]

I think you’re alluding to something like the trans-Planckian problem where the stress-energy at the horizon diverges.

But yes, the distant light is redshifted relative to where it’s emitted which is outside the horizon.

[u/Little_Vehicle_6671 → u/Optimal_Mixture_7327]

Ok ! This sounds new. Btw Optimal Mixture is such a ridiculously cool name.

Do you enjoy combustion engines? Or do you have more interest in fundamental chemistry.

[u/Optimal_Mixture_7327 → u/Little_Vehicle_6671]

The name was assigned to me by Reddit. Sadly I know very little about chemistry and my graduate studies were in gravitational physics, and thanks!

[u/Little_Vehicle_6671 → u/Optimal_Mixture_7327]

Its so cool lol. Maybe its your optimal mixture though. I drive tiny vehicles soo its also a weird convergence 😁

[u/MergingConcepts]

Its the other way around. We created time as a metric to compare rates of increasing entropy in different systems. The winding down of a watch spring is calibrated to the turning of the Earth in rotation. We then use the watch to plan for and anticipate entropy changes in other things, such as the time to cook dinner.

[u/Little_Vehicle_6671 → u/MergingConcepts]

This is …Philosophically amazing. I wish I could get better at math and physics because honestly this still pisses me off because I see no way to solve it.

It also implies that “Should entropy reverse” then time reverses soo

To me Neither can exist without the other.

And reverse entropy and reverse time means no intelligent structures or data can persist ….

One CANNOT think about the PAST they are moving into , if they are CONSTANTLY moving into the past.

Because that means forming data structures is IMPOSSIBLE …

[u/MergingConcepts → u/Little_Vehicle_6671]

Relax. The direction of entropy cannot reverse in our part of the universe. However, it must do so somewhere. Perhaps it does inside black holes.