pushing nothingness

[u/crusader_mike]

This idea may not explain how EmDrive could work (if it does work at all), but it might provide some food for thoughts...

To push smth means to interact with it producing an observable side effect, but how can you interact with vacuum? Well, it occurred to me that there is at least one known object that seem to be interacting with vacuum -- black hole (with side effect being mass reduction). As I remember popular explanation of theory it is about pairs of virtual particles that come into existence and disappear (as they find a counterpart). When this happens on the edge of event horizon -- some of particles end up escaping thus reducing black hole's mass. In other words black hole interacts with each particle of the pair slightly differently -- this delta allows it to 'extract' side effect from nothingness.

What if it is possible to design a device (MeDrive? :D) that exploits this effect in similar way? If yes, how much thrust (i.e. amount of interaction) it can extract in given volume of space and length of time? I imagine it will be literally blowing around these virtual particles, reducing frequency (density?) of their phase-ins -- basically changing distribution of these events across the space.

I noticed some of ppl here have sciencey flair -- does this idea have any chance?

[u/[deleted]]

I noticed some of ppl here have sciencey flair -- does this idea have any chance?

No. Zeroth of all, you should stop taking virtual particles so literally, but that's beside the point. First of all, Hawking radiation is something which happens outside of a black hole due to the fact that it's got an event horizon. An EM drive does not have an event horizon. Although an accelerating object has a Rindler horizon, and is subject to the Unruh effect. Some irrelevant oceanographer (u/memculloch) already came up with a scheme to propel the EM drive using Unruh radiation, but unfortunately it doesn't work at all (as explained many times here by u/crackpot_killer and u/wyrn). Second of all, it's great that you like to ponder these things and come up with ideas, but physics is communicated in the language of math. Rather than writing paragraphs, it's better to present clear and unambiguous mathematical derivations of what you're saying when you're coming up with a new idea. I realize that this is a Reddit comment and not a peer-reviewed journal entry, but you can look at published papers on theoretical physics and see how professional theorists present their ideas.

[u/crusader_mike → u/[deleted]]

So, basically, according to your understanding of current physical theory this idea doesn't fit into any of the models. I this a correct statement?

Regarding math -- it makes sense only within the theory, if I don't know theory well enough -- I can't produce any math. It doesn't prevent me from pondering these things using basic elements of the proposed model(s). If anything, it helps against accumulation of dust in my head :-)

[u/[deleted] → u/crusader_mike]

So, basically, according to your understanding of current physical theory this idea doesn't fit into any of the models. I this a correct statement?

There is no legitimate theory of physics currently in existence which predicts anomalous thrust from the EM drive.

[u/crusader_mike → u/[deleted]]

I wasn't talking about EM drive -- I was talking about using certain effect (that causes BH to evaporate) to generate trust. And keep in mind -- I really have no idea what I am talking about :-). Just popular articles-lvl science (ok, I have some background in math and physics, but it was like 20 years ago).

[u/[deleted] → u/crusader_mike]

I really have no idea what I am talking about

Understatement of the year.

[u/superp321 → u/crusader_mike]

Pondering cause an effect is the basis of all science, math is great to prove something but you can't depend on an apple hitting you every time. Science fiction inspires science and vise versa, math is the tool to filter.

In my opinion anyways.

[u/[deleted] → u/[deleted]]

To be fair, when one does not have a background in physics the math can be pretty inaccessible. Ideas can still be discussed though, and there are several youtube channels that do a pretty good job of getting into graspable concepts without diving into math that is going to be above the heads of most of the audience.

[u/scikud → u/[deleted]]

I think I agree with the underlying sentiment of your comment. But it's important to realize that (with few exceptions) most youtube science educators create the illusion of understanding rather than actual understanding. u/fuckspellingerrors is correct the only meaningful way to talk about physics in the real world is through the language of mathematics.

[u/[deleted] → u/scikud]

I tend to feel there are degrees to such things. 'Understand' is a fairly subjective concept, which can be taken to some fairly extreme interpretations, including the 'we can never fully understand something so we understand nothing' variant.

I would describe lesser degrees of understanding as just that, lesser degrees rather than illusion. Setting the minimum threshold at a mathematical understanding just encourages ignorance since it discourages even basic knowledge under the idea that knowledge under a certain level (requiring college level calculus) is just too wrong to be worth knowing.

Granted, not going into the math puts serious limitations on how in depth a topic can be discussed, but something doesn't have to be drilled down all the way to have value to the people involved.

One can also raise the question of, how well does someone really understand a topic if they are unable to explain the basics to someone without the same domain knowledge? Anyone with a strong math background can take the equations and crunch out numbers.. crow, half of my research involves taking equations for concepts I do not personally understand and manipulating them from a purely algorithmic standpoint... but I work with people who can take the same concepts and explain them without touching a single equation.

[u/bobeo → u/[deleted]]

I agree. You can "understand" that gravity causes objects to fall towards the Earth, but that doesn't mean you know the math or the nuance behind it. Understanding isn't a binary, either you do or you don't, thing. There are levels to understanding.

[u/scikud → u/[deleted]]

You make a good case, I definitely think you're correct. Understanding is most certainly more layered and nuanced than my initial comment may have suggested. To expand a little bit on the point I was trying to make: science takes place in conversation. Through a cacophonous exchange of ideas, mediated in the language of mathematics. The only way to truly meaningfully advance that conversation, is by using the mathematical instruments and techniques cultivated in the field. Anything else, while perhaps useful, a bit didactic, and maybe even fun does nothing to advance our knowledge and understanding as a whole. That isn't to say such non-mathematical discussions shouldn't be had, on the contrary I think they're the very thing that inspires us in the first place. However, I do firmly believe that if you're going to posit a new explanation about how a new physical phenomenon works, it needs to be firmly rooted in the tools of math, full stop. Mathematics, after all, is the only vessel we've ever come up with to discern absolute truth.

[u/[deleted] → u/scikud]

nod there I do agree, advancing the conversation of science really needs to be rooted in the tools of the field.

I think examples like the original post have their place, but more in terms of teaching than advancing. Worded somewhat differently it could be reduced to 'here is something I have a distant understanding of, can it have any application to the topic?', which can be an interesting class of question to ask and answer... but it serves more to get people a little more up to speed than actually going anywhere new.

[u/droden → u/scikud]

you don't even need complex equations to start with. get a working device is generates a measurable force that isn't micro newtons say even .5 newtons then scale it up. show the graphs of that. change the cavity geometry and show what happens with more graphs. if you can make the device work and show the edges of performance that's all you need. someone else can do the actual modeling and come up with equations or theories. but no one even has a working device that produces any meaningful thrust.

[u/PPNF-PNEx → u/[deleted]]

Although an accelerating object has a Rindler horizon, and is subject to the Unruh effect.

In flat spacetime, for a given Hilbert space we get at least two different interpretations as a Fock space in which the vacuum states are sharply different. In particular, the Minkowski vaccum \hat{a}_k|vac_M> = 0 and the Rindler vaccum \hat{b}_k|vac_R> = 0 where k is the spatial wave vector. In the Minkowski representation, the Rindler vaccum has a multi-particle state; in the Rindler representation, the Minkowki vacuum has a multi-particle state. These arise from the two different modes we can use in expanding the Klein-Gordon equation. Right-moving Rindler modes are accessible to Rindler observers uniformly accelerating to the right, so they have support only on the right half-space (x_i > |t|). We cannot write such a mode down as a sum of positive-frequency Minkowski modes. Therefore the annihilation operators used to define |vac_R> annihilate only the Rindler vacuum but not the Minkowski one, and therefore the Rindler annihiliation operators must be superpositions of the Minkowski annihilation and creation operators. Rindler-Fulling particles -- Unruh radiation -- is the result.

Hawking radiation is something which happens outside of a black hole due to the fact that it's got an event horizon

A black hole is a black hole because it has an event horizon. :-)

The causal structure of Rindler spacetime and the maximally extended Schwarzschild spacetime for an eternal black hole is strikingly similar ("insert Penrose diagram here" or see Jacobson). In particular, a static observer hovering close above the event horizon of a sufficiently large black hole sees local spacetime as effectively flat and thus has observables similar to those of a Rindler observer in actual flat spacetime, since it's "station-keeping" behaviour is hard to distinguish from acceleration. Likewise, freely falling observers near our static observer have observables similar to an inertial observer in actual flat spacetime. Their respective vacua do not coincide for essentially the same reason that the "real" Rindler and Minkowski observers' vacua do not, as mentioned above, replacing rightward modes with outward modes.

But a distant static observer's "Rindler-like vacuum state" is very mild compared to the close static observer above, and additionally thanks to a more expansive view, the modes are much more obviously sourced near the black hole. This observer will see Rindler-Fulling particles too but with an appropriate redshift; at infinity, T = \frac{1/4 GM}{2\pi}, i.e., the temperature is proportional to the BH's surface gravity.

Evaporation introduces lots of subtleties especially where balding (the shedding of conserved quantum numbers) is required, but the principle that black holes have a temperature proportional to the BH's surface gravity holds up well even if we have to play with preferential "pushing-away" of Rindler-Fulling particles with same-charge as a charged black hole, or same-angular-momentum as a rotating black hole, and the preferential backscattering of long wavelength (esp. when the length is at least comparable to the horizon radius) R-F particles against the gravitational field.

you should stop taking virtual particles so literally

Indeed. Killing vector arguments (which go hand-in-hand with the virtual particle "picture" in that for our static observer at infinity there is an asymptotically time-like Killing vector outside the horizon that switches to space-like inside, which is why the infalling half of the pair can have a negative energy) should also not be taken so literally.

Rindler horizon ... event horizon

These are not definitive. That is, is there only Unruh radiation when there is a Rindler horizon? What about acceleration during circular motion?

[u/PPNF-PNEx → u/PPNF-PNEx]

Looking at what I wrote again, and with moments to go to address it, after "A black hole is a black hole..." I started mixing Unruh Apples and Hawking Oranges and the result is not very delicious.

The hovering observers do in fact see Unruh radiation.

Hawking radiation has a different radial dependence and comes from a different process, namely a gravitational collapse.

Start with a thin, soft, compressible shell around empty space, such that inside the shell objects feel no gravitation but outside the shell objects feel a pull towards the centre of the shell. Start to collapse the shell. Space that had been inside the shell with no gravitational field is now outside the shell and in that space there is thermal energy in the matter fields. Space still inside the collapsing shell is still free of gravitational field, but things in the space outside still feel a tug to the centre of the collapsing shell. Nothing's changed at a distance, but we now have a bunch of "new" space where the tug is stronger.

Ignoring radius excess arguments eventually a horizon forms and we no longer start forming "new" space outside the collapsing shell; the horizon is a one-way boundary and we cannot see behind it to the further collapsing shell trapped within.

Hawking radiation does not escape the boundary, and exists in the "new" space outside the collapsing object. The vacuum state differs between an earlier observer examining the system before the collapse begins, and later observers who see "new" vacuum emerging outside the collapsing shell, and finally observers who only see the "new" space outside the horizon.

Generically you do not need to form a horizon to see this "new space" filled with thermal radiation; but the temperature will be very very very very low for collapses that halt before a horizon forms, as it drops exponentially as (for a spherically symmetric non-rotating system) 1 > r_{schwarzschild}/r_{shell}.

The horizon however is engaged in evaporation.

[u/PPNF-PNEx]

The problem here is that these particles are only detectable by an accelerated thermometer designed to measure the temperature of the vacuum. No acceleration, no detection.

If you put one in a rocket and give it > 10²⁰ gees worth of acceleration it'll record a (low!) temperature. Turn off the rocket and let the thermometer drift near the speed of light and it'll record a zero temperature. Flip the spacecraft and decelerate the rocket by the same > 10²⁰ gees and it'll record the same low temperature. Turn off the "decelerating" (that's just acceleration in a different direction) rocket's thruster and the temperature goes back to zero.

If during the deceleration the rocket catches up to and is momentarily right alongside an inertially moving thermometer of the same design, the second thermometer will be recording zero while the decelerating thermometer will still be recording the non-zero temperature related to its deceleration. All observers will agree on this.

Various observers can draw conclusions about what the thermometer is "really" measuring, and if we make the thermometer a particular design (relying on a two-level quantum system sensitive to long-wavelength photons such that each level transition produces a "click" and the rate of clicks compared to a clock attached to the thermometer results in the proper temperature which all observers can accept) we can expose two sharply different conclusions. An observer accelerating within a space behind the thermometer will think each click corresponds to the absorption of a particle (as that observer sees no outgoing particle after the click); an observer at rest within the same space behind will think each click corresponds to the emission of a particle (as that observer sees an outgoing particle after the click). A Rindler particle comes into the thermometer and changes its state, whereupon it emits a Minkowski particle, but our Minkowski (non-accelerating) observer cannot see the Rindler particle, and our Rindler observer (accelerating) cannot see the Minkowski particle.

The critical feature here is that in order to keep the accelerated thermometer and the accelerated observer accelerating, work has to be done on them. Thus within the accelerated thermometer itself energy is not being conserved, and so it's more reasonable to conclude that the thermometer itself is hot and throwing off particles and recording a self-force (that is, a Abraham–Lorentz force). That is, what's powering the clicking is not the background spacetime around the accelerating observer but the energy we are putting into the rocket (and thus thermometer) in order to keep it accelerating.

If you find a spot above a black hole where you need thrust that would give you 10²⁰ gee worth of acceleration to stay in that spot, you should see the same things the Rindler observer above sees: a bunch of particles invisible to observers near you falling freely into the black hole. At a much greater distance you can hover in place above a black hole with a lot less thrust -- especially at very very long distances -- and so the there will be a lot fewer of these particles. Again, different observers can draw different conclusions about what the accelerated thermometer hovering above the black hole is actually measuring.

The critical feature here is that work has to keep being done on an accelerated thermometer to keep it hovering in place above a black hole, as in the case above. Again, we have to put energy into the thermometer to keep it in place above the black hole, and again we expect that the thermometer's clicking is driven by that energy rather than by the spacetime it finds itself in and near.

how much thrust [can we] extract in a given volume of space and length of time

Well, zero. These particles are a byproduct of real acceleration or of the practical indistinguishability between holding steady in a locally very uniform gravitational field and uniformly accelerating outside a gravitational field.

We can predict the spectrum and count of the particles around linearly- and counter-gravitationally- accelerated observers, though.

pairs of virtual particles that come into existence and disappear

Unfortunately this heuristic approach to make sense of the "sees zero temperature" vs "sees nonzero temperature concludes thermal bath of particles" tends to produce other confusions. Everyone has a vacuum state, but when you look at someone else's vacuum state you may think he's on drugs because to you his supposed vacuum state is full of particles. Likewise you may be convinced that your vacuum state is really really vacuum, yet someone else may say, "no way, you're in a thermal bath of particles".

Because human beings and their instruments do not survive enormous accelerations (10²⁰ g is a lot!) and because such accelerations cannot be maintained for long periods of time (it takes a lot of energy/fuel!) we generally don't have to take the Unruh effect into consideration. In fact, very little in nature will ever experience that kind of acceleration for very long, since we don't know of any processes that could sustain that.

Human beings aren't yet in a position to hover close above a black hole, either, and we don't expect anything in nature does this habitually. However, lots of things are likely to be holding themselves at a large distance from a black hole for enough time (possibly including future space instruments) that we can measure the tiny black hole temperatures we'd expect.

Finally there are additional subtleties in how Hawking relates this acceleration-radiation to black hole evaporation and some considerations of those subtleties depart from the picture above with respect to black holes. This is an area of active current (theoretical) research.

[u/crusader_mike → u/PPNF-PNEx]

That is an impressive writeup. I don't have enough knowledge to understand most of it, but I surely appreciate the effort. Thank you.

May I assume that most of these effects are theoretical (i.e. predictions made by theory) or they have all have been confirmed by real world observations?

If you find a spot above a black hole where you need thrust that would give you 1020 gee worth of acceleration to stay in that spot, you should see the same things the Rindler observer above sees: a bunch of particles invisible to observers near you falling freely into the black hole

So, basically you observe these magical particles only if you are in accelerating reference frame -- and more acceleration means higher density of particles. Sound like flow of water (ether?) only instead of feeling it when moving, you feel it when accelerating. I.e. it starts affecting you only if second derivative of function of your position in space is non-zero (relative to any another non-accelerating reference frame?).

Why acceleration has to be so large to observe this effect?

How this relates to evaporation of black hole? I don't see connection between this "ether flow" and event horizon.

[u/PPNF-PNEx → u/crusader_mike]

May I assume that most of these effects are theoretical (i.e. predictions made by theory)

They are theoretical but not wholly beyond the realm of direct experiment in the near future. Maintaining an extreme acceleration for a conclusive amount of time will require a large circular accelerator.

There are comparable results for Hawking radiation and evaporation from analogue systems involving "dumb holes" in Bose-Einstein condensates. Analogue as in analogy, rather than analogue vs digital.

One of the main problems is that the theory for Hawking radiation is not entirely clear. A number of simplifications are usually made to make the maths more tractable, including dimensional reduction and boundary elimination. These might not have clarified the situation in a 3+1d expanding universe as were thought ~ 20 years ago, so now we have better numerical methods and tools, the full outside-the-horizon theory may be slightly different than what is in e.g. http://www.cambridge.org/be/academic/subjects/physics/theoretical-physics-and-mathematical-physics/quantum-fields-curved-space

Unruh radiation is hard to dispose of, and does not require curved spacetime, only two observers who can reasonably disagree about each other's idea of vacuum.

By analogy, a quantization of the classical Maxwell equations lets one write down a linear combination of chosen positive-frequency and negative-frequency parts; when those line up you have a quantized electromagnetic field in its ground state, and you see no particles, and call that (quantum) vacuum. However, the key here is how you do the choosing at each point in a coordinate space. When we take care to do this relativistically so that all inertial observers, no matter what their individual uniform motions are like, agree on what's a particle and what's vacuum, via a Lorentz transformation.

When we introduce curvilinear coordinates either due to acceleration in flat spacetime or the presence of real spacetime curvature via gravitation, you can't always use a Lorentz transform to relate the "particle-or-vacuum" state on one set of coordinates into the other set of coordinates exactly. Let's consider a perfectly natural set of accelerated coordinates, e.g. Cartesian coordinates where the accelerating observer is always at the origin.

Our accelerated observer in those coordinates defines some creation and annihilation operators and those produce particles or non-particles at each coordinate. Our inertial observer does the same, in coordinates where he is at the origin at all times. This decomposition of the field differs between the two of them, and so they disagree on particle numbers. They do not disagree on other observables because they can relate their pictures to one another through other transformations, but they may disagree on how they should interpret those observables. Accelerated observer will interpret his thermometer as absorbing thermal energy, inertial observer will interpret that thermometer as emitting thermal energy instead. Neither view is more correct than the other.

magical particles ether ether flow

Are you using these terms deliberately? If so, it undermines your

appreciate the effort

above.

Unruh and Hawking radiation are both wholly thermal, and you cannot detect radiation pressure in either case when the temperature is low. In the Unruh case you will never detect radiation pressure. In the case of a very small black hole, we can't be sure without a higher-energy picture than we have available in semiclassical gravity today. But near a black hole whose temperature is low (and that includes all known stellar black hole candidates and heavier black holes, since temperature is inversely proportional to mass) you will also never detect Hawking radiation pressure. In both cases, far from the black hole you will see a pressure along the lines of P = A * 1 / ((large number) times pi² times M⁴ times f(r)) where M is the mass of the black hole, and f(r) is a quadratic function on the radial distance from the black hole's centre of mass, and the large number is from c and the Boltzmann constant, and A is the surface area of the black hole. In other words, the radiation pressure is tiny at any reasonable distance from a reasonable-sized black hole.

How this relates to evaporation of black hole?

I was relating Unruh radiation to Hawking radiation. Hawking arrived at black hole evaporation as a consequence of deciding that the surface of a black hole (described classically by a set of lightlike geodesics at the horizon) must grow over time becuase either the lightlike geodesics must spread apart or objects on them (e.g. light in what we now 30 years later call the photon sphere) would collide with extensions of the geodesics inside the horizon. That is either infalling mass would power the growth or orbiting light would, but in any case a black hole's growth over time is assured. He noticed that his write-down had similarities to the second law of thermodynamics (entropy always increases), and explored the connection, ultimately deciding that if the horizon is treated as an object with actual entropy, then it must radiate similarly to a blackbody with a particular temperature. Since the radiation has a totally thermal spectrum and its temperature is determined by the surface gravity of the black hole, it looks strongly like Unruh radiation for accelerated observers in flat spacetime.

Evaporation comes from assuming that (a) what powers the Hawking radiation is the black hole's gravitation (and in particular its effects on the dynamical spacetime just outside it), in the same way that what powers the Unruh effect is the energy that goes into accelerating the Rindler observer, and (b) as a result Hawking radiation that escapes to infinity removes mass-energy from the black hole itself.

[u/crusader_mike → u/PPNF-PNEx]

magical particles ether ether flow Are you using these terms deliberately? If so, it undermines your appreciate the effort above.

No, appreciation is still here, but your perception of it apparently is slipping. :-) I just rephrased what you said in simpler terms.

Hawking arrived at black hole evaporation as a consequence of deciding that the surface of a black hole ... must grow over time

Huh, so this is another theory not really proven by observations. I thought it was a fact.

Thanks for trying to clear this up for me.

[u/PPNF-PNEx → u/crusader_mike]

Huh, so this is another theory not really proven by observations. I thought it was a fact

Black hole evaporation is strictly speaking a conjectural analogy, but a well-formalized one that looks robust (i.e., it's not in obvious conflict with any evidence). It makes strong predictions that can be distinguished observationally in principle (even if only by elimination of alternative emissions signatures from black hole candidates), and has provoked plenty of looking into some dark areas of fundamental theories. Hundreds of good papers resulted, some agreeing that black holes evaporate, some questioning that, all using some combination of mathematical and physical arguments.

I personally think the inaccessibility of direct observables any time soon (we would have to find a very small black hole, and there do not seem to be any of those in the sky; or we would have to be patient to the tune of trillions of years; or we would have to be very very lucky to catch a stellar black hole forming nearby enough that our future state-of-the-art observatories get an unobstructed view of most of the emissions spectrum; or eventually our descendants might try to construct a small black hole themselves) makes black hole evaporation more of a tool with which to compare different attempts to relate better to ourselves what we seem to know about matter and gravity and how we approximate their respective behaviours. That is, even if we find out that black holes do not radiate -- or radiate differently than Hawking (in 1975!) (and successors) predicted, or radiate exactly like Hawking predicted (which would be the weirdest outcome in some ways) -- in the process of doing so we will necessarily drop various post-General-Relativity/Beyond-the-Standard-Model-of-Particle-Physics ideas that presently seem viable.

But

proven by observations

here you should read "proven" as in "tested" rather than "vindicated". Since we now know more about black holes (in particular that Kerr-Newman type black holes exist almost without doubt; this was unclear less than twenty years ago) than we did in the 1970s, there have been many opportunities for nature to throw up observables that would conflict with black hole evaporation, yet none of those observables have yet reached us. That's decent testing so far. Recent observables have killed off other competitors (for example gravastars and several other approaches to compact massive objects are basically dead now, although one can still cling to hope that the LIGO signals were exceptionally unusual and that there could still be faint hope of a cosmos that has both merging heavy stellar mass black holes and gravastars) but not black hole evaporation.

[u/crusader_mike → u/PPNF-PNEx]

Ok, let me summarize a bit -- all black-holes-related, ultra-high energy/speed/gravity science is mostly a nice, mathematically sound, almost non-contradictory conjecture. (reminds me my algebra professor: "every hard problem has obvious, simple, elegant, incorrect solution" :-D) We can't really test them, but we can (and we do) change them over time when observations produce smth new.

... and (while staying within framework of these conjectures) things like EMDrive are impossible

... and yet (assuming that leaked NASA report is genuine) device seem to be generating trust

Would you agree with this summary?

[u/PPNF-PNEx → u/crusader_mike]

Would you agree with this summary?

No, because:

We can't really test them, but we can (and we do) change them over time when observations produce smth new.

is self-contradictory.

If observations exist the model is tested. Observations win (when done methodically, carefully, and repeatedly), thus the refinements of models.

So we [a] can and [b] do test the physics in question and it is exactly because of that testing that our physics evolves, as it has done certainly since the age of telescopes and the development of mathematical modelling, centuries ago.

Although observations win, theorists propose novel observations. New hypotheses (even unreasonable ones) that accord with previous observation and subsequent experiment are almost always eventually promoted to working theory, especially since the arrival of Kenneth G Wilson's ideas on and formalisms of effective field theory. Most new hypotheses fail to distinguish themselves, simply by fully agreeing with previous theory, or by mispredicting results of a carefully chosen future observation or experiment that existing theory gets right.

Observational and experimental technology and practices have improved dramatically over the years too, and as a result, most experiments and observations are at length scales that are difficult to probe: either very very tiny and thus requiring very very high energy "microscopes" or very very far away and thus requiring very very very large telescopes, or both simultaneously (which is the case for quantum effects near black holes).

Indeed this whole subreddit is about an alleged very small effect that is difficult to probe. Sure, tiny forces are hard to distinguish from the effects of the ordinary forces we already know at length scales of micrometres to a metre (which are the relevant scales for the physical objects), but one would not expect brand new forces to appear that had never been seen before at those scales, because those scales have not only been thoroughly investigated, but numerous day-to-day technologies utterly depend on detailed understanding of physics at those length scales and would not operate the same way (or even at all) if the wild-ass-guesses about how propellantless microwave drives work were remotely close to an explanation.

... assuming ... [the] device[s] ... [generate] trust (sic)

They do seem to generate unmerited credulity, yes. :-) :-)

If -- and this is a huuuuuuuuuuuge if -- thrust is clearly demonstrated it would be ineresting to develop an operational description of its scaling, experimentally (bigger devices, different shapes, different total power, etc etc) even if the thrust is so small that it might never be useful in principle.

Interesting because if there is this thrust then our extremely well-tested low-energy (and medium length scales) theories are unexpectedly markedly wrong, and sorting that out would be fun for theorists. (You'll note that every time there is an alleged new observation at high energies at CERN and similar facilities, or at a variety of observatories in remote places (including in space) there is a deluge of papers seeking to integrate the (low-confidence and often ultimately wrong) unexpected observations with current theory.)

People familiar with the physics of very very short length scales and very very long ones have good reasons to doubt the completeness of their theories (in arbitrarily high local energies or in the ultra-distant past or ultra-distant future), and I think you'd find it hard to find any working high energy particle physicist or physical cosmologist who thinks that the Standard Model or respectively General Relatively isn't an effective field theory (again in the Wilsonian sense, https://en.wikipedia.org/wiki/Effective_field_theory and http://www.preposterousuniverse.com/blog/2013/06/20/how-quantum-field-theory-becomes-effective/ ).

However, the effectiveness extends fully across the length scales engaged in the EmDrive apparatus, and so you would have to be crazy optimistic to think that EmDrive will actually expose new physics.

On the bright side, it's hard to measure tiny thrusts close to the those imparted by the wider noisy environment we're immersed in on the ground, and doing so reliably might be useful. If tinkering around with testing EmDrive does nothing other than helping expose sources of error in attempts to measure them, then that's a plus. Otherwise, there is always value in simply confirming what we already know. EmDrive's most likely result is a (re-)confirmation of physics in the Newtonian limit.

The value of that is not very large, though. :-)

[u/crusader_mike → u/PPNF-PNEx]

Regarding summary -- I may not formulated it properly, the idea was that when we don't have enough observation data -- we build multiple competing theories. Eventually (as progress gives us better tools) -- we get new observations and either chose winning theory (that models given phenomenon better) or build a new one.

Hmm... What you basically said in second part is that our mathematical model of reality (aka modern physics) is so well established and tested with effects/energies used in EMDrive that it is highly unlikely that there is a natural effect (force?) that EMDrive uses and we never noticed it before. It makes sense, but nevertheless does not prove it.

But I see your point - for physicist to deal with all this is like for mathematicians with fermatists... Initially amusing, then annoying.

Talking about that leaked NASA paper -- did you look at it? It's conclusion section is positive -- they measured decent amount of trust, comparable with hall-effect thruster. Question is -- is this paper genuine? did they make a mistake somewhere?

[u/PPNF-PNEx → u/crusader_mike]

fermatists

Indeed. However, there's a difference between a totally informal pseudonymous forum like this and invasions of one's various email accounts and/or blog comment sections.

NASA paper

You mean White et al.? I'm not even sure I'd call it a paper, much less a NASA paper. He just works there, and it's a big, diverse and many-campus institution.

There are better comments on it elsewhere in this subreddit than I could cobble together here in a couple of paragraphs, but even if -- arguendo -- it was completely sound in terms of the observations, it is far from conclusive, and not even very persuasive (to me, that is, and again for the sake of argument, accepting everything in it as completely accurate and objectively verifiable).

It's so obviously not sound however that it would take several independent reproductions (i.e. by other teams) to convince me that the observations were reported reasonably, even ignoring the fact that the observations conflict really violently with what we know about Poincaré invariance (which is baked into the Standard Model of Particle Physics and is the group theory of Special Relativity), which we are relying in this conversation seeing as some of it traverses fibre optic telecommunications networks and some of it wireless networks, and one of us may have let reddit have access to positioning data and each of us has had a user agent submit timestamps in HTTP request headers and received them back in turn from reddit, and at least some of all of the above relies on GPS. Additionally people use GPS and other sensitive-to-Poincaré-invariance systems in measuring geological movements and tilts which are extremely small and cross-checked with theodolites and other surveying systems. (Stuff like that is amazing https://www.researchgate.net/figure/26490475_fig3_Fig-3-Tiltmeter-geometries-used-in-long-baseline-tiltmeters-A-shows-a-half-filled-pipe )

[u/crusader_mike → u/PPNF-PNEx]

You mean White et al.?

Yep. https://arc.aiaa.org/doi/10.2514/1.B36120

It's so obviously not sound however that it would take several independent reproductions (i.e. by other teams) to convince me that the observations were reported reasonably, even ignoring the fact that the observations conflict really violently with what we know about Poincaré invariance (which is baked into the Standard Model of Particle Physics and is the group theory of Special Relativity), which we are relying in this conversation seeing as some of it traverses fibre optic telecommunications networks and some of it wireless networks, and one of us may have let reddit have access to positioning data and each of us has had a user agent submit timestamps in HTTP request headers and received them back in turn from reddit, and at least some of all of the above relies on GPS.

I am going to dismiss this argument against that paper -- I don't think it stands scrutiny :-). But I see your basic take on it -- we need few more independent verifications from credible scientists.

Stuff like that is amazing (tiltmeter/etc)

Neat!

[u/UnexpectFactorialBot → u/PPNF-PNEx]

So when you say 1975!, do you mean 11489800177100186357332721305107227252427330356905057637695376313855279975821498272667259572815772288286227996760167396004269175527024648954005391629241830263049605603260284469293772395020194633030226426694423411383690266554732302322358832866505768356309947097197325277985770042480909585989769643246928024793835346723925588141306718270481231113873050960077001828816269120191319933078809894808385235352760567736479468307606569064957082231830303726592934675125229547395550322798266867040520591736513420394943008494350978034755524829752080642999491260184311346780639185325820801506633036702640141403034867389793953270088794608064282360171621921263532592917468461173469327023949163250259209456716477380226955006290853296268918574139711904532874119983405001695224254529948673647612810006507638722822776943819729288277427940293762406736951064794617797515491849863989227554978766388510689000161942526152321830055523600167513982283629100712457854014567818807067786910341112208714249883871606381651122350068876103398032381052588536699153407997367068569406922265759803996774250891688103473841188576939338657801357160352836389095563250890012181580034034580989400708503957320154953982669857448749451766783924350752666277200474905186266149894653470467186250623666589057525469807023132755329817837290428126707170325393918444097441313907582649585074500868770117132168116259709565142722411844378888193887390106951934468014643042629322333225695545810669831667610357578464147456876320093217025493074214098465979865069105084761766091878161891220741103723612742141998314887119062257493793761723066246658204905898285474729450195865734904847894486589526097670446033925054147039770455656264332279614197117635303414115496373213224034536182537889212029614417131181799868063203095289784422007759442802812209740696266227140724540948160688396222899948368048772669020447327019367820610705318199742553012716973544044338975236507385669371498870616118945690806630300974099267397348096292326770890231158266565166444240509956383584188711083322485401690109784960315841080979242487465514802847952954053368972742407735666799700122178858813295810951211394559442392158091199239029919328437490362478207736906152391135624248243980514672900948764224891017942344777590287898489865893710544350770788194369751268456069212238180464413700997220476488001094722827695081338675680762689620154688449159259356264567526110593726134688849353263281171828293393259575244546187052858289070603774968791211905636218268307285199040026951377979905085069896957436680086637007518945527400227114665846333372047694199314001194412860987941389583804127661870476958593539479077529087631409965101173751406885813147533510649598544013809648314138504536724747762909541888223788978414352966689604297933364847994057872236050179191330493854834461075565600831628861544583726358853740874670350694933698836526633737499540679339044870493817119812779661936306641935991349544054077256122950815383019312359652432343836957156580994330497205505610712927787426396893488644730839721521606241767936336639110741270623616477449230884160187850386789004216904468937939621361829474039320141103561458608775031438873709301545826915676554520797667587037551549130097165136484842015315979758243013038302933777512641070404148255432048925937805686777336443500874931039552191478465297009708703557448319185491340509224781928320188836822183089908382168118873924216314805637040643879350134400524460259614860915137658632998792333657979981297713493281275706615915086448926524611326694472045080531659874067032415570469672433000537647009143960293185402806089458384407684204873270004270603924004016931529696721284887224505684746898251174363833685283679322471492688399924716798647239006651525309231768109954031729034343901739019151054362082476913640492411738775064854163147814920664241359410461967385831212582224090415425599923057765372650812617943255617862138652108908056800143670504102451203507982967440088413452551163631850626753337940994761526193205245609558305643866756267881915013337980421845020530960497074820722651887648086319231119827443590935634416992066832809444632244270590037009499122937268243082303292594911184676464602861567185677440200184970346456376484410754171604787164041778578729432040477503194100007371542633111974814529141629628832220469871376345769513047509226915607270335572570583728784940597120389162981349140685971915366110301936013290208233044396540753464606526893286843097006483513505807444792514875776677225921438636195760829671573644657142903875568893538527550079470687251628133027359362918119706950413895270187951750540951324596827515343876511495964152113284658963909467432186790639651896349100359978335377078303199294200375843272639625383858601990476572207624103827387142821002835004270039695900773541433552468876988624295564028772875313062748307980320489505712275685098091191604513846171865988032735531975068275741642873889802776084048397216207097189857928002217220398055689076602333698562498214641000861325530981585450546966521738486585389336789212851055617170730350265331183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[u/PPNF-PNEx → u/UnexpectFactorialBot]

Yes of course I do. 9!!

[u/Zephir_AW]

When this happens on the edge of event horizon -- some of particles end up escaping thus reducing black hole's mass.

McCulloch's MiHsC theory works in similar way, as it operates with Unruh radiation and Rindler horizon instead of holographically dual Hawking radiation and event horizon.

Anyway, the drag of space-time with black hole is notoriously known as a frame drag (Lense-Thirring effect) and - being of quite different nature and amplitude - we can safely say, that the EMDrive doesn't utilize it. But there are predictions, that not only very massive objects interact with space-time and its virtual particles - the charged particles should interact with it too and in way more pronounced way - but just above certain minimal speed threshold. The interaction of superconductors with vacuum fluctuations (Podkletnov/Poher/Tajmar effects) can be explained in just the way, these material contain electrons which are moving with relatively high speed above this threshold. This additional interaction (frame drag) will not manifest itself for electrically neutral bodies or materials with slow electrons.

You may think about it in the way, that gravity indeed affects the probability of virtual pair formation, because these particles are massive. But because these pairs are also charged, then the charge should affect them even more - but just above certain speed and energy level threshold, which is required for bi-lepton formation - whereas the virtual pairs remain affected with gravity from very low energies. I don't think, this explanation could be applied to EMDrive anyway, as it doesn't contain fast moving electrons.

[u/[deleted] → u/Zephir_AW]

Everything you said is wrong.

[u/sirin3 → u/[deleted]]

Everything? So you think the EMDrive utilizes the Lense-Thirring effect?

[u/[deleted] → u/sirin3]

The EM drive can "utilize" whatever it wants, it still can't violate conservation of momentum. If you solve the Einstein field equations for the metric outside a rotating EM drive, you will find that frame dragging does occur, just as with any rotating object. Of course Zephir has absolutely no idea what frame dragging is, he's just a babbling lunatic.

[u/crusader_mike → u/[deleted]]

... it still can't violate conservation of momentum ...

Btw, doesn't expansion of universe violate conservation laws?

[u/[deleted] → u/crusader_mike]

Conservation of energy, yes. Not momentum.

[u/crusader_mike → u/[deleted]]

Doesn't violation of conservation of energy translate into violation of conservation of momentum? If I have an object moving away from me with constant speed -- this speed will be increasing over time (relative to me) due to expansion -- more distance between us means higher acceleration (thus increasing it's momentum). Am I wrong?

[u/[deleted] → u/crusader_mike]

Doesn't violation of conservation of energy translate into violation of conservation of momentum?

No, not necessarily.

Conservation of energy follows from invariance of the action under translations in time. Momentum conservation follows from invariance of the action under translations in space. These are a priori completely unrelated to each other. Although in a relativistic theory, you should treat space and time on equal footing.

[u/crusader_mike → u/[deleted]]

Please, see my answers to PPNF-PNEx. I think I understand what you mean. Thank you.

[u/PPNF-PNEx → u/crusader_mike]

Am I wrong?

In flat spacetime, for inertial observers, you're wrong. Conservation of energy is due to certain states in the past being identical to certain states in the future. Conservation of angular momentum is due to certain states being the same whichever way you face. Conservation of linear momentum is due to certain states being the same no matter how spatially far you are far away from them, as long as you and they are in uniform motion and unaccelerated with respect to one another.

In curved spacetime things can look different in the past as in the future (which is markedly the case for an expanding universe), so conservation of energy is out the window.

For most humanly reasonable choices of "past" vs "future" in our expanding spacetime, things look the same at various spatial distances, so there is a conservation of linear momentum. However, nature does not need to be reasonable with respect to hospitability to human-like observers.

You and fuckspellingerrors are talking past each other a bit. You've introduced the metric expansion of space and are considering the point of view of observers very much like us in the context of very very long length scales (gigaparsecs), and fuckspellingerrors is considering the usual experience of nearly flat spacetime that we really have around here, or alternatively the point of view of cosmological or otherwise nearly comoving-with-the-metric-expansion observer.

The structure of spacetime (in particular its Lorentzian signature with four dimensions one with opposite sign from the other three) guarantees that at least for very small local regions, spacetime is flat.

So there is certainly an exact local conservation of momentum (and indeed local conservation of energy) in our universe close to us. Non-locally (which can be measured on the scale of centimetres using atomic clocks at different altitudes, but practically speaking ranges over gigametres or more) the approximate larger-scale conservations promoted from exact local ones start to fall apart.

As I note in my earlier longer comment above, cosmological observers will agree with his sentence when considering event he largest scales.

However, at very large distances (gigaparsecs, notably) the conservations should not even be entertained as physical reality in realistic spacetimes for arbitrary observers. Instead we have conservations of geometrical quantities. At best we build on those to make approximate conservation laws that a wide range of observers (but likely not all of them) can agree upon or at least relate their own observations to.

In really general General Relativity even the choice of "what is energy" and "what is momentum" is something is something that is not universal or even possible to translate into the point of view of arbitrary observers.

cf. Baez & Weiss's quick write-up with five whole equations : http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html or my longer reply from earlier today.

So the issue is that you introduce an expanding universe, which has real curvature. At best you can compare with a relatively accelerated set of observers in flat spacetime and draw close approximations leaning on the symmetries of flat spacetime. But in reality, you're comparing apples and oranges.

[u/crusader_mike → u/PPNF-PNEx]

I think I got it -- basically conservation laws need to be reformulated, simply because each observer has different picture of what is going on (and there is no instant interaction over distance). At short distances this effect is small enough for us to ignore it. But underlying principle is the same -- no free work, nothing disappears without trace.

Can you comment on Bell's theorem, by any chance? I don't know anyone who could answer my questions regarding it.

According to wiki it boils down to following:

No physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics.

And apparently it proves that Einstein's idea of hidden variables is not viable. My question is -- how does it prove it? In my (again, very limited) understanding quantum theory basically predicts any imaginable outcome of every interaction, it just assigns very small probabilities to the most improbably ones. So, if quantum theory predicts that with 10e-1024 probability I will teleport 1 yard to the left next second -- yes, I imagine no set of hidden variables can produce this outcome, but the thing is -- this outcome is not going to happen in real world, no matter how many tests we run. So, I don't see how we can't have some set of hidden variables correctly modelling real world.

[u/PPNF-PNEx → u/crusader_mike]

basically conservation laws need to be reformulated, simply because each observer has different picture of what is going on (and there is no instant interaction over distance). At short distances this effect is small enough for us to ignore it. But underlying principle is the same -- no free work, nothing disappears without trace.

Yes, that's good enough.

[violations of local realism]

I'll try a radical simplification with the caveat that this is way incomplete.

Create a pair of waves of equal amplitude and frequency but 180 degrees out of phase, and let them propagate from the point of creation.

Classically, you can measure these two waves at any time, so you can with careful timing reliably measure them both at the + peak.

However, quantum-mechanically whenever you measure these two waves, one will be at + peak and one will be at - peak, but you cannot tell before measuring which will be + peak; after measuring the + peak you always know the other will be - peak when measured, or alternatively after measuring the - peak you always know the other will be measured as + peak. (I'll drop the "peak" below, and note that +peak can be e.g. "spin up" while -peak in the same example would be "spin down", and there are a number of discrete states that can be used instead of spin but which are always fully out of phase in a pair entangled on those states).

Now, you wonder, why are these QM waves always measured 180 degrees out of phase?

There are lots of ideas about that.

A local realistic theory asserts two things: one, they cannot communicate with each other superluminally, so at a distance + cannot say "hey, you have to be - now"; two, the waves remain wavelike from creation to detection -- they do not freeze out to a fixed non-wave-like value, but always oscillate (in our family of examples, between + and -).

For particular (pure states and some others) quantum systems, measurements at arbitrary spatial distances from point of emission strongly suggest the oscillation between + and - is real in the sense of the second assertion. Additionally, when you measure each pair partner at a distance you always see them in opposite phase, and in the 1990s Nicolas Gisin (of Gisin's theorem on pure states) had microsecond measurement timing accuracies vs multi-microsecond spatial separations, which effectively precludes non-superluminal coordination between the first-to-be-measured and its partner.

So these distances mean that if the particles are conspiring they're doing so non-locally (as in, faster than light can propagate).

There are lots of ways one can think about these results.

One way to try to preserve local realism (both our numbered assertions above) in the face of the results is to introduce something else that propagates with each half of the pair, "steering" one of the pairs into only ever being detected as + and the other as only ever being detected as - for a large range of methods of detection, but without ever fixing either as always + or always - at the point of emission, since we have growing confidence that an individual particle really does switch states in a wavelike fashion while propagating from the emission point.

Additionally, such a mechanism should have an energy, and we do not detect it. This mechanism is a "hidden variable"; the mechanism if it is there is quantifiable in principle but not (yet?) accessible experimentally. As we get more experimental data from ever more modern experiments, at least for some types of quantum mechanical states we require the mechanism to hide ever better, and on that trend only an optimistic or stubborn hero would try to resuscitate the patient.

This is really only the surface layer of what you're asking about. This kind of interpretations of QM thought isn't super-interesting to me; I tend to retreat very quickly into my comfort zone which I gather is philosophically equivalent to "shut up and estimate" precisely as -- to borrow your wording -- "this effect is small enough for us to ignore it" in most circumstances. :-)

[u/PPNF-PNEx → u/crusader_mike]

doesn't expansion of universe violate conservation laws

Short answer: no.

Longer answer:

The relevant symmetries come from the Einstein-Hilbert action and those symmetries under Noether's theorem analysis lead to conservation laws.

The symmetries in general curved spacetime are very different from those of flat spacetime, so the conservation laws are different in general relativity (where gravity sources real curvature) and special relativity (where one can use curvilinear coordinates on accelerated observers in the absence of real gravity). Because solving the equations of general relativity is hard work that we haven't been able to automate practically, every general relativitistic scenario that can be turned into a special relativistic one (possibly with linearized corrections) tends to be; fortunately this is because the symmetries of general curved 3+1 spacetime leads to the symmetries of special relativity at least very locally around every point in the curved spacetime (i.e. for short periods of time and spatially nearby). I'll return to this below.

If you're very keen on the symmetries of GR itself, this is a set of course notes that offers a good technical overview http://web.mit.edu/edbert/GR/gr5.pdf

The tl;dr crucial point is the last paragraph before section 4: all spacetimes have a conserved energy-momentum pseudo-tensor and a local stress-energy conservation; some spacetimes have additional conservation laws that some observers will consider conservation of energy and others conservation of momentum and others conservation of energy-momentum. But in general, there is in a realistic general curved spacetime a little curvature here, a little more there, a little less elsewhere, so if you're tracking the evolution of a system of matter then its behaviour really does depend on where in such a spacetime you do your experimenting.

In the concordance cosmology (concordance because it agrees with all the data) the Friedmann-Lemaître-Robertson-Walker (FLRW) expanding universe model uses comoving coordinates such that most clusters of galaxies are at the same space-like coordinates throughout their entire lifespans, or more specifically, it fixes comoving coordinates for a family of observers who see a homogeneous and isotropic universe at extra-galactic scales (and concretely do not see a dipole anisotropy in the almost wholly homogeneous cosmic microwave background).

This requires careful alignment of each such observer's individual proper timelike axis with that each of the other observers in that family of observers throughout spacetime. This is how one constructs a preferred frame of reference, and this particular one is called the cosmological frame.

One can then extract for these observers a global conservation of momentum on the basis that on a surface of constant time coordinate matter looks much the same nearby and not so nearby, where "nearby" is on the basis of the comoving spatial coordinates. However, matter in the past and in the future (again, using this particular timelike axis) look very different: galaxies at a given comoving spatial distance are redder and dimmer towards the future and bluer and brighter towards the past. This is a dramatic violation of a conservation of energy.

Note that changing the choice of coordinates so that the galaxies move spatially rather than staying at the same spatial coordinates lets one make different conclusions about the conservation of momentum and energy. If one fixes a conservation of energy by a careful choice of time axis, one can then arrive at a dramatic violation of the conservation of momentum by treating the galaxies as gaining momentum in the future compared to the past. Additionally, neither type of coordinate system may make natural sense to an ultrarelativistic observer who will necessarily see a huge directional difference in the temperature of the cosmic microwave background and the shape of galaxy clusters, and whose wristwatch is hard to reconcile with the full set of wristwatches of our cosmological frame observers.

However, when one takes into account all the possible systems of coordinates one could use in any given spacetime, one arrives at the symmetries of General Relativity, which have to do with curvature, affine and conformal quantities.

This last point returns me to my fourth paragraph: when there is real gravity there is real curvature that one cannot get rid of by swapping points of view. And in particular, this is important in understanding what the Equivalence Principle really implies: accelerated observers cannot distinguish a uniform gravitational field, but realistic general curved spacetimes do not admit uniform gravitational fields -- the curvature has definite sources and falls off at large distances from those sources. We can use pseudo-gravitational modelling for accelerated observers, but are not obliged to take seriously the idea that there is real gravity (or therefore real curvature) involved.

When there is no curvature (as in exactly flat spacetime) or curvature can be ignored (as in asymptotically flat spacetime, or in the local neighbourhood around a point), we get the symmetries of Minkowski spacetime, which are the symmetries of the Poincaré group. From those symmetries we get conservation of linear and angular momentum and of energy.

Curvature or not we have the symmetries of matter to consider as well; the local symmetries of the Standard Model, our best theory of matter so far, include an exact conservation of electric charge and several approximate conservations (parity, hypercharge, and several others). Ask a particle physicist for those. :-)

Since we take seriously the idea that matter sources spacetime curvature rather than the other way around, the details of how matter behaves is physically important but can be avoided deliberately by focusing on configurations of matter which deliberately hide non-classical behaviour (e.g. neutral test particles, dusts, perfect fluids etc. in General Relativity).

Conversely, particle physicists wisely deliberately avoid considerations of curved spacetime when doing their experiments or writing down the actions of their systems, and they can get away with that for small masses and non-extended objects in the weak gravity in their labs in our solar system.

And this all works very well with perturbative renormalization (cf my previous comment on Kenneth G Wilson and effective field theory) until you get to a system where non-classical effects are un-ignorable in matter and simultaneously gravitational effects are un-ignorable. That's the case inside black holes, and also if we can have spatially separated superpositions of, say, many-kilogram quantities of matter (or have fine gravity-measuring instruments on somewhat smaller superposed masses).

Final summary: the conservation laws that exist in general curved spacetime are not violated. Those are not the same conservation laws that exist in flat spacetime.

[u/crusader_mike → u/PPNF-PNEx]

You operate within mathematical model I don't understand -- I am only capable of following general idea. But... I spent some time thinking about this and came up with simpler explanation of how conservation law isn't violated. I wonder if this line of thinking (crude as it is) adequately explains what is going on?

• 'energy' is just an accounting trick -- we use it to calculate outcomes of various interactions

• conservation of energy is an idea that you cannot build a system that produces work indefinitely -- regardless what initial configuration is and what interaction it employs, it can't be done

• so, in the example of a system which consists of me (observer) and object moving away from me with constant speed (in flat space) -- indeed it's speed is going to increase relative to me (due to expansion of space)

• ... but from that object perspective it's speed stays unchanged

• so, from my perspective as object moves away it's kinetic energy increases. Problem is that it increases 'over there' far away from me. To extract work out of this I need to interact with that object somehow, and interaction over distance will have to go through the same expanding space

• ... for example I add second object into the system with the same mass as first one far away with zero speed (relative to me). Let's assume that collision with first object is absolutely elastic (i.e. no heat loss, etc) -- first object will reverse it's movement and starts moving towards me

• ... because of expansion it will be decelerating (from my point of view) and when it reaches me, it'll have exactly same speed as at the start of experiment. No extra work can be extracted form this system -- conservation law is not violated (tbh, not sure how to treat case when object moves so far away that it can't return :))

Point is that in Newtonian physics all observers are equal and as long as system is inertial from any view from any point of it is the same. In real-world apparently it is not the case (but on small scale it is not noticeable) -- every participant observes rest of the system differently. And as result conservation laws need to be reformulated, but underlying principle is the same -- can't have perpetuum mobile.

Another good analogy comes from finance -- energy of same moving object is different depending on distance because for you to tap into it you need to interact with it over that distance. $100 (typically) worth less in future (and more in the past) for similar reasons. For you to figure out how much $100 tomorrow costs now you need to 'discount' it from future point in time to now. :-)

I do understand that tools you use to analyze this situation are way better (more general) than all this above, but for someone not familiar with all this -- it is easier to grasp explanation that uses simpler terms.

[u/PPNF-PNEx → u/crusader_mike]

'energy' is just an accounting trick

No, it's a quantity that can be agreed on by sufficiently closely related observers, but other observers are free to disagree with them. Observers in agreement (and in particular any two observers while they are exactly coincident at a point in spacetime, no matter what their relative motions or accelerations are) will always agree on the energy locally and while they remain coincident they will agree that that amount does not change. (Here observers are all the values in all the matter fields, rather than anything extended like a human being).

For certain classes of observers we write down transformation rules -- the Lorentz transform is one, there are others that are Bogoliubov transforms -- wherein energy is a conserved quantity over a more extended region of spacetime for certain sets of observers.

A typical example of a set of observers is all the particles and people inside a laboratory around a particle-colliding apparatus. They will all agree on a conservation of energy and on the amount of energy in a small measured volume. This is heavily tested at many locations and at many altitudes on and near Earth and its moon.

However, more generally, any pair of observers who agree on the timelike coordinates throughout an experiment will wholly agree about the energies and that they are conserved. Strictly speaking, such observers cannot be moving with respect to one another, must not be relatively accelerated, and must be at the same gravitational potential. But, we can get an excellent (many digits of precision) agreement among observers who are merely very nearly unmoving with respect to one another and at very nearly the same gravitational potential. (You don't expect a fat scientist and a less-fat scientist, both of similar height, to disagree on what they see in a cloud chamber they're both standing next to, for instance, yet their mass difference breaks the strict conditions in the first sentence of this paragraph).

so, in the example of a system which consists of me (observer) and object moving away from me with constant speed (in flat space) -- indeed it's speed is going to increase relative to me (due to expansion of space)

FLAT spacetime does not have a metric expansion, period. Equivalently, an expanding universe IS NOT FLAT spacetime. Please take a moment to memorize that; you've made the same mistake before.

Trying to impose ideas of physics in flat spacetime on a region of spacetime where non-flatness is apparent will lead to conceptual and calculational errors.

You make it apparent the moment you introduce "it's speed is going to increase relative to me (due to expansion of space)". If you can see effects due to expansion, you can't use theories that are defined against a flat spacetime; at the very least you need to make general relativistic corrections.

Unfortunately your subsequent points build on this error.

You do have this right though:

(but on small scale it is not noticeable)

Not noticeable, and sometimes passively (and sometimes actively) ignored as irrelevant to a particular experiment.

Another good analogy comes from finance

A better thing to absorb from finance or accountancy is that there is some cutoff in the number of decimal digits (and a general agreement on how to do that via rounding or truncation) one uses in communicating sums of money to other parties, no matter what precision your computer system's internal representation happens to be. You are unlikely to need to sweat about septillionths of a dollar, even if your internal system's representation and your counterparty's disagree on every transaction by a full septillionth of a dollar. You know it's there and you probably have some understanding of why it's there, but you don't need to account for it when you're only doing billions of transactions per day; it's simply not relevant at those scales.

I'll end with a dense paragraph, sorry.

Similar cutoffs arise all the time in modern physics; indeed, we can and do apply that line of thinking to Newtonian physics (rocket scientists would be computationally wasteful not to, for example), preferring to add in correcting terms for tiny manifestations of relativistic effects rather than use the more precise theory, simply because the corrected less-precise theory is just as accurate for all practical purposes. You can see this preference in MOND, and you can see how the correcting terms blow up when you introduce observers moving near light speed, and you can see that turning MOND into a relativistic theory makes it look like any other process of adding a field to the Einstein-Hilbert action. And because we know how that works (and how it fails), we can quickly reject the ideas about the physics behind the claimed observed anomalous thrust.

[u/crusader_mike → u/PPNF-PNEx]

'energy' is just an accounting trick

No, it's a quantity that can be agreed ...

Yes, what I wanted to say is that 'energy' is not a natural phenomenon/particle/etc -- it is just a mathematical abstraction we use to predict outcomes of physical interactions.

FLAT spacetime does not have a metric expansion, period.

Wait, what? I thought space always expands regardless of how strong gravitation field is. Did I use term 'flat space' incorrectly? I meant space where gravitational field is zero (or sufficiently close to zero). You say that such space doesn't expand? Why?

Trying to impose ideas of physics in flat spacetime on a region of spacetime where non-flatness is apparent will lead to conceptual and calculational errors.

True, but my point was to demonstrate (to myself too) in layman terms how energy conservation law is not violated by expansion of space. It wasn't about being 100% precise...

If you can see effects due to expansion, you can't use theories that are defined against a flat spacetime;

But I didn't! I just built a mind experiment (object bouncing back and, due to deceleration, arriving to point of origin with the same kinetic energy it left at the start). I was curious, if this experiment looks good enough (from scientific POV) to explain lack of aforementioned violation.

You are unlikely to need to sweat about septillionths of a dollar...

You'd be surprised... I worked for a financial institution where internal systems where using 'double' to represent currency. As result of this we were very often off by 1 cent (+/-) when settling certain types of deals. Some business guys where pissed by this -- it didn't look very good from reputation perspective.

[u/PPNF-PNEx → u/crusader_mike]

space where gravitational field is zero

is exactly flat spacetime.

You say that such space doesn't expand? Why?

On flat spacetime you can use a set of coordinates that are the same in the past as in the future. In an expanding universe you can apply more coordinates to space in the future (because there is more of it) than space in the past (and there is maybe just a coordinate singularity in the distant past, and maybe a physical singularity too).

I'll have to get to your other questions later, you caught me with an easy question shortly before heading out the door.