Markus Hanke

For a wavefunction to be physically meaningful, one of the conditions it has to fulfil is that it needs to be normalised: [math]\displaystyle{\int_{-\infty }^{\infty}\psi^{*}\psi dV=1}[/math] The squared norm of such a wavefunction can therefore never exceed 1 - this should be obvious, since such a concept as “more than 100% probability” does not make much sense. This does not follow, and is not possible either way.

No. The notion of curvature - in particular the intrinsic curvature used in General Relativity - makes sense only on smooth, differential manifolds. A topological construct with non-integer Hausdorff dimension cannot be a differential manifold (I know this can be formally proven, though I forgot the name of the theorem). You would also find it hard to define events and their separation on such a topological construct, never even mind pulling that all together into a self-consistent model that represents gravity as we see it in the real world. It’s an interesting idea though, but not mathematically workable so far as I can see.

What I was referring to is the energy-momentum tensor, which is the source term in the Einstein field equation. It physically represents the distribution of energy-momentum in spacetime. It’s called the “energy-momentum tensor” because it encapsulates both the distribution of energy and momentum in a system.

Spacetime is not created, so I am unsure what you mean by this. If you meant whether photons have themselves a gravitational effect, then the answer is yes they do, because they carry energy-momentum - which is the source of gravity (not just mass). That depends on the observer. No, because the blueshift is an observer-dependent phenomenon. Locally in a small enough spacetime neighbourhood of the photon itself, nothing changes.

It initially appears bizarre only because it runs contrary to how we as humans, in our human domain of everyday life, experience the world. It’s a habit of perception that keeps us “stuck” in a particular world view. But it is possible to transcend that Newtonian paradigm, and with a bit of practice the relativistic world view becomes quite natural after a while.

I forgot to mention earlier - it is in fact possible to observationally test GR on scales much larger than the solar system. Here is just one recent example: https://arxiv.org/abs/1806.08300 Needless to say that all of these tests are consistent with GR predictions.

The sun. Yes, just like any other type of matter too. And the weak and strong interactions also play their role. Generally speaking, which of these interactions has the strongest effect depends on the scale; for example, on atomic scales the EM interaction will be dominant, on subatomic scales the weak and strong interactions, and on macro scales it will be gravity. But in any case, they are all present. I am not aware of any laboratory experiments that measure plasma to have gravitational effects different from what GR predicts. Can you provide a citation please? Actually, you are asking the wrong question. We already know that - using GR - the observational data we have is consistent with the existence of dark matter. Without dark matter, it won’t be. The thing with this is that we have absolutely no reason to believe that the laws of gravity are scale-dependent; we know GR works very well on scales of the order of the solar system, so it is reasonable to assume that they also do on larger scales. It follows that the existence of dark matter is a more reasonable explanation, than a modified gravity law. There is a possibility that gravity is indeed scale-dependent; these are concepts that are being investigated (refer e.g. to Verlinde’s “Emergent Gravity”). At the moment though, none of these alternatives has proven very workable. As for electromagnetism, it is evidently very different from gravity, both in terms of its nature and behaviour. The idea that gravity is an electromagnetic effect is very old, and self-evidently false, which is why it isn’t part of modern science. Let me ask you in return - can you provide a model based purely on electromagnetism that correctly replicates all aspects of gravity? I can tell you for a fact that you can’t, because EM does not have a sufficient number of degrees of freedom to do so.

Because the process of quantisation leads to a new theory, not just an amendment to the original one (which remains standing within its own domain of applicability). The original theory becomes thus the classical limit of the new quantum one - meaning it is implied by, but not identical to, the quantum version.

This doesn’t actually follow. Much like the other fundamental interactions, General Relativity can be written as a Yang-Mills gauge field theory, using the Ashtekar variables; it is thus quite natural to assume that spacetime is ultimately quantised, i.e. granular on small scales. We are in fact able to perform a full quantisation of this field theory, and the result is a model called Loop Quantum Gravity (LQG). This is currently a work in progress, since we do not yet fully understand all dynamics of this theory, and hence it is too early to tell whether it is a good description of quantum gravity, or not. Nonetheless, this model seems like a pretty strong contender. There are also other clues that spacetime is not infinitely divisible; most especially thermodynamics. Stephen Hawking has shown that black hole event horizons have a finite entropy associated with them - but since entropy is a statistical measure of microstates, it follows that the vacuum cannot be continuous on small scales. It must have a discrete structure. Interestingly, this entropy can be computed from aforementioned LQG, which does indeed yield Hawking’s entropy formula.

I have to be honest and say that you would be better off investing the time you spend on YouTube into studying a proper textbook on GR. There are two main reasons for this: 1. GR is a 4-dimensional model. As such, no visual representation will ever allow you to gain a full understanding of gravity, since it is not possible to accurately embedd a 4D manifold into a 2D+1 screen representation. Any such attempt will necessarily be flawed, and can thus lead to serious misunderstandings of what GR actually says. 2. YouTube is not a valid source of scientific data. How do you know that what you see in a video is a an accurate representation of GR, especially if you are unfamiliar with the model? I do realise that the maths of GR seem very intimidating at first, and I do not deny that some considerable effort is initially needed to get your head around the formalism. But once you do, you no longer have to rely on incomplete and flawed analogies; the meaning and physics of GR become self-evident, once you know how to read the formulas. And that’s all you need to be able to do - understand the physical meaning of the equations. For a layperson it is not necessary to be able to work with them. But understanding them is not such a tall order. No! What is described in the video does not represent the current scientific consensus on gravity. It is a mixture of established facts, hypothetical/unconfirmed ideas from current research into quantum gravity, and personal speculations by the author which have no basis in established physics at all. It would be difficult and time consuming now to try and disentangle these strands for you, so I won’t try. Suffice to say that this is the reason why you shouldn’t rely on random YouTube videos when trying to understand GR. I have no doubt that there will be decent YouTube presentations on the topic, though I can’t give you any links, since I seldom use that platform; I self-study only from textbooks, since in my opinion that is the only way to really develop a proper understanding of the subject matter. I’m afraid there are simply no shortcuts here. At the danger of getting myself into trouble with the moderators here (please delete if not allowed), I will link you to a “First Primer for Laypeople” style introduction to GR, which I wrote some years ago. It contains almost no math at all, but does present the main ideas of GR in a way that I hope is understable even for a complete newbie: http://www.markushanke.net/general-relativity-for-laypeople-a-first-primer/ Hopefully this is helpful to you. There is also a link there to another article of mine, which is a (more or less) gentle introduction to the mathematics of GR. You may wish to have a read there, too.

But the maths aren’t off. What happens is that some of the original mass-energy of the disc gets radiated away as heat, and some of it does not accumulate in the central star, but stays “outside” (that’s the bit from which planets can later form). We can account for all of these things. The “approximately” just indicated that not all of the original mass ends up in the star, but that does not mean it somehow disappears. Modern cosmology does not propose any boundary to spacetime, so it is not a surprise that this is never mentioned. The notion of “outside”, when applied to the universe, is simply meaningless. Flat does not mean 2-dimensional. Space always has three dimensions, regardless of its geometry. The “flat” means that on average there is no intrinsic curvature in the spatial dimensions, meaning that, if you pick three arbitrary points that are far enough apart, then the angle sum of the resultant triangle will be 180 degrees. Yes, it is - but only in the classical domain. But that’s fine for now, because GR is a model of classical gravity only; it does not incorporate any quantum effects. When we look further “out”, towards quantum gravity, things become very much more complicated. But I suggest for now we stick to GR, because you can’t progress further unless you fully understand this first. Probably yes, because rhythmic cycles like that are very common in nature, and also occur in many other contexts. Yes, it would affect our aging compared to a reference clock someplace else. Time dilation is a relationship between clocks in spacetime, not something that “happens” to just one clock. Note that gravitational time dilation is very well established effect, backed up by a vast body of experimental data. Beliefs are irrelevant, only the scientific method counts. Gravitational time dilation is very easy to test experimentally. That was a belief that couldn’t be supported by experimental and observational evidence. That is why it was eventually abandoned. Gravitational time dilation on the other hand is supported by lots of experimental evidence. It is even used in everyday engineering applications, so we know it works. It would age less, compared to a reference rock which does not travel. This can be easily ascertained by comparing the ratios of radioactive isotopes (which are naturally occurring in all rocks) between the two. Or simply by attaching a time piece to the rock before it embarks on its journey.

Excellent explanation, Janus. The fundamental problem with all threads of this nature is the OP’s tacit assumption that space and time are both separable and absolute. This is the Newtonian paradigm, as established back in the 1600’s. But of course, we know today that space and time are neither separable, nor can they be absolute, since these assumptions lead to contradictions and inconsistencies. Relativity rectifies these problems by recognising that notions of space and time are purely observer-dependent and local. At the frontiers of modern research, we are now also beginning to understand at a fundamental level just why that must be so.

The laws of gravity do not depend on the state of matter at all. They depend only on the distribution of energy-momentum.

Since the g{tt} component of the metric tensor contains the factor c, and hence “dominates” the metric in a certain sense, it is not a surprise that it makes a large contribution to the overall geodesic deviation, at least under some circumstances. And the bit in bold is the key, because the relationships between the metric tensor components in the field equations are of a highly non-linear nature. This non-linearity is small in the weak-field vacuum regime (such as the Earth), but becomes increasingly noticeable in strong field regimes. It also becomes noticeable when the spacetime in question is not stationary, and in particular when you go from vacuum to the interior of energy-momentum distributions. Under such circumstances, tidal forces (which mostly arise from the spatial part of the metric, instead of the temporal one) play as much, or even more, of a role than gravitational time dilation. In my humble opinion it makes no sense at all to attempt to separate these effects, except perhaps as pedagogical aids, or as approximations in special cases to simplify the maths. Other than that, spacetime is the gravitational field - you can’t meaningfully separate them. And why would you want to? It is precisely that identification of spacetime with the gravitational field, which makes GR so powerful.

Yes, you have stumbled across your own ongoing inability to stop looking at time and space as being independent and absolute. This has been known to not be workable for well over a 100 years now - it’s time for you to catch up at last, don’t you think? Based on the fact that you seem to have completely ignored everything that was already explained to you in the other threads you had opened on this topic, I see no reason to go through the actual calculation again. It would serve no purpose, since you’ll ultimately ignore it anyway. Also, had you actually read the Wiki article, you’d be able to do the numbers yourself - it’s just the usual length contraction formulas, plus a bit of trigonometry, since your observer sits off-side from the line of motion. Instead of wasting our time here, let me ask you something in return - is there anything at all that we could say to you or show you, that could convince you of the validity of the theory of relativity? It seems obvious that giving actual answers to your questions isn’t enough. Please just be honest - if there isn’t anything we can say that would convince you, then that’s fine - at least we’ll all know where we stand. Well, why don’t you? No one is going to stop you from doing this. Perhaps it would be a very illuminating exercise for you.

A spacetime being “flat” means that neighbouring events (i.e. events that are close to each other in space and time) are always related to each other in the exact same way, no matter where and when you are. When a spacetime has curvature, the relationship between neighbouring events changes depending on where and when you are. That’s all there is to it. Potentially yes, but this is not yet a sufficient condition to establish intrinsic curvature. See below. What you are hinting at here is the difference between extrinsic and intrinsic curvature. The two are not the same, and largely independent concepts. A cylinder for example is extrinsically curved, but intrinsically flat. Extrinsic curvature happens when a surface is embedded in a higher dimensional space, whereas intrinsic curvature is independent of any embedding. GR uses intrinsic curvature. The concept of intrinsic curvature is defined by what happens when you parallel-transport a tangent vector along a closed curve in your space that covers all possible directions. If the space has intrinsic curvature, then the final transported vector at the end of the manoeuvre will not coincide with the original vector you started with. That’s true, which is why the definition of intrinsic curvature uses closed curves spanning all possible directions, rather than just parallel lines. That is because there are quantities called “constants of motion”, which are similar to the conserved quantities in Newtonian physics. Orbital angular momentum is one of them. If a planet has orbital angular momentum at the time when it first forms, it will retain this orbital angular momentum unless something happens that transfers this energy away (e.g. a major collision, or friction due to gases etc). This is way their orbit is largely stable. In GR speak, the geodesics that a body in free fall traces out are determined by initial and boundary conditions. Because the moon is very close, so the influence of the Earth is very much stronger than that of the sun. It will stay mostly the same. I’m not sure what you mean by “see a line”. But anyway, the universe appears flat in space, but it’s not flat in spacetime, because of its ongoing expansion. Mass is always warping spacetime, so I am not sure what you mean by this. Mass does not just appear out of nowhere - it only changes form. For example, a star forms from a disk of gas through self-contraction. The original disk of gas has the same total mass (approximately) as the star that forms from it. It’s just distributed differently. So it is just a matter of spacetime geometry slowly changing over time - it’s not a matter of it being flat at one moment, and then suddenly curved at the next. That’s not possible, because curvature itself - in a certain sense - is also a conserved quantity. It can change, but it can’t be created or destroyed. You can see this by trying to smoothly transform a sphere into a flat sheet - no matter how you twist and deform it, cut and paste it, the result will never be a completely flat and seamless sheet. That’s because you cannot eliminate the original curvature inherent in the sphere. The reverse is also true - you can’t make a perfect sphere from a flat sheet. This is physically meaningless, because you cannot do this. All you can do is change how the energy-momentum of the sun is distributed, and the geometry of spacetime will change accordingly. But you cannot destroy or create it out of nothing. I’m struggling to understand what you mean by this. In the absence of any other sources of gravity, the body will just continue on in its motion, in the same way as it does in Newtonian physics. However, it nonetheless deforms spacetime around it - so if you bring a test particle near to that body, it will “feel” the effects of its gravity. As an additional remark - GR is a simple application for mathematics that have existed since the 1800s, so all the mathematical concepts you can find in GR are rigorously defined, fully self-consistent, and very well understood. There is no room for interpretations or uncertainties, so far as the maths are concerned. Einstein did not invent any of this, he just made use of something that was already there since the times of Bernhard Riemann, in order to describe the physics of gravity. The area of mathematics used here is Riemann geometry, which is a subset of the broader area of differential geometry.

Well, it’s a valid conclusion, at least in the context of our current level of knowledge and understanding. We even have a model that can directly describe how this entropy comes about - loop quantum gravity. It is possible to do the maths via LQG, and obtain the Bekenstein-Hawking entropy equation. This is a very fascinating thing, because if we take LQG at face value, then we will be forced to completely rethink the nature of space and time. It would be a major paradigm shift. No, because that model only describes the vacuum and gravity, but does not unify the other fundamental interactions. No, String Theory assumes a smooth and continuous background spacetime from the beginning, so it doesn’t explain how such a spacetime comes about. It only explains how its geometry emerges, which isn’t quite the same thing. The approach in this paper on the other hand models an emergence of spacetime itself from more fundamental principles. Yes, at present it would be difficult to directly test such proposals. However, there may be ways to test it indirectly through observations - for example, just as there is a CMBR left over from the BB, there should also be a background of gravitational wave echos. It may (!) be possible that such a background provides clues as to the quantum structure of spacetime in the earliest moments of the universe.

Yes, that is absolutely correct. However, unlike String Theory, General Relativity has been extensively studied and experimentally and observationally tested over the past 100 years or so. We know now that it is a good description of gravity, and we understand the model very well. At this point in time, the same is not true for String Theory - but since physics is a science in constant progress, this may well change in the future. Or perhaps we’ll end up abandoning String Theory altogether, since there are a number of other models that may be better descriptions of the world. It’s rather the other way around - precisely because of our understanding of quantum physics are we now able to start building quantum computers. That would not be possible if we didn’t understand the quantum world to the degree that we do. With this I am not claiming that we have it all figured out (we haven’t) - but we do already know a great deal. This is certainly true. But we need to remember that the reverse is not true - not everyone who is considered ridiculous is necessarily on to something valuable; the vast majority of people simply aren’t. It’s really important to keep this in mind - major paradigm shifts are what drives our understanding of the world, but these are very rare events brought about by exceptional and rare people. Also, such paradigm shifts are not usually based on a rejection of what we already know, but rather on developing a new perspective on known facts. Einstein is a good example - he never rejected Newtonian physics (Newtonian gravity is still the asymptotic limit of GR), he simply put it into a new light by relaxing certain assumptions we have had about the nature of space and time. This opened up a new way to understand gravity and spacetime. The next paradigm shift will be similar - GR will remain standing as the classical limit, but quantum gravity will force us to once again look at space and time in a completely different light. And so it goes on.

By “locally” we mean in a very small region in and around a point in spacetime - small enough so that curvature can be neglected. This is as opposed to “global”, which signifies a larger region that may not be flat. It does not mean that the Earth is in any way special, since it is true for any point in spacetime, not just here. String theory - in spite of its name - is actually only a hypothesis, not a fully worked out model. General Relativity on the other hand is a proper theory, because it has been tested extensively over the past 100 years or so, and found to give the right predictions. We know it works.

The ability of a system to store energy is not the same as that system being able to do work. That being said, I think it is important to realise that magnetism isn’t fundamental - it’s the electromagnetic field that is the fundamental entity. Splitting this entity up into electric and magnetic components is quite an arbitrary and observer-dependent procedure. It can be useful to do so for specific scenarios, but it can also create a lot of unnecessary confusion. The EM field has a well defined energy density, but how this breaks down into “E” and “B” parts depends on how you observe it. Personally I think it is best to not break it down at all, and just stick with the fundamental EM field.

This puts me in a difficult position, because it is not so easy to demonstrate these things without the maths. Basically, the problem with your idea (and it is commendable that you think about these issues so deeply, so kudos!) is that you are thinking about it in terms of Newtonian physics - you speak of kinetic energy, friction, conservative forces, conservation of energy etc etc. Unfortunately the universe at large scales is not a Newtonian system - many of the concepts you use are meaningless and not defined in this domain. To understand the dynamics and behaviour of the universe at large scales, you really need to use relativistic physics, specifically General Relativity, which is based on the geometry of spacetime. To give just an isolated example - the total amount of energy in a region of non-trivial spacetime (which the universe at large scales is) is a difficult to define quantity; there are in fact several different notions of that energy content, depending on your boundary conditions. What’s more, there is also no global law of energy conservation in such regions of spacetime, there are only locally applicable laws. So like I said, it’s commendable effort on your part, but it won’t lead anywhere - sorry, but I have to say it as it is.

I’m sorry to be harsh, but the above is completely meaningless nonsense - mathematically as well as physically. You might as well have posted a child’s drawing of a pink unicorn, for all the difference it would have made. And before you question it, the answer is yes, I am well versed in both mathematics and physics, so I can actually read a mathematical statement when I see one, and understand its physical meaning (or absence thereof). Like I said, I do not set out to be harsh to anyone, but at the same time I will say it as it is.

I think this should be SR, not GR. Standard QFT is formulated on a Minkowski background, basically to ensure CPT invariance. Transposing this to a situation with a non-Minkowski background is a formidable task, which I don’t think this thread is about.

This statement is completely devoid of any meaning, on all levels. YouTube is not a valid source of scientific data. Apart from this, water in the real world behaves exactly like described by the dynamics of General Relativity - as does everything else in the classic domain. GR has become such an integral part of physics, simply because it works very well. The experiments are quite sound. Also, many GR effects can be directly observed in everyday engineering applications, and require no special funding or setups. It would seem to me that the problem isn’t with physics, but with your own attitudes and belief systems. I must admit that many of the things you have posted here on this forum are, to me, an outward expression of a deeply troubled mind, that has fallen victim to some very insidious cognitive distortions. As such you are unlikely to be receptive to anything we say to you. I find this very sad, and hope that perhaps one day you will realise the pain you are causing yourself with this. There’s certainly no peace in being so deeply rooted in delusion.

This sub-forum is intended as a (I quote) As such the OP is completely off-topic, since it is in no way a rational exploration of religion.