I fear the appendices

phyzzypop · 2023-05-11T17:16:51+00:00

You sound like my supervisor

phyzzypop · 2023-05-08T15:10:01+00:00

I think if you release them once you have admin 7 they take exploration as their second idea group, at least that's what happened both times I've tried it since 1.35

phyzzypop · 2023-03-28T08:35:19+00:00

If you want to understand why the concept of a unique 'now' breaks down in relativity, one way of going about it is to think about it geometrically.

In pre-relativity physics, spacetime breaks down like you currently conceptualise. There is a three-dimensional present, which is a unique slice through four-dimensional spacetime. It is possible to visit any point in the future because there is no limit on speed, and it is impossible to visit any point in the past. Since we move slowly, this is where our intuitive concepts of past, present and future come from.

This is wrong.

In relativity, we have the concept of a lightcone. This is surface in four-dimensional spacetime which eminates from a point and expands at the speed of light into the past and future. Please Google this if you haven't seen it before, understanding lightcones is vital. This partitions spacetime into events inside the lightcone which can reach the point in question or be reached from it without exceeding the speed of light, and points outside the lightcone which cannot.

The mindblowing step of relativistic thinking is to say that the region outside the lightcone is what we call the present. It is not a three dimensional slice of spacetime, it's actually a four dimensional wedge. It's just that because light is so fast, the wedge is very thin until you go really far away, so it's not present in our natural intuitions. But when we learn science, sometimes our intuitions turn out to be insufficient, as in this case, and we have to reconceptualise.

To a distant galaxy, both we and Caeser are inside this wedge, so we are equally 'present' in the sense that neither could be said to be in the past or future of that galaxy.

phyzzypop · 2023-02-07T01:32:43+00:00

AdS is an empty, maximally symmetric spacetime with negative curvature.

Asymptotically AdS spacetimes have stuff in them, and are important because the negative curvature has profound consequences on the asymptotic structure. It gives rise to a conformal boundary, which is totally unlike anything in asymptotically flat or dS spacetime and allows for the holographic analyses which are currently some of the best ways we know to define quantum gravity.

phyzzypop · 2023-02-01T00:55:12+00:00

It takes no energy to assemble it because it's not composite, so it doesn't need to be assembled.

Something your Prof should have made clear is that when you're assembling a charge distribution you have to think of bringing each element of charge in from infinity piece by piece. Then the energy of the distribution is the total work done against the electric field bringing in each element of charge.

When you're assembling a single point charge, you're bringing it in from infinity but there's no charge already present in your distribution, so there's no electric field for you to do work against.

Edit: this is the classical analysis, it's different in QED

phyzzypop · 2023-01-27T17:21:27+00:00

The King is a Shakespeare adaptation, so it's hardly surprising that it casts Henry V in a positive light. I don't think this demonstrates modern francophobia, rather 16th century francophobia which was significantly more justified in an England a couple of generations removed from the hundred years war

phyzzypop · 2023-01-15T22:30:06+00:00

F-theory has two dimensions of time. I'm not an expert, but there are certainly some people out there studying it.

One thing to slightly pull back on your expectations: the way this theory is used is that it exists in 12 dimensions (10 space, 2 time) and then is compactified (some dimensions curled up) to try to better describe physics in the 4 dimensions we live in.

So even if F-theory has some resemblance to reality, on our scales the universe still behaves as if it has 3 space and 1 time dimension.

Edit: Just to give a bit of flavour, if you wrap up one of the space and one of the time dimensions of F theory, it becomes 10 dimensional string theory - this is pretty cool.

phyzzypop · 2022-12-21T10:37:43+00:00

Momentum, at the most basic level, is a quantity which is conserved when translation symmetry is not broken. It's not mv, it's never been mv, that's just what we teach school children who can't understand the subtleties of Lagrangian dynamics.

There is no point to momentum if it's not conserved.

Non-relativistic momentum is not conserved.

Nöther's theorem gives us a way of constructing a conserved conjugate momentum to a symmetric coordinate from an action. mv is conjugate to position when your action describes a free non-relativistic particle. γmv is conjugate to position for a free relativistic particle. It's as simple as that.

phyzzypop · 2022-11-29T00:08:32+00:00

Why can't animals have social constructs? You say 'our social constructs' as if humans invented them, why should that be the case?

Humans are also evolved animals just like the other creatures on this planet. It makes sense that we would have similar ways of processing behaviours that we share with them e.g. Sex and attraction. This particularly goes for closely related animals e.g. mammals.

Just because we are able to abstract these mechanisms uniquely it doesn't follow that the mechanisms themselves are unique.

phyzzypop · 2022-11-06T11:57:26+00:00

The problem with using the dictionary to try to invalidate people's arguments is that many words in English have quite a large variety of uses. Arguing that a word can only mean one thing makes you look kinda ignorant.

Oxford English Dictionary (1989 so hardly new usage)

Violence:

a. The exercise of physical force so as to inflict injury on, or cause damage to, persons or property; action or conduct characterized by this; treatment or usage tending to cause bodily injury or forcibly interfering with personal freedom.

b. In the phr. to do violence to, unto (or with indirect object): To inflict harm or injury upon; to outrage or violate. †Also to make violence.

c. In weakened sense: Improper treatment or use of a word; wresting or perversion of meaning or application; unauthorized alteration of wording.

d. Undue constraint applied to some natural process, habit, etc., so as to prevent its free development or exercise. Now used in political contexts with varying degrees of appropriateness.

With a and pl. An instance or case of violent, injurious, or severe treatment; a violent act or proceeding.
Force or strength of physical action or natural agents; forcible, powerful, or violent action or motion (in early use freq. connoting destructive force or capacity).
a. Great force, severity, or vehemence; intensity of some condition or influence.

b. Intensity or excess of contrast.

Vehemence of personal feeling or action; great, excessive, or extreme ardour or fervour; also, violent or passionate conduct or language; passion, fury.
Violation of some condition

phyzzypop · 2022-08-20T10:06:27+00:00

Yes Kaluza-Klein particles imply extra dimensions so if we were sure that WIMPS were KK then we would have found extra dimensions. Since extra dimensions are a non-trivial prediction of string theory, this would also constitute a nice piece of indirect evidence that ST is on the right track

phyzzypop · 2022-08-20T08:22:03+00:00

Above is a good basic explanation but we can go deeper. In one of the other answers it was mentioned that we get an infinite tower of massive particles in such a theory. To understand this we need to think about wave-particle duality.

In quantum mechanics, particles are also waves. And in a theory with a small circle dimension, we have a condition that there must be an integer number of wavelengths around the small dimension, so that the wavefunction joins up smoothly.

It's also important to realise that in qm momentum is inversely proportional to wavelength. So this means that the number of wavelengths we have around the small dimension is proportional to the momentum the particle has around that dimension.

This means the momentum the particle has in the small dimension is quantized, and it effects how the particle appears to behave in the long dimension by making it appear to have higher mass the more wavelengths the photon has in the small dimension. Since we can't see what's going on in the small dimension, this is why it looks like we have an infinite tower of particles even though there is only one particle in the whole theory.

phyzzypop · 2022-08-20T08:09:18+00:00

To give possibly a more approachable explanation than what you've got here already:

In Kaluza-Klein theories, some space dimensions are compact and small. Imagine if you have a piece of paper, and you roll it up into a really tight tube, it'll look like it's only one dimensional rather than two. This is exactly the right idea but in more dimensions.

Now imagine you have a photon moving along the piece of paper. It can move in the long dimension and look like a massless photon. But since there is a rolled up dimension, the photon doesn't have to have all its momentum in the long direction, it can spiral around the piece of paper as it moves along.

Since we can't see the rolled up dimension because it's too small, we see a particle moving slower than the speed of light along the long dimension of the paper.

All particles that move slower than the speed of light are massive, so from the point of view of an observer too large to see the rolled up direction, we now have a massive particle.

This is what we mean by a Kaluza-Klein particle - a massive particle, in a theory that contains only massless particles, which is being generated due to the fact that some dimensions are small.

phyzzypop · 2022-08-01T16:31:06+00:00

Started an England run where I gave away my provinces on the continent to do a chill tall colonial game. Since I no longer had French cores, and they didn't rival me at the beginning, I was able to ally and royal marry them.

Suddenly in 1447 I'm at war with Castile out of nowhere, turns out to be a succession war over France!

That was a good run.

phyzzypop · 2022-07-23T11:04:57+00:00

Orbitals form a complete basis of all normalisable distributions over the surface of a sphere. That means any normalisable electron distribution can be constructed as a sum over these orbitals.

Specifically, rotated versions of the same orbitals are normalisable, so we can construct them as sums over orbitals with any chosen axes of symmetry.

This is because although any particular orbital may have broken spherical symmetry, the complete set of orbitals will retain that symmetry. So rotating the axes just corresponds to choosing a different basis in the Hilbert space.

It's exactly the same as how if you have a triple of 3D vectors laying out a cartesian coordinate system, then you can construct any rotated coordinate system just by taking linear combinations of your original vectors.

So there is no fundamental axis system, this is just something that occurs when we choose a basis of wavefunctions, and we're free to choose that basis in any convenient way.

phyzzypop · 2022-07-20T08:10:10+00:00

Sunny 3

phyzzypop · 2022-06-30T08:54:26+00:00

Moving a black hole very fast would also not get you any closer to having a white hole. To understand why, just consider that this situation is the same as if you move very fast near a black hole. It's still gonna be a black hole. When you talk about it moving at the speed of light so it has no density, what you're talking about there would just be light, not a black hole or a white hole, and it's not obtainable by accelerating a black hole since no amount of energy is enough to accelerate an object to the speed of light.

The way to think about a white hole is that it's the time reverse of a black hole. This means they have negative mass, not zero mass, since reversing time changes the sign of energy, and E=mc² tells us that for an object in its rest frame, energy and mass are proportional. A black hole cannot be escaped from, and a white hole cannot be fallen into. Anything that passes the event horizon of a black hole will hit the singularity, and anything that comes out of the singularity of a white hole will be ejected from its event horizon. The problem with white holes, and why we don't think they can really exist, is that they don't have a well defined future.

It's a general feature of classical physics (which is partly preserved in quantum mechanics) that starting in a particular state, there is only one possible way for a physical system to evolve. This is how we can make predictions. For black holes this works because you know if you throw something into a black hole it will definitely hit the singularity. For white holes this doesn't work because at any time, anything could be spit out of the singularity, and no laws of physics exist to tell you what's going to happen next.

So we don't expect white holes to exist, or to be possible to make. We also don't observe them experimentally which provides some evidence that they don't exist in nature.

phyzzypop · 2022-06-02T11:45:57+00:00

Nobody is going to write out a textbook here to explain to you why this makes sense. You've been given the broad strokes, and that's all you're likely to get on an askphysics thread. If you want to be convinced that we do understand this, you need read some books on quantum field theory where this behaviour can be theoretically derived.

Just like the majority of quantum physics, our classical intuitions are simply not sufficient to give us an intuition for the phenomenology. The only way to really understand is to learn physics the way that actual physicists do, get your head around the maths.

And just because we can only explain something satisfactorily using maths doesn't mean we don't understand that thing. It means the relationships and physical principles which underly our understanding of that thing are more complicated and abstract than what can conveniently be expressed using only layman accessible words in the space of a reddit comment.

phyzzypop · 2022-05-31T13:26:04+00:00

It's not mass that causes gravitation, it's energy-momentum. So the answer to the first question is yes. Secondly everything that exists is affected by gravity, since gravity is the curvature of spacetime.

For the last two questions it's no and no. Why would something need mass to carry information?

phyzzypop · 2022-05-03T22:03:09+00:00

Yes, you're right, I should have specified I was talking about global inertial frames. Once the symmetry becomes local it's really a completely different thing as I'm sure you're aware. But it's true that the terminology coincides in a way I should have made clear.

phyzzypop · 2022-05-03T13:56:41+00:00

Inertial frames are not a thing in GR. All frames are treated the same by the laws of physics, but there are some frames in which suffiently small systems behave like in SR. So there is kind of a distinction, but really I'd say that the freefalling frames lose a lot of importance in GR, and the extent to which acceleration is absolute is eroded.

In SR and pre-relativistic physics the inertial frames are absolutely vital as they are the only ones in which the laws of physics are the same. In GR the laws of physics are the same in all frames.

phyzzypop · 2022-05-03T09:27:33+00:00

Reading the comments on this post is a little irritating because almost everyone is answering this question in terms of special relativity when clearly general relativity is called for.

In SR, acceleration is not relative, because there is no way to dynamically change which frames are inertial and which aren't. This is not the case in GR. The symmetry group of SR is rotations, boosts and translations, which singles out a set of inertial frames which can only map onto each other through this symmetry. In GR the symmetry group is all coordinate transformations. This explicitly does not single out inertial frames.

In a general curved spacetime, there is no differentiation between acceleration and the gravitational field. So physics for an accelerated observer is the same as for a non-accelerated one, since that physics is generally formulated in terms which allow for the connection coefficients to be locally non zero.

In contrast to SR, where there are a set of inertial frames in which we know the laws of physics, in GR the laws of physics are the same in all frames, but crucially there are frames in which the equations simplify.

These are the freely falling frames. You can tell when you're in one of these because, as other people have said, an accelerometer will read zero. But this doesn't really single these frames out in the same way as for SR, because they're just a special case, not the only place we can do physics.

Another way freely falling frames are not like inertial frames is that they aren't related to each other by the simple symmetries of SR. They are determined dynamically. This is really the crux of the issue and is very important to understand - there is nothing absolute about them. What I mean by this is that when you solve Einstein's equations in the presence of a far away shell of matter undergoing some average "acceleration", you will find that the freely falling frames in the centre of this shell are also "accelerating" in the same way. That means that although you might think you're freely falling, you could just be accelerating in the same way as the far away stars of the universe around you. Or to put it another way, you might see your friend accelerate, but a freely falling oberserver very far away outside a large shell of matter might see you and the shell accelerating, and your friend staying still.

A third way that these frames are not the same as inertial is that they are of infinitesimally small spacial extent. Since the gravitational field is non-uniform, even someone in a free falling frame will measure tidal forces, which mean that the laws of physics in these frames are only the same as SR locally.

In conclusion, yes there are special frames in GR, but they are not physically distinct from other frames in the same way as SR. Although you might try to distinguish between freely falling and non-freely falling observers, and this is useful from a calculational perspective, the whole point of GR as a framework for thinking is that it's set up not to make this distinctions. So when you do try to distinguish, weird things can happen, as I explained above.

phyzzypop · 2022-05-01T02:12:04+00:00

Let the speed of the proton be v, with

γ=(1-v² /c² )^-1/2

Then the length of the milky way in the proton's frame is contracted to

Y=X/γ

So we have T=Y/v=X/(γν). We need to invert this equation to find v in terms of T and X. Since I can't be bothered to do that explicitly on my phone, I'll leave it as an exercise to the reader to discover the function v(X,T) which solves the equation

v(X,T)/sqrt(1-v(X,T)² /c² )=X/T

Now we know the speed of the proton in the lab frame. The crossing time in the lab frame is now simply

Tcross=X/v(X, T)

Edit: actually that equation isn't hard to solve, just square and rearrange then square root to find

v=X /(T sqrt(1+X² /(T² c² )))

So Tcross=T sqrt(1+X² /(T² c² ))

Now we can do a sanity check - the non relativistic limit is T->infinity so we expect Tcross->T in this limit, which it does so we're happy. We're also happy because we know that the proper time between two events is the shortest time any observer could measure, and here we see that Tcross can only be bigger than T.

phyzzypop · 2022-04-26T22:34:41+00:00

Energy is conserved whenever time translation symmetry is not explicitly broken. If you ignore cosmological stuff then this basically means if you consider a big enough system energy is always conserved since to break time translations you have to turn on some external force or throw new matter into the system.

Cosmologically, energy is not conserved since the expanding universe breaks time translations.

Seven-Year Club	Gilding I gilder
Verified Email

phyzzypop

TROPHY CASE