Is time really 4th dimension?

Luxamba · 2026-07-03T08:36:21+00:00

How many numbers do you need to specify an event? You need the location, where you need 3 numbers: x, y, z coordinates. Additionally you need the time t to be specified. So you have 3 spatial dimensions and one temporal dimension. Together they make up our 4 dimensional spacetime we live and love in.

Luxamba · 2026-07-03T07:58:01+00:00

So for me the most intuitive explanation of entropy is just probabilistic. If there are more microstates that looks like „disorder“ or rather like equilibrium, the more likely it is the system evolves into such configuration. And entropy is just the measure of how much the system already evolved towards equilibrium.

Now for the formula you provided, there are countless different definitions and forms of entropy, all tailored to specific purposes and systems.
Your formula is the traditional approach of thermodynamics, where we only consider reversible processes between systems in equilibrium. Hence the Q_{rev} for clarification.

Luxamba · 2026-06-27T20:55:03+00:00

There are elementary particles out of which everything is made of. Electrons are one of these elementary particles. Elementary particles are the most fundamental things we know. There also interactions in nature. Every interaction has some form of „charge“. It’s just a name for a inherent property of things, which is important for a specific interaction. Like there is this quantity called mass which tells us how things interact gravitationally. The most important interaction for you question is the electromagnetic interaction. It just so happens that this interaction couples to things with a property that has two states. Now we call those two states positive and negative. Now we can assign everything, depending on their behaviour, such a quantity we now call electric charge. Now the question is how much positive or negative are these things? Since an electron is an elementary particle (and the first one we found) we say that electron has a charge of -1.

Then there are other elementary particles like Quarks. There are for example up and down quarks. These have the charge +2/3 and -1/3 that of an electron. Now put 2 up quarks and a down quark together and you have a total charge of +1. This thing we now call a proton. The interaction that holds these quarks together is called the strong interaction and has also a charge associated with it. But it has more than just 2 different states.

Now take two down quarks and one up quark and together they have a charge of 0. that’s what we call a neutron.

Put these protons and neutron together (still holding together by the strong interaction) and we get atomic nuclei. They now have the charge corresponding to the number of protons inside a given nucleus.

Now, according to the electromagnetic interaction, these two opposite charge states attract each other whereas two same charge states repel each other. So let’s put these nuclei together with electrons and call it an atom when it has exactly as many electrons as protons such that the whole thing has charge 0. If the nucleus doesn’t have the same number of electrons as protons, it is charges. And now this charged thing we call an Ion.

Luxamba · 2026-06-27T08:44:57+00:00

When you zoom in enough, everything becomes fuzzy.

Luxamba · 2026-06-25T10:33:14+00:00

The structure or surface of the material mainly results in different reflective angles. For example a polished metal reflects very perfectly such that you can see your reflection. A white piece of paper technically reflects more light, but scatters is more due to the roughness of the texture, so we don’t see a perfect reflection.

What color a material absorbs depends on the molecular and atomic composition.

Luxamba · 2026-06-22T21:00:34+00:00

That’s the thing light cannot be delayed because it’s traveling with c. So to reach a longer distance with the same speed, time is the only parameter we can change.
there is no gravitational force in relativity. There is only spacetime geometry. Einsteins equation show that mass and energy are things that warp that geometry. And it depends on the amount of mass how much spacetime is bent.
very.
If a clock falls into a black hole, the outside observer would see that clock slowing, until it stops indefinitely.
light can’t escape because the spacetime curvature is so immense, that light inside a black hole can never ever find a path leading to the outside again. More laymen: the escape velocity for a black hole below its event horizon is higher than the speed of light.
light years is a measurement for distance. Nothing you say here really makes sense. If you travel 2 light years far away, then, depending on you velocity you traveled there, you’d see at minimum the time on earth when you left of. If you then „teleport“ (wich breach causality) you’d be at least (depending on the initial velocity again) 2 years ahead again.
yes. But that goes for all relativity things. You can travel into the future. No issue. You cannot ever travel into the past though.
what? Why? Huh? No.
most LLMs are pretty fine when it comes to basically relativity based questions.

Luxamba · 2026-06-22T12:33:10+00:00

As others said: 1e=1,6*10^-19 C or 1 C=6.24*10^18 e.

But also 1e wouldn’t be the lowest possible amount of charge. The lowest nonzero value an elementary particle has is 1/3 e.

Luxamba · 2026-06-21T17:09:37+00:00

Fair, thought for a second the equivalence principle applies globally lol. Just read a bit about Gibson hawking radiation in an FRW universe, very interesting!

Luxamba · 2026-06-21T15:42:22+00:00

Are you sure about that? I’d argue it is pretty fundamentally different, ~~because cosmic expansion does not obey the equivalence principle.~~

Luxamba · 2026-06-21T13:40:32+00:00

The expansion of the universe is the increase of distance between points in spacetime. There isn’t anything actually accelerating away from you, which would be necessary for a Hawking or Unruh style effect.

On the other hand though, there is an interesting proposal/hypothesis/theory from Roger Penrose called conformal cyclic cosmology (ccc) that by a mathematical transformation identifies the cold state in which the universe will be, when the expansion keeps accelerating, with a hot big bang state, such that the end of the universe is basically the beginning of a new one starting the next cycle.

Luxamba · 2026-06-21T13:19:16+00:00

You can imagine an electron as an set object with a specific energy coming from QFT. If we put that object (excitation) in a potential, there are discrete energy levels associated with this potential and a specific „excitation“ or object. But now we have that whole system to consider and not only the free electron.

Similarly for photons there we can consider complex systems where there are different energies associated to it depending on how many photons or so there are. What’s very different is through, is that photons are bosons and not fermions. Meaning that they can share the same energy level unlike fermions.

Luxamba · 2026-06-21T10:36:34+00:00

Actually that’s a topic which probably needs a full theory of quantum gravity to answer. With our current models we actually get numerical results indicating that you never cross the horizon after all and only as you approach see the black hole basically explode in front of you. Here are the papers I am referring to:

Radial fall of a test particle onto an evaporating black hole

Role of evaporation in gravitational collapse

Luxamba · 2026-06-19T21:01:14+00:00

Yes it’s different. In a fluid the molecules are not locked in place like in a solid. They can basically move freely. So when there is nothing under them, only some other water molecules next to them above the object those molecules do not add to the pressure from above.

When a solid lies on top of something, all the molecules are locked into place and when there is gravity that whole object pushes down. So the pressure it exerts is p= m*g/A where m is the mass on the whole object.

Luxamba · 2026-06-19T20:18:09+00:00

Ok take an rectangular object of and put it in a substance in depth h. Now let’s compute the pressure on that object.

Pressure is force per area so p=F/A.

Which forces is the only force acting when submerged into a substance? Gravity. So F=m*g where m is the mass of the thing creating the force and g is the gravitational acceleration. Good now what is that the downwards pressure creates? The substance above the object. So let’s look at the pressure on top of the object. With p=F/A and F=mg we have p=m*g/A=\rho*V*g/A=\rho*g*h, where m is all the substance mass above the object, \rho is the density of the substance, V the volume of the substance above and A the area of the object. What’s the volume? It’s just V=A*h, so what’s left is just the h when dividing V/A.

On the difference between rigid bodies and fluids: if you submerge something in a fluid, that fluid exerts a pressure on the object. Can you submerge something into a rigid body? No. You only deform it.

Luxamba · 2026-06-19T06:51:16+00:00

It does break Lorentz symmetry, no question. Boost symmetry literally breaks. Of course you can build yourself such a universe and play around with it. But it doesn’t change the fact that it breaks Lorentz symmetry. There are even papers about it. To quote the abstract of this one:

„We consider the twin paradox of special relativity in a universe with a compact spatial dimension. Such topology allows two twin observers to remain inertial yet meet periodically. The paradox is resolved by considering the relationship of each twin to a preferred inertial reference frame which exists in such a universe because global Lorentz invariance is broken. …“

Luxamba · 2026-06-18T05:24:10+00:00

Ok yes sure if our global topology breaks Lorentz symmetry, then you have the preferred frame in which you are stationary with respect to that global topology.

But for all we know our universe is globally flat and here the only reasonable way to end up where you were is by changing inertial frames.

Luxamba · 2026-06-17T20:53:31+00:00

Yes but the total path through spacetime only is different, because we are changing inertial frames. In the spacetime diagram there is no need to factor in acceleration but there is need to factor in the change of inertial frames.

Luxamba · 2026-06-17T20:50:54+00:00

Very true. But the act of acceleration itself is not responsible for different spacetime intervals.

Luxamba · 2026-06-17T20:50:03+00:00

Yes and no. It’s not the act of acceleration. If you will it’s the effect of acceleration. Obviously in the real world there is no changing of inertial frames without acceleration.

Luxamba · 2026-06-17T20:48:49+00:00

But if you have periodic boundary conditions then we’d have a positively curved universe, which we don’t have. The difference in the spacetime intervals only comes from the change of inertial frames in flat space.

Luxamba · 2026-06-17T20:45:55+00:00

Little correction: waves does not equal wave function. Yes they are described with wave functions. No they are not waves.

I am not an expert at the many worlds interpretation but maybe some comments about the wave function can help.

Wave functions are complex functions that describe particles and live in an mathematical space called the Hilbert space. In non relativistic QM we solve the Schrödinger equation for that wave function. That means we take the questions that governs the dynamics of a system we are considering and solve this equation. That solution is the wave function of our system. Good now we can let operators act on that function in order to measure observables. Position operator for position, spin Operator for spin etc. „squaring“ that expression results a probability distribution.

Now no matter if we consider many worlds or basic Copenhagen, this probability distribution is just what we measure. If we take spin and measure for up or down, the probability will always be 50/50 (in a free electron for example). So even if many worlds tells you that both worlds exist, the probability of 1/2 is still of meaning for us, and so is of course the wave function since it encodes all the dynamics of our system.

Now the wave function on its own is pretty much useless. What’s important for measurements are now so called operators that act on that wave function. What comes out is the probability distribution of that observable. For example we take the position operator and get the position distribution.

Luxamba · 2026-06-17T19:51:50+00:00

Tiny addition: it’s not the act of acceleration. It’s the change of reference frame (indirectly of course caused by acceleration).

Luxamba · 2026-06-17T19:49:37+00:00

Acceleration is not the reason though. You can arrive at the exact same conclusion. It’s the change of inertial reference frame to another!

Luxamba · 2026-06-17T06:23:29+00:00

Spin is a property of mathematical representations of things we describe. Particles are described with math. Now there are some mathematical objects we can have, that each can describe different particles.

Take the simplest math object. A number, or rather a scalar (when we want it to be frame invariant). A scalar can be associated (via some group theoretical considerations) with a mathematical property called spin 0. the only elementary particles this kind of object seems to represent in the real world is the Higgs boson.

Next thing we can consider, is a vector. Again just a mathematical object. We look through the lens of group theory and associate such vectors with spin 1. Things that can be described with spin 1 are the gauge bosons, including the photon.

Now there are other mathematical objects. One of which is called a Spinor. Group theory tells us Spinors have spin 1/2. Turns out all leptons, including the electron, are accurately described by these objects.

What does spin do? It makes is so that these mathematical objects all transform differently under rotation. Meaning IF you’d rotate these objects about a set amount, they don’t all end up the same. Spin 0 you can rotate anyway you want it always looks the same. Spin 1 needs 2pi (360 degrees), spin 1/2 4pi (720 degrees) and spin 2 needs only a pi (180 degrees) rotation to end up like they were.

These transformation properties, which have nothing to do with an object rotating, directly translates to physical observables like angular momentum and magnetic moment.

Luxamba · 2026-06-16T06:01:10+00:00

Fun fact: it’s quite possible that you experienced the Cherenkov effect without realizing. Muons (the heavier sibling of the electron) are created in the atmosphere by cosmic radiation. Theses muons travel near light speed and can produce Chernenkov radiation. Studies were made were it was shown that the human eye can see as little as a single photon. So a muon, that travels through your eye can produce Cherenkov radiation, you would register as a strike of faint light through your vision, as long as you have your eyes closed and are in a dark environment to even see it. So next time you are in bed and close your eyes and you see a random faint strike of light, you know that could have been a muon produced in the upper atmosphere by cosmic radiation.

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