We all know the derivation of the path integral by a transition amplitude (or from a trace) by chopping time into discrete steps and inserting a basis at each step, leading to a Trotter product. But the measure itself is ill-defined in the limit.

How does one justify its use from a mathematical perspectice?

I have currently 3 points of view (not very precisely formulated, but you get the idea):

1. It lives actually on an underlying Lattice (or a range of lattices) and we should first calculate it on there and then take the continuum limit.

2. The initial way is ill-defined to begin with and the RG flow is actually the proper starting point.

3. Here I need euclidean: The whole concept is probabilistic anyway and just like there is an associated distribution for a random variable, there is one for the function spaces/stochastic processes.

Please share your thoughts, since I would love to read of more reasons and maybe more rigour :))

Comment: The Feynman argument that you split your „space into (double) slit experiments“ is for the derivation, but not an answer for the limit.

Disclaimer: I am in NO WAY a quantum expert, or even a beginner. Take whatever i say with a grain of salt. ALSO, i know FTL can't exist. I just want to know why what i wrote below won't work

I think(?) I have a setup that THEORITICALLY can facilitate FTL Information transfer. Obviously the physical problems of actually getting entangled particles so far apart that light speed becomes a factor is the biggest issue, but ignoring that, this is the method. Please prove me wrong, cause there is no way such a simple thing can exist and break the speed limit

Assumption: (please debunk these if they are wrong, i did like 15 min of googling(or binging if we wanna be exact) and i don't see(?) any reason why these can be wrong)

1: Entanglement can exist at long distances(so one half of a qubit pair on earth and other half on mars)

2: If you observe one half of a entangled pair of particles(qubits from now on), its other half INSTANTLY falls out of entanglement, and loses any property that arises from entanglement

3: Qubits, those used in quantum computers, must be entangled to be able to run simultaneous calculations(parrallisms)

4: If said entanglement of Qubits break, the quantum computer's calculations break and/or stop performing at peak speeds.

So why can't this exist:

Alice and Bob want to exchange a signal. They make a entangled pair of Qubits,

Then one half of the qubit pair is constantly running simultaneous calculations, or any other thing/operation that only a entangled half of a pair of entangled particles can run. A computer is kept always looking at the OUTCOMES of the calculations the qubit is doing(not the qubit itself), and will sound an alarm in Alice's lab on Earth(thats where this half of the machine is) if it stops/deviates/slows down

The 2nd half of the pair is kept trapped under a mechanism that can observe it with the press of a button.

So Bob takes the observing button(2nd half) and goes to mars. Then, Can he, with the press of that button, instantly ring the alarm at Alice's Lab?

If the above is not blatantly wrong, then, can we send hundreds of these qubit halfs(kinda as ammunition/tickets) upto Mars with Bob, and he can use Morse Code to ring the alarm at set times, so like BEEP BEEP BEEP BEEEEEEEEEEEEEEP. BEEP BEEEEEEEEP? and then you can scale this upto practically internet leves? with Binary and all?

This bypasses the problem of the spin, since we are not actually looking at the qubit itself, we are just looking at the emergent properties, and we don't need to send any instructions using classical methods since we have it predetermined?

I tried this with both Co-Pilot and ChatGPT, and both either just bug out(as in it doesn't understand its contradictions) or just choose to forget or just stop answering and then have amnesia

Edit: so apparently the calculations I was mentioning is not possible on a single qubit. But we know that quantum computers exist, so can we make a waaay bigger but more cumbersome method of basically using a quantum computer but then breaking the superposition from far away?

So I understand that in order for energy to be conserved as our universe splits, it splits into another skinnier universe and ours also gets skinnier, why isn’t this noticeable to us? For this idea to be true it must mean that the universe is constantly splitting? And if our universe is constantly splitting and thus constantly getting skinnier why haven’t we noticed?? I clearly do not understand

I have no actual credentials in quantum physics or actual basic physics for that matter. I've been teaching myself going back from the beginning when they first made up quantum physics and learning about the theories, laws, formulas, etc. Idk what the guys name is but he brought made up string theory. How do we not have endless dimensions we can't see? For every subatomic particle it has to be bouncing off a geometrical shape because if it wasnt it would then change the makeup of the entire nucleus, atom, molecule etc. I'm just a welder with a background in metallurgy. For steel the atoms bond together making a crystalline structure. For example, Ferrite (Alpha Iron) has a BBC unit cell, on a (110)plane, has 48 slip systems which has 12 planes, 4directions. When we cut into a piece of metal/element and view it close up they all have different types of crystalline structures but all connecting to where it is a BBC, FCC, HCP, etc. Why wouldnt it be the same if someone was able to cut open any subatomic particle. There has to be a geometrical pattern the string is vibrating off of. If someone were to make up a formula to figure out the coordinates each time the string vibrated. You could graph the coordinates onto a x,y,z graph. How we do with figuring out the structure within elements. It would show the geometrical shape inside the subatomic particle. That it's not randomly bouncing around. Proving that we live in a world with endless dimensions that we just cannot see. Like I said before I am not going into quantum physics. I'm just a machinist, welder, and understand basic physics do to understanding how and why machines work and how to build tthem. If anyone could tell me if this is feasible or why it wouldnt work that would be great

I'm not a physicist, mathematician, or going to school for quantum physics/mechanics. I just like to learn and study in my own. For dark matter how do we not have it? Obviously I know its everywhere in space. If CERN made an electromagnetic field with a tunnel and they throw in photons moving at the speed of light or any subatomic particle for that matter. The second they collided together gravitons and other particles would have been expelled. Dark matter has a force so wouldnt they have been able to collect the data showing that their is force proving that theyve created dark matter?

Hello, I've found arXiv email update format quite unreadable so I've built a simple webpage that presents last day submissions (https://arxiv.org/list/quant-ph/new) in a hopefully cleaner way. Below is the link:

https://arxiv.archeota.org/

It is free and I do not plan to put this behind any sort of paywall. In future I'd like to add more features to help researches and hobbyists increase signal to noise ratio when going through the papers. I'd be glad if you could drop me a DM (or simply a comment below) what features you'd like to see added.

In a typical Compton scattering experiment, we assume an incident photon with a very well-defined momentum, in our calculations. That is, we talk about a monochromatic incident radiation. But in reality, do photons even have well-defined momentum? Aren't they always associated with a wave packet with a spread in k no matter how narrow? Perfect monochromatic radiation do not exist in reality as far I understand(Such a thing would have to have an infinite extent in space). So, the calculations are therefore very much idealized.

So, the question is what exactly happens in a "real" Compton scattering experiment with incident photons with a spread in momentum values?

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Context: THE STEP POTENTIAL (ENERGY LESS THAN STEP HEIGHT)

Did anyone study this portion from Resnick Eisberg's Quantum Mechanics book?

So I didn't understand what exactly is this experiment trying to do. Can anyone elaborate on this? I am extremely sorry I have no clue on exactly how elaborate exactly what thing I don't understand. I am confused by the whole damn thing...

Things might sound bogus but let me try to write some of my problems...

For example, what do they mean by localizing the particle? Are they creating a localized wavefunction in the region x>0 or what? And if so, why do they need to create this localization in such a small range? The region V=V_0 literally extends to +infinity... Why are they even referring to the result of a different distribution (The statement "Since the probability density for x > 0 is appreciable only in a range of length delx...". This is obtained from the calculation of energy definite eigenstates/eigenfunctions/wavefunctions which are, by the way, not physically realizable as they cannot be normalized...) ? And where's the part of mathematics which tells that this localization is in the x>0 region? I seriously don't understand this. The author has missed important details. See, I am too confused.

Also then how does an uncertainty of V_0-E ensure the E cannot be said to be definitely less than V_0. We have no info regarding the distribution of E... Imagine V_0-E to be sufficiently small compared to V_0. Then I can definitely have a distribution with a standard deviation of V_0-E which is well below V_0(well within the range [0,V_0]), isn't it? The author didn't provide details regarding the positioning of the distribution. How do I know that the distribution is positioned in such a way that an uncertainty of V_0-E takes it beyond V_0...?

I guess my elaboration is too confusing too... But if anybody could help?

I just completely bombed my quantum mechanics final. It was a graduate level class that somewhat follows the second half of Sakurai, but the professor taught scattering, relativity, and basic fields from his own notes. I felt I had a pretty good understanding of QM, until we covered those three topics which I didn’t understand a lick of. Now I don’t feel like thinking about quantum ever again, let alone taking a QFT course.

I guess my question is, are those topics (scattering, relativity, intro to QFT) really just THAT much harder than the rest of QM? I want to take QFT but not if the math is going to be at a level I have no chance of comprehending, which is how I’ve felt the past two months in my class.

If anybody’s been in this situation before I would love to hear your story.

hi! i just study the quantum harmonic oscillator and i want to understand the idea behind this concept and how is it represented in reality

In the past, phenomena like the motion of celestial bodies were considered random until explained by scientific theories. However, the question arises: how can we be certain of quantum randomness?

While historical examples showcase our evolving understanding, what distinguishes quantum randomness as truly unpredictable? Looking for insights and discussions on this intriguing topic.

This can sound like a very silly question for you but as a biologist, it’s been puzzling my mind. Any nudge in the right direction is well appreciated!

I have a large interest in quantum physics, not through studying in a relevant course, but through personal hobbies/interests, most documentaries impress me, however I find when I want to discuss particular things, or reword it in a bid to explain it to someone else I get stumped, on basic terminology and I find it difficult to explain what I mean.

Anyways in terms of vocabulary appropriate to the subject can anyone recommend me a good book for starters interested in the subject, if anyone is studying a relevant course that knows of a good guide book, course book, that would be awesome, thanks:)!!.

Modern physics traditionally posits that the boundary of the universe is found at the largest scales, dating back to the Planck epoch, seconds after the Big Bang. During this epoch, the universe is theorized to have been nearly two-dimensional—a property inferred from the progressive two-dimensional appearance of the universe as one looks back to earlier times closer to the Big Bang. This correlation is illustrated by the Cosmic Microwave Background (CMB), which, despite depicting the universe 380,000 years after the Big Bang, supports the notion that at greater scales (and thus closer in time to the Big Bang), the universe appears almost two-dimensional. This compelling argument suggests that the universe's boundary exists on these vast scales.

However, this initial boundary, linked to the universe's very first moments, existed 13.8 billion years ago. This raises a question: Is there a present-day boundary? What if this boundary is located at today's Planck scales, just as it was at the very beginning of the universe when everything was condensed to Planck scales? (basically the boundary has always been on the planck scales)

According to the holographic principle, the information content of a region of space can be described by a theory on its boundary. Applying this principle and the AdS/CFT correspondence, will it be possible to relate a D-dimensional bulk spacetime to a (D-1)-dimensional boundary CFT at the Planck scale?

This suggests that the Planck scale could serve as a natural boundary for the universe, with the effective boundary dimension reducing to two. Such a boundary would be everywhere, existing on the planck scales in every "point" of 3dimensional space.

What are your thoughts on this idea? Could the Planck scale really be a viable candidate for the universe's present-day boundary?

Sorry... maybe a laymen's question but...

If a photon's energy is E = (Planck Const * Freq) and it's momentum is p = (Planck Const * wavelength), then why is the energy of the photon not considered in Einstein's E^2 = pc^2 + (mc^2)^2?

The mass of a photon = 0 and that cancels the latter part of the equation.

The momentum is pc^2.

So where is the photon's energy (i.e., (Planck Const * Freq))?

Shouldn't (Planck Const * Freq)^2 = pc^2 + (mc^2)^2 ?

But with mass = 0... that would make E = (Planck Const * Freq)^2 = pc^2 !! And that is messed up :-)

Maybe we are talking about different kinds of energy (i.e., Photon v Mass)?

I'm in a dilemma right now. I'm ending my second year of college right now and I'm majoring in mathematics and have recently declared a second major in chemistry. I always thought about making my second major physics, but I was slightly deterred because I enjoyed chemistry more than physics in high school. I'm only finishing up gen chem I, but I can't help but feel like maybe this isn't for me. Or maybe it's too early to tell.

I've been finding chemistry boring thus far. It's not that it's too "easy," but it just feels so...random? Arbitrary? I don't like how you can't really predict chemical reactions or bonds. Obviously at this level I can to some degree, but once it gets too complex (which happens fairly quickly) I have no idea what to do. I have to blindly trust whatever my professor and textbook are saying.

But I recently reached the chapter about quantum theory and the electronic structure of atoms, and I'm finally enjoying it. I feel like this is what I really love. Maybe this is coming from the math purist in me, but I like how we build off of more fundamental concepts, even if they start off from observational findings.

On the other hand, I also partially dislike physics. Classical physics feels like dry math to me. I don't know why I never found it interesting. I do have to take calculus based mechanics and E&M, so maybe that will be more interesting? I have no idea.

Either way. I don't have much time to decide which of the two is better for me. Can a bachelor's in chemistry lead to quantum mechanics, say, as a Master's/PhD, especially with a strong background in math? Or is physics better for that? It seems that they both eventually converge, if I go along the right path.

I have heard that the Many Worlds Interpretation is a bit popular, and that eternalism is also a bit popular. But I was wondering if there was some overlap and how much there was a response to criticism of these ideas.

This is really a question that sits at the intersection of quantum and nuclear physics.

Does Breit-wigner single resonance formula with h-bar instead of \sigma exist? Does anyone know where I could find it?

Or is there a derivation going from de Broglie wavelength to microscopic cross section?

Thanks

Premise: not very technical post and more of a suggestiveness, stop here if you don't want to be annoyed by the probable insignificance of the content.

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Roughly speaking, general relativity predicts that when an observer in a low-gravity environment observes an object in a high-gravity one, the observer will see time pass more slowly for the object.

When an observer in a high-gravity environment observes an object in a low-gravity environment, the observer will see time pass more rapidly for the object.

For example, from an observer’s point of view, as an object approaches the event horizon of a black hole (very high gravitational effects), time will appear to slow down for the object to the point that the external observer will never see the object actually cross the event horizon (even if, from the object's own perspective and time frame of reference, it has already "fallen into the black hole singularity").

On the other hand, from an observer's point of view, as the object approaches the size of a photon (almost irrelevant gravitational effect), time will speed up for the object to the point the observer will never be able to measure the position and the velocity of the object at the same time , and the object will appear in a superposition of states (even if, from the object's own perspective and time frame of reference, it might always be a specific place and state).

What is a measurement? What is the measurement problem? In QM measurement might simply mean to unify the perspective and the time frame of reference of both the observer/measurement device and the object/particle.

To achieve some kind of artificial, aproximate "temporal synchronization" between the observer and the object. When we measure a particle (with some measurement device), we artificially put ourselves and a particle in a single time frame of reference (our, from our perspective). This is why a particle is always measured in a specific position or with a specific spin, with "classical features"so to speak, and not in a superposition.

By measuring, we impose our time frame of reference upon a particle.

All the oddities of QM might not be inherent in the ‘quantum world’, but oddities born from relating the two worlds, the classical and the quantum, and especially their respective, very different, time frame of reference.

Stupid and probably wrong example: If my smallest possible conceivable unit of time is 𝑋, and within 𝑋, only one note at the time can be played, while for you, the smallest possible unit of time is 0.1𝑋, allowing you to play one note every 0.1𝑋, then from my tempo/perspective (where I cannot go below 𝑋), I will inevitably be forced to conceive and describe your music as a series of chord, a superposition of sounds.

Only by making you play your music at my tempo of X, I will be able to hear every a single note at a time. But in doing so, I will never be able to apprehend the symphony in its entirety (Heisenberg principle).

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Sorry, I go home now.

I was watching a veritasium video about quantum computers (How Quantum Computers Break The Internet... Starting Now) and he mentioned

...but you can't simply read out this superposition. When you make a measurement, you only get a single value from the superposition basically at random, and all the other information is lost. So in order to harness the power of a quantum computer, you need a smart way to convert a superposition of states into one that contains only the information you want. This is an incredibly difficult task, which is why for most applications, quantum computers are useless...

this is the direct quote from the video. noticeably to my eyes, he does not say impossible, simply extremely difficult. My mind went to two ideas then, either what he thought when writing the video was "best not to say impossible in case it ever happens" or "some people theorized ways to convert the information but it's all theoretical so I won't mention it."

It got me thinking and brought me here: is there possible ways for superposition to be converted into desired outputs? maybe have multiple quantum computers do the same work and compare or something? I'm curious and I think it's really cool but the closest i get to physics is some basic electronics calculations with resistors and voltages lol.

thanks for explaining if you can! :)

hello, i recently watched interstellar and it interested me a lot, I have a lot of curiosity in quantum physics and don't know where to learn it. i am a business major and want to be educated and learn. please drop a book or something I can learn from and if your a quantum physicist please message me. Thank you.