Space is the boundless three-dimensional extent in which objects and events have relative position and direction. In classical physics, physical space is often conceived in three linear dimensions, although modern physicists usually consider it, with time, to be part of a boundless four-dimensional continuum known as spacetime. The concept of space is considered to be of fundamental importance to an understanding of the physical universe. However, disagreement continues between philosophers over whether it is itself an entity, a relationship between entities, or part of a conceptual framework.
Debates concerning the nature, essence and the mode of existence of space date back to antiquity; namely, to treatises like the Timaeus of Plato, or Socrates in his reflections on what the Greeks called khôra (i.e. "space"), or in the Physics of Aristotle (Book IV, Delta) in the definition of topos (i.e. place), or in the later "geometrical conception of place" as "space qua extension" in the Discourse on Place (Qawl fi al-Makan) of the 11th-century Arab polymath Alhazen. Many of these classical philosophical questions were discussed in the Renaissance and then reformulated in the 17th century, particularly during the early development of classical mechanics. In Isaac Newton's view, space was absolute—in the sense that it existed permanently and independently of whether there was any matter in the space. Other natural philosophers, notably Gottfried Leibniz, thought instead that space was in fact a collection of relations between objects, given by their distance and direction from one another. In the 18th century, the philosopher and theologian George Berkeley attempted to refute the "visibility of spatial depth" in his Essay Towards a New Theory of Vision. Later, the metaphysician Immanuel Kant said that the concepts of space and time are not empirical ones derived from experiences of the outside world—they are elements of an already given systematic framework that humans possess and use to structure all experiences. Kant referred to the experience of "space" in his Critique of Pure Reason as being a subjective "pure a priori form of intuition".
In the 19th and 20th centuries mathematicians began to examine geometries that are non-Euclidean, in which space is conceived as curved, rather than flat. According to Albert Einstein's theory of general relativity, space around gravitational fields deviates from Euclidean space. Experimental tests of general relativity have confirmed that non-Euclidean geometries provide a better model for the shape of space.
Science fiction is of course full of all kind of futuristic ideas about interstellar space travel and ways of propulsion, some more physically plausible then others.
But within the current realm of what is physical possible, what could interstellar space travel be like?
First you need a source...
If an infinite amount of energy were available to create the lift mechanism for a space launch. What would be required to fire a 200lb object into low Earth orbit(160km) after speeding it up in a way similar to how the large hadron collider speeds up a particle.
Assuming the launch vehicle...
I attatched an example plot where I created the histogram for the differential distribution with respect to the energy of the d-quark produced in the scattering process. My conception is that the phase space generator can "decide" how much of the available energy it assigns to the respective...
What do you guys think of this soberly elegant proposal by Sean Carroll?
Reality as a Vector in Hilbert Space
Fundamental reality lives in Hilbert space and everything else (space, fields, particles...) is emergent. Seems to me a step in the right conceptual direction.
So carbon nanotubes are incredible. Is a macrtube a possibility? If we stretched one out for centuries, and landed it on another planet, would it transfer gravity?
Hi,
How do I left align the text below? Also, how do I create vertical spaces above and below the line stating "Subbing the following expressions..."? Could you please help me with it?To derive 14(ii) m_{0} \gamma^{2} \frac{d^{2} y}{d t^{2}}=e E_{y}^{\prime} from 13(ii) m_{0} \frac{d^{2}...
Summary:: Given a known closed space/apparatus ( e.g. constant volume, pressure, density, current, temperature, voltage, spark gap distance - let me know if I missed something) how would I compute the change in gas temperature.
Hello,
Given a known closed space/apparatus ( e.g. constant...
Is the following a correct demonstration that quantum mechanics can be done in a real vector space?
If you simply stack the entries of density matrices into a column vector, then the expression ##\textrm{Tr}(AB^\dagger)## is the same as the dot product in a complex vector space (Frobenius inner...
Hello, I have problems with this exercise
Let $(X,\mathcal{B} , \mu)$ a measurement space, consider
$\bar{\mathcal{B}} = \{ A \subseteq{X} \; : \; A\cap{B} \in \mathcal{B}$ for all that satisfies $\mu(B) < \infty \}$, and
for $A \in \bar{\mathcal{B}}$ define
$\bar{\mu}(A) = \left \{...
It is said that: It is not possible to write a position vector in a curved space time. What is the reason?
How can one describe a general vector in a curved space time?
Can you please suggest a good textbook or an article which explains this aspect?
I consider three material points O, O', M, in uniform rectilinear motion in a common direction, so that in relation to the point O, the points O' and M move in the same direction with the constant velocities v and u (u>v>0). Assuming that at the initial moment (t0=0), the points O, O', M were in...
From "standard" formula we have that the gravity acceleration a = GM/r^2 and that the Schwarzschild radius rs = 2 GM / c^2
Is it possible to compute the gravity acceleration at Schwarzschild radius putting r = rs?
In this case we will have a = c^4 / (4GM) This mean that a very very...
So I am a layman in physics, I admit I am trying to grasp big ideas piecemeal via articles, wikipedia and YouTube. I don't pretend to be educated in this regard but I am curious and willing to learn!
The idea of the multiverse intrigues me. Sidestepping for a second the fact that the idea has...
From: https://en.wikipedia.org/wiki/Mathematical_formulation_of_quantum_mechanics
In the section, "Effect of measurement on the state" (aka Postulate 5), it says:
If this is just a fancy way of talking about our very own space in which we live (ie, in which an observation has been made), then...
Since it asks for the time evolution of the wavefunction in the momentum space, I write : ##\tilde{\Psi}(k,t) = < p|U(t,t_{0})|\Psi> = < U^\dagger(t,t_{0})p|\Psi>##
Since ##U(t,t_{0})^\dagger = e^{\frac{i}{\hbar}\frac{\hat{p^2}t}{2m}}##, the above equation becomes
##\tilde{\Psi}(k,t) =...
I've been trying for a very long time to show that the following integral:
$$ I_D=2{\displaystyle \int} \, {\displaystyle \prod_{i=1}^3} d \Pi_i \, (2\pi
)^4\delta^4(p_H-p_L-p_R) |{\cal M}({e_L}^c e_R \leftrightarrow h^*)|^2
f_{L}^0f_{R}^0(1+f_{H}^0). $$
can be reduced to one dimension:
$$
I_D...
It's probably more kind of math question.
I consider a wave function of a harmonic oscillator, i.e. a particle in a parabolic well of potential. We know that the Hamiltonian is a Hermitian operator, and so its eigenstates constitute a full basis in the Hilbert space of the wave function states...
I first saw note of this about a week ago and I don't think it has gotten enough attention:
https://www.cnn.com/2021/06/30/opinions/hubble-telescope-glitch-opinion-lincoln/index.html
While I don't want to eulogize too soon, I'm wondering where the HST ranks in the annals of the most...
Please help me understand why this is a concept that has not been studied? The laser sail is really the only info I can find in this area using a laser from a fixed source. Using liquid nitrogen to cool the mirrors and reflecting lasers off of them for propulsion. I'm a Doctor of Pharmaceutical...
Summary:: You have a spacecraft the size of a cube (2x2x2 m^3, m=3000 kg. It has 24 thrusters (2N each) and one main engine. For preparing your spacecraft for maneuvers, you want to rotate by 180 degrees. For the rotation, you'll use n=4 attitude thrusters per burn.
What am I doing wrong...
Electrostatic energy involves a volume integral and a surface integral
The question is how to apply this formula to a finite space in which case the 1st term (surface integral) won't vanish. Let's apply to a capacitor and enclose the capacitor by a closed surface. Calculate the energy integral...
Hi PF, I've one question about vector spaces. There is only one way to define the operations of a vector space? For example if V is a vector space there is other way to define their operations like scalar multiplication or the sums of their elements and that the result is also a vector space?
I can calculate the fields generated by the cylinder and the wire but I don't know how to calculate their vector sum to evaluate it at point A.
Cylinder field inside: ρR^2/2rε
Cylinder field outside: ρr/2ε
Field generated by the wire: λ/2πr
I should break the fields into components but I don't...
Hi and thank you for answering questions on complex subjects like this. I’m a non-scientist who is jealous of your brain capacity!
Recently, in a discussion with a chemist, he said the particles appearing from nothing might have been the initial cause of the universe. I’m familiar with the...
I've heard it and I've read* it before, so I just want to make sure I understand this so I never have to wonder about it again.
So, are tidal forces exactly curvature of space?
Here's why I think the answer to that is yes:
.I've seen a spacetime interval equation which has a coefficient on...
I read this in the wiki article about Wick rotation:
Note, however, that the Wick rotation cannot be viewed as a rotation on a complex vector space that is equipped with the conventional norm and metric induced by the inner product, as in this case the rotation would cancel out and have no...
Let's play this game, let's assume the infinite Hilbert Space, the operators and all the modern machinery introduced by Von Neuman were not allowed.
How would be the formalism?
Thanks
Hi,
I was reading the following article.
Source: https://www.forbes.com/sites/startswithabang/2019/01/31/dark-energy-may-not-be-a-constant-which-would-lead-to-a-revolution-in-physics
How come the density of dark energy remains constant? Yes, if it's intrinsic to the space itself and more...
Freshly Made Plutonium From Outer Space Found On Ocean Floor
May 13, 2021
[discussion split off from here: https://www.physicsforums.com/threads/what-is-theoretically-the-heaviest-isotope-that-the-r-process-could-produce.1000056/ ]
The Earth is spinning and orbiting the Sun, and that is orbiting the center of the Milky Way, and that too moving in some way...
Say I were to hop in a spaceship and travel in such a way that it counters all of this motion, leaving me and the spaceship completely motionless,
would anything...
Heloo guys, diego here,
I was wondering if there exist multiple space dimensions, and we can only see in the 3th dimension, it is entirely possible to have multiple time dimensions.
And another thing, we all learn(simplified version coming) 1 dimension is basically a point, 2nd dimension is a...
Hi there, first post here!
I'm working on a story and at one point there is a ship traveling at 40% of C. The characters are on a long trip, fifteen years or so, I'm wondering in a ship far from any star system going at a % of C, what kind of interesting experiments could one do. The ship has...
I am not sure how does the integral was did here. More preciselly, How to go from the first line to the second line? Shouldn't it be $$\frac{4 \pi}{(2 \pi)^3} \int _{0} ^{\infty} p^2 e^{ip*r}/(2 E_p)$$ ? (x-y is purelly spatial)
I'm trying to figure out alternative ways to lift the roof on a pop-up camper that I'm refurbishing. There is limited space, and it needs to be lifted from beneath. I'm trying to avoid completely gutting it if possible which is what I'd have to do with a standard cable system. Any ideas?
It...
In Anthony French's book, Newtonian Mechanics, while explaining the non-Euclidean nature of the 3-d space, he poses a problem (I have rephrased it slightly):
Suppose you are on Earth's equator (r = 6,400 km) at the prime meridian (point I).
You first walk along the equator 1000 miles east and...
It has been stated unequivocally that there are no naturally occurring elements beyond uranium anywhere else in the universe but on Earth then I read that plutonium has been discovered in space. Assuming it wasn't put there by humans who's right?
One place I used to visit every year was Green Cove Springs Florida. Once there, I could hardly ignore this artifact near the river bank.
It has been there since 2013. It is privately owned, so presumably it could be for sale. If you don't recognize it, this picture may help.
In the...
I am trying to draw the Poynting vector field for a single electron in free space between two capacitor plates. The electron is moving (and accelerating) to the positive plate at the right. I expected the Poynting vector field lines to converge to the electron, because that is where the work...
I’ve read that the human brain capacity has 2.5 petabytes worth of memory storage. I have an excellent memory for details; even super obscure things that happened decades ago. I only have an average IQ but my recall is very good especially when my memory is jogged or if I had read something...
it's been 60 years since humanity entered space. What are your favorite things about space or hidden space history tidbits?
mine is On the 12 April 1961, the first man in space, Yuri Gagarin asked the bus driver to stop on the route to the launchpad and urinated against the right-hand back tire...