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.
Homework Statement
Given ##\hat{x} =i \hbar \partial_p##, find the position operator in the position space. Calculate ##\int_{-\infty}^{\infty} \phi^*(p) \hat{x} \phi(p) dp ## by expanding the momentum wave functions through Fourier transforms. Use ##\delta(z) = \int_{\infty}^{\infty}\exp(izy)...
Homework Statement
Problem- Determine if the set of all function y(t) which have period 2pi forms a vector space under operations of function addition and multiplication of a function by a constant.
What I know- So I know this involves sin, cos, sec, and csc. Also I know that a vector space...
Two stationary masses will attract each other. That is, they start moving towards each other. For example, a stationary apple will fall to earth.
I can see bent space affecting the trajectory of a moving object.
...but how does bent space explain that stationary objects start moving?
A question arose over a simplification I wrote on another subject. My i information say's that matters antimatter pairs are generated in what is known to be very empty space such as the voids within the cosmic web. When I read about this it was considered anomalous but definitely verified.
Now...
Right now, I am studying Advanced Calculus (proof based), and it is hard thinking through some of the definitions without first thinking about it concretely (meaning how to visualize it better geometrically, if that makes any sense?). I need help with this definition.
Definition
Let X be a...
I am currently solving a problem where I need to find the gravity in the ISS (distance 400km from Earth with Radius 6371km). I am using the formula g=GM/R^2 . One way to solve it would be to find GM by multiplying g(which is 9.81) and R^2 (which is known) and then to use it in GM/(R+400)^2 and...
We have a simple table , for example a kitchen table, with some objects on it. If we consider the table having two dimension (1) does the table with objects represent an affine space ? Why ?
I want to do some calculation, so i choose a point as origin and i place a vector space in the affine...
Imagine that the CMB did not exist. What observational evidence exists to support the theory of the metric expansion of spacetime, as opposed to having a static spacetime and it's the matter distribution that is expanding - as it would in an explosion?
Homework Statement
Homework EquationsThe Attempt at a Solution
Substituting x = ## r \cos{ \theta } ## and y = ## r \sin \theta ## into the equation y = 3x +2,
I got r = ## \frac { -3 \cos{\theta} \pm \sqrt{ 4 – 31 ( \cos{\theta} )^2 } } { 10 ( \cos{\theta} ) ^2 – 1} ##Plotting...
Homework Statement
a) research the space elevator concept. Consider the environment in which the cable must operate. Recommend two physical and one chemical property that the cable should have. Justify your choices.
b) Based on what you have learned about bonding and forces in solids, which...
Please, moderator, just delete this question if it is too silly.
I am wondering what is happening in anyone point in the SpaceTime field. That's what it is called, I think?
Because my simple understanding is that we see colours/light because of propagated electromagnetic radiation at...
Does space have its own density?
i.e. a mass density distinct from the mass density of 'particles' in it?
or may it have a uniform density of some kind of vast particle(s)?
If so, would the effect on observable masses largely cancel out?
One answer from...
Evaluate
$\displaystyle \int_C(x+y)ds$
where C is the straight-line segment
$x=t, y=(1-t), z=0, $
from (0,1,0) to (1,0,0)
ok this is due tuesday but i missed the lecture on it
so kinda clueless.
i am sure it is a easy one.
Good afternoon,
I'm trying to search only based on bibliography or numerical and theoretical calculations the change of the thermal optical properties, namely the solar absorptivity, of a polyimide-based plastics (VESPEL SP-1) in space conditions (considering radiation, atomized oxygen atoms...
how do you describe the speed of an object in momentum space (energy, momentum as the 2 axes) where there is no distance or time? Can you give an example?
Hi all,
This is my first time posting on this forum. I'm not sure if this is the right place to ask this question so apologies in advance. Perhaps someone could recommend a more appropriate forum for me to post this on.
I'm working on creating documentation for a simulation. It's an Apollo...
Massive Space Structures Have Surprising Connection to Quantum Mechanics Math
Reading my daily science news I came across an interesting article that talks about how massive space objects have unexpected relationships to quantum mechanical mathematics.
I was quite surprised to hear this, as I...
Can momentum space also able to handle spin and polarizations?
I'm understanding it that in QM, you have position, momentum, spin, polarization as observables. Position and momentum can be equivalent via Fourier transform. So if you use momentum space instead of position, how do you handle...
Regarding the expansion of space...
In one book I've read the diameter of the universe is more than 100B light years across, even though the age of the universe is only roughly 14B years old. This is due to accelerated expansion of space.
In another book it says that space is expanding in a...
I am no smart person like the rest of you, but I find it fascinating about how physics works. I am deeply motivated to know about how we would solve this problem about gravity and space flight. Would a particle accelerator be used to help solve this problem or am I way off base?
I am reading "Multidimensional Real Analysis I: Differentiation by J. J. Duistermaat and J. A. C. Kolk ...
I am focused on Chapter 1: Continuity ... ...
I need help with an aspect of Lemma 1,1,7 (iv) ...
Duistermaat and Kolk"s Lemma 1.1.7 reads as follows...
I am reading "Multidimensional Real Analysis I: Differentiation by J. J. Duistermaat and J. A. C. Kolk ...
I am focused on Chapter 1: Continuity ... ...
I need help with an aspect of Lemma 1,1,7 (iv) ...
Duistermaat and Kolk"s Lemma 1.1.7 reads as follows:
At the start of the proof of (iv)...
as we know light travel in vacuum because of oscillation of electric and magnetic field and both are perpendicular to each other. But i don understand how these electric and magnetic fields get generated in vacuum. as electric filed can vary by oscillating charge and that generate varying...
$\textsf{An advertisement claims that a centrifuge takes up only $0.127 m$ of bench space}$
$\textsf{but can produce a radial acceleration of $4100 \, g$ at $6830 \, rev/min$}$
$\textsf{a. Calculate the requested radius of the centrifuge}$
OK the only thing I can guess here is...
When I see stuff on Netflix (yes not real), and yet I look stuff up on the Net (real)
and they try and create a spaceship capable of travellng anywhere else in the solar system,
they always come up with standard missile design and go "new and improved.."
When they then show failure to actually...
Hi PF!
A text states that the following two functions
$$
\psi^o_k = \sin(\pi(k-1/2)x)\cosh(\pi(k-1/2)(z+h)): k\in\mathbb{N},\\
\psi^e_k = \cos(\pi kx)\cosh(\pi k(z+h)): k\in\mathbb{N}
$$
each form complete orthogonal systems in two mutually orthogonal subspaces, which compose the Hilbert...
Entangled states are only separable relative to certain basis states. So does that mean that reference frames have importance beyond those in spacetime?
hi
I am studying algebra and i have a question.
why is important that something is a vector space?, i mean, what implications have?
matrix, complex numbers , functions , n-tuples.
What do these have in common, apart from being a vector space?
why is so important that a certain set of...
Hello, Hola, hajimemashite physics family,
Well do you know what It takes to start a space exploration company such as making cubesats , satellites or launching vehicles? :wideeyed:o_O:woot: Give your suggestions please :oldeyes::oldbiggrin::angel:
Regards.
NASA decided to stop *WFIRST and concentrate on Mars project (send humans to Mars).
What do you think about it?
In my opinion, since a lot of ventures have begun space developments such as SpaceX and this proves that rockets make money, NASA should tackle WFIRST. Generally, we cannot earn...
I believe the electric flux within a closed space can be found with the equation phi = Q/ε0. Can this be used for volume and area, or just volume?
Also what good does this do. Why would I want to know the electric flux of something?
What is the practical feasibility of changing the International Space Station's orbital inclination to match the orbit of the Moon?
Major future missions beyond the Earth-Moon system (ie: space colonization) will likely require in-orbit assembly of components from multiple launches. And...
Sorry for the possible double post. I really need help with this...anyway let's assume we have chances of winning "something" anything...can be the lotto or whatever. We have A, B, C, D, E and each have a different chance of winning. We will also give them each a value, and the chance of winning...
In trying to explain the concept of curved space, many books use the example of the surface of a sphere, which can be considered as a curved 2D space embedded in a higher dimensional, 3D space. I could derive, starting from ##a^2=x^2+y^2+z^2##, that the metric, or the line element, on the...
I have some questions about the curvature of space (NB not of spacetime) near a planet like Earth. Unambiguously defining space curvature requires choice of a coordinate system, so I choose the Swarzschild system. Here are my questions:
Would constant-time hypersurfaces under the Swarzschild...
Homework Statement [/B]
The International Space Station (ISS) has a mass of 400,000 kg and orbits 408 km
above the Earth’s surface. The ISS is 109 m across.
Homework Equations : [/B]
R=a(semimajoraxis) cubedroot(m2/3M1)The Attempt at a Solution : [/B]
ive tried multiple ways with multiple...
Homework Statement
Derive, using the canonical commutation relation of the position space representation of the fields φ(x) and π(y), the corresponding commutation relation in momentum space.Homework Equations
[φ(x), π(y)] = iδ3(x-y)
My Fourier transforms are defined by: $$ φ^*(\vec p)=\int...
Has the spectrum of light that is reflected off planet Earth ever been measured from outer space? (In the same sense that we measure spectra of the light emitted/reflected from other celestial bodies in astronomy). If so, would it be possible that there could be dips in the spectrum resulting...
Homework Statement
So I have these two Matrices:
M = \begin{pmatrix}
a & -a-b \\
0 & a \\
\end{pmatrix}
and
N =
\begin{pmatrix}
c & 0 \\
d & -c \\
\end{pmatrix}
Where a,b,c,d ∈ ℝ
Find a base for M, N, M +N and M ∩ N.
Homework Equations
I know the 8 axioms about the vector spaces.
The...
the problem:
Say we have the entire space uniformly charged. Then, the E field experienced by any point is zero, from symmetry.*
But, it means that for any Gaussian surface, the flux though it is zero even though the charge enclosed is clearly not. Gauss' law seems to disagree with symmetry, but...
I am trying to follow modern QFT by Tom Banks and I am having an issue with literally the first equation.
He claims that beginning from ## |p_1 , p_2, ... , p_k> \: = \: a^\dagger (p_1) a^\dagger (p_2) \cdots a^\dagger (p_k)|0> ## with the commutation relation ##[a (p),a^\dagger (q)]_\pm \: =...
Hello
In our Quantum Mechanics lecture we have been discussing a simplified model of the Stern-Gerlach experiment. Let ##|+>## and ##|->## denote an electron that is "spin up" and "spin down" (with respect to ##\hat{z}##), respectively. Our professor then asserted that ##|+>## and ##|->## acted...
Regarding curvature of spacetime/space: At some given point in a gravitational field, spacetime is curved at that point and this is a constant. (I'm assuming this is true).
Although we can talk about the curvature of spacetime, I never hear anyone talking about the curvature of space. Can...
Homework Statement
A 50 g, 420 mw laser pointer is floating in outer space (don’t ask how it got there) at rest with respect to an observer. The laser pointer is turned on and let go. If the battery runs continuously for 250 hours before dying, what is the final speed achieved by the laser...
Hey I'm new to Physics. I have a question. Is it possible to use the force generated when air entera a vacuum tube to launch something into space? Can anybody throw some light on this in simple words please. Thank You.
Homework Statement
Find the complement C' of the set C with respect to the space U if:
1. U = {(x,y,z) : x^2+y^2+z^2 ≤1}, C = {(x,y,z) : x^2+y^2+z^2 = 1}
2. U = {(x,y) : |x| + |y| ≤ 2}, C = {(x,y) : x^2 + y^2 < 2}
Homework Equations
Definition of complement: The elements of the space that...
Heisenberg's uncertainty relation says:
$$\Delta x \Delta p \ge \hbar$$
If we assume a massless quantum object then we have the relationship ##\Delta E = c\Delta p## so that the above uncertainty relationship becomes
$$\Delta E \ge \frac{\hbar c}{\Delta x}.\tag{1}$$
I understand that if we have...