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.
Hello!
As the topic suggests I´m interested which functions space square waves span?
Lets say we define them as https://wikimedia.org/api/rest_v1/media/math/render/svg/5b8953debf86627276f45bf8822140ff2bbaee56 .
Do they span the same space as the sines and cosines in Fourier analysis? :/
Thanks!
Hi everyone. I'm a skydiver. i would like to know the maximum altitude from where i can jump from the space and to be able to free fall back to Earth without geting lost in space. i think the actual record is 41425m. here is a brief story about world record spacedive...
I am not sure this question has been asked here before but I am curious about it. From the Modern Physics Course, I learned that we need a nucleus to create an electron and positron pair (with a photon). And the reason is stated as to conserve linear momentum. If this is the case then how the...
It seems that the entanglement of two particles does not change with time and can cross long distanced as long an neither particle decoheres with the environment. This makes me wonder if the wave function for that entanglement can have any time or space dependence? I only did a brief search for...
Hello everyone,
I have calculated the received power for free space optic (FSO) using the equation:
Lsystem (system loss) is set to 8dB. PTotal can be calculated as:
where Ntx (number of receiver) = 1 and PTx (transmitted power) =7.78 dBm. LGeo can be calculated as:
where d2R (receiver...
Answer is probably not, but is there some connection between the inhomogeneous wave equation with a constant term and the spacetime interval in Minkowski space?
$$
1) ~~ \nabla^2 u - \frac{1}{c^2} \frac{\partial^2 u}{\partial t^2} = \sum_{i=0}^2 \frac{\partial^2 u}{\partial x_i^2} -...
Assume that there are 2 rockets in deep space or a place where there is nothing around to compare their motion to. Rocket A starts its thrusters but the observer in rocket A doesn't know about it. So my question is, if rocket A is considered to be stationary by the observer then how can he...
I'm hoping I can get my idea debunked or with some words of encouragement, continue my investigation in what could be an ideal way to solve some propulsion issues in space travel.
What I'm suggesting is building a large circular "maglev" accelerator in space, similar to CERN, which wouldn't...
I'm confused (what else is new) about L2.
While watching a video from PBS Digital Spacetime about the latest data drop from Gaia Space Telescope, Matt O'Dowd showed a CGI animation of the telescope leaving Earth then circling/orbiting L2 perpendicular to the Earth/sun plane.
I thought that the...
I have read numerous times that the overall curvature of space in extremely large regions -1000s of megaparsecs say - is zero. I also keep reading that the expansion rate of the universe is increasing, and that the universe is resultantly positively curved. I would be interested in a...
This has been bothering me for some time, and would like to get a physicist's view of it.
If my understanding or contention is in error, please correct me (gently). I only have under grad
physics from 1970, and was a microbiologist, though am interested in quantum physics, cosmology.
My...
I was looking at the following proof of Louviles theorem :
we define a velocity field as V=(dpi/dt, dqi/dt). using Hamilton equations we find that div(V)=0. using continuity equation we find that the volume doesn't change.
I couldn't figure out the following :
1- the whole point was to show...
Given a basis of a vector space $(V,O_1,O_2)$ can it represent two different non-isomorphic graphs.Any other inputs kind help. It will improve my knowledge way of my thinking.
Another kind help with this question is suppose (V,O_1,O_2) and (V,a_1,a_2) are two different vector spaces on the...
If space only had one dimension would Einstein's speed of light postulate still lead to Lorentz transformation for motion along that one dimension?
Relativity of simultaneity can obviously be demonstrated in one dimension (lightning bolts hitting opposite ends of stationary and moving train)...
I'm just trying to figure somethings out concerning the accelerating expansion of the universe and the measured redshift, etc.
If a light emitting object moves away from us, because of the expansion of the universe, the speed of that object causes a redshift in this light. But this light, from...
The metric of a 3-D positively curved space is dr2+ Sk(r)2(dθ2+sin2θdΦ2).
Now if this space expands with a scale factor a(t) from r to r'.
Whether the change in the radial component be a(t)dr and angular component be Sk(r')dθ and Sk(r')sinθdΦ since the change due to expansion is already...
This is a problem from Tensor Calculus:Barry Spain on # 69
Prove that a space with Schwarzschild's metric is an Einstein space, but not a space of constant curvature.
The metric as given in the book is $$d\sigma^2=-\bigg(1-\frac{2m}{c^2r}\bigg)^{-1}dr^2-r^2d\theta^2-r^2\sin^2 \theta...
Hello,
i use mathtype 7.3 in word - in office 365 for equations. Everything is okay, but when inserting an inline equation, an extra space is inserted after the equation in Word. It looks ugly. i found http://dessci.com/en/support/mathtype/tsn/tsn143.htm but it didnt help me. It does not work...
Homework Statement
given I am required to proove or disprove:[/B]
Homework Equations
rank
dim
null space
The Attempt at a Solution
I tried to base my answer based on the fact that null A and null A^2 is Contained in F (n)
and
dim N(A)+rank(A)=N
same goes for A^2.
Hello,
Basically, I use a portable electric space heater to keep my room warm during the winter, and it works quite well, except it makes a very loud hum that keeps me awake, so my options right now are poor sleep due to hum or having my room drop to about 12 C over night if I turn the heater...
Homework Statement [/B]Homework Equations
Doing this problem like e.g setting the determinant of potential matrix and the ω2*kinetic matrix equal to 0 ,det(V-ω2T)=0,I got the frequency of the normal modes of vibration to be 2ω0 and ω0 where ω0 is the natural frequency,
But sir how to treat...
Homework Statement
Homework Equations
Doing this problem like e.g setting the determinant of potential matrix and the ω2*kinetic matrix equal to 0 ,det(V-ω2T)=0,I got the frequency of the normal modes of vibration to be 2ω0 and ω0 where ω0 is the natural frequency,
But sir how to treat this...
Hi,
As I understand it the theory that the universe is expanding is in part based off the red light shift. My question is could atoms in space, dust etc cause the red light to travel faster. I realize that space isn’t a medium, but could the aforementioned atoms and dust exist in such...
I have been studying primordial black hole formation through inflation for a while and I was curious to know how the parameters in an inflation model are determined such that they are consistent with CMB constraints. In my literature reviews, there are quite a few models that exhibit an...
In the big bang theory, inevitably we have the end of space. Expansion ratio is same everywhere in space. The end of the universe moves from us at the very high speed, but there space also hardly expands(Ho << 1). Then what happens to the light that arrives at the end of space? Will it stop...
I am reading Loring W.Tu's book: "An Introduction to Manifolds" (Second Edition) ...
I need help in order to fully understand Theorem 2.2 and the remarks after the theorem ...Theorem 2.2 and the remarks after the theorem read as follows:
My questions on the above text from Tu are as follows...
Homework Statement
Instead of pumping heat into the cabaret air from the outside air, you could simply put an electric space heater inside the cabaret. A space heater turns electrical energy directly into thermal energy. Why would operating a space heater consume more electric power than...
Given a finite-dimensional normed linear space ##(L,\lVert \cdot \rVert)##, is there anything that suggests that at every point ##x_0 \in L##, there exists a direction ##\delta \in L## such that that ##\lVert x_0 + t\delta \rVert \geqslant \lVert x_0 \rVert## for all ##t \in \mathbb{R}##?
Homework Statement
The payload of a spaceship accounts for 20% of its total mass. The ship is traveling in a straight line at 2100km/hr relative to some inertial observer O. When the time is right, the spaceship ejects the payload, which is moving away from the ship at 500km/hr immediately...
Hi.
If a function f is normalizable ,ie f→0 as | x | → infinity or r→ infinity then I presume the following surface integral f dS over infinite space is zero ?
But I thought about this again and it seems like a case of zero x infinity. The function is zero at the infinite surface but the area...
Hey,
I'm designing an HVAC system for a laundry building. I have vacuum equipment (Vacuum press and Vacuum Ironing boards ) in the space which have a vacuum outlet the is taken outside the building through individual ducts. When all machines are operational, 877 l/s of hot air and moisture would...
Homework Statement
[/B]
The total mass of a space shuttle and its launch vehicle is
M=2000t.
a) What must be the minimum size of the thrust force, to make the rocket move?
b) The actual thrust of the rocket is F=30MN. What is its acceleration in the beginning?
c) Assume that a mass of a...
Hey! :o
We consider the $\mathbb{F}_2$-vector space $(2^M, +, \cap)$, where $M$ is non-empty set and $+ : 2^M\times 2^M \rightarrow 2^M: (X,Y)\mapsto (X\cup Y)\setminus (X\cap Y)$.
I want to show that $(2^M, +, \cap )$ for $\mathbb{K}=\{\emptyset , M\}$ satisfies the axioms of a vector space...
Hey! :o
Let $1\leq n\in \mathbb{N}$ and let $U_1, U_2$ be subspaces of the $\mathbb{R}$-vector space $\mathbb{R}^n$.
I want to prove or disprove the following:
The set $\{f\in \mathbb{R}^{\mathbb{R}} \mid \exists x\in \mathbb{R} : f(x)=0_{\mathbb{R}}\}$ is a subspace of...
I have an assignment to show that specific intensity over frequency cubed \frac{I}{\nu^3}, is Lorentz invariant and one of the main topics there is to show that the phase space is Lorentz invariant. I did it by following J. Goodman paper, but my professor wants me to show this in another way...
Hi,
I am studying some material related to Grassmannians and in particular how to represent k-subspaces of ℝn as "points" in another space.
I think understood the general idea behind the Plücker embedding, however, I recently came across another type of embedding (the "Projection embedding")...
I was thinking about the fact that space contains all sorts of matter and that these objects have temperatures. But then I read that space itself has a temperature depending on where you are. The cosmic background radiation for example has a temperature of 2.7K. Can someone explain what that...
Hi!
I have a question about space suits on Mars. I've done a google search and find conflicting information.
In my YA novel the protagonist makes a quick stop on Mars (just for a couple of minutes).
I wonder if it's possible for a human to visit Mars surface for a couple of minutes with just...
Could it be possible for light to not move at all but remain still while space and time moves past it? The light would just exists as the continuum of space time moves past light.
Hi good day. I am trying to find the general Inverted Pendulum on a cart nonlinear state space equations with two degrees of freedom with x, x_dot, theta, theta_dot which represents displacement, velocity, pendulum angle from vertical, angular velocity. However from research, I am seeing...
A question came up about deducing the number of possible energy states within a certain momentum ##p## using momentum space.
To make my question easier to understand, I deliberately chose ##p## and not a particular increment ##dp## and I assume a 2 dimensional momentum space with coordinates...
I always had a tough time understanding how QFT relates to reality. Are these quantum fields (electron field, ect) physically real? Are they things that exist in space or are they just mathematical abstractions that help use calculate things?
Hi all.
I was wondering if time is dilated whilst traveling in a stable magnetic field that is generated by the object travelling, and if so, does this vary if you reduce or intensify the magnetic field?
Also, what happens if the object is generating two opposing magnetic fields, would...
Let's consider two inertial frame S and S'. S' moves with speed v w.r.t S along x-axis towards the right. Now we can draw the two co-ordinates system.
The t' axes will make an angle arctan(v/c) with t axes rotated towards x-axis and similarly the x' axis will be tilted towards the t axes...
It is often proposed that gravity could be simulated on a space station by rotating around an axis, such that the astronaut experiences the centripetal force of the space station wall, analogously to gravity. It is usually mentioned that the radius of rotation must be very large to avoid...
Russia has developed a micronized nuclear powered drive for ballistic misiles and cruize misiles. This is obviously a very aggressive and environment polluting action.
However, could such nuclear powered drive be used for space ships, that would start in space and do not touch the atmosphere of...
So I'm an Software Engineer, not a physicist, nor a mathematician. So I like to work in the qualitative, not the quantitative.
Today I hit on a problem. I've been trying to remove the concept of "down" or "inward" from my thinking of gravity and GR.
When people show the concept of space/time...