As a consequence of the Lorentz transformations, time and space transform into each other when changing reference frame. This calls for a unified description: Minkowski spacetime.

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Kleppner derivation of Lorentz transformation

I am reading Kleppner.(Lorentz transformations) He said,we take the most general transformation relating the coordinates of a given event in the two systems to be of the form $$x'=Ax +Bt, y'=y, z'=z, ...
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62 views

Visualizing gravity in 3D

We've all seen the depiction of gravity bending space downwards, and so attracting objects into the dent it creates, cf. e.g. this and this Phys.SE posts. That's intuitive and makes a lot of sense, ...
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50 views

Can two distinct events occur at precisely the same moment in time?

I am writing a simulation and am having difficulty resolving the order in which two distinct forces occur. The simulation will give different results if the forces are applied to the state in ...
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39 views

How time is formed? Is it the result of expansion of three dimensional space? [on hold]

How time is formed? Is it the result of expansion of three dimensional space?
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74 views

Why is time considered a dimension? [on hold]

Why is time considered to be a dimension (instead of something else, like possibly a "force")? The unidirectionality of time (as I understand it) seems to be a unique property that makes it unlike ...
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1answer
78 views

A Theory of Almost Everything? [on hold]

Before I present this theory, I ask that you take the time to read this disclaimer. I do not claim to have an excellent knowledge of physics, it is actually rather limited. Therefore, I am not ...
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31 views

Is time depending on the observer in string theory?

I heard that in the theory of relativity the time of an action is depending on the observer. But in string theory, is the time also depending on the observer? Are strings acting according to the ...
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1answer
27 views

The nature of universal forces [on hold]

When we speak of universal forces, do these forces constitute a form a matter? Are they consistent forces throughout the universe? Meaning, are there regions of space where these rules don't hold up ...
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3answers
281 views

A sees B's clock running slow and B sees A's clock running slow? [duplicate]

This paradox is very common it seems, in which A sees B's clock running slow and B sees A's clock running slow. Here is the question a little more concretely. Let's say B flies by A's spaceship. If ...
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25 views

Is the future purely a construct of the human mind or is the flow of time an Universe phenomena? [on hold]

Is it mathematically proven that the future exists already somewhere in the time-space continuum? Do past and present exist in the Universe or is it just one "long thread" of time? Why do we travel ...
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3answers
54 views

Space time curvature bends back

If our perception of space-time curvature is gravitation and Reduced Gravity Plane can reach weightlessness on some point of its trajectory, doesn't that mean that when Reduced Gravity plane reaches ...
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1answer
139 views

Is imaginary time a fifth dimension? [duplicate]

I've read that by introducing the concept of imaginary time, the dimension of time can be treated like a spatial dimension mathematically. Assuming, without imaginary time, one considers the universe ...
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2answers
92 views

Does spacetime have a “mass” value? or What is “Spacetime” made out of?

When measuring the MASS within the Universe, does "space" or "spacetime" have a value? I only ask, because when speaking of expansion, space is expanding. Could it be possible, to reverse the ...
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55 views

Alternate theories of space and time [closed]

Do mainstream theories in physics make implicit assumptions about the nature of space and time? In particular, are there any theories which implicitly assume that space and time are continuous, or is ...
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31 views

Does a body curve spacetime at higher velocities? [duplicate]

Suppose we have two objects where the distance over time decreases. Now, as I understand it, general relativity says that we can observe the Universe from the perspective of both objects an get a ...
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0answers
33 views

Does infinity really exist? [duplicate]

Does infinity really exist, or is it just part of the fabric of our imaginations? Great mathematicians, like Gauss or Pointcaré, said that actual infinity does not exist.infinity is mathematical ...
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28 views

Relative time dilation in Schwarzschild metric

Let's say we use the Schwarzschild metric to model the curved spacetime around a planet of mass $M$ and radius $R_0$. One clock $A$ is hovering at distance $R_A$ > $R_0$ with the help of rockets, a ...
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1answer
588 views

Gravity is curved geometry: A fact of nature or model-dependent interpretation?

We are regularly taught in high-schools and universities that, according to General Relativity (GR), gravity is nothing but a manifestation of space-time curvature (which, in its turn, is caused by ...
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2answers
34 views

What are the end points in the action integral of field theory?

In the mechanics of particles when we apply the principle of the least action the two end points are two spatial coordinates. Therefore, if we consider the variation of the action with respect to the ...
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1answer
34 views

Infinite Universe and Big Bang

A common view now in the physics community is that the Universe is infinite in extent (which makes Hubble sphere an infinitely small part of the Universe). On the other hand, there is the Big Bang ...
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1answer
62 views

What happens to black holes if/when the universe “ends”

I've heard several ideas about what happens to the universe when it dies, and they range from infinite expansion and heat death, to a "big crunch". In the event that something like a "big crunch" ...
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2answers
202 views

Spacetime diagram of a collapse of a rotating star

There is a well-known "standard" spacetime diagram (Kruskal and Penrose) for the collapse of a spherically symmetric star to a Schwarzschild black hole (for example here, or here in EF), which stands ...
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1answer
42 views

What it would look like to observe people with a different time flows?

As I learned, that the bigger gravity source you are influenced by the more slow time ticks for you, the farther away you are from a gravity source the faster times ticks. So Imagine two different ...
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1answer
55 views

Why is $\mathbb{R}^1$ different than Euclidean space $\mathbb{E}^1$? Roger Penrose road to reality

In Roger's book, the following is stated: (I'm paraphrasing because my book is in spanish) "We consider time as part of a space, namely $\mathbb{E}^1$, instead of it just being a copy of the line ...
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1answer
38 views

Convergent series in the real world with equal time for each term

A few months ago someone was explaining a philosophical principle in Aikido (a martial art) which involved a convergent series. The analogy he used was that, say you have a pool, and each day the pool ...
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48 views

Visualizing bending of Spacetime around a heavy object

The commonly used example of viewing bent SpaceTime around a heavy object such as the Sun is the Trampoline. However, this image is limited as it shows only the bending below the Sun. What about the ...
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1answer
35 views

The Higgs field and spacetime intervals

The Higgs field imparts a rest mass to certain fundamental particles, but it also seems to do something more interesting. Particles that don't couple to the Higgs field, i.e. the rest-massless, are ...
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2answers
60 views

Gravitational force of several massive bodies, from the viewpoint of general relativity

According to Wald's GR, "absolute gravitation force has no meaning". The text goes on to describe two cases: one where a gravitational force can be defined, and one in which it cannot. I'd like to ...
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22 views

Do three spacelike separated events on the same lightcone satisfy the triangle inequality?

If three events are (pairwise) spacelike related to each other then their interval ratios do not necessarily satisfy the triangle inequality. (For example, consider the case that two of the three ...
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1answer
32 views

Higgs field and the null geodesic

How does coupling to the Higgs field take a particle with a spacetime interval of zero and give it a non-zero value, i.e, how does it move it off the null geodesic? [of course, the Higgs field is ...
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1answer
56 views

A true singularity at $t=0$, coordinate independent Big Bang

Consider a flat Robertson-Walker metric. When we say that there is a singularity at $t=0$, clearly it is a coordinate dependent statement. So it is a "candidate" singularity. In principle there is ...
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3answers
80 views

Is it possible to express various nonlinear motions as straight lines in transformed spacetime?

I am trying to understand simple examples of space-time curvature. Assume for the moment that $c$ is infinite (classical curvature due to Newton's laws). Also, I will only consider 1+1-dimensional ...
4
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3answers
94 views

Is acceleration caused by curvature or space or time or both?

I'm trying to get a hold of the idea of gravity in general relativity and spacetime. I've seen plenty of demonstrations of the rubber mat analogy to describe gravity and spacetime curvature. Is this ...
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39 views

Is time dilation a mechanical slowdown only? [duplicate]

I've recently read about the time dilation occurs at very high speeds. But I'm really wondering if it is just a mechanical slowdown of the clock only? What if we use clocks that does not use moving ...
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2answers
67 views

Meaning of general covariance

Quoting from Wald's GR: In the context of special relativity, the principle of general covariance states that the spacetime metric $\eta_{ab}$, is the only quantity pertaining to spacetime ...
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1answer
93 views

Einsteins gravity Space time

I'm having a difficulty in understanding Einstein's version of gravity as "space time curvature" (I could be a total physics idiot, please point out !). How does an object on the surface of earth ...
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3answers
82 views

Is the world we are living in discretized? [duplicate]

I do not know how to use professional words to ask my question, so I will try to use a layman language. Please bear with me for a moment. A ROUGH GUESS The world our eyes are seeing every moment is ...
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1answer
58 views

What will I see if I travelled to a distant planet in 100 times faster than speed of light and look back? [closed]

Consider this scenario. I enter a space ship at 10:00 AM, it starts to move at a speed 100 times faster than light, I travel for 55 mins. And then slow down to very much less than speed of light and ...
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1answer
636 views

Questions after watching the movie Interstellar [closed]

Awesome movie, but as a physics student, some questions do crop up When they travel to the watery planet, they say that 1 hour on this planet is 7 yrs om earth. How is this possible? Is the planet ...
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45 views

Examples of warped product manifolds?

Bishop and O'Neil defined warped product manifolds. Space-times are good examples of such warped product manifolds. Is there a famous and important example of space-times $I×M$ where $M$ is itself a ...
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4answers
71 views

Question about dot product of four vectors?

I am looking back over some old notes and see that I have written $\bar{p}=\left(\overset{E}{\vec p}\right)$ and $\bar{x}=\left(\overset{t}{\vec x}\right)$ (using Plank units) And then $\bar{p} ...
2
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1answer
63 views

Does space-time cause time dilation at relativistic speeds?

I'm trying to understand the concept of the space-time continuum and it's effect on time dilation but am having difficulty with parts of it. To me there seems to be two separate components to time ...
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1answer
29 views

Direction of formation of Black Hole

When Black holes are getting formed, in which direction in space they form? For example, I have read that formation of Black Holes is same as forming a hole on a rubber sheet by a spherical ball, so ...
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2answers
91 views

Is space-time a property of mass?

Imagine looking at a quasar millions of light years away. From your perspective, a photon emitted by the quasar has spent millions of years travelling through space, and its trajectory has been ...
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1answer
51 views

Newtonian tidal forces and curvature

Today in my physics class, my lecturer said something which confused me. He said: "Newtonian tidal forces are reinterpreted as a manifestation of curvature in General Relativity". Now I know what ...
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61 views

Topological implications of symbolic represenation of the relativity

I have seen in the online Stanford Encyclopedia of Philosophy in the entry on Copenhagen Interpretation of Quantum Mechanics that Niels Bohr had argued that the theory of relativity is not a literal ...
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2answers
78 views

Why does Einstein's equation of relativity exclude space and time? [closed]

Taking $E={m}{c^2}$, we have mass and energy but no space and time. What is the best way of understanding the ways that space and time are passive and therefore unaccountable as mass and energy?
2
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74 views

How does matter interact with spacetime? [closed]

It's easy to see how matter interacts with itself but how does it interact with spacetime which is "not" matter? Einstein showed us that mass and energy cause a curvature in spacetime, which intern ...
2
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72 views

Does a mass gain inertia against movement in all directions as it approaches the speed of light?

If a mass moves along the x axis at near the speed of light, does it take as much energy to additionally accelerate the mass along the y axis as it does to accelerate it along the x axis by the same ...