14

The concept of absolute time was perhaps more of a postulate, rather than an axiom. If Newton's physics were based on any axioms, it would have to be the principle of relativity, which is perhaps the most profound concept, fundamental to his laws of motion. This principle was first stated by Galileo$^1$. It states that the laws of physics should be the same ...


13

The two different formulas are based on different assumptions. The time dilation formula assumes that there are two events in spacetime and that the two events are in the same position in one reference frame. The length contraction formula assumes that there are two worldlines in spacetime and that the two worldlines are at rest in one reference frame. For ...


12

Since you're trying to understand, I'll show you how to figure it out, instead of just telling you the answer. You don't need to know what a matrix is, and you don't need trigonomotry. Algebra is sufficient. To avoid unenlightening distractions, I'll using units in which the speed of light is $c=1$. If you want to restore factors of $c$, just replace every $...


11

Newton and others did not think necessary to state that the time was absolute (at least not as a postalate$^1$), because they considered this self-evident. Indeed, if they doubted this, they would have come with something similar to (special) relativity much earlier. I think the assumption about absolute nature of time is most obvious when deriving Galilean ...


7

Light itself moves only through space, so it doesn't move at all in time. I think this is where your misunderstanding lies. In relativity, elapsed time depends on the reference frame in which it is measured. It is true that the proper time along a path followed by a light ray in vacuum is constant. So, relative to its own reference frame no time elapses for ...


6

The question of how strings build up spacetime is not limited to the string field theory formalism. I won't reproduce the entire resolution, which is substantively answered here, here, and links therein, but the crux is that the strings themselves do not "build up" the spacetime background. Rather, deformations of this background can be generated ...


5

The answer from Nihar Karve provides useful information on how to describe spacetime in string theory, and I would like to add another perspective. Closed string field theory describes spacetime curvature in (almost – see below) the same way as general relativity. In general relativity, the dynamics of the metric $g_{\mu\nu}$ and the curvature of spacetime ...


5

The standard physics answers are that there is no way to cancel out your momentum and no reasonable way to travel faster than light. I would expect either that the observers are mistaken in what they saw, or there is an mundane explanation. But without better information, it is hard to say. I wouldn't take explanations such as aliens, particularly aliens ...


5

However, from what I take away from these explanations is that it only “appears” as though (as in “observed”) backwards time travel was achieved. … So my first question here is, is my understanding here correct or not? You have misunderstood the whole point of relativity. The Lorentz transform, which is what Andrew Steane used to produce those diagrams, ...


4

can I not sit down and say that something is happening everywhere in the universe right now You can, but it will be from your point of view. You can also sit down and declare that your point of view is the best point of view and this will define absolute simultaneity. The problem is others can do this too and they will arrive at different notion of ...


4

The very first step, where you assume that you can apply the transform simultaneously in two directions is wrong. If you first transformed from $(t,x,y,z)$ to $(t',x',y',z')$, and then applied a second boost with the new $t'$, then at least you'd know that your result was physical, even if the overall boost you get is incorrect. But you tried to smoosh the ...


4

From this and your previous question, I suspect your confusion stems from the interpretation of $L$ in the length contraction formula. In fact this is something that confused me a lot when I was starting out. Consider two observers attached to frames $S$ and $S^\prime$, with $S^\prime$ moving at speed $v$ relative to $S$ in the $x$-direction. Let their ...


3

Now, how do I show a similar argument for time? It is actually easier to argue both together. We are trying to find the form of a transformation between inertial frames. An inertial frame is one where Newton’s 1st law holds: an isolated object moves in a straight line at a constant speed. Such a path is a straight line in spacetime. Therefore, we are ...


3

Absolute time means there is unique procedure to determine which events are simultaneous and this is present everywhere in Newtonian mechanics. Take for example third Newton law. It states, that if object A acts on object B with some force, so does the object B on object A with force equal in magnitude and opposite in direction. But if the force is changing ...


2

Backwards time travel due to FTL would not merely be "seen", it would be a real effect. That is, if the principle of relativity is absolutely true, and if FTL travel is possible, then a person armed with both an FTL and STL (slower than light) drive could travel back in time and meet herself. Note that the STL part is necessary -- it's because of ...


2

I read the previous answers and I think they both miss the point, which is this: without that minus sign there would be no difference between time and space. (I don't know much about general relativity so I'll restrict my answer to the special theory, i.e. Euclidean vs. Minkowski space.) In Euclidean space, e.g. our three-dimensional space at a fixed point ...


2

Every straight line is a geodesic in flat space. So, if two flat lines have nonzero geodesic deviation, this means that they come to some closest distance (which can be an intersection, but they don't have to be in a common plane), and then, the distance between them linearly increases. But not all pairs of straight lines are mutually parallel.


2

It is impossible to use Reissner-Nordström black holes in you scenario, because these black holes assume spherical symmetry of spacetime. This is a good approximation if other sources are far away and produce only small distortions around the black hole (BH) you analyze, but in your case the symmetry is highly broken. Just the fact that the two event ...


2

The problem you pose in this question is, I think, quite a general and interesting one: we have a definition for a physical quantity and we wish to measure it, but the definition assumes "isolation" from the outside world, whose influence in practice will never be precisely zero. This is an experimental problem, and it is "solved" only by ...


2

The limit you want is the https://en.m.wikipedia.org/wiki/Bekenstein_bound bekenstien limit. This limit states that the amount of information a given volume can contain is proportional to the surface area of that volume. Specifically it is 1 bit of information for every 4 plank areas. Note that because the limit is a surface area proportional to $r^2$ and ...


2

Curvature represents tidal effects, and the equivalence principle is by definition only applicable to regions of spacetime where tidal effects are too small to notice. So the equivalence principle on its own cannot tell you about curvature. However, if you couple the equivalence principle with some basic observations then you can infer that curvature is ...


2

The choice of Riemannian metric $h_{\mu \nu}$ is itself arbitrary, since there are multiple inequivalent rank-2 non-degenerate tensors on an arbitrary space; and different choices of $h_{\mu \nu}$ will lead to different "preferred time directions." For example, consider the following two rank-2 tensors on Minkowski space with coordinates $t$, $x$, ...


2

Regardless of the validity of Woodward hypothesis (which might or might not been experimentally refuted already), for his argument to work in order to provide an inertia-like contribution to mass, he is relying on the fact that cosmological sources of mass are mostly positive, and their net rough contribution is: $$\phi_g = \frac{GM}{R}$$ with $M$ and $R$ ...


2

You can just displace the origin of the chosen co-ordinate axes along the time axis. When you displace the origin, the time co-ordinates of all the events change a bit. Now consider the fact that the choice of origin is arbitrary. By changing the origin, you've merely changed the time-labels that you're attributing to the events. Physics doesn't care about ...


2

This might just be vocabulary, but you do not have absolute time even in special relativity. In classical mechanics, absolute time means that if you synchronizes everybody's clocks, they stay synchronized. It doesn't matter which frame of reference you use, everybody agrees on what time it is. You are getting at a similar idea by choosing one frame of ...


1

It may help to look at a case where both length contraction and time dilation are relevant in analyzing the motion of light, and how the formulas are consistent when correctly applied. Consider a "light clock", a channel in which a light pulse reflects back and forth. In its rest frame, the channel has length $0.5$ and so light takes time $1$ to ...


1

Just like you can say "x is the place where this tree is" or "y is the place where my house is" you could also say that "event z is when supernova A exploded" or something. Hence you have your "coordinate free way" of representing spacetime, to stay with your example. Practical physics is always done in specific ...


1

... is it possible (that is not falsified) that in these other laws there is time, life, intelligent beings, technology, etc.? Many, many things are possible, in the sense that they have not been shown to be impossible. Some of these things, such as Russell’s teapot, are very difficult to disprove. Science (and, in particular, physics) deals with what can ...


1

One way to look at strings is that everything happens in a fixed spacetime background. No spacetime dynamics at all. However, there is a type of excitation (called graviton) which interacts with all other types of excitations (and itself) in such a way as if the spacetime is actually different from the said fixed background and that it is dynamic. And this ...


1

A quick trip to Wikipedia and a look at Speed of Light will tell you that the speed of light is now, by international agreement, defined to be an exact value. Formerly, it was not exactly defined, so that had implications for the definitions of other units of measurement, particularly the meter. Definitions of measurement units have changed over the years in ...


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