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14

1) No, because it's actually going slower from your perspective. In special relativity, "the fastest wristwatch is always your own". 2) Yes, but remember that it's farther away from us now, so it will take some time to get to us (if it was travelling at 0.5c it will take 50% longer to get to us). 3) Mostly in that as an observer the redshift effect would ...


11

Why does time stop in black holes? Time according to whom? The fact is that, in special and general relativity, there is no universal time. Indeed, time is a coordinate in relativity so one must be careful to specify the coordinate system when asking questions like this. Now, every entity also has an associated proper time which is not a coordinate ...


7

Since you only mention acceleration to 0.5c, we'll assume we're dealing with special relativity alone. In this case, your accelerating computer 'loses time' -- its clock moves slower. Computers ultimately work on clock cycles. Thus it is fair to say that, as its clocking is ticking slower -- from your point of view -- the computer on your desk will finish ...


5

It's my understanding that the invention of the metric system during the turbulence following the French Revolution also included a switch to decimal time, with ten hours per day, etc., but that it didn't take. There's a certain amount of cultural inertia that has to be overcome; as you're probably aware, those of us in the United States still have many ...


5

Short answer: It doesn't stop. Slightly longer answer: The case of a non-rotating, non-charged black hole is described by the Schwarzschild solution. It is now the case that, if you draw the worldline of a particle falling into a black hole, you will find that the coordinate time in the Schwarzschild metric grows infinite as the particle approaches the ...


5

It is a reasonable question at the elementary particle physics level , since the mathematical formulae of all the models we have are reversible as to time. It is in the thermodynamic manifestation of the laws that an arrow of time appears, and in special relativity which separates observations in timelike and spacelike regions. So it is one of those ...


3

You're asking two separate questions. To take your second question first, the existance of seven extra spacelike dimensions is a requirement for the consistency of string theory and we have no experimental evidence that extra dimensions exist or that string theory is a good description of reality. So it's impossible to make any definitive comment about why ...


3

Why time is considered to be a dimension? Because, to the extent of the empirical evidence, relatively moving inertial observers are related by the Lorentz transformation. But, the Lorentz transformation mixes time and space coordinates in a particular way. If time were not a dimension, if time were just a universal parameter, this mixing would not be ...


3

it doesn't move in time, so no time will have past when the light arrives at it's "destination". Right? A photon does 'move in time'. It just that, for a photon, the displacement in time, $c \Delta t$, equals the displacement in space, $\Delta x$. However, there is no proper time for a photon. Your proper time is, in words, the elapsed time ...


3

You're thinking about gravitational time dilation. Time machines do exists. If you go in a space ship and travel around the supermassive blackhole in the center of Milky Way, close enough to not fall in it, and then come back to Earth, you just traveled to the future (relative to the space further from you). So in that thinking line, if you want to make a ...


3

You shouldn't use the "subjective/objective" distinction for a place where "relative/absolute" is much more appropriate, because they mean different things. For something to be subjective, it must be dependent on the knowledge or state of mind of an observer. As an example, suppose we define "depth" as "length along the direction an observer is facing". ...


3

The quantity that tells you what time an observer travelling along a path $\gamma : [t_0,t_1] \rightarrow \mathbb{R}^4$ experiences is the proper time $$ \tau = \int_\gamma \sqrt{\mathrm{d}x_\mu\mathrm{d}x^\mu}$$ Assuming flat spacetime, i.e Minkowski metric/special relativity, this reduces to $$ \tau = \int_\gamma\sqrt{\mathrm{d}t^2 - ...


2

Almost none. Let's be much more generous than your idea of human-carrying craft. Let's just use the fastest probe. The Helios II craft, after nearing the sun, reached a heliocentric speed somewhere near 70 km/s. Obviously, its speed was more due to the gravitational influence of the sun than its engines. $$t = \frac{t_o}{\sqrt{1 - \frac{v^2}{c^2}}} $$ ...


2

So let's just say that the spacecraft can accelerate until it's moving away from the Earth at the speed of the fastest currently-existing spacecraft First, note that the fastest speed, relative to Earth, that a spacecraft has obtained is an exceedingly small fraction of the $c$ and, thus, one should not expect significant time dilation. For ...


2

Your reasoning seems to be that because $\frac{t}{\sqrt{1-v^2}}\to \infty$ when $v\to 1$, it must be the case that $\frac{t}{\sqrt{1-v^2}}\to 0$ as $v\to 0$. But in fact when $v=0$ we have $$ \frac{t}{\sqrt{1-v^2}} = \frac{t}{\sqrt{1-0^2}} = \frac{t}{\sqrt{1}} = \frac{t}{{1}} = t. $$ So time does not pass infinitely rapidly but instead passes at exactly its ...


2

The French Revolutionary Gov't did try to move towards a decimalized system of time measurement, with a second defined as one-one hundred thousandths of a day (along with decimal hours, minutes and a new calander), around the same time as it introduced the proto-metric system. But unlike the rest of the metric system, the new time keeping system and ...


2

Ok, before we fill up the comment section with this, I will write this as an answer: Proper time $\tau$ along a path $\gamma$ is $$ \tau := \int_\gamma \sqrt{\mathrm{d}x^\mu\mathrm{d}x_\mu}$$ and a clock moving along $\gamma$ will have $\tau$ as its elapsed time at the end of the path. Yet, the definition of proper time $\tau$ involves such clocks not ...


2

It means that time is no longer an absolute concept, yes. The time a specific observer experiences in a specific frame of reference, i.e. his proper time depends on the path (worldline) he takes through spacetime. In other words, it depends on his state of motion, the way he accelerates. This is the reason for the famous twin paradoxon: the resolution is ...


2

If you think of the future as a probabilistic distribution of events, for the far future there are an infinite number of possible events. As you approach those events in time, past (and present) actions force the future to collapse to a single event (assuming two can't happen simultaneously). You could think (and even predict) one event would happen over ...


2

There are many devices that can measure rate of a quantity without using approximate derivative and integral. I will give some example here: Pitot tube Pitot tube is a device used to measure velocity of a body with respect to flow. This device uses Bernoulli's equation. For computing the velocity using Pitot tube, the total pressure and static pressure ...


2

Years ago, the speedometer in a car moved the needle by spinning a magnet. The physical rotation of the driveshaft turned the cable inside the assembly. The spinning cable is attached to a magnet. The needle is mounted on a disk attached to a spring which provides rotational counter-force. The spinning magnet attempts to spin the disk, but the spring ...


1

If someone is falling in a black hole, the nearer he/she gets to black hole the slower time will pass and when he/she reaches the edge of event horison, time it would take for an observer to see him/her to cross event horison will be infinite (in other words if their friend was watching him/her he would never see him/her crossing the event horison). ...


1

Comment to the question (v2): Globally within an inertial frame $I$ in Special Relativity, there is a theoretical (as well as practical) procedure using light rays, known as Einstein synchronization, to synchronize clocks in each space point of the inertial frame $I$, so that at least theoretically, it makes sense to assign a common global time $t$ within an ...


1

The function $U = U(x_1, x_2, \dots x_k, t)$ would be an example of a potential energy function explicitly dependent on time. In your case, you have the function $U = U(x_1, x_2,\dots x_k)$, where it is understood that for each $x_i,\, i \in \left\{1,\dots k\right\}$, we have an implicit dependence $x_i = x_i(t)$. The total derivative of $U$ is $$dU = ...


1

Lets make up an example. $$U(x,y,z,t) = E_0\left(x^2+y^2+\alpha\,z^4 -\beta\,t\,z^2\right)$$ In that case parital derivatives are: $$\frac{\partial U}{\partial x} = 2xE_0,\; \frac{\partial U}{\partial x} = 2yE_0,\; \frac{\partial U}{\partial z} = \left(4\alpha z^3 -2\beta z\right)E_0,\; \frac{\partial U}{\partial t} = -\beta\,z^2E_0 $$ Now you have a ...


1

Even if there is no agreement in the physics community about what is special about "NOW", I believe that most physicists that believe in a block universe would agree with your statement that there are an infinite number of me's at every point in time, all experiencing their own now. Not only that, there is an infinite number of mathematical universes (see ...


1

This is essentially the same effect that you get in special relativity as the velocity approaches the speed of light. If you take a clock and accelerate it towards the speed of light then it will run slowly. If you could get the clock to the speed of light (which you can't of course) then it would stop completely. To use your words for any infinitesimally ...


1

There isn't a hyperbolic time chamber on reality, so one could only guess as to what this might mean. As for increased gravity, consider that astronauts in microgravity lose muscle mass, so it could be that increased gravity would indeed have the effect you discussed.


1

The reason that the worked examples in textbooks arrange the length of the light clock perpendicular to the axis of travel is that lengths perpendicular to the axis are not Lorentz contracted. If you orient the clock along the direction of travel you have both time dilation and length contraction to contend with. You can still derive the Lorentz ...


1

The common definition of "time" is a type of measurement, like size. No. The common definition of "time", certainly in the context of physics, is as one indication of one participant, or also as the ordered set of all indications of one participant. As Einstein put it: "[... that instead] of "time" we substitute "the position of the little hand of my ...



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