New answers tagged

1

The argument goes as follows. First we model the universe as isotropic and homogeneous on the largest scale (i.e. smooth and the same in all directions and locations). Next we define a global reference frame, it is the one in which the matter in the universe does not move. The field equation of general relativity then provides a differential equation ...


3

Did you ever seen this obstruction stated like that (i.e. bolded sentence) before? Where? Is it relevant? As pointed out by knzhou in a comment, this is a point that comes up at the level of QFT on a flat spacetime, before we even start talking about quantum mechanics of curved spacetime. If you look at discussions of quantum gravity that are written for ...


-3

I gues the same reference as of today's ignoring the time dilation it's how much space formation was taking up per second that is defined by the excitation of the caesium isotope. The possibility of the dilation to have been felt by an intelligent organism was no existent. The exited state of matter back then was in form of the pure fundamental forces that ...


0

The reason for your misunderstanding is a common one- it crops up in many of the questions about special relativity- and arises because you are focussing upon the phenomenon of time dilation while forgetting to consider the related effect known as the relativity of simultaneity. If you and I are in the same reference frame we have a common time. If it is 10....


2

In the special relativity case, neither frame is privileged. You can take either as at rest and the other moving. Or neither at rest, choosing some other frame as the origin. You can move between them with a simple change of velocity. You can't do that with the observer on the surface of the planet. The planet breaks the symmetry. That observer is in a ...


0

Time is not slowing down, that any one could be aware of, if time ran differently for you, your clock, and the rest of the Universe, how would you know, how would it matter? However time is relative to the frame of reference. In higher gravity, time can be dilated (run slower) compared to an observer in lesser gravity. At higher speeds time can be dilated ...


-4

No, the time is not slowing down. Time only slows down for an observer travelling beyond the speed of light, which is only possible when the observer go through a blackhole.


6

A velocity-dependent generalized potential $U=U({\bf r},{\bf v},t)$ satisfies by definition $$ {\bf F}~=~\frac{d}{dt} \frac{\partial U}{\partial {\bf v}} - \frac{\partial U}{\partial {\bf r}}.\tag{1} $$ If there is no velocity-dependence but possible explicit time dependence, this simplifies to the well-known gradient form $$ {\bf F}~=~ - \frac{\partial U}{...


2

For a truly uniform gravitational field see this article I don’t think that I would describe the result on that page as “truly uniform”. That is the exterior field of a fixed mass as the radius goes to infinity. As such it has curvature everywhere which goes to zero in the limit. Aren't both situations equivalent and as such will time for both men walk ...


0

The greater the gravitational field, the greater time is dilated, whether you are in freefall or not. Time would seem to pass normally for each man in their own reference frame.


2

The definitions are both trying to say the same thing, but they are not quite managing to avoid all scope for misunderstanding. For a non-technical appreciation of the meaning of proper time you should start with the principle that proper time is the time experienced at any point in one's own reference frame. As you sit at your desk marvelling at the clarity ...


2

You are correct when you say that our speed (us who have rest mass) in the spatial dimensions affects our speed in the temporal dimension, and this is because you just have to accept that the universe is built up so and the four vector (velocity) is built up so. In physics, in particular in special relativity and general relativity, a four-velocity is a ...


0

It’s a meaningless question. Intervals of the cosmological time used in the Friedmann metric don’t change, but intervals of conformal time do. You can use any time coordinate you want in cosmology, and can make coordinate time intervals get longer, shorter, or stay the same relative to proper time intervals as the universe evolves. Precisely because “space ...


2

In the Lagrangian formalism, the Lagrangian is a function $L(x, \dot{x}, t)$. The notation $\frac{\partial L}{\partial t}$ means nothing but "the partial derivative of L with respect to its third argument". The partial derivative notation always means differentiating a function with respect to a certain "argument slot", regardless of what you put in the slot ...


4

Explicit dependence would mean $\partial_tL\ne0$. Note that $\partial_t\dot{x}=0$.


0

The people on the larger planet would marvel at how quickly those on the smaller planet got things done. Those on the small planet would marvel at how long those on the larger planet live.


30

In ancient civilizations, astronomy was a serious business (among other reasons, to accurately predict the seasons), so there were a lot of scientists making very careful measurements. Even with the naked eye, you can make quite accurate observations, and the ancients used these observations well. The first really accurate determination of the length of the ...


0

Concentrations of matter cause time dilation. The current hypothesis is that prior to the Big Bang all matter was "together" with no space between. This situation would mean that according to the laws of physics time was completely stopped. We could therefore say that time began with the Big Bang. Time itself has a value of 13.8 billion in terms of our years....


1

In the right frame, all the galaxies are approximately stationary. That is - the relative velocity of the galaxies is mostly due to the expansion of space. So, the age of the universe can be computed consistently from the point of view of the galaxies in general, since they all share the same time frame. This is a contingent fact - if half the galaxies were ...


0

From https://en.wikipedia.org/wiki/Second#%22Atomic%22_second : "Since 1967, the second has been defined as exactly "the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom" (at a temperature of 0 K)." Assuming that the second is based of a physical ...


9

I asked my friend, and he told me, if he'd have to do it, he would simply watch at the stars, and map them, and do that until he came back to the exact same position of the first night. Is that realistic ? I don't think the position would differ so much that the eye could see it. Am I right ? No light pollution Please remember there was no light ...


4

Relativity has ways to make time pass arbitrarily slow, but no ways to make it pass arbitrarily fast. So if you are uncomfortable with defining what it means to "move with the universe", there is another way. You can define the age of the universe as the longest possible time any observer can need to get from the big bang to our current position in space-...


2

In order to find out how the topic evolved in the past 1000's of year, the proper search on the Internet is about the different calendar systems that people employed in the past. Generally, calendars evolved between better and better precision and different attempts to fit the seasons and the moon phases around some easy calculatable numbers (12, 30, 360, ...


9

You are correct, there is no absolute time in the universe. This is as per SR, time is relative. Now to whom is the universe 13.8 billion years old? To a comoving observer with zero comoving velocity (peculiar velocity). The "age of the Universe" of about 14Gyr you frequently hear about is a good approximation for any observer whose peculiar velocity is ...


10

First, you're quite wrong about Bob --- when he returns, he shares Alice's frame, and so agrees with Alice that the universe is 14.8 billion years old --- and that he once spent one billion of those years traveling, during which time he aged only .1 billion years, though this has nothing to do with how long ago the Big Bang occurred. The person you want to ...


1

You are basically thinking about time dilation, that is a difference in elapsed time measured by two clocks caused by: having a relative velocity of the two clocks by there being a gravitational potential difference between their locations https://en.wikipedia.org/wiki/Time_dilation Now the answer is that the crew on the spaceship will just use their own ...


2

It is not that simple. It takes tools such as Stonehenge to accurately time the passage of stars. You may then notice that the Sun's passage across the sky varies with a period of 365.25 days.


16

If you would capture sun position in the sky at the same time each day of year - you would get a periodic figure, called Analemma which shows sun's path in a sky through a whole year :


29

Observe where the Sun rises and sets, and how high it gets in the sky at midday. These things repeat after 365 days.


-2

It is a lot simpler. In Europe we have four seasons. The same season returns about 365 days later. Over time the measurement got more and more exact. The reason we have seasons is that the earth axis is slightly inclined compared to the movement around the sun.


2

Your proposed chaining method is inappropriate. To understand why, consider a simple analogy. Suppose I am holding a metre rule. You are standing at some distance from me, so that the rule appears to be half its length, ie 50cm. Suppose your friend is standing the same distance from you, so that a metre rule you are holding appears 50cm to her. You cannot '...


2

$t_a=t_c\sqrt{1-u^2/c^2}\sqrt{1-v^2/c^2}$ is incorrect. The proper time formula can't be chained up like that. The reason is a little subtle - it's because $A$ isn't in the same position at the start than when $t_B$ has passed in the $B$ frame. Because of that, you need the full machinery of the Lorentz transformation to go from $B$ to $C$. If you chain up ...


2

The fist thing to mention is that the uncertainty relation between energy and time is in this sense different from position and momentum that in quantum mechanics time is a parameter and not a dynamical variable (like position and momentum, which depend on this parameter). Beside that, there is no intuitive hermitian time-operator $\hat T$ which is canonical ...


0

Apply the operator of an observable to a wave function that is a pure state of the Hamiltonian and then multiply by the complex conjugate of the wave function, you'll eliminate the time dependence of the probability of getting a given value of the observable. Further, by The Ehrenfest Theorem, if an observable and its square both commute with the ...


3

In the Schrödinger picture if $\left|\Psi\right>$ is an energy eigenstate, then $e^{-iHt}\left|\Psi\right> = e^{-iEt}\left|\Psi\right>$. That is, time-evolving the state gives back the same state (sinces states are only defined up to phases). So the state can't change with time and in particular could not be localized in time. I'm not sure why you ...


-1

Maybe have a look at the uncertainty principle, if a state's energy is known ('localized'), then you cannot simultaneously be localized in time. Another nice thing to look into are stationary states, which are energy eigenstates: https://en.wikipedia.org/wiki/Stationary_state


2

There is no evidence - either direct or indirect - of matter or antimatter suddenly appearing anywhere in our universe. The only theoretical mechanism that we know of that could connect distant points in spacetime is an Einstein-Rosen bridge. This has also never been observed, and it has such unusual properties that many physicists think it is physically ...


0

Many quantities in physics depend on derivatives of functions as evaluated at a specific point in time. It makes perfect sense to assert the existence of an instant in time in this context because it allows you to solve for the value of that derivative.


3

Time and space are modeled in most physics theories as continua because there is no evidence that they are discrete. Models are just models. We may eventually discover, or become convinced theoretically, that time and space are discrete and not continuous. An instant is not an infinitely-small time interval. It is a zero-size time interval, the analog of a ...


0

The answer to your question is that we don't remember the future because we haven't yet stored any memory of it. Your memories arise from connections wired in your brain as a consequence of experience. You have not yet experienced the future, so the configuration of your brain has not been affected by it. You can, of course anticipate and imagine the ...


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