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I think it is important to emphasize that the notion of 'virtual particles' is a very dangerous one, which seems to lead to countless (unnecessary) misconceptions. It appears to have originated from the diagrammatic technique that can be used to carry out perturbative quantum field theoretic computations (i.e. Feynman diagrams), but it is crucial to keep in ...


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It's a trick to get the negative sign in the Pythagorean measure of distance. "Stick an $i$ here" vs "use a negative sign here" in the rules of how to figure things. It's not another different dimension nor is time a complex value. It's an x i t in the function of the interval, where $x$ is a real number. Of the several posts nominated as duplicates of ...


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I was doing a question about if a train fits in a tunnel. Did the question assignment include a specific consistent definition of what's meant there by "to fit", in the first place? Presumably, in the setup which is typically considered, the ends of the tunnel (say participants $A$ and $B$) are supposed to be at rest to each other, the ends of the ...


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The site rules forbid us from giving the answers to homework problems, but this problem illustrates a fundamental issue in relativity so I think it's worth some general comments. Incidentally you may be interested to read the Wikipedia article on the ladder/barn paradox, though in it's efforts to be comprehensive I think the article gets a bit confusing. ...


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Time is not directly related to energy itself, but it is definitely related to many aspects of energy. For example, the direction of time (from past to future) can be determined by the flow of energy in the universe. This concept is known as entropy. Our universe is gradually moving from a state of energy concentration (where some regions of our universe ...


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Here is a model for the relation between energy and momentum, based on classical physics: A particle at rest receives a linear acceleration. After this acceleration process it is moving, it has kinetic energy which corresponds to a momentum. For calculating the energy, you consider the length of the path the force of acceleration was applied: ekin = f x s ...


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Energy is the name physicists give to the Noether Charge that is conserved when a physical system's description through its Lagrangian is unchanged by time shifts. Or, in more everyday language, most physics does not depend on where one puts the $t=0$ time co-ordinate origin. The laws are invariant when we shift our time origin back and forth. Noether's ...


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The units of energy is $\dfrac{ML^2}{T^2}$ so that way energy is inversely proportional to square of time. But in most equations of energy, time is never present. Energy is a simpler way to relate work done in complicated systems with variable force. That is found by work-energy theorem. Work is $$\text{force*distance}$$. There is also Noether's theorem ...


0

Em, it will be no "image deformation" if your question is about it, just the biggest mass of the big planet will more curves the space time around it and the light will need more time to escape the big planet since the space time curvature will induce a longer distance for the light to travel throught.


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I don't see the difference between your "coordinate time" and just time. Yes, time is relative. Since time is relative, it is incorrect to find a reason (or cause). A cause is, by definition, some local event in the past, which affects some other event (consequence) in the future. Time relativity is not an event. It is not local, and is not in the past. ...


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At the research of the answer, I would recommend to consider the example of an astronaut going very far in a lifetime (example: moving near speed of light, he reaches a star 5000 light years away in only 50 years). I would ask the reversal of "Why is coordinate time frame dependent?": why proper time is passing slower than the observer's dilated time? It ...


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Tilting an object in space changes its apparent dimension (think of trying to get furniture through a door: the width of an object depends on its orientation). Objects in relative motion are tilted in space and time (or rather, spacetime), and different observers will see things unfold under different perspectives. Personally, I find relativity of ...


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One reason for the difference is time dilation--a given coordinate clock at rest in one frame will be running slow as measured by coordinate clocks at rest in another frame. It can be demonstrated that this follows logically from the two postulates of special relativity, using the "light-clock" thought-experiment detailed here. The second postulate says that ...


1

This alleged problem falls apart as soon as you do a rigorous analysis. It should be clear that with such random accidents there is no causation. If event A really causes event B, then that's reflected in the state of the system. You'll have a state of the form 1/sqrt(1+|u|^2)[|A B> + u |not(A) not(B)>], so an entangled state containing information about the ...


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Many-world interpretation can be consistent with the second law of thermodynamics. It is not a problem. Now, about this hypothetical time travel: If you went back in time to tell Shakespeare about his work and he published it after, it looks consistent but it is ultimately a paradox because where does that knowledge come from? Information, or strictly ...


0

A couple of things first... 1) Time dilation is not a consequence of high speeds, but of ANY speed - it just the effects grow large rapidly within about 10% the speed of light. Low speeds can have measurable consequences as is the case with magnetic fields for example. 2) All identical clocks "tick" away at the same rate under all circumstances,** metering ...


0

Imagine, for example, that two different inertial observers, one sitting on a train moving through a station with uniform velocity $v$ with respect to ground. The experiment will consist of turning on a flashlight aimed at a mirror directly above on the ceiling and measuring the time it takes the light to travel up and be reflected back on its starting ...


1

The most helpful path to getting your mind wrapped around physics of your question is to examine how you pose the question itself. Most importantly, you write: "...with acceleration instead of a constant velocity, because one of you is experiencing time dilation" This is wrong on a few counts: Time dilation occurs whenever there is relative motion, whether ...


1

I looked at the previous discussion that you had about this here in the comments and I think I may have an idea about what is going on here, but I expect someone else will post a better reply here. First I want to quote three of John Rennie's comments. See this article on the block universe. Note that most us regard this as philosophy not physics ...


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If I do not misunderstand your question, what you are asking refers to what is called block universe. In the block universe, time does not unfold, but is equivalent to the the spatial coordinates in the sense that all the time past present and future already exists, in the same way that the negative axis, the origin, and the positive axis direction in space ...


1

Confusion about Length Contraction [...] if one object is moving at a speed relative to another object, shouldn't this movement affect [...] Talk about "length contraction" (or "time dilation") is inherently confusing; it is improper and should be avoided. In the typical "cosmic ray generated atmospheric muon" example we have the following unambiguous ...


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the key is the word "perception" no person can get another person's perception of anything. the question could be re-worded to be more amenable to physics by asking something about the physical world of matter and energy not one's internal perceptions, just a suggestion.


3

Whether or not time is continuous or has some sort of discrete time step, consider the following. Imagine you had a very powerful computer at your disposal, or that the laws of physics happened to be simple enough that we could simulate something as complex as a sentient, self-aware organism using it. Now, we hit "start" on our simulation, and wait a few ...


0

I think we're getting into the philosophical and metaphysical. Perhaps the flow of time is an illusion in the sense we believe it to be. If we take the points on a graph, we can see a proportionate of them simultaneously, whereas we don't perceive "all time" instantly. Not only can we record a point in the past, time appears to flow from the past, into the ...


1

Length is contracted the other way, we just don't notice it because muons are pointlike particles (as far as anyone knows), and a length of zero is still zero no matter how much you contract it. If you had a beam of muons spaced a fixed distance apart (and yet somehow their "decay counters" only start at $50\text{ km}$ altitude), then it would be a ...


2

Don't confuse time dilation and length contraction,(even if length contraction is a consequence of time dilation) because there is no length contraction for the distance between two reference frames. The length (or distance) must be found in one reference frame, and the observer must be in another reference frame, he may not be part of the reference frame of ...


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Short answer: Yes, length contraction is a symmetric transformation between reference frames. However... You may not like this answer, but I think it's far easier to regard muon decay via the concept of time dilation rather than length of contraction. Reason is, from the standpoint of the muon it's not moving (and yes the Eath is moving but it's not ...


1

Well, Lorentz transformation and whole special relativity gives us short qualitative answer - time dilation and length contraction are very similar. Sitting on Earth we see muons with slower decay rate, because of time dilatation. Being a muon, we calculate time in our own frame of reference - so to keep calculations clear, we need to contract length ...


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Two questions and two errors: The (hypothetical) point of view of the photon is not "frozen" because you need time to perceive something frozen. But the photon has proper time zero, everything is reduced to one instant, thus nothing can be frozen. "Dodge" a photon: Information is transmitted with light speed. As the photon is moving with light speed it is ...


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A photon cannot be said to have its own inertial reference frame, because inertial reference are defined to be a family of coordinate systems that satisfy the two fundamental postulates of SR, one of which is that light moves at c in all frames. You could construct a coordinate system where the photon was at rest, but since this coordinate system wouldn't be ...


1

The "g-force" you would experience if you were to "hover" at Schwarzschild coordinate $r$ away from a spherical body of mass $M$ is given by: $$g=\frac{GM}{r^2 \sqrt{1-\frac{2GM}{c^2r}}}$$ (This only applies to bodies held at a fixed value of $r$. A body in freefall experiences no acceleration, for example. If $r$ is changing in some fashion then then ...


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There are two types of time dilation: dilation caused by being near a large body, and dilation caused by traveling very fast relative to another observer. Relativistic time dilation plays a bigger role for astronauts aboard a space station similar to the ISS. Even though velocity and gravity produce opposite time dilation, in this scenario, time dilation due ...


1

Have a look at my answer to Time Dilation Effects from simply being on a spinning planet orbiting a star in a rotating galaxy in an expanding universe.. Compared to an observer far from the Earth, time at the Earth's surface runs more slowly by a factor of 0.9999999993. Over a 70 year lifespan this makes a difference of about 1.5 seconds. So the man in ...



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