# Tag Info

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User Sahil Chadha has already answered the question, but here's the math and a pretty picture for anyone who is unconvinced that you're right. Since the train is accelerating, from the perspective of an observer on the train, the ball will experience a (fictitious) force in the direction opposite the train's travel having magnitude $ma$ where $m$ is the ...

6

Suppose you pick two people at random. From one, you pluck a single hair from their head. Is it possible to tell who had the hair plucked by weighing the people? Technically, plucking a hair makes a person very slightly lighter, so you get a tiny bit of information about who had the hair plucked by weighing the people. But the information is very slight ...

5

We need to untangle this a bit but first: the cause of time dilation is the geometry of spacetime which is such that there is an invariant speed c. Now, remember that velocity or speed is not a property of an object; there is no absolute rest. Further, consider the case of three objects in uniform relative motion with respect to each other. If I choose ...

4

If the twins never meet, but just continue travelling in a straight line at constant velocity then each twin will see the other as being younger. The *paradox*$^1$ only occurs if one or both of the twins is accelerated, which of course is necessary for the twins to meet again. $^1$ it's not a paradox of course, just an unintuitive result!

4

It depends on how you define orthogonality, or, as OSE puts it in his comment, "Orthogonality is usually tested using some defined inner product." I'll expand on this a bit. In order to mathematically answer the question Is direction A orthogonal to direction B? we need a definition of the terms "direction" and "orthogonal." The standard ...

4

If you say that earth's velocity around the sun is 67,000 mi/h, your reference point is the sun itself, which makes the aeroplane's velocity 68,000 mi/h, not 1000. Using special relativity only, and (A) observing from the sun, a clock on the plane would seem to run slower than a clock on earth. A person (B) on earth would measure also measure an ...

3

In the frame of reference of the body, is the centripetal force felt or is only the centrifugal force felt? It depends on what you mean exactly. Consider, for example, the amusement park ride Dumbo at Disneyland: . On this ride, passengers sit in mini Dumbo replicas and are swung around in a circle. What forces do they feel? Well, firstly, they ...

3

I'd like to answer as far as buckets are concerned but leave the CMBR to a cosmologist or a real relativity-ist. Mopping the floor up after the chaos left by my children, I think of myself as an expert on the former! In GR it is immaterial whether one describes a "force" as an "inertial force" or a gravitational field. All one "knows" is whether one is ...

3

Let's assume that this whole setup is being viewed from an inertial frame and that if there is gravity, then it points perpendicular to the plane of the disk, then The disk will slide under the pebble, and the pebble will stay where it is. Why? Well in an inertial frame, Newton's second law holds. Since the force on the pebble tangent to the surface of ...

3

The only way to do it is to put you temporarily in free fall. But as for the room you describe, I can only think of one type. Bring a scale with you next time you go down an elevator, and watch artificial gravity reduction at work! Heh heh.

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The simplest way to think about the helium balloon in the accelerating car is to invoke Einstein's Principle of Equivalence: a constant acceleration is the same, in all respects, as a gravitational force. To make matters as simple as possible, we'll ignore the real force of gravity (i.e. what's pulling the car toward the Earth) and just think about the ...

2

It always helps to draw the right picture. This picture assumes that Boxguy is standing next to the lamp, and that the flash leaves the lamp just as it passes PlatGirl. (If, for example, BoxGuy were standing next to the mirror, the picture would look a little different.) The black vertical line is Platgirl's worldline, and any black horizontal line is ...

2

Time dilation (and also length contraction) always occurs with respect to an observer in a different frame of reference. You, in your own inertial frame, will not notice any difference. However, when you compare your measurement to that of an external observer, you will see a discrepancy in the results. If you enter a spaceship and go on a journey through ...

2

Partly because the magnitude of the gravitational force decreases as $\frac{1}{r^2}$, so as the distance from the center of the earth, $r$, increases, the magnitude decreases. The bigger reason for spacecraft is because they are constantly in free fall, and there is no way to feel gravity when you are falling freely. The spacecraft are falling and moving ...

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I've never been at a theme park where you can mount into a plane at free fall. The photo that you posted is inside a reduced gravity aircraft. So you don't modify gravity, you are just falling.

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why we always choose the center of gravity of the bicycle be the rotational center. We do not do that always, sometimes it is better to use the point in contact with the ground or some other point. We use center of mass when it leads to simpler equations than the other points. In problems dealing with torques or rotations we use the theorem T: the sum ...

2

What if without meeting they send a light pulse to each other, such that they can know each other's age The result will still be the same - each twin judges the other twin to be ageing more slowly than themselves. However, sending a light pulse to each other involves other factors that must be taken into account such as time of flight and ...

2

All the previous answers are correct. Let me add just some mathematics. Take a look at the equation for Fermi normal coordinates, for example in the original article by Misner and Manasse [1] or here. These coordinates provide an example of a local Lorentz frame, that is, a reference frame with a locally flat metric. As you can find in these articles, Fermi ...

2

First of all your statement "because pseudo forces can (locally) be interpreted as gravitational fields and it is therefore impossible for the local experimenter to decide whether he is moving, or being accelerated, or motionless." is incorrect. I will paraphrase MTW's 'Gravitation', section 13.6, page 327: We have a very small man inside a very small, ...

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Is there any significance in saying an observer as an imaginary entity? Yes. From Wikipedia: Physicists use the term "observer" as shorthand for a specific reference frame from which a set of objects or events is being measured. Speaking of an observer in special relativity is not specifically hypothesizing an individual person who is ...

1

Let me present a slightly different perspective to Alfred's answer, although I'm basically saying the same thing. I suspect you've got hung up on the idea that velocity causes the relativistic effects like time dilation, but the underlying cause is something different. All the weird effects in SR are caused by a fundamental symmetry of spacetime, which is ...

1

Basically, the universe has a speed limit. No object can ever exceed the speed of light. Now imagine you decide to prove Einstein wrong by building a train capable of nearly reaching the speed of light, and then shooting a bullet forward in that train, so that the bullet will break the speed of light. In order to preserve this speed limit, time for you and ...

1

Great question; I remember being so confused by this when I first took analytic mechanics. The components of the angular velocity "in the body frame" aren't zero because when one writes these components, one isn't referring to measurements of the motions of the particles in the body frame (because, of course, the particles are stationary in this frame). ...

1

GR treats all free-fall reference frames as equivalent. Also, a reference frame is a local thing, as you said. A rotating bucket filled with water is a non-local thing. Anyway, you can go down a very deep rabbit hole by looking up Mach's principle, but I'm not sure I would advise this (I think it may be antiquated). Finally, assuming the universe is ...

1

This term is used all the time in introductory classical physics. In that context, stationary usually means not moving in the laboratory frame. Thus, a block sitting on a table not doing much would be referred to as being stationary. If one studies relative motion, then stationary could mean not moving in whatever frame you're discussing.

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We know that a moving charge produces a magnetic field. We know that a field that is purely electric in one frame of reference will, in general, be a mix of electric and magnetic fields in relatively moving reference frames. In a frame of reference in which an isolated point charge is not moving, the field of the point charge is purely electric. But, ...

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Think about this In your brain there is a clock too. In other words, everything has a clock in itself. The clock in this meaning is the electron and molecule activity. Both gear and battery is electron and molecule activity. And inside your brain is another kind of electron and molecule activity Time dilation is about the reality that all electron and ...

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How do we prove that any directions are orthogonal? [...] we can use the pythagorean theorem. This involves of course a definition of (how to measure or compare) "angle(s)" in the first place; such that one may comprehend statements about (distinct) angles being "equal" (or else: "not equal") for instance in Euclid's 4th axiom (on "right angles") or in ...

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