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51

It travels forwards instead of backwards in an accelerating car for the same reason that a helium balloon travels upwards instead of downwards under the influence of gravity. Why is that? In an accelerating car, for all intents and purposes the acceleration can be considered a change in the amount and direction of gravity, from pointing straight down to ...

36

When your car accelerates forward, the air inside moves back relative to the car. This creates a slightly high pressure in the rear of the vehicle and a low pressure up front. Since helium is lighter than air, it moves away from the region of high pressure. A similar balloon filled with $CO_2$ would move back, since it is heavier than the surrounding air

12

Fun question. Here's my "me-too" answer. Suppose the car has just emerged from a river, so there's a lot of water in it, and the balloon is tied to the floor. Then you drive away. The air in the car is just like a bunch of water :)

11

Everything moves in geodesics, unless acted on by a non-inertial force. Ok. Everything moves in geodesics This just means it takes a path in spacetime, with this path satisfying the geodesic equation:  \frac{\mbox d^2x^\rho}{\mbox ...

11

It acts precisely like water in a cup. Or, more specifically, like the air in the cup. Since the helium is a much lower density than the nitrogen and other gasses in your car, it can be visualized like an air bubble in a bottle. The container for the helium(the balloon) has negligible mass. When you accelerate forward, the water in a bottle will move ...

10

Your question is a natural one to ask, but it has no answer. It is a bit like asking by what mechanism the angles of a triangle always wind up adding to 180 degrees (in Euclidean geometry). There is no mechanism for that - no one is going around checking all the triangles to make sure their angles add up right. It is just a logical consequence of the theory ...

9

Fermat's principle is a bit more complicated than what you state: it says that in travelling from $A$ to $B$, light will go along the paths that will minimize the time taken to get there - and these may or may not be straight lines. (See e.g. Wikipedia.) That said, the gravitational lensing of light does not operate quite like that. Since it is in vacuum, ...

9

Firstly you need to understand Newton's law's. basically the second law. Concisely second law is :"whenever we apply a force on an object this force changes object's velocity's magnitude if it is in the same direction as that of the direction of motion and changes the direction of motion if the applied force is not in the direction of motion." When an ...

7

In special relativity there is no way you can see someone elses time going faster. This is because in SR all motion is relative. There is no notion of an absolute state of rest. In dmckee's example of the muon experiment, we see time moving more slowly for the muons. However the muons (if they were sentient) would see time moving more slowly for us. This ...

7

You assert that special relativity is valid only under constant speed while the speeds of electrons in quantum mechanics vary with positions This is a very misleading statement. What is true is that via Poincare transformations, special relativity describes precisely how the observations of different inertial observers are connected. It is also the ...

7

It's one of the postulates of the special theory of relativity that the speed of light is $c=299,792,458\,{\rm m/s}$ in all inertial reference frames, regardless of the speed of the source and the speed of the observer. This would conflict with other principles in Newtonian physics because one may always make light move faster or slower by adding the speed ...

7

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

When it comes to light any analogy with water is doomed to be completely wrong. I word this so strongly because it is a common misconception that frustrated all of physics for several decades back around the turn of the 20th century. People kept trying to make analogies with water, and the result was always wrong. What you are describing is what is known ...

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 ...

6

So when people say: 'I am approaching the speed of light, and to get to 100% light I would need infinite energy' they are essentially saying that this situation is impossible? Yes. I read this in Hawking's book and confused me because I assume when he says 99.9% speed of light, he means 99.9% speed of light in relation to someone outside observing? ...

6

A centripetal force is not a fundamental force. We call any force a centripetal force if it is acting towards the center of the direction of rotation, perpendicular to the direction of motion. Rotating a rock tied on a string? Centripetal force = tension in the string Satellite orbiting Earth? Centripetal force = gravity Charged object rotating around an ...

5

There can be at least two different flavors of paradoxes. In one, a result such as 2+2=5 is proved, and the problem must be either incorrect reasoning or a set of assumptions that was invalid. In the other type, exemplified by the EPR paradox, the correct result of an argument is so surprising that it seems like it must be a mistake. Based on the ...

5

I put my negative comment in the from of the answer. Here are the very basics of the simultaneity implications (or causes) of relativity: According to the special theory of relativity, it is impossible to say in an absolute sense whether two distinct events occur at the same time if those events are separated in space, such as a car crash in London ...

5

That is exactly right. A fundamental tenet of physics is that all inertial reference frames are equivalent and indistinguishable.1 Furthermore, given one inertial frame (standing at rest2), any other frame moving with respect to it with a constant velocity is also inertial. The frame "moving at terminal velocity" is just as inertial as "sitting still" and so ...

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 ...

5

NO, They do not cancel out each other, while centripetal (center seeking force) is generally provided by some other agency/force, like for revolution of planets it is provided by gravitational force, centrifugal force(outward force) is a pseudo force which is felt in the reference frame of the revolving/rotating body. Clearly since the two forces belong in ...

4

The general diffeomorphism symmetry in the target space is not a symmetry of the world line theory or, analogously, the world sheet theory! A general spacetime diffeomorphism changes the metric tensor $g_{\mu\nu}(X^\alpha)$ which plays the role of the "coupling constants" (coefficients defining the action, e.g. your exponent) in the world line or world sheet ...

4

Lenny is confused, I think. They're closely related, pretty much the same thing. Light front dynamics is pretty much the same approach as "light cone gauge" except that "light front dynamics" etc. is used by people close to nuclear physics and "light cone gauge" is used by the stringy and nearby researchers. In both cases, we want to slice the spacetime ...

4

in relation to anything else that can make such measurements. As the speed of light is universal, nothing can see any other massive field moving at the speed of light (which is reserved for massless fields) your 0.51 number suggests that you expect that naive addition of velocities holds when velocities approach the speed of light. This is wrong. Here is ...

4

Moving away from earth at some speed can mean moving faster in space OR moving slower in space and thus also mean slower or faster time flow than the one on the earth. There is no speed relative to space, there is just relative motion between objects. But since the earth already travels at some always varying speed and thus is not standing ...

4

It is an axiom of general relativity. A basic assumption. A more accurate statement would be that light always travels along a spacetime geodesic. The classical addition of speeds in newtonian meachanics doesn't work inrelativity (light is the most extreme case). That is the source of all weird stuff in relativity

4

This actually is not so much a relativistic effect but only a consequence of light travelling at a finite speed What you see is the image of the object as it was 10 years ago, this doesn't mean the object is actually "in the past", it only means that any information (photons) sent by the object will reach you 10 years after it has been emitted. (and ...

4

General relativity is not going to help you 'live forever'. Sure, you might develop the technology to hover a tiny distance above the horizon of a black hole. Your aging will slow down. People on earth will observe you outlive your parent by many millions of years. By any number of years really. However, this doesn't help you live 'forever'. All physical ...

4

The net force on the water at the zenith is indeed downwards. However a net force downwards does not mean that the motion will be downwards, only the acceleration. And the water is indeed accelerated downwards at that brief instant, which is why it continues in a circular motion, rather than flying off horizontally as it would if there were neither ...

4

The simple answer is that because you are the traveller and therefore have to slow down, stop, accelerate in the opposite direction and come back again. The situation is not therefore symmetric as the Earthbound observers do not accelerate. You accelerate, so you are NOT in an inertial frame at all times. The easiest calculation is therefore done in the ...

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