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10122023, 04:19 AM
Question about Special Relativity
I have heard about Einstein's theory of special relativity but never really understood it, so I watched some YouTube videos.
I think I have a grasp of its basic ideas but there is a nagging question that I can't really find the answer to.
Special Relativity states that the faster and object is moving, the slower time is from its point of view. However, when there's know object of reference, you can't know which object is moving and which is not. So what decides an object's speed, and it's perception of time?
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10122023, 05:36 AM
Question about Special Relativity
(10122023, 04:19 AM)Jarsa Wrote: ... what decides an object's speed, and it's perception of time ... ?
Velocity will be the net result of all the acceleration vectors an object underwent from its beginning; no external reference is necessary. The experience of time passage does not change for the entity; it experiences time the same regardless of its velocity. But an external observer will perceive a time differential between itself and what it's observing if their mutual velocities differ, with the faster entity perceiving time for the slower entity as passing more quickly. An astronaut will age more slowly compared to people on earth traveling more slowly than the astronaut. The film "Interstellar" demonstrates this principal at extreme differences.
Again, velocity is a function of net total accelerations, not apparent velocity compared to something else.
Someone please correct me if I'm wrong here.
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10122023, 12:31 PM
Question about Special Relativity
(10122023, 04:19 AM)Jarsa Wrote: I have heard about Einstein's theory of special relativity but never really understood it, so I watched some YouTube videos.
I think I have a grasp of its basic ideas but there is a nagging question that I can't really find the answer to.
Special Relativity states that the faster and object is moving, the slower time is from its point of view. However, when there's know object of reference, you can't know which object is moving and which is not. So what decides an object's speed, and it's perception of time?
In special relativity, there is only relative motion, no absolute motion.
So, suppose that Alice is moving past Jack at 75% of the speed of light in Jack's reference frame. Then Jack is moving at 75% of the speed of light past Alice in Alice's reference frame.
So, Jack sees Alice's clocks as moving slower. But, also, Alice sees Jack's clocks as moving slower. Both see the clocks of those moving *in their reference frame* as moving slower.
Yes, it sounds paradoxical. But the math actually works out. The point is that *both* space and time measurements are affected in relative motion. So, what Alice sees as being 'at the same place' and 'different times', Jack sees as being at different places and times. The same happens in reverse.
An analogy is with rotation of coordinate systems. Suppose you set up an xy coordinate system in the plane. A point will then have both x and y coordinates. if you rotate the coordinate system, that same point will have different coordinates.
Now, suppose you take *two* points with the same x values but different y values. In the rotated system, those two points will have both x and y values different. Also, the difference in y values will be less.
In reverse, if you take two points that have the same y values in the rotated system, they will have different x and y values in the original system, with the difference in y values smaller in the original.
So, there is 'y contraction' (as opposed to 'time dilation') in going from either system to the other.
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10122023, 12:33 PM
Question about Special Relativity
(10122023, 05:36 AM)airportkid Wrote: (10122023, 04:19 AM)Jarsa Wrote: ... what decides an object's speed, and it's perception of time ... ?
Velocity will be the net result of all the acceleration vectors an object underwent from its beginning; no external reference is necessary. The experience of time passage does not change for the entity; it experiences time the same regardless of its velocity. But an external observer will perceive a time differential between itself and what it's observing if their mutual velocities differ, with the faster entity perceiving time for the slower entity as passing more quickly. An astronaut will age more slowly compared to people on earth traveling more slowly than the astronaut. The film "Interstellar" demonstrates this principal at extreme differences.
Again, velocity is a function of net total accelerations, not apparent velocity compared to something else.
Someone please correct me if I'm wrong here.
You are wrong here.
Time dilation works both ways: each observer sees the clocks going slower for those moving *in their frame of reference*.
There is no such thing as absolute motion in special relativity.
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10122023, 03:42 PM
Question about Special Relativity
(10122023, 12:31 PM)polymath257 Wrote: (10122023, 04:19 AM)Jarsa Wrote: I have heard about Einstein's theory of special relativity but never really understood it, so I watched some YouTube videos.
I think I have a grasp of its basic ideas but there is a nagging question that I can't really find the answer to.
Special Relativity states that the faster and object is moving, the slower time is from its point of view. However, when there's know object of reference, you can't know which object is moving and which is not. So what decides an object's speed, and it's perception of time?
In special relativity, there is only relative motion, no absolute motion.
So, suppose that Alice is moving past Jack at 75% of the speed of light in Jack's reference frame. Then Jack is moving at 75% of the speed of light past Alice in Alice's reference frame.
So, Jack sees Alice's clocks as moving slower. But, also, Alice sees Jack's clocks as moving slower. Both see the clocks of those moving *in their reference frame* as moving slower.
Yes, it sounds paradoxical. But the math actually works out. The point is that *both* space and time measurements are affected in relative motion. So, what Alice sees as being 'at the same place' and 'different times', Jack sees as being at different places and times. The same happens in reverse.
An analogy is with rotation of coordinate systems. Suppose you set up an xy coordinate system in the plane. A point will then have both x and y coordinates. if you rotate the coordinate system, that same point will have different coordinates.
Now, suppose you take *two* points with the same x values but different y values. In the rotated system, those two points will have both x and y values different. Also, the difference in y values will be less.
In reverse, if you take two points that have the same y values in the rotated system, they will have different x and y values in the original system, with the difference in y values smaller in the original.
So, there is 'y contraction' (as opposed to 'time dilation') in going from either system to the other.
Thanks!
Another question I have is why is the speed of light same for all observers. I have seen this in multiple articles but I can't find how Einstein came to this conclusion
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10122023, 04:39 PM
(This post was last modified: 10122023, 04:42 PM by polymath257.)
Question about Special Relativity
(10122023, 03:42 PM)Jarsa Wrote: (10122023, 12:31 PM)polymath257 Wrote: In special relativity, there is only relative motion, no absolute motion.
So, suppose that Alice is moving past Jack at 75% of the speed of light in Jack's reference frame. Then Jack is moving at 75% of the speed of light past Alice in Alice's reference frame.
So, Jack sees Alice's clocks as moving slower. But, also, Alice sees Jack's clocks as moving slower. Both see the clocks of those moving *in their reference frame* as moving slower.
Yes, it sounds paradoxical. But the math actually works out. The point is that *both* space and time measurements are affected in relative motion. So, what Alice sees as being 'at the same place' and 'different times', Jack sees as being at different places and times. The same happens in reverse.
An analogy is with rotation of coordinate systems. Suppose you set up an xy coordinate system in the plane. A point will then have both x and y coordinates. if you rotate the coordinate system, that same point will have different coordinates.
Now, suppose you take *two* points with the same x values but different y values. In the rotated system, those two points will have both x and y values different. Also, the difference in y values will be less.
In reverse, if you take two points that have the same y values in the rotated system, they will have different x and y values in the original system, with the difference in y values smaller in the original.
So, there is 'y contraction' (as opposed to 'time dilation') in going from either system to the other.
Thanks!
Another question I have is why is the speed of light same for all observers. I have seen this in multiple articles but I can't find how Einstein came to this conclusion
The answer to this requires a bit of history.
Newton's laws of motion actually obey a type of 'relativity': they are invariant under what is known as Galilean transformations. In essence, any uniformly moving system can *think* of itself at rest and the laws of physics will still apply. So, even though the sun is moving, the planets still orbit as if it was at rest.
Then, in the middle 19th century, Maxwell proposed his laws of electromagnetism and discovered that they predicted waves moving at what was discovered to be the speed of light. In this way, we learned that light is an electromagnetic phenomenon.
But, it turns out that Maxwell's equations are NOT invariant under Galilean transformations. So this produced a conflict between Newtonian physics and the understanding of light. It was proposed that some 'absolute frame' was the 'correct' one for Maxwell's equations.
But this meant that we should be able to detect the motion of the Earth by looking at how light moves in different directions (it should be slightly different perpendicular to the motion than parallel to it). The Michelson Morley experiment was designed to measure this motion of the Earth.
But, in a result that surprised everyone at the time, no motion was found. This has been called one of the most important null results in the history of science. Many people tried to explain it.
What Einstein proposed was to take the Maxwell equations as correct for *all* reference frames and deduce what sorts of transformations would be allowed for them (not Galilean). His paper going through the details was called 'On the electrodynamics of moving bodies' and was where special relativity was first described.
it turns out that the 'correct' transformations are those proposed by Lorentz and are thereby called the Lorentz transformations. it is these that describe the 'rotation' produced in reference frames by relative motion.
But one of the consequences of taking the Maxwell equations seriously is that the speed of light would be the same in all reference frames.
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10132023, 06:42 AM
(This post was last modified: 10132023, 06:50 AM by Cavebear.)
Question about Special Relativity
(10122023, 03:42 PM)Jarsa Wrote: (10122023, 12:31 PM)polymath257 Wrote: In special relativity, there is only relative motion, no absolute motion.
So, suppose that Alice is moving past Jack at 75% of the speed of light in Jack's reference frame. Then Jack is moving at 75% of the speed of light past Alice in Alice's reference frame.
So, Jack sees Alice's clocks as moving slower. But, also, Alice sees Jack's clocks as moving slower. Both see the clocks of those moving *in their reference frame* as moving slower.
Yes, it sounds paradoxical. But the math actually works out. The point is that *both* space and time measurements are affected in relative motion. So, what Alice sees as being 'at the same place' and 'different times', Jack sees as being at different places and times. The same happens in reverse.
An analogy is with rotation of coordinate systems. Suppose you set up an xy coordinate system in the plane. A point will then have both x and y coordinates. if you rotate the coordinate system, that same point will have different coordinates.
Now, suppose you take *two* points with the same x values but different y values. In the rotated system, those two points will have both x and y values different. Also, the difference in y values will be less.
In reverse, if you take two points that have the same y values in the rotated system, they will have different x and y values in the original system, with the difference in y values smaller in the original.
So, there is 'y contraction' (as opposed to 'time dilation') in going from either system to the other.
Thanks!
Another question I have is why is the speed of light same for all observers. I have seen this in multiple articles but I can't find how Einstein came to this conclusion
As best I understand it, Einstein looked at a village clock from some distance and considered that the light reflecting off it took "some time" to reach his eyes. And he thought if it was closer it would take "less time". So he considered "time" as a way of considering "speed of light" as a basic measurement.. Since nothing could seem to movr faster than light. it was a constant. Thereby, a "constant" in equations.
All forms of electromagnetic radiation, including visible light, travel at the speed of light.
I have no idea "why" lightspeed is a maximum or why it can't be exceeded, but that seems to be the case. I hope any of that helps...
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10132023, 01:00 PM
Question about Special Relativity
(10132023, 06:42 AM)Cavebear Wrote: (10122023, 03:42 PM)Jarsa Wrote: Thanks!
Another question I have is why is the speed of light same for all observers. I have seen this in multiple articles but I can't find how Einstein came to this conclusion
As best I understand it, Einstein looked at a village clock from some distance and considered that the light reflecting off it took "some time" to reach his eyes. And he thought if it was closer it would take "less time". So he considered "time" as a way of considering "speed of light" as a basic measurement.. Since nothing could seem to movr faster than light. it was a constant. Thereby, a "constant" in equations.
All forms of electromagnetic radiation, including visible light, travel at the speed of light.
I have no idea "why" lightspeed is a maximum or why it can't be exceeded, but that seems to be the case. I hope any of that helps... It seems that all massless particles will move at the same speed (according to quantum field theory). Since photons (the particle for light) are massless, that is the speed they move.
One way to intuit this is that massless particles instantly accelerate to the top speed possible.
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10132023, 02:32 PM
Question about Special Relativity
(10132023, 06:42 AM)Cavebear Wrote: (10122023, 03:42 PM)Jarsa Wrote: Thanks!
Another question I have is why is the speed of light same for all observers. I have seen this in multiple articles but I can't find how Einstein came to this conclusion
As best I understand it, Einstein looked at a village clock from some distance and considered that the light reflecting off it took "some time" to reach his eyes. And he thought if it was closer it would take "less time". So he considered "time" as a way of considering "speed of light" as a basic measurement.. Since nothing could seem to movr faster than light. it was a constant. Thereby, a "constant" in equations.
All forms of electromagnetic radiation, including visible light, travel at the speed of light.
I have no idea "why" lightspeed is a maximum or why it can't be exceeded, but that seems to be the case. I hope any of that helps... It was my understanding that lightspeed is a maximum because light doesn't have mass. If anything else tried to go that fast, it would need energy to support its mass, which then has to be stored, which gives the object more mass, and so on. So an object would need infinite energy to travel a lightspeed.
What I don't understand is why the speed of light is the same for all observers. A car going 40 miles an hour is going to appear moving to a guy on the street, but to the guy in the car, its stationary. But light travels and the same speed no matter what the observer is doing.
Perplexing.
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10132023, 08:13 PM
Question about Special Relativity
(10132023, 01:00 PM)polymath257 Wrote: (10132023, 06:42 AM)Cavebear Wrote: As best I understand it, Einstein looked at a village clock from some distance and considered that the light reflecting off it took "some time" to reach his eyes. And he thought if it was closer it would take "less time". So he considered "time" as a way of considering "speed of light" as a basic measurement.. Since nothing could seem to movr faster than light. it was a constant. Thereby, a "constant" in equations.
All forms of electromagnetic radiation, including visible light, travel at the speed of light.
I have no idea "why" lightspeed is a maximum or why it can't be exceeded, but that seems to be the case. I hope any of that helps... It seems that all massless particles will move at the same speed (according to quantum field theory). Since photons (the particle for light) are massless, that is the speed they move.
One way to intuit this is that massless particles instantly accelerate to the top speed possible.
One could argue that, since photons are energy, then by E=MC2, there must be mass. But what do I know...?
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10132023, 08:21 PM
Question about Special Relativity
(10132023, 02:32 PM)Jarsa Wrote: (10132023, 06:42 AM)Cavebear Wrote: As best I understand it, Einstein looked at a village clock from some distance and considered that the light reflecting off it took "some time" to reach his eyes. And he thought if it was closer it would take "less time". So he considered "time" as a way of considering "speed of light" as a basic measurement.. Since nothing could seem to movr faster than light. it was a constant. Thereby, a "constant" in equations.
All forms of electromagnetic radiation, including visible light, travel at the speed of light.
I have no idea "why" lightspeed is a maximum or why it can't be exceeded, but that seems to be the case. I hope any of that helps... It was my understanding that lightspeed is a maximum because light doesn't have mass. If anything else tried to go that fast, it would need energy to support its mass, which then has to be stored, which gives the object more mass, and so on. So an object would need infinite energy to travel a lightspeed.
What I don't understand is why the speed of light is the same for all observers. A car going 40 miles an hour is going to appear moving to a guy on the street, but to the guy in the car, its stationary. But light travels and the same speed no matter what the observer is doing.
Perplexing.
I recently rewatched Cosmos. Sagan had a piece where 2 objects travelling at different speeds saw events the same regardless of the direction of motion. IOW, lightspeed is not affected to the motion of objects.
Yeah, beats the hell out of me too. I imagined recently that a ship was moving at lightspeed and had its headlights on. Would it gradually become enclosed in a fog of light because both were moving at the same speed? According to theory, apparently not. Light moves out at its own speed. But wouldn't that mean light was still moving faster than the lightspeed ship?
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10132023, 09:42 PM
Question about Special Relativity
(10132023, 08:13 PM)Cavebear Wrote: (10132023, 01:00 PM)polymath257 Wrote: It seems that all massless particles will move at the same speed (according to quantum field theory). Since photons (the particle for light) are massless, that is the speed they move.
One way to intuit this is that massless particles instantly accelerate to the top speed possible.
One could argue that, since photons are energy, then by E=MC2, there must be mass. But what do I know...?
E=mc^2 is only for particles at rest. The full equation is
E^2 =m^2 c^4 +p^2 c^2
where p is the momentum of the particle. For photons, m=0 and E=pc.
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10132023, 09:53 PM
Question about Special Relativity
(10132023, 09:42 PM)polymath257 Wrote: (10132023, 08:13 PM)Cavebear Wrote: One could argue that, since photons are energy, then by E=MC2, there must be mass. But what do I know...?
E=mc^2 is only for particles at rest. The full equation is
E^2 =m^2 c^4 +p^2 c^2
where p is the momentum of the particle. For photons, m=0 and E=pc.
WOW! I never realized there was more. Thank you so much.
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10132023, 09:54 PM
(This post was last modified: 10132023, 09:55 PM by polymath257.)
Question about Special Relativity
(10132023, 02:32 PM)Jarsa Wrote: (10132023, 06:42 AM)Cavebear Wrote: As best I understand it, Einstein looked at a village clock from some distance and considered that the light reflecting off it took "some time" to reach his eyes. And he thought if it was closer it would take "less time". So he considered "time" as a way of considering "speed of light" as a basic measurement.. Since nothing could seem to movr faster than light. it was a constant. Thereby, a "constant" in equations.
All forms of electromagnetic radiation, including visible light, travel at the speed of light.
I have no idea "why" lightspeed is a maximum or why it can't be exceeded, but that seems to be the case. I hope any of that helps... It was my understanding that lightspeed is a maximum because light doesn't have mass. If anything else tried to go that fast, it would need energy to support its mass, which then has to be stored, which gives the object more mass, and so on. So an object would need infinite energy to travel a lightspeed.
What I don't understand is why the speed of light is the same for all observers. A car going 40 miles an hour is going to appear moving to a guy on the street, but to the guy in the car, its stationary. But light travels and the same speed no matter what the observer is doing.
Perplexing.
It is tricky to get an intuition on what is going on. Let's do a quick discussion on how to add speeds.
So, if you are in a car going down the highway at 40 mph, you appear to be at rest in your reference frame. Another car that appears to you to go by at 20 mph will be going at 40+20=60 mph with respect to the ground. This is ordinary (Galilean) addition of velocities. In this, V=v1+v2.
But, in relativity, it isn't quite that easy. The formula is now
V=(v1+v2)/(1+v1*v2)
where v1 and v2 are given as fractions of the speed of light.
So, you are moving past the Earth at 40% of the speed of light and another ship goes by you at 60% of the speed of light (according to your reference frame), the speed of the second ship with respect to Earth would be
(.6+.4)/(1+.6*.4) = .806,
so 80.6% of the speed of light.
So why the difference? Well, speeds like 60 mph are very, very small fractions of the speed of light, so that denominator is *very* close to 1, making V=v1+v2 to a very good approximation.
At the other extreme, if v1=1, we get V=1 as well no matter what v2 is. So light going past at the speed of light also is going past at the speed of light in all frames.
Why do velocities in relativity add that way? It has to do with the details of the Lorentz transformations. I'd prefer not to try to do the math in this forum.
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10212023, 01:56 PM
Question about Special Relativity
(10122023, 12:33 PM)polymath257 Wrote: (10122023, 05:36 AM)airportkid Wrote: Velocity will be the net result of all the acceleration vectors an object underwent from its beginning; no external reference is necessary. The experience of time passage does not change for the entity; it experiences time the same regardless of its velocity. But an external observer will perceive a time differential between itself and what it's observing if their mutual velocities differ, with the faster entity perceiving time for the slower entity as passing more quickly. An astronaut will age more slowly compared to people on earth traveling more slowly than the astronaut. The film "Interstellar" demonstrates this principal at extreme differences.
Again, velocity is a function of net total accelerations, not apparent velocity compared to something else.
Someone please correct me if I'm wrong here.
You are wrong here.
Time dilation works both ways: each observer sees the clocks going slower for those moving *in their frame of reference*.
There is no such thing as absolute motion in special relativity.
This may be tangential somewhat, but, assuming there is no privileged frame of reference, how do we determine their frame of reference?
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10212023, 02:14 PM
Question about Special Relativity
(10212023, 01:56 PM)tomilay Wrote: (10122023, 12:33 PM)polymath257 Wrote: You are wrong here.
Time dilation works both ways: each observer sees the clocks going slower for those moving *in their frame of reference*.
There is no such thing as absolute motion in special relativity.
This may be tangential somewhat, but, assuming there is no privileged frame of reference, how do we determine their frame of reference?
It’s the frame where they are at rest.
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11032023, 07:06 PM
Question about Special Relativity
(10132023, 09:53 PM)Cavebear Wrote: (10132023, 09:42 PM)polymath257 Wrote: E=mc^2 is only for particles at rest. The full equation is
E^2 =m^2 c^4 +p^2 c^2
where p is the momentum of the particle. For photons, m=0 and E=pc.
WOW! I never realized there was more. Thank you so much.
For an object at rest, the momentum p=0, and it reduces to the simpler equation.
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11032023, 07:22 PM
(This post was last modified: 11032023, 07:33 PM by pythagorean.)
Question about Special Relativity
(10132023, 06:42 AM)Cavebear Wrote: [quote="Jarsa" pid='409253' dateline='1697125355']
I have no idea "why" lightspeed is a maximum or why it can't be exceeded, but that seems to be the case. I hope any of that helps...
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11042023, 03:51 AM
Question about Special Relativity
(11032023, 07:06 PM)pythagorean Wrote: (10132023, 09:53 PM)Cavebear Wrote: WOW! I never realized there was more. Thank you so much.
For an object at rest, the momentum p=0, and it reduces to the simpler equation.
Forgive the ignorance, but how is an object ever actually at rest? Everything is moving. And I've never understood why C is squared...
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11042023, 03:59 AM
(This post was last modified: 11042023, 04:04 AM by Chas.)
Question about Special Relativity
(11042023, 03:51 AM)Cavebear Wrote: (11032023, 07:06 PM)pythagorean Wrote: For an object at rest, the momentum p=0, and it reduces to the simpler equation.
Forgive the ignorance, but how is an object ever actually at rest? Everything is moving. And I've never understood why C is squared...
An object is only at rest relative to other objects and defines its frame of reference.
The c is squared for the same reason v is squared in K.E. = 1/2 m v²
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11042023, 05:26 AM
(This post was last modified: 11042023, 05:40 AM by pythagorean.)
Question about Special Relativity
(11042023, 03:51 AM)Cavebear Wrote: (11032023, 07:06 PM)pythagorean Wrote: For an object at rest, the momentum p=0, and it reduces to the simpler equation.
Forgive the ignorance, but how is an object ever actually at rest? Everything is moving. And I've never understood why C is squared...
Massive objects (in special relativity) are at rest with respect to a coordinate system that moves along with them.
Massless objects (like photons) are moving too fast for any coordinate system to keep up with them.
That is, somebody thinks that the massive object is at rest (and that's all it takes, since the more general formula is invariant under the Poincaré group, and the only reason for looking at that particular coordinate system was to make p=0, so the formula would be psychologically simpler), but nobody thinks that the photon is at rest.
We like the coordinate system that moves along with the massive object for our own psychological reasons, not because of any physical reasons.
But if there ain't one (like in the case of the photon), then there ain't one. We're just forced to deal with our psychological discomfort, because we can't just magically transform that discomfort away and make it disappear, like we can with massive objects.
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11042023, 05:29 AM
Question about Special Relativity
(11042023, 03:59 AM)Chas Wrote: (11042023, 03:51 AM)Cavebear Wrote: Forgive the ignorance, but how is an object ever actually at rest? Everything is moving. And I've never understood why C is squared...
An object is only at rest relative to other objects and defines its frame of reference.
The c is squared for the same reason v is squared in K.E. = 1/2 m v²
OK, I expected "at rest" would be relative to the immediate location.
But, as I haven't the slightest idea why C is squared in E=MC^2, I also have no idea why v is squared in K.E. = 1/2 m v². And at least I understand what kinetic energy is!
I'm not asking for a math class here. Just something a bit more in plain English. I am better with geometry than physics formulas. I can intuitively grasp why light diminishes at the square of the distance, that F=MA, and that a spaceship can gain speed slingshotting around a planet (time in the gravitywell).
But I (and maybe others) don't know " why" kinetic energy = 1/2 momentum times velocity squared". Why "1/2"? Why is "velocity" squared? Give us a little help here.
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11042023, 05:42 AM
Question about Special Relativity
(11042023, 05:26 AM)pythagorean Wrote: (11042023, 03:51 AM)Cavebear Wrote: Forgive the ignorance, but how is an object ever actually at rest? Everything is moving. And I've never understood why C is squared...
Massive objects (in special relativity) are at rest with respect to a coordinate system that moves along with them.
Massless objects (like photons) are moving too fast for any coordinate system to keep up with them.
That is, somebody thinks that the massive object is at rest, but nobody thinks that the photon is at rest.
Poincaré group  Wikipedia
OK, so a black hole basically is "at rest" as it relates to itself and its gravitational influence.
Massless particles are never at rest (relative to anything)?
Why is C squared?
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11042023, 06:09 AM
(This post was last modified: 11042023, 06:37 AM by pythagorean.)
Question about Special Relativity
(11042023, 05:29 AM)Cavebear Wrote: Kinetic energy = 1/2 momentum times velocity squared". Why "1/2"? Why is "velocity" squared? Give us a little help here.
KE = (1/2) m v^2 = (1/2) m s'(t)^2
(where s=position)
d/dt (KE) = (1/2) m 2(s'(t)) s''(t) = m a(t) = F(t)
according to Newton (F=ma), where a(t) is acceleration, and F(t) is force.
I'm no physicist, but think that 1/2 is there just to cancel out the 2.
I don't think it's any deeper than that.
But what do I know? Best to ask this dude. He's a Physicist.
Of course, IMNSHO, it would have been nice of him to point out that "motor proteins throwing off heat" presumably involves speeding up molecules by applying a force thru a distance, but that's a different issue. (It's not really F dx where dx=0, as you can feel yourself, just by spending all that time in your body. You really are doing work, even if you aren't moving the bar.)
OK, I just watched it again. Did he say "zero delta x"? I'm pretty sure that was a blooper. I think he meant F delta x where delta x =0.
A force is being applied, but the bar isn't moving, not the other way around.
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11042023, 06:12 AM
(This post was last modified: 11042023, 06:14 AM by pythagorean.)
Question about Special Relativity
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