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Buckethead
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From a frame of reference outside of a gravitational field, does the mass of an object near a gravitational field increase?
Just to be clear, I'm not referring to rest mass. Since time dilates and mass increases for an object that has a velocity relative to an observer, it lead me to wonder if mass also increases (since time dilates) for an object in a gravitational field relative to an observer outside that field.timmdeeg said:No it doesn't. Mass is invariant which means it is not coordinate dependent.
Please don't say that. "Mass" means invariant mass. Say "relativistic mass" if you must use the term; better to call it total energy (divided by ##c^2## if you like).Buckethead said:mass increases for an object that has a velocity relative to an observer,
Ibix said:Please don't say that. "Mass" means invariant mass. Say "relativistic mass" if you must use the term; better to call it total energy (divided by ##c^2## if you like).
How are you planning to measure the mass of this thing from far away?
The concept of relativistic mass is misleading, insteadBuckethead said:Since time dilates and mass increases for an object that has a velocity relative to an observer, it lead me to wonder ...
Ibix said:So you are going to combine a time measurement in one place with a measurement of the spring constant (which includes a dimension of time) in another. That won't produce anything meaningful.
Ibix said:In this planet experiment you are comparing a gravitational acceleration where G is defined using time local to the planet to a centripetal acceleration caclulated using your watch. You know that your watch and the clocks on the planet (used to define G) run at different rates. But you are ignoring this and attributing the resultant mismatch in measurements to a change in mass.
Ibix said:Again, you are just using funny time units. They're consistent this time, so things will work out. The numbers are different, but they'd be different if you switched to using minutes instead of seconds.
It's not recommended to do this in relativity because the ratio of my clock rate to yours isn't generally well defined in curved spacetime. You get away with it here because it's possible to write the Schwarzschild metric in a time-independent way. In general, though, you need to make all measurements (time and otherwise) locally or derive the local measurements from your remote observations.
Klystron said:If you have time before your lecture for research, Lee Smolin and James Gleick have written popular books on time that you could skim at the library.
Klystron said:Please consider following the mentors' suggestions: mass particularly change in mass may not be the best concept to help you explain "Flow of Time".
Look again at post #4 from Ibix. Big hint: Energy may be a useful concept to help understand time, rather than mass. Thanks.
Buckethead said:To measure the relativistic mass
Buckethead said:Since the watch fulcrum would be moving more slowly, it would indicate it's mass would have to have increased so as not to violate m=f/a since the force available in the spring itself would be constant.
Buckethead said:From the point of view of the observer in a strong gravitational field (near a black hole for example) according to her watch the Earth is rotating too fast.
Maybe there is such an higher order effect :Buckethead said:From a frame of reference outside of a gravitational field, does the mass of an object near a gravitational field increase?
PeterDonis said:The term "relativistic mass" is not correct for the (hypothetical, it doesn't actually happen--see below) effect you are describing a measurement of. "Relativistic mass" refers specifically to an effect of relative motion. The mass inside the gravitational field in your scenario is at rest relative to the observer well outside the field. So any effect on mass due to a gravitational field, such as you are asking about (and there actually isn't any--see below) would not be correctly described as "relativistic mass".
PeterDonis said:This is not correct. Force "redshifts" the same way energy does, i.e., by the time dilation factor, so the slower motion is due to the reduced force, not to any change in mass.
PeterDonis said:You are making the common mistake of throwing around different scenarios without first getting a proper understanding of the original one. Throwing in the black hole plus the rotating Earth is too much. You need to get a handle on the simplest case--a non-rotating source of gravity and a test mass in its gravitational field--first.
Buckethead said:This would correlate with what Idex said in post #9 about G changing due to time dilation.
Buckethead said:it does seem things "pony up" to keep Newtonian laws working in the way I had hoped they would.
Buckethead said:An observer in a gravitational field notes that the Earth (outside the strong gravitational field of the observer) is spinning too fast (or a watch is ticking too fast).
Buckethead said:Time is actually moving faster and is a physical change that can be verified upon meeting up and comparing watches.
Buckethead said:That being the case, I find Newtonian laws would be violated unless something else also changed.
Buckethead said:I originally thought it might be Mass that changed, but this error has been corrected. It seems instead that it is the force that changes which includes the force in a watch spring and the force due to G and in any other force.
Ibix said:G is defined using time local to the planet
Buckethead said:It seems instead that it is the force that changes which includes the force in a watch spring and the force due to G and in any other force. The so called "redshift" in the force. Is this correct?
You have to be careful here - there are some some dubious assumptions hidden in the innocent-sounding words "real observation" and "too fast".Buckethead said:An observer in a gravitational field notes that the Earth (outside the strong gravitational field of the observer) is spinning too fast (or a watch is ticking too fast). This observation is a real event. i.e. Time is actually moving faster and is a physical change that can be verified upon meeting up and comparing watches.
Buckethead said:The so called "redshift" in the force.
I'm attributing it to a change of units in G, I think. If I am a distant observer using time on my wristwatch to analyse something happening at some more-or-less constant altitude far below me in a Schwarzschild metric, that's the same as an observer local to the experiment using a watch that ticks Schwarzschild coordinate time at that altitude, surely? It's just funny time units.PeterDonis said:G isn't defined using anyone's local notion of time. It's a universal constant. So the explanation you are offering, that the distant observer's observations should be attributed to a change in G, does not work.
Ibix said:I'm attributing it to a change of units in G, I think
Ibix said:If I am a distant observer using time on my wristwatch to analyse something happening at some more-or-less constant altitude far below me in a Schwarzschild metric, that's the same as locally using a watch that ticks Schwarzschild coordinate time, surely?
Ibix said:It's just funny time units.
I think that's a matter of interpretation of the original question. My reading of #5 is basically that Buckethead is looking down at a mass on a spring and using his own watch to time its oscillations. He isn't correcting for redshift, which is how he can say the spring is moving slowly.PeterDonis said:No, it's different curves through spacetime having different lengths. The units measuring the length along each curve are the same.
But I don't think that's a precise analogy to Buckethead's experiment. Buckethead's worldline and that of the spring never meet. It's more like Buckethead walking a line of constant latitude near the pole and wondering how he's staying ahead of a sprinter on the equator. What he really should be doing is using metre rules on the equator to measure the distance covered by the sprinter. But what he's doing is more like projecting the ends of his own metre rules along lines of constant longitude down to the equator. Which, in this highly symmetric case, would be a perfectly valid procedure if only he didn't call the projected length of his ruler a metre.PeterDonis said:Consider the analogy I made in response to @Buckethead in post #18: two people travel from New York to Los Angeles along different routes.
Nugatory said:That is, our "real observation" is of the proper time along our worldline between the receipt of successive flashes, not the proper time the Earth takes to make one rotation.
Ibix said:I think that's a matter of interpretation of the original question.
Ibix said:My reading of #5 is basically that Buckethead is looking down at a mass on a spring and using his own watch to time its oscillations.
Ibix said:He isn't correcting for redshift, which is how he can say the spring is moving slowly.
Ibix said:Buckethead's worldline and that of the spring never meet.
No. Under the conditions you have specified, the reception events will be separated by less than one day of proper time along our worldline (assuming that a "day" is defined to be the number of cesium-clock seconds that will be counted by a clock on Earth during one rotation).Buckethead said:Just a quick clarification before I answer everyone's posts more extensively. Are you saying we will measure the pulses of light to occur at the rate of once per day proper time (i.e. according to the time on my watch)?
Well how about an observer in a very deep gravity well observing a clock that is located far above, and wondering how the clock hands do not break, as they are going around like crazy?Buckethead said:I'm sorry, but I don't understand this. Without the black hole plus the rotating Earth I have no question. I have to use the two together as that is my question. Just to be clear, my core question now (not my original question) is this: An observer in a gravitational field notes that the Earth (outside the strong gravitational field of the observer) is spinning too fast (or a watch is ticking too fast). This observation is a real event. i.e. Time is actually moving faster and is a physical change that can be verified upon meeting up and comparing watches. That being the case, I find Newtonian laws would be violated unless something else also changed. If this were not the case, the Earth would fly apart from spinning too fast. I originally thought it might be Mass that changed, but this error has been corrected. It seems instead that it is the force that changes which includes the force in a watch spring and the force due to G and in any other force. The so called "redshift" in the force. Is this correct?
Nugatory said:No. Under the conditions you have specified, the reception events will be separated by less than one day of proper time along our worldline (assuming that a "day" is defined to be the number of cesium-clock seconds that will be counted by a clock on Earth during one rotation).
Define a "day" to be the time measured by a cesium clock on Earth during one rotation of the Earth (using the definition of "rotation" I used in #21 above). That's some number of cesium clock cycles on earth. Your handy wristwatch cesium clock, deeper in the potential well, will count fewer cycles between consecutive pulses; that is, less than a day's worth of proper time will pass between the reception events.Buckethead said:I'm confused. Isn't proper time my time (standing standing near this black hole)? If so why did you say "less than one day of proper time" only to say "assuming a day is a day as measured by an Earth bound clock?
PeterDonis said:What do you mean, "too fast"? How does the observer in the gravitational field know this?
PeterDonis said:The difference in elapsed time on watches of people who followed different paths through spacetime does not mean "time is actually moving faster". It just means their paths through spacetime had different lengths. It's no different from two people taking two routes from New York to Los Angeles and finding different elapsed distances on their odometers when they meet again: that doesn't mean "distance is actually moving faster" for one of them.
PeterDonis said:Nope. Locally the laws are the same everywhere. But you are trying to apply local laws to situations that aren't local. That doesn't work.
Buckethead said:By looking through a scope toward the Earth and seeing that it is spinning more than once a day according to the watch on the hand of the observer?
Buckethead said:I would have thought you could do a Lorentz transform from a non local environment to a local environment
Nugatory said:We conclude from this observation (it helps if the transmitted light signals include the time on Earth at which they are sent) that the proper time the Earth takes to make one rotation is greater than the proper time between our receipt of successive flashes. But how does that have to mean that the Earth is spinning "too fast", or equivalently that too little time is passing between revolutions? We have two time intervals. One is longer than the other, but we can interpret this as the longer one being too long, the shorter one being too short, or (best) both of them being just right for what they are.
PeterDonis said:How does the observer know how long a "day" is? How does he know that the time 86,400 seconds has some special significance for the Earth? It doesn't have any special significance in his own observations.
PeterDonis said:You thought wrong. You can't. A Lorentz transformation only works between inertial frames, and in a curved spacetime (i.e., in the presence of gravity), there are no global inertial frames, only local ones
Yes, the mass of an object does affect its gravitational pull. The more mass an object has, the stronger its gravitational pull will be. This is because mass is one of the factors that determines the strength of the gravitational force between two objects.
No, the mass of an object does not increase in a stronger gravitational field. The mass of an object remains constant, regardless of the strength of the gravitational field it is in. However, the weight of an object may change in a stronger gravitational field, as weight is a measure of the force of gravity on an object.
The mass of an object does not affect its acceleration in a gravitational field. According to Newton's second law of motion, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This means that in a gravitational field, all objects will experience the same acceleration regardless of their mass.
No, the mass of an object does not change when it is in orbit. The mass of an object remains constant, regardless of its location or motion. However, the weight of an object may change in orbit due to the changing strength of the gravitational field.
No, an object cannot have a negative mass in a gravitational field. Mass is a fundamental property of matter and it cannot be negative. Objects with negative mass would violate the laws of physics and are not possible in our universe.