The discussion revolves around the concept of time dilation in the context of special relativity (SR) and its generalization beyond light. Participants explore how time dilation is understood, its implications for particles like muons, and the relationship between different reference frames in relativistic physics.
Participants do not reach a consensus on the interpretation of time dilation and its implications across different reference frames. Multiple competing views remain regarding the nature of time dilation and the effects of relativistic speeds on measurements.
Limitations in the discussion include unresolved assumptions about the frames of reference, the applicability of special relativity versus general relativity, and the complexities introduced by the expansion of space.
Päällikkö said:How has it been shown that time dilation is not a property of light? I've only seen the equation derived from a light clock or something dealing with light. How can time dilation (along with other predictions of special relativity) be generalized to everything as a property of time itself?
I am familiar with this experiment, however I do have a question concerning the time dilation as you interpret it. First of all, the muon is moving constantly until it decays and never decelerates, correct? Since this muon never decelerates to the Earth frame in which it is observed, how can time dilation be observed by the muon if we are to assume that either the muon or the Earth can be considered at rest? That is, to the muon, the Earth's time is dilated - but to the Earth, the muon's time is dilated by the fact that it is shown to live longer than a muon at rest in the Earth frame would. If you go to my thread on special relativity, this is exactly opposite the view touted by posters there in which the moving frame doesn't agree that it's time is dilating until it accelerates to another frame that says that the previously moving frame was dilated.pervect said:Muons generated in the upper atmoshphere by cosmic rays have such a short lifetime that they could not reach the Earth's surface even if they moved at the speed of light before they decayed.
However, muons are observed at the Earth's surface.
The explanation for this is that they don't decay as quickly because of time dilation.
Other particles routinely generated by high energy particle accelerators are also moving at relativistic velocities, and show the same effect of time dilation on their lifetimes.
In the muon's frame the Earth's clocks are running slow, but the distance from the upper atmosphere to the surface is also shrunk due to Lorentz contraction, so in this frame you should still predict that the muon will reach the surface before its onboard "decay clock" runs out. The whole point of relativity is that you should get the same answer to all physical questions no matter which inertial frame you use, and the question of what a clock will read at the moment it reaches the same position as another physical object (like the surface of the earth) is such a physical question.Aer said:I am familiar with this experiment, however I do have a question concerning the time dilation as you interpret it. First of all, the muon is moving constantly until it decays and never decelerates, correct? Since this muon never decelerates to the Earth frame in which it is observed, how can time dilation be observed by the muon if we are to assume that either the muon or the Earth can be considered at rest? That is, to the muon, the Earth's time is dilated - but to the Earth, the muon's time is dilated by the fact that it is shown to live longer than a muon at rest in the Earth frame would. If you go to my thread on special relativity, this is exactly opposite the view touted by posters there in which the moving frame doesn't agree that it's time is dilating until it accelerates to another frame that says that the previously moving frame was dilated.
Special relativity is derived without reference to light in the following papers:Päällikkö said:How has it been shown that time dilation is not a property of light? I've only seen the equation derived from a light clock or something dealing with light.
According to a muon moving through the atmosphere as previously described (I'm not sure of the exact speed, I suppose I could look it up...) what is the length of the known universe? Let's assume the known universe is 15 billion light years across.JesseM said:In the muon's frame the Earth's clocks are running slow, but the distance from the upper atmosphere to the surface is also shrunk due to Lorentz contraction,
The size of the observable universe is actually a lot larger than 15 billion light years due to the expansion of space--about 156 billion light years according to the latest estimates. http://www.glenbrook.k12.il.us/gbssci/phys/Class/relativity/u7l2e2muon.html says a muon created in the upper atmosphere travels at around 0.998c relative to the earth, which gives a length contraction factor of around 0.0632. So, if the distance between the furthest points that we can see along the muon's axis of motion is 156 billion light years in our frame, in the muon's frame the distance between these points would be 9.86 billion light years according to a straightforward SR calculation, although this probably isn't completely legitimate when dealing with GR where spacetime can't be treated as flat as is assumed in SR (and even if space is pretty close to flat, the expansion of space means that spacetime is curved).Aer said:According to a muon moving through the atmosphere as previously described (I'm not sure of the exact speed, I suppose I could look it up...) what is the length of the known universe? Let's assume the known universe is 15 billion light years across.
Yes I agree with the comment about GR. However, the same situation can be applied in a region of space where GR is negligible and the same results should apply. Does this mean that the muon can see points further in the universe than the Earth?JesseM said:The size of the observable universe is actually a lot larger than 15 billion light years due to the expansion of space--about 156 billion light years according to the latest estimates. http://www.glenbrook.k12.il.us/gbssci/phys/Class/relativity/u7l2e2muon.html says a muon created in the upper atmosphere travels at around 0.998c relative to the earth, which gives a length contraction factor of around 0.0632. So, if the distance between the furthest points that we can see along the muon's axis of motion is 156 billion light years in our frame, in the muon's frame the distance between these points would be 9.86 billion light years according to a straightforward SR calculation, although this probably isn't completely legitimate when dealing with GR where spacetime can't be treated as flat as is assumed in SR (and even if space is pretty close to flat, the expansion of space means that spacetime is curved).
I'm not too well-versed in how cosmological horizons work...does anyone know if two observers who are currently at the same location in space but moving apart with a large velocity will have the same horizon or not?Aer said:Yes I agree with the comment about GR. However, the same situation can be applied in a region of space where GR is negligible and the same results should apply. Does this mean that the muon can see points further in the universe than the Earth?
Thank you, this is exactly what I was looking for.Perspicacious said:Special relativity is derived without reference to light in the following papers:
http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=AJPIAS000043000005000434000001
http://arxiv.org/PS_cache/physics/pdf/0302/0302045.pdf
Reference 3
Note that if you try to derive relativity without referring to light, you'll get an equation that, depending whether a certain parameter is set equal to zero or not, will either give you something like relativity's Lorentz transform or will just give you Newtonian physics' Galilei transform, in which there is no time dilation. So you still need experimental confirmation that this parameter is nonzero to show that time dilation will happen, and you also need additional confirmation that this parameter is equal to 1/(speed of light) and thus that the speed of light is the same in all frames.Päällikkö said:Thank you, this is exactly what I was looking for.
So, as long as you suppose that all inertial observers see the laws of physics working the same way, and that this includes Maxwell's laws of electromagnetism which say that the velocity of electromagnetic waves is c regardless of the velocity of the source, then there is no way to avoid these conclusions about time dilation. Of course, it's conceivable one of these premises could be false--in the 19th century physicists believed that Maxwell's laws would only work exactly in a specific preferred reference frame, the rest frame of the "luminiferous ether" which was supposed to be the medium that electromagnetic waves were a vibration in. It was imagined that if our velocity was v relative to the rest frame of the ether, light waves would move at velocity c+v relative to us in one direction, and c-v relative to us in the other. But experiments to detect light traveling at different speeds at different points in the Earth's orbit had failed, so this was part of the experimental justification for thinking the assumptions of relativity were true. Since then, all the most fundamental laws of physics that have been discovered have had the mathematical property of "Lorentz-invariance" which insures they will appear the same in all inertial reference frames. Also, there have been experimental observations of time dilation involving things like particles taking longer to decay when their velocity is close to c, and even atomic clocks placed on board the space shuttle which were initially synchronized with clocks on Earth but came back a few microseconds behind.The simple but essential point is that the double diagonal path that we see the photon traverse is longer than the straight up-and-down path taken by the photon in the stationary clock; in addition to traversing the up-and-down distance, the photon in the sliding clock must also travel to the right, from our perspective. Moreover, the constancy of the speed of light tells us that the sliding clock's photon travels at exactly the same speed as the stationary clock's photon. But since it must travel farther to achieve one tick it will tick less frequently. This simple argument establishes that the moving light clock, from our perspective, ticks more slowly than the stationary light clock. And since we have agreed that the number of ticks directly reflects how much time has passed, we see that the passage of time has slowed down for the moving clock.
You might wonder whether this merely reflects some special feature of light clocks and would not apply to grandfather clocks or Rolex watches. Would time as measured by these more familiar clocks also slow down? The answer is a resounding yes, as can be seen by an application of the principle of relativity. Let's attach a Rolex watch to the top of each one of the light clocks, and rerun the preceding experiment. As discussed, a stationary light clock and its attached Rolex measure identical time durations, with a billion ticks on the light clock occurring for every one second of elapsed time on the Rolex. But what about the moving light clock and the attached Rolex? Does the rate of ticking on the moving Rolex slow down so that it stays synchronized with the light clock to which it is attached? Well, to make the point most forcefully, imagine that the light clock-Rolex watch combination is moving because it is bolted to the floor of a windowless train compartment gliding along perfectly straight and smooth tracks at constant speed. By the principle of relativity, there is no way for an observer on this train to detect any influence of the train's motion. But if the light clock and the Rolex were to fall out of synchronization, this would be a noticeable influence indeed. And so the moving light clock and its attached Rolex must still measure equal time durations; the Rolex must slow down in exactly the same way that the light clock does. Regardless of brand, type, or construction, clocks that are moving relative to one another record the passage of time at different rates.