Speed of light and dark matter

[mfarineau]

First off, I'm not a physicist (as I'm sure is evident by my multi-part question), but I'm hoping someone will be kind enough to explain this in basic terms.

Part the first: I'm wondering if someone can explain to me in layman's terms why the speed of light is essentially the universal speed limit?

Part the second: Why does dark matter have to respect the speed of light speed-limit (and how do we know that it does?)

Thanks!

 

[mathman]

The simple answer is that it would take an infinite amount of energy to speed up anything to the speed of light (relativity theory). This applies to all matter (dark and ordinary).

 

[ravikannaujiya]

the speed of light is a universal speed limit because no one could measure the speed of anything more than that of light, not even of the light.

 

[Dale]

the speed of light is a universal speed limit because no one could measure the speed of anything more than that of light, not even of the light.

That isn't true. Simply set up some synchronized clocks a known distance apart and check the time on each as the object goes by. That will give you the speed regardless of if it is slower or faster than light.

 

[Parlyne]

First off, I'm not a physicist (as I'm sure is evident by my multi-part question), but I'm hoping someone will be kind enough to explain this in basic terms.

Part the first: I'm wondering if someone can explain to me in layman's terms why the speed of light is essentially the universal speed limit?

The way you're thinking about this is a little inside out. The universal speed limit is a property of the geometry of spacetime. The fact that light travels at the speed limit really is telling us something about light, not something about the speed limit. What it's telling us is that light is massless. We can see this by considering how energy works in special relativity. And object of mass m moving at speed v will have energy given by
$$E = \frac{mc^2}{\sqrt{1-\left(\frac{v}{c}\right)^2}}.$$

If we examine this equation, we can see that, when v=c, the energy becomes infinite unless the object's mass is 0. And, we can also see that the energy of an object with m=0 will be 0 unless v=c. In the case where v=c and m=0, this equation is actually indeterminate, which turns out to happen because massless objects can actually have any amount of energy without it changing their speed.

So, it isn't that something about light affects how everything else moves. It's that a property of the way the universe works both determines how fast light moves and, for the same reason, restricts how everything else moves, as well.

Part the second: Why does dark matter have to respect the speed of light speed-limit (and how do we know that it does?)

Thanks!

Dark matter has to obey the speed limit for the same reason that everything else does - the speed limit is an underlying property of spacetime itself.

 

[ravikannaujiya]

@ DaleSpam
As far as I know the concept of synchronization of clocks is lost at the relativistic speed and we can not measure the absolute time and distance so measuring the speed is not simply division of distance and time but we need to take account of frame of reference, time delation and the whole special relativity. And it says that nothing can move faster than the light. for simplicity just try to do a thaught experiment:
let's say two observer O1 and O2 are close to each other and they synchronised their clocks. Now they go away from each other with their clock at a distance 300000 km. for which light takes almost 1 sec. to travel. Now if they are able to see the clocks of each other, observer O1 would find that the clock of O2 is 1 sec behind of his own clock and same would go for observer O2.
Now suppose, an object is moving with infinite speed, i.e. a particle reaches instantenously to observer O2 whenever it is realsed by the observer O1. It will take no time but as the clocks are showing the time difference of 1 sec., so, for both the observers, it will take 1 sec to travel the distance as they have their clocks synchronised locally. Thus both the observer will find the speed of the particle is same as the speed of light.

 

[ash64449]

@ DaleSpam

It will take no time but as the clocks are showing the time difference of 1 sec., so, for both the observers, it will take 1 sec to travel the distance as they have their clocks synchronised locally. Thus both the observer will find the speed of the particle is same as the speed of light.

But it is not possible to measure infinite speed. But i agree with DaleSpam is that we can measure something below infinite speed.If something travels faster than light,it will take less than 1 second and both observer will agree on it as their clocks go at the same rate. You used the context of infinite speed,we cannot measure infinite speed as we can't know what is the answer for 1 divided by 0.

 

[Nugatory]

@ DaleSpam
As far as I know the concept of synchronization of clocks is lost at the relativistic speed and we can not measure the absolute time and distance so measuring the speed is not simply division of distance and time but we need to take account of frame of reference, time delation and the whole special relativity

You have misunderstood Dalespam's answer. Synchronization is only lost between clocks that are moving relative to one another. It's OK to have two synchronized clocks one kilometer apart and not moving relative to each other; they will remain synchronized and one km apart for as long as I need them, and that's what Dalespam is describing.

If I'm standing next to one clock when it reads zero, and I shoot a bullet at the other clock... The bullet hits the other clock and stops it. I then slowly walk over to the other clock and look at it, and see that it read one second when it was stopped by the bullet. I know that the speed of the bullet was 1 km/sec in a frame of reference in which I and the clocks are at rest, and I've used my synchronized clocks to discover this.

 

[ravikannaujiya]

@ash64449 and Nugatory
First I would like to address that the synchronisation is lost when no observer is moving. for this I take example of three spaceship at rest observing a star:

Suppose we have three spaceship A, B, and C. The spaceship is not at the same distance from star as shown in the figure above. Every pilot has synchronised his clock with others. One night they observed an abnormal event on a star. Next day, they met with each other and discussed the events took place on the star. They agreed on everything except timing of the event (we can easily figure it out why it is so). And I see that the synchronisation is lost anyway.
Now take the example of bullet. At the speed of bullet we never take relativistic correction. But when we talk about the velocity of light we must take care of relativity.

In case of bullet the distance between the target and firing position is remain same, i.e. X=X₀. But when bullet would be moving comparable with the speed of light then,
X=X₀*√(1-(v²/c²). Now the distace between the two point is function of the speed. So if you say that we can measure the speed of a particle (we are mesuring because the velocity is unknown) that is heigher than or cmparable to the speed of light, then I doubt how we can find the speed when we do not know the relativistic distance between them as it is a function of velocity itself. The same we can have if we measure the time between the two events, i.e. it also needs relativistic correction.

 

[1977ub]

Next day, they met with each other and discussed the events took place on the star. They agreed on everything except timing of the event (we can easily figure it out why it is so). And I see that the synchronisation is lost anyway.

Not if they have the least understand of physics. The light from the star will reach them at different times. Of course all along they have slightly different measurement of the distance to the star, and so the differing times of observation for them are understood in terms of that different distance for A, B, and C so they come up with the same time for the initial event, before its light was sent to each of them. What you said is true only if they imagine the speed of light to be infinite.

 

[Nugatory]

@Next day, they met with each other and discussed the events took place on the star. They agreed on everything except timing of the event (we can easily figure it out why it is so).

No, they still agree about the timing of the events on the star. The light from the events on the star hits their eyes at different times, but because they know about light travel time, they also understand that the the events happened sometime before the light hit their eyes. So the guy who is four light-minutes away from the star sees something happen at four minutes past midnight, the guy who is two light-minutes away from the star sees something happen at two minutes past midnight, and they both agree that it really happened at the same time time, midnight - as long as they are at rest relative to one another so can maintain clock synchronization.

Time dilation, length contraction, relativity of simultaneity are what's left over after you've allowed for light transmission times.

 

[Nugatory]

In case of bullet the distance between the target and firing position is remain same, i.e. X=X₀. But when bullet would be moving comparable with the speed of light then,
X=X₀*√(1-(v²/c²). Now the distace between the two point is function of the speed. So if you say that we can measure the speed of a particle (we are mesuring because the velocity is unknown) that is heigher than or cmparable to the speed of light, then I doubt how we can find the speed when we do not know the relativistic distance between them as it is a function of velocity itself. The same we can have if we measure the time between the two events, i.e. it also needs relativistic correction.

Now you're making an easy problem difficult. Speed is defined to be distance traveled divided by time of travel (using a reference frame in which the observer is at rest - speed is a frame-dependent quantity even in ordinary classical physics). The relativistic effects of the bullet's speed are irrelevant unless we want to calculate how things look to the bullet.

 

[ravikannaujiya]

Not if they have the least understand of physics. The light from the star will reach them at different times. Of course all along they have slightly different measurement of the distance to the star, and so the differing times of observation for them are understood in terms of that different distance for A, B, and C so they come up with the same time for the initial event, before its light was sent to each of them. What you said is true only if they imagine the speed of light to be infinite.

No, they still agree about the timing of the events on the star. The light from the events on the star hits their eyes at different times, but because they know about light travel time, they also understand that the the events happened sometime before the light hit their eyes. So the guy who is four light-minutes away from the star sees something happen at four minutes past midnight, the guy who is two light-minutes away from the star sees something happen at two minutes past midnight, and they both agree that it really happened at the same time time, midnight - as long as they are at rest relative to one another so can maintain clock synchronization..

if the speed of light were infinite, the time of observing the event would be same as it reaches to A, B and C simultaneously irrespective to their distance from the star.
you guys again assuming the distance to be known. :)

 

[ravikannaujiya]

Now you're making an easy problem difficult. Speed is defined to be distance traveled divided by time of travel (using a reference frame in which the observer is at rest - speed is a frame-dependent quantity even on ordinary classical physics). The relativistic effects of the bullet's speed are irrelevant unless we want to calculate how things look to the bullet.

Relativity matters only when speed of the bullet is comparable to the speed of light whether we see how things look like to the bullet or to our position as the bullet is moving w.r.t to us and we are moving w.r.t. to the bullet with the same speed.

 

[ZapperZ]

Relativity matters only when speed of the bullet is comparable to the speed of light whether we see how things look like to the bullet or to our position as the bullet is moving w.r.t to us and we are moving w.r.t. to the bullet with the same speed.

This is incorrect. Do you use relativistic addition all the time? After all, according to an observer in another galaxy, you are moving very, very, very fast!

If the bullet is not moving relative to you, no matter how fast it looks from another frame, that bullet isn't relativistic to you.

Zz.

 

[Nugatory]

if the speed of light were infinite, the time of observing the event would be same as it reaches to A, B and C simultaneously irrespective to their distance from the star.

yes, of course. And then the correction for light travel time would be even easier because the travel time would always be zero. But I'm not sure of the significance of this point because no one in this thread is suggesting that the speed of light might be infinite.

you guys again assuming the distance to be known. :)

Of course we are... Because in principle the distance can always be measured.

 

[1977ub]

if the speed of light were infinite, the time of observing the event would be same as it reaches to A, B and C simultaneously irrespective to their distance from the star.
you guys again assuming the distance to be known. :)

I see my error regarding infinite speed. The issue is that people do not make determination of when an event occurred without knowing how far away something is.

 

[1977ub]

If A, B, and C have synchronized their clocks, they presumably have measurements regarding how far away they are from one another. If they all agree to send out pulses of light at time t1, each will receive the others' pulses at different times. This won't confuse them about their clocks being in synch because they know the light has to travel to get to them.

 

[ravikannaujiya]

This is incorrect. Do you use relativistic addition all the time? After all, according to an observer in another galaxy, you are moving very, very, very fast!

If the bullet is not moving relative to you, no matter how fast it looks from another frame, that bullet isn't relativistic to you.

Zz.

yes .. if the speed of the bullet is high enough (comparable to the speed of light), relativity is always there to play a role. But when speed is very low even 1000km/s, there is no need to take relativistic corrction. You can see when we deal with the nutrinos or high energy particles from outer space falling on the atmosphere of the earth, we take relativistic correction.

 

[ZapperZ]

yes .. if the speed of the bullet is high enough (comparable to the speed of light), relativity is always there to play a role. But when speed is very low even 1000km/s, there is no need to take relativistic corrction. You can see when we deal with the nutrinos or high energy particles from outer space falling on the atmosphere of the earth, we take relativistic correction.

But what does this have anything to do with what I was responding to. You clearly stated that it doesn't matter as long as something is moving close to c in any frame. I'm saying it does! If the bullet is moving at 0.9 c in some frame, but I am in the same ref. frame as the bullet, I see the bullet is not moving, and I do not have to use any relativistic correction of any kind!

Zz.

 

[ravikannaujiya]

But what does this have anything to do with what I was responding to. You clearly stated that it doesn't matter as long as something is moving close to c in any frame. I'm saying it does! If the bullet is moving at 0.9 c in some frame, but I am in the same ref. frame as the bullet, I see the bullet is not moving, and I do not have to use any relativistic correction of any kind!

Zz.

yes ... if the bullet is moving at 0.9 c and observer moving with the bullet with same speed, then both are at the rest with each other and obsly why one would take relativity when observer and observable are not moving with each other. but I am talking when there is relative speed.

 

[ZapperZ]

yes ... if the bullet is moving at 0.9 c and observer moving with the bullet with same speed, then both are at the rest with each other and obsly why one would take relativity when observer and observable are not moving with each other. but I am talking when there is relative speed.

Then maybe what you wrote earlier is not what it turned out to be:

Relativity matters only when speed of the bullet is comparable to the speed of light whether we see how things look like to the bullet or to our position as the bullet is moving w.r.t to us and we are moving w.r.t. to the bullet with the same speed.

Zz.

 

[Dale]

Wow ravikannaujiya, that is an impressive amount of misinformation in one post.

As far as I know the concept of synchronization of clocks is lost at the relativistic speed

Not true. The concept is not the lost, it is just that different frames disagree on whether or not two specific events are synchronized. Relativistically moving clocks can still have a well-defined notion of synchronization.

and we can not measure the absolute time and distance so measuring the speed is not simply division of distance and time

The premises are correct (we cannot measure absolute time and distance) but the conclusion is incorrect and does not follow from the premises. Speed is simply the division of distance and time. The premises show that it speed is not absolute, not that the forumla is any different.

but we need to take account of frame of reference, time delation and the whole special relativity. And it says that nothing can move faster than the light.

No matter or information can move faster than light, but that doesn't place a limitation on speeds that are measurable. For instance, you can measure the superluminal speed of a "laser dot" sweeping across some known distance by using synchronized clocks with a photosensitive trigger. No matter or information is superluminal, but the measured speed of the dot is.

for simplicity just try to do a thaught experiment:
let's say two observer O1 and O2 are close to each other and they synchronised their clocks. Now they go away from each other with their clock at a distance 300000 km. for which light takes almost 1 sec. to travel. Now if they are able to see the clocks of each other, observer O1 would find that the clock of O2 is 1 sec behind of his own clock and same would go for observer O2.

True, but irrelevant. All of the SR effects are what remain after accounting for the finite speed of light. O1 and O2 would know that their clocks are still synchronized precisely because they are 1 light second away and the visual image they see is 1 second late.

Now suppose, an object is moving with infinite speed, i.e. a particle reaches instantenously to observer O2 whenever it is realsed by the observer O1. It will take no time but as the clocks are showing the time difference of 1 sec., so, for both the observers, it will take 1 sec to travel the distance as they have their clocks synchronised locally. Thus both the observer will find the speed of the particle is same as the speed of light.

No, this is silly. The time that O2 sees the release by O1 has nothing to do with the speed of the released particle. The particle will reach O2 before the image of O1 releasing it, thus O2 will immediately know it was FTL, just like getting hit by a bullet before hearing the shot is a sure indication that the bullet was supersonic.

 

[ravikannaujiya]

Then maybe what you wrote earlier is not what it turned out to be:



Zz.

hmm that bold letters were my fault...

 

[ravikannaujiya]

@ daleSpam, then pls clarify me
If we can not measure absolute time and distance in relativistic case, how two observer can have their clocks synchronised with each other moving in different frames of reference? If I consider they had their clocks synchronised before entering into their frames of refernce, why should they have their clocks remained synchronised? As we can see the twin paradox, where twins had their clocks synchronsed before leaving the Earth but when one of them returnes their clocks are no more synchronised so their age.
If they ar not moving but very far away from each other, is there any kind of observation that could show that their clocks are still synchronised? And I think for both of them it would be like looking into past whenever they observe the clocks of each other. If you say why they need such observation, Then I think the very nature of science is to prove your previous data with current experiments. If you say that they know their distance between each other so they can find the exact time deleting all posiblity of misconception. For this you must assume the speed of light is fixed and cannot exceed the value of c if it exceeds then again c becomes unknown and to find the exact time is out of hand. If you say anyother particle may exceed the speed of light, then the particle would not be observable until light reaches to our eyes and it shows that the light came before the particle because that was the light which made the particle observable, again destroying the idea that particle moved faster than light. this thing goes with Cherenkov effect where light reaches before the particle instead particle moved faster than light.
If there is no limitation to measure the speed and we can measure the speed of an object more than that of light, what would you say about second postulate of special theory of reativity?
If the formula for speed is simple distance upon time, why do we need to take relativistic correction when we tackle with the particles with very high speed? Why the Newtonian physics becomes irrelevant while it gives the formula for speed as distance upon time?

 

[Nugatory]

If you say that they know their distance between each other so they can find the exact time deleting all posiblity of misconception. For this you must assume the speed of light is fixed and cannot exceed the value of c if it exceeds then again c becomes unknown and to find the exact time is out of hand

Yes, we must assume that the speed of light is the same for all observers. This is the second of Einstein's two postulates; all of relativity theory is based on this assumption. Of course Einstein didn't just pull this assumption out of thin air; both experiment (Michelson-Morley) and various theoretical considerations pointed that way, and subsequent experiments have vindicated it.

 

[ravikannaujiya]

Yes, we must assume that the speed of light is the same for all observers. This is the second of Einstein's two postulates; all of relativity theory is based on this assumption. Of course Einstein didn't just pull this assumption out of thin air; both experiment (Michelson-Morley) and various theoretical considerations pointed that way, and subsequent experiments have vindicated it.

yes...and that's why speed of light becomes cosmic speed limit.

 

[Dale]

ravikannaujiya, please consider spending a little more effort on your posts. Instead of just asking everything that comes to your mind, narrow it down to one or two key points. Then present those points using paragraphs to organize your thoughts in a logical manner.

@ daleSpam, then pls clarify me
If we can not measure absolute time and distance in relativistic case, how two observer can have their clocks synchronised with each other moving in different frames of reference? If I consider they had their clocks synchronised before entering into their frames of refernce, why should they have their clocks remained synchronised? As we can see the twin paradox, where twins had their clocks synchronsed before leaving the Earth but when one of them returnes their clocks are no more synchronised so their age.

None of this is relevant to the topic at hand. For measuring speed, the two synchronized clocks are at rest wrt each other a known distance apart.

If they ar not moving but very far away from each other, is there any kind of observation that could show that their clocks are still synchronised?

Yes, the Einstein synchronization method, or any equivalent method.

For this you must assume the speed of light is fixed

Yes, of course we assume this. It is the second postulate. A postulate is an assumption. The postulate is well-confirmed experimentally so we can be quite confident making that assumption: http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html

If you say anyother particle may exceed the speed of light, then the particle would not be observable until light reaches to our eyes and it shows that the light came before the particle because that was the light which made the particle observable, again destroying the idea that particle moved faster than light.

This is simply not correct. Suppose there is some tachyon that moves at 10 c which we can detect as it passes through some detector block which emits a flash of light as the tachyon passes through.

Now, suppose that we have a tachyon emitter aligned with two detector blocks. The detector blocks are separated by 1000 ft (in the x direction) and 1 ft away (in the y direction) from each detector block is a clock and a high-speed camera which can see both blocks and the time on the other clock. The clocks are synchronized using Einstein's convention (c=1ft/ns).

The following observations are made: at t=1ns the near camera records a tachyon flash in the near block, at t=101ns the far camera records a tachyon flash in the far block, at t=1001ns the far camera records a flash in the near block when the near clock read 1ns, and at t=1101ns the near camera records a flash in the far block when the far clock read 101ns.

From those observations the experimenters can tell that the tachyon hit the near block at t=0ns and the far block at t=100ns. Then they determine its speed as 1000ft/100ns=10c.

If there is no limitation to measure the speed and we can measure the speed of an object more than that of light, what would you say about second postulate of special theory of reativity?

I would say it is well-confirmed experimentally. The second postulate is a postulate about the speed of light, not a postulate about a limitation of measuring devices.

If the formula for speed is simple distance upon time, why do we need to take relativistic correction when we tackle with the particles with very high speed? Why the Newtonian physics becomes irrelevant while it gives the formula for speed as distance upon time?

I am not aware of a relativistic correction for speed. Can you please provide a mainstream scientific reference for the correction you are thinking about?

 

[ravikannaujiya]

you are saying two contradictory things at the same time. Special relativity and exisitance of tachyon. First if second postulate is correct, then there would be no tachyon. If there is tachyon then the second postulate is incorrect. If there is tachyon, then the case is no more relevant to anykind of light detector which is the fastest way of detecting by now, and there must be tachyon detector. If we put light detector anyway then the detectors would only recognise the light first, before coming the tachyon as Chereknov effect.

 

[Dale]

you are saying two contradictory things at the same time. Special relativity and exisitance of tachyon. First if second postulate is correct, then there would be no tachyon. If there is tachyon then the second postulate is incorrect.

This is not true. You can have any two of tachyons, relativity, and causality. So tachyons do not by themselves contradict relativity.

However, that is not the point. The point is that our measuring devices are not limited to only being able to measure subluminal speeds as you incorrectly claimed in post 3. I demonstrated a set up where, IF there were a tachyon traveling at 10 c, the superluminal speed could be correctly measured. The fact that nothing we know of goes at 10 c does not stem from a limitation of our measuring devices to measuring v<c.

ravikannaujiya, if you believe that it is impossible to measure a superluminal speed due to some fundamental limitation of all measuring devices then please post a mainstream scientific reference which describes that fundamental limitation of measuring devices. Note, this is not the same as a reference that nothing can travel at v>c, but a reference that no device can measure v>c.

If you cannot post such a reference then further comments to that effect are deliberate personal speculation.

 

[1977ub]

"Speed is only a number." All one would need to do in order to detect a speed greater than c is make two measurements. Note the locations and the times in your IRF. Then do simple division of the distance change divided by the time change
and that is the speed. There is *no* specific measurement apparatus that needs to be to used calculate speed.

[edited had initially left out *no*]

$$\frac{\Delta d}{\Delta t}$$

 

[ravikannaujiya]

Read first three chapters of "On Time: An Investigation into Scientific Knowledge and Human Experience" by Michael Shallis and First chapte of "Concepts of Modern Physics" Arthur Beiser.
about tachyon and SR you can read first few lines on Wikipedia by typing Tachyon whether they contradict or not.

 

[1977ub]

Trying to *cause* tachyon radiation and *use* it in a meaningful way would violate relativity and generate potential causality violations.

 

[Dale]

Read first three chapters of "On Time: An Investigation into Scientific Knowledge and Human Experience" by Michael Shallis

That is a pop-sci book, not a valid scientific reference.

and First chapte of "Concepts of Modern Physics" Arthur Beiser.

I didn't see anything there that said that our measuring devices could not detect any v>c. You are inserting your own personal speculation into your reading and not learning what the author is actually saying.

about tachyon and SR you can read first few lines on Wikipedia by typing Tachyon whether they contradict or not.

Nothing there supports your position of post 3 either.

 

[ravikannaujiya]

you are saying two contradictory things at the same time. Special relativity and exisitance of tachyon. First if second postulate is correct, then there would be no tachyon. If there is tachyon then the second postulate is incorrect. If there is tachyon, then the case is no more relevant to anykind of light detector which is the fastest way of detecting by now, and there must be tachyon detector. If we put light detector anyway then the detectors would only recognise the light first, before coming the tachyon as Chereknov effect.

that's what wikipedia says:
A tachyon (pron.: /ˈtæki.ɒn/) or tachyonic particle is a hypothetical particle that always moves faster than light. The word comes from the Greek: ταχύς or tachys, meaning "swift, quick, fast, rapid", and was coined by Gerald Feinberg.[1] Most physicists think that faster-than-light particles cannot exist because they are not consistent with the known laws of physics.[2][3] If such particles did exist, they could be used to build a tachyonic antitelephone and send signals faster than light, which (according to special relativity) would lead to violations of causality.[3] Potentially consistent theories that allow faster-than-light particles include those that break Lorentz invariance, the symmetry underlying special relativity, so that the speed of light is not a barrier.
what you have said: