Challenge Questions

The short answer is the biological clock of humans and a "nornal" clock that uses the vibration of a crystal or a spring mass sytem would show the same affects. The hard part would be accelerating a person to high enough speed for the affects to be of significance. Maybe on a spacecraft but surely not anywhere on planet earth.

Absolutely! That is the whole crux of the famous Twin Paradox.

Jorrie - very glad you answered this as you did above. Good answer.

I was originally displeased with the question to the point where I felt it useless to even answer. Especially with good stuff readily available on wiki.

http://en.wikipedia.org/wiki/Special_relativity

Also, I would like to point out that since travelling at speeds near c (speed of light) is required, there are many more problematic factors involved in reaching such speeds.

Of course!

Einstein used the example of a man in an elevator cubicle, conducting experiments involving time and distance, to explain the Principle of Equivalence. Regardless of whether the elevator cubicle was sitting 'at rest' on the surface of the Earth and experience a 'gravitational pull' of 1 g, or whether the elevator cubicle was out in space experiencing an upwards acceleration of 1 g, the results of the experiments would be the same -- the Principle of Equivalence. And it applies to all clocks biological, mechanical, electronic, atomic, et cetera.

I do not quite agree with Einstein's example. He said (if I am wrong say so) that a man in free fall will feel no force acting upon him. If a man is say near a very massive object then surely because of the massive g , g will change significantly over say 2 meters, because g is proportional to the inverse square of the distance between the two objects in question. A man falling towards this object will feel like he is being stretched because of the difference in g from his head to his toes. Let me demonstrate.

mass of planet = m = 10^90 kg

G = 6.674x10^-11

Distance to planet centre = r1 = 10 000 000m

my length = 2 m therefore r2= 10 000 002m

At distance r1 g1 = Gm/r/r = 6.674x10^79/r/r = 6.674x10^65 N

At distance r2 we have g2 = 6.6739973x19^65N

Therefore the difference is g1-g2=2.66x10^59N

This is the difference in force you will feel between your head and toes. You will be ripped apart.

Or am I barking up the wrong tree here?

Hi Carel. Technically you are right - it is called tidal forces. Einstein's remark was in relation to Earth, where the tidal forces over a human length are too feeble to notice.

BTW, your example, using m = 10^90 kg is quite unrealistic. The whole observable universe weighs in at around 10^55 kg only! A distance of r1 = 10 000 000m is also very far inside the event horizon of such an unrealistic black hole. To be more realistic, use a black hole of about 10^33 kg or so, which is about a thousand solar masses. You will find that at the horizon of the hole (~ 1.5x10^6 m) the tidal forces are still quite small - it is the small black holes that can tear you apart near their event horizons. The big ones can only do it deep inside the event horizon.

Jorrie

I do not agree even if apparently you seem to be right.

let us demonstrate:

For the sake of simplicity assume you have 2 bodies with same mass at the distance of "a" m connected with a mass less element.

The first body is at R from planet center and the second at R+a

Thus the gravity will be go for the first and goxR/(R+a) for the second. The Forces are the product between gravity and mass so that force (weight) of 1st mass will be Fo=Mxgo and for the second mass F1= MxgoxR/(R+a). The tear force will be the difference DF= Fo-F1= Mxgox(1-R/(R+a))= Mxgoxa/(R+a).

With the values you considered DF= Mxgox2/(10 000 002).

It seams a bit too low to "tear" a part. This tear force is proportional to the gravity gradient which is a lot more important in the case of "black holes" since their mass is big and their radius small. in their neighbourhood the gradient will be tremendous and a tear can occur. In the case that black holes do exist and that one could come near to them.

Hi nick name, I think you left out something important in your calculations. Have you noticed the extreme mass used? (10^90 kg)

The tidal force on each of your masses is given by TF ~ 2GmMa/r³, where m is the mass at each end of your mass-less rod of length a and r is the distance of the center of the rod to the center of the gravitating mass M (valid for r >> a).

I think you will find the same extreme forces that the respondent got, because he was working very deep inside of a black hole!

Jorrie

You are right I played with symbols not with numbers. It was an other error since I forgot to consider the R^-3. At low range the "g" evolution is almost linear but not when distances are important. I did it too fast, some times it happens. No body's perfect with the exception of those who believe in Tesla and dark matter, free energy aso.

I had a look the mass in the example is 1E90, the sun has a mass of 2E30! Ratio = 5E59.

Thanks for the notice.

As Jorrie pointed out relativity does not state that motion reduces the speed at which a clock marks time. It states that time at a location will be observed to go slower when measured by someone who is moving relative to that location, ie, who is in a different inertial frame of reference. Since time itself is affected it doesn't matter whether it is a clock or the aging process or chemical reactions or nuclear decay, etc.

According to theory, most certainly. If one of a pair of twins traveled at close to the speed of light to a distant object and back he would return to find his twin much older than himself.

According to theory, most certainly. If one of a pair of twins traveled at close to the speed of light to a distant object and back he would return to find his twin much older than himself.

It has already been proven that the affects of gravity provide a time differential in relation to time at sea level. The biological clocks of humans that travel to the top of Mount Everest, The ISS, or even the moon clearly indicates that time is relative.

That being said my wife apparently has complete control of time since her benchmarks regarding household chores appear to pass before she tells me to achieve them..

Thankfully she is half Cuban so I can apply the same time differencial to lovin.

Hi

The simple answer is that a living organism traveling along with that clock will experience the same passage of time as does that clock. In fact, the clock and life form would not have any sense that they were moving at all, except for references to other objects that are moving at different velocities.

Unstated, but assumed, is that the conditions such as acceleration are within the viable range for the life form, sort of like doing a chemistry experiment at standard temperature and pressure. The processes in biochemistry, and thus ageing, obey the rules of chemistry and changing the body's temperature would change the rate of the chemical reactions and metabolism by roughly twice or half the original for a rise or drop in temperature, respectively.

With regard to relativistic velocities, the clicking of chemical reactions and the clicking of the clock would keep a fixed ratio and thus the biological -chemical- clock and mechanical clock would stay in synchrony.

The metaphysical or mental sense of the passage of time would be altered by many things, but the clock in the person's pocket would still be the correct reference for comparison.

I hope we advance space propulsion systems to the point where we empirically demonstrate this result on a regular basis.

Have fun,

Ed

No the biological clock of humans will not slow down nor will a clock.

Speed is only relitive to a person observing that speed, which at the speed of light he wont even see, however the person traveling at the speed of light is still governed by the original clock.

Yes all he is doing is covering a great distance in a short space of time.

Who is relative to who?

Would not the person traveling at the speed of light, if he could see the othe person standing still see him in fact traveling at that speed?

the clock remains the same only the distance varies.

Regards additive

The "time flow" is not "unconnected" from the "biological clock". It is implied to any physical procedure. And biological procedures are physical procedures too.

When a friend of us is moving in relativistic speed (relative to us) we observe that his clock "clicks" the time in a slower rate than our clock does. And if we could observe (somehow) our friend, we would see him aging in a slower rate too.

[Of course, if we were standing in his inertial system (on his spaceship or on another spaceship comoving in the same speed as his) we would see him aging in a normal rate (the same as ours).]

In other words: if his trip will last for a "lifetime" we'll see him living for e.g. 150 years, while from his point of view (relative to his inertial system) he will live only 100 years. If he wasn't moving relative to us (during all his lifetime) we would see him living for 100 years too. So the conclusion is that he doesn't live longer relative to himself, but he lives longer relative to us.

( Of course, he will observe the same concerning us: He will see us aging in a slower rate and live longer.)

Hi George. What you wrote is only partially correct, IMO. If both "our friend and us" remained inertial in free space, there is no way anyone could confirm that the other one is aging slower of faster - because of the symmetry of the situation, as you mentioned in your final paragraph: "( Of course, he will observe the same concerning us: He will see us aging in a slower rate and live longer.)"

In order to actually observe a difference in age (or clock readings), there must be an asymmetry in the test, e.g., like the "twin paradox", where one twin stays inertial and the other one makes a (partially) non-inertial round trip. Only when two clocks can be directly compared twice can any conclusions be made on actual differences in clock rates.

Jorrie

Hi Jorrie. You wrote that

"In order to actually observe a difference in age (or clock readings), there must be an asymmetry in the test, e.g., like the "twin paradox", where one twin stays inertial and the other one makes a (partially) non-inertial round trip".

I think you probably didn't mean to use the word observe as you can observe a difference in aging between any two inertial frames of reference even if there is no asymmetry. In this case both observers see the other as aging slower and both are right. It is only when one of the reference frames acelerates to join the other that there is a difference between their ages that they can both agree on.

Hi BobD, you wrote: "I think you probably didn't mean to use the word observe as you can observe a difference in aging between any two inertial frames of reference even if there is no asymmetry."

I suppose it depends on how one defines "observe". I define it as the result after a straight measurement has been corrected for things like light travel time and other known phenomena. The result is that I do not classify reciprocal "aging" as an observation.

Secondly, there is no way in which two purely inertial observers in free space can ever directly compare clocks more than once, so they can't observe which one ages slower - by my definition...

Jorrie

Hi Jorrie, this is really very trivial nit-picking but since the question has already been adequately answered what else is there to do.

Lets take the example of two space travelers with identical clocks who send light pulses to each other every second (as indicated on their clocks) and who are in different relativistic inertial frames of reference. Each will observe the time between the others pulses and after correcting for time of light travel, etc will note that the other's clock is going slower than theirs. Each travellers observation is valid and is no different in principle to observations made by earth astronomers on other objects in space which are in different inertial reference frames. Certainly I would not call such observations invalid.

Bob

Hi Bob. Not really "trivial nit-picking", I think, because there may be some deep implications in what you wrote!

When an observer measures a red/blue shift in signals coming from a nearby source (i.e. not at cosmological distances), she can safely deduce the relative radial opening/closing speed of that object, using the one-way relativistic Doppler shift fromula:^[1]

where x-dot = v/c, a positive (opening) radial speed, λ_Tx the transmitter wavelength and Δλ the wavelength shift at the receiver. To extract a time dilation from that measurement is pure conjecture, not observation, IMHO. Special Relativity does not care whether it is the source or the receiver that moves, the result remains the same, dependent only on relative speed. So perhaps it is the observer that moves and hence time dilated...

Jorrie

[1] Equation from Relativity-4-Engineers eBook.

Hi Jorrie, I am not sure how the doppler shift formula is relevant to my example from previous entry. While the frequency of the light pulse from each traveller would be doppler shifted and you could determine the relative speeds (if you knew the emitted frequency) you would take this into account (in addition to taking into account the extra distance the light would have to travel between each pulse) for each measurement so that the resulting measurement would be the time between pulses of the distant clock relative to your reference frame. The time dilation is not extracted from the doppler shift measurement. I recall a previous challenge question where the lifetime of (pions?) generated in the upper atmosphere and travelling towards the earth at relativistic speeds was greatly extended from the earth reference frame which was purely due to the high relative speed of the pions and not from any acceleration. In that example the (pion?) would also observe the earth as aging slower right up to the time when its lifetime expired.

Bob

Hi Hob, I agree that "The time dilation is not extracted from the doppler shift measurement", but my point is that you have nothing absolute to unequivocally extract it from in a symmetric case.

The only quasi-absolute method that I know of is to have synchronized clocks in each frame and then read the other frame's passage of time as each pass the others clocks. As you know, this method will depend on how the clocks are synchronized in each frame and the two frame's observers will not agree on the others clock synchronization.

In the case of the muon experiment, imagine an inertial frame moving with the particle from altitude to ground level. The only way an observer in such a frame has to 'measure' that the Earth ages slower, is by reading static, Earth synchronized clocks at the top and the bottom of the trajectory in question. It is easy to set up a thought experiment to prove that this is caused purely by the difference in clocks synchronization used in the two frames and hence, unfortunately, rules out determining who ages faster and who ages slower.

I'll respond to the 'aging of the muons' in my next post and attempt to show that it is not a symmetrical situation.

Jorrie

Jorrie, I remember this statement of yours (in a former blog entry). But still is sth not perfectly clarified by you.

I mean, in the "twin paradox" example, twins must meet each other, again, in order to observe the final result of the trip: the one who made the trip is much older than his brother (and this happens because of the partialy non-inertial situation, as you said).

But this is sth different. Now we speak about inertial systems and if there is a way to observe the time dilation due to the SR. And this can be done. As an example: it is possible our friend (who travels in relativistic speed relative to us) to transmit light pulses e.g. 1pulse/sec. But instead of seeing 1pulse/sec, we see his transmission rate to be 1pulse every 2sec. So we conclude that the time on his inertial frame is retarded. Of course (because of the symmetrical situation) our friend will observe exactly the same time dilation on our inertial frame, if we, also, transmit such light pulses.

Actually, neither the time of ours nor the time of our friend is retarded in an objective and absolute way (as there is no such way). Is retarded in a subjective and relative way, meaning with respect to each other.

Let's give you another example: The relativistic time dilation is observable in the collisions of the particles that take place in the big accelerators (like LHC): We observe that some particles -produced after the collisions- "live" longer because of the very high speed that they have.

Any comments???

Hi George, apart from my comments to Bob above, a comment on your second example: "The relativistic time dilation is observable in the collisions of the particles that take place in the big accelerators (like LHC): We observe that some particles -produced after the collisions- "live" longer because of the very high speed that they have."

This is in some way equivalent to the "twin paradox", because the particles are accelerated out of our frame of reference and there is no symmetry, hence we observe an absolute time dilation. Not so for purely inertial observers, as you said...

Jorrie

Hi Jorrie. I certainly respect your opinion (afterall, you are a Guru in SR issues) but, still, I cannot understand your persistence that "two inertial observers have to meet each other twice in order to compare their clocks and to verify any lag of time".

BTW, BobD in his today's post #33 refer to the "light pulses" issue (as a way to observe the time dilation due to SR) like I did in my yesterday's post #28 (probably Bob didn't notice that I had already mentioned this). The point is that we both agree on this. It is an observation of the time dilation (despite your objection of "what does an observation mean").

Also, I'm not sure that I understood your explanation about my 2nd example (concerning the observation of the longer "lifetime" of the very fast moved particles).

I'd like some more comments from you.

Thanks.

Hi George, you wrote: "I cannot understand your persistence that "two inertial observers have to meet each other twice in order to compare their clocks and to verify any lag of time"."

Similarly, I cannot understand how you would determine which clock lose or gain time without bringing them together for a second time. Sending light or other EM pulses between observers does not tell you unequivocally how the passage of time has changed for any of them, because it may be (and IMO is) a function of how light/EM propagates in spacetime.

The mere fact that the purely inertial situation is symmetrical/reciprocal casts doubt on the "observation" that one clock ticks slower than the other.

I'll post separately on your 2nd example (concerning the observation of the longer "lifetime" of the very fast moved particles).

Jorrie

Hi Geoge, on your: "Also, I'm not sure that I understood your explanation about my 2nd example (concerning the observation of the longer "lifetime" of the very fast moved particles)."

I wrote: "This is in some way equivalent to the "twin paradox", because the particles are accelerated out of our frame of reference and there is no symmetry, hence we observe an absolute time dilation."

I meant that if we could have accelerated an observer together with the particles, then there is an obvious asymmetry between that observer and us, the un-accelerated observers. Hence an absolute difference in clock rates, decay times, etc. could be observed. This is exactly what the twin paradox also provides...

I the end, I think it boils down to this: certain time dilations are absolute, while some are just relative and has no absolute meaning. As an example of the latter, if two observers are accelerated identically out and back, but in opposite directions, they will "observe" relative time dilations, but when they get together again, their clocks will still be in sync (reading the same time).

Jorrie

Hi Jorrie, I should have read George's comments before posting mine it would have saved a lot of duplication as we have similar views. I also used the extended lifetime as an example. I think that your argument is that since the particle was accelerated from our frame of reference to a different frame of reference we can measure the extra lifetime due to time dilation because the case is assymetric. I submit that if you could create a particle with a known lifetime and at the moment of its creation it had a relativistic velocity relative to you you would still be able to measure an extended lifetime of the particle even though there was no assymetry in the situation. This is similar to my example of muons (not pions as in my post) created in the upper atmosphere with a relativistic velocity and having greatly extended lifetime.

Bob.

Hi Bob, on the issue of the muon lifetime and symmetry:

I submit that such a situation is asymmetrical on the grounds of the immense energy of the cosmic ray protons that are partially imparted upon the muons (via the pions) and not upon the reference muons in the lab. (The "moving" muons receive E=mc²+½mv², loosely speaking).

Additionally, I have never seen the situation being described as symmetrical in the literature. Here is a small excerpt^[1] of the usual description:

"... Alternatively, one can envision the muon at rest and the earth in motion toward it. In the rest frame of the muon, the earth is moving at  = 0.994, and its atmosphere is contracted by the Lorentz factor, 9.14 with respect its rest length of 15 km."

I don't think you will find a reference that describes Earth's clocks as "ticking slower than the muon's..."

On the other hand, I understand the difficulty in some situations, like: two inertial frame are in relative high speed motion and a "static" muon is created in each frame. Now the situation will be symmetrical and there can be reciprocal observations, but no "real" difference in lifetimes of the muons. Then again, it depends on what one classifies as real...

Jorrie

[1] http://web.mit.edu/lululiu/Public/pixx/not-pixx/muons.pdf

Hi Jorrie. You wrote "if two observers are accelerated identically out and back, but in opposite directions, they will "observe" relative time dilations, but when they get together again, their clocks will still be in sync".

What do you suppose happens if they just accelerate out (but not back) and then meet on the other side of the universe? Would their clocks be in sync?

Hi Guest, you asked: "What do you suppose happens if they just accelerate out (but not back) and then meet on the other side of the universe?"

If this was possible, their clocks should still have been roughly in sync, due to the fact that their situations were symmetrical and roughly identical. This feat is not possible though (even in principle) in a universe with dark energy, i.e. an accelerating expansion, where even in an infinite time you cannot even get close to halfway around...

No because the biological time is relative to the person, so the biological time runs at the same "speed" of the time the observer is running.

I believe that any theory that respects acceleration and decay with a beginning and ending point would suffice. Relativity and motion don't directly fall into this bag of joy and misery and death. Unless somehow it involves the potential passing of my mother inlaw.

Biological clock? Are you asking if a childless woman approaching middle age is accelerated to the speed of light will she be less prone to panicking?

The biological clock of humans is a function of their location in the universe which happens to be Earth..Hence the circadian rythm established tends to follow the rotation of the earth relative to other universal pulls on the contained protoplasm making up a human being with the sun and moon being the largest external to the earth mass bodies..Even small changes in pressure/working shifts etc can throw our biological clocks off ...The chemistries happeningwithin our contained protoplasmic entities are a function of inputs and outputs choreographed by an amazing array of homeostatic seeking organs/tissues/cells functioning in concert..The reaction rates are dictated by chemical availability and these rates happen exceedingly quickly(femto or picoseconds)makingeven the speed of light rate just another extraneous number as we as a body are travelling fairly quickly already(rotation rate/solar system velocity rate/local part of the galaxy velocity rate/galaxy velocity rate/this part of the universe as we know it velocity rate)...The truly remarkable question is that we are now....The speed of light and relativity are human constructs to understanding..all that is..In short i believe,with no stochastic proof that biology will continue at its own pace regardless of relative velocity as biology provided inputs and outputs can be maintained to support lfe will continue at its own rate determined(rate being determined by the usual chemical parameter of concentration/temperature/pressure of reactants involved)..So no the theory does not affect the biological clock if the reactants for that biologcal clock are continually available..

Regards,Marty Wolf

As noted, the speed at which the clock in motion is reduced is only lessened in relation to another clock that is not in motion. The physico-chemical processes that constitute what we call a "biological clock" would also be reduced in speed when in motion, but only in relation to processes not in motion. Both the moving clock and the moving human would not notice the change in and of themselves, but only relative to a stationary reference. Perhaps this is why it is called the "theory of relativity"?

Yes , human biological clocks are affected , but only Female Clocks , and proportional to the rate at which the Female in question is approaching Thirty.

Hi Jorrie, (wish I had your knowledge and expertise!)

I have been trying to understand time and space to myself with
the analogy of "snap shots" and may I ask your opinion please?

i.e. Imagine the whole of space is a series of scenes, portrayed
as pictures; (and not specifying a "time") Similar to the rotary
cards of flick machines where each "snap shot" shows a slight
movement in the drawing to create the movement in the "film"

Now, imagine a "standing" universe of these pictures, billions of them,
which could be "flicked" (played) in any direction to form a continuation
of life, as we, and others, may see it. (and live it)
(it is not the "time" that we use and know of now; i.e. secs. mins. etc.)

It's in the unknown one; THE "time" of the universe, as pertaining to
the flow of the scenes. (in my first paragraph) Were we impinge our "time"
on these pics., attributing our references to the "scenes" as we see or live it.
e.g. different to say; a dog, crocodile, or whatever. Also, this description
(of scenes) would show multi-different directions, each going in an instance
of our "time" which could explain the different points of reference.

I haven't got much further with this, as I'm not that clever, but I do feel
that there may be a "key" here to understanding how space / time works.
What do you think please? (forgive me if I appear simple, it's a natural talent)

jt.

Hi jt, a very philosophical line of reasoning!

In a way, the real world/universe may just be "a series of scenes, portrayed as pictures", as you wrote. However, those scenes seem to run only in the forward direction. As Stephen Hawking (and possibly others, paraphrased) wrote about the "arrow of time": we can visualize observing a glass of milk being spilt onto the floor, but we do not expect to observe the milk to gather itself up from the floor and end up in the glass again.

You wrote: "... but I do feel that there may be a "key" here to understanding how space / time works."

It seems that space and time are interwoven so that the one can be traded off for the other - not one-for-one, but according to the Lorentz transformations. Your image may perhaps be a "key" to understand this fully, but I'm not so sure...

Jorrie

Thank you for your reply Jorrie.

My understanding is very elemental. (negligible)

So I am captivated to read your replies!

Many thanks.

jt.

I say, it seems that you have confused biological clocks with relatavistic clocks. Clocks, mechanical and so on, only "slow down" when the clock itself is traveling at a large fraction of the speed of light, or when subjected to extreme gravity. Biological clocks can be assumed to ALSO slow down IF the organism or person is also traveling at a large fraction of light speed, likely in a space ship, or in a very intense gravitational field.

A person living in deep space traveling in a space ship would undoubtedly age faster due to the living conditions...So the biological clock would be accelerated...Since you cannot accelerate to a speed that would significantly slow time, chances are you would age quicker, even though you may have shaved a few minutes off your chronological time..

Does the theory of relativity affect the biological clock of humans? Is that the question we are addressing? Then we must understand what is meant by a biological clock. From http://dictionary.reference.com/browse/biological%20clock we get the following two definitions of biological clock.

noun

1. An internal mechanism in organisms that controls the periodicity of various functions or activities, such as metabolic changes, sleep cycles, or photosynthesis.
2. The progression or time period from puberty to menopause, marking a woman's ability to bear children.

The first definition is related to the 24 hour daily circadian rhythm which if a function of the rising and setting of the sun. This is related to alternating periods of light and dark. The biological clock in this context is related more to the way we as biological entities mark the passage of time. The biological clock is a mechanism in our brains that is related to how we perceive time.

The second definition is related to how the female human body progresses through the various stages of life as it relates to the ability to have children. Many environmental things can affect the rate of progression of this biological clock.

How would a human traveling at very high speeds have their biological clocks affected? If their environment was otherwise similar except for their relative speed, no real changes would be evident. However, I contend that with the resources ever to be available to humans, traveling at speeds high enough to test this theory will not be possible is a real sense. Perhaps in theory but not in reality. Accelerating a human to high enough speed to matter in terms of relativity would require an unobtainable amount of energy. And then, the environment to which the person would be subjected would cause significant changes in the running of the biological clock. A twin confined to a spaceship would not be in any thing like the environment of the twin who stayed on earth. Even identical twins that live close to each other undergo different aging rates due to differences in environmental factors. Even small changes in environment early in life can have huge changes later in life. In theory, if two identical twins were in two environments that were exactly the same except that one was accelerated up to a high rate of speed and then decelerated back so the two twins could meet again, their biological clocks would have seen a difference. However, since we can not provide the same environment of earth on a spaceship, there is no way to do this experiment at all.

Could the theory of relativity affect the biological clock of humans? I'd say yet. Could the reality of relativity affect the biological clocks of humans? I'd say no.

There was a young woman named Bright, Who traveled much faster than light. She set out one day In a relative way, And returned on the previous night...author unknown

I don't know does the wind chill gfactor affect inanimate objects. At bleast they would survive without artificial help.

Fascinating discussion. Wow.

My watch is supposed to be accurate to one sec in a million years - according to the guarantee that is!

If it turns out to be more than one second out in a million years time, I can see I will be out-manoeuvred by profound arguments when I ask for my money back.

I will probably have to think twice about taking a flight on the Richard Branson space shuttle.