e=mc�

[ll_billym]

I watched this program on C4 last night and I found it very enlightening, however I would like someone to clarify the following 2 points that I didn't fully understand....

 

1) If you are travelling at the speed of light (or indeed any speed), why will light still move away from you at the same speed as it always does?  This is different from any physical object.

 

2) When the lead balls were dropped in the clay, doubling the height they were dropped from squared the depth of the impression made but this was only done over short distances.  Surely this is to do with the acceleration (speed) the balls gained (i.e. gravity at work).  If 1 ball was dropped from 3/4 up a skyscraper and another from the top, would the impressions be exactly the same due to the maximum speed a falling object can obtain?

Thanks......

[Loosehead]

1) The faster you go the slower time goes. To take this to extremes as an object approaches the speed of light then time slows right down so that the speed of light is still perceived as the same. Current thinking is that  the speed of light is the maximum, if an object could attain this then time would stop, for that object.

2) .... to follow

[Loosehead]

2) This cannot be a general rule as it depends on what they land on, sand, clay, water, cast iron.... etc Acceleration due to gravity is constant regardless of mass but when an atmosphere is present then things change. Ie a terminal velocity can be reached, even with a lead ball. In the example you give I would say that a 1/4 of a skyscraper would probably not be enough for the falling speed to equalise given the density and shape of the material but the general point is valid, if you dropped a lead ball from 15000 feet and another from 30000 they would probably both have reached terminal velocity but that's just an estimate as I have'nt actually calculated it. For meaningful data though you have to remove the atmosphere.  

[Clanad]

I found the following link sometime ago... with it you can conduct your own experiment(s) concerning the effects of air resistance, change in gravity, etc., as it applies to terminal velocity.  Be sure to loacte the sub-link under the title  named Terminal velocity simulation...

http://www.materialworlds.com/sims/TerminalVelocity/worksheet2.html

[ll_billym]

Thanks for the response Loosehead, I still require some more clarification though if you have the time (this presumably depends on how fast you are moving!!)....

1.1)  How does this fit in with the Time=Distance/Speed formula?

1.2) Can you verify my understanding:  If you are travelling at an incredible speed and time slows down by half for you (compared to Earth time) then this just gives light twice as long (relatively) do do the same distance, therefore its speed is the same no matter how fast you are going.

2) The reason I used the balls in clay example was because it was featured in the programme as being one of the discoveries that lead to E=MC�.  When the distance the ball was dropped from was doubled, the depth of the impression squared.  Your reply stating that this is not a general rule confuses me even more as to why this is a fundemental part of the above equation.

[Loosehead]

1.1) The Time distance speed formula does not take account of the time dilation mainly because in the situations that it is used the effect is negligible. For example how long will it take a jumbo jet travelling at 500mph to fly to las vegas. Using the traditional calculation will yeild an answer as accurate as we are likely to want. Also if we included a factor for the time dialation then we would get different figures for different postions, eg the time as the pilot perceives it will be slightly short than the ground crew in heathrow! Day to day calculations generally do not include relativity variables as in the observable sqherer they are negligible.

1.2) Yes that has been my understanding as a layman.

2) e=mc squared is the general rule regardless of the situation. Dropping lead balls into clay in this experiment is the yard stick in this case. Essentially they are using the indentation as a measure of energy to verify the equation. In doing so they are not making any claims about a general, dropping of lead balls situation. If for example instead of clay they used steel then you would get a dent and the balls would squash. measuring the dent and the amount of squashing would provide the same yard stick all be it with more work to do on the calculation.      

[fo3nix]

light moves at constant velocity because it is travelling at the speed of light, c, which is some special intrinsic property of the universe (dont ask why the value of c is what it is, no-one really knows, yet. string theory may hold the key).

however, are you familiar with the exponential function in maths? something like this:
http://people.bath.ac.uk/ma3rgc/Work/rd_decay.gif

as the graph goes down, towards the x-axis, it gets closer and closer. but, it never quite touches. its forever getting closer and closer.

velocity is similar in this regard. you can keep going faster and faster and faster, but you'll never quite get to the speed of light. you can be going very near to the speed of light, and go a bit faster, but you'll still just be that bit nearer to it. you can't ever reach it. this is because you have mass. only massless things (such as the photon, the particle light is made up of), can travel at the speed of light.

for something like a photon though, in some sense there is no time. and thus it moves at a constant velocity. all this because it is massless. this is why it is different from any physical object. "any physical object" is not massless.

[Gef]

I watched the program but was very disappointed with it. It seemed to set out only to describe what each of the terms (energy, mass and velocity of light squared) meant. Some of the individual stories were fascinating but Lavoisier's work on the Law of Conservation of Mass in chemical reactions really had nothing to do with Einstein's work. The "lead ball" experiment was used to show that in some equations a variable has to be squared but did not explain why Einstein used c2 in his equation.