Monday, April 21, 2008

From Leonard Susskind to Everyone:

A number of years ago I became aware of the large number of physics enthusiasts out there who have no venue to learn modern physics and cosmology. Fat advanced textbooks are not suitable to people who have no teacher to ask questions of, and the popular literature does not go deeply enough to satisfy these curious people. So I started a series of courses on modern physics at Stanford University where I am a professor of physics. The courses are specifically aimed at people who know, or once knew, a bit of algebra and calculus, but are more or less beginners.

The response was overwhelming and it was suggested that Stanford put them up on the internet. You can find them at

Since the videos went up, I have received many emails with good questions. Some are about the material in the courses. Some are more broadly about physics and science. Here is the place to ask them. If I know the answer to your question I will post it. If not perhaps someone else can answer.

Leonard Susskind


«Oldest   ‹Older   401 – 590 of 590
MarkP said...

I have a stupid question that I cannot get rid of.
If anything falling towards a black hole will become slower and slower from an outside point of view, but never reaches the event horizon, how could the same thing from its own perspective actually fall in?
Shouldn´t that thing see the outside universe evolve faster and faster as it gets closer to the event horizon so that outside an infinite amount of time goes by before it would reach the event horizon?
There´s a theory that a black hole will loose a few particles every now and then, so in some google+ years a black hole will vanish.
Google+ years is a long time, but not infinite.
Wouldn´t that mean that anything falling towards a black hole will see the black hole loosing more and more material until the black hole disappears before that thing reaches it?

Mobius01010 said...

I am in the middle of working on what I hope is a Theory of Everything. I'm not sure if it's correct or not, but if it is... well, if it's wrong, I will have spent years of my life learning things that are essentially useless to me (I'm an artist, not a mathematician), and I need help from a true dyed in the wool physicist, like yourself, but I also have barely scratched the Riemannian surface, and don't yet know if my little epiphany was right or wrong, because all the physics questions involving "why" (supersymmetry, entanglement, dark matter, the Pioneer anomaly, etc) point in my direction now, and feeling like a singularity is somewhat... overwhelming? Either way, I don't want to work for years for a reward that may not exist - if I'm wrong, you would know. I just wanted to know if you still looked after this blog and I could share some of your time. Thank you.

Obaid Qureshi said...

Hi Respected Sir Leonard suskind!

I am undergraduate student of physics, University of Karachi,Pakistan. I am studying particle physics and find out different integrated cross-section of leptonic family but when I integrate the differential cross-section of electron-electron elastic scattering cross-section, in result, I got infinity due to sintheta which is in denominator of differential cross-section, so may you please tell me. Is that possible to calculate integrated cross-section of electron-electron scattering?

Thank you,

Kindest regards,

RobTommasi said...

Hello Professor Susskind,
I have a background in Theoretical Physics from Padua University in Italy.
I am very interested in a personal interpretation on Feynman-Kac formulation of Euclidean Partition Function in QFT. As a result of analytic continuation of time, Euclidean Lagrangian is nothing but Euclidean Hamiltonian and the formula sums up on all periodic boundary conditions of closed loops starting and ending at each eigenstate of position. In my opinion first consequence is that periodic behaviour means that degrees of freedom x(euclidean time) can be thought as harmonic oscillators. Then for each given extremal euclidean time and each oscillation mode x, the sum over all closed loops on x gives an envelope made up of the only contributions surviving. This is definitely a family of closed loops surrounding x and weighted by its euclidean action S. But this means that contributions to euclidean partition function Z by each x come from the behaviour around it. Equation of motion for x degrees of freedom must satisfy then Laplace’s equation with respect to Euclidean time and the other coordinate sigma we can think to parameterize periodically the path surrounding point x. So we can say finally that each point x can be represented by an oscillator X(euclidean time, sigma) on a closed envelope (string?) and Feynman-Kac formula for euclidean Z is nothing but a sum over all strings for all energies and all boundary conditions. It could be interesting to prove that it is equivalent to Dedekind's eta function. I hope to have been clear enough and I ask your opinion about this interpretation that naturally takes strings in QFT.
Thank you very much in advance.
Roberto Tommasi.

Unknown said...

Hello Dr. Susskind,

I've been watching your lectures on Quantum Mechanics and now String Theory. This is a dawn of a new age. You and your associates are doing an amazing thing.

I have a few questions. Unfortunately, this might not be the place, but here I go.

1) Quantum Mechanics: In the double slit experiment that exhibits the property of superposition, has the possibility of entanglement between particles fired from the source device been excluded as a cause of interference? In other words, the next particle fired is entangled with the previous one(s) leading to interference.

2) Black hole Evaporation: I've read about Hawking evaporation where a virtual anti-particle that crosses the event horizon, converts some of the black hole’s mass into energy. Is this the mechanism that would cause the black hole to evaporate when the background temperature of space is less than the black hole temperature? How else would a black hole radiate energy when all carriers of energy are stuck behind the horizon?

3) Gravity: Besides the view that matter warps space-time, is the ultimate source of gravity simply the pressure of surrounding expanding space on matter? Does the space between an electron and the center of an atom expand with the expansion of the universe?

And finally…

4) Has there been any advancement on connecting M.O.N.D. to a physical theory?

Kindest regards and thank you for your valuable time! I look forward to learning more.

Gerry said...

Dear Prof Susskind,
First thank you for these lectures. They're fun.
I have a question about the twins paradox. It sounds ok if you think of one twin setting off and everyone waving and the earth is there etc. But suppose the universe were empty except for the twins. You'd be able to tell which one went on a trip. is that because his frame is non-inertial? If so then it seems to me there is an absolute something. It isn't position or velocity but it does seem to be acceleration.
Is that right?

Ohad Asor said...
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Ohad Asor said...

Dear Prof. Susskind,
I wish I had the words to thank you for what your lectures gave (and still giving) to me, while I live in Israel.
I'm studying by myself, so I don't have anyone to consult with regarding my thoughts.
I would admire if you could take a look on this document:


Ohad Asor said...
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Ohad Asor said...
This comment has been removed by the author.
Jet said...

There is a new theory that the origin of stars is the super massive black hole in the center of the host galaxy. It follows that the origin of planets is the host star they orbit. We know coronal mass ejections are violent, on the order of 100 billion atomic bombs. A planetary ejection would be even more violent, thus creating the heavy elements. In an expanding universe, this concept is so much more plausible compared to the idea that stars and planets are formed by a condensing process. It is time to end the mystery of black holes and realize that they are highly compressed photon matter that are spinning so fast that there is no way stars could ever be absorbed by them. With this new theory, everything we see and know as fact is explained. On the other hand, current theory does not explain even the most basic observable facts like why galaxies spin, are flat and spiral shaped. With the recent discovery of planets outside our solar system, we do see certain anomalies, but planets tend to orbit at the host stars equator. They do so because of equatorial discharge. We see the same effect as stars flow out of their host black hole. Atoms are created from this process, not from condensing radiation. The accretion theory is dead. Our origins lie not in nebula dust and gas but in super massive black holes. This ends the great mystery of black holes. They are 'liquid light', chipped from a central core of solid light. All we need to do is stop kidding ourselves thinking of black holes as some mysterious entity. Just because Relativity does not explain them, it does not mean there is an answer. Forget about E equals MC squared. Energy is the wave and all waves contain particles. Light, gravity and electromagnetic waves all contain particles. There is a true fundamental particle and it is very small. 10 to the neg. 34 meters. We must put an end to this idea that in the beginning there was a big bang. That is no explanation for galaxies upon galaxies. What is ever created from an explosion? Only when the universe has expanded fully and begins to contract will matter begin to condense. Yes, I have a question. Can we end this absurd idea that accreation in an expanding universe is the answer?

Mudassir said...

Respected Sir,
I want to ask a question regarding mass spring system.

mẍ+kx=0 →(A) is an equation which represents mass spring system. It is a linear equation of second order. If I want to make it non-linear I make it like
mẍ+kx+k1(x^3)=0, i.e. I add another term k1(x^3). Why can’t I add k1(x^2) to (A) to make it non-linear?

Elijah said...

I think that potential energy depends not only on position but on velocity. I haven't got the maths or physics to explain it but isn't it the case that as soon as a force acts on a body then it has potential energy, in the case of hitting a baseball, both the position and velocity of the baseball affects the force acting on it and the same would be true of a field, is the potential energy reduced by gamma?

rudugro said...

Dear Prof Susskind!
Recently I watched the 9th lecture on "Topics on String Theory". I found the Hawking temperature of de Sitter horizont pretty paradoxial, because I live right at the horizont of other observers but I dont feel high Hawking temperature .. yet the observers detect different (high?)temperature at my place.. The lecture did not cover this topic..

Wasif said...

dear Susskind please read this article on arXiv:1203.2510 to know how time dilation is possible in nuclear and chemical reactions.

Lee Jamison said...

Dr Susskind,

I hope you are still following this thread. I have watched your lecture series as I had time and listened as I was working on painting projects (though not viewing makes for quite a loss of information) and I came up against an issue I find very perplexing.

When you are discussing the creation of matter and antimatter the standard discussion treats the issue as though this occurs at a pretty specific time. But it can't.

Protons and electrons form at very different energies in the experiments we do in modern times. There is roughly three orders of magnitude in energy level between them. What we know now is that protons and electrons appear to balance out to create the charge neutrality of the universe, but between the period when protons and anti-protons were created and when electrons and positrons were created SOMETHING else either provided charge neutrality or the story we're hearing is way less complicated than what really happened.

Can you shed some light on the gap between the two easily understandable eras of charge neutrality?

Lee Jamison

Fred D. said...

Respected Dr. Susskind,
I am so grateful for the youtube lectures that you have provided. I have learned general relativity, cosmology, quantum mechanics and particle physics from you. Is there any book signings or public appearances you will be making in the near future? If so, when and where? Is this information posted regularly on the internet?

Thank you,
Fred De prosse ( B.S. Computer engineering, U.C. Davis, 1985)

Fred D. said...

Dr. Susskind,
Cosmology question: What caused inflation to end? I saw an article on the concept of hybrid scalar fields so instead of the one scalar field there is also a second one that basically oscillates to a point of tachyonic instability once the original field drops below a certain threshold. Do you agree with this hybrid scalar field theory?
Second question is regarding metric tensor in general relativity. So based on cosmological constant there is no pure minkowski space because there is alway a little vacuum energy to cause curvature even if no mass is present. True? Also, some physics "play" with the metric tensor to create warp engines my merely making the coefficient of metric tensor functions of dx, dy, dz, and dt. You can moosh space up any way you want basically are there any limits with this or just the imagination.
Lastly, I have a theory that the universe could within a sub heisenberg constant unit of time be collapsing a re-expanding periodically, but we would not detect it because of the small time slice with which it happens. This is how space travel could exist. To catch a ride as universe collapses and expands.
Thank you,
Fred De Prosse (UC Davis engineering, 1985)

zhenchang said...

Dear Professor Susskind,
I have a fundamental question about field theory. Field theory assumes that the fields are continous. However, Fields are made by corresponding particles, which are discontinous. How can you explain the conflict?
best wish

nabla said...

Hello mr. Susskind.
Have a question:
I wonder why three body problem (in general N body problem)- can not analitically be solved, I mean what is, say in equation of motion (F=ma), preventing us to determine exact solutions to the equation.

nabla said...

Hello mr. Susskind.
Have a question:
I wonder why three body problem (in general N body problem)- can not analitically be solved, I mean what is, say in equation of motion (F=ma), preventing us to determine exact solutions to the equation.

slackjaw said...

Dear Prof. Susskind,
Thanks for taking the trouble to put your lectures on line. They are great. I have a question, though, about the principle of least action. I understand the derivation of the Euler-Lagrange equations formally, but I feel like one should also be able to derive them by looking at the geometry of a small deviation from the action-minimizing path, figuring out all the first-order ways in which this small deviation might affect the action, then setting the sum of those ways equal to zero.
Consider a one-dimensional problem, with only t and x(t). To make a small perturbation in the path, you’d have to add some small amount Ѳ to the slope dx/dt, between time t-Δt and time t. Then you’d subtract the same amount from the slope between time t and t+Δt. You would then have formed a little tent-like structure above the curve, where the curve is raised up by a small amount Ԑ at time t, i.e., raised up from x(t) to x(t)+Ԑ. And you would have also increased the slope in the increment of time just before t, and decreased the slope in the increment just after t. (I say the “slope,” but really it’s the velocity, dx/dt.) Certainly, the lifting up of the curve at time t gives rise to a change in the action by an amount Ԑ ∙ ∂L/∂x ∙ Δt, which is where one term in the Euler-Lagrange equation comes from.
But what about the other term? It seems like the other term is saying this: You increased the slope by a small amount Ѳ just to the left of t, and you decreased it by the same thing just to the right of t. So the affect on the action is a wash, except if the Lagrangian is slightly "more sensitive to slope" to the right of t than it is to the left of t, and that is where you get the term “d/dt (∂L/∂ẋ).” But what puzzles me is this: In order to get x(t) to rise up by Ԑ (which is first-order small) between t-Δt and time t, you need a change in slope that is zeroth-order small -- in other words, Ѳ must be a macroscopic number, since it manages to increase x by an amount Ԑ even though it only acts over a very small time, Δt. So, I don’t get why you can use the derivative ∂L/∂ẋ, as if ẋ were just varying slightly. Unfortunately I can't draw a picture of what I'm talking about. It's kind of hard to describe.

Unknown said...

LS! I have my own thoughts/philosophy on the nature of all that is! I refrain from using the term "universe" or "multiverse" because I find them to be extremely limiting concepts; as is the concept of matter. Matter is a word/concept scientists seem incapable of getting away from, as in "dark matter," no matter how many dimensions they can postulate (pun intended). I believe the scientific method of observation to be the limiting stumbling block scientists struggle with in attempts to comprehend "all that is!" Is it not possible that infinity includes limitless non-matter existence, that is not observable by humans in a physical state? I postulate that the experience of existing in a non-physical state, as in meditation, allows sight not with eyes, but with consciousness. I ask, "What is thought?" Is it physical? Is it matter? If not, if it is simply non-physical consciousness, then it may be the door to perception of the true nature of "All That Is!" I would like to send you my thoughts on the matter! :)

Unknown said...

I'm not unknown. Followup comments will be emailed to me. :)

Karthik said...

How would a ball look like if its de broglie wave length was high, something like 2 meters ?

saito200 said...

Dear Prof Susskind and all the followers of this blog. I am a PhD student of quantum chemistry. I followed the entire lectures about QM and there's something about the role of complex numebrs which I don't quite glimpse and I'm curious about it.

The first postulate is usually recited as something like: "Quantum systems are described by a wave-function in the compex (Hilbert) space".
Why does it have to be complex? What is the physical reason that justifies using complex numbers? Just because we can't represent quantum systems mathematically in another way? In particular, if one had to describe "i" from a quantum-physical point of view and not from a mathematical stand-point, what could one say? And what about the value of "y" in the general expression "z = x + iy"?

Thank you

Kamran said...

hello...I am 16 years years of age, and I have great love for physics.
I have a question... in the lectures of special relativity, professor susskind said..
I would be using # to represent "fi", and ^ and * to represent super-index, and sub-index respectively...
#^ has all the normal space components and one positive time component, and #* all normal space components and one negative time component. Then he multipled these two and got a quantity which was invaient.
Does that mean that if +ve and -ve time is mixed, then nothing would vary, or in other words, nothing would happen if -ve time goes hand in hand with +ve time...
or does that mean that it is applicable to a photon of light, who does not experience any time in order to view the other photon travelling at the same speed of light, with respect to the first photon.
Or does invarient here mean something else ?

SCPR said...

hai all
Is their any place in the universe where large scale conversion of energy to matter take place?

Jan A. said...

Dear Professor Susskind,
Your book found me and I laughed at the Holographic Principle and gave it to a physics graduate to read. The next book that pushed itself on me was Gary R. Renard's book "The Disappearance of the Universe, Straight Talk about Illusions,......
If you have not read it, it may interest you with its' positing of the Holographic Principle. Fascinating. I have just reclaimed and reread your book. Thank you so much.

Jan A. said...

Dear Professor Susskind,

An after thought. The foreword of Gary Renard's book is not to be missed.

If and when you read "The Disappearance of the Universe", you will read of a text called A Course in Miracles,(don't stop!) not a religious text but an explanation of our temporal reality, time space continuum and so much more.

I am not a "holy roller" but feel the need to share with others, as with any good book such as yours.

I apologise if this is not the correct forum for such a posting. I do not mean to offend anyone. That is not my intention. End of story!

Saurabh said...

Dear Prof. Susskind,
With reference to Lecture 1, Special Relativity, is the invariance of the term (x^2 - t^2) a mere coincidence or experimental fact (like Lorentz Force) or is there a physical meaning attached to it?

Lalit Pradhan said...

I have really got myself confused between these two statements

Speed of light is a constant in every frame of reference and is equal to c.

the speed of light is different in different medium and their ratio is refractive index.

aaronwemple/tweetme said...

Let me know what you think about this new theoretical physics book 'I R Physics' for a wonderful change to classical physics with the most comprehensive study of clean free energy systems (even for catalyst free & polution free power), dark matter solved, and many other wonderful scientific quagmires better explained.

z said...

I have been reading some of Dirac's papers from the 20s. What does he mean by "Einstein's" A's and B's? Is this similar to his references to "q numbers" and "c numbers"?

z said...

The above post is regarding Dirac's paper:P.A.M. Dirac, Proc. Roy. Soc., A114, 243, The Quantum Theory of the Emission and
Absorption of Radiation.
P. A. M. Dirac, St. John’s College,
Cambridge, and Institute for Theoretical Physics, Copenhagen.
(Communicated by N. Bohr, For. Mem. R.S. – Received February 2, 1927.)

z said...

Quote from paper:.....We shall now show that the Hamiltonian (30) leads to the correct expressions
for Einstein’s A’s and B’s. We must first modify slightly the analysis
of § 5 so as to apply to the case when the system has a large number of
discrete stationary states instead of a continuous range. Instead of equation
(21) we shall now have
ih ˙a( 0) = 00V ( 0 00)a( 00).
If the system is initially in the state 0 we must take the initial value of
a( 0) to be 0 0 , which is now correctly normalised. This gives for a first
ih ˙a( 0) = V ( 0 0) = v( 0 0)ei[W( 0)−W( 0)]t/h,
which leads to
iha( 0) = 0 0 + v( 0 0)
ei[W( 0)−W( 0)]t/h − 1
i[W( 0) −W( 0)]/h
corresponding to (22). If, as before, we transform to the variables
2 . . .
u−1, we obtain (when
0 6=
0) = v(W0,
0; W0,
0)[1 − ei(W0−W0)t/h]/(W0 −W0).
The probability of the system being in a state for which each
k equals.....

rjs said...

Professor Susskind, I have been watching your lectures on gravitation and relativity and have a question regarding gravity not specifically discussed. In a spherically symmetric gravitational field, the speed of an orbiting mass is such that (or so it seems to me) the smaller the radius of its orbit, the greater its speed. But, if this is true, then it seems to imply that in order to raise an orbiting satellite to a higher orbit, it would fire a retro-rocket, not an accelerating rocket. This seems counterintuitive. Thanks so much.

Michael Garofano said...

Hey Susskind, where did you go? Anyways, I think it may be worth looking into the relationship between black holes and the fact the suck everything into a singularity vs. the fact the big bang exploded from a singularity. I'm a professional from NYC, certainly no physicist, but I have a feeling there may be a connection. Has this already been explored?

Soumya Dhawan said...

Hello Dr. Susskind
I really want to thank you for uploading these lectures.
I have a doubt regarding lecture 8 of particle physics : basic which the dirac equation predicts negative energy solutions and two spin states by the pauli matrices. This seems to only work for spin 1/2 particles as i think for a spin 1 particle alpha's & betas would be a 5X5 matrix, but nowhere did we assume the particle was an electron, or even a fermion....where am i going wrong?

André-Marie Glaize said...

Dear Leonard,
As many people I discovered your lectures by pure chance and it is really a real pleasure to listen to you. I wish I had such courses when I was a student something like 40 years ago!
Anyway I as would like to learn Quantum Mechanics I managed to do two scripts (not exhaustive) of 2 lectures on QM 2008 and Particle Physics 2009. For people interested I would be happy to give copy of them on request (e-mail address = gandremarie[at]gmail[dot]com)

Thank you again Leonard for your excellent job

Geoffrey Robertson said...

many years ago it occurred to me, whilst looking down a boulevard, that the lines of perspective converging are illusion. if you imagine the view without them, then suddenly space itself is an illusion. Tonight whilst watching a documentary entitled "what is reality" i thought how this "vision" might relate to your "holographic principle" in a conceptual way.Recently i thought to my self that the only actual "separation" in our universe is "time". obviously i'm not a mathematician, but i do enjoy thinking about things and i thank you for helping us all make sense of the world we live in.

Geoffrey Robertson said...

Many years ago it occurred to me, whilst looking down a boulevard, that the lines of perspective converging are illusion. if you imagine the view with these lines "corrected" then our 3-d view is flattened, space itself is an illusion. Tonight whilst watching a documentary entitled "what is reality" i thought how this "vision" might relate to your "holographic principle" in a conceptual way. then i have the question is the only "separation" or "distance" time.

amam said...

Sir, I am a graduate student from India. I would like to know how to proceed to derive an equation to find the time period of a horizontally oscillating spring with a mass attached to its free end. Hoping for your help...

Jarbas Novaes said...

Dear Mr. Susskind,
I have a degree in Law, and also a degree in Philosophy, and I would like to stress a few comments regarding space and time, as we learn in Philosophy, and could be related to modern physics.
In modern physics, we understand space and time as patterns, creating an equation for the constant space-time. When we do so, I mean, when we think space as something that can be distorted, like a curved space-time deformation caused by the Sun, lies within the idea that space and time are “things”, just like a matter that could be changed by cosmic events, or maybe distorted by men. In fact, we consider space-time as if they are both “Substances”, things that we can manipulate. From this Idea, the next level is to travel in time and the worm holes.
I would like to offer a new view about this subject.
First of all, I would like to state that space is the opposite of all other things, or better, space is the place where things rest. Space itself can’t be made out of ether, plasma, or any kind of element. Those are things, and those things are all present in space, but they are not THE space, just because we’ve stated that things and space are completely different. Gravity is also a force created by things, so this force can alter all other things nearby, but it doesn’t make a distortion in the space, it affects only the things that are in space, specially creating optical issues.
I would like to know your opinion about this.
If we notice we are in the right path, I will describe time.

Alf Salte said...

I have been watching your lectures of standford university. I have seen the classical mechanics and special relativity and now started on the general relativity. First off, is there any place a list of which of these lectures comes first etc - I am not sure if I skip over anyone I shouldn't have skipped or if I see them in the wrong sequence. Secondly, I have a question concerning the second part of the general relativity lecture - about the moving frames of reference. You say it is impossible to simulate gravity using acceleration due to divergence. Well, what if you had a universe without gravity but where you were on a planet which grew in size in an accelerated way - everything in the universe grew in the same way so a meter stick would also grow so the people in it would not notice they grew but when they dropped an object their planet grew up to meet the object so that they measured a downward acceleration. Wouldn't they then be justified in calling this "gravity"? In what manner would it differ from regular gravity as we know it?

Alf Salte said...

I have been watching your lectures of standford university. I have seen the classical mechanics and special relativity and now started on the general relativity. First off, is there any place a list of which of these lectures comes first etc - I am not sure if I skip over anyone I shouldn't have skipped or if I see them in the wrong sequence. Secondly, I have a question concerning the second part of the general relativity lecture - about the moving frames of reference. You say it is impossible to simulate gravity using acceleration due to divergence. Well, what if you had a universe without gravity but where you were on a planet which grew in size in an accelerated way - everything in the universe grew in the same way so a meter stick would also grow so the people in it would not notice they grew but when they dropped an object their planet grew up to meet the object so that they measured a downward acceleration. Wouldn't they then be justified in calling this "gravity"? In what manner would it differ from regular gravity as we know it?

Rhythm Sharma said...

feel great to be a part of this blog

Rhythm Sharma said...
This comment has been removed by the author.
Rhythm Sharma said...
This comment has been removed by the author.
kaavya said...

what caused light to acquire such a high speed??

pedro juan said...

Dear Professor Leonard Susskind,

Please add a lecture concerning to Tensors and its applications especially on electromagnetics theory with numeric solutions.



pedro juan said...

Dear Professor Leonard Susskind,

Please add a lecture concerning to Tensors and its applications especially on electromagnetics theory with numeric solutions.



Alf Salte said...

Just watching your cosmology lecture and I have a question. It refers to the equation: (da/dt/a)**2 = some constant (when w=-1) and with the solution a = exp(sqrt(some consant)*t). However as it is squared you also have the possible solution of exp(-sqrt(some constant)*t) but this solution seems to not be considered, why is that and if it were considered what would the expansion look like? seems to me it would continue to expand but the expansion would asymptotically slow down over time.

Cristián Varela Bruce said...

What happend if the space-time does not exist?

For me is hard to belive in a time dependent system...

A human have less than 80 years to understand a million of years.

maybe is cycle

Jose Limérez said...

Dear Professor: In your lecture of special relativity, I can understand the concept of Proper time, but not its mathematical expression.
It seems to me that dt2-dx2 is just an arbitrary definition, not coming from a mathematical deduction and that it has been selected only because it is invariant under Loretz transformations. So, as a crazy idea for my clarification, why not using ds, that is also invariant, or any other, to define the proper time.
Thaks for your great help. Jose Manuel-Spain.

khalfa abdelkader said...

question out physics:
why is friday a bad day for you professor lecture 7 (2008) 1:47:27

nihal3994 said...

what does the unification theory aim to do?Is it a field equation that can represent all forces/interactions in the universe?

AudreyER said...

About black holes. I believe a black hole is just an underpass enclosed in the space-time with the characteristics of proper space and proper time and 0 time-point. I believe it is a stop-point for our understanding because we have not any conscious experience of similar conditions but it is not a stop-point for theoretical physics.

Eleana Geo said...

Hi!First of all forgive my bad english.I was watching an episode of "through the wormhole" documentary,it was about black holes..I dont know anything about physics so my Q is probably sily and im sorry for that :)(actually i have 3 Q's)
1)Black holes swallow everything?
2)If they do swallow everything and one another what happens when is nothing left to swallow?could it be another Big bang?
Im so confused .

Mike - NZ said...

I've come to this blog and the lectures late, but am enjoying the series on Strings. Occasionally i think 'i get that' and worlds open up. Thank you for this.

Len said...

I think I got the right title: In your video "The World As Hologram" I understand the actual universe may be 1000 times that of the
observable universe. Would that have any effect on the actual age of the universe?

Len said...

Bad boy of physics? Have you been banned from Physorg? Do a search on "ynot1 physorg".

kshitij kumar pandey said...

dr, susskind
i want to ask you that what is the conclusion of string theory,i mean after combining quantum mechanics and general relativity what we will get to know ?

Len said...

Are multiverses unfalsifiable? Yes if there is no other way of disproving them.

Len said...

@kshitij kumar pandey - Let me guess. Only universes similar to ours can replicate.

Len said...

@kshitij kumar pandey - or, perhaps, the most likely to replicate.

TheRealCygnus said...

Hello Professor Susskind,
Much thanks for the mind candy video lectures. In the recent long awaited General Relativity lecture #10...
specifically regarding gravity waves....a student asked about frequency....& another looked it up...& said 7.5 hrs. as a it only the relative rotation of the binaries that contribute to detectable frequencies ? I would guess that would only produce ELF waves such as the 7.5hr....but I recently read in a physics world article about the LIGO experiment and it mentioned that it filtered the wave data to only pass KHz ranges & that if it was sound waves it would be in the audible range ! ....why KHz & not ELF ? or are many ranges produced ? & how ? maybe the detection method cant use low-pass as a limitation ?...Perhaps you can clear this up ? also is the Energy proportion to frequency the same as in EM ?...BTW...have you seen the Wince Vs. Susskind youtube video?
Its a philosophy Major that has a Theory called existics that makes small corrections to Special Relativity & other things mainly via introducing 3 dimensional time...I'm no expert but the logic & math seem pretty solid ....he claims to have predicted the FTL neutrino mistake at CERN with it....the "Vs Susskind." thing I think was because of the video about Richard Feynman bashes philosophy...anyway I think the theory is serious...has anyone else checked this out or have any comments about any of this ?

Len said...

The World as a Hologram - It seems like the event horizon could be limited in its capacity to store information. That is, the storage capacity of the event horizon could not be more than the number of Planck areas that could form on the surface of the event horizon. If the radius of a black hole doubles and its volume density remains the same, the bit density of the surface area doubles. Eventually as the black hole grows there must be some limit on the event horizon bit density and if this limit is exceeded it would seem the horizon would collapse and as it approached the singularity the pressure and temperature would increase enough to form another big bang.

Since we know the Planck area, if we knew the number of bits in the universe we could then calculate the size of the black hole required to trigger the big bang. If this critical bit density is unique to our position in the landscape, it might rule out many other possibilities. Nevertheless a unique critical density of the event horizon assures that all replications of our universe would have the same size. Seems interesting.

Abdalrahman Abdallah said...
This comment has been removed by the author.
Abdalrahman Abdallah said...

Dear Prof.Susskind

Thanks alot for your great physics courses. Please I want to ask if you are going to give a course in electrodynamics.

Kazi Ranjibul Islam said...

i am currently following the itunes quantum mech course. operator represents observables. but how does one construct an operator corresponding to an observable?i give any observable quantity and ask what is its corresponding operator? how does one determine that?

the engineer said...

hello professor susskind
how can i prove that electron in vacum cant radiate??

GCapp5893 said...

Is this blog still active???

Rouph Mouph said...

Dr. Susskind,

I have two questions, if you find the time to reply.

I'm confused exactly how to explain the difference between states and bits with regard to quantum bits. I do not understand exactly how to explain the relationship between the two. Is it the case that a bit is like a coin with two sides and the state is one of those sides, whichever is the reality of that observable?

Also, in Quantum Entanglement, Part 1, video #8 you say that entropy doesn't add. Is it the case that entropy is additive, but entanglement entropy is not additive? The formula for entropy has a summation so that really threw me off. I just assumed that you meant entanglement entropy.

Thank you for these videos!


Audrey E Randles said...

The Universe contains infinity of these “temporal fields” creating streams and rivers of time. Space sometimes is looking flat and time move the world. Masses associated with visible space are rotated by centrifugal force inside temporal Space-Time Matrixes, around their mass centres at “0” time-points of our understanding, like the surface of water rotating in a bucket. Space-Time flux changes properties, builds channels, path shorting and bringing forth spaces close together or further from us. FromThe Theory Of Matrix, New Concepts of Self and Reality. Psychology of Cosmology and Astrophysics.

vgptgupta said...
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vgptgupta said...
This comment has been removed by the author.
vgptgupta said...


I have a very stupid but basic question that's been bothering me for sometime.
My question is if physical laws are made to be obeyed then what makes the objects obey them. I mean if say an electron is moving under an magnetic or electric field then how does it know about the presence of the field and accordingly why does it act the way it acts under those fields.

I hope my point is clear.

lukka karthik said...

I have a small doubt on band theory of solids. It is a quantum mechanical model.

It always says like this " Energy is required for electron excitation not force or electric field."

For example, Can band theory account for Electric breakdown of insulators at room temperature ?

The primary difference looks like this

"Whenever there is an electron with higher energy and conduction band with less energy gap, it can participate in conduction"


"whenever an higher energy electron is loosely bound by nucleus, with a sufficient electric field we can make a current to flow".

find7truth said...

Hi sir Susskind , all my respects for your work ; so inspiring to see people working hard for their ideas.

I just wanted to say that Iam a believer I do believe in the existance of a creator this world ; it just cant be the result of chaos ;chaos cant create symetry and intelligence in my opinion; so yes sir when you say that this world is a kind of hologram ; which means that everything is written in two dimensions out of the universe ( which I belieave is a multiverse )past present and futur and every bit every information every partucule is written there ... I do belieave this cause I believe that the creator never leaves his creatures without a guidance.

Quran 34/3 " not even the weight of an atom (or a small ant) or less than that or greater, escapes His Knowledge in the heavens or in the earth, but it is in a CLEAR BOOK "

Quran 27/75 " There is nothing hidden in the heavens and the earth that is not (recorded) in a manifest book. "

Heavens means universes and we believe that there is seven .

I hope every reader to know that the Quran is full of such pre-science truths ; peace on you all.

find7truth said...

Hi sir Susskind , all my respects for your work ; so inspiring to see people working hard for their ideas.

I just wanted to say that Iam a believer I do believe in the existance of a creator this world ; it just cant be the result of chaos ;chaos cant create symetry and intelligence in my opinion; so yes sir when you say that this world is a kind of hologram ; which means that everything is written in two dimensions out of the universe ( which I belieave is a multiverse )past present and futur and every bit every information every partucule is written there ... I do belieave this cause I believe that the creator never leaves his creatures without a guidance.

Quran 34/3 " not even the weight of an atom (or a small ant) or less than that or greater, escapes His Knowledge in the heavens or in the earth, but it is in a CLEAR BOOK "

Quran 27/75 " There is nothing hidden in the heavens and the earth that is not (recorded) in a manifest book. "

Heavens means universes and we believe that there is seven .

I hope every reader to know that the Quran is full of such pre-science truths ; peace on you all.

Orthomentor said...

What on Maslow's B-values in re holarchic nidi for the physicist?
Also, if the perimeter membrane is asymptotic, wouldn't it take analog thinking to ken its elasticity?

Fahad said...

In your book TBHW on page 248 you said that the Hsisenberg principle applies to a proton, an atom or balling ball. I bet you i can very accurately measure a balling ball speed and position on a balling ally. I sending this question not to prove you wrong rather to make sure that my understanding is correct.

John McAndrew said...

Dear Prof. Susskind,
Since the gravity attraction depends on the inverse of the square of the distance between, for instance, two masses, when they collide the distance is 0, so the force should be infinite... How to overcome this empasse? Do I have to take into consideration Newton's third law? I think of the two masses in the open space, and m1=m2.

Thanks for a possible response.
federico coda form Italy

Windscar said...

I have been wondering why Hawking would attempt to show conservation of black holes using particle pair production that violates conservation of energy in itself. Does this imply that particle pair production is directly related to black holes? That they have to produce particle pairs everywhere so that everything in physics can be shown to be conserved? What would it matter if black holes are conserving energy or information if the particle pairs that allow this to happen have not even been shown to obey conservation laws?

CharlieAndy said...

Professor Susskind,

CP violation has been observed and, if CPT is conserved, that implies T violation. In your desciption of the progression of the states of the universe you disallow ambiguity in predecessor states, i.e. every state has only one predecessor. I am confused about CP, i.e. T violation. Does T violation imply ambiguity in predecessor states? Thank you.

CharlieAndy said...

CP is violated in some interactions. This implies T violation (if CPT is conserved). You have pointed out that each state of the universe has but one predecessor. Doesn't T violation pose a problem there?

Eshita Joshi said...

Hi sir, I'm currently in grade 11 and I'm doing higher level physics in the IB program..

Recently I read this article ( ) about how in 1999 they slowed light down to about 38 miles per hour using a really cold super atomic cloud with temperatures close to that of the absolute zero.
I was watching your video lectures on iTunesU on special relativity and how according to Maxwell's equations it is a law that the speed of light is always equal to c? Is that only for all frames of references as long as the temperature is constant? I really don't understand how this works..

Also, I was a bit confused by why does light slow down during refraction and I searched online about it to find that light doesn't slow down, but it gets absorbed and transmitted so it appears to slow down but it doesn't because light always moves at light speed..

Then how can it be that light slowed down by a factor of 20 million just by cooling it to temperatures near absolute zero? Is it because the photons have no energy in them? but then, doesn't a photon have zero mass? so k.e. and p.e. would be zero anyway?

I'm really confused about how it is possible for light to slow down when: 1) Maxwell's equations and s.relativity say that light always moves at light speed (c)
2) photons have no rest mass

Thanks, Eshita.

CharlieAndy said...

Two unentangled black holes, Alice and Bob, evaporate. The products of the evaporation condense together to create Charlie. If C is a composite of A and B, does that mean that A and B become entangled then?
Since everything was interacting at the time of the Big Bang, does that mean that everything is entangled? Is Mach's principle also an artifact of that primordial entanglement?

CharlieAndy said...

Eshita, In reading the Harvard article about Lena Hau, I saw that the author, William J. Cromie, not Hau, makes a mistake when he says that relativity only puts an upper limit on the speed of light. No, like you describe light "slowing" in a refractive medium, the light is absorbed and re-emitted some time later. It still travels at c between atoms. Ms. Hau has managed to create a Bose-Einstein condensate of atoms that delay this re-emission quite a lot.

Eshita Joshi said...

That makes sense..
but then again, why does the temperature affect the time taken for the light to be absorbed and transmitted?

Eshita Joshi said...

(not sure if this might be asking for too much) but..
how did they find out that light was just being absorbed and transmitted by the atoms of the medium during refraction? I mean, how did they do the experiment? You can measure the speed of light directly..So how did they know that its travelling at speed c between the atoms but get absorbed by them and is transmitted later on?
And even if they did this mathematically (not sure if they did or not..) how did they confirm this experimentally?
I'm really curious..
Thanks, Eshita.

Eshita Joshi said...

I mean *you can't measure the speed of light directly
(atleast, I am not aware of any such methods)

CharlieAndy said...

Eshita, The speed of light has been measured many times, in vacuo. Your question about the speed of light between atoms in a solid or in a Bose-Einstein condensate is not so easy to answer. I can't imagine that that has been measured directly. (I may be wrong though.) The reason the speed of light is assumed to be constant and the same for all inertial observers is that the Theory of Relativity depends on it being so. And that theory has never been found to be erroneous. It has been tested many many times too.

The condensate cannot be created except as a very cold collection of bosons so that's the reason it has to be cold. Heisenberg's uncertainty principle is ∆E⋄∆t=h/2π. If ∆E can be made very small then ∆t, the time between emissions, can be made small. A very cold condensate has a very low and fairly constant temperature, i.e. energy.

I encourage you to do more research on this and on the measurements of the speed of light. Keep going. You're on to something.

Eshita Joshi said...

Actually in IB we're supposed to do an Extended Essay in a subject of our choice (and on a topic of our choice)..
its kind of like a thesis, so you do your research and write a 4000 word paper on it..
I'm really interested in modern physics and so I follow Professor Susskind's lectures..
and from there I got the idea of doing my Extended Essay on the slowing down of light during refraction, but I cant think of a way to actually do this.
The most I got from the internet was atomic absorption/emission spectroscopy.

CharlieAndy said...

Eshita, Try to get in touch with Lene Hau, the professor at Harvard that made the Bose-Einstein condensate where light "travels slowly." I bet she'd be glad to help.

CharlieAndy said...

Eshita, Here's a link that explains mathematically how the slow-down works.

It talks about a 'medium' like glass or a Bose-Einstein condensate. It doesn't say much about what's going on with the particles of the medium as the electromagnetic wave traverses it. You have picked a topic that requires some real study. Good luck!

אריק לקאר said...

Hi Professor Susskind.
I watched your lectures on quantum mechanics and i saw how you derived the position wave function for a particle of definite momentum as an eigenstate of the momentum operator: Y = A*e^(ikx)
Y - position wave function.
but the same thing can be done using the time independent schrodinger equation: HY(x) = EY(x)
if you let H = (p^2)/2m and solve
you get: Y = A*e^(i*k*x)
so that wave function is both an eigenstate of the momentum and eigenstate of the hamiltonian and it makes sense because if H only depends on the momentum/velocity so [H,P] = 0
but if the hamiltonian has a potential energy in it so [H,P] != 0 (H and P don't commute) and in that case solving HY = EY will give a different wave function from solving by finding the Y which is the eigenstate of the momentum operator(PY = pY) and it's probably because H and Y don't commute if H depends on position.
but my question is if the eigenstate of the momentum operator is still a valid wave function for the system with the potential energy?

Thank you.

Eshita Joshi said...

CharlieAndy, Thank you so very much!

John McAndrew said...
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John McAndrew said...

Combinatorics. Egr. Prof. Leonard Susskind,have You never tought to teach the basics of combinatorics that can be useful in counting states and populate correctly the space of states of a system?! There are courses on probability and statistics but somehow none of the teachers have your ability to make simple very complex things, in even the more more complicated physical subjects. It would be a blessing if you could share your knowledge also on the realm of statistic and probability! I hope you will kindly consider this possibility... Best regards Federico Coda (Italy)

Eshita Joshi said...
This comment has been removed by the author.
bulldoggy said...

At the beginning of Lecture 5 in Classical Mechanics,Lenny Susskind mentioned recommended books.
I'm Japanese.
It's difficult to speculate spelling of author and book titles because I don't have enough experiances to speculate.
Can you tell me the book title and author name?

Micke Långberg said...

I was thinking,. wondering,..

A Vector is just a set of values put together because it makes sense, right?

And it makes sense to put together the three coordinates of space x,y,z for example if you want to describe a field.
A scalar field then describes a values at a x,y,z.
And the reason you put them together is because
it describes the field at time t, right?

But is it ok to say that the positions x,y,z are all at the same time t? simultaneously?

Does the Lorenz transform account that un-simultioneousness?


jack geisler said...

this is a test

jack geisler said...

I have two questions pertaining to the theory of the early universe.

It is said that the redshift that the CMB has undergone is 1,000; that is,
Here I have used S for the scale factor, set=1 today. From this we have the result that S(temit)=.001, and when multiplied by 13.7 bly, we get 13.7 mly. This is said to be the distance of the surface of last scattering from us at the time the photons set out for us. So far, OK.
One small question here. How is this redshift determined? I would like to say that there must be one or more absorption lines in the observed CMB spectrum, but this is never mentioned or shown in diagrams of the the spectrum.

So, I'll take the 1,000 on faith and proceed from the observed spectrum,via this redshift number to infer lambda(emit) at the spectral peak, and then from Wein's Law to get the peak T of 3000K. This is the vital anchor point for extrapolating T back in time via the lambda~1/S(t) connection.

Now anger-producing confusion rushes in like a tsunami. First of all, it seems to be gospel that the surface of last scattering, which is the place we start our back extrapolation of T must begin, is situated at 480,000 years. Where does that number come from? Furthermore, all of the diagrams of that epoch say that S(t) is around 0.1 at this time. Where does that come from? How can such an assertion be reconciled with the earlier-stated result that S=.001 at the surface of last scattering or with the fact that if you divide 480,000 ly by 13.7 bly, you get 3.5x 10^-5 for the scale factor, not 0.1?

Jim Shilleto said...

This comment is regarding the derivation of Maxwell's equations in the section on special relativity.

An essential part of quantum physics is the invariance under phase shifts and an essential of E&M is the use of the vector and scalar potential. Requiring these plus Lorentz invariance plus the least action principle produces Maxwell's equations.

Would people agree that this is a fair summary?

nick canning said...

A question about the two slit experiment:

Suppose Bob is located at hole 2 with a mechanism that can instantly close the hole or open it. Sue is located on the screen plane a large distance, D , from the slits and at the position of the first interference fringe towards hole 1, where the probability of particle detection is zero when both holes are open. Bob closes hole 2, so the probability distribution for detecting a particle at Sue’s position changes from (=0) to  > 0 . Does this change occur instantly? or does the effect propagate from Bob to Sue with the velocity of the particles? taking a time equal to the time of flight t = mD/p
where m= particle mass, p= particle momentum?

If the change in probability distribution at Sue’s location is instantaneous ( as I suspect that it is *) can Bob use this to instantly modulate the number of particles per second received by Sue and hence send a signal faster than light? Why not?

*Delayed choice experiments suggest that the change in probability at Sue’s position is instantaneous: i.e. If both holes are open at the moment the particle is detected at the screen then the probability is , but if hole 2 is closed at the moment of detection the probability is Is this correct?

Instantaneous change would make no sense if we could locate the particle as having definitely passed through the slits before Bob closed hole 2 but we can’t locate them precisely enough due to the uncertainty in the position of the particles which have well-defined momentum (hence debroglie wavelength. So even particles which are detected very short times, t, after Bob closed the hole (where t<< time of flight mD/p) are governed by statistics of the one hole case. Is this correct?

nick canning said...
This comment has been removed by the author.
nick canning said...

A question about the time at which a measurement has occurred:

A similar question concerning when we can consider a measurement to have occurred arises in the following experiment: A beam of spin ½ particles of well defined momentum and pure state |+z> enter a Stern gerlach loop like those in Feynman’s lectures lec5 vol3. The loop is oriented to select |+x> and |-x> states depending on which channel of the loop is blocked, if neither is blocked the loop passes the |+z> unchanged. Suppose we block the |-x> channel and measure the spin of the emerging particle; with certainty it is |+x>. Now remove the detector far from the loop so that most of the flight time of a particle to the detector occurs after passing the filter. Can we say there is a time after which the particle has passed the filter and is thus definitely in the |+x> state but has yet to be detected? What if at the last moment, just before detection, the blocked channel of the filter was opened so that when the detection takes place both channels were open? In that case if we detect |+z> with certainty rather than |+x> we cannot assign a time at which the particle interacted with the original filter apparatus. Is the state of the whole apparatus which the particle may have passed through only considered at the time at which the particle is detected and so irreversibly removed from play? This seems very odd.

In this case do we in fact detect |+z> with certainty? Have I missunderstood something here?

Jack Bidnik said...

I found this quotation in an old book called Vector Analysis, by Joseph George Coffin, which was copyrighted in 1911. The footnote after the asterisk is very interesting, it is about something called the Vortex Atom Theory of Matter, by Lord Kelvin:

" Taylor's theorem. because all of its derivatives vanish at
a certain instant. This theorem due to Helmholtz says that if no vorticity exists in any incompressible, frictionless fluid at any time it is impossible to produce any by means of a conservative system of forces, and the motion will remain forever non-vortical.

* If the ether he considered to be a frictionless medium, then a vortex once set up in it would be indestructible; and conversely, if no vortices existed, it would be impossible to create any. It is conceivable, however, that some "Cataclysm" might have rendered the ether temporarily viscous to some extent. By this we mean that it is conceivable, for example, that under extraordinary conditions say of temperature the ether might acquire unusual properties, in which case, if it became frictionless again after vortical motion had been produced in it while in this state, such vortical motion would persist forever. This speculation is of interest in connection with the vortex-atom theory of matter."

This looks like the essential purpose of the Higgs phenomenon. Instead of Cataclysm, read Spontaneous Symmetry Breaking. The more things change, the more they stay the same.

lukka karthik said...

I want to ask something about spinning top.The angular momentum gets change only in direction due to the torque due to weight.Sir,but This is the explanation one generally gives about spinning.I have a small query.why does not the top fall to ground as there is force acting.So the center of mass of top can be accelerated downwards similar to the fashion of free fall.Sir,If u can reply me I am thankful to u.

lukka karthik said...

Sir,I have a small query regarding classical mechanics on spinning top. the torque due to weight will change angular momentum continuously.This is the explanation given to it.Why can't happen the other way? Due to force of gravity , why doesn't the top fall to ground? Please explain me! It's a sincere request.

lukka karthik said...

Sir,I have a small query regarding classical mechanics on spinning top. the torque due to weight will change angular momentum continuously.This is the explanation given to it.Why can't happen the other way? Due to force of gravity , why doesn't the top fall to ground? Please explain me! It's a sincere request.

bumpker (Ron Reynolds) said...

Hey what do u think about subjective information. Here's what I mean. If I write a word on the chalkboard, that's information. I could erase it with an eraser. Or I could lay the chalkstick sideways and smear more chalk on it. The information is held by the shapes of the letters (and by the intelligence to recognize the info).
So by using the chalk I have removed the information by eliminating the visibility of the shapes of the letters. For anyone looking at it that is. But what about for the information itself. Suppose it is aware of itself. It would still be there for itself, if I didn't use the eraser. I know how that sounds but I think physicists mostly beleive that a "self" is a mass of information.
But they don't talk about subjectivity. Now what about (instead of chalk) the energy field a moment after the big bang. Before it has even distinguished itself into particles. I'm not sure how much information would have to be in there for it to be self aware,
BUT But since 'self aware' is subjectivity the info is already in there as far as the info itself is concerned. the info can be it's own genesis (all manner of energy configurations (which can be info)are potentially there. It doesn't need to be discernible, it's very nature is awareness itself so it's so ,for itself it is there. Put another way: If there were a shape I could draw on the chalkboard that would be aware of itself, I don't need to know the shape. I could just smear chalk. That shape is in there somewhere, not for me but for itself it is because it's very shape is self awareness. THE SUBJECTIVE PRINCIPLE So perhaps the big bang would automatically create a vast superintelligence. Know one knows what the self awareness is, even though it is the most immediately familiar thing for any individual. And information does one thing very well. It makes more information. Look at what twenty six alphabet characters can do. Now this vast superintelligence which is self aware would remember that it's self aware. In fact, let's say that remembering itself is also built into it's "shape". Could this condition of remembering account for the arrow of time? thx, Ron Reynolds

bumpker (Ron Reynolds) said...

I forgot to say this. Our universe could be a process in the unconscious side of that vast intelligence. Ron Reynolds

bijan shariat said...

TO: L. SUSSKIND 11/25/2013
STANFORD, CALIF 94303-4060

FROM: BIJAN SHARIAT TEL – 310 210 1604
1668 COLBY AV #1
LA, CA 90025


rpons said...


I have been following various developments in the multi-dimensions, gravity, and quantum mechanics at a modest level, however, the question always arises that perhaps the reason that uncertainty comes up in all of the equations and outcomes is that perhaps we are not looking at it from the right vantage point. In engineering class we used to refer to it as the Control Volume. As I look at all of the outcomes at the quantum level may not be uncertain if we develop the Control Volume to include the other dimensions. By including the other universes, there may not in fact be any uncertainty. It is only by including the other dimensions and/or universes that the quantum effects can be explained. A good example would be quantum entanglement; looking at it from multi-dimensions, perhaps the particles interface between dimensions in and out, giving them the spooky effect of interacting at distances. Gravity may also be interacting inter=dimensionally. Can you comment on my observations, reasoning and errors in oversight, if any?

Bhandaru Rohith said...

sir , i am really curious to learn concepts in particle physics , quantum physics. i am currently studying electrical engineering at IIT Madras.i have doubt regarding the intersection of two phase space curves. here is my argument " consider normal one dimension system(system 1).now we know its fate at each and every consider another body with different velocity(system 2).in the phase space diagram ,as we plot a point for system 1 we know the magnitude of velocity and position of the body at that instant.if at all the system 2 also has the same magnitude of velocity at that position , its future is already determined. which implies that system 1 and system 2 can have a point in common.there is no ambiguity at the point of intersection for the system 1 because its path is already determined and so it moves in that path only which is governed by the laws. the same applies to system 2. Wher is the flaw?" sorry for my poor english. hope that you understand my argument.

James Nordblom said...

Has anyone considered the idea that the "shape" of the Multiverse might be the Mandelbrot set, perhaps in a 3 or more dimensional version?
That is the picture that I have in my mind when I try to grasp the idea.
Jim Nordblom

Asya Skal said...

3. Dear Prof. leonard Sasskind
4. I have solved Navier Stokes equation and obtain from it NEW LORENTZ force
5. and published papers:
7. 1. Skal AS (2011) ‘Does a physically reasonable solution of the Navier Stokes equation exist?”,Journal of Engineering and Technology Research vol. 3(6). Pp 168-170, June , 2011. (see online
8. At http//
9. 2. Skal A.S “The New Fundamental Equation of turbulent phase transition."
10. American Journal of Mathematics and Statistics p-ISSN: 2162-948X e-ISSN: 2162-8475 2012; 2(1): 13-15 doi: 10.5923/j.

jesuswebes said...

I studied Quantum Mechanics at University but after following your QM 2012 video lessons, I din´t know how little I knew of it. It´s been a pleasure and I really apreciate your kindness of sharing your deep knowledge and capability of teaching it with all of us ( me included)through your video lessons.
Now I think I really understand this strange but wonderful thing called QM.
Thank you from Spain. Jesús

franx said...

I do have a question.
Where is Leonard Susskind?

Samik Sarkar said...

Dear Professor,

As per The Uncertainty Principle, it is not possible to measure momentum & position accurately & simultaneously of a particle. Is this indicates human's defeciency to measure these two basic parameters or it is a nature's law irrespective of human error.

For example, we performing an experiment of measuring position & momentum of a ceiling fan's blades. When fan is not rotating at that moment, we can accurately measure the position & momentum of each blade. But if we gradually increase the fan's speed, then it is very hard to measure position & momentum accurately. But whatever the measure data we have in different time, the actual position of blade is fixed after same time interval.

I hope, I can make you understand my query.

Jack Bidnik said...

In response to franx:

Leonard Susskind is no doubt revisiting the study of Gravitation, in light of recent insights.

theoretical physics said...

I'm Mustapha.Mekhfi a professor of theoretical physics at Oran, Algeria university. I would like by this mail to thank you for the set of video lectures called the theoretical minimun I discoved recently. l thank you for many reasons - The free  availability of these lectures for people outside standford university and especially for africans  and arabs who lack good conferences and exceptional teachers like you- Your broad knowledge in physics-Your simplicity and humanity-Your sense of  humour- Your love for  physics and for your studentsAnd the list goes .May God Almighty give you health and long life that we can have other conferences in the future.

周鍾揚 said...
This comment has been removed by the author.
周鍾揚 said...

Dear Professor Susskind,
My name is Roger Chow from Hong Kong ~ Thank you very much for your lectures in Physics ~ It is great and wonderful and I enjoy it very much ~ Thanks ~ :)

A'me Bower said...

Professor Susskind,

The Lorentz transformation in SR bothers me deeply. There are several reasons. The one on mind right now is the what happens to the denominator in 1/sqrt1-v^2/c^2 when v=the speed of light. The speed of light=1, right? I did understand that correctly? That means that the whole thing is undefined.

Would that not mean that even light can't travel at the speed of light?

Markay said...

Thank you

John Smith said...

I am also a physics professor. You have to make it fun!

Herb Roseman said...

This is probably a naive question. I am probably confused.

The way the Lorentz transform is usually presented is that there is a clock with time t on a moving frame of velocity v. The time t' in the observers frame is computed using a formula which is a function of t and v in the moving frame. But v is also a function of time (dx/dt). Is the time associated with v the time in the moving frame?

Moreover, it is impossible to measure time without some rate of movement in the measuring instrument. So how can we determine the velocity involved in the measurement of t'. Do we need still another time, t'', which needs still another velocity?

Is there a regress or are the variables in the Lorentz transform just taken to be primitives?

Dhrubanka Sarma said...

Dear sir,
i have gone through your lecture of the proper time but could not visualize and understood it . will you make it more simpler or can you give me a link where i can understand and visualize the concept of proper time ?

faisal raeme said...


If there is anything wrong with this theory please do not judge my lack of knowlege, i am just 18 years old first year of high school but so into science. If this is possible there is a brightness coming to human race if not then please correct the ugly looking parts.

An object is made of atoms, when breaking down every small piece is still made of atoms, now if we see it through quantum physics, the atoms that form this object are not together there is a space between them, and they are probably hold to gether by the strong force also this object is made by chemical bonds, in a bond most of electron are not moving the same direction, the same time and in the same point of space, in other words they are moving oppositly, acting in different space and time (quantum law). If we look at the angular momentum of this operation that the electrons involve in formation of an object is balanced, now Einstein saw space as a bubble, in this bubble the atom and electrons of this object is acting in a way to keep the space between the atoms of the object in such a scale to let an object form a geometric or non-geometric sturcture. In other words i would like brief that if the electrons around the atoms of the object in that of the bond were to move in one direction say if it was moving clockwise it would pentrate the bubbly space with too much pressure and might explod and if it was moving counter-clockwise it would spread and make space to the bubbly space to expand and expand. Naturally we can see such a process happening to a cancerous cell, cancer spreads through out our body if we dont take the tumor out on a right time. According to my above theory cancer spreads because a cancerous cell spinns in a right turning spirall so quantumlly it is the electrons around the atoms of the cancerous cell moving clockwise and spreading space between the atoms and making gaps for the bubbly space to expand, so it expands and destroys the nieghboring cells. A treatment to this is to generate molecules to work in a way so the expansion stops in other words the right moving electrons canceling out the force or energy of opening gaps for the bubbly space with the left moving generated electrons. This process can be applied when a cancerous cell is dicovered in a human body or even before the desease starts to grow, a human body is a set of chemical bonds and it is balanced through this theory one can come up with a medicin that we could use it once in our lifetime and it would hunt down the uncontrollability.

dboggs said...

I have just discovered your lectures on cosmology and are enjoying them tremendously. So far have only made it through lecture 2, in which you made a statement that runs counter to something very fundamental that I THOUGHT I knew. You stated that, if a galaxy is so far away that it is receding faster than the speed of light, we would NEVER see it no matter how long we waited.

I had thought the following: Although the emitted light initially loses its race towards earth--i.e. it just gets further away--it DOES make progress locally by advancing (at the speed of light) through the local space in which the galaxy "rests." Thus, after some time it will have advanced into a new region of space that is not receding as fast as the space where it originally started. After yet another increment of time the light will have made it into space that is receding even more slowly, and so on. Eventually it will have made it into space that is receding from Earth only at the speed of light, and since it is advancing through THIS space towards Earth at c, it will momentarily appear to stay still from us. But continuing, the light will soon find itself traveling through space that is receding at sub-light speed, and it begins to actually approach the earth. Eventually it finds itself nearing the space close to earth, which is hardly receding at all, and it ends up getting to us at precisely the speed of light through our local space which is not receding at all.

Am I missing something? I am largely self-taught when it comes to cosmology. Do I need to do some re-learning?

Daryl Boggs

Bharat Kuchhal said...
This comment has been removed by the author.
Bharat Kuchhal said...

Dear Professor Susskind,
I was recently watching your lecture on classical mechanics where you say that the only allowable states in classical physics are those whose future is deterministic as well as their past can be re-traced back. But if I consider an object at a height from the ground at rest, its initial state is undetermined. It could either be at rest because the ball could be in an airplane, or it could have been thrown up to a height from the ground (as we all know that the velocity of an object thrown up is zero at its maximum height). This example is very famous and comes under classical physics. But this also contradicts what you told us about principles in classical mechanics which need to have a known past. Please clarify my doubt.
Bharat Kuchhal

Mary said...

Does anyone know where to get answers to the exercises in "Quantum Mechanics-The theoretical minimum"?

suman subedi said...

i am watching your lecture on modern physics special relativity.On your second lecture you said the value of the spring constant increases if you cut the spring to half.I think the value of spring constant remains the same as you cut to half but it increases if you compress it to half.


An electron gains energy and moves
up the orbital. But in the process of
transition it should get accelerated
(while it is moving up to an orbital of
higher energy). We know that an
accelerated electron(or any charge
particle for that matter) radiates em
waves and hence energy. So an
electron gains energy and in the
process of moving up it loses energy
(via radiation due to acceleration).
We also know that the electron starts
moving when it receives energy just
equal to the difference of energy
between two orbitals. In the given
situation the electron should never
be able to move up an orbital. How
do u explain? Or..where am I wrong?

Bill Man said...

First, I offer my deepest and most profound thanks, Mr. Susskind, for authoring Black Hole Wars and The Cosmic Landscape. I have read many authors regarding this type of information, but you have the knack of explaining it so that people with even a minimal scientific background get it. You also you bring theoretical physics alive with your anecdotes of working with some of the other giants in physics, with just the right amount of humor making your work very readable. I am so happy that you have discovered such a large number of people with this interest, and after reading your book, I don't see how anyone could not be hooked.

After reading Black Hole Wars, I became fascinated by cosmic event horizons, even more so than black hole event horizons because for one thing, cosmic event horizons are so much more abundant.

I was wondering, what effect do cosmic event horizons have with local space, considering that if our cosmic event horizon is 15 BLY away, what effects can we see knowing that every location on earth intersects with a cosmic event horizon. Would these horizons have any effect on local physics, can any experiments be performed that can detect strings that extend onto the horizon since they would be on the horizon in a holographic sense? What if anything would you expect an experiment to detect the existence of a cosmic horizon?

Also, one last question, since information can't be lost in the universe, does that mean the cosmic event horizon contains more information than our visible universe due to inflation,and would that information have energy that exceeds the mass of the visible universe, minus the CMB? Maybe I think I understand what you wrote better than I actually do, and the question makes no sense, but any information would be great.

Also, when are you going to author a book on cosmic event horizons? I am waiting with baited breath. In the mean time, are there any books out there that you know of that written at the level similar to Black Hole Wars? Also, it would be monumentally fortuitous if you found the time to make some quality television programming to talk about the Holographic Principle, because I truly believe that between that and some of the complementarity/duality aspects of quantum mechanics and cosmology, nobody will look at the universe the same again, or without a grin from ear to ear.

Bill Man said...

Oops, I forgot to add if you knew any books written at the same level as Black Hole Wars about cosmic event horizons. Sorry I forgot to add that.

Calia said...

It's very weird to imagine an
object like black hole which
is a phantasmagoric gravitational hole upon 4 dimensional
spacetime when I stick to the common sense that universe is material reality.
But, thinking inversely, that is,
a black hole being something like a projector generating 4D event space as we are mathematically abstracting it, it becomes
little bit natural to regard the universe as holographic projection in which we has insatiable desire
to look hard into the blackened source of which everything we call real is only a reflection.

My question is : Are black holes
hypothesized to be storing the information of the universe we live in?

Paul the LionHeart said...

G'day Professor Susskind,
I have been thrilled by your lectures.
I have a question about photons.
If photons are the boson that carry the electric force, does that mean that there are lots of photons within each atom to hold the electrons in orbit around the nucleons? How many are there? How often do they exchange between the electrons and the nucleons? Are you able to describe a Feynman diagram for this process?

Many thanks, Paul from Australia

Island Girl said...

Hello, I'm looking for help! I need to understand how an electromagnetic field/wave function, and if there is an easily explainable way of canceling an electromagnetic wave or field. This is for my writing research... Is there an electromagnetic geek willing to enlighten me, for art's sake? Thank you so much!

Ron Todosychuk said...

Richard Krause thinks that when a electron kicks out a photon - where there was no photon before - that is something from nothing. I have trouble with this statement. Do you think this constitutes something from nothing. Seems to me the photon came from the electron. And a follow up - can you explain how an electron can create a photon?

Baktash amini said...
This comment has been removed by the author.
Baktash amini said...

hi dear sir.
this is baktash amini, i am working on my research about the schroidinger equation,i saw lots of books and the way they derived the shroidinger equation, i wana ask you that can we find the wave function by the supperpostion of plane waves by fourier transform????? please respond me as soon as you can cause i don't have much time

Brenda Akers said...

Hey, I've really enjoyed your posts here. It was exciting and informative to read your post. I appreciate your great efforts, just keep doing.

Dan Bowlds said...

Dear Dr. Susskind,
Thank you so much for the opportunity to converse with you on this blog. I am a retired engineer and have always been fascinated with physics and the workings of the Universe, how it came to be, what makes it continue to exist, etc.

One thing that always popped up in my mind when thinking about matter and its properties, is, what makes the properties exist? Is the cause of gravity, the same thing that causes inertia? Also, what causes time to pass and space to exist? What is the connection between energy, time, and space?

One day I had an epiphany. What if the manifestation of matter with its properties, energy, time, space, and all that we can perceive as existing in the Universe, originates from some unseen independent variable/invisible dimension that is causing all of this to exist? We can only physically sense things that exhibit Universe properties through the use of those same properties. But that doesn't mean that other things can't exist.

I propose that the entire Universe (including all of space) is made up of a finite amount of only one kind of invisible particle, even though the number of them is inconceivably large. These particles are in intimate contact with one another throughout the Universe with no voids between them, and although they are similar to each other, each particle has a unique volume of its primary material that cannot be shared with another. The boundaries of the particles are formed by their own material.

Now here's a secret: Within each particle is a creative source trying to generate more of its unique particle space. But its expansion (which would be into a forth dimension that we cannot see) is limited by the surrounding particles that it is in intimate contact with (they cannot share space). These particles comprising the Universe are like an expanding foam all sharing sides with one another in complex polyhedron configurations. "Clumps" of particles form visible matter with properties of mass. More freely expanding portions of them make up our "space", and also these portions are expanding at what we call the speed of light. Time passes by virtue of an overall expansion of a given quantity of particles into the unseen forth dimension. The 3D space expansion that we see is a differential expansion between two portions of the Universe. All of the properties of the Universe can be explained by using this continuing unseen expansion model where the Universe is growing more 4D space through the expansion of the particles.

If the source within each particle "dies", the Universe will cease to exist, time will be no more, and the Universe will "never" have been.

ravi panchal said...

Dear Sir

I am a mathematics student working on relativity. I feel happy to watch your videos on General Relativity. It helped me a lot to understand things.

I am just beginner in GR and I have made Mathematica programs for the computations in GR.

Ravi Panchal

Tullio Cicero said...

Dear Sir,

I am no theoretical physicist just an ordinary person with some knowledge in mathematics and physics due to my studies. I am fascinated by your lessons and explanations. I am intrigued by black holes. I recently had the chance to follow on line your lecture concerning what is inside a black hole. My question is more related to philosophy than physics.
Why do the world insist in calling black holes such as when we do know that they are not holes at all?
All the theories I heard of are referring to an empty space between the horizon of the events and the singularity at the center.
What if there is no hole at all and horizon of the events coincides with the edge of the singularity. If we compare the escape velocity to the speed of light the hearth would be a black hole of the size of a tennis ball and the mass will be concentrated in the core, tennis ball size, so where is the hole in all this.

I just feel a bit lost between theoretical physics and philosophical approach.

thank you for your time and sorry for bothering.

Jack Bidnik said...

The challenge:

If you use the formula for force in Newton 's Gravitational Equation: F =G Mm/r ^ 2,
on the proton and electron of the Hydrogen atom you will find that the attraction is a very small number, compared to the electrostatic force.
If , however, instead of G, you use the following expression:

Gs = (1/ (M+m))*r*Vo^2*c^4/(Vo^2 +c^2)^2 ,

where Vo is orbital velocity, c is speed of light, and Gs is what I call Special G, thus:
F =Gs* M*m/r ^ 2,
you will find that the calculation yields exactly the accepted figure for the electrostatic force of the Bohr Hydrogen atom.
In fact, if you use Gs instead of G for the equation of force for any planet, with r being the length of the semi-major axis and Vo being the average orbital speed, then the result will be the same as if you had used only G, Newtons constant, in the first place, for under those conditions Gs=G.
This is a result of the equation's dependency on the orbital speed; in the atomic case, this speed is high, and it translates to a much larger attraction, while in the planetary case the speed is slow relative to the speed of light, giving the classical force value.

This is not a trick, or a mere mathematical oddity. It is a fact of nature, derived from physical laws and equations.
In fact, from understanding how these equations have been derived one can see that this establishes the relationship between gravity and electrostatics and, by extension, electromagnetic forces .

m=9.1e-31 ,mass of the electron kg
M=m*1836.15 ,mass of proton
r=5.29172e-11 ,radius of H, Bohr radius, meters
c=2.99792458e8 ,speed of light in M/s
ke=8.99e9 ,Coulomb's constant NM^2/C^2
q1,q2=1.6e-19 , charge of electron and proton in H atom
Vo=sqr((ke*q1^2)/(m*r)) = 2.186153e6 m/s ,orbital speed
Force from electrostatic formula, fe= ke* q1*q2/ r^2 = 8.21875e-8
Force from Special G formula, Fg=Gs* M*m/r ^ 2 = 8.2134e-8
ke=8.99e9 ,Coulomb's constant NM^2/C^2
q1,q2=1.6e-19 , charge of electron and proton in H atom
For planetary cases: F =Gs* M*m/r ^ 2, a few examples:
Sun's mass M= 1.9891e30 kg, Newton's G=0.667384e-10
For Earth m= 5.97219e24, r= 1.49598262e11, Vo= 29788, F= 3.53e22, Gs=.66735e-10
Mars m=.641693e24, r= 2.27943824e11, Vo= 24136, F= 1.64e21, Gs=.66759e-10
Jupiter m=1898.130e24, r= 7.78340821e11, Vo= 13065, F= 4.1589e23, Gs=.66732e-10
Saturn m= 568.319e24, r= 1.426666422e12, Vo= 9647.7, F= 3.7067e22, Gs=.66732e-10

Igor Giterman said...

Good evening Professor,

I am watching your video lectures on SPECIAL THEORY OF RELATIVITY.

My question is why Lorenz transformations you show are the only valid one?

I have modified the transformation and it seems to satisfy all the basic requirements and assumptions (see below)

Please explain where my assumptions are incorrect.

Inertial System moves with constant velocity V
All laws of physics are preserved in all inertial systems (observer S and S’ will see same things)
All observers see “Speed of Light as C”
For V=0, S and S’ will merge (X’=X, t’=t)

Premises 1, 2 and 3 are satisfied
Velocity can be any value


Premises 1, 2 and 3 are satisfied
Velocity is limited by speed of light C (3·10^8m/sec)
γ = f(V) is a multiplies to force C to be universal absolute maximum velocity in all frames of reference.
γ at velocity ZERO must satisfy f(0)=1

γ=1/√(1-V^2/C^2 )

X'=(X-V*t)/√(1-V^2/C^2 )

t'=(t-V/C^2 *X)/√(1-V^2/C^2 )

Premises 1, 2 and 3 are satisfied
α is universal constant
Velocity not limited by speed of light C (3·10^8m/sec)

X^'=(α*X-V*t)/√(α^2-V^2/C^2 )

t^'=(α*t-V/C^2 *X)/√(α^2-V^2/C^2 )

John Fistere said...

I have just finished watching your video "Demystifying the Higgs Boson", and I am left with with an elementary (perhaps) question. I think I now have somewhat of a feel for the conditions that create mass, and how certain particles participate in that process, but it is not clear to me why the oscillation of a particle by emitting and absorbing a particle from a condensate results in the first particle having mass.

Can you help me bridge this "intuitive gap"?

Also, as a particle is oscillating, is the mass constant during the oscillations?

Thank you for considering this question.
John Fistere

Shubham Bhatt said...

I've just completed reading your book 'The cosmic Landscape'. It was
the most beautiful 1 week of my life, and the most bizarre and surreal
at the same time. I was all excited and confused at the same time.
Sir, I am an undergraduate, and Quantum World never ceases to amaze
me. My brain was coming up with theories of its own. I would be
privileged and blessed if you could read this, and get your guidance.
It will be the best motivation for me to move forward, Sir.

Why we are not pondering on the fact that the kind of universe we are
living, with particular fixed value of constants, are or can only
makes humans exist. its the evolution within these narrow range of
constants, that only made human species florish. And i strongly
subscribe to the fact(and would it be right to do so) that its the
human brain that is making these thought experiment and all. And
whatever theory and observation we are coming up with are processed by
our brain, which is capable of processing the 3 dimensional world.

And talking about fishysicists which you mentioned sir, What if the
fishysicists capable of viewing more dimensions. They can have a brain
that can process the world completely differently. May be more closer
to the ultimate reality. So, would it be right to believe that, we
are confined by our brain. We are only coming up with theories and
experiments that can be processed by our brain. What if our brain is
not that complex to understand the ultimate reality. What if what our
brain processes, is only a projection of the ultimate reality which
may be of multiple dimensions?

So what i think is that we humans and our intelligence is confined and
limited to our brains. What if the brain dspite of being the most
complex of all, is not that complex to understand the ultimate
reality(with more beauties).

If we start believing in the theory of megaverse(not multiverse as you
would like), then Sir, just as this universe with all the constant
and elementary particles is conducive for we humans to live, is it not
possible that other universes with completely different constansts and
elementary particles are conducive for other creatures to live, with
completely different anatomy, and there existence is also the
result of millions of years of evolution,just as that of Darwins on Earth.

There's one more thing which is giving me a food for thought Sir, is
there a possibility that we are already living in some small
as stated by String Theory, and there are bigger dimensions instead of
small which we cannot perceive or think of.

Like I said said sir, i would be motivated to move forward and study
Quantum world in more detail, if i get your guidance.

Blair Storkamp said...

Dear Mr. Susskind,
I have been looking at the existence of dark energy and have an alternative theory to run by you. Is it possible that rather than being a "negative" force of unknown energy, that perhaps it is simply gravitational effects between all particles, planets, galaxies, etc..? This would explain why the universe is expanding at a measureable rate. As everything gets farther apart, The overall gravitational force between everything is weaker. The universe then continues to expand at a faster rate. Am I missing something? Thanks, Blair Storkamp

Snow girl said...

Why there is not a subtitles for the new lectures ?

Daniel Sigg said...

Hi all,

Loving the book on quantum mechanics, and thought I would share a little insight I obtained from considering a bit further the delightfully simple model proposed by Prof. Susskind of spin entanglement with a 3-state measuring apparatus (Chapter 7.8).

The dynamical laws as described in the chapter are: |u,b> -> |u,1> and |d,b> -> |d,-1>.
These rules are insufficient to describe in full the 6 x 6 evolution matrix E describing the measurement process. In order to specify E one must have 6 rules, one for each starting basis.

My first idea was that the measuring apparatus could send every “up” spin into the |u,1> state, regardless of the starting point of the apparatus, and every “down” spin could enter into the |d,-1> state. These dynamics are irreversible in the sense described in Prof. Susskind’s first book, meaning that they describe the future, but not the past. I quickly realized that the resulting E matrix is non-unitary!

A better set of laws is given by:
|u,b> -> |u,1> |u,1> -> |u,b> |u,-1> -> |u,-1>
|d,b> -> |d,-1> |d,-1> -> |d,b> |d,1> -> |d,1>

Under these laws, which are reversible, there are four cycles. Two of the cycles describe the toggling of the measuring apparatus from d to +1 or -1, depending on the starting point of the system, “spin-up” or “spin-down”. Repeated measurement of the |u,b> state, for example, yields for the apparatus: b, 1, b, 1,b, 1…. For the |d,b> initial state, we would obtain the sequence: b, -1, b ,-1, b, -1,….

The other two cycles (last column) represent the fate of the improperly prepared states |u,-1> and |d,1>, which simply repeat forever.

The 6 x 6 evolution matrix E for the above set of reversible rules is thankfully unitary. Application of E to an arbitrary ket is easily achieved through matrix multiplication.

Using the example described in the text, where the initial ket is: |Yo> = a|u,b> + b|d,b>, it is straightforward to compute successive kets. From these the 6 x 6 density matrix for the combined system, as well as the reduced 2 x 2 matrix for the spin, can be computed using the formulas supplied in the text.

As stated in the text, after one measurement, the spin system, which was initially in a pure state, becomes entangled with the apparatus, and is therefore a mixed state. However, following a second measurement, the spin system state reverts back to its original “pure” state! This cycle of alternating pure and mixed states continues forever.

I thought to myself, how does one make the apparatus irreversible without violating the laws of physics, so that, after registering “1” for example, it continues to register “1” for repeated measurements?

One solution is to provide 2N states to the apparatus in addition to the “b” state, that is, N measurement states for each of the two spin states, yielding either “-1” or “1” (there would obviously be a lot degenerate eigenvalues). For example, starting in the “spin-up” state, one would continuously cycle around the sequence |u,b> -> |u,1A> -> |u,1B> -> -> -> |u,1N> -> |u,b>. A similar cycle occurs for the “spin-down” states. The improperly prepared states |u,-1A…> and |d,1A…> endlessly revert back to themselves, as before.

For this expanded spin-N-state-apparatus system, the spin state, after the initial measurement, stays entangled during the N steps taken by the apparatus before the entire process repeats itself, at which point the spin system again finds itself momentarily in a pure state. The so-called “Poincare period” is N+1. By setting N to a very large number, the process becomes essentially irreversible (the system state has “collapsed”).

The idea of a measurement “collapsing” the wave function has bugged me ever since my last exposure to the subject in college. Thanks to the authors for presenting in very simple terms a possible “way out” of this unsavory aspect of quantum mechanics!

- Dan Sigg

Daniel Sigg said...

Sorry, the tabbing in the last comment did not work out so well.

The dynamical rules should appear:

|u,b> -> |u,1>; |u,1> -> |u,b>; |u,-1> -> |u,-1>
|d,b> -> |d,-1>; |d,-1> -> |d,b>; |d,1> -> |d,1>

Hope that is clearer!

- Dan

Daniel Sigg said...

Hi all,

A couple of more thoughts on another gem in the QM book. In chapter 2.4, the need for complex probability amplitudes when dealing with two-dimensional spin states is explained.

I thought perhaps another way to make the argument is to first imagine we live in a one-dimensional world. The components making up a ket could then be actual (classical) probabilities. For example |Y> = Pu|u> + Pd|d>, where Pu = and Pd = are the probabilities of measuring "spin-up" and "spin-down" in the z-direction.

A two-dimensional universe requires the use of probability amplitudes (i.e. square roots of probabilities), but they can be real. To wit, |Y> = Pu^1/2|u> + Pd^1/2|d> in the z-basis, where the x-basis vectors are |r> = (1/2)^1/2|u> + (1/2)^1/2|d> and |l> = (1/2)^1/2|u> - (1/2)^1/2|d>.

In going to three dimensions, the addition of two more orthogonal basis vectors in the y-direction require the use of complex amplitudes to satisfy the constraints placed on the system by a two-level spin, as explained in the text.

I am wondering if this line of reasoning cannot be extended into the relativistic domain with four dimensions, and whether the outcome would be the Dirac spinors and the requirement for antiparticles. Does anybody want to try making this argument? (Since time is distinct from the spatial dimensions in that spin states are not thought as being oriented in time, I am somewhat skeptical, but not being well versed in relativity theory, I am keeping an open mind!)

- Dan Sigg

Timothy Takemoto said...

Dear Professor Susskind,

Is possible that the universe is flat (hollographic in parallel with our visual field (Mach) which is ellipsoidal (Cea), flat (Susskind ,1995), tilted
(Atrio-Barandela, Kashlinsky), and having a tao shaped "axis"?



Timothy Takemoto
Yamaguchi University

Erwin Marschall said...

Dear Prof. Susskind,

you surely read:
"How to Recover a Qubit That Has Fallen Into a Black Hole" (Submitted on 13 Jul 2015)
by Aidan Chatwin-Davies, Adam S. Jermyn, Sean M. Carroll

Do you agree with the conclusions?
I think this "recover of a qubit" is not possible and is in contradiction
with what I've heard from different talks/courses of yours.
I'm astonished finding Sean Carroll as a co-author !

Erwin Marschall

Leonid said...

Dear Prof. Susskind,

I am from a different field, but I am very much fascinated with your lectures, particularly the ones about the holographic principal. I have two questions on the subject, if I may, please, ask. One is concerning gravity and one -- black holes.

A question concerning black holes and the holographic principle -
As matter falls into a black hole and information is encoded on the event horizon, might we imagine a situation in which as we pile up information on the event horizon it happens to encode another massive object - let’s say another new star - all encoded on the even horizon of the original black hole from all the matter that falls into that black hole. And let’s say that the new star is massive enough to collapse into a singularity and form an event horizon of it own. For Bob (who has flown into the original black hole), the newly formed star collapsing into a singularity would look like a black hole. But for Alice waiting outside of the original black hole, would the new black hole that’s formed on the event horizon actually expose the information hidden in the original black hole?

A question concerning gravity -
Can gravity (at least in part) be attributed to the Universe’s expanding at an accelerating rate? If we take an analogy of a balloon — we pump in air into a balloon with an accelerated rate, any objects we attach to the surface of the balloon would dent the surface of the balloon against the force of the accelerated expansion.
Wouldn’t objects in a space that’s undergoing an accelerated expansion counter-act the expanding force causing the space to bend around these objects? If so, might gravity be a consequence of the expansion?

Thank you in advance for your time,



Ckurz7000 said...

Dear Prof. susskind,

I have recently gotten into a discussion about gravitational lensing and got myself confused about something which ought to be trivial.

A photon has a mass according to its energy, E=mc2=hf. Therefor tha tmass ought to interact with gravity and cause a deflection which is dependent on the photon energy.

On the other hand, a photon follows a geodesic of curved space, which is independent of the photon energy.

The first approach suggests gravitational lenses have chromatic aberration whereas the latter seems to say they don't. Of course, the mass of the photon will contribute something to local spacetime curvature but that ought to be negligible, right?

Can you shed some light on this?

Thank you very much (I am an avid listener of your online classes), -- Chris.

Ezio said...

Dear Prof. Susskind,

I am following your lecture series on Quantum Entanglement. I was wondering if probability distribution of radiation made by an electron in magnetic field can be implemented practically using the following procedure:-

1. 1 mol (or some number) of electrons are "prepared" in some direction say THETA w.r.t. measuring magnetic field lines.

If this is not the case, then please elaborate on how can we be make only one electron suspend in the magnetic field. Wouldn't it violate the Heisenberg UP as I would know it is standing still (Vel=0) and hence at a constant position?

Can we use a hydrogen atom as we can calculate the magnetic moment using Bohr's theory?

2. Then a vertical magnetic field is applied.

3. Finally we measure the intensity per unit time of the radiation and divide it by the number of electrons taken to get the probability density. We can use precise instruments to measure intensity per unit time and find out the approximate curve for the decay and probability density w.r.t time.

Thus we can talk about the average time of emission.

Ezio said...

Dear Prof. Susskind,

I am following your lecture series on Quantum Entanglement. Thank you for putting up such a wonderful lecture series online. I wanted to know why you defined probability as the product of components and their complex.


ZT said...

Is prof. gone from the blog? I dont see his replies....

Jack Bidnik said...

There is an interesting corollary to the relation that I posted above on March 11,2015, where I showed
that the same equation can describe both the gravitational force on planets, and the electrostatic force between proton and electron in the Bohr hydrogen atom.

The equation is: F =Gs* M*m/r ^ 2, where

Gs = (1/ (M+m))*r*Vo^2*c^4/(Vo^2 +c^2)^2

and where Vo is orbital velocity, c is speed of light, and Gs is what I call Special G.

The surprising corollary is that this equation also applies to stars in orbit about galaxies,
thus indicating there is no need to postulate dark matter, as the equation dispels the problem of
insufficient force using the Newtonian constant.
The equation speaks for itself, but those who want to get further insight into its derivation
can go to :

Loadedice said...

Please do an Electromagnetic Theory series...

Shanti Ettien said...

Univers got mathématic parametre as big thing can get or the smallest neutrino, if it's a multiunivers it get parametre as well So univers got life parametre So it Will stop growing when it Will get is maturite. It Will get is univers shape is suppose to get.

Jack Bidnik said...
This comment has been removed by the author.
Tian Kun said...

Dear Leonard Suskind,
I am a graduate student .It is quit excited to contact you here . I want to have a deeper learning of string theory and superstring theory . Can you give me a recomendation of some textbooks .(P.S : My major are mathematics and physics as a undergraduate student before ).

Tian Kun said...
This comment has been removed by the author.
Oliver Falk said...

I just watched the video about universe being a hologram and id just like to say it sounds more to me like ur saying our universe is a blackhole in another universe.


Prudhvi Raj Varma Ch said...

Sub: Regarding Energy Momentum Tensor in General Relativity

Dear Professor Susskind,

First of all, thank you for making your lessons accessible to everyone. I was going through your classes on General Relativity and in one of the classes you mentioned that the gravitational waves are an example of Energy Momentum Tensor and therefore, Ricci tensor being zero while the Riemann curvature tensor is non-zero.

I was wondering if either dark matter or the dark energy could be another possible example for the same case because I read somewhere that even though both of their (dark matter & dark energy) effects are observed, they are not visible. Please do correct me if my assumptions are wrong.


Abhishek Verma said...
This comment has been removed by the author.
Ben said...

I've been watching the lectures of particle physics. I have a question. Are there any baryons similar to the proton and neutron having a spin of 1/2 and three quarks having the same flavor? Why doesn't the proton decay into a spin 1/2 baryon having three up quarks?

Unknown said...

it's it as possible to do it on a x y plan ,as in visual bacic
circle(X +-a,Y+-b)Ri-+ri1(Red-+red[limit1],0,0)
circle(X +-a,Y+-b)Ri-+ri2(0,Green-+green[limit2],0)
circle(X +-a,Y+-b)Ri-+ri3(0,o,Blue-+blue[limit3])
i hope so because that the program Im trying to put to together to study it
love the lectures great chatting with you :)

Bernard Kamau said...

I am following

Sayan Datta said...

Dear Professor Susskind,

My name is Sayan Datta and I am writing from India.

I have watched most of your lectures; and many of them more than once. I always had a strong desire to understand some advanced physics, and your lectures were my first genuine introduction to the field after some failed attempts with some books and courses. I thank you for the lectures, which to me were excellent not only because of the ease with which it covered difficult material, but also because they were a deeply honest and genuine effort at reaching out.
I have also read your two books based on the lectures and have been eagerly waiting for the third. I hope it comes out soon.

Thanks again,

Eran Sinbar said...

Dear Professor Susskind,
Thank you for believing that deep understanding of physics should be available to all those who seek it.
I deeply enjoy viewing your Stanford lectures.
please review my latest publications in slide share regarding the missing anti matter and the non locality of entanglement.

I think you will find it very interesting.
I am very interested to hear you opinion.
Thank you so much
Eran Sinbar

happy loser said...

Both Dr. Hawkings and Dr. Susskind are correct that information is both conserved and destroyed.
To elaborate, discrete particle information is destroyed over time due to entropy but the information of where, when and how the particle existed over time is essentially preserved in the standing quantum wave functions. When one wave function collapses upon observation another more complex, more information containing wave function is created waiting to interact with the next observed wave/particle duality outcome. For example, the double slit experiment with single release events.
Information that exists as a continuous analogue form as a quantum wave function represents the imaginary component* of the information stored in what is the white hole spherical surface of an expanding sphere (as often described in the holographic model) and this wave function has no discrete singularities but oscillates possibly on the plank scalre and on the rebound so to speak for all intents and purposes this goes backwards in time as limited by HUP.
* (please see subscript below for excerpt from the above lecture) Ref 1
The above information is what is used by QED to “keep track” of the individual discrete particles that make up the universe and represent for all intents and purposes a physical digital (discrete elementary particles) that exist in two states until observed by or interacted with another analoque wave function.
Now the interesting aspect of this comes from Dr. Edward Fredkin and his work on “reversible computing”:……………his quote :” In 1982 Fredkin and Toffoli proposed the Billiard ball computer, a mechanism using classical hard spheres to do reversible computations at finite speed with zero dissipation, but requiring perfect initial alignment of the balls' trajectories, and Bennett's review[7] compared these "Brownian" and "ballistic" paradigms for reversible computation.” Is basically identical to his billiard ball computer but we are suggesting the universe and its discrete individual particles represent a three dimensional billiard table that behaves more like a digital abacus where information is temporarily encoded as three dimensional objects that behave like both a particle and wave until observed.
Reversible computing is a model of computing where the computational process to some extent is reversible, i.e., time-invertible. In a computational model that uses transitions from one state of the abstract machine to another, a necessary condition for reversibility is that the relation of the mapping from states to their successors must be one-to-one. Reversible computing is generally considered an unconventional form of computing.

Now the interesting part is what Dr. Brian Greene blah blah says (wow this is going to be hard to find) (at seven minutes) “layer based on information” this is consistent with Dr. Hawkings online lecture “by virtue of that object having been there but moved on”.

Ref 1
In fact, James Hartle of the University of California Santa Barbara, and I have proposed that space and imaginary time together, are indeed finite in extent, but without boundary. They would be like the surface of the Earth, but with two more dimensions. The surface of the Earth is finite in extent, but it doesn't have any boundaries or edges. I have been round the world, and I didn't fall off.
This says that in the imaginary time direction, space-time is finite in extent, but doesn't have any boundary or edge. The predictions of the no boundary proposal seem to agree with observation. The no boundary hypothesis also predicts that the universe will eventually collapse again. However, the contracting phase, will not have the opposite arrow of time, to the expanding phase. So we will keep on getting older, and we won't return to our youth. Because time is not going to go backwar

Benjamin Brown said...

If there was a simple axiomatic way to describe a whole universe, where according to a few rules everything we saw around us was emergent and if it was short to, about 15 or so pages, would you like read about it?

marjan gajovic said...

Dear Professor Susskind,
Is it not, that every entengled pair of particles creates its own wormhole to send informations through time and space... Information passage through time and space is instant, that means entenglment between particles worped time and space to send information... Thats definition of wormhole by default... I would like to get your intell about this...
Btw you can use entenglment for communication device during the deep exploration of cosmos... Informations from our probes can use communication device which carry entegled pairs of particles with ones at the Earth and send informations much faster then using electromagnetic signals or any velocity limited ways of travel... I hope my idea help u construct something usefull ...

Jonas Brønd said...

Dear Leonard Susskind

Recently I read your magnificent book; "The Black Hole War".

I enjoyed reading it even though I daily work as a clerk within tax law and valuation in Denmark.

Two questions kept bothering me all the way through. I hope you will take a little time to clarify these for me:

1) How does the premise that entropy is connected to heat (excited molecules rumbling around in a tub of water) cohere with heat created from high pressure? I imagine that heat produced in mid-earth would have very low entropy given that atoms/molecules are fixed and locked by dense pressure. Geologists expect large crystals to be found in mid-earth, and these crystals would have no entropy at all. How to explain this difference with heat/entropy?

2) From Bob's point of view objects falling through the horizon of a black hole are stuck on the horizon. As I understand it, this phenomena is caused by time gradually slowing down as the objects approach the horizon. Am I correct to assume that light doesn't play a role on the perception of these objects being stuck, given that the gravity of the black hole cannot slow down the speed of light - only at most deplete its energy?

Finally I want to thank you for a wonderful reading experience.


Jonas Brønd, Denmark

Abhishek Verma said...

Sir, i'm curious to know if Principle of Least Action is an axiom or it has got some proof. How can one check the validity of Principle of Least Action for some generalised case.

Shivani Singh said...


In your presentation on 'Why is Time a One- Way Street?' Published on YouTube on July 16, 2013 ( ) you have very well explained how time is a one way street but I am getting confused since space-time is treated as one then how would you explain the same phenomena for space-time as one? Can one way street of time be defined as a consequence of homogeneity of space as every point in space is center? Can you please recommend me some paper so that I can understand this concept better?

Thank you !


Dear Prof. Susskind,
The spin operator in x direction applied on |u> state will give either |r> or |l> with 50 % chance. But in Lecture 6 and in appendix(The theoretical minimum- Quantum Mechanics), it's shown to produce a |d> state. How can be it possible, when a measurement in x direction will only give |r> or |l>. The blog seems dead for a long time, but I like to get the answer.

Unknown said...

I am sabelo zwana from sa doing my first at mathematics and mathematical statistics i have been trying to understand theory of relativity can u please explain it to me in detail

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